Abstract:
A short length LDPC (Low Density Parity Check) code and modulation adapted for high speed Ethernet applications. In some instances, the short length-LDPC code and modulation may be employed within the recommended practices currently being developed by the IEEE 802.3an (10GBASE-T) Task Force. The IEEE 802.3an (10GBASE-T) Task Force has been commissioned to develop and standardize communications protocol adapted particularly for Ethernet operation over 4 wire twisted pair cables. A new LDPC code, some possible embodiments of constellations and the corresponding mappings, as well as possible embodiments of various parity check matrices, H, of the LDPC code are presented herein to provide for better overall performance than other proposed LDPC codes existent in the art of high speed Ethernet applications. Moreover, this proposed LDPC code may be decoded using a communication device having much less complexity than required to decode other proposed LDPC codes existent in this technology space.

Description:
CROSS REFERENCE TO RELATED PATENTS/PATENT APPLICATIONS  
     Provisional Priority Claim  
       [0001]     The present U.S. Utility patent application claims priority pursuant to 35 U.S.C. § 119(e) to the following U.S. Provisional Patent Applications which are hereby incorporated herein by reference in their entirety and made part of the present U.S. Utility Patent Application for all purposes:  
         [0002]     1. U.S. Provisional Application Ser. No. 60/602,553, “A short length LDPC (Low Density Parity Check) code and modulation adapted for high speed Ethernet applications,” (Attorney Docket No. BP4008), filed Wednesday, Aug. 18, 2004 (Aug. 18, 2004), pending.  
         [0003]     2. U.S. Provisional Application Ser. No. 60/602,692, “A short length LDPC (Low Density Parity Check) code and modulation adapted for high speed Ethernet applications,” (Attorney Docket No. BP4008.1), filed Thursday, Aug. 19, 2004 (Aug. 19, 2004), pending. 
     
    
     BACKGROUND OF THE INVENTION  
       [0004]     1. Technical Field of the Invention  
         [0005]     The invention relates generally to communication systems; and, more particularly, it relates to coding (including encoding and/or decoding) of signals within such communication systems.  
         [0006]     2. Description of Related Art  
         [0007]     Data communication systems have been under continual development for many years. One such type of communication system that has been of significant interest lately is a communication system that employs turbo codes. Another type of communication system that has also received interest is a communication system that employs LDPC (Low Density Parity Check) code. Each of these different types of communication systems is able to achieve relatively low BERs (Bit Error Rates).  
         [0008]     A continual and primary directive in this area of development has been to try continually to lower the error floor within a communication system. The ideal goal has been to try to reach Shannon&#39;s limit in a communication channel. Shannon&#39;s limit may be viewed as being the data rate to be used in a communication channel, having a particular SNR (Signal to Noise Ratio), that achieves error free transmission through the communication channel. In other words, the Shannon limit is the theoretical bound for channel capacity for a given modulation and code rate.  
         [0009]     LDPC code has been shown to provide for excellent decoding performance that can approach the Shannon limit in some cases. For example, some LDPC decoders have been shown to come within 0.3 dB (decibels) from the theoretical Shannon limit. While this example was achieved using an irregular LDPC code of a length of one million, it nevertheless demonstrates the very promising application of LDPC codes within communication systems.  
         [0010]     The use of LDPC coded signals continues to be explored within many newer application areas. For example, the use of LDPC coded signals has been of significant concern within the IEEE (Institute of Electrical &amp; Electronics Engineers) P802.3an (10GBASE-T) Task Force. This IEEE P802.3an (10GBASE-T) Task Force has been created by the IEEE to develop and standardize a copper 10 Giga-bit Ethernet standard that operates over twisted pair cabling according the IEEE 802.3 CSMA/CD Ethernet protocols. Carrier Sense Multiple Access/Collision Detect (CSMA/CD) is the protocol for carrier transmission access in Ethernet networks. IEEE 802.3an (10GBASE-T) is an emerging standard for 10 Gbps (Giga-bits per second) Ethernet operation over 4 wire twisted pair cables. More public information is available concerning the IEEE P802.3an (10GBASE-T) Task Force at the following Internet address: 
        “http://www.ieee802.org/3/an/”.        
 
         [0012]     This high data rate provided in such applications is relatively close to the theoretical maximum rate possible over the worst case 100 meter cable. Near-capacity achieving error correction codes are required to enable 10 Gbps operation. The latency constraints, which would be involved by using traditional concatenated codes, simply preclude their use in such applications.  
         [0013]     Clearly, there is a need in the art for some alternative coding type and implementation that can provide near-capacity achieving error correction.  
       BRIEF SUMMARY OF THE INVENTION  
       [0014]     The present invention is directed to apparatus and methods of operation that are further described in the following Brief Description of the Several Views of the Drawings, the Detailed Description of the Invention, and the claims. Other features and advantages of the present invention will become apparent from the following detailed description of the invention made with reference to the accompanying drawings. 
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0015]      FIG. 1  and  FIG. 2  are diagrams illustrating various embodiments of communication systems that may be built in accordance with certain aspects of the invention.  
         [0016]      FIG. 3  is a diagram illustrating an embodiment of an LDPC (Low Density Parity Check) code bipartite graph.  
         [0017]      FIG. 4  is a diagram illustrating an embodiment of decomposition of a parity check matrix, H, according to certain aspects of the invention.  
         [0018]      FIG. 5A  and  FIG. 5B  are diagrams illustrating embodiment of a size 4 loop and a size 6 loop, respectively, that may exist within an LDPC code bipartite graph according to certain aspects of the invention.  
         [0019]      FIG. 6  is a diagram illustrating an embodiment of a system that employs LDPC coding with 3 uncoded bits and 4 coded bits according to certain aspects of the invention.  
         [0020]      FIG. 7  is a diagram illustrating an embodiment of a doughnut 128 2-D 12-PAM (Pulse Amplitude Modulation) constellation.  
         [0021]      FIG. 8  is a diagram illustrating an embodiment of a substantially evenly distributed 128 2-D (128 2-Dimensional) constellation according to certain aspects of the invention.  
         [0022]      FIG. 9  is a diagram illustrating one possible embodiment of a Gray code mapping for the 16 constellation points associated with the uncoded bits  000  according to certain aspects of the invention.  
         [0023]      FIG. 10  is a diagram illustrating one possible embodiment of a Gray code mapping for the 16 constellation points associated with the uncoded bits  001  according to certain aspects of the invention.  
         [0024]      FIG. 11  is a diagram illustrating an embodiment of performance comparison of decoding of an LDPC coded signal employing the substantially evenly distributed 128 2-D constellation, implemented according to certain aspects of the invention, with decoding of an LDPC coded signal employing the doughnut 128 2-D 12-PAM constellation.  
         [0025]      FIG. 12  is a flowchart illustrating an embodiment of a method for transmit processing of LDPC coded signals in accordance with certain aspects of the invention.  
         [0026]      FIG. 13  and  FIG. 14  are flowcharts illustrating embodiments of methods for receive processing of LDPC coded signals in accordance with certain aspects of the invention.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0027]     The goal of digital communications systems is to transmit digital data from one location, or subsystem, to another either error free or with an acceptably low error rate. As shown in  FIG. 1 , data may be transmitted over a variety of communications channels in a wide variety of communication systems: magnetic media, wireless, fiber, copper, and other types of media as well.  
         [0028]      FIG. 1  and  FIG. 2  are diagrams illustrating various embodiments of communication systems,  100  and  200 , respectively, that may be built in accordance with certain aspects of the invention.  
         [0029]     Referring to  FIG. 1 , this embodiment of a communication system  100  is a communication channel  199  that communicatively couples a communication device  110  (including a transmitter  112  having an encoder  114  and including a receiver  116  having a decoder  118 ) situated at one end of the communication channel  199  to another communication device  120  (including a transmitter  126  having an encoder  128  and including a receiver  122  having a decoder  124 ) at the other end of the communication channel  199 . In some embodiments, either of the communication devices  110  and  120  may only include a transmitter or a receiver. There are several different types of media by which the communication channel  199  may be implemented (e.g., a satellite communication channel  130  using satellite dishes  132  and  134 , a wireless communication channel  140  using towers  142  and  144  and/or local antennae  152  and  154 , a wired communication channel  150 , and/or a fiber-optic communication channel  160  using electrical to optical (E/O) interface  162  and optical to electrical (O/E) interface  164 )). In addition, more than one type of media may be implemented and interfaced together thereby forming the communication channel  199 .  
         [0030]     To reduce transmission errors that may undesirably be incurred within a communication system, error correction and channel coding schemes are often employed. Generally, these error correction and channel coding schemes involve the use of an encoder at the transmitter and a decoder at the receiver.  
         [0031]     Referring to the communication system  200  of  FIG. 2 , at a transmitting end of a communication channel  299 , information bits  201  are provided to a transmitter  297  that is operable to perform encoding of these information bits  201  using an encoder and symbol mapper  220  (which may be viewed as being distinct functional blocks  222  and  224 , respectively) thereby generating a sequence of discrete-valued modulation symbols  203  tat is provided to a transmit driver  230  that uses a DAC (Digital to Analog Converter)  232  to generate a continuous-time transmit signal  204  and a transmit filter  234  to generate a filtered, continuous-time transmit signal  205  that substantially comports with the communication channel  299 . At a receiving end of the communication channel  299 , continuous-time receive signal  206  is provided to an AFE (Analog Front End)  260  that includes a receive filter  262  (that generates a filtered, continuous-time receive signal  207 ) and an ADC (Analog to Digital Converter)  264  (that generates discrete-time receive signals  208 ). A metric generator  270  calculates symbol metrics  209  that are employed by a decoder  280  to make best estimates of the discrete-valued modulation symbols and information bits encoded therein  210 .  
         [0032]     The communication devices of either of the previous embodiments may be implemented to include various aspects of the invention therein. In addition, several of the following Figures describe other and particular embodiments (some in more detail) that may be used to support the devices, systems, functionality and/or methods that may be implemented in accordance with certain aspects of the invention. One particular type of signal that is processed according to certain aspects of the invention is an LDPC coded signal. Before more details are provided below, a general description of LDPC codes is provided.  
         [0033]     Several of the following Figures describe other and particular embodiments (some in more detail) that may be used to support the devices, systems, functionality and/or methods that may be implemented in accordance with certain aspects of the invention. One particular type of signal that is processed according to certain aspects of the invention is an LDPC coded signals. Before more details are provided below, a general description of LDPC codes is provided.  
         [0034]      FIG. 3  is a diagram illustrating an embodiment of an LDPC (Low Density Parity Check) code bipartite graph  300 . In the art, an LDPC bipartite graph may also sometimes be referred to as a Tanner graph. An LDPC code may be viewed as being a code having a binary parity check matrix such that nearly all of the elements of the matrix have values of zeroes (e.g., the binary parity check matrix is sparse). For example, H=(h i,j ) M×N  may be viewed as being a parity check matrix of an LDPC code with block length N.  
         [0035]     The number of 1&#39;s in the i-th column of the parity check matrix may be denoted as d v (i), and the number of 1&#39;s in the j-th row of the parity check matrix may be denoted as d c (j). If d v (i)=d v  for all i, and d c (j)=d c  for all j, then the LDPC code is called a (d v ,d c ) regular LDPC code, otherwise the LDPC code is called an irregular LDPC code.  
         [0036]     LDPC codes were introduced by R. Gallager in [I] referenced below and by M. Luby et al. in [2] also referenced below. 
    [1] R. Gallager,  Low - Density Parity - Check Codes , Cambridge, Mass.: MIT Press, 1963.     [2] M. Luby, M. Mitzenmacher, M. A. Shokrollahi, D. A. Spielman, and V. Stemann, “Practical Loss-Resilient Codes”, Proc. 29 th  Symp. on Theory of Computing, 1997, pp. 150-159.    
 
         [0039]     A regular LDPC code can be represented as a bipartite graph  300  by its parity check matrix with left side nodes representing variable of the code bits (or alternatively as the “variable nodes” (or “bit nodes”)  310  in a bit decoding approach to decoding LDPC coded signals), and the right side nodes representing check equations (or alternatively as the “check nodes”  320 ). The bipartite graph  300  of the LDPC code defined by H may be defined by N variable nodes (e.g., N bit nodes) and M check nodes. Every variable node of the N variable nodes  310  has exactly d v (i) edges (an example edge shown using reference numeral  330 ) connecting the bit node, v i    312 , to one or more of the check nodes (within the M check nodes). The edge  310  is specifically shown as connecting from the bit node, v i    312 , to the check node, c j    322 . This number of d v  edges (shown as d v    314 ) may be referred to as the degree of a variable node i. Analogously, every check node of the M check nodes  1520  has exactly d c (j) edges (shown as d c    324 ) connecting this node to one or more of the variable nodes (or bit nodes)  310 . This number of edges, d c , may be referred to as the degree of the check node j.  
         [0040]     An edge  330  between a variable node v i  (or bit node b i )  312  and check node c j    322  may be defined by e=(i,j). However, on the other hand, given an edge e=(i,j), the nodes of the edge may alternatively be denoted as by e=(v(e),c(e)) (or e=(b(e c(e))). Given a variable node v i  (or bit node be), one may define the set of edges emitting from the node v i  (or bit node b i ) by E v  (i)={e|v(e)=i} (or by E b (i)={e|b(e)=i}). Given a check node c j , one may define the set of edges emitting from the node c j  by E c (j)={e|c(e)=j}. Continuing on, the derivative result will be |E v (i)|=d v  (or |E b (i)|=d b ) and |E c (i)|=d c .  
         [0041]     Generally speaking, any codes that can be represented by a bipartite graph may be characterized as graph codes. It is also noted that an irregular LDPC code may also described using a bipartite graph. However, the degree of each set of nodes within an irregular LDPC code may be chosen according to some distribution. Therefore, for two different variable nodes, v i     1   , and v i     2   , of an irregular LDPC code, |E v (i 1 )| may not equal to |E v (i 2 )|. This relationship may also hold true for two check nodes. The concept of irregular LDPC codes was originally introduced within M. Luby et al. in [2] referenced above.  
         [0042]     In general, with a graph of an LDPC code, the parameters of an LDPC code can be defined by a degree of distribution, as described within M. Luby et al. in [2] referenced above and also within the following reference [3]: 
    [3] T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check code under message-passing decoding,”  IEEE Trans. Inform. Theory , Vol. 47, pp. 599-618, February 2001.    
 
         [0044]     This distribution may be described as follows:  
         [0045]     Let λ i  represent the fraction of edges emanating from variable nodes of degree i and let ρ i  represent the fraction of edges emanating from check nodes of degree i. Then, a degree distribution pair (λ,ρ) is defined as follows:  
           λ   ⁡     (   x   )       =         ∑     i   =   2       M   v       ⁢       λ   i     ⁢     x     i   -   1       ⁢           ⁢   and   ⁢           ⁢     ρ   ⁡     (   x   )           =       ∑     i   =   2       M   c       ⁢       ρ   i     ⁢     x     i   -   1               ,       
 
 where M v  and M c  represent the maximal degrees for variable nodes and check nodes, respectively. 
 
         [0046]     While many of the illustrative embodiments described herein utilize regular LDPC code examples, it is noted that certain aspects of the invention are also operable to accommodate both regular LDPC codes and irregular LDPC codes.  
         [0047]      FIG. 4  is a diagram illustrating an embodiment of decomposition of a parity check matrix, H,  400  according to certain aspects of the invention. As described above, a parity check matrix (e.g., H=(h i,j ) M×N ) is used to perform coding of an LDPC coded signal.  
         [0048]     A (1280,1024) LDPC code is presented herein that is a rate 4/5 binary code with 256 redundancy bits. The parity check matrix H is a 256×1280 LDPC matrix. The LDPC code has 4 different bit node degrees, namely, 1 degree one bit node, 255 degree two bit nodes, 768 degree three bit nodes and 256 degree seven bit nodes.  
         [0049]     All of the check nodes of the LDPC code, but one, have degree 18. The other check node has degree 17. Therefore, the LDPC bipartite graph of the LDPC code has 4607 edges. The parity check matrix H can further be decomposed to 3 parts as follows: 
 
H=[H 7 ,H 3 ,Hd]  (EQ 5) 
 
         [0050]     1. The sub-matrix H d  is a 256×256 matrix constructed as follows:  
               H   d     =     [         1                                                                                   1       1                                                                                   1       1                                                                                               ⋯                                                                                               1                                                                                   1       1                                                                                   1       1         ]             (     EQ   ⁢           ⁢   6     )             
        where the empty entry stands for “0”. This construction is a convention. The advantage of using this structure are many, including: 1) the code constructed by this sub-matrix is systematic; 2) encoding and decoding can share the same parity check matrix; and 3) it provides a large unclosed loop is the LDPC bipartite graph of the corresponded LDPC code.        
 
         [0052]     2. The sub-matrix H 7  is a 256 by 256 matrix. Every column of H 7  has seven is. Furthermore, this matrix is further decomposed to another two sub-matrices, as follows: 
 
H 7 =[H 7,1 ,H 7,2 ]  (EQ 7) 
 
         [0053]     The sub-matrix H 7,i  is a 2-cyclic matrix. At first, 7 positions among the positions 0 to 255 are randomly chosen. The first column of the matrix is defined by these 7 positions. The entries of the chosen positions are 1 and the others are 0. The following columns of H 7,i  constructed by cyclic shift two positions of the previous column.  
         [0054]     3. The sub-matrix H 3  is a 256 by 768 matrix. Every column of H 3  has three 1s. Matrix is decomposed to 6 sub-matrices, as follows: 
 
H 3 =[H 3,1 , H 3,2 , H 3,3 , H 3,4 , H 3,5 , H 3,6 ]  (EQ 8) 
 
         [0055]     The sub-matrix H 3,i  is a 2-cyclic matrix. At first, 3 positions among 0 to 255 are randomly chosen. The first column of the matrix is defined by these 3 positions. The entries of the chosen positions are 1 and the others are 0. The following columns of H 3,i  is constructed by cyclic shift two position of the previous column.  
         [0056]     4. Further criteria of the construction are: 
        a) The 8 sets of random number should be chosen in the way that after 2-cyclic shift that the number of 1&#39;s in every rows of [H 7 , H 3 ] should exactly equal to 16;     b) The bipartite graph of the code should have no size 4 loops.        
 
         [0059]     Below, several embodiments of possible parity check matrices are provided, according to the approach given above.  
         [0060]     Of the first example parity check matrix constructed according to the approach provided above, the LDPC bipartite graph of this code has no size 4 loop. It has 50298 size 6 loops. A size 4 loop and a size 6 loop can be depicted as shown within the following diagrams.  
         [0061]      FIG. 5A  and  FIG. 5B  are diagrams illustrating embodiment of a size 4 loop and a size 6 loop, respectively, that may exist within an LDPC code bipartite graph according to certain aspects of the invention.  
         [0062]     As can be seen in  FIG. 5A , a size 4 loop  500  is shown as having two bit nodes and two check nodes appropriately interconnected via edges. Analogously, as can be seen in  FIG. 5B , a size 6 loop  505  is shown as having three bit nodes and three check nodes appropriately interconnected via edges.  
         [0063]     Referring back to the  FIG. 4 , the operations depicted above with respect to steps 2 and 3 may be generalized even more (as shown by 2′ and 3′ below).  
         [0064]     2′. The sub-matrix H 7  is decomposed to n(n≧1) sub-matrices, as follows: 
 
H 7 =[H 7,1 , . . . , H 7,n ]  (EQ 9) 
 
         [0065]     The sub-matrix H 7  is a n-cyclic matrix. At first, 7 positions among 0 to 255 are randomly chosen. The first column of the matrix is defined by these 7 positions. The entries of the chosen positions are 1 and the others are 0. The following columns of H 7,i  constructed by cyclic shift n positions of the previous column.  
         [0066]     3′. The sub-matrix H 3  is decomposed to 3n (n≧1) sub-matrices, as follows: 
 
H 3 =[H 3,1 , . . . , H 3,n , . . . , H 3,3n ]  (EQ 10) 
 
         [0067]     The sub-matrix H 3,i  is a n-cyclic matrix. At first, 3 positions among 0 to 255 are randomly chosen. The first column of the matrix is defined by these 3 positions. The entries of the chosen positions are 1 and the others are 0. The following columns of H 3,i  is constructed by cyclic shift n position of the previous column.  
         [0068]     In the following referenced paper, a regular LDPC code is constructed based on two codewords of a R-S (Reed-Solomon) code. 
    [4] I. Djurdjevic, J. Xu, K. Abdel-Ghaffar and S. Lin, “A Class of Low-Density Parity-Check Codes Constructed Based on Reed-Solomon Codes With Two Information Symbols,”  IEEE Communications Letter , vol. 7, no. 7, pp. 317-319, July 2003.    
 
         [0070]     Consider a code (1024, 833), which has rate 8.13 constructed using the approach of the Djurdjevic, et al., paper [4] as identified above. Every bit node of the code has degree 10 and every check node has degree 32. Therefore the code has 10240 edges. Furthermore, the bipartite graph of the code has 2286604 size 6 loops.  
         [0071]     Therefore, a (1280,1024) LDPC code, which has 4607 edges, constructed as described according to certain aspects of the invention is less complex; several examples of such codes are provided below as well. Therefore, a (1280, 1024) code would save a considerable amount of hardware with reduced complexity within an actual device.  
         [0072]      FIG. 6  is a diagram illustrating an embodiment of a system  600  that employs LDPC coding with 3 uncoded bits and 4 coded bits according to certain aspects of the invention.  
         [0073]     This diagram shows an embodiment where uncoded information bits  610  and LDPC coded bits  620  are provided and subsequently arranged to form 7 bit symbols. These 7 bit symbols have 128 possible values (e.g., 2 7 =128). Each of these 7 bit symbols included 3 uncoded bits (selected form the uncoded information bits  610 ) and 4 LDPC coded bits (selected from the LDPC coded bits  620 ) that are provided to this system  600 . These 7 bit symbols are operable to be symbol mapped according to a substantially evenly distributed 128 2-D constellation  650 . Some possible embodiments of such an substantially evenly distributed 128 2-D constellation are provided below with respect to some other of the embodiments disclosed herein.  
         [0074]      FIG. 7  is a diagram illustrating an embodiment of a doughnut 128 2-D 12-PAM (Pulse Amplitude Modulation) constellation  700 . In a presentation “Modifications to LDPC Proposal offering Lower Symbol Rate and Lower Latency,” by D. Dabiri, J. Tellado of Teranetics (IEEE 802.3an (10GBASE-T) March 2004 meeting) a 128 2-D 12-PAM constellation is constructed as depicted in this diagram.  
         [0075]     This document is publicly available at the following Internet address:  
         [0076]     “http://www.ieee802.org/3/an/public/mar04/dabiri — 1 — 0304.pdf”.  
         [0077]     This constellation is referred to herein as a “doughnut” constellation. The labeling of every constellation point is for uncoded bits. In fact, every signal point will transmit 7 bits which include 3 uncoded bits and 4 coded bits from an LDPC code.  
         [0078]     Since the center part of this construction is taken out, the distributional of the “doughnut” constellation is not even. Let E be the average power of 1-D 12-PAM constellation. Then the noise variance is as follows: 
 
σ 1   =E/SNR   1   (EQ 11) 
 
         [0079]     Since the doughnut 2D-constellation is not exactly 2-D 12-PAM, (EQ 11) cannot be used to compute the noise variance with this constellation. In fact, with the average power E 2  of the 2-D constellation the variance should be as follows: 
 
σ 2   =E   2 /2 SNR   2   (EQ 12) 
 
         [0080]     If the 2D Constellation is exact 2-D 12-PAM which has 144 signals, then E 2 =95.333 and thus SNR, =SNR 2  when σ 2 =σ 1 . However, the doughnut constellation only has 128 signals. Moreover, the average power of the constellation is E 2 =106. Thus, when σ 1 =σ 2 , then  
           SNR   2     =       106   95.333     ⁢     SNR   1         ,       
 
 i.e. in dB (decibels). 
 
 SNR   2 =0.46 +SNR   1  (dB)  (EQ 13) 
 
         [0081]      FIG. 8  is a diagram illustrating an embodiment of a substantially evenly distributed 128 2-D (128 2-Dimensional) constellation  800  according to certain aspects of the invention. The inventors have developed a different modulation (constellation and mapping) whose constellation points are substantially evenly distributed when compared to the constellation points of the “doughnut” constellation described above. The constellation points of this modulation may be referred to as a substantially evenly distributed 128 2-D constellation.  
         [0082]     The construction and placement of the constellation points of this substantially evenly distributed 128 2-D constellation is made in the following way.  
         [0083]     1. Set-partitioning of the total 144 possible signals of a true 2-D 12-PAM to 9 regions with 16 constellation points within each of the 9 regions.  
         [0084]     2. Delete  1  signal from every region so that the distributional of the deleted signals is as even as possible.  
         [0085]     The mapping of these constellation points is based on the set-partition of the left 8 signals in every subset. With this new 2-D 128 constellation, the average power is provided as follows: 
 
E 2 =92.75  (EQ 14) 
 
         [0086]     Thus, when σ 1 =σ 2 , then  
           SNR   2     =       92.75   95.333     ⁢     SNR   1         ,       
 
 i.e. in dB. 
 
 SNR   2   =SNR   1 −0.1193 (dB)  (EQ 15) 
 
         [0087]     Because of this, the new “substantially evenly distributed 128 2-D constellation” outperforms the “doughnut” constellation described above. The following diagram depicting performance gives the comparison of the two constellations and the two LDPC codes described above.  
         [0088]     This substantially evenly distributed 128 2-D constellation  800  may be viewed as being a constellation that is generated from a 2-D 12-PAM (2-Dimensional 12-Pulse Amplitude Modulation) constellation that includes all 144 possible constellation points. These 144 constellation points are then evenly partitioned into 9 regions such that each region includes 16 possible constellation points therein. Of these 9 regions, 8 of the 9 regions comprise 14 constellation points therein, and 1 of the 9 regions comprises all 16 possible constellation points therein. As can also be seen, the uncoded bit assignment is provided as shown in each of the remaining 128 constellation point locations. It can be seen that there are 16 corresponding constellation points for each 3 valued uncoded bit symbol. For example, the uncoded bits  000  have 16 corresponding constellation points; the uncoded bits  001  have 16 corresponding constellation points; and so on for all of the 8 possible 3 bit symbols composed of the uncoded bits. Each of these 3 uncoded bits indicate which subset, among 8 subsets each containing the corresponding 16 constellation points, to which the 4 coded bits correspond and are symbol mapped. As can be seen in this embodiment, for 7 of the 8 subsets, the 16 constellation points therein are distributed among at least 2 of the 9 regions. For 1 of the 8 subsets, all of the 16 possible constellation points are included within the same region (i.e., of the 9 possible regions that are generated by dividing up the 144 constellation points of the 2-D 12-PAM constellation.  
         [0089]      FIG. 9  is a diagram illustrating one possible embodiment of a Gray code mapping  900  for the 16 constellation points associated with the uncoded bits  000  according to certain aspects of the invention. Generally speaking, a working definition of a “Gray code” is as follows:  
         [0090]     Gray code: a binary sequence with the property that only one bit changes between any two consecutive elements (i.e., the two codes have a Hamming distance of one).  
         [0091]     As mentioned above, some of the 16 constellation points corresponding to each of the 8 subsets may have different mappings may be deleted and distributed among other of the possible constellation point locations. As for the uncoded bits  000 , two of the 16 constellation points of this subset are located outside of the region that includes the 16 possible constellation point locations. Specifically, the LDPC coded bits  0000  and  0111  correspond to constellation point locations outside of the region that includes the majority of the constellation points corresponding to the uncoded bits  000 . The remaining 14 constellation points are all located within the same region. The 4 bit assignment of the other of the LDPC coded bits corresponding to the uncoded bits  000  are as depicted in the diagram.  
         [0092]      FIG. 10  is a diagram illustrating one possible embodiment of a Gray code mapping  1000  for the 16 constellation points associated with the uncoded bits  001  according to certain aspects of the invention.  
         [0093]     Again, some of the 16 constellation points corresponding to each of the 8 subsets may have different mappings may be deleted and distributed among other of the possible constellation point locations. As for the uncoded bits  001 , three of the 16 constellation points of this subset are located outside of the region that includes the 16 possible constellation point locations. Specifically, the LDPC coded bits  0000 ,  0001 , and  1010  correspond to constellation point locations outside of the region that includes the majority of the constellation points corresponding to the uncoded bits  001 . The remaining 13 constellation points are all located within the same region. The 4 bit assignment of the other of the LDPC coded bits corresponding to the uncoded bits  001  are as depicted in the diagram.  
         [0094]     It is noted that there are a wide variety of possible Gray code mappings that may be employed to map the 16 constellation points of each of the 16 constellation points within each of the 8 subsets of uncoded bits depicted herein. These diagrams shown within the  FIG. 9  and the  FIG. 10  are just one possible embodiment of Gray code mapping of the 16 constellation points within each of the 8 subsets corresponding to the uncoded bit groups. Clearly, there are other mappings (including non-Gray code mappings) that may alternatively be employed for each of the 16 constellation points. If desired, each of the groups of 16 constellation points corresponding to each of the 8 subsets may have a common mapping; alternatively, each (or some) of the groups of 16 constellation points corresponding to each of the 8 subsets may different mappings.  
         [0095]      FIG. 11  is a diagram illustrating an embodiment of performance comparison  1100  of decoding of an LDPC coded signal employing the substantially evenly distributed 128 2-D constellation, implemented according to certain aspects of the invention, with decoding of an LDPC coded signal employing the doughnut 128 2-D 12-PAM constellation.  
         [0096]     This performance comparison diagram is described in the context of BER (Bit Error Rate) versus E b /N o  (ratio of energy per bit E b  to the Spectral Noise Density N o ). This term E b /N o  is the measure of SNR (Signal to Noise Ratio) for a digital communication system. When looking at these performance curves, the BER may be determined for any given E b /N o  (or SNR) thereby providing a relatively concise representation of the performance of the decoding approach.  
         [0097]     As can be seen, LDPC coded signals (shown as using the substantially evenly distributed constellation  1102  (e.g., the substantially evenly distributed 128 2-D constellation) and using the substantially evenly distributed constellation  1103  (e.g., the substantially evenly distributed 128 2-D constellation)) that employ the new “substantially evenly distributed 128 2-D constellation” provide for a much lower BER than the “doughnut” constellation described above (shown as using the “doughnut” constellation  1101 ) when operating at the same E b /N o  (or SNR). As such, it can be seen that by selecting an appropriate generator matrix, G, and its corresponding parity check matrix, H, for use with the LDPC code, and by selecting an appropriate modulation (i.e., constellation and mapping), a significant improvement in performance may be achieved.  
         [0098]      FIG. 12  is a flowchart illustrating an embodiment of a method for transmit processing of LDPC coded signals  1200  in accordance with certain aspects of the invention.  
         [0099]     The method involves receiving 1 or more information bits, as shown in a block  1210 . The method then involves encoding the 1 or more information bits into a sequence of discrete-valued modulation symbols according to an LDPC generator matrix, G, having a corresponding LDPC parity check matrix, H, thereby generating discrete-time transmit signals, as shown in a block  1220 . This may be performed by employing the substantially evenly distributed 128 2-D constellation presented above, as shown in a block  1222 . This may also involve employing 1 or more uncoded information bits when forming a sequence of discrete-valued modulation symbols, as shown in a block  1224 .  
         [0100]     The method then involves inserting the discrete-time transmit signals at a modulation rate into means (e.g., using a DAC) to generate a continuous-time transmit signal, as shown in a block  1230 . The method then involves filtering the continuous-time transmit signal (e.g., using a transmit filter), as shown in a block  1240 . The method then involves launching the filtered, continuous-time transmit signal into a communication channel, as shown in a block  1250 .  
         [0101]      FIG. 13  and  FIG. 14  are flowcharts illustrating embodiments of methods for receive processing of LDPC coded signals in accordance with certain aspects of the invention Referring to  FIG. 13 , the method  1300  involves receiving a continuous time signal, as shown in a block  1310 . The information bits that have been encoded within this continuous time signal have been encoded using LDPC encoding in accordance with certain aspects of the invention. Upon the receiving of this continuous time signal, it is also noted that the method may involve performing any necessary down-conversion of a first continuous time signal (e.g., the originally received continuous time signal) thereby generating a second continuous time signal, as shown in a block  1312 . This down conversion may be performed by direct conversion from carrier frequency to baseband, or it may alternatively be performed by passing through an IF (Intermediate Frequency) as well without departing from the scope and spirit of the invention. Moreover, this may also include performing any appropriate receive filtering as well.  
         [0102]     The method then involves sampling the first (or second) continuous time signal (e.g., using an ADC) thereby generating a discrete time signal and extracting I, Q (In phase, Quadrature) components there from, as shown in a block  1320 . The method then also involves demodulating the I, Q components and performing symbol mapping of the I, Q components thereby generating a sequence of discrete-valued modulation symbols, as shown in a block  1330 . In doing this, this may be performed by employing the substantially evenly distributed 128 2-D constellation presented above, as shown in a block  1332 .  
         [0103]     The method then involves performing edge message updating with respect to LDPC bipartite graph according to the parity check matrix, H, as shown in a block  1340 . This is performed for predetermined number of decoding iterations within this particular embodiment. This updating may be performed a number of ways. For example, the method may involve employing likelihood for both edges messages with respect to check nodes and edges messages with respect to bit nodes, as shown in a block  1342 . Alternatively, the method may involve employing likelihood ratio for edges messages with respect to bit nodes, as shown in a block  1344 .  
         [0104]     The method also involves making hard decisions based on soft information corresponding to the finally updated edge messages, as shown in a block  1350 . Using these hard decisions, the method then involves outputting a best estimate of the transmitted codeword (having at least one information bit included therein) that is extracted from the received continuous time signal, as shown in a block  1360 .  
         [0105]     Referring to  FIG. 14 , initially, this particular method  1400  operates very similarly to the embodiment described above with respect to the  FIG. 13 . The method involves receiving a continuous time signal, as shown in a block  1410 . The information bits that have been encoded within this continuous time signal have been encoded using LDPC encoding. Upon the receiving of this continuous time signal, it is also noted that the method may involve performing any necessary down-conversion of a first continuous time signal (e.g., the originally received continuous time signal) thereby generating a second continuous time signal, as shown in a block  1412 . This down conversion may be performed by direct conversion from carrier frequency to baseband, or it may alternatively be performed by passing through an IF (Intermediate Frequency) as well without departing from the scope and spirit of the invention. Again, this may also include performing any appropriate receive filtering as well.  
         [0106]     The method then involves sampling the first (or second) continuous time signal (e.g., using an ADC) thereby generating a discrete time signal and extracting I, Q (In phase, Quadrature) components there from, as shown in a block  1420 . The method then also involves demodulating the I, Q components and performing symbol mapping of the I, Q components thereby generating a sequence of discrete-valued modulation symbols, as shown in a block  1430 . In doing this, this may be performed by employing the substantially evenly distributed 128 2-D constellation presented above, as shown in a block  1432 .  
         [0107]     The method then involves performing edge message updating with respect to LDPC bipartite graph according to parity check matrix, H, as shown in a block  1440 . This updating may be performed a number of ways. For example, the method may involve employing likelihood for both edges messages with respect to check nodes and edges messages with respect to bit nodes, as shown in a block  1442 . Alternatively, the method may involve employing likelihood ratio for edges messages with respect to bit nodes, as shown in a block  1444 .  
         [0108]     However, this method now departs from the operation of the method of the  FIG. 13 . In this particular embodiment, the method involves making hard decisions based on soft information corresponding to edge messages to produce a current estimate of the codeword, as shown in a block  1446 . It is noted that this is performed after bit engine processing has finished at least one decoding iteration. After this current estimate of the codeword is made, then the method involves performing syndrome checking of the current estimate of the codeword, as shown in a block  1450 . This is performed to determine if this current estimate of the codeword indeed passes the syndrome check. If the syndrome check does NOT pass, as shown in a block  1454 , then the method involves returning to the edge message updating using only multiplication (or log domain addition) on both sides of LDPC bipartite graph. However, if it is found that the syndrome check does in fact pass, as shown in a block  1452 , then the method involves outputting a best estimate of the transmitted codeword (having at least one information bit included therein) that is extracted from the received continuous time signal, as shown in a block  1460 .  
         [0109]     Various examples of possible parity check matrices, H, are provided in the Appendix A and Appendix B below that may be constructed in accordance with certain aspects of the invention.  
         [0110]     It is also noted that the methods described within the preceding figures may also be performed within any of the appropriate system and/or apparatus designs (communication systems, communication transmitters, communication receivers, communication transceivers, and/or functionality described therein) that are described above without departing from the scope and spirit of the invention.  
         [0111]     In view of the above detailed description of the invention and associated drawings, other modifications and variations will now become apparent. It should also be apparent that such other modifications and variations may be effected without departing from the spirit and scope of the invention.  
       Appendix Introduction  
       [0112]     Several examples of various parity check matrices are provided in this Appendix.  
         [0113]     These parity check matrices are provided and presented with respect to the matrices depicted above.  
         [0114]     In the following tables depicting these parity check matrices, “b” stands for the bit node number, and “c” stands for the check node number in the context of an LDPC bipartite graph.  
       Appendix A  
       [0115]     1. One possible embodiment of a parity check matrix of a (1280, 1024) LDPC code is presented below.  
         [0116]     The following presents a another possible embodiment of a (1280,1024) LDPC code parity check matrix that is constructed in accordance with certain aspects of the invention. The parity check matrix is presented in the following format:  
         [0117]     H=[H(7,1), H(7,2), H(3,1), H(3,3), H(3,4), H(3,5), H(3,6), H(d)] 
                                                                                   TABLE 1                           H(7, 1)            b   c   c   c   c   c   c   c                    1   1   194   177   143   65   61   123       2   3   196   179   145   67   63   125       3   5   198   181   147   69   65   127       4   7   200   183   149   71   67   129       5   9   202   185   151   73   69   131       6   11   204   187   153   75   71   133       7   13   206   189   155   77   73   135       8   15   208   191   157   79   75   137       9   17   210   193   159   81   77   139       10   19   212   195   161   83   79   141       11   21   214   197   163   85   81   143       12   23   216   199   165   87   83   145       13   25   218   201   167   89   85   147       14   27   220   203   169   91   87   149       15   29   222   205   171   93   89   151       16   31   224   207   173   95   91   153       17   33   226   209   175   97   93   155       18   35   228   211   177   99   95   157       19   37   230   213   179   101   97   159       20   39   232   215   181   103   99   161       21   41   234   217   183   105   101   163       22   43   236   219   185   107   103   165       23   45   238   221   187   109   105   167       24   47   240   223   189   111   107   169       25   49   242   225   191   113   109   171       26   51   244   227   193   115   111   173       27   53   246   229   195   117   113   175       28   55   248   231   197   119   115   177       29   57   250   233   199   121   117   179       30   59   252   235   201   123   119   181       31   61   254   237   203   125   121   183       32   63   256   239   205   127   123   185       33   65   2   241   207   129   125   187       34   67   4   243   209   131   127   189       35   69   6   245   211   133   129   191       36   71   8   247   213   135   131   193       37   73   10   249   215   137   133   195       38   75   12   251   217   139   135   197       39   77   14   253   219   141   137   199       40   79   16   255   221   143   139   201       41   81   18   1   223   145   141   203       42   83   20   3   225   147   143   205       43   85   22   5   227   149   145   207       44   87   24   7   229   151   147   209       45   89   26   9   231   153   149   211       46   91   28   11   233   155   151   213       47   93   30   13   235   157   153   215       48   95   32   15   237   159   155   217       49   97   34   17   239   161   157   219       50   99   36   19   241   163   159   221       51   101   38   21   243   165   161   223       52   103   40   23   245   167   163   225       53   105   42   25   247   169   165   227       54   107   44   27   249   171   167   229       55   109   46   29   251   173   169   231       56   111   48   31   253   175   171   233       57   113   50   33   255   177   173   235       58   115   52   35   1   179   175   237       59   117   54   37   3   181   177   239       60   119   56   39   5   183   179   241       61   121   58   41   7   185   181   243       62   123   60   43   9   187   183   245       63   125   62   45   11   189   185   247       64   127   64   47   13   191   187   249       65   129   66   49   15   193   189   251       66   131   68   51   17   195   191   253       67   133   70   53   19   197   193   255       68   135   72   55   21   199   195   1       69   137   74   57   23   201   197   3       70   139   76   59   25   203   199   5       71   141   78   61   27   205   201   7       72   143   80   63   29   207   203   9       73   145   82   65   31   209   205   11       74   147   84   67   33   211   207   13       75   149   86   69   35   213   209   15       76   151   88   71   37   215   211   17       77   153   90   73   39   217   213   19       78   155   92   75   41   219   215   21       79   157   94   77   43   221   217   23       80   159   96   79   45   223   219   25       81   161   98   81   47   225   221   27       82   163   100   83   49   227   223   29       83   165   102   85   51   229   225   31       84   167   104   87   53   231   227   33       85   169   106   89   55   233   229   35       86   171   108   91   57   235   231   37       87   173   110   93   59   237   233   39       88   175   112   95   61   239   235   41       89   177   114   97   63   241   237   43       90   179   116   99   65   243   239   45       91   181   118   101   67   245   241   47       92   183   120   103   69   247   243   49       93   185   122   105   71   249   245   51       94   187   124   107   73   251   247   53       95   189   126   109   75   253   249   55       96   191   128   111   77   255   251   57       97   193   130   113   79   1   253   59       98   195   132   115   81   3   255   61       99   197   134   117   83   5   1   63       100   199   136   119   85   7   3   65       101   201   138   121   87   9   5   67       102   203   140   123   89   11   7   69       103   205   142   125   91   13   9   71       104   207   144   127   93   15   11   73       105   209   146   129   95   17   13   75       106   211   148   131   97   19   15   77       107   213   150   133   99   21   17   79       108   215   152   135   101   23   19   81       109   217   154   137   103   25   21   83       110   219   156   139   105   27   23   85       111   221   158   141   107   29   25   87       112   223   160   143   109   31   27   89       113   225   162   145   111   33   29   91       114   227   164   147   113   35   31   93       115   229   166   149   115   37   33   95       116   231   168   151   117   39   35   97       117   233   170   153   119   41   37   99       118   235   172   155   121   43   39   101       119   237   174   157   123   45   41   103       120   239   176   159   125   47   43   105       121   241   178   161   127   49   45   107       122   243   180   163   129   51   47   109       123   245   182   165   131   53   49   111       124   247   184   167   133   55   51   113       125   249   186   169   135   57   53   115       126   251   188   171   137   59   55   117       127   253   190   173   139   61   57   119       128   255   192   175   141   63   59   121                  
 
         [0118]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                   
               
               
                 H(7, 2) 
               
             
          
           
               
                 b 
                 c 
                 c 
                 c 
                 c 
                 c 
                 c 
                 c 
               
               
                   
               
             
          
           
               
                 129 
                 2 
                 253 
                 142 
                 250 
                 124 
                 90 
                 202 
               
               
                 130 
                 4 
                 255 
                 144 
                 252 
                 126 
                 92 
                 204 
               
               
                 131 
                 6 
                 1 
                 146 
                 254 
                 128 
                 94 
                 206 
               
               
                 132 
                 8 
                 3 
                 148 
                 256 
                 130 
                 96 
                 208 
               
               
                 133 
                 10 
                 5 
                 150 
                 2 
                 132 
                 98 
                 210 
               
               
                 134 
                 12 
                 7 
                 152 
                 4 
                 134 
                 100 
                 212 
               
               
                 135 
                 14 
                 9 
                 154 
                 6 
                 136 
                 102 
                 214 
               
               
                 136 
                 16 
                 11 
                 156 
                 8 
                 138 
                 104 
                 216 
               
               
                 137 
                 18 
                 13 
                 158 
                 10 
                 140 
                 106 
                 218 
               
               
                 138 
                 20 
                 15 
                 160 
                 12 
                 142 
                 108 
                 220 
               
               
                 139 
                 22 
                 17 
                 162 
                 14 
                 144 
                 110 
                 222 
               
               
                 140 
                 24 
                 19 
                 164 
                 16 
                 146 
                 112 
                 224 
               
               
                 141 
                 26 
                 21 
                 166 
                 18 
                 148 
                 114 
                 226 
               
               
                 142 
                 28 
                 23 
                 168 
                 20 
                 150 
                 116 
                 228 
               
               
                 143 
                 30 
                 25 
                 170 
                 22 
                 152 
                 118 
                 230 
               
               
                 144 
                 32 
                 27 
                 172 
                 24 
                 154 
                 120 
                 232 
               
               
                 145 
                 34 
                 29 
                 174 
                 26 
                 156 
                 122 
                 234 
               
               
                 146 
                 36 
                 31 
                 176 
                 28 
                 158 
                 124 
                 236 
               
               
                 147 
                 38 
                 33 
                 178 
                 30 
                 160 
                 126 
                 238 
               
               
                 148 
                 40 
                 35 
                 180 
                 32 
                 162 
                 128 
                 240 
               
               
                 149 
                 42 
                 37 
                 182 
                 34 
                 164 
                 130 
                 242 
               
               
                 150 
                 44 
                 39 
                 184 
                 36 
                 166 
                 132 
                 244 
               
               
                 151 
                 46 
                 41 
                 186 
                 38 
                 168 
                 134 
                 246 
               
               
                 152 
                 48 
                 43 
                 188 
                 40 
                 170 
                 136 
                 248 
               
               
                 153 
                 50 
                 45 
                 190 
                 42 
                 172 
                 138 
                 250 
               
               
                 154 
                 52 
                 47 
                 192 
                 44 
                 174 
                 140 
                 252 
               
               
                 155 
                 54 
                 49 
                 194 
                 46 
                 176 
                 142 
                 254 
               
               
                 156 
                 56 
                 51 
                 196 
                 48 
                 178 
                 144 
                 256 
               
               
                 157 
                 58 
                 53 
                 198 
                 50 
                 180 
                 146 
                 2 
               
               
                 158 
                 60 
                 55 
                 200 
                 52 
                 182 
                 148 
                 4 
               
               
                 159 
                 62 
                 57 
                 202 
                 54 
                 184 
                 150 
                 6 
               
               
                 160 
                 64 
                 59 
                 204 
                 56 
                 186 
                 152 
                 8 
               
               
                 161 
                 66 
                 61 
                 206 
                 58 
                 188 
                 154 
                 10 
               
               
                 162 
                 68 
                 63 
                 208 
                 60 
                 190 
                 156 
                 12 
               
               
                 163 
                 70 
                 65 
                 210 
                 62 
                 192 
                 158 
                 14 
               
               
                 164 
                 72 
                 67 
                 212 
                 64 
                 194 
                 160 
                 16 
               
               
                 165 
                 74 
                 69 
                 214 
                 66 
                 196 
                 162 
                 18 
               
               
                 166 
                 76 
                 71 
                 216 
                 68 
                 198 
                 164 
                 20 
               
               
                 167 
                 78 
                 73 
                 218 
                 70 
                 200 
                 166 
                 22 
               
               
                 168 
                 80 
                 75 
                 220 
                 72 
                 202 
                 168 
                 24 
               
               
                 169 
                 82 
                 77 
                 222 
                 74 
                 204 
                 170 
                 26 
               
               
                 170 
                 84 
                 79 
                 224 
                 76 
                 206 
                 172 
                 28 
               
               
                 171 
                 86 
                 81 
                 226 
                 78 
                 208 
                 174 
                 30 
               
               
                 172 
                 88 
                 83 
                 228 
                 80 
                 210 
                 176 
                 32 
               
               
                 173 
                 90 
                 85 
                 230 
                 82 
                 212 
                 178 
                 34 
               
               
                 174 
                 92 
                 87 
                 232 
                 84 
                 214 
                 180 
                 36 
               
               
                 175 
                 94 
                 89 
                 234 
                 86 
                 216 
                 182 
                 38 
               
               
                 176 
                 96 
                 91 
                 236 
                 88 
                 218 
                 184 
                 40 
               
               
                 177 
                 98 
                 93 
                 238 
                 90 
                 220 
                 186 
                 42 
               
               
                 178 
                 100 
                 95 
                 240 
                 92 
                 222 
                 188 
                 44 
               
               
                 179 
                 102 
                 97 
                 242 
                 94 
                 224 
                 190 
                 46 
               
               
                 180 
                 104 
                 99 
                 244 
                 96 
                 226 
                 192 
                 48 
               
               
                 181 
                 106 
                 101 
                 246 
                 98 
                 228 
                 194 
                 50 
               
               
                 182 
                 108 
                 103 
                 248 
                 100 
                 230 
                 196 
                 52 
               
               
                 183 
                 110 
                 105 
                 250 
                 102 
                 232 
                 198 
                 54 
               
               
                 184 
                 112 
                 107 
                 252 
                 104 
                 234 
                 200 
                 56 
               
               
                 185 
                 114 
                 109 
                 254 
                 106 
                 236 
                 202 
                 58 
               
               
                 186 
                 116 
                 111 
                 256 
                 108 
                 238 
                 204 
                 60 
               
               
                 187 
                 118 
                 113 
                 2 
                 110 
                 240 
                 206 
                 62 
               
               
                 188 
                 120 
                 115 
                 4 
                 112 
                 242 
                 208 
                 64 
               
               
                 189 
                 122 
                 117 
                 6 
                 114 
                 244 
                 210 
                 66 
               
               
                 190 
                 124 
                 119 
                 8 
                 116 
                 246 
                 212 
                 68 
               
               
                 191 
                 126 
                 121 
                 10 
                 118 
                 248 
                 214 
                 70 
               
               
                 192 
                 128 
                 123 
                 12 
                 120 
                 250 
                 216 
                 72 
               
               
                 193 
                 130 
                 125 
                 14 
                 122 
                 252 
                 218 
                 74 
               
               
                 194 
                 132 
                 127 
                 16 
                 124 
                 254 
                 220 
                 76 
               
               
                 195 
                 134 
                 129 
                 18 
                 126 
                 256 
                 222 
                 78 
               
               
                 196 
                 136 
                 131 
                 20 
                 128 
                 2 
                 224 
                 80 
               
               
                 197 
                 138 
                 133 
                 22 
                 130 
                 4 
                 226 
                 82 
               
               
                 198 
                 140 
                 135 
                 24 
                 132 
                 6 
                 228 
                 84 
               
               
                 199 
                 142 
                 137 
                 26 
                 134 
                 8 
                 230 
                 86 
               
               
                 200 
                 144 
                 139 
                 28 
                 136 
                 10 
                 232 
                 88 
               
               
                 201 
                 146 
                 141 
                 30 
                 138 
                 12 
                 234 
                 90 
               
               
                 202 
                 148 
                 143 
                 32 
                 140 
                 14 
                 236 
                 92 
               
               
                 203 
                 150 
                 145 
                 34 
                 142 
                 16 
                 238 
                 94 
               
               
                 204 
                 152 
                 147 
                 36 
                 144 
                 18 
                 240 
                 96 
               
               
                 205 
                 154 
                 149 
                 38 
                 146 
                 20 
                 242 
                 98 
               
               
                 206 
                 156 
                 151 
                 40 
                 148 
                 22 
                 244 
                 100 
               
               
                 207 
                 158 
                 153 
                 42 
                 150 
                 24 
                 246 
                 102 
               
               
                 208 
                 160 
                 155 
                 44 
                 152 
                 26 
                 248 
                 104 
               
               
                 209 
                 162 
                 157 
                 46 
                 154 
                 28 
                 250 
                 106 
               
               
                 210 
                 164 
                 159 
                 48 
                 156 
                 30 
                 252 
                 108 
               
               
                 211 
                 166 
                 161 
                 50 
                 158 
                 32 
                 254 
                 110 
               
               
                 212 
                 168 
                 163 
                 52 
                 160 
                 34 
                 256 
                 112 
               
               
                 213 
                 170 
                 165 
                 54 
                 162 
                 36 
                 2 
                 114 
               
               
                 214 
                 172 
                 167 
                 56 
                 164 
                 38 
                 4 
                 116 
               
               
                 215 
                 174 
                 169 
                 58 
                 166 
                 40 
                 6 
                 118 
               
               
                 216 
                 176 
                 171 
                 60 
                 168 
                 42 
                 8 
                 120 
               
               
                 217 
                 178 
                 173 
                 62 
                 170 
                 44 
                 10 
                 122 
               
               
                 218 
                 180 
                 175 
                 64 
                 172 
                 46 
                 12 
                 124 
               
               
                 219 
                 182 
                 177 
                 66 
                 174 
                 48 
                 14 
                 126 
               
               
                 220 
                 184 
                 179 
                 68 
                 176 
                 50 
                 16 
                 128 
               
               
                 221 
                 186 
                 181 
                 70 
                 178 
                 52 
                 18 
                 130 
               
               
                 222 
                 188 
                 183 
                 72 
                 180 
                 54 
                 20 
                 132 
               
               
                 223 
                 190 
                 185 
                 74 
                 182 
                 56 
                 22 
                 134 
               
               
                 224 
                 192 
                 187 
                 76 
                 184 
                 58 
                 24 
                 136 
               
               
                 225 
                 194 
                 189 
                 78 
                 186 
                 60 
                 26 
                 138 
               
               
                 226 
                 196 
                 191 
                 80 
                 188 
                 62 
                 28 
                 140 
               
               
                 227 
                 198 
                 193 
                 82 
                 190 
                 64 
                 30 
                 142 
               
               
                 228 
                 200 
                 195 
                 84 
                 192 
                 66 
                 32 
                 144 
               
               
                 229 
                 202 
                 197 
                 86 
                 194 
                 68 
                 34 
                 146 
               
               
                 230 
                 204 
                 199 
                 88 
                 196 
                 70 
                 36 
                 148 
               
               
                 231 
                 206 
                 201 
                 90 
                 198 
                 72 
                 38 
                 150 
               
               
                 232 
                 208 
                 203 
                 92 
                 200 
                 74 
                 40 
                 152 
               
               
                 233 
                 210 
                 205 
                 94 
                 202 
                 76 
                 42 
                 154 
               
               
                 234 
                 212 
                 207 
                 96 
                 204 
                 78 
                 44 
                 156 
               
               
                 235 
                 214 
                 209 
                 98 
                 206 
                 80 
                 46 
                 158 
               
               
                 236 
                 216 
                 211 
                 100 
                 208 
                 82 
                 48 
                 160 
               
               
                 237 
                 218 
                 213 
                 102 
                 210 
                 84 
                 50 
                 162 
               
               
                 238 
                 220 
                 215 
                 104 
                 212 
                 86 
                 52 
                 164 
               
               
                 239 
                 222 
                 217 
                 106 
                 214 
                 88 
                 54 
                 166 
               
               
                 240 
                 224 
                 219 
                 108 
                 216 
                 90 
                 56 
                 168 
               
               
                 241 
                 226 
                 221 
                 110 
                 218 
                 92 
                 58 
                 170 
               
               
                 242 
                 228 
                 223 
                 112 
                 220 
                 94 
                 60 
                 172 
               
               
                 243 
                 230 
                 225 
                 114 
                 222 
                 96 
                 62 
                 174 
               
               
                 244 
                 232 
                 227 
                 116 
                 224 
                 98 
                 64 
                 176 
               
               
                 245 
                 234 
                 229 
                 118 
                 226 
                 100 
                 66 
                 178 
               
               
                 246 
                 236 
                 231 
                 120 
                 228 
                 102 
                 68 
                 180 
               
               
                 247 
                 238 
                 233 
                 122 
                 230 
                 104 
                 70 
                 182 
               
               
                 248 
                 240 
                 235 
                 124 
                 232 
                 106 
                 72 
                 184 
               
               
                 249 
                 242 
                 237 
                 126 
                 234 
                 108 
                 74 
                 186 
               
               
                 250 
                 244 
                 239 
                 128 
                 236 
                 110 
                 76 
                 188 
               
               
                 251 
                 246 
                 241 
                 130 
                 238 
                 112 
                 78 
                 190 
               
               
                 252 
                 248 
                 243 
                 132 
                 240 
                 114 
                 80 
                 192 
               
               
                 253 
                 250 
                 245 
                 134 
                 242 
                 116 
                 82 
                 194 
               
               
                 254 
                 252 
                 247 
                 136 
                 244 
                 118 
                 84 
                 196 
               
               
                 255 
                 254 
                 249 
                 138 
                 246 
                 120 
                 86 
                 198 
               
               
                 256 
                 256 
                 251 
                 140 
                 248 
                 122 
                 88 
                 200 
               
               
                   
               
             
          
         
       
     
         [0119]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 1) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 257 
                 1 
                 96 
                 245 
               
               
                   
                 258 
                 3 
                 98 
                 247 
               
               
                   
                 259 
                 5 
                 100 
                 249 
               
               
                   
                 260 
                 7 
                 102 
                 251 
               
               
                   
                 261 
                 9 
                 104 
                 253 
               
               
                   
                 262 
                 11 
                 106 
                 255 
               
               
                   
                 263 
                 13 
                 108 
                 1 
               
               
                   
                 264 
                 15 
                 110 
                 3 
               
               
                   
                 265 
                 17 
                 112 
                 5 
               
               
                   
                 266 
                 19 
                 114 
                 7 
               
               
                   
                 267 
                 21 
                 116 
                 9 
               
               
                   
                 268 
                 23 
                 118 
                 11 
               
               
                   
                 269 
                 25 
                 120 
                 13 
               
               
                   
                 270 
                 27 
                 122 
                 15 
               
               
                   
                 271 
                 29 
                 124 
                 17 
               
               
                   
                 272 
                 31 
                 126 
                 19 
               
               
                   
                 273 
                 33 
                 128 
                 21 
               
               
                   
                 274 
                 35 
                 130 
                 23 
               
               
                   
                 275 
                 37 
                 132 
                 25 
               
               
                   
                 276 
                 39 
                 134 
                 27 
               
               
                   
                 277 
                 41 
                 136 
                 29 
               
               
                   
                 278 
                 43 
                 138 
                 31 
               
               
                   
                 279 
                 45 
                 140 
                 33 
               
               
                   
                 280 
                 47 
                 142 
                 35 
               
               
                   
                 281 
                 49 
                 144 
                 37 
               
               
                   
                 282 
                 51 
                 146 
                 39 
               
               
                   
                 283 
                 53 
                 148 
                 41 
               
               
                   
                 284 
                 55 
                 150 
                 43 
               
               
                   
                 285 
                 57 
                 152 
                 45 
               
               
                   
                 286 
                 59 
                 154 
                 47 
               
               
                   
                 287 
                 61 
                 156 
                 49 
               
               
                   
                 288 
                 63 
                 158 
                 51 
               
               
                   
                 289 
                 65 
                 160 
                 53 
               
               
                   
                 290 
                 67 
                 162 
                 55 
               
               
                   
                 291 
                 69 
                 164 
                 57 
               
               
                   
                 292 
                 71 
                 166 
                 59 
               
               
                   
                 293 
                 73 
                 168 
                 61 
               
               
                   
                 294 
                 75 
                 170 
                 63 
               
               
                   
                 295 
                 77 
                 172 
                 65 
               
               
                   
                 296 
                 79 
                 174 
                 67 
               
               
                   
                 297 
                 81 
                 176 
                 69 
               
               
                   
                 298 
                 83 
                 178 
                 71 
               
               
                   
                 299 
                 85 
                 180 
                 73 
               
               
                   
                 300 
                 87 
                 182 
                 75 
               
               
                   
                 301 
                 89 
                 184 
                 77 
               
               
                   
                 302 
                 91 
                 186 
                 79 
               
               
                   
                 303 
                 93 
                 188 
                 81 
               
               
                   
                 304 
                 95 
                 190 
                 83 
               
               
                   
                 305 
                 97 
                 192 
                 85 
               
               
                   
                 306 
                 99 
                 194 
                 87 
               
               
                   
                 307 
                 101 
                 196 
                 89 
               
               
                   
                 308 
                 103 
                 198 
                 91 
               
               
                   
                 309 
                 105 
                 200 
                 93 
               
               
                   
                 310 
                 107 
                 202 
                 95 
               
               
                   
                 311 
                 109 
                 204 
                 97 
               
               
                   
                 312 
                 111 
                 206 
                 99 
               
               
                   
                 313 
                 113 
                 208 
                 101 
               
               
                   
                 314 
                 115 
                 210 
                 103 
               
               
                   
                 315 
                 117 
                 212 
                 105 
               
               
                   
                 316 
                 119 
                 214 
                 107 
               
               
                   
                 317 
                 121 
                 216 
                 109 
               
               
                   
                 318 
                 123 
                 218 
                 111 
               
               
                   
                 319 
                 125 
                 220 
                 113 
               
               
                   
                 320 
                 127 
                 222 
                 115 
               
               
                   
                 321 
                 129 
                 224 
                 117 
               
               
                   
                 322 
                 131 
                 226 
                 119 
               
               
                   
                 323 
                 133 
                 228 
                 121 
               
               
                   
                 324 
                 135 
                 230 
                 123 
               
               
                   
                 325 
                 137 
                 232 
                 125 
               
               
                   
                 326 
                 139 
                 234 
                 127 
               
               
                   
                 327 
                 141 
                 236 
                 129 
               
               
                   
                 328 
                 143 
                 238 
                 131 
               
               
                   
                 329 
                 145 
                 240 
                 133 
               
               
                   
                 330 
                 147 
                 242 
                 135 
               
               
                   
                 331 
                 149 
                 244 
                 137 
               
               
                   
                 332 
                 151 
                 246 
                 139 
               
               
                   
                 333 
                 153 
                 248 
                 141 
               
               
                   
                 334 
                 155 
                 250 
                 143 
               
               
                   
                 335 
                 157 
                 252 
                 145 
               
               
                   
                 336 
                 159 
                 254 
                 147 
               
               
                   
                 337 
                 161 
                 256 
                 149 
               
               
                   
                 338 
                 163 
                 2 
                 151 
               
               
                   
                 339 
                 165 
                 4 
                 153 
               
               
                   
                 340 
                 167 
                 6 
                 155 
               
               
                   
                 341 
                 169 
                 8 
                 157 
               
               
                   
                 342 
                 171 
                 10 
                 159 
               
               
                   
                 343 
                 173 
                 12 
                 161 
               
               
                   
                 344 
                 175 
                 14 
                 163 
               
               
                   
                 345 
                 177 
                 16 
                 165 
               
               
                   
                 346 
                 179 
                 18 
                 167 
               
               
                   
                 347 
                 181 
                 20 
                 169 
               
               
                   
                 348 
                 183 
                 22 
                 171 
               
               
                   
                 349 
                 185 
                 24 
                 173 
               
               
                   
                 350 
                 187 
                 26 
                 175 
               
               
                   
                 351 
                 189 
                 28 
                 177 
               
               
                   
                 352 
                 191 
                 30 
                 179 
               
               
                   
                 353 
                 193 
                 32 
                 181 
               
               
                   
                 354 
                 195 
                 34 
                 183 
               
               
                   
                 355 
                 197 
                 36 
                 185 
               
               
                   
                 356 
                 199 
                 38 
                 187 
               
               
                   
                 357 
                 201 
                 40 
                 189 
               
               
                   
                 358 
                 203 
                 42 
                 191 
               
               
                   
                 359 
                 205 
                 44 
                 193 
               
               
                   
                 360 
                 207 
                 46 
                 195 
               
               
                   
                 361 
                 209 
                 48 
                 197 
               
               
                   
                 362 
                 211 
                 50 
                 199 
               
               
                   
                 363 
                 213 
                 52 
                 201 
               
               
                   
                 364 
                 215 
                 54 
                 203 
               
               
                   
                 365 
                 217 
                 56 
                 205 
               
               
                   
                 366 
                 219 
                 58 
                 207 
               
               
                   
                 367 
                 221 
                 60 
                 209 
               
               
                   
                 368 
                 223 
                 62 
                 211 
               
               
                   
                 369 
                 225 
                 64 
                 213 
               
               
                   
                 370 
                 227 
                 66 
                 215 
               
               
                   
                 371 
                 229 
                 68 
                 217 
               
               
                   
                 372 
                 231 
                 70 
                 219 
               
               
                   
                 373 
                 233 
                 72 
                 221 
               
               
                   
                 374 
                 235 
                 74 
                 223 
               
               
                   
                 375 
                 237 
                 76 
                 225 
               
               
                   
                 376 
                 239 
                 78 
                 227 
               
               
                   
                 377 
                 241 
                 80 
                 229 
               
               
                   
                 378 
                 243 
                 82 
                 231 
               
               
                   
                 379 
                 245 
                 84 
                 233 
               
               
                   
                 380 
                 247 
                 86 
                 235 
               
               
                   
                 381 
                 249 
                 88 
                 237 
               
               
                   
                 382 
                 251 
                 90 
                 239 
               
               
                   
                 383 
                 253 
                 92 
                 241 
               
               
                   
                 384 
                 255 
                 94 
                 243 
               
               
                   
                   
               
             
          
         
       
     
         [0120]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 2) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 385 
                 2 
                 157 
                 192 
               
               
                   
                 386 
                 4 
                 159 
                 194 
               
               
                   
                 387 
                 6 
                 161 
                 196 
               
               
                   
                 388 
                 8 
                 163 
                 198 
               
               
                   
                 389 
                 10 
                 165 
                 200 
               
               
                   
                 390 
                 12 
                 167 
                 202 
               
               
                   
                 391 
                 14 
                 169 
                 204 
               
               
                   
                 392 
                 16 
                 171 
                 206 
               
               
                   
                 393 
                 18 
                 173 
                 208 
               
               
                   
                 394 
                 20 
                 175 
                 210 
               
               
                   
                 395 
                 22 
                 177 
                 212 
               
               
                   
                 396 
                 24 
                 179 
                 214 
               
               
                   
                 397 
                 26 
                 181 
                 216 
               
               
                   
                 398 
                 28 
                 183 
                 218 
               
               
                   
                 399 
                 30 
                 185 
                 220 
               
               
                   
                 400 
                 32 
                 187 
                 222 
               
               
                   
                 401 
                 34 
                 189 
                 224 
               
               
                   
                 402 
                 36 
                 191 
                 226 
               
               
                   
                 403 
                 38 
                 193 
                 228 
               
               
                   
                 404 
                 40 
                 195 
                 230 
               
               
                   
                 405 
                 42 
                 197 
                 232 
               
               
                   
                 406 
                 44 
                 199 
                 234 
               
               
                   
                 407 
                 46 
                 201 
                 236 
               
               
                   
                 408 
                 48 
                 203 
                 238 
               
               
                   
                 409 
                 50 
                 205 
                 240 
               
               
                   
                 410 
                 52 
                 207 
                 242 
               
               
                   
                 411 
                 54 
                 209 
                 244 
               
               
                   
                 412 
                 56 
                 211 
                 246 
               
               
                   
                 413 
                 58 
                 213 
                 248 
               
               
                   
                 414 
                 60 
                 215 
                 250 
               
               
                   
                 415 
                 62 
                 217 
                 252 
               
               
                   
                 416 
                 64 
                 219 
                 254 
               
               
                   
                 417 
                 66 
                 221 
                 256 
               
               
                   
                 418 
                 68 
                 223 
                 2 
               
               
                   
                 419 
                 70 
                 225 
                 4 
               
               
                   
                 420 
                 72 
                 227 
                 6 
               
               
                   
                 421 
                 74 
                 229 
                 8 
               
               
                   
                 422 
                 76 
                 231 
                 10 
               
               
                   
                 423 
                 78 
                 233 
                 12 
               
               
                   
                 424 
                 80 
                 235 
                 14 
               
               
                   
                 425 
                 82 
                 237 
                 16 
               
               
                   
                 426 
                 84 
                 239 
                 18 
               
               
                   
                 427 
                 86 
                 241 
                 20 
               
               
                   
                 428 
                 88 
                 243 
                 22 
               
               
                   
                 429 
                 90 
                 245 
                 24 
               
               
                   
                 430 
                 92 
                 247 
                 26 
               
               
                   
                 431 
                 94 
                 249 
                 28 
               
               
                   
                 432 
                 96 
                 251 
                 30 
               
               
                   
                 433 
                 98 
                 223 
                 32 
               
               
                   
                 434 
                 100 
                 225 
                 34 
               
               
                   
                 435 
                 102 
                 1 
                 36 
               
               
                   
                 436 
                 104 
                 3 
                 38 
               
               
                   
                 437 
                 106 
                 5 
                 40 
               
               
                   
                 438 
                 108 
                 7 
                 42 
               
               
                   
                 439 
                 110 
                 9 
                 44 
               
               
                   
                 440 
                 112 
                 11 
                 46 
               
               
                   
                 441 
                 114 
                 13 
                 48 
               
               
                   
                 442 
                 116 
                 15 
                 50 
               
               
                   
                 443 
                 118 
                 17 
                 52 
               
               
                   
                 444 
                 120 
                 19 
                 54 
               
               
                   
                 445 
                 122 
                 21 
                 56 
               
               
                   
                 446 
                 124 
                 23 
                 58 
               
               
                   
                 447 
                 126 
                 25 
                 60 
               
               
                   
                 448 
                 128 
                 27 
                 62 
               
               
                   
                 449 
                 130 
                 29 
                 64 
               
               
                   
                 450 
                 132 
                 31 
                 66 
               
               
                   
                 451 
                 134 
                 33 
                 68 
               
               
                   
                 452 
                 136 
                 35 
                 70 
               
               
                   
                 453 
                 138 
                 37 
                 72 
               
               
                   
                 454 
                 140 
                 39 
                 74 
               
               
                   
                 455 
                 142 
                 41 
                 76 
               
               
                   
                 456 
                 144 
                 43 
                 78 
               
               
                   
                 457 
                 146 
                 45 
                 80 
               
               
                   
                 458 
                 148 
                 47 
                 82 
               
               
                   
                 459 
                 150 
                 49 
                 84 
               
               
                   
                 460 
                 152 
                 51 
                 86 
               
               
                   
                 461 
                 154 
                 53 
                 88 
               
               
                   
                 462 
                 156 
                 55 
                 90 
               
               
                   
                 463 
                 158 
                 57 
                 92 
               
               
                   
                 464 
                 160 
                 59 
                 94 
               
               
                   
                 465 
                 162 
                 61 
                 96 
               
               
                   
                 466 
                 164 
                 63 
                 98 
               
               
                   
                 467 
                 166 
                 65 
                 100 
               
               
                   
                 468 
                 168 
                 67 
                 102 
               
               
                   
                 469 
                 170 
                 69 
                 104 
               
               
                   
                 470 
                 172 
                 71 
                 106 
               
               
                   
                 471 
                 174 
                 73 
                 108 
               
               
                   
                 472 
                 176 
                 75 
                 110 
               
               
                   
                 473 
                 178 
                 77 
                 112 
               
               
                   
                 474 
                 180 
                 79 
                 114 
               
               
                   
                 475 
                 182 
                 81 
                 116 
               
               
                   
                 476 
                 184 
                 83 
                 118 
               
               
                   
                 477 
                 186 
                 85 
                 120 
               
               
                   
                 478 
                 188 
                 87 
                 122 
               
               
                   
                 479 
                 190 
                 89 
                 124 
               
               
                   
                 480 
                 192 
                 91 
                 126 
               
               
                   
                 481 
                 194 
                 93 
                 128 
               
               
                   
                 482 
                 196 
                 95 
                 130 
               
               
                   
                 483 
                 198 
                 97 
                 132 
               
               
                   
                 484 
                 200 
                 99 
                 134 
               
               
                   
                 485 
                 202 
                 101 
                 136 
               
               
                   
                 486 
                 204 
                 103 
                 138 
               
               
                   
                 487 
                 206 
                 105 
                 140 
               
               
                   
                 488 
                 208 
                 107 
                 142 
               
               
                   
                 489 
                 210 
                 109 
                 144 
               
               
                   
                 490 
                 212 
                 111 
                 146 
               
               
                   
                 491 
                 214 
                 113 
                 148 
               
               
                   
                 492 
                 216 
                 115 
                 150 
               
               
                   
                 493 
                 218 
                 117 
                 152 
               
               
                   
                 494 
                 220 
                 119 
                 154 
               
               
                   
                 495 
                 222 
                 121 
                 156 
               
               
                   
                 496 
                 224 
                 123 
                 158 
               
               
                   
                 497 
                 226 
                 125 
                 160 
               
               
                   
                 498 
                 228 
                 127 
                 162 
               
               
                   
                 499 
                 230 
                 129 
                 164 
               
               
                   
                 500 
                 232 
                 131 
                 166 
               
               
                   
                 501 
                 234 
                 133 
                 168 
               
               
                   
                 502 
                 236 
                 135 
                 170 
               
               
                   
                 503 
                 238 
                 137 
                 172 
               
               
                   
                 504 
                 240 
                 139 
                 174 
               
               
                   
                 505 
                 242 
                 141 
                 176 
               
               
                   
                 506 
                 244 
                 143 
                 178 
               
               
                   
                 507 
                 246 
                 145 
                 180 
               
               
                   
                 508 
                 248 
                 147 
                 182 
               
               
                   
                 509 
                 250 
                 149 
                 184 
               
               
                   
                 510 
                 252 
                 151 
                 186 
               
               
                   
                 511 
                 254 
                 153 
                 188 
               
               
                   
                 512 
                 256 
                 155 
                 190 
               
               
                   
                   
               
             
          
         
       
     
         [0121]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 3) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 513 
                 1 
                 178 
                 19 
               
               
                   
                 514 
                 3 
                 180 
                 21 
               
               
                   
                 515 
                 5 
                 182 
                 23 
               
               
                   
                 516 
                 7 
                 184 
                 25 
               
               
                   
                 517 
                 9 
                 186 
                 27 
               
               
                   
                 518 
                 11 
                 188 
                 29 
               
               
                   
                 519 
                 13 
                 190 
                 31 
               
               
                   
                 520 
                 15 
                 192 
                 33 
               
               
                   
                 521 
                 17 
                 194 
                 35 
               
               
                   
                 522 
                 19 
                 196 
                 37 
               
               
                   
                 523 
                 21 
                 198 
                 39 
               
               
                   
                 524 
                 23 
                 200 
                 41 
               
               
                   
                 525 
                 25 
                 202 
                 43 
               
               
                   
                 526 
                 27 
                 204 
                 45 
               
               
                   
                 527 
                 29 
                 206 
                 47 
               
               
                   
                 528 
                 31 
                 208 
                 49 
               
               
                   
                 529 
                 33 
                 210 
                 51 
               
               
                   
                 530 
                 35 
                 212 
                 53 
               
               
                   
                 531 
                 37 
                 214 
                 55 
               
               
                   
                 532 
                 39 
                 216 
                 57 
               
               
                   
                 533 
                 41 
                 218 
                 59 
               
               
                   
                 534 
                 43 
                 220 
                 61 
               
               
                   
                 535 
                 45 
                 222 
                 63 
               
               
                   
                 536 
                 47 
                 224 
                 65 
               
               
                   
                 537 
                 49 
                 226 
                 67 
               
               
                   
                 538 
                 51 
                 228 
                 69 
               
               
                   
                 539 
                 53 
                 230 
                 71 
               
               
                   
                 540 
                 55 
                 232 
                 73 
               
               
                   
                 541 
                 57 
                 234 
                 75 
               
               
                   
                 542 
                 59 
                 236 
                 77 
               
               
                   
                 543 
                 61 
                 238 
                 79 
               
               
                   
                 544 
                 63 
                 240 
                 81 
               
               
                   
                 545 
                 65 
                 242 
                 83 
               
               
                   
                 546 
                 67 
                 244 
                 85 
               
               
                   
                 547 
                 69 
                 246 
                 87 
               
               
                   
                 548 
                 71 
                 248 
                 89 
               
               
                   
                 549 
                 73 
                 250 
                 91 
               
               
                   
                 550 
                 75 
                 252 
                 93 
               
               
                   
                 551 
                 77 
                 254 
                 95 
               
               
                   
                 552 
                 79 
                 256 
                 97 
               
               
                   
                 553 
                 81 
                 2 
                 99 
               
               
                   
                 554 
                 83 
                 4 
                 101 
               
               
                   
                 555 
                 85 
                 6 
                 103 
               
               
                   
                 556 
                 87 
                 8 
                 105 
               
               
                   
                 557 
                 89 
                 10 
                 107 
               
               
                   
                 558 
                 91 
                 12 
                 109 
               
               
                   
                 559 
                 93 
                 14 
                 111 
               
               
                   
                 560 
                 95 
                 16 
                 113 
               
               
                   
                 561 
                 97 
                 18 
                 115 
               
               
                   
                 562 
                 99 
                 20 
                 117 
               
               
                   
                 563 
                 101 
                 22 
                 119 
               
               
                   
                 564 
                 103 
                 24 
                 121 
               
               
                   
                 565 
                 105 
                 26 
                 123 
               
               
                   
                 566 
                 107 
                 28 
                 125 
               
               
                   
                 567 
                 109 
                 30 
                 127 
               
               
                   
                 568 
                 111 
                 32 
                 129 
               
               
                   
                 569 
                 113 
                 34 
                 131 
               
               
                   
                 570 
                 115 
                 36 
                 133 
               
               
                   
                 571 
                 117 
                 38 
                 135 
               
               
                   
                 572 
                 119 
                 40 
                 137 
               
               
                   
                 573 
                 121 
                 42 
                 139 
               
               
                   
                 574 
                 123 
                 44 
                 141 
               
               
                   
                 575 
                 125 
                 46 
                 143 
               
               
                   
                 576 
                 127 
                 48 
                 145 
               
               
                   
                 577 
                 129 
                 50 
                 147 
               
               
                   
                 578 
                 131 
                 52 
                 149 
               
               
                   
                 579 
                 133 
                 54 
                 151 
               
               
                   
                 580 
                 135 
                 56 
                 153 
               
               
                   
                 581 
                 137 
                 58 
                 155 
               
               
                   
                 582 
                 139 
                 60 
                 157 
               
               
                   
                 583 
                 141 
                 62 
                 159 
               
               
                   
                 584 
                 143 
                 64 
                 161 
               
               
                   
                 585 
                 145 
                 66 
                 163 
               
               
                   
                 586 
                 147 
                 68 
                 165 
               
               
                   
                 587 
                 149 
                 70 
                 167 
               
               
                   
                 588 
                 151 
                 72 
                 169 
               
               
                   
                 589 
                 153 
                 74 
                 171 
               
               
                   
                 590 
                 155 
                 76 
                 173 
               
               
                   
                 591 
                 157 
                 78 
                 175 
               
               
                   
                 592 
                 159 
                 80 
                 177 
               
               
                   
                 593 
                 161 
                 82 
                 179 
               
               
                   
                 594 
                 163 
                 84 
                 181 
               
               
                   
                 595 
                 165 
                 86 
                 183 
               
               
                   
                 596 
                 167 
                 88 
                 185 
               
               
                   
                 597 
                 169 
                 90 
                 187 
               
               
                   
                 598 
                 171 
                 92 
                 189 
               
               
                   
                 599 
                 173 
                 94 
                 191 
               
               
                   
                 600 
                 175 
                 96 
                 193 
               
               
                   
                 601 
                 177 
                 98 
                 195 
               
               
                   
                 602 
                 179 
                 100 
                 197 
               
               
                   
                 603 
                 181 
                 102 
                 199 
               
               
                   
                 604 
                 183 
                 104 
                 201 
               
               
                   
                 605 
                 185 
                 106 
                 203 
               
               
                   
                 606 
                 187 
                 108 
                 205 
               
               
                   
                 607 
                 189 
                 110 
                 207 
               
               
                   
                 608 
                 191 
                 112 
                 209 
               
               
                   
                 609 
                 193 
                 114 
                 211 
               
               
                   
                 610 
                 195 
                 116 
                 213 
               
               
                   
                 611 
                 197 
                 118 
                 215 
               
               
                   
                 612 
                 199 
                 120 
                 217 
               
               
                   
                 613 
                 201 
                 122 
                 219 
               
               
                   
                 614 
                 203 
                 124 
                 221 
               
               
                   
                 615 
                 205 
                 126 
                 223 
               
               
                   
                 616 
                 207 
                 128 
                 225 
               
               
                   
                 617 
                 209 
                 130 
                 227 
               
               
                   
                 618 
                 211 
                 132 
                 229 
               
               
                   
                 619 
                 213 
                 134 
                 231 
               
               
                   
                 620 
                 215 
                 136 
                 233 
               
               
                   
                 621 
                 217 
                 138 
                 235 
               
               
                   
                 622 
                 219 
                 140 
                 237 
               
               
                   
                 623 
                 221 
                 142 
                 239 
               
               
                   
                 624 
                 223 
                 144 
                 241 
               
               
                   
                 625 
                 225 
                 146 
                 243 
               
               
                   
                 626 
                 227 
                 148 
                 245 
               
               
                   
                 627 
                 229 
                 150 
                 247 
               
               
                   
                 628 
                 231 
                 152 
                 249 
               
               
                   
                 629 
                 233 
                 154 
                 251 
               
               
                   
                 630 
                 235 
                 156 
                 253 
               
               
                   
                 631 
                 237 
                 158 
                 255 
               
               
                   
                 632 
                 239 
                 160 
                 1 
               
               
                   
                 633 
                 241 
                 162 
                 3 
               
               
                   
                 634 
                 243 
                 164 
                 5 
               
               
                   
                 635 
                 245 
                 166 
                 7 
               
               
                   
                 636 
                 247 
                 168 
                 9 
               
               
                   
                 637 
                 249 
                 170 
                 11 
               
               
                   
                 638 
                 251 
                 172 
                 13 
               
               
                   
                 639 
                 253 
                 174 
                 15 
               
               
                   
                 640 
                 255 
                 176 
                 17 
               
               
                   
                 641 
                 2 
                 237 
                 12 
               
               
                   
                 642 
                 4 
                 239 
                 14 
               
               
                   
                 643 
                 6 
                 241 
                 16 
               
               
                   
                 644 
                 8 
                 243 
                 18 
               
               
                   
                 645 
                 10 
                 245 
                 20 
               
               
                   
                 646 
                 12 
                 247 
                 22 
               
               
                   
                 647 
                 14 
                 249 
                 24 
               
               
                   
                 648 
                 16 
                 251 
                 26 
               
               
                   
                 649 
                 18 
                 253 
                 28 
               
               
                   
                 650 
                 20 
                 255 
                 30 
               
               
                   
                 651 
                 22 
                 1 
                 32 
               
               
                   
                 652 
                 24 
                 3 
                 34 
               
               
                   
                 653 
                 26 
                 5 
                 36 
               
               
                   
                 654 
                 28 
                 7 
                 38 
               
               
                   
                 655 
                 30 
                 9 
                 40 
               
               
                   
                 656 
                 32 
                 11 
                 42 
               
               
                   
                 657 
                 34 
                 13 
                 44 
               
               
                   
                 658 
                 36 
                 15 
                 46 
               
               
                   
                 659 
                 38 
                 17 
                 48 
               
               
                   
                 660 
                 40 
                 19 
                 50 
               
               
                   
                 661 
                 42 
                 21 
                 52 
               
               
                   
                 662 
                 44 
                 23 
                 54 
               
               
                   
                 663 
                 46 
                 25 
                 56 
               
               
                   
                 664 
                 48 
                 27 
                 58 
               
               
                   
                 665 
                 50 
                 29 
                 60 
               
               
                   
                 666 
                 52 
                 31 
                 62 
               
               
                   
                 667 
                 54 
                 33 
                 64 
               
               
                   
                 668 
                 56 
                 35 
                 66 
               
               
                   
                 669 
                 58 
                 37 
                 68 
               
               
                   
                 670 
                 60 
                 39 
                 70 
               
               
                   
                 671 
                 62 
                 41 
                 72 
               
               
                   
                 672 
                 64 
                 43 
                 74 
               
               
                   
                 673 
                 66 
                 45 
                 76 
               
               
                   
                 674 
                 68 
                 47 
                 78 
               
               
                   
                 675 
                 70 
                 49 
                 80 
               
               
                   
                 676 
                 72 
                 51 
                 82 
               
               
                   
                 677 
                 74 
                 53 
                 84 
               
               
                   
                 678 
                 76 
                 55 
                 86 
               
               
                   
                 679 
                 78 
                 57 
                 88 
               
               
                   
                 680 
                 80 
                 59 
                 90 
               
               
                   
                 681 
                 82 
                 61 
                 92 
               
               
                   
                 682 
                 84 
                 63 
                 94 
               
               
                   
                 683 
                 86 
                 65 
                 96 
               
               
                   
                 684 
                 88 
                 67 
                 98 
               
               
                   
                 685 
                 90 
                 69 
                 100 
               
               
                   
                 686 
                 92 
                 71 
                 102 
               
               
                   
                 687 
                 94 
                 73 
                 104 
               
               
                   
                 688 
                 96 
                 75 
                 106 
               
               
                   
                 689 
                 98 
                 77 
                 108 
               
               
                   
                 690 
                 100 
                 79 
                 110 
               
               
                   
                 691 
                 102 
                 81 
                 112 
               
               
                   
                 692 
                 104 
                 83 
                 114 
               
               
                   
                 693 
                 106 
                 85 
                 116 
               
               
                   
                 694 
                 108 
                 87 
                 118 
               
               
                   
                 695 
                 110 
                 89 
                 120 
               
               
                   
                 696 
                 112 
                 91 
                 122 
               
               
                   
                 697 
                 114 
                 93 
                 124 
               
               
                   
                 698 
                 116 
                 95 
                 126 
               
               
                   
                 699 
                 118 
                 97 
                 128 
               
               
                   
                 700 
                 120 
                 99 
                 130 
               
               
                   
                 701 
                 122 
                 101 
                 132 
               
               
                   
                 702 
                 124 
                 103 
                 134 
               
               
                   
                 703 
                 126 
                 105 
                 136 
               
               
                   
                 704 
                 128 
                 107 
                 138 
               
               
                   
                 705 
                 130 
                 109 
                 140 
               
               
                   
                 706 
                 132 
                 111 
                 142 
               
               
                   
                 707 
                 134 
                 113 
                 144 
               
               
                   
                 708 
                 136 
                 115 
                 146 
               
               
                   
                 709 
                 138 
                 117 
                 148 
               
               
                   
                 710 
                 140 
                 119 
                 150 
               
               
                   
                 711 
                 142 
                 121 
                 152 
               
               
                   
                 712 
                 144 
                 123 
                 154 
               
               
                   
                 713 
                 146 
                 125 
                 156 
               
               
                   
                 714 
                 148 
                 127 
                 158 
               
               
                   
                 715 
                 150 
                 129 
                 160 
               
               
                   
                 716 
                 152 
                 131 
                 162 
               
               
                   
                 717 
                 154 
                 133 
                 164 
               
               
                   
                 718 
                 156 
                 135 
                 166 
               
               
                   
                 719 
                 158 
                 137 
                 168 
               
               
                   
                 720 
                 160 
                 139 
                 170 
               
               
                   
                 721 
                 162 
                 141 
                 172 
               
               
                   
                 722 
                 164 
                 143 
                 174 
               
               
                   
                 723 
                 166 
                 145 
                 176 
               
               
                   
                 724 
                 168 
                 147 
                 178 
               
               
                   
                 725 
                 170 
                 149 
                 180 
               
               
                   
                 726 
                 172 
                 151 
                 182 
               
               
                   
                 727 
                 174 
                 153 
                 184 
               
               
                   
                 728 
                 176 
                 155 
                 186 
               
               
                   
                 729 
                 178 
                 157 
                 188 
               
               
                   
                 730 
                 180 
                 159 
                 190 
               
               
                   
                 731 
                 182 
                 161 
                 192 
               
               
                   
                 732 
                 184 
                 163 
                 194 
               
               
                   
                 733 
                 186 
                 165 
                 196 
               
               
                   
                 734 
                 188 
                 167 
                 198 
               
               
                   
                 735 
                 190 
                 169 
                 200 
               
               
                   
                 736 
                 192 
                 171 
                 202 
               
               
                   
                 737 
                 194 
                 173 
                 204 
               
               
                   
                 738 
                 196 
                 175 
                 206 
               
               
                   
                 739 
                 198 
                 177 
                 208 
               
               
                   
                 740 
                 200 
                 179 
                 210 
               
               
                   
                 741 
                 202 
                 181 
                 212 
               
               
                   
                 742 
                 204 
                 183 
                 214 
               
               
                   
                 743 
                 206 
                 185 
                 216 
               
               
                   
                 744 
                 208 
                 187 
                 218 
               
               
                   
                 745 
                 210 
                 189 
                 220 
               
               
                   
                 746 
                 212 
                 191 
                 222 
               
               
                   
                 747 
                 214 
                 193 
                 224 
               
               
                   
                 748 
                 216 
                 195 
                 226 
               
               
                   
                 749 
                 218 
                 197 
                 228 
               
               
                   
                 750 
                 220 
                 199 
                 230 
               
               
                   
                 751 
                 222 
                 201 
                 232 
               
               
                   
                 752 
                 224 
                 203 
                 234 
               
               
                   
                 753 
                 226 
                 205 
                 236 
               
               
                   
                 754 
                 228 
                 207 
                 238 
               
               
                   
                 755 
                 230 
                 209 
                 240 
               
               
                   
                 756 
                 232 
                 211 
                 242 
               
               
                   
                 757 
                 234 
                 213 
                 244 
               
               
                   
                 758 
                 236 
                 215 
                 246 
               
               
                   
                 759 
                 238 
                 217 
                 248 
               
               
                   
                 760 
                 240 
                 219 
                 250 
               
               
                   
                 761 
                 242 
                 221 
                 252 
               
               
                   
                 762 
                 244 
                 223 
                 254 
               
               
                   
                 763 
                 246 
                 225 
                 256 
               
               
                   
                 764 
                 248 
                 227 
                 2 
               
               
                   
                 765 
                 250 
                 229 
                 4 
               
               
                   
                 766 
                 252 
                 231 
                 6 
               
               
                   
                 767 
                 254 
                 233 
                 8 
               
               
                   
                 768 
                 256 
                 235 
                 10 
               
               
                   
                   
               
             
          
         
       
     
         [0122]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 5) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 769 
                 1 
                 64 
                 110 
               
               
                   
                 770 
                 3 
                 66 
                 112 
               
               
                   
                 771 
                 5 
                 68 
                 114 
               
               
                   
                 772 
                 7 
                 70 
                 116 
               
               
                   
                 773 
                 9 
                 72 
                 118 
               
               
                   
                 774 
                 11 
                 74 
                 120 
               
               
                   
                 775 
                 13 
                 76 
                 122 
               
               
                   
                 776 
                 15 
                 78 
                 124 
               
               
                   
                 777 
                 17 
                 80 
                 126 
               
               
                   
                 778 
                 19 
                 82 
                 128 
               
               
                   
                 779 
                 21 
                 84 
                 130 
               
               
                   
                 780 
                 23 
                 86 
                 132 
               
               
                   
                 781 
                 25 
                 88 
                 134 
               
               
                   
                 782 
                 27 
                 90 
                 136 
               
               
                   
                 783 
                 29 
                 92 
                 138 
               
               
                   
                 784 
                 31 
                 94 
                 140 
               
               
                   
                 785 
                 33 
                 96 
                 142 
               
               
                   
                 786 
                 35 
                 98 
                 144 
               
               
                   
                 787 
                 37 
                 100 
                 146 
               
               
                   
                 788 
                 39 
                 102 
                 148 
               
               
                   
                 789 
                 41 
                 104 
                 150 
               
               
                   
                 790 
                 43 
                 106 
                 152 
               
               
                   
                 791 
                 45 
                 108 
                 154 
               
               
                   
                 792 
                 47 
                 110 
                 156 
               
               
                   
                 793 
                 49 
                 112 
                 158 
               
               
                   
                 794 
                 51 
                 114 
                 160 
               
               
                   
                 795 
                 53 
                 116 
                 162 
               
               
                   
                 796 
                 55 
                 118 
                 164 
               
               
                   
                 797 
                 57 
                 120 
                 166 
               
               
                   
                 798 
                 59 
                 122 
                 168 
               
               
                   
                 799 
                 61 
                 124 
                 170 
               
               
                   
                 800 
                 63 
                 126 
                 172 
               
               
                   
                 801 
                 65 
                 128 
                 174 
               
               
                   
                 802 
                 67 
                 130 
                 176 
               
               
                   
                 803 
                 69 
                 132 
                 178 
               
               
                   
                 804 
                 71 
                 134 
                 180 
               
               
                   
                 805 
                 73 
                 136 
                 182 
               
               
                   
                 806 
                 75 
                 138 
                 184 
               
               
                   
                 807 
                 77 
                 140 
                 186 
               
               
                   
                 808 
                 79 
                 142 
                 188 
               
               
                   
                 809 
                 81 
                 144 
                 190 
               
               
                   
                 810 
                 83 
                 146 
                 192 
               
               
                   
                 811 
                 85 
                 148 
                 194 
               
               
                   
                 812 
                 87 
                 150 
                 196 
               
               
                   
                 813 
                 89 
                 152 
                 198 
               
               
                   
                 814 
                 91 
                 154 
                 200 
               
               
                   
                 815 
                 93 
                 156 
                 202 
               
               
                   
                 816 
                 95 
                 158 
                 204 
               
               
                   
                 817 
                 97 
                 160 
                 206 
               
               
                   
                 818 
                 99 
                 162 
                 208 
               
               
                   
                 819 
                 101 
                 164 
                 210 
               
               
                   
                 820 
                 103 
                 166 
                 212 
               
               
                   
                 821 
                 105 
                 168 
                 214 
               
               
                   
                 822 
                 107 
                 170 
                 216 
               
               
                   
                 823 
                 109 
                 172 
                 218 
               
               
                   
                 824 
                 111 
                 174 
                 220 
               
               
                   
                 825 
                 113 
                 176 
                 222 
               
               
                   
                 826 
                 115 
                 178 
                 224 
               
               
                   
                 827 
                 117 
                 180 
                 226 
               
               
                   
                 828 
                 119 
                 182 
                 228 
               
               
                   
                 829 
                 121 
                 184 
                 230 
               
               
                   
                 830 
                 123 
                 186 
                 232 
               
               
                   
                 831 
                 125 
                 188 
                 234 
               
               
                   
                 832 
                 127 
                 190 
                 236 
               
               
                   
                 833 
                 129 
                 192 
                 238 
               
               
                   
                 834 
                 131 
                 194 
                 240 
               
               
                   
                 835 
                 133 
                 196 
                 242 
               
               
                   
                 836 
                 135 
                 198 
                 244 
               
               
                   
                 837 
                 137 
                 200 
                 246 
               
               
                   
                 838 
                 139 
                 202 
                 248 
               
               
                   
                 839 
                 141 
                 204 
                 250 
               
               
                   
                 840 
                 143 
                 206 
                 252 
               
               
                   
                 841 
                 145 
                 208 
                 254 
               
               
                   
                 842 
                 147 
                 210 
                 256 
               
               
                   
                 843 
                 149 
                 212 
                 2 
               
               
                   
                 844 
                 151 
                 214 
                 4 
               
               
                   
                 845 
                 153 
                 216 
                 6 
               
               
                   
                 846 
                 155 
                 218 
                 8 
               
               
                   
                 847 
                 157 
                 220 
                 10 
               
               
                   
                 848 
                 159 
                 222 
                 12 
               
               
                   
                 849 
                 161 
                 224 
                 14 
               
               
                   
                 850 
                 163 
                 226 
                 16 
               
               
                   
                 851 
                 165 
                 228 
                 18 
               
               
                   
                 852 
                 167 
                 230 
                 20 
               
               
                   
                 853 
                 169 
                 232 
                 22 
               
               
                   
                 854 
                 171 
                 234 
                 24 
               
               
                   
                 855 
                 173 
                 236 
                 26 
               
               
                   
                 856 
                 175 
                 238 
                 28 
               
               
                   
                 857 
                 177 
                 240 
                 30 
               
               
                   
                 858 
                 179 
                 242 
                 32 
               
               
                   
                 859 
                 181 
                 244 
                 34 
               
               
                   
                 860 
                 183 
                 246 
                 36 
               
               
                   
                 861 
                 185 
                 248 
                 38 
               
               
                   
                 862 
                 187 
                 250 
                 40 
               
               
                   
                 863 
                 189 
                 252 
                 42 
               
               
                   
                 864 
                 191 
                 254 
                 44 
               
               
                   
                 865 
                 193 
                 256 
                 46 
               
               
                   
                 866 
                 195 
                 2 
                 48 
               
               
                   
                 867 
                 197 
                 4 
                 50 
               
               
                   
                 868 
                 199 
                 6 
                 52 
               
               
                   
                 869 
                 201 
                 8 
                 54 
               
               
                   
                 870 
                 203 
                 10 
                 56 
               
               
                   
                 871 
                 205 
                 12 
                 58 
               
               
                   
                 872 
                 207 
                 14 
                 60 
               
               
                   
                 873 
                 209 
                 16 
                 62 
               
               
                   
                 874 
                 211 
                 18 
                 64 
               
               
                   
                 875 
                 213 
                 20 
                 66 
               
               
                   
                 876 
                 215 
                 22 
                 68 
               
               
                   
                 877 
                 217 
                 24 
                 70 
               
               
                   
                 878 
                 219 
                 26 
                 72 
               
               
                   
                 879 
                 221 
                 28 
                 74 
               
               
                   
                 880 
                 223 
                 30 
                 76 
               
               
                   
                 881 
                 225 
                 32 
                 78 
               
               
                   
                 882 
                 227 
                 34 
                 80 
               
               
                   
                 883 
                 229 
                 36 
                 82 
               
               
                   
                 884 
                 231 
                 38 
                 84 
               
               
                   
                 885 
                 233 
                 40 
                 86 
               
               
                   
                 886 
                 235 
                 42 
                 88 
               
               
                   
                 887 
                 237 
                 44 
                 90 
               
               
                   
                 888 
                 239 
                 46 
                 92 
               
               
                   
                 889 
                 241 
                 48 
                 94 
               
               
                   
                 890 
                 243 
                 50 
                 96 
               
               
                   
                 891 
                 245 
                 52 
                 98 
               
               
                   
                 892 
                 247 
                 54 
                 100 
               
               
                   
                 893 
                 249 
                 56 
                 102 
               
               
                   
                 894 
                 251 
                 58 
                 104 
               
               
                   
                 895 
                 253 
                 60 
                 106 
               
               
                   
                 896 
                 255 
                 62 
                 108 
               
               
                   
                   
               
             
          
         
       
     
         [0123]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 6) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 897 
                 2 
                 73 
                 199 
               
               
                   
                 898 
                 4 
                 75 
                 201 
               
               
                   
                 899 
                 6 
                 77 
                 203 
               
               
                   
                 900 
                 8 
                 79 
                 205 
               
               
                   
                 901 
                 10 
                 81 
                 207 
               
               
                   
                 902 
                 12 
                 83 
                 209 
               
               
                   
                 903 
                 14 
                 85 
                 211 
               
               
                   
                 904 
                 16 
                 87 
                 213 
               
               
                   
                 905 
                 18 
                 89 
                 215 
               
               
                   
                 906 
                 20 
                 91 
                 217 
               
               
                   
                 907 
                 22 
                 93 
                 219 
               
               
                   
                 908 
                 24 
                 95 
                 221 
               
               
                   
                 909 
                 26 
                 97 
                 223 
               
               
                   
                 910 
                 28 
                 99 
                 225 
               
               
                   
                 911 
                 30 
                 101 
                 227 
               
               
                   
                 912 
                 32 
                 103 
                 229 
               
               
                   
                 913 
                 34 
                 105 
                 231 
               
               
                   
                 914 
                 36 
                 107 
                 233 
               
               
                   
                 915 
                 38 
                 109 
                 235 
               
               
                   
                 916 
                 40 
                 111 
                 237 
               
               
                   
                 917 
                 42 
                 113 
                 239 
               
               
                   
                 918 
                 44 
                 115 
                 241 
               
               
                   
                 919 
                 46 
                 117 
                 243 
               
               
                   
                 920 
                 48 
                 119 
                 245 
               
               
                   
                 921 
                 50 
                 121 
                 247 
               
               
                   
                 922 
                 52 
                 123 
                 249 
               
               
                   
                 923 
                 54 
                 125 
                 251 
               
               
                   
                 924 
                 56 
                 127 
                 253 
               
               
                   
                 925 
                 58 
                 129 
                 255 
               
               
                   
                 926 
                 60 
                 131 
                 1 
               
               
                   
                 927 
                 62 
                 133 
                 3 
               
               
                   
                 928 
                 64 
                 135 
                 5 
               
               
                   
                 929 
                 66 
                 137 
                 7 
               
               
                   
                 930 
                 68 
                 139 
                 9 
               
               
                   
                 931 
                 70 
                 141 
                 11 
               
               
                   
                 932 
                 72 
                 143 
                 13 
               
               
                   
                 933 
                 74 
                 145 
                 15 
               
               
                   
                 934 
                 76 
                 147 
                 17 
               
               
                   
                 935 
                 78 
                 149 
                 19 
               
               
                   
                 936 
                 80 
                 151 
                 21 
               
               
                   
                 937 
                 82 
                 153 
                 23 
               
               
                   
                 938 
                 84 
                 155 
                 25 
               
               
                   
                 939 
                 86 
                 157 
                 27 
               
               
                   
                 940 
                 88 
                 159 
                 29 
               
               
                   
                 941 
                 90 
                 161 
                 31 
               
               
                   
                 942 
                 92 
                 163 
                 33 
               
               
                   
                 943 
                 94 
                 165 
                 35 
               
               
                   
                 944 
                 96 
                 167 
                 37 
               
               
                   
                 945 
                 98 
                 169 
                 39 
               
               
                   
                 946 
                 100 
                 171 
                 41 
               
               
                   
                 947 
                 102 
                 173 
                 43 
               
               
                   
                 948 
                 104 
                 175 
                 45 
               
               
                   
                 949 
                 106 
                 177 
                 47 
               
               
                   
                 950 
                 108 
                 179 
                 49 
               
               
                   
                 951 
                 110 
                 181 
                 51 
               
               
                   
                 952 
                 112 
                 183 
                 53 
               
               
                   
                 953 
                 114 
                 185 
                 55 
               
               
                   
                 954 
                 116 
                 187 
                 57 
               
               
                   
                 955 
                 118 
                 189 
                 59 
               
               
                   
                 956 
                 120 
                 191 
                 61 
               
               
                   
                 957 
                 122 
                 193 
                 63 
               
               
                   
                 958 
                 124 
                 195 
                 65 
               
               
                   
                 959 
                 126 
                 197 
                 67 
               
               
                   
                 960 
                 128 
                 199 
                 69 
               
               
                   
                 961 
                 130 
                 201 
                 71 
               
               
                   
                 962 
                 132 
                 203 
                 73 
               
               
                   
                 963 
                 134 
                 205 
                 75 
               
               
                   
                 964 
                 136 
                 207 
                 77 
               
               
                   
                 965 
                 138 
                 209 
                 79 
               
               
                   
                 966 
                 140 
                 211 
                 81 
               
               
                   
                 967 
                 142 
                 213 
                 83 
               
               
                   
                 968 
                 144 
                 215 
                 85 
               
               
                   
                 969 
                 146 
                 217 
                 87 
               
               
                   
                 970 
                 148 
                 219 
                 89 
               
               
                   
                 971 
                 150 
                 221 
                 91 
               
               
                   
                 972 
                 152 
                 223 
                 93 
               
               
                   
                 973 
                 154 
                 225 
                 95 
               
               
                   
                 974 
                 156 
                 227 
                 97 
               
               
                   
                 975 
                 158 
                 229 
                 99 
               
               
                   
                 976 
                 160 
                 231 
                 101 
               
               
                   
                 977 
                 162 
                 233 
                 103 
               
               
                   
                 978 
                 164 
                 235 
                 105 
               
               
                   
                 979 
                 166 
                 237 
                 107 
               
               
                   
                 980 
                 168 
                 239 
                 109 
               
               
                   
                 981 
                 170 
                 241 
                 111 
               
               
                   
                 982 
                 172 
                 243 
                 113 
               
               
                   
                 983 
                 174 
                 245 
                 115 
               
               
                   
                 984 
                 176 
                 247 
                 117 
               
               
                   
                 985 
                 178 
                 249 
                 119 
               
               
                   
                 986 
                 180 
                 251 
                 121 
               
               
                   
                 987 
                 182 
                 253 
                 123 
               
               
                   
                 988 
                 184 
                 255 
                 125 
               
               
                   
                 989 
                 186 
                 1 
                 127 
               
               
                   
                 990 
                 188 
                 3 
                 129 
               
               
                   
                 991 
                 190 
                 5 
                 131 
               
               
                   
                 992 
                 192 
                 7 
                 133 
               
               
                   
                 993 
                 194 
                 9 
                 135 
               
               
                   
                 994 
                 196 
                 11 
                 137 
               
               
                   
                 995 
                 198 
                 13 
                 139 
               
               
                   
                 996 
                 200 
                 15 
                 141 
               
               
                   
                 997 
                 202 
                 17 
                 143 
               
               
                   
                 998 
                 204 
                 19 
                 145 
               
               
                   
                 999 
                 206 
                 21 
                 147 
               
               
                   
                 1000 
                 208 
                 23 
                 149 
               
               
                   
                 1001 
                 210 
                 25 
                 151 
               
               
                   
                 1002 
                 212 
                 27 
                 153 
               
               
                   
                 1003 
                 214 
                 29 
                 155 
               
               
                   
                 1004 
                 216 
                 31 
                 157 
               
               
                   
                 1005 
                 218 
                 33 
                 159 
               
               
                   
                 1006 
                 220 
                 35 
                 161 
               
               
                   
                 1007 
                 222 
                 37 
                 163 
               
               
                   
                 1008 
                 224 
                 39 
                 165 
               
               
                   
                 1009 
                 226 
                 41 
                 167 
               
               
                   
                 1010 
                 228 
                 43 
                 169 
               
               
                   
                 1011 
                 230 
                 45 
                 171 
               
               
                   
                 1012 
                 232 
                 47 
                 173 
               
               
                   
                 1013 
                 234 
                 49 
                 175 
               
               
                   
                 1014 
                 236 
                 51 
                 177 
               
               
                   
                 1015 
                 238 
                 53 
                 179 
               
               
                   
                 1016 
                 240 
                 55 
                 181 
               
               
                   
                 1017 
                 242 
                 57 
                 183 
               
               
                   
                 1018 
                 244 
                 59 
                 185 
               
               
                   
                 1019 
                 246 
                 61 
                 187 
               
               
                   
                 1020 
                 248 
                 63 
                 189 
               
               
                   
                 1021 
                 250 
                 65 
                 191 
               
               
                   
                 1022 
                 252 
                 67 
                 193 
               
               
                   
                 1023 
                 254 
                 69 
                 195 
               
               
                   
                 1024 
                 256 
                 71 
                 197 
               
               
                   
                   
               
             
          
         
       
     
         [0124]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                   
               
               
                 H(d) 
               
             
          
           
               
                 b 
                 c 
                 c 
               
               
                   
               
             
          
           
               
                 1025 
                 1 
                 2 
               
               
                 1026 
                 2 
                 3 
               
               
                 1027 
                 3 
                 4 
               
               
                 1028 
                 4 
                 5 
               
               
                 1029 
                 5 
                 6 
               
               
                 1030 
                 6 
                 7 
               
               
                 1031 
                 7 
                 8 
               
               
                 1032 
                 8 
                 9 
               
               
                 1033 
                 9 
                 10 
               
               
                 1034 
                 10 
                 11 
               
               
                 1035 
                 11 
                 12 
               
               
                 1036 
                 12 
                 13 
               
               
                 1037 
                 13 
                 14 
               
               
                 1038 
                 14 
                 15 
               
               
                 1039 
                 15 
                 16 
               
               
                 1040 
                 16 
                 17 
               
               
                 1041 
                 17 
                 18 
               
               
                 1042 
                 18 
                 19 
               
               
                 1043 
                 19 
                 20 
               
               
                 1044 
                 20 
                 21 
               
               
                 1045 
                 21 
                 22 
               
               
                 1046 
                 22 
                 23 
               
               
                 1047 
                 23 
                 24 
               
               
                 1048 
                 24 
                 25 
               
               
                 1049 
                 25 
                 26 
               
               
                 1050 
                 26 
                 27 
               
               
                 1051 
                 27 
                 28 
               
               
                 1052 
                 28 
                 29 
               
               
                 1053 
                 29 
                 30 
               
               
                 1054 
                 30 
                 31 
               
               
                 1055 
                 31 
                 32 
               
               
                 1056 
                 32 
                 33 
               
               
                 1057 
                 33 
                 34 
               
               
                 1058 
                 34 
                 35 
               
               
                 1059 
                 35 
                 36 
               
               
                 1060 
                 36 
                 37 
               
               
                 1061 
                 37 
                 38 
               
               
                 1062 
                 38 
                 39 
               
               
                 1063 
                 39 
                 40 
               
               
                 1064 
                 40 
                 41 
               
               
                 1065 
                 41 
                 42 
               
               
                 1066 
                 42 
                 43 
               
               
                 1067 
                 43 
                 44 
               
               
                 1068 
                 44 
                 45 
               
               
                 1069 
                 45 
                 46 
               
               
                 1070 
                 46 
                 47 
               
               
                 1071 
                 47 
                 48 
               
               
                 1072 
                 48 
                 49 
               
               
                 1073 
                 49 
                 50 
               
               
                 1074 
                 50 
                 51 
               
               
                 1075 
                 51 
                 52 
               
               
                 1076 
                 52 
                 53 
               
               
                 1077 
                 53 
                 54 
               
               
                 1078 
                 54 
                 55 
               
               
                 1079 
                 55 
                 56 
               
               
                 1080 
                 56 
                 57 
               
               
                 1081 
                 57 
                 58 
               
               
                 1082 
                 58 
                 59 
               
               
                 1083 
                 59 
                 60 
               
               
                 1084 
                 60 
                 61 
               
               
                 1085 
                 61 
                 62 
               
               
                 1086 
                 62 
                 63 
               
               
                 1087 
                 63 
                 64 
               
               
                 1088 
                 64 
                 65 
               
               
                 1089 
                 65 
                 66 
               
               
                 1090 
                 66 
                 67 
               
               
                 1091 
                 67 
                 68 
               
               
                 1092 
                 68 
                 69 
               
               
                 1093 
                 69 
                 70 
               
               
                 1094 
                 70 
                 71 
               
               
                 1095 
                 71 
                 72 
               
               
                 1096 
                 72 
                 73 
               
               
                 1097 
                 73 
                 74 
               
               
                 1098 
                 74 
                 75 
               
               
                 1099 
                 75 
                 76 
               
               
                 1100 
                 76 
                 77 
               
               
                 1101 
                 77 
                 78 
               
               
                 1102 
                 78 
                 79 
               
               
                 1103 
                 79 
                 80 
               
               
                 1104 
                 80 
                 81 
               
               
                 1105 
                 81 
                 82 
               
               
                 1106 
                 82 
                 83 
               
               
                 1107 
                 83 
                 84 
               
               
                 1108 
                 84 
                 85 
               
               
                 1109 
                 85 
                 86 
               
               
                 1110 
                 86 
                 87 
               
               
                 1111 
                 87 
                 88 
               
               
                 1112 
                 88 
                 89 
               
               
                 1113 
                 89 
                 90 
               
               
                 1114 
                 90 
                 91 
               
               
                 1115 
                 91 
                 92 
               
               
                 1116 
                 92 
                 93 
               
               
                 1117 
                 93 
                 94 
               
               
                 1118 
                 94 
                 95 
               
               
                 1119 
                 95 
                 96 
               
               
                 1120 
                 96 
                 97 
               
               
                 1121 
                 97 
                 98 
               
               
                 1122 
                 98 
                 99 
               
               
                 1123 
                 99 
                 100 
               
               
                 1124 
                 100 
                 101 
               
               
                 1125 
                 101 
                 102 
               
               
                 1126 
                 102 
                 103 
               
               
                 1127 
                 103 
                 104 
               
               
                 1128 
                 104 
                 105 
               
               
                 1129 
                 105 
                 106 
               
               
                 1130 
                 106 
                 107 
               
               
                 1131 
                 107 
                 108 
               
               
                 1132 
                 108 
                 109 
               
               
                 1133 
                 109 
                 110 
               
               
                 1134 
                 110 
                 111 
               
               
                 1135 
                 111 
                 112 
               
               
                 1136 
                 112 
                 113 
               
               
                 1137 
                 113 
                 114 
               
               
                 1138 
                 114 
                 115 
               
               
                 1139 
                 115 
                 116 
               
               
                 1140 
                 116 
                 117 
               
               
                 1141 
                 117 
                 118 
               
               
                 1142 
                 118 
                 119 
               
               
                 1143 
                 119 
                 120 
               
               
                 1144 
                 120 
                 121 
               
               
                 1145 
                 121 
                 122 
               
               
                 1146 
                 122 
                 123 
               
               
                 1147 
                 123 
                 124 
               
               
                 1148 
                 124 
                 125 
               
               
                 1149 
                 125 
                 126 
               
               
                 1150 
                 126 
                 127 
               
               
                 1151 
                 127 
                 128 
               
               
                 1152 
                 128 
                 129 
               
               
                 1153 
                 129 
                 130 
               
               
                 1154 
                 130 
                 131 
               
               
                 1155 
                 131 
                 132 
               
               
                 1156 
                 132 
                 133 
               
               
                 1157 
                 133 
                 134 
               
               
                 1158 
                 134 
                 135 
               
               
                 1159 
                 135 
                 136 
               
               
                 1160 
                 136 
                 137 
               
               
                 1161 
                 137 
                 138 
               
               
                 1162 
                 138 
                 139 
               
               
                 1163 
                 139 
                 140 
               
               
                 1164 
                 140 
                 141 
               
               
                 1165 
                 141 
                 142 
               
               
                 1166 
                 142 
                 143 
               
               
                 1167 
                 143 
                 144 
               
               
                 1168 
                 144 
                 145 
               
               
                 1169 
                 145 
                 146 
               
               
                 1170 
                 146 
                 147 
               
               
                 1171 
                 147 
                 148 
               
               
                 1172 
                 148 
                 149 
               
               
                 1173 
                 149 
                 150 
               
               
                 1174 
                 150 
                 151 
               
               
                 1175 
                 151 
                 152 
               
               
                 1176 
                 152 
                 153 
               
               
                 1177 
                 153 
                 154 
               
               
                 1178 
                 154 
                 155 
               
               
                 1179 
                 155 
                 156 
               
               
                 1180 
                 156 
                 157 
               
               
                 1181 
                 157 
                 158 
               
               
                 1182 
                 158 
                 159 
               
               
                 1183 
                 159 
                 160 
               
               
                 1184 
                 160 
                 161 
               
               
                 1185 
                 161 
                 162 
               
               
                 1186 
                 162 
                 163 
               
               
                 1187 
                 163 
                 164 
               
               
                 1188 
                 164 
                 165 
               
               
                 1189 
                 165 
                 166 
               
               
                 1190 
                 166 
                 167 
               
               
                 1191 
                 167 
                 168 
               
               
                 1192 
                 168 
                 169 
               
               
                 1193 
                 169 
                 170 
               
               
                 1194 
                 170 
                 171 
               
               
                 1195 
                 171 
                 172 
               
               
                 1196 
                 172 
                 173 
               
               
                 1197 
                 173 
                 174 
               
               
                 1198 
                 174 
                 175 
               
               
                 1199 
                 175 
                 176 
               
               
                 1200 
                 176 
                 177 
               
               
                 1201 
                 177 
                 178 
               
               
                 1202 
                 178 
                 179 
               
               
                 1203 
                 179 
                 180 
               
               
                 1204 
                 180 
                 181 
               
               
                 1205 
                 181 
                 182 
               
               
                 1206 
                 182 
                 183 
               
               
                 1207 
                 183 
                 184 
               
               
                 1208 
                 184 
                 185 
               
               
                 1209 
                 185 
                 186 
               
               
                 1210 
                 186 
                 187 
               
               
                 1211 
                 187 
                 188 
               
               
                 1212 
                 188 
                 189 
               
               
                 1213 
                 189 
                 190 
               
               
                 1214 
                 190 
                 191 
               
               
                 1215 
                 191 
                 192 
               
               
                 1216 
                 192 
                 193 
               
               
                 1217 
                 193 
                 194 
               
               
                 1218 
                 194 
                 195 
               
               
                 1219 
                 195 
                 196 
               
               
                 1220 
                 196 
                 197 
               
               
                 1221 
                 197 
                 198 
               
               
                 1222 
                 198 
                 199 
               
               
                 1223 
                 199 
                 200 
               
               
                 1224 
                 200 
                 201 
               
               
                 1225 
                 201 
                 202 
               
               
                 1226 
                 202 
                 203 
               
               
                 1227 
                 203 
                 204 
               
               
                 1228 
                 204 
                 205 
               
               
                 1229 
                 205 
                 206 
               
               
                 1230 
                 206 
                 207 
               
               
                 1231 
                 207 
                 208 
               
               
                 1232 
                 208 
                 209 
               
               
                 1233 
                 209 
                 210 
               
               
                 1234 
                 210 
                 211 
               
               
                 1235 
                 211 
                 212 
               
               
                 1236 
                 212 
                 213 
               
               
                 1237 
                 213 
                 214 
               
               
                 1238 
                 214 
                 215 
               
               
                 1239 
                 215 
                 216 
               
               
                 1240 
                 216 
                 217 
               
               
                 1241 
                 217 
                 218 
               
               
                 1242 
                 218 
                 219 
               
               
                 1243 
                 219 
                 220 
               
               
                 1244 
                 220 
                 221 
               
               
                 1245 
                 221 
                 222 
               
               
                 1246 
                 222 
                 223 
               
               
                 1247 
                 223 
                 224 
               
               
                 1248 
                 224 
                 225 
               
               
                 1249 
                 225 
                 226 
               
               
                 1250 
                 226 
                 227 
               
               
                 1251 
                 227 
                 228 
               
               
                 1252 
                 228 
                 229 
               
               
                 1253 
                 229 
                 230 
               
               
                 1254 
                 230 
                 231 
               
               
                 1255 
                 231 
                 232 
               
               
                 1256 
                 232 
                 233 
               
               
                 1257 
                 233 
                 234 
               
               
                 1258 
                 234 
                 235 
               
               
                 1259 
                 235 
                 236 
               
               
                 1260 
                 236 
                 237 
               
               
                 1261 
                 237 
                 238 
               
               
                 1262 
                 238 
                 239 
               
               
                 1263 
                 239 
                 240 
               
               
                 1264 
                 240 
                 241 
               
               
                 1265 
                 241 
                 242 
               
               
                 1266 
                 242 
                 243 
               
               
                 1267 
                 243 
                 244 
               
               
                 1268 
                 244 
                 245 
               
               
                 1269 
                 245 
                 246 
               
               
                 1270 
                 246 
                 247 
               
               
                 1271 
                 247 
                 248 
               
               
                 1272 
                 248 
                 249 
               
               
                 1273 
                 249 
                 250 
               
               
                 1274 
                 250 
                 251 
               
               
                 1275 
                 251 
                 252 
               
               
                 1276 
                 252 
                 253 
               
               
                 1277 
                 253 
                 254 
               
               
                 1278 
                 254 
                 255 
               
               
                 1279 
                 255 
                 256 
               
               
                 1280 
                 256 
               
               
                   
               
             
          
         
       
     
       Appendix B  
       [0125]     2. Another embodiment of a parity check matrix of a (1280, 1024) LDPC code is presented below.  
         [0126]     The following presents another possible embodiment of a (1280,1024) irregular LDPC code parity check matrix that is constructed in accordance with certain aspects of the invention. The parity check matrix is presented in the following format:  
         [0127]     H=[H(7,1), H(7,2), H(3,1), H(3,3), H(3,4), H(3,5), H(3,6), H(d)] 
                                                                                   TABLE 1                           H(7, 1)            b   c   c   c   c   c   c   c                    1   1   203   21   57   85   42   191       2   3   205   23   59   87   44   193       3   5   207   25   61   89   46   195       4   7   209   27   63   91   48   197       5   9   211   29   65   93   50   199       6   11   213   31   67   95   52   201       7   13   215   33   69   97   54   203       8   15   217   35   71   99   56   205       9   17   219   37   73   101   58   207       10   19   221   39   75   103   60   209       11   21   223   41   77   105   62   211       12   23   225   43   79   107   64   213       13   25   227   45   81   109   66   215       14   27   229   47   83   111   68   217       15   29   231   49   85   113   70   219       16   31   233   51   87   115   72   221       17   33   235   53   89   117   74   223       18   35   237   55   91   119   76   225       19   37   239   57   93   121   78   227       20   39   241   59   95   123   80   229       21   41   243   61   97   125   82   231       22   43   245   63   99   127   84   233       23   45   247   65   101   129   86   235       24   47   249   67   103   131   88   237       25   49   251   69   105   133   90   239       26   51   253   71   107   135   92   241       27   53   255   73   109   137   94   243       28   55   1   75   111   139   96   245       29   57   3   77   113   141   98   247       30   59   5   79   115   143   100   249       31   61   7   81   117   145   102   251       32   63   9   83   119   147   104   253       33   65   11   85   121   149   106   255       34   67   13   87   123   151   108   1       35   69   15   89   125   153   110   3       36   71   17   91   127   155   112   5       37   73   19   93   129   157   114   7       38   75   21   95   131   159   116   9       39   77   23   97   133   161   118   11       40   79   25   99   135   163   120   13       41   81   27   101   137   165   122   15       42   83   29   103   139   167   124   17       43   85   31   105   141   169   126   19       44   87   33   107   143   171   128   21       45   89   35   109   145   173   130   23       46   91   37   111   147   175   132   25       47   93   39   113   149   177   134   27       48   95   41   115   151   179   136   29       49   97   43   117   153   181   138   31       50   99   45   119   155   183   140   33       51   101   47   121   157   185   142   35       52   103   49   123   159   187   144   37       53   105   51   125   161   189   146   39       54   107   53   127   163   191   148   41       55   109   55   129   165   193   150   43       56   111   57   131   167   195   152   45       57   113   59   133   169   197   154   47       58   115   61   135   171   199   156   49       59   117   63   137   173   201   158   51       60   119   65   139   175   203   160   53       61   121   67   141   177   205   162   55       62   123   69   143   179   207   164   57       63   125   71   145   181   209   166   59       64   127   73   147   183   211   168   61       65   129   75   149   185   213   170   63       66   131   77   151   187   215   172   65       67   133   79   153   189   217   174   67       68   135   81   155   191   219   176   69       69   137   83   157   193   221   178   71       70   139   85   159   195   223   180   73       71   141   87   161   197   225   182   75       72   143   89   163   199   227   184   77       73   145   91   165   201   229   186   79       74   147   93   167   203   231   188   81       75   149   95   169   205   233   190   83       76   151   97   171   207   235   192   85       77   153   99   173   209   237   194   87       78   155   101   175   211   239   196   89       79   157   103   177   213   241   198   91       80   159   105   179   215   243   200   93       81   161   107   181   217   245   202   95       82   163   109   183   219   247   204   97       83   165   111   185   221   249   206   99       84   167   113   187   223   251   208   101       85   169   115   189   225   253   210   103       86   171   117   191   227   255   212   105       87   173   119   193   229   1   214   107       88   175   121   195   231   3   216   109       89   177   123   197   233   5   218   111       90   179   125   199   235   7   220   113       91   181   127   201   237   9   222   115       92   183   129   203   239   11   224   117       93   185   131   205   241   13   226   119       94   187   133   207   243   15   228   121       95   189   135   209   245   17   230   123       96   191   137   211   247   19   232   125       97   193   139   213   249   21   234   127       98   195   141   215   251   23   236   129       99   197   143   217   253   25   238   131       100   199   145   219   255   27   240   133       101   201   147   221   1   29   242   135       102   203   149   223   3   31   244   137       103   205   151   225   5   33   246   139       104   207   153   227   7   35   248   141       105   209   155   229   9   37   250   143       106   211   157   231   11   39   252   145       107   213   159   233   13   41   254   147       108   215   161   235   15   43   256   149       109   217   163   237   17   45   2   151       110   219   165   239   19   47   4   153       111   221   167   241   21   49   6   155       112   223   169   243   23   51   8   157       113   225   171   245   25   53   10   159       114   227   173   247   27   55   12   161       115   229   175   249   29   57   14   163       116   231   177   251   31   59   16   165       117   233   179   253   33   61   18   167       118   235   181   255   35   63   20   169       119   237   183   1   37   65   22   171       120   239   185   3   39   67   24   173       121   241   187   5   41   69   26   175       122   243   189   7   43   71   28   177       123   245   191   9   45   73   30   179       124   247   193   11   47   75   32   181       125   249   195   13   49   77   34   183       126   251   197   15   51   79   36   185       127   253   199   17   53   81   38   187       128   255   201   19   55   83   40   189                  
 
         [0128]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                   
               
               
                 H(7, 2) 
               
             
          
           
               
                 b 
                 c 
                 c 
                 c 
                 c 
                 c 
                 c 
                 c 
               
               
                   
               
             
          
           
               
                 129 
                 2 
                 180 
                 54 
                 122 
                 188 
                 225 
                 144 
               
               
                 130 
                 4 
                 182 
                 56 
                 124 
                 190 
                 227 
                 146 
               
               
                 131 
                 6 
                 184 
                 58 
                 126 
                 192 
                 229 
                 148 
               
               
                 132 
                 8 
                 186 
                 60 
                 128 
                 194 
                 231 
                 150 
               
               
                 133 
                 10 
                 188 
                 62 
                 130 
                 196 
                 233 
                 152 
               
               
                 134 
                 12 
                 190 
                 64 
                 132 
                 198 
                 235 
                 154 
               
               
                 135 
                 14 
                 192 
                 66 
                 134 
                 200 
                 237 
                 156 
               
               
                 136 
                 16 
                 194 
                 68 
                 136 
                 202 
                 239 
                 158 
               
               
                 137 
                 18 
                 196 
                 70 
                 138 
                 204 
                 241 
                 160 
               
               
                 138 
                 20 
                 198 
                 72 
                 140 
                 206 
                 243 
                 162 
               
               
                 139 
                 22 
                 200 
                 74 
                 142 
                 208 
                 245 
                 164 
               
               
                 140 
                 24 
                 202 
                 76 
                 144 
                 210 
                 247 
                 166 
               
               
                 141 
                 26 
                 204 
                 78 
                 146 
                 212 
                 249 
                 168 
               
               
                 142 
                 28 
                 206 
                 80 
                 148 
                 214 
                 251 
                 170 
               
               
                 143 
                 30 
                 208 
                 82 
                 150 
                 216 
                 253 
                 172 
               
               
                 144 
                 32 
                 210 
                 84 
                 152 
                 218 
                 255 
                 174 
               
               
                 145 
                 34 
                 212 
                 86 
                 154 
                 220 
                 1 
                 176 
               
               
                 146 
                 36 
                 214 
                 88 
                 156 
                 222 
                 3 
                 178 
               
               
                 147 
                 38 
                 216 
                 90 
                 158 
                 224 
                 5 
                 180 
               
               
                 148 
                 40 
                 218 
                 92 
                 160 
                 226 
                 7 
                 182 
               
               
                 149 
                 42 
                 220 
                 94 
                 162 
                 228 
                 9 
                 184 
               
               
                 150 
                 44 
                 222 
                 96 
                 164 
                 230 
                 11 
                 186 
               
               
                 151 
                 46 
                 224 
                 98 
                 166 
                 232 
                 13 
                 188 
               
               
                 152 
                 48 
                 226 
                 100 
                 168 
                 234 
                 15 
                 190 
               
               
                 153 
                 50 
                 228 
                 102 
                 170 
                 236 
                 17 
                 192 
               
               
                 154 
                 52 
                 230 
                 104 
                 172 
                 238 
                 19 
                 194 
               
               
                 155 
                 54 
                 232 
                 106 
                 174 
                 240 
                 21 
                 196 
               
               
                 156 
                 56 
                 234 
                 108 
                 176 
                 242 
                 23 
                 198 
               
               
                 157 
                 58 
                 236 
                 110 
                 178 
                 244 
                 25 
                 200 
               
               
                 158 
                 60 
                 238 
                 112 
                 180 
                 246 
                 27 
                 202 
               
               
                 159 
                 62 
                 240 
                 114 
                 182 
                 248 
                 29 
                 204 
               
               
                 160 
                 64 
                 242 
                 116 
                 184 
                 250 
                 31 
                 206 
               
               
                 161 
                 66 
                 244 
                 118 
                 186 
                 252 
                 33 
                 208 
               
               
                 162 
                 68 
                 246 
                 120 
                 188 
                 254 
                 35 
                 210 
               
               
                 163 
                 70 
                 248 
                 122 
                 190 
                 256 
                 37 
                 212 
               
               
                 164 
                 72 
                 250 
                 124 
                 192 
                 2 
                 39 
                 214 
               
               
                 165 
                 74 
                 252 
                 126 
                 194 
                 4 
                 41 
                 216 
               
               
                 166 
                 76 
                 254 
                 128 
                 196 
                 6 
                 43 
                 218 
               
               
                 167 
                 78 
                 256 
                 130 
                 198 
                 8 
                 45 
                 220 
               
               
                 168 
                 80 
                 2 
                 132 
                 200 
                 10 
                 47 
                 222 
               
               
                 169 
                 82 
                 4 
                 134 
                 202 
                 12 
                 49 
                 224 
               
               
                 170 
                 84 
                 6 
                 136 
                 204 
                 14 
                 51 
                 226 
               
               
                 171 
                 86 
                 8 
                 138 
                 206 
                 16 
                 53 
                 228 
               
               
                 172 
                 88 
                 10 
                 140 
                 208 
                 18 
                 55 
                 230 
               
               
                 173 
                 90 
                 12 
                 142 
                 210 
                 20 
                 57 
                 232 
               
               
                 174 
                 92 
                 14 
                 144 
                 212 
                 22 
                 59 
                 234 
               
               
                 175 
                 94 
                 16 
                 146 
                 214 
                 24 
                 61 
                 236 
               
               
                 176 
                 96 
                 18 
                 148 
                 216 
                 26 
                 63 
                 238 
               
               
                 177 
                 98 
                 20 
                 150 
                 218 
                 28 
                 65 
                 240 
               
               
                 178 
                 100 
                 22 
                 152 
                 220 
                 30 
                 67 
                 242 
               
               
                 179 
                 102 
                 24 
                 154 
                 222 
                 32 
                 69 
                 244 
               
               
                 180 
                 104 
                 26 
                 156 
                 224 
                 34 
                 71 
                 246 
               
               
                 181 
                 106 
                 28 
                 158 
                 226 
                 36 
                 73 
                 248 
               
               
                 182 
                 108 
                 30 
                 160 
                 228 
                 38 
                 75 
                 250 
               
               
                 183 
                 110 
                 32 
                 162 
                 230 
                 40 
                 77 
                 252 
               
               
                 184 
                 112 
                 34 
                 164 
                 232 
                 42 
                 79 
                 254 
               
               
                 185 
                 114 
                 36 
                 166 
                 234 
                 44 
                 81 
                 256 
               
               
                 186 
                 116 
                 38 
                 168 
                 236 
                 46 
                 83 
                 2 
               
               
                 187 
                 118 
                 40 
                 170 
                 238 
                 48 
                 85 
                 4 
               
               
                 188 
                 120 
                 42 
                 172 
                 240 
                 50 
                 87 
                 6 
               
               
                 189 
                 122 
                 44 
                 174 
                 242 
                 52 
                 89 
                 8 
               
               
                 190 
                 124 
                 46 
                 176 
                 244 
                 54 
                 91 
                 10 
               
               
                 191 
                 126 
                 48 
                 178 
                 246 
                 56 
                 93 
                 12 
               
               
                 192 
                 128 
                 50 
                 180 
                 248 
                 58 
                 95 
                 14 
               
               
                 193 
                 130 
                 52 
                 182 
                 250 
                 60 
                 97 
                 16 
               
               
                 194 
                 132 
                 54 
                 184 
                 252 
                 62 
                 99 
                 18 
               
               
                 195 
                 134 
                 56 
                 186 
                 254 
                 64 
                 101 
                 20 
               
               
                 196 
                 136 
                 58 
                 188 
                 256 
                 66 
                 103 
                 22 
               
               
                 197 
                 138 
                 60 
                 190 
                 2 
                 68 
                 105 
                 24 
               
               
                 198 
                 140 
                 62 
                 192 
                 4 
                 70 
                 107 
                 26 
               
               
                 199 
                 142 
                 64 
                 194 
                 6 
                 72 
                 109 
                 28 
               
               
                 200 
                 144 
                 66 
                 196 
                 8 
                 74 
                 111 
                 30 
               
               
                 201 
                 146 
                 68 
                 198 
                 10 
                 76 
                 113 
                 32 
               
               
                 202 
                 148 
                 70 
                 200 
                 12 
                 78 
                 115 
                 34 
               
               
                 203 
                 150 
                 72 
                 202 
                 14 
                 80 
                 117 
                 36 
               
               
                 204 
                 152 
                 74 
                 204 
                 16 
                 82 
                 119 
                 38 
               
               
                 205 
                 154 
                 76 
                 206 
                 18 
                 84 
                 121 
                 40 
               
               
                 206 
                 156 
                 78 
                 208 
                 20 
                 86 
                 123 
                 42 
               
               
                 207 
                 158 
                 80 
                 210 
                 22 
                 88 
                 125 
                 44 
               
               
                 208 
                 160 
                 82 
                 212 
                 24 
                 90 
                 127 
                 46 
               
               
                 209 
                 162 
                 84 
                 214 
                 26 
                 92 
                 129 
                 48 
               
               
                 210 
                 164 
                 86 
                 216 
                 28 
                 94 
                 131 
                 50 
               
               
                 211 
                 166 
                 88 
                 218 
                 30 
                 96 
                 133 
                 52 
               
               
                 212 
                 168 
                 90 
                 220 
                 32 
                 98 
                 135 
                 54 
               
               
                 213 
                 170 
                 92 
                 222 
                 34 
                 100 
                 137 
                 56 
               
               
                 214 
                 172 
                 94 
                 224 
                 36 
                 102 
                 139 
                 58 
               
               
                 215 
                 174 
                 96 
                 226 
                 38 
                 104 
                 141 
                 60 
               
               
                 216 
                 176 
                 98 
                 228 
                 40 
                 106 
                 143 
                 62 
               
               
                 217 
                 178 
                 100 
                 230 
                 42 
                 108 
                 145 
                 64 
               
               
                 218 
                 180 
                 102 
                 232 
                 44 
                 110 
                 147 
                 66 
               
               
                 219 
                 182 
                 104 
                 234 
                 46 
                 112 
                 149 
                 68 
               
               
                 220 
                 184 
                 106 
                 236 
                 48 
                 114 
                 151 
                 70 
               
               
                 221 
                 186 
                 108 
                 238 
                 50 
                 116 
                 153 
                 72 
               
               
                 222 
                 188 
                 110 
                 240 
                 52 
                 118 
                 155 
                 74 
               
               
                 223 
                 190 
                 112 
                 242 
                 54 
                 120 
                 157 
                 76 
               
               
                 224 
                 192 
                 114 
                 244 
                 56 
                 122 
                 159 
                 78 
               
               
                 225 
                 194 
                 116 
                 246 
                 58 
                 124 
                 161 
                 80 
               
               
                 226 
                 196 
                 118 
                 248 
                 60 
                 126 
                 163 
                 82 
               
               
                 227 
                 198 
                 120 
                 250 
                 62 
                 128 
                 165 
                 84 
               
               
                 228 
                 200 
                 122 
                 252 
                 64 
                 130 
                 167 
                 86 
               
               
                 229 
                 202 
                 124 
                 254 
                 66 
                 132 
                 169 
                 88 
               
               
                 230 
                 204 
                 126 
                 256 
                 68 
                 134 
                 171 
                 90 
               
               
                 231 
                 206 
                 128 
                 2 
                 70 
                 136 
                 173 
                 92 
               
               
                 232 
                 208 
                 130 
                 4 
                 72 
                 138 
                 175 
                 94 
               
               
                 233 
                 210 
                 132 
                 6 
                 74 
                 140 
                 177 
                 96 
               
               
                 234 
                 212 
                 134 
                 8 
                 76 
                 142 
                 179 
                 98 
               
               
                 235 
                 214 
                 136 
                 10 
                 78 
                 144 
                 181 
                 100 
               
               
                 236 
                 216 
                 138 
                 12 
                 80 
                 146 
                 183 
                 102 
               
               
                 237 
                 218 
                 140 
                 14 
                 82 
                 148 
                 185 
                 104 
               
               
                 238 
                 220 
                 142 
                 16 
                 84 
                 150 
                 187 
                 106 
               
               
                 239 
                 222 
                 144 
                 18 
                 86 
                 152 
                 189 
                 108 
               
               
                 240 
                 224 
                 146 
                 20 
                 88 
                 154 
                 191 
                 110 
               
               
                 241 
                 226 
                 148 
                 22 
                 90 
                 156 
                 193 
                 112 
               
               
                 242 
                 228 
                 150 
                 24 
                 92 
                 158 
                 195 
                 114 
               
               
                 243 
                 230 
                 152 
                 26 
                 94 
                 160 
                 197 
                 116 
               
               
                 244 
                 232 
                 154 
                 28 
                 96 
                 162 
                 199 
                 118 
               
               
                 245 
                 234 
                 156 
                 30 
                 98 
                 164 
                 201 
                 120 
               
               
                 246 
                 236 
                 158 
                 32 
                 100 
                 166 
                 203 
                 122 
               
               
                 247 
                 238 
                 160 
                 34 
                 102 
                 168 
                 205 
                 124 
               
               
                 248 
                 240 
                 162 
                 36 
                 104 
                 170 
                 207 
                 126 
               
               
                 249 
                 242 
                 164 
                 38 
                 106 
                 172 
                 209 
                 128 
               
               
                 250 
                 244 
                 166 
                 40 
                 108 
                 174 
                 211 
                 130 
               
               
                 251 
                 246 
                 168 
                 42 
                 110 
                 176 
                 213 
                 132 
               
               
                 252 
                 248 
                 170 
                 44 
                 112 
                 178 
                 215 
                 134 
               
               
                 253 
                 250 
                 172 
                 46 
                 114 
                 180 
                 217 
                 136 
               
               
                 254 
                 252 
                 174 
                 48 
                 116 
                 182 
                 219 
                 138 
               
               
                 255 
                 254 
                 176 
                 50 
                 118 
                 184 
                 221 
                 140 
               
               
                 256 
                 256 
                 178 
                 52 
                 120 
                 186 
                 223 
                 142 
               
               
                   
               
             
          
         
       
     
         [0129]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 1) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 257 
                 1 
                 24 
                 179 
               
               
                   
                 258 
                 3 
                 26 
                 181 
               
               
                   
                 259 
                 5 
                 28 
                 183 
               
               
                   
                 260 
                 7 
                 30 
                 185 
               
               
                   
                 261 
                 9 
                 32 
                 187 
               
               
                   
                 262 
                 11 
                 34 
                 189 
               
               
                   
                 263 
                 13 
                 36 
                 191 
               
               
                   
                 264 
                 15 
                 38 
                 193 
               
               
                   
                 265 
                 17 
                 40 
                 195 
               
               
                   
                 266 
                 19 
                 42 
                 197 
               
               
                   
                 267 
                 21 
                 44 
                 199 
               
               
                   
                 268 
                 23 
                 46 
                 201 
               
               
                   
                 269 
                 25 
                 48 
                 203 
               
               
                   
                 270 
                 27 
                 50 
                 205 
               
               
                   
                 271 
                 29 
                 52 
                 207 
               
               
                   
                 272 
                 31 
                 54 
                 209 
               
               
                   
                 273 
                 33 
                 56 
                 211 
               
               
                   
                 274 
                 35 
                 58 
                 213 
               
               
                   
                 275 
                 37 
                 60 
                 215 
               
               
                   
                 276 
                 39 
                 62 
                 217 
               
               
                   
                 277 
                 41 
                 64 
                 219 
               
               
                   
                 278 
                 43 
                 66 
                 221 
               
               
                   
                 279 
                 45 
                 68 
                 223 
               
               
                   
                 280 
                 47 
                 70 
                 225 
               
               
                   
                 281 
                 49 
                 72 
                 227 
               
               
                   
                 282 
                 51 
                 74 
                 229 
               
               
                   
                 283 
                 53 
                 76 
                 231 
               
               
                   
                 284 
                 55 
                 78 
                 233 
               
               
                   
                 285 
                 57 
                 80 
                 235 
               
               
                   
                 286 
                 59 
                 82 
                 237 
               
               
                   
                 287 
                 61 
                 84 
                 239 
               
               
                   
                 288 
                 63 
                 86 
                 241 
               
               
                   
                 289 
                 65 
                 88 
                 243 
               
               
                   
                 290 
                 67 
                 90 
                 245 
               
               
                   
                 291 
                 69 
                 92 
                 247 
               
               
                   
                 292 
                 71 
                 94 
                 249 
               
               
                   
                 293 
                 73 
                 96 
                 251 
               
               
                   
                 294 
                 75 
                 98 
                 253 
               
               
                   
                 295 
                 77 
                 100 
                 255 
               
               
                   
                 296 
                 79 
                 102 
                 1 
               
               
                   
                 297 
                 81 
                 104 
                 3 
               
               
                   
                 298 
                 83 
                 106 
                 5 
               
               
                   
                 299 
                 85 
                 108 
                 7 
               
               
                   
                 300 
                 87 
                 110 
                 9 
               
               
                   
                 301 
                 89 
                 112 
                 11 
               
               
                   
                 302 
                 91 
                 114 
                 13 
               
               
                   
                 303 
                 93 
                 116 
                 15 
               
               
                   
                 304 
                 95 
                 118 
                 17 
               
               
                   
                 305 
                 97 
                 120 
                 19 
               
               
                   
                 306 
                 99 
                 122 
                 21 
               
               
                   
                 307 
                 101 
                 124 
                 23 
               
               
                   
                 308 
                 103 
                 126 
                 25 
               
               
                   
                 309 
                 105 
                 128 
                 27 
               
               
                   
                 310 
                 107 
                 130 
                 29 
               
               
                   
                 311 
                 109 
                 132 
                 31 
               
               
                   
                 312 
                 111 
                 134 
                 33 
               
               
                   
                 313 
                 113 
                 136 
                 35 
               
               
                   
                 314 
                 115 
                 138 
                 37 
               
               
                   
                 315 
                 117 
                 140 
                 39 
               
               
                   
                 316 
                 119 
                 142 
                 41 
               
               
                   
                 317 
                 121 
                 144 
                 43 
               
               
                   
                 318 
                 123 
                 146 
                 45 
               
               
                   
                 319 
                 125 
                 148 
                 47 
               
               
                   
                 320 
                 127 
                 150 
                 49 
               
               
                   
                 321 
                 129 
                 152 
                 51 
               
               
                   
                 322 
                 131 
                 154 
                 53 
               
               
                   
                 323 
                 133 
                 156 
                 55 
               
               
                   
                 324 
                 135 
                 158 
                 57 
               
               
                   
                 325 
                 137 
                 160 
                 59 
               
               
                   
                 326 
                 139 
                 162 
                 61 
               
               
                   
                 327 
                 141 
                 164 
                 63 
               
               
                   
                 328 
                 143 
                 166 
                 65 
               
               
                   
                 329 
                 145 
                 168 
                 67 
               
               
                   
                 330 
                 147 
                 170 
                 69 
               
               
                   
                 331 
                 149 
                 172 
                 71 
               
               
                   
                 332 
                 151 
                 174 
                 73 
               
               
                   
                 333 
                 153 
                 176 
                 75 
               
               
                   
                 334 
                 155 
                 178 
                 77 
               
               
                   
                 335 
                 157 
                 180 
                 79 
               
               
                   
                 336 
                 159 
                 182 
                 81 
               
               
                   
                 337 
                 161 
                 184 
                 83 
               
               
                   
                 338 
                 163 
                 186 
                 85 
               
               
                   
                 339 
                 165 
                 188 
                 87 
               
               
                   
                 340 
                 167 
                 190 
                 89 
               
               
                   
                 341 
                 169 
                 192 
                 91 
               
               
                   
                 342 
                 171 
                 194 
                 93 
               
               
                   
                 343 
                 173 
                 196 
                 95 
               
               
                   
                 344 
                 175 
                 198 
                 97 
               
               
                   
                 345 
                 177 
                 200 
                 99 
               
               
                   
                 346 
                 179 
                 202 
                 101 
               
               
                   
                 347 
                 181 
                 204 
                 103 
               
               
                   
                 348 
                 183 
                 206 
                 105 
               
               
                   
                 349 
                 185 
                 208 
                 107 
               
               
                   
                 350 
                 187 
                 210 
                 109 
               
               
                   
                 351 
                 189 
                 212 
                 111 
               
               
                   
                 352 
                 191 
                 214 
                 113 
               
               
                   
                 353 
                 193 
                 216 
                 115 
               
               
                   
                 354 
                 195 
                 218 
                 117 
               
               
                   
                 355 
                 197 
                 220 
                 119 
               
               
                   
                 356 
                 199 
                 222 
                 121 
               
               
                   
                 357 
                 201 
                 224 
                 123 
               
               
                   
                 358 
                 203 
                 226 
                 125 
               
               
                   
                 359 
                 205 
                 228 
                 127 
               
               
                   
                 360 
                 207 
                 230 
                 129 
               
               
                   
                 361 
                 209 
                 232 
                 131 
               
               
                   
                 362 
                 211 
                 234 
                 133 
               
               
                   
                 363 
                 213 
                 236 
                 135 
               
               
                   
                 364 
                 215 
                 238 
                 137 
               
               
                   
                 365 
                 217 
                 240 
                 139 
               
               
                   
                 366 
                 219 
                 242 
                 141 
               
               
                   
                 367 
                 221 
                 244 
                 143 
               
               
                   
                 368 
                 223 
                 246 
                 145 
               
               
                   
                 369 
                 225 
                 248 
                 147 
               
               
                   
                 370 
                 227 
                 250 
                 149 
               
               
                   
                 371 
                 229 
                 252 
                 151 
               
               
                   
                 372 
                 231 
                 254 
                 153 
               
               
                   
                 373 
                 233 
                 256 
                 155 
               
               
                   
                 374 
                 235 
                 2 
                 157 
               
               
                   
                 375 
                 237 
                 4 
                 159 
               
               
                   
                 376 
                 239 
                 6 
                 161 
               
               
                   
                 377 
                 241 
                 8 
                 163 
               
               
                   
                 378 
                 243 
                 10 
                 165 
               
               
                   
                 379 
                 245 
                 12 
                 167 
               
               
                   
                 380 
                 247 
                 14 
                 169 
               
               
                   
                 381 
                 249 
                 16 
                 171 
               
               
                   
                 382 
                 251 
                 18 
                 173 
               
               
                   
                 383 
                 253 
                 20 
                 175 
               
               
                   
                 384 
                 255 
                 22 
                 177 
               
               
                   
                   
               
             
          
         
       
     
         [0130]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 2) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 385 
                 2 
                 239 
                 140 
               
               
                   
                 386 
                 4 
                 241 
                 142 
               
               
                   
                 387 
                 6 
                 243 
                 144 
               
               
                   
                 388 
                 8 
                 245 
                 146 
               
               
                   
                 389 
                 10 
                 247 
                 148 
               
               
                   
                 390 
                 12 
                 249 
                 150 
               
               
                   
                 391 
                 14 
                 251 
                 152 
               
               
                   
                 392 
                 16 
                 253 
                 154 
               
               
                   
                 393 
                 18 
                 255 
                 156 
               
               
                   
                 394 
                 20 
                 1 
                 158 
               
               
                   
                 395 
                 22 
                 3 
                 160 
               
               
                   
                 396 
                 24 
                 5 
                 162 
               
               
                   
                 397 
                 26 
                 7 
                 164 
               
               
                   
                 398 
                 28 
                 9 
                 166 
               
               
                   
                 399 
                 30 
                 11 
                 168 
               
               
                   
                 400 
                 32 
                 13 
                 170 
               
               
                   
                 401 
                 34 
                 15 
                 172 
               
               
                   
                 402 
                 36 
                 17 
                 174 
               
               
                   
                 403 
                 38 
                 19 
                 176 
               
               
                   
                 404 
                 40 
                 21 
                 178 
               
               
                   
                 405 
                 42 
                 23 
                 180 
               
               
                   
                 406 
                 44 
                 25 
                 182 
               
               
                   
                 407 
                 46 
                 27 
                 184 
               
               
                   
                 408 
                 48 
                 29 
                 186 
               
               
                   
                 409 
                 50 
                 31 
                 188 
               
               
                   
                 410 
                 52 
                 33 
                 190 
               
               
                   
                 411 
                 54 
                 35 
                 192 
               
               
                   
                 412 
                 56 
                 37 
                 194 
               
               
                   
                 413 
                 58 
                 39 
                 196 
               
               
                   
                 414 
                 60 
                 41 
                 198 
               
               
                   
                 415 
                 62 
                 43 
                 200 
               
               
                   
                 416 
                 64 
                 45 
                 202 
               
               
                   
                 417 
                 66 
                 47 
                 204 
               
               
                   
                 418 
                 68 
                 49 
                 206 
               
               
                   
                 419 
                 70 
                 51 
                 208 
               
               
                   
                 420 
                 72 
                 53 
                 210 
               
               
                   
                 421 
                 74 
                 55 
                 212 
               
               
                   
                 422 
                 76 
                 57 
                 214 
               
               
                   
                 423 
                 78 
                 59 
                 216 
               
               
                   
                 424 
                 80 
                 61 
                 218 
               
               
                   
                 425 
                 82 
                 63 
                 220 
               
               
                   
                 426 
                 84 
                 65 
                 222 
               
               
                   
                 427 
                 86 
                 67 
                 224 
               
               
                   
                 428 
                 88 
                 69 
                 226 
               
               
                   
                 429 
                 90 
                 71 
                 228 
               
               
                   
                 430 
                 92 
                 73 
                 230 
               
               
                   
                 431 
                 94 
                 75 
                 232 
               
               
                   
                 432 
                 96 
                 77 
                 234 
               
               
                   
                 433 
                 98 
                 79 
                 236 
               
               
                   
                 434 
                 100 
                 81 
                 238 
               
               
                   
                 435 
                 102 
                 83 
                 240 
               
               
                   
                 436 
                 104 
                 85 
                 242 
               
               
                   
                 437 
                 106 
                 87 
                 244 
               
               
                   
                 438 
                 108 
                 89 
                 246 
               
               
                   
                 439 
                 110 
                 91 
                 248 
               
               
                   
                 440 
                 112 
                 93 
                 250 
               
               
                   
                 441 
                 114 
                 95 
                 252 
               
               
                   
                 442 
                 116 
                 97 
                 254 
               
               
                   
                 443 
                 118 
                 99 
                 256 
               
               
                   
                 444 
                 120 
                 101 
                 2 
               
               
                   
                 445 
                 122 
                 103 
                 4 
               
               
                   
                 446 
                 124 
                 105 
                 6 
               
               
                   
                 447 
                 126 
                 107 
                 8 
               
               
                   
                 448 
                 128 
                 109 
                 10 
               
               
                   
                 449 
                 130 
                 111 
                 12 
               
               
                   
                 450 
                 132 
                 113 
                 14 
               
               
                   
                 451 
                 134 
                 115 
                 16 
               
               
                   
                 452 
                 136 
                 117 
                 18 
               
               
                   
                 453 
                 138 
                 119 
                 20 
               
               
                   
                 454 
                 140 
                 121 
                 22 
               
               
                   
                 455 
                 142 
                 123 
                 24 
               
               
                   
                 456 
                 144 
                 125 
                 26 
               
               
                   
                 457 
                 146 
                 127 
                 28 
               
               
                   
                 458 
                 148 
                 129 
                 30 
               
               
                   
                 459 
                 150 
                 131 
                 32 
               
               
                   
                 460 
                 152 
                 133 
                 34 
               
               
                   
                 461 
                 154 
                 135 
                 36 
               
               
                   
                 462 
                 156 
                 137 
                 38 
               
               
                   
                 463 
                 158 
                 139 
                 40 
               
               
                   
                 464 
                 160 
                 141 
                 42 
               
               
                   
                 465 
                 162 
                 143 
                 44 
               
               
                   
                 466 
                 164 
                 145 
                 46 
               
               
                   
                 467 
                 166 
                 147 
                 48 
               
               
                   
                 468 
                 168 
                 149 
                 50 
               
               
                   
                 469 
                 170 
                 151 
                 52 
               
               
                   
                 470 
                 172 
                 153 
                 54 
               
               
                   
                 471 
                 174 
                 155 
                 56 
               
               
                   
                 472 
                 176 
                 157 
                 58 
               
               
                   
                 473 
                 178 
                 159 
                 60 
               
               
                   
                 474 
                 180 
                 161 
                 62 
               
               
                   
                 475 
                 182 
                 163 
                 64 
               
               
                   
                 476 
                 184 
                 165 
                 66 
               
               
                   
                 477 
                 186 
                 167 
                 68 
               
               
                   
                 478 
                 188 
                 169 
                 70 
               
               
                   
                 479 
                 190 
                 171 
                 72 
               
               
                   
                 480 
                 192 
                 173 
                 74 
               
               
                   
                 481 
                 194 
                 175 
                 76 
               
               
                   
                 482 
                 196 
                 177 
                 78 
               
               
                   
                 483 
                 198 
                 179 
                 80 
               
               
                   
                 484 
                 200 
                 181 
                 82 
               
               
                   
                 485 
                 202 
                 183 
                 84 
               
               
                   
                 486 
                 204 
                 185 
                 86 
               
               
                   
                 487 
                 206 
                 187 
                 88 
               
               
                   
                 488 
                 208 
                 189 
                 90 
               
               
                   
                 489 
                 210 
                 191 
                 92 
               
               
                   
                 490 
                 212 
                 193 
                 94 
               
               
                   
                 491 
                 214 
                 195 
                 96 
               
               
                   
                 492 
                 216 
                 197 
                 98 
               
               
                   
                 493 
                 218 
                 199 
                 100 
               
               
                   
                 494 
                 220 
                 201 
                 102 
               
               
                   
                 495 
                 222 
                 203 
                 104 
               
               
                   
                 496 
                 224 
                 205 
                 106 
               
               
                   
                 497 
                 226 
                 207 
                 108 
               
               
                   
                 498 
                 228 
                 209 
                 110 
               
               
                   
                 499 
                 230 
                 211 
                 112 
               
               
                   
                 500 
                 232 
                 213 
                 114 
               
               
                   
                 501 
                 234 
                 215 
                 116 
               
               
                   
                 502 
                 236 
                 217 
                 118 
               
               
                   
                 503 
                 238 
                 219 
                 120 
               
               
                   
                 504 
                 240 
                 221 
                 122 
               
               
                   
                 505 
                 242 
                 223 
                 124 
               
               
                   
                 506 
                 244 
                 225 
                 126 
               
               
                   
                 507 
                 246 
                 227 
                 128 
               
               
                   
                 508 
                 248 
                 229 
                 130 
               
               
                   
                 509 
                 250 
                 231 
                 132 
               
               
                   
                 510 
                 252 
                 233 
                 134 
               
               
                   
                 511 
                 254 
                 235 
                 136 
               
               
                   
                 512 
                 256 
                 237 
                 138 
               
               
                   
                   
               
             
          
         
       
     
         [0131]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 3) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 513 
                 1 
                 36 
                 219 
               
               
                   
                 514 
                 3 
                 38 
                 221 
               
               
                   
                 515 
                 5 
                 40 
                 223 
               
               
                   
                 516 
                 7 
                 42 
                 225 
               
               
                   
                 517 
                 9 
                 44 
                 227 
               
               
                   
                 518 
                 11 
                 46 
                 229 
               
               
                   
                 519 
                 13 
                 48 
                 231 
               
               
                   
                 520 
                 15 
                 50 
                 233 
               
               
                   
                 521 
                 17 
                 52 
                 235 
               
               
                   
                 522 
                 19 
                 54 
                 237 
               
               
                   
                 523 
                 21 
                 56 
                 239 
               
               
                   
                 524 
                 23 
                 58 
                 241 
               
               
                   
                 525 
                 25 
                 60 
                 243 
               
               
                   
                 526 
                 27 
                 62 
                 245 
               
               
                   
                 527 
                 29 
                 64 
                 247 
               
               
                   
                 528 
                 31 
                 66 
                 249 
               
               
                   
                 529 
                 33 
                 68 
                 251 
               
               
                   
                 530 
                 35 
                 70 
                 253 
               
               
                   
                 531 
                 37 
                 72 
                 255 
               
               
                   
                 532 
                 39 
                 74 
                 1 
               
               
                   
                 533 
                 41 
                 76 
                 3 
               
               
                   
                 534 
                 43 
                 78 
                 5 
               
               
                   
                 535 
                 45 
                 80 
                 7 
               
               
                   
                 536 
                 47 
                 82 
                 9 
               
               
                   
                 537 
                 49 
                 84 
                 11 
               
               
                   
                 538 
                 51 
                 86 
                 13 
               
               
                   
                 539 
                 53 
                 88 
                 15 
               
               
                   
                 540 
                 55 
                 90 
                 17 
               
               
                   
                 541 
                 57 
                 92 
                 19 
               
               
                   
                 542 
                 59 
                 94 
                 21 
               
               
                   
                 543 
                 61 
                 96 
                 23 
               
               
                   
                 544 
                 63 
                 98 
                 25 
               
               
                   
                 545 
                 65 
                 100 
                 27 
               
               
                   
                 546 
                 67 
                 102 
                 29 
               
               
                   
                 547 
                 69 
                 104 
                 31 
               
               
                   
                 548 
                 71 
                 106 
                 33 
               
               
                   
                 549 
                 73 
                 108 
                 35 
               
               
                   
                 550 
                 75 
                 110 
                 37 
               
               
                   
                 551 
                 77 
                 112 
                 39 
               
               
                   
                 552 
                 79 
                 114 
                 41 
               
               
                   
                 553 
                 81 
                 116 
                 43 
               
               
                   
                 554 
                 83 
                 118 
                 45 
               
               
                   
                 555 
                 85 
                 120 
                 47 
               
               
                   
                 556 
                 87 
                 122 
                 49 
               
               
                   
                 557 
                 89 
                 124 
                 51 
               
               
                   
                 558 
                 91 
                 126 
                 53 
               
               
                   
                 559 
                 93 
                 128 
                 55 
               
               
                   
                 560 
                 95 
                 130 
                 57 
               
               
                   
                 561 
                 97 
                 132 
                 59 
               
               
                   
                 562 
                 99 
                 134 
                 61 
               
               
                   
                 563 
                 101 
                 136 
                 63 
               
               
                   
                 564 
                 103 
                 138 
                 65 
               
               
                   
                 565 
                 105 
                 140 
                 67 
               
               
                   
                 566 
                 107 
                 142 
                 69 
               
               
                   
                 567 
                 109 
                 144 
                 71 
               
               
                   
                 568 
                 111 
                 146 
                 73 
               
               
                   
                 569 
                 113 
                 148 
                 75 
               
               
                   
                 570 
                 115 
                 150 
                 77 
               
               
                   
                 571 
                 117 
                 152 
                 79 
               
               
                   
                 572 
                 119 
                 154 
                 81 
               
               
                   
                 573 
                 121 
                 156 
                 83 
               
               
                   
                 574 
                 123 
                 158 
                 85 
               
               
                   
                 575 
                 125 
                 160 
                 87 
               
               
                   
                 576 
                 127 
                 162 
                 89 
               
               
                   
                 577 
                 129 
                 164 
                 91 
               
               
                   
                 578 
                 131 
                 166 
                 93 
               
               
                   
                 579 
                 133 
                 168 
                 95 
               
               
                   
                 580 
                 135 
                 170 
                 97 
               
               
                   
                 581 
                 137 
                 172 
                 99 
               
               
                   
                 582 
                 139 
                 174 
                 101 
               
               
                   
                 583 
                 141 
                 176 
                 103 
               
               
                   
                 584 
                 143 
                 178 
                 105 
               
               
                   
                 585 
                 145 
                 180 
                 107 
               
               
                   
                 586 
                 147 
                 182 
                 109 
               
               
                   
                 587 
                 149 
                 184 
                 111 
               
               
                   
                 588 
                 151 
                 186 
                 113 
               
               
                   
                 589 
                 153 
                 188 
                 115 
               
               
                   
                 590 
                 155 
                 190 
                 117 
               
               
                   
                 591 
                 157 
                 192 
                 119 
               
               
                   
                 592 
                 159 
                 194 
                 121 
               
               
                   
                 593 
                 161 
                 196 
                 123 
               
               
                   
                 594 
                 163 
                 198 
                 125 
               
               
                   
                 595 
                 165 
                 200 
                 127 
               
               
                   
                 596 
                 167 
                 202 
                 129 
               
               
                   
                 597 
                 169 
                 204 
                 131 
               
               
                   
                 598 
                 171 
                 206 
                 133 
               
               
                   
                 599 
                 173 
                 208 
                 135 
               
               
                   
                 600 
                 175 
                 210 
                 137 
               
               
                   
                 601 
                 177 
                 212 
                 139 
               
               
                   
                 602 
                 179 
                 214 
                 141 
               
               
                   
                 603 
                 181 
                 216 
                 143 
               
               
                   
                 604 
                 183 
                 218 
                 145 
               
               
                   
                 605 
                 185 
                 220 
                 147 
               
               
                   
                 606 
                 187 
                 222 
                 149 
               
               
                   
                 607 
                 189 
                 224 
                 151 
               
               
                   
                 608 
                 191 
                 226 
                 153 
               
               
                   
                 609 
                 193 
                 228 
                 155 
               
               
                   
                 610 
                 195 
                 230 
                 157 
               
               
                   
                 611 
                 197 
                 232 
                 159 
               
               
                   
                 612 
                 199 
                 234 
                 161 
               
               
                   
                 613 
                 201 
                 236 
                 163 
               
               
                   
                 614 
                 203 
                 238 
                 165 
               
               
                   
                 615 
                 205 
                 240 
                 167 
               
               
                   
                 616 
                 207 
                 242 
                 169 
               
               
                   
                 617 
                 209 
                 244 
                 171 
               
               
                   
                 618 
                 211 
                 246 
                 173 
               
               
                   
                 619 
                 213 
                 248 
                 175 
               
               
                   
                 620 
                 215 
                 250 
                 177 
               
               
                   
                 621 
                 217 
                 252 
                 179 
               
               
                   
                 622 
                 219 
                 254 
                 181 
               
               
                   
                 623 
                 221 
                 256 
                 183 
               
               
                   
                 624 
                 223 
                 2 
                 185 
               
               
                   
                 625 
                 225 
                 4 
                 187 
               
               
                   
                 626 
                 227 
                 6 
                 189 
               
               
                   
                 627 
                 229 
                 8 
                 191 
               
               
                   
                 628 
                 231 
                 10 
                 193 
               
               
                   
                 629 
                 233 
                 12 
                 195 
               
               
                   
                 630 
                 235 
                 14 
                 197 
               
               
                   
                 631 
                 237 
                 16 
                 199 
               
               
                   
                 632 
                 239 
                 18 
                 201 
               
               
                   
                 633 
                 241 
                 20 
                 203 
               
               
                   
                 634 
                 243 
                 22 
                 205 
               
               
                   
                 635 
                 245 
                 24 
                 207 
               
               
                   
                 636 
                 247 
                 26 
                 209 
               
               
                   
                 637 
                 249 
                 28 
                 211 
               
               
                   
                 638 
                 251 
                 30 
                 213 
               
               
                   
                 639 
                 253 
                 32 
                 215 
               
               
                   
                 640 
                 255 
                 34 
                 217 
               
               
                   
                   
               
             
          
         
       
     
         [0132]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 4) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 641 
                 2 
                 127 
                 216 
               
               
                   
                 642 
                 4 
                 129 
                 218 
               
               
                   
                 643 
                 6 
                 131 
                 220 
               
               
                   
                 644 
                 8 
                 133 
                 222 
               
               
                   
                 645 
                 10 
                 135 
                 224 
               
               
                   
                 646 
                 12 
                 137 
                 226 
               
               
                   
                 647 
                 14 
                 139 
                 228 
               
               
                   
                 648 
                 16 
                 141 
                 230 
               
               
                   
                 649 
                 18 
                 143 
                 232 
               
               
                   
                 650 
                 20 
                 145 
                 234 
               
               
                   
                 651 
                 22 
                 147 
                 236 
               
               
                   
                 652 
                 24 
                 149 
                 238 
               
               
                   
                 653 
                 26 
                 151 
                 240 
               
               
                   
                 654 
                 28 
                 153 
                 242 
               
               
                   
                 655 
                 30 
                 155 
                 244 
               
               
                   
                 656 
                 32 
                 157 
                 246 
               
               
                   
                 657 
                 34 
                 159 
                 248 
               
               
                   
                 658 
                 36 
                 161 
                 250 
               
               
                   
                 659 
                 38 
                 163 
                 252 
               
               
                   
                 660 
                 40 
                 165 
                 254 
               
               
                   
                 661 
                 42 
                 167 
                 256 
               
               
                   
                 662 
                 44 
                 169 
                 2 
               
               
                   
                 663 
                 46 
                 171 
                 4 
               
               
                   
                 664 
                 48 
                 173 
                 6 
               
               
                   
                 665 
                 50 
                 175 
                 8 
               
               
                   
                 666 
                 52 
                 177 
                 10 
               
               
                   
                 667 
                 54 
                 179 
                 12 
               
               
                   
                 668 
                 56 
                 181 
                 14 
               
               
                   
                 669 
                 58 
                 183 
                 16 
               
               
                   
                 670 
                 60 
                 185 
                 18 
               
               
                   
                 671 
                 62 
                 187 
                 20 
               
               
                   
                 672 
                 64 
                 189 
                 22 
               
               
                   
                 673 
                 66 
                 191 
                 24 
               
               
                   
                 674 
                 68 
                 193 
                 26 
               
               
                   
                 675 
                 70 
                 195 
                 28 
               
               
                   
                 676 
                 72 
                 197 
                 30 
               
               
                   
                 677 
                 74 
                 199 
                 32 
               
               
                   
                 678 
                 76 
                 201 
                 34 
               
               
                   
                 679 
                 78 
                 203 
                 36 
               
               
                   
                 680 
                 80 
                 205 
                 38 
               
               
                   
                 681 
                 82 
                 207 
                 40 
               
               
                   
                 682 
                 84 
                 209 
                 42 
               
               
                   
                 683 
                 86 
                 211 
                 44 
               
               
                   
                 684 
                 88 
                 213 
                 46 
               
               
                   
                 685 
                 90 
                 215 
                 48 
               
               
                   
                 686 
                 92 
                 217 
                 50 
               
               
                   
                 687 
                 94 
                 219 
                 52 
               
               
                   
                 688 
                 96 
                 221 
                 54 
               
               
                   
                 689 
                 98 
                 223 
                 56 
               
               
                   
                 690 
                 100 
                 225 
                 58 
               
               
                   
                 691 
                 102 
                 227 
                 60 
               
               
                   
                 692 
                 104 
                 229 
                 62 
               
               
                   
                 693 
                 106 
                 231 
                 64 
               
               
                   
                 694 
                 108 
                 233 
                 66 
               
               
                   
                 695 
                 110 
                 235 
                 68 
               
               
                   
                 696 
                 112 
                 237 
                 70 
               
               
                   
                 697 
                 114 
                 239 
                 72 
               
               
                   
                 698 
                 116 
                 241 
                 74 
               
               
                   
                 699 
                 118 
                 243 
                 76 
               
               
                   
                 700 
                 120 
                 245 
                 78 
               
               
                   
                 701 
                 122 
                 247 
                 80 
               
               
                   
                 702 
                 124 
                 249 
                 82 
               
               
                   
                 703 
                 126 
                 251 
                 84 
               
               
                   
                 704 
                 128 
                 253 
                 86 
               
               
                   
                 705 
                 130 
                 255 
                 88 
               
               
                   
                 706 
                 132 
                 1 
                 90 
               
               
                   
                 707 
                 134 
                 3 
                 92 
               
               
                   
                 708 
                 136 
                 5 
                 94 
               
               
                   
                 709 
                 138 
                 7 
                 96 
               
               
                   
                 710 
                 140 
                 9 
                 98 
               
               
                   
                 711 
                 142 
                 11 
                 100 
               
               
                   
                 712 
                 144 
                 13 
                 102 
               
               
                   
                 713 
                 146 
                 15 
                 104 
               
               
                   
                 714 
                 148 
                 17 
                 106 
               
               
                   
                 715 
                 150 
                 19 
                 108 
               
               
                   
                 716 
                 152 
                 21 
                 110 
               
               
                   
                 717 
                 154 
                 23 
                 112 
               
               
                   
                 718 
                 156 
                 25 
                 114 
               
               
                   
                 719 
                 158 
                 27 
                 116 
               
               
                   
                 720 
                 160 
                 29 
                 118 
               
               
                   
                 721 
                 162 
                 31 
                 120 
               
               
                   
                 722 
                 164 
                 33 
                 122 
               
               
                   
                 723 
                 166 
                 35 
                 124 
               
               
                   
                 724 
                 168 
                 37 
                 126 
               
               
                   
                 725 
                 170 
                 39 
                 128 
               
               
                   
                 726 
                 172 
                 41 
                 130 
               
               
                   
                 727 
                 174 
                 43 
                 132 
               
               
                   
                 728 
                 176 
                 45 
                 134 
               
               
                   
                 729 
                 178 
                 47 
                 136 
               
               
                   
                 730 
                 180 
                 49 
                 138 
               
               
                   
                 731 
                 182 
                 51 
                 140 
               
               
                   
                 732 
                 184 
                 53 
                 142 
               
               
                   
                 733 
                 186 
                 55 
                 144 
               
               
                   
                 734 
                 188 
                 57 
                 146 
               
               
                   
                 735 
                 190 
                 59 
                 148 
               
               
                   
                 736 
                 192 
                 61 
                 150 
               
               
                   
                 737 
                 194 
                 63 
                 152 
               
               
                   
                 738 
                 196 
                 65 
                 154 
               
               
                   
                 739 
                 198 
                 67 
                 156 
               
               
                   
                 740 
                 200 
                 69 
                 158 
               
               
                   
                 741 
                 202 
                 71 
                 160 
               
               
                   
                 742 
                 204 
                 73 
                 162 
               
               
                   
                 743 
                 206 
                 75 
                 164 
               
               
                   
                 744 
                 208 
                 77 
                 166 
               
               
                   
                 745 
                 210 
                 79 
                 168 
               
               
                   
                 746 
                 212 
                 81 
                 170 
               
               
                   
                 747 
                 214 
                 83 
                 172 
               
               
                   
                 748 
                 216 
                 85 
                 174 
               
               
                   
                 749 
                 218 
                 87 
                 176 
               
               
                   
                 750 
                 220 
                 89 
                 178 
               
               
                   
                 751 
                 222 
                 91 
                 180 
               
               
                   
                 752 
                 224 
                 93 
                 182 
               
               
                   
                 753 
                 226 
                 95 
                 184 
               
               
                   
                 754 
                 228 
                 97 
                 186 
               
               
                   
                 755 
                 230 
                 99 
                 188 
               
               
                   
                 756 
                 232 
                 101 
                 190 
               
               
                   
                 757 
                 234 
                 103 
                 192 
               
               
                   
                 758 
                 236 
                 105 
                 194 
               
               
                   
                 759 
                 238 
                 107 
                 196 
               
               
                   
                 760 
                 240 
                 109 
                 198 
               
               
                   
                 761 
                 242 
                 111 
                 200 
               
               
                   
                 762 
                 244 
                 113 
                 202 
               
               
                   
                 763 
                 246 
                 115 
                 204 
               
               
                   
                 764 
                 248 
                 117 
                 206 
               
               
                   
                 765 
                 250 
                 119 
                 208 
               
               
                   
                 766 
                 252 
                 121 
                 210 
               
               
                   
                 767 
                 254 
                 123 
                 212 
               
               
                   
                 768 
                 256 
                 125 
                 214 
               
               
                   
                   
               
             
          
         
       
     
         [0133]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 5) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 769 
                 1 
                 82 
                 53 
               
               
                   
                 770 
                 3 
                 84 
                 55 
               
               
                   
                 771 
                 5 
                 86 
                 57 
               
               
                   
                 772 
                 7 
                 88 
                 59 
               
               
                   
                 773 
                 9 
                 90 
                 61 
               
               
                   
                 774 
                 11 
                 92 
                 63 
               
               
                   
                 775 
                 13 
                 94 
                 65 
               
               
                   
                 776 
                 15 
                 96 
                 67 
               
               
                   
                 777 
                 17 
                 98 
                 69 
               
               
                   
                 778 
                 19 
                 100 
                 71 
               
               
                   
                 779 
                 21 
                 102 
                 73 
               
               
                   
                 780 
                 23 
                 104 
                 75 
               
               
                   
                 781 
                 25 
                 106 
                 77 
               
               
                   
                 782 
                 27 
                 108 
                 79 
               
               
                   
                 783 
                 29 
                 110 
                 81 
               
               
                   
                 784 
                 31 
                 112 
                 83 
               
               
                   
                 785 
                 33 
                 114 
                 85 
               
               
                   
                 786 
                 35 
                 116 
                 87 
               
               
                   
                 787 
                 37 
                 118 
                 89 
               
               
                   
                 788 
                 39 
                 120 
                 91 
               
               
                   
                 789 
                 41 
                 122 
                 93 
               
               
                   
                 790 
                 43 
                 124 
                 95 
               
               
                   
                 791 
                 45 
                 126 
                 97 
               
               
                   
                 792 
                 47 
                 128 
                 99 
               
               
                   
                 793 
                 49 
                 130 
                 101 
               
               
                   
                 794 
                 51 
                 132 
                 103 
               
               
                   
                 795 
                 53 
                 134 
                 105 
               
               
                   
                 796 
                 55 
                 136 
                 107 
               
               
                   
                 797 
                 57 
                 138 
                 109 
               
               
                   
                 798 
                 59 
                 140 
                 111 
               
               
                   
                 799 
                 61 
                 142 
                 113 
               
               
                   
                 800 
                 63 
                 144 
                 115 
               
               
                   
                 801 
                 65 
                 146 
                 117 
               
               
                   
                 802 
                 67 
                 148 
                 119 
               
               
                   
                 803 
                 69 
                 150 
                 121 
               
               
                   
                 804 
                 71 
                 152 
                 123 
               
               
                   
                 805 
                 73 
                 154 
                 125 
               
               
                   
                 806 
                 75 
                 156 
                 127 
               
               
                   
                 807 
                 77 
                 158 
                 129 
               
               
                   
                 808 
                 79 
                 160 
                 131 
               
               
                   
                 809 
                 81 
                 162 
                 133 
               
               
                   
                 810 
                 83 
                 164 
                 135 
               
               
                   
                 811 
                 85 
                 166 
                 137 
               
               
                   
                 812 
                 87 
                 168 
                 139 
               
               
                   
                 813 
                 89 
                 170 
                 141 
               
               
                   
                 814 
                 91 
                 172 
                 143 
               
               
                   
                 815 
                 93 
                 174 
                 145 
               
               
                   
                 816 
                 95 
                 176 
                 147 
               
               
                   
                 817 
                 97 
                 178 
                 149 
               
               
                   
                 818 
                 99 
                 180 
                 151 
               
               
                   
                 819 
                 101 
                 182 
                 153 
               
               
                   
                 820 
                 103 
                 184 
                 155 
               
               
                   
                 821 
                 105 
                 186 
                 157 
               
               
                   
                 822 
                 107 
                 188 
                 159 
               
               
                   
                 823 
                 109 
                 190 
                 161 
               
               
                   
                 824 
                 111 
                 192 
                 163 
               
               
                   
                 825 
                 113 
                 194 
                 165 
               
               
                   
                 826 
                 115 
                 196 
                 167 
               
               
                   
                 827 
                 117 
                 198 
                 169 
               
               
                   
                 828 
                 119 
                 200 
                 171 
               
               
                   
                 829 
                 121 
                 202 
                 173 
               
               
                   
                 830 
                 123 
                 204 
                 175 
               
               
                   
                 831 
                 125 
                 206 
                 177 
               
               
                   
                 832 
                 127 
                 208 
                 179 
               
               
                   
                 833 
                 129 
                 210 
                 181 
               
               
                   
                 834 
                 131 
                 212 
                 183 
               
               
                   
                 835 
                 133 
                 214 
                 185 
               
               
                   
                 836 
                 135 
                 216 
                 187 
               
               
                   
                 837 
                 137 
                 218 
                 189 
               
               
                   
                 838 
                 139 
                 220 
                 191 
               
               
                   
                 839 
                 141 
                 222 
                 193 
               
               
                   
                 840 
                 143 
                 224 
                 195 
               
               
                   
                 841 
                 145 
                 226 
                 197 
               
               
                   
                 842 
                 147 
                 228 
                 199 
               
               
                   
                 843 
                 149 
                 230 
                 201 
               
               
                   
                 844 
                 151 
                 232 
                 203 
               
               
                   
                 845 
                 153 
                 234 
                 205 
               
               
                   
                 846 
                 155 
                 236 
                 207 
               
               
                   
                 847 
                 157 
                 238 
                 209 
               
               
                   
                 848 
                 159 
                 240 
                 211 
               
               
                   
                 849 
                 161 
                 242 
                 213 
               
               
                   
                 850 
                 163 
                 244 
                 215 
               
               
                   
                 851 
                 165 
                 246 
                 217 
               
               
                   
                 852 
                 167 
                 248 
                 219 
               
               
                   
                 853 
                 169 
                 250 
                 221 
               
               
                   
                 854 
                 171 
                 252 
                 223 
               
               
                   
                 855 
                 173 
                 254 
                 225 
               
               
                   
                 856 
                 175 
                 256 
                 227 
               
               
                   
                 857 
                 177 
                 2 
                 229 
               
               
                   
                 858 
                 179 
                 4 
                 231 
               
               
                   
                 859 
                 181 
                 6 
                 233 
               
               
                   
                 860 
                 183 
                 8 
                 235 
               
               
                   
                 861 
                 185 
                 10 
                 237 
               
               
                   
                 862 
                 187 
                 12 
                 239 
               
               
                   
                 863 
                 189 
                 14 
                 241 
               
               
                   
                 864 
                 191 
                 16 
                 243 
               
               
                   
                 865 
                 193 
                 18 
                 245 
               
               
                   
                 866 
                 195 
                 20 
                 247 
               
               
                   
                 867 
                 197 
                 22 
                 249 
               
               
                   
                 868 
                 199 
                 24 
                 251 
               
               
                   
                 869 
                 201 
                 26 
                 253 
               
               
                   
                 870 
                 203 
                 28 
                 255 
               
               
                   
                 871 
                 205 
                 30 
                 1 
               
               
                   
                 872 
                 207 
                 32 
                 3 
               
               
                   
                 873 
                 209 
                 34 
                 5 
               
               
                   
                 874 
                 211 
                 36 
                 7 
               
               
                   
                 875 
                 213 
                 38 
                 9 
               
               
                   
                 876 
                 215 
                 40 
                 11 
               
               
                   
                 877 
                 217 
                 42 
                 13 
               
               
                   
                 878 
                 219 
                 44 
                 15 
               
               
                   
                 879 
                 221 
                 46 
                 17 
               
               
                   
                 880 
                 223 
                 48 
                 19 
               
               
                   
                 881 
                 225 
                 50 
                 21 
               
               
                   
                 882 
                 227 
                 52 
                 23 
               
               
                   
                 883 
                 229 
                 54 
                 25 
               
               
                   
                 884 
                 231 
                 56 
                 27 
               
               
                   
                 885 
                 233 
                 58 
                 29 
               
               
                   
                 886 
                 235 
                 60 
                 31 
               
               
                   
                 887 
                 237 
                 62 
                 33 
               
               
                   
                 888 
                 239 
                 64 
                 35 
               
               
                   
                 889 
                 241 
                 66 
                 37 
               
               
                   
                 890 
                 243 
                 68 
                 39 
               
               
                   
                 891 
                 245 
                 70 
                 41 
               
               
                   
                 892 
                 247 
                 72 
                 43 
               
               
                   
                 893 
                 249 
                 74 
                 45 
               
               
                   
                 894 
                 251 
                 76 
                 47 
               
               
                   
                 895 
                 253 
                 78 
                 49 
               
               
                   
                 896 
                 255 
                 80 
                 51 
               
               
                   
                   
               
             
          
         
       
     
         [0134]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                   
               
               
                 H(3, 6) 
               
             
          
           
               
                   
                 b 
                 c 
                 c 
                 c 
               
               
                   
                   
               
             
          
           
               
                   
                 897 
                 2 
                 251 
                 226 
               
               
                   
                 898 
                 4 
                 253 
                 228 
               
               
                   
                 899 
                 6 
                 255 
                 230 
               
               
                   
                 900 
                 8 
                 1 
                 232 
               
               
                   
                 901 
                 10 
                 3 
                 234 
               
               
                   
                 902 
                 12 
                 5 
                 236 
               
               
                   
                 903 
                 14 
                 7 
                 238 
               
               
                   
                 904 
                 16 
                 9 
                 240 
               
               
                   
                 905 
                 18 
                 11 
                 242 
               
               
                   
                 906 
                 20 
                 13 
                 244 
               
               
                   
                 907 
                 22 
                 15 
                 246 
               
               
                   
                 908 
                 24 
                 17 
                 248 
               
               
                   
                 909 
                 26 
                 19 
                 250 
               
               
                   
                 910 
                 28 
                 21 
                 252 
               
               
                   
                 911 
                 30 
                 23 
                 254 
               
               
                   
                 912 
                 32 
                 25 
                 256 
               
               
                   
                 913 
                 34 
                 27 
                 2 
               
               
                   
                 914 
                 36 
                 29 
                 4 
               
               
                   
                 915 
                 38 
                 31 
                 6 
               
               
                   
                 916 
                 40 
                 33 
                 8 
               
               
                   
                 917 
                 42 
                 35 
                 10 
               
               
                   
                 918 
                 44 
                 37 
                 12 
               
               
                   
                 919 
                 46 
                 39 
                 14 
               
               
                   
                 920 
                 48 
                 41 
                 16 
               
               
                   
                 921 
                 50 
                 43 
                 18 
               
               
                   
                 922 
                 52 
                 45 
                 20 
               
               
                   
                 923 
                 54 
                 47 
                 22 
               
               
                   
                 924 
                 56 
                 49 
                 24 
               
               
                   
                 925 
                 58 
                 51 
                 26 
               
               
                   
                 926 
                 60 
                 53 
                 28 
               
               
                   
                 927 
                 62 
                 55 
                 30 
               
               
                   
                 928 
                 64 
                 57 
                 32 
               
               
                   
                 929 
                 66 
                 59 
                 34 
               
               
                   
                 930 
                 68 
                 61 
                 36 
               
               
                   
                 931 
                 70 
                 63 
                 38 
               
               
                   
                 932 
                 72 
                 65 
                 40 
               
               
                   
                 933 
                 74 
                 67 
                 42 
               
               
                   
                 934 
                 76 
                 69 
                 44 
               
               
                   
                 935 
                 78 
                 71 
                 46 
               
               
                   
                 936 
                 80 
                 73 
                 48 
               
               
                   
                 937 
                 82 
                 75 
                 50 
               
               
                   
                 938 
                 84 
                 77 
                 52 
               
               
                   
                 939 
                 86 
                 79 
                 54 
               
               
                   
                 940 
                 88 
                 81 
                 56 
               
               
                   
                 941 
                 90 
                 83 
                 58 
               
               
                   
                 942 
                 92 
                 85 
                 60 
               
               
                   
                 943 
                 94 
                 87 
                 62 
               
               
                   
                 944 
                 96 
                 89 
                 64 
               
               
                   
                 945 
                 98 
                 91 
                 66 
               
               
                   
                 946 
                 100 
                 93 
                 68 
               
               
                   
                 947 
                 102 
                 95 
                 70 
               
               
                   
                 948 
                 104 
                 97 
                 72 
               
               
                   
                 949 
                 106 
                 99 
                 74 
               
               
                   
                 950 
                 108 
                 101 
                 76 
               
               
                   
                 951 
                 110 
                 103 
                 78 
               
               
                   
                 952 
                 112 
                 105 
                 80 
               
               
                   
                 953 
                 114 
                 107 
                 82 
               
               
                   
                 954 
                 116 
                 109 
                 84 
               
               
                   
                 955 
                 118 
                 111 
                 86 
               
               
                   
                 956 
                 120 
                 113 
                 88 
               
               
                   
                 957 
                 122 
                 115 
                 90 
               
               
                   
                 958 
                 124 
                 117 
                 92 
               
               
                   
                 959 
                 126 
                 119 
                 94 
               
               
                   
                 960 
                 128 
                 121 
                 96 
               
               
                   
                 961 
                 130 
                 123 
                 98 
               
               
                   
                 962 
                 132 
                 125 
                 100 
               
               
                   
                 963 
                 134 
                 127 
                 102 
               
               
                   
                 964 
                 136 
                 129 
                 104 
               
               
                   
                 965 
                 138 
                 131 
                 106 
               
               
                   
                 966 
                 140 
                 133 
                 108 
               
               
                   
                 967 
                 142 
                 135 
                 110 
               
               
                   
                 968 
                 144 
                 137 
                 112 
               
               
                   
                 969 
                 146 
                 139 
                 114 
               
               
                   
                 970 
                 148 
                 141 
                 116 
               
               
                   
                 971 
                 150 
                 143 
                 118 
               
               
                   
                 972 
                 152 
                 145 
                 120 
               
               
                   
                 973 
                 154 
                 147 
                 122 
               
               
                   
                 974 
                 156 
                 149 
                 124 
               
               
                   
                 975 
                 158 
                 151 
                 126 
               
               
                   
                 976 
                 160 
                 153 
                 128 
               
               
                   
                 977 
                 162 
                 155 
                 130 
               
               
                   
                 978 
                 164 
                 157 
                 132 
               
               
                   
                 979 
                 166 
                 159 
                 134 
               
               
                   
                 980 
                 168 
                 161 
                 136 
               
               
                   
                 981 
                 170 
                 163 
                 138 
               
               
                   
                 982 
                 172 
                 165 
                 140 
               
               
                   
                 983 
                 174 
                 167 
                 142 
               
               
                   
                 984 
                 176 
                 169 
                 144 
               
               
                   
                 985 
                 178 
                 171 
                 146 
               
               
                   
                 986 
                 180 
                 173 
                 148 
               
               
                   
                 987 
                 182 
                 175 
                 150 
               
               
                   
                 988 
                 184 
                 177 
                 152 
               
               
                   
                 989 
                 186 
                 179 
                 154 
               
               
                   
                 990 
                 188 
                 181 
                 156 
               
               
                   
                 991 
                 190 
                 183 
                 158 
               
               
                   
                 992 
                 192 
                 185 
                 160 
               
               
                   
                 993 
                 194 
                 187 
                 162 
               
               
                   
                 994 
                 196 
                 189 
                 164 
               
               
                   
                 995 
                 198 
                 191 
                 166 
               
               
                   
                 996 
                 200 
                 193 
                 168 
               
               
                   
                 997 
                 202 
                 195 
                 170 
               
               
                   
                 998 
                 204 
                 197 
                 172 
               
               
                   
                 999 
                 206 
                 199 
                 174 
               
               
                   
                 1000 
                 208 
                 201 
                 176 
               
               
                   
                 1001 
                 210 
                 203 
                 178 
               
               
                   
                 1002 
                 212 
                 205 
                 180 
               
               
                   
                 1003 
                 214 
                 207 
                 182 
               
               
                   
                 1004 
                 216 
                 209 
                 184 
               
               
                   
                 1005 
                 218 
                 211 
                 186 
               
               
                   
                 1006 
                 220 
                 213 
                 188 
               
               
                   
                 1007 
                 222 
                 215 
                 190 
               
               
                   
                 1008 
                 224 
                 217 
                 192 
               
               
                   
                 1009 
                 226 
                 219 
                 194 
               
               
                   
                 1010 
                 228 
                 221 
                 196 
               
               
                   
                 1011 
                 230 
                 223 
                 198 
               
               
                   
                 1012 
                 232 
                 225 
                 200 
               
               
                   
                 1013 
                 234 
                 227 
                 202 
               
               
                   
                 1014 
                 236 
                 229 
                 204 
               
               
                   
                 1015 
                 238 
                 231 
                 206 
               
               
                   
                 1016 
                 240 
                 233 
                 208 
               
               
                   
                 1017 
                 242 
                 235 
                 210 
               
               
                   
                 1018 
                 244 
                 237 
                 212 
               
               
                   
                 1019 
                 246 
                 239 
                 214 
               
               
                   
                 1020 
                 248 
                 241 
                 216 
               
               
                   
                 1021 
                 250 
                 243 
                 218 
               
               
                   
                 1022 
                 252 
                 245 
                 220 
               
               
                   
                 1023 
                 254 
                 247 
                 222 
               
               
                   
                 1024 
                 256 
                 249 
                 224 
               
               
                   
                   
               
             
          
         
       
     
         [0135]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                   
               
               
                 H(d) 
               
             
          
           
               
                 b 
                 c 
                 c 
               
               
                   
               
             
          
           
               
                 1025 
                 1 
                 2 
               
               
                 1026 
                 2 
                 3 
               
               
                 1027 
                 3 
                 4 
               
               
                 1028 
                 4 
                 5 
               
               
                 1029 
                 5 
                 6 
               
               
                 1030 
                 6 
                 7 
               
               
                 1031 
                 7 
                 8 
               
               
                 1032 
                 8 
                 9 
               
               
                 1033 
                 9 
                 10 
               
               
                 1034 
                 10 
                 11 
               
               
                 1035 
                 11 
                 12 
               
               
                 1036 
                 12 
                 13 
               
               
                 1037 
                 13 
                 14 
               
               
                 1038 
                 14 
                 15 
               
               
                 1039 
                 15 
                 16 
               
               
                 1040 
                 16 
                 17 
               
               
                 1041 
                 17 
                 18 
               
               
                 1042 
                 18 
                 19 
               
               
                 1043 
                 19 
                 20 
               
               
                 1044 
                 20 
                 21 
               
               
                 1045 
                 21 
                 22 
               
               
                 1046 
                 22 
                 23 
               
               
                 1047 
                 23 
                 24 
               
               
                 1048 
                 24 
                 25 
               
               
                 1049 
                 25 
                 26 
               
               
                 1050 
                 26 
                 27 
               
               
                 1051 
                 27 
                 28 
               
               
                 1052 
                 28 
                 29 
               
               
                 1053 
                 29 
                 30 
               
               
                 1054 
                 30 
                 31 
               
               
                 1055 
                 31 
                 32 
               
               
                 1056 
                 32 
                 33 
               
               
                 1057 
                 33 
                 34 
               
               
                 1058 
                 34 
                 35 
               
               
                 1059 
                 35 
                 36 
               
               
                 1060 
                 36 
                 37 
               
               
                 1061 
                 37 
                 38 
               
               
                 1062 
                 38 
                 39 
               
               
                 1063 
                 39 
                 40 
               
               
                 1064 
                 40 
                 41 
               
               
                 1065 
                 41 
                 42 
               
               
                 1066 
                 42 
                 43 
               
               
                 1067 
                 43 
                 44 
               
               
                 1068 
                 44 
                 45 
               
               
                 1069 
                 45 
                 46 
               
               
                 1070 
                 46 
                 47 
               
               
                 1071 
                 47 
                 48 
               
               
                 1072 
                 48 
                 49 
               
               
                 1073 
                 49 
                 50 
               
               
                 1074 
                 50 
                 51 
               
               
                 1075 
                 51 
                 52 
               
               
                 1076 
                 52 
                 53 
               
               
                 1077 
                 53 
                 54 
               
               
                 1078 
                 54 
                 55 
               
               
                 1079 
                 55 
                 56 
               
               
                 1080 
                 56 
                 57 
               
               
                 1081 
                 57 
                 58 
               
               
                 1082 
                 58 
                 59 
               
               
                 1083 
                 59 
                 60 
               
               
                 1084 
                 60 
                 61 
               
               
                 1085 
                 61 
                 62 
               
               
                 1086 
                 62 
                 63 
               
               
                 1087 
                 63 
                 64 
               
               
                 1088 
                 64 
                 65 
               
               
                 1089 
                 65 
                 66 
               
               
                 1090 
                 66 
                 67 
               
               
                 1091 
                 67 
                 68 
               
               
                 1092 
                 68 
                 69 
               
               
                 1093 
                 69 
                 70 
               
               
                 1094 
                 70 
                 71 
               
               
                 1095 
                 71 
                 72 
               
               
                 1096 
                 72 
                 73 
               
               
                 1097 
                 73 
                 74 
               
               
                 1098 
                 74 
                 75 
               
               
                 1099 
                 75 
                 76 
               
               
                 1100 
                 76 
                 77 
               
               
                 1101 
                 77 
                 78 
               
               
                 1102 
                 78 
                 79 
               
               
                 1103 
                 79 
                 80 
               
               
                 1104 
                 80 
                 81 
               
               
                 1105 
                 81 
                 82 
               
               
                 1106 
                 82 
                 83 
               
               
                 1107 
                 83 
                 84 
               
               
                 1108 
                 84 
                 85 
               
               
                 1109 
                 85 
                 86 
               
               
                 1110 
                 86 
                 87 
               
               
                 1111 
                 87 
                 88 
               
               
                 1112 
                 88 
                 89 
               
               
                 1113 
                 89 
                 90 
               
               
                 1114 
                 90 
                 91 
               
               
                 1115 
                 91 
                 92 
               
               
                 1116 
                 92 
                 93 
               
               
                 1117 
                 93 
                 94 
               
               
                 1118 
                 94 
                 95 
               
               
                 1119 
                 95 
                 96 
               
               
                 1120 
                 96 
                 97 
               
               
                 1121 
                 97 
                 98 
               
               
                 1122 
                 98 
                 99 
               
               
                 1123 
                 99 
                 100 
               
               
                 1124 
                 100 
                 101 
               
               
                 1125 
                 101 
                 102 
               
               
                 1126 
                 102 
                 103 
               
               
                 1127 
                 103 
                 104 
               
               
                 1128 
                 104 
                 105 
               
               
                 1129 
                 105 
                 106 
               
               
                 1130 
                 106 
                 107 
               
               
                 1131 
                 107 
                 108 
               
               
                 1132 
                 108 
                 109 
               
               
                 1133 
                 109 
                 110 
               
               
                 1134 
                 110 
                 111 
               
               
                 1135 
                 111 
                 112 
               
               
                 1136 
                 112 
                 113 
               
               
                 1137 
                 113 
                 114 
               
               
                 1138 
                 114 
                 115 
               
               
                 1139 
                 115 
                 116 
               
               
                 1140 
                 116 
                 117 
               
               
                 1141 
                 117 
                 118 
               
               
                 1142 
                 118 
                 119 
               
               
                 1143 
                 119 
                 120 
               
               
                 1144 
                 120 
                 121 
               
               
                 1145 
                 121 
                 122 
               
               
                 1146 
                 122 
                 123 
               
               
                 1147 
                 123 
                 124 
               
               
                 1148 
                 124 
                 125 
               
               
                 1149 
                 125 
                 126 
               
               
                 1150 
                 126 
                 127 
               
               
                 1151 
                 127 
                 128 
               
               
                 1152 
                 128 
                 129 
               
               
                 1153 
                 129 
                 130 
               
               
                 1154 
                 130 
                 131 
               
               
                 1155 
                 131 
                 132 
               
               
                 1156 
                 132 
                 133 
               
               
                 1157 
                 133 
                 134 
               
               
                 1158 
                 134 
                 135 
               
               
                 1159 
                 135 
                 136 
               
               
                 1160 
                 136 
                 137 
               
               
                 1161 
                 137 
                 138 
               
               
                 1162 
                 138 
                 139 
               
               
                 1163 
                 139 
                 140 
               
               
                 1164 
                 140 
                 141 
               
               
                 1165 
                 141 
                 142 
               
               
                 1166 
                 142 
                 143 
               
               
                 1167 
                 143 
                 144 
               
               
                 1168 
                 144 
                 145 
               
               
                 1169 
                 145 
                 146 
               
               
                 1170 
                 146 
                 147 
               
               
                 1171 
                 147 
                 148 
               
               
                 1172 
                 148 
                 149 
               
               
                 1173 
                 149 
                 150 
               
               
                 1174 
                 150 
                 151 
               
               
                 1175 
                 151 
                 152 
               
               
                 1176 
                 152 
                 153 
               
               
                 1177 
                 153 
                 154 
               
               
                 1178 
                 154 
                 155 
               
               
                 1179 
                 155 
                 156 
               
               
                 1180 
                 156 
                 157 
               
               
                 1181 
                 157 
                 158 
               
               
                 1182 
                 158 
                 159 
               
               
                 1183 
                 159 
                 160 
               
               
                 1184 
                 160 
                 161 
               
               
                 1185 
                 161 
                 162 
               
               
                 1186 
                 162 
                 163 
               
               
                 1187 
                 163 
                 164 
               
               
                 1188 
                 164 
                 165 
               
               
                 1189 
                 165 
                 166 
               
               
                 1190 
                 166 
                 167 
               
               
                 1191 
                 167 
                 168 
               
               
                 1192 
                 168 
                 169 
               
               
                 1193 
                 169 
                 170 
               
               
                 1194 
                 170 
                 171 
               
               
                 1195 
                 171 
                 172 
               
               
                 1196 
                 172 
                 173 
               
               
                 1197 
                 173 
                 174 
               
               
                 1198 
                 174 
                 175 
               
               
                 1199 
                 175 
                 176 
               
               
                 1200 
                 176 
                 177 
               
               
                 1201 
                 177 
                 178 
               
               
                 1202 
                 178 
                 179 
               
               
                 1203 
                 179 
                 180 
               
               
                 1204 
                 180 
                 181 
               
               
                 1205 
                 181 
                 182 
               
               
                 1206 
                 182 
                 183 
               
               
                 1207 
                 183 
                 184 
               
               
                 1208 
                 184 
                 185 
               
               
                 1209 
                 185 
                 186 
               
               
                 1210 
                 186 
                 187 
               
               
                 1211 
                 187 
                 188 
               
               
                 1212 
                 188 
                 189 
               
               
                 1213 
                 189 
                 190 
               
               
                 1214 
                 190 
                 191 
               
               
                 1215 
                 191 
                 192 
               
               
                 1216 
                 192 
                 193 
               
               
                 1217 
                 193 
                 194 
               
               
                 1218 
                 194 
                 195 
               
               
                 1219 
                 195 
                 196 
               
               
                 1220 
                 196 
                 197 
               
               
                 1221 
                 197 
                 198 
               
               
                 1222 
                 198 
                 199 
               
               
                 1223 
                 199 
                 200 
               
               
                 1224 
                 200 
                 201 
               
               
                 1225 
                 201 
                 202 
               
               
                 1226 
                 202 
                 203 
               
               
                 1227 
                 203 
                 204 
               
               
                 1228 
                 204 
                 205 
               
               
                 1229 
                 205 
                 206 
               
               
                 1230 
                 206 
                 207 
               
               
                 1231 
                 207 
                 208 
               
               
                 1232 
                 208 
                 209 
               
               
                 1233 
                 209 
                 210 
               
               
                 1234 
                 210 
                 211 
               
               
                 1235 
                 211 
                 212 
               
               
                 1236 
                 212 
                 213 
               
               
                 1237 
                 213 
                 214 
               
               
                 1238 
                 214 
                 215 
               
               
                 1239 
                 215 
                 216 
               
               
                 1240 
                 216 
                 217 
               
               
                 1241 
                 217 
                 218 
               
               
                 1242 
                 218 
                 219 
               
               
                 1243 
                 219 
                 220 
               
               
                 1244 
                 220 
                 221 
               
               
                 1245 
                 221 
                 222 
               
               
                 1246 
                 222 
                 223 
               
               
                 1247 
                 223 
                 224 
               
               
                 1248 
                 224 
                 225 
               
               
                 1249 
                 225 
                 226 
               
               
                 1250 
                 226 
                 227 
               
               
                 1251 
                 227 
                 228 
               
               
                 1252 
                 228 
                 229 
               
               
                 1253 
                 229 
                 230 
               
               
                 1254 
                 230 
                 231 
               
               
                 1255 
                 231 
                 232 
               
               
                 1256 
                 232 
                 233 
               
               
                 1257 
                 233 
                 234 
               
               
                 1258 
                 234 
                 235 
               
               
                 1259 
                 235 
                 236 
               
               
                 1260 
                 236 
                 237 
               
               
                 1261 
                 237 
                 238 
               
               
                 1262 
                 238 
                 239 
               
               
                 1263 
                 239 
                 240 
               
               
                 1264 
                 240 
                 241 
               
               
                 1265 
                 241 
                 242 
               
               
                 1266 
                 242 
                 243 
               
               
                 1267 
                 243 
                 244 
               
               
                 1268 
                 244 
                 245 
               
               
                 1269 
                 245 
                 246 
               
               
                 1270 
                 246 
                 247 
               
               
                 1271 
                 247 
                 248 
               
               
                 1272 
                 248 
                 249 
               
               
                 1273 
                 249 
                 250 
               
               
                 1274 
                 250 
                 251 
               
               
                 1275 
                 251 
                 252 
               
               
                 1276 
                 252 
                 253 
               
               
                 1277 
                 253 
                 254 
               
               
                 1278 
                 254 
                 255 
               
               
                 1279 
                 255 
                 256 
               
               
                 1280 
                 256