Patent Document

CROSS REFERENCE TO RELATED PATENTS/PATENT APPLICATIONS 
   Provisional Priority claim 
   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: 
   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,” , filed Wednesday, Aug. 18, 2004 (Aug. 18, 2004), pending. 
   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,” , filed Thursday, Aug. 19, 2004 (Aug. 19, 2004), pending. 

   BACKGROUND OF THE INVENTION 
   1. Technical Field of the Invention 
   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. 
   2. Description of Related Art 
   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). 
   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. 
   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. 
   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/”. 
   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. 
   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 
   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 
       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. 
       FIG. 3  is a diagram illustrating an embodiment of an LDPC (Low Density Parity Check) code bipartite graph. 
       FIG. 4  is a diagram illustrating an embodiment of decomposition of a parity check matrix, H, according to certain aspects of the invention. 
       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. 
       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. 
       FIG. 7  is a diagram illustrating an embodiment of a doughnut 128 2-D 12-PAM (Pulse Amplitude Modulation) constellation. 
       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. 
       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. 
       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. 
       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. 
       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. 
       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 
   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. 
     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. 
   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 . 
   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. 
   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 . 
   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. 
   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. 
     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. 
   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. 
   LDPC codes were introduced by R. Gallager in [1] 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. 
   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. 
   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 b i ), 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 . 
   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. 
   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. 
   This distribution may be described as follows: 
   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.
 
   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. 
     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. 
   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. 
   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)
 
   1. The sub-matrix H d  is a 256×256 matrix constructed as follows: 
   
     
       
         
           
             
               
                 
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   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. 
   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)
 
   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. 
   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)
 
   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. 
   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. 
   Below, several embodiments of possible parity check matrices are provided, according to the approach given above. 
   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. 
     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. 
   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. 
   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). 
   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)
 
   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. 
   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)
 
   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. 
   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. 
   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. 
   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. 
     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. 
   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. 
     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. 
   This document is publicly available at the following Internet address: 
   “http://www.ieee802.org/3/an/public/mar04/dabiri — 1 — 0304.pdf”. 
   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. 
   Since the center part of this construction is taken out, the distribution 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)
 
   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)
 
   If the 2D Constellation is exact 2-D 12-PAM which has 144 signals, then E 2 =95.333 and thus SNR 1 =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) 
     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. 
   The construction and placement of the constellation points of this substantially evenly distributed 128 2-D constellation is made in the following way. 
   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. 
   2. Delete 1 signal from every region so that the distribution of the deleted signals is as even as possible. 
   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)
 
   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) 
   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. 
   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. 
     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: 
   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). 
   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. 
     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. 
   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. 
   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. 
     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. 
   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. 
   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. 
     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. 
   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 . 
   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 . 
     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. 
   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 . 
   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 . 
   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 . 
   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. 
   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 . 
   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 . 
   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 . 
   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. 
   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. 
   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 
   Several examples of various parity check matrices are provided in this Appendix. 
   These parity check matrices are provided and presented with respect to the matrices depicted above. 
   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 
   1. One possible embodiment of a parity check matrix of a (1280, 1024) LDPC code is presented below. 
   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:
         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 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               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 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               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 
   2. Another embodiment of a parity check matrix of a (1280, 1024) LDPC code is presented below. 
   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:
         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 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               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 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               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 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               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 
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Technology Category: 5