Abstract:
The present invention comprises memory devices, apparatuses and systems including multiple bit per cell memory cells and methods for operating same. The multiple bit per cell memory cells of the present invention have higher memory densities than conventional single bit per cell memory cells. Additionally, spare states in multiple bit per cell memory devices that remain unmapped to binary data bits may be advantageously used.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]    This application is a continuation-in-part of application Ser. No. 09/758,476, filed Jan. 11, 2001, pending. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    The present invention relates generally to memory devices with storage cells capable of storing more than one bit of data, i.e., more than two voltage levels. More particularly, the present invention is a memory device with storage cells capable of storing 1.5 bits of data, or three voltage levels, and methods using same.  
           [0003]    Most conventional memory devices, including programmable read-only memory (PROM), electrically-erasable PROM (EEPROM), flash EEPROM, random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM) and the like, are capable of storing a single bit of data in a single memory cell. The memory cell of a conventional memory device may represent a data bit with a logical state of true or high voltage in the presence of stored charge in the memory cell. Conversely, the absence of charge may be representative of a data bit with a logical state false or low voltage.  
           [0004]    Memory devices with more than one bit of data per cell are also known in the art. For example, U.S. Pat. No. 5,043,940 to Harrari defines multilevel states in a single memory cell in terms of the threshold voltage V t  of a split-channel flash EEPROM memory cell. Harrari discloses using four discrete voltage levels to store two bits of data per memory cell by applying multiple programming pulses to each memory cell. U.S. Pat. No. 5,163,021 to Mehrota et al. also discloses a multi-level memory system wherein each memory cell is capable of four threshold voltage levels.  
           [0005]    U.S. Pat. No. 5,566,125 to Fazio et al. discloses a method and circuitry for storing discrete amounts of charge in a single flash memory cell. Fazio et al. also discloses programming a flash memory cell to one of at least three amounts of charge, wherein the amount of charge placed in the flash memory cell is increased by increasing the voltage level of a programming pulse applied to the memory cell.  
           [0006]    U.S. Pat. No. 5,574,879 to Wells et al. discloses addressing modes for a dynamic single bit per cell to multiple bit per cell memory. Wells et al. also discloses a memory system containing switch control for selecting between standard cell addressing modes and multi-level cell addressing modes. U.S. Pat. No. 5,594,691 to Bashir discloses address transition detection sensing circuitry for flash memory having multi-bit cells and methods for using same. U.S. Pat. No. 5,612,912 to Gillingham discloses a method of sensing and restoring voltages in a multi-level DRAM cell.  
           [0007]    However, none of these patents appears to disclose memory devices, apparatuses, systems and methods of using multi-bit memory cells to provide parity bits or methods of storing and retrieving partial bits of data from a single memory cell. Thus, there exists a need in the art for memory devices, apparatuses, systems and methods of using multi-bit memory cells to provide parity bits in a memory device based on multiples of 8 bits.  
         BRIEF SUMMARY OF THE INVENTION  
         [0008]    The present invention comprises memory devices, apparatuses and systems including multiple bit per cell memory cells and methods for using same. The multiple bit per cell memory cells of the present invention have higher memory densities than conventional single bit per cell memory cells. Additionally, spare states in multiple bit per cell memory devices that remain unmapped to binary data bits may be advantageously used for storing information. While multiple bit per cell memory cells having more than three states are contemplated, a memory cell with three states is preferable to a memory cell with four or more states because of the added difficulty in distinguishing four or more memory states in a given voltage range versus only three states, i.e., reliability decreases with narrower voltage margins between cell states.  
           [0009]    An embodiment of a multiple bit per cell memory device in accordance with the present invention includes a command and address decode block connected to a command bus and an address bus, a data input/output (I/O) block connected to the command and address decode block and connected to a data bus, and a memory array of multiple bit memory cells connected to the command and address decode block and the data I/O block.  
           [0010]    An embodiment of a memory card in accordance with the present invention includes a substrate for mounting and interconnecting integrated circuits, and at least one multiple bit per cell memory device integrated circuit mounted on the substrate, wherein the at least one multiple bit per cell memory device integrated circuit includes a command and address decode block connected to a command bus and an address bus, a data input/output (I/O) block connected to the command and address decode block and connected to a data bus, and a memory array of multiple bit memory cells connected to the command and address decode block and the data I/O block.  
           [0011]    An embodiment of a computer system in accordance with the present invention includes an input device, an output device, a processor connected to the input device and the output device, a memory device connected to the processor device and including at least one multiple bit per cell memory device, wherein each of the at least one multiple bit per cell memory device includes a command and address decode block connected to a command bus and an address bus, a data input/output (I/O) block connected to the command and address decode block and connected to a data bus, and a memory array of multiple bit memory cells connected to the command and address decode block and the data I/O block.  
           [0012]    An embodiment of a semiconductor substrate in accordance with the present invention includes at least one multiple bit per cell memory device mounted on the substrate, wherein the at least one multiple bit per cell memory device includes a command and address decode block connected to a command bus and an address bus, a data input/output (I/O) block connected to the command and address decode block and connected to a data bus, and a memory array of multiple bit memory cells connected to the command and address decode block and the data I/O block.  
           [0013]    A method embodiment for mapping states of a multiple bit per cell memory device to binary data bits is disclosed. Method embodiments for operating a multiple bit per cell memory device are also disclosed.  
           [0014]    These devices, apparatuses, systems and methods and attendant advantages of the present invention will be readily understood by reading the following detailed description in conjunction with the accompanying figures of the drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS  
       [0015]    In the drawings, which illustrate what is currently regarded as the best mode for carrying out the invention and in which like reference numerals refer to like parts in different views or embodiments:  
         [0016]    [0016]FIG. 1 is a voltage diagram of an embodiment of a multiple bit memory cell in accordance with the present invention.  
         [0017]    [0017]FIG. 2 is a block diagram of a multiple bit per cell memory device in accordance with the present invention.  
         [0018]    [0018]FIG. 3 is a block diagram of a memory card including at least one multiple bit per cell memory device of the present invention.  
         [0019]    [0019]FIG. 4 is a block diagram of a computer system including the multiple bit per cell memory device of the present invention.  
         [0020]    [0020]FIG. 5 is a plan view of a semiconductor substrate including at least one integrated circuit die having at least one multiple bit per cell memory device in accordance with the present invention.  
         [0021]    [0021]FIG. 6 is a flow chart of a method of mapping the unique states of a multiple bit per cell memory cell to unique states of binary data bits and assigning spare states for erased, default or invalid data states.  
         [0022]    [0022]FIG. 7 is a flow chart of a method of operating a multiple bit per cell memory device in accordance with the invention.  
         [0023]    [0023]FIG. 8 is a flow chart of a method of erasing data in a multiple bit per cell memory device in accordance with the present invention.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0024]    U.S. Pat. Nos. 5,566,125 to Fazio et al., 5,574,879 to Wells et al., 5,594,691 to Bashir and 5,612,912 to Gillingham are each expressly incorporated herein by reference for all purposes. The primary advantage of the multiple bit per cell memory cells disclosed herein is greater memory density relative to conventional single bit per cell memory cells or, alternatively, reduced semiconductor die real estate relative to conventional single bit per cell memory cells.  
         [0025]    [0025]FIG. 1 is a voltage diagram of an embodiment of a multiple bit memory cell in accordance with the present invention. In particular, FIG. 1 illustrates a 1.5 bit memory cell  100  in accordance with the present invention. The 1.5 bit memory cell  100  includes three states, 0, 1 and 2, corresponding roughly to the voltage regions between a power source, V CC , and ground potential, GND, as indicated. The three states are separated by two reference voltages, V R1  and V R2 . Memory devices including memory cells with 2 bits per cell (or four states) in Flash EEPROM and DRAM technologies and methods for manufacturing same are known in the art. For this reason, further detail regarding the storage of more than two states in a memory cell will not be included herein.  
         [0026]    Table 1 below, is an exemplary mapping of two 1.5 bit memory cells, CELL0-CELL1, each with three states, to three binary bits, BIT0-BIT2. In order to retrieve data from a cell which stores a fraction of a data bit, it is necessary to read at least two cells. The nine possible states of the two cells are mapped into eight data states representing three binary data bits, and one spare state. The ninth state, State 8, is a spare state. The spare state may be used as an erased or unwritten state, or as an error state (data is invalid). As can be seen from Table 1 below, the mapping of two 1.5 bit memory cells, CELL0-CELL 1, each with three states to three binary bits, BIT0-BIT1, is a mapping of base 3 numbers (two 1.5 bit cells each cell having three states) to base 2 numbers (three binary bits), each unique mapping representing a state.  
                                           TABLE 1                                   State   CELL0   CELL1   BIT2   BIT1   BIT0                           0   0   0   0   0   0           1   0   1   0   0   1           2   0   2   0   1   0           3   1   0   0   1   1           4   1   1   1   0   0           5   1   2   1   0   1           6   2   0   1   1   0           7   2   1   1   1   1           8   2   2   X   X   X                      
 
         [0027]    The example mapping shown in Table 1, above, may be extended to any number of cells. Table 2, at the end of this specification, is a table illustrating one possible mapping of six 1.5 bit memory cells, C0-5, to nine binary data bits, B0-8. The left-most column of the table in Table 2, is the state column with a unique number of each of the 729 possible states in a group of six, 3-state memory cells. The six 1.5 bit memory cells are referred to herein as a “group of 1.5 bit memory cells” or alternatively as a “group of 3-state memory cells.” The nine binary data bits, B0-8, mapped from the group of 1.5 bit memory cells may be arranged as eight data bits and one parity bit. Note that there are extra or “spare states,” specifically, states 512-728, denoted by an “X” in the bit columns, B0-8. These 217 spare states may be powered up in an invalid data state, or may be erased into the invalid data state. Groups of 1.5 bit memory cells may be arranged in any suitable topology to form multiple bit per cell memory devices. Thus, Table 2, like Table 1, is a mapping of base 3 numbers (six 1.5 bit cells each cell having 3 states) to base 2 numbers (nine binary data bits).  
         [0028]    [0028]FIG. 2 is a block diagram of a multiple bit per cell memory device  200  in accordance with the present invention. The multiple bit per cell memory device  200  includes a command and address decode block  202  connected to a data input/output (I/O) block  204 , and a memory array  206  connected to both the command and address decode block  202  and the data I/O block  204 . The command and address decode block  202  may be connected externally to a command bus and to an address bus. The data I/O block  204  may be connected externally to a bidirectional data bus. The memory array  206  further includes at least one group  208  of multiple bit per cell memory cells  210  and a parity generator  212 . Although only one group  208  and one multiple bit per cell memory cell  210  are shown, one of ordinary skill in the art will recognize that the group  208  and multiple bit per cell memory cell  210  may be arranged and scaled to accommodate virtually any configuration of memory array. The parity generator  212  allows on-chip parity generation and checking for any memory states within the multiple bit per cell memory cells  210  that are invalid data states. Parity generator  212  may also include circuitry for generating error-correcting codes, applying the generated error-correcting codes, detecting errors and correcting errors detected.  
         [0029]    Multiple bit per cell memory cell  210  may be a 1.5 bit per cell memory cell as depicted in FIG. 1. A group  208  may contain any number of multiple bit per cell memory cells  210 . Advantageously, group  208  may include six 1.5 bit per cell memory cells mapped to eight data bits and one parity bit as illustrated in Table 2.  
         [0030]    Other multiple bit per cell memory cells are within the scope of the present invention, for example, and not by way of limitation, a five state, 2.5 bit per cell memory cell. The more states per memory cell, the greater the memory density of the memory device. However, as noted above, for a given rail-to-rail voltage differential (i.e., ground potential, GND, to supply voltage, V CC ), a three-state memory cell is easier to reliably manufacture than a memory cell with four or more states because the voltage thresholds that separate the various states are wider for a three-state memory cell than for higher-state memory cells.  
         [0031]    The multiple bit per cell memory cell  210  of the present invention may be used in conventional memory device architectures such as dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), RAMBUS® DRAM (RDRAM®), extended data-out DRAM,(EDO DRAM), fast-page-mode DRAM (FPM DRAM), static random access memory (SRAM), SyncBurst™ SRAM, Zero Bus Turnaround™ SRAM (ZBT™ SRAM), Quad Data Rate™ SRAM (QDR™ SRAM), DDR synchronous SRAM (DDR SRAM) and nonvolatile electrically block-erasable programmable read only memory (Flash).  
         [0032]    [0032]FIG. 3 is a block diagram of a memory card  300  including at least one multiple bit per cell memory device  200  of the present invention. The term “memory card” is synonymous with “memory circuit card” or “memory module” as known to one of ordinary skill in the art. The memory card  300  of FIG. 3 is shown with a substrate  302  and five multiple bit per cell memory devices  200 . However, any number of multiple bit per cell memory devices  200  may be included on a given memory card  300 . Memory card  300  also includes an interface to external devices. FIG. 3 illustrates a system bus interface; however, a memory bus or other dedicated electrical bus interface is also contemplated within the scope of the invention. Substrate  302  may be a circuit card or other substrate for mounting integrated circuits.  
         [0033]    The memory card  300  may be configured for compatibility with conventional memory module architectures, for example and not by way of limitation, single in-line memory module (SIMM), RAMBUS® in-line memory module (RIMM™), dual in-line memory module (DIMM), accelerated graphics port (AGP) in-line memory module (AIMM), and small-outline DIMM (SODIMM).  
         [0034]    [0034]FIG. 4 is a block diagram of a computer system  400  including the multiple bit per cell memory device  200  of the present invention. Computer system  400  includes an input device  402 , an output device  404 , a processor device  406  connected to the input device  402  and the output device  404 , and a memory device  408  connected to the processor device. Input device  402  may be a keyboard, mouse, joystick or other computer input device. Output device  404  may be a monitor, printer or storage device, such as a disk drive. Processor device  406  may be a microprocessor or a circuit card including hardware for processing computer instructions.  
         [0035]    Memory device  408  includes at least one multiple bit per cell memory device  200  in accordance with the present invention. Memory device  408  may be a memory card  300  as described above and shown in FIG. 3.  
         [0036]    [0036]FIG. 5 is a plan view of a semiconductor substrate  500  including at least one integrated circuit die  502  having at least one multiple bit per cell memory device  200  in accordance with the present invention.  
         [0037]    The semiconductor technology employed is not a limiting factor in the application of the multiple bit per cell memory device of the present invention. While silicon is the preferred bulk semiconductor material for commercial electronic devices, gallium arsenide and indium phosphide substrates may also be employed. Of course, it will be understood that the multiple bit per cell memory device of the present invention may be fabricated on other semiconductor substrates as well, including, for example, silicon-on-glass (SOG) substrates, silicon-on-insulator (SOI) substrates, and silicon-on-sapphire (SOS) substrates.  
         [0038]    [0038]FIG. 6 is a flow chart of a method  600  for mapping the unique states of a multiple bit per cell memory cell to unique states of binary data bits and assigning spare states as invalid data states in accordance with the present invention. The method  600  includes providing  602  a memory device with x memory cells, each with y states, assigning  604  a unique state to each of the y x  possible states of the memory device, mapping  606  each unique state to a unique binary state of n binary bits, where 2 n &lt;y x  and n is an integer, and designating  608  the y x −2 n  spare states as invalid data states. As an example of the above method, refer again to Table 2. For a multiple bit per cell memory device with 6 cells (x=6), each memory cell with 3 states (y=3), there are 3 6 =729 unique states (y x ). To satisfy the inequality, 2 n &lt;y x , for the largest integer n, select n=9 (i.e., 512&lt;729). The remaining y x −2 n  or 729−512=217 spare states may be designated as erased, default, or invalid data states.  
         [0039]    [0039]FIG. 7 is a flow chart of a method  700  of operating a multiple bit per cell memory device in accordance with the present invention. The method  700  includes providing  702  a multiple bit per cell memory device with x memory cells, each with y states, where y&gt;2, applying power  704  to the multiple bit per cell memory device, running  706  a self-test on each of y x  possible states of the memory device to identify z faulty states, where z≧0, assigning  708  a unique state to each of the y x −z working states of the memory device, mapping  710  each assigned unique state to a unique binary state of n binary bits, where 2 n &lt;y x  and n is an integer, and designating  712  the y x −z−2 n  spare states for erased, default, or invalid data states.  
         [0040]    [0040]FIG. 8 is a flow chart of a method  800  of erasing data in a multiple bit per cell memory device in accordance with the present invention. Method  800  includes providing  802  a multiple bit per cell memory device with x multiple bit per cell memory cells, each with y states, assigning  804  a unique state to each of y x  possible states of the multiple bit per cell memory device, mapping  806  each assigned unique state to a unique binary state of n binary bits, where 2 n &lt;y x  and n is an integer, utilizing  808  at least one of y x −2 n  spare states for indicating erased memory cells, reading  810  each of the indicated erased memory cells to determine whether it is erased or not erased, and erasing  812  each of the indicated erased memory cells only if it is not erased.  
                                                                                                                                             TABLE 2                       STATE   C5   C4   C3   C2   C1   C0   B8   B7   B6   B5   B4   B3   B2   B1   B0                                0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0       1   0   0   0   0   0   1   0   0   0   0   0   0   0   0   1       2   0   0   0   0   0   2   0   0   0   0   0   0   0   1   0       3   0   0   0   0   1   0   0   0   0   0   0   0   0   1   1       4   0   0   0   0   1   1   0   0   0   0   0   0   1   0   0       5   0   0   0   0   1   2   0   0   0   0   0   0   1   0   1       6   0   0   0   0   2   0   0   0   0   0   0   0   1   1   0       7   0   0   0   0   2   1   0   0   0   0   0   0   1   1   1       8   0   0   0   0   2   2   0   0   0   0   0   1   0   0   0       9   0   0   0   1   0   0   0   0   0   0   0   1   0   0   1       10   0   0   0   1   0   1   0   0   0   0   0   1   0   1   0       11   0   0   0   1   0   2   0   0   0   0   0   1   0   1   1       12   0   0   0   1   1   0   0   0   0   0   0   1   1   0   0       13   0   0   0   1   1   1   0   0   0   0   0   1   1   0   1       14   0   0   0   1   1   2   0   0   0   0   0   1   1   1   0       15   0   0   0   1   2   0   0   0   0   0   0   1   1   1   1       16   0   0   0   1   2   1   0   0   0   0   1   0   0   0   0       17   0   0   0   1   2   2   0   0   0   0   1   0   0   0   1       18   0   0   0   2   0   0   0   0   0   0   1   0   0   1   0       19   0   0   0   2   0   1   0   0   0   0   1   0   0   1   1       20   0   0   0   2   0   2   0   0   0   0   1   0   1   0   0       21   0   0   0   2   1   0   0   0   0   0   1   0   1   0   1       22   0   0   0   2   1   1   0   0   0   0   1   0   1   1   0       23   0   0   0   2   1   2   0   0   0   0   1   0   1   1   1       24   0   0   0   2   2   0   0   0   0   0   1   1   0   0   0       25   0   0   0   2   2   1   0   0   0   0   1   1   0   0   1       26   0   0   0   2   2   2   0   0   0   0   1   1   0   1   0       27   0   0   1   0   0   0   0   0   0   0   1   1   0   1   1       28   0   0   1   0   0   1   0   0   0   0   1   1   1   0   0       29   0   0   1   0   0   2   0   0   0   0   1   1   1   0   1       30   0   0   1   0   1   0   0   0   0   0   1   1   1   1   0       31   0   0   1   0   1   1   0   0   0   0   1   1   1   1   1       32   0   0   1   0   1   2   0   0   0   1   0   0   0   0   0       33   0   0   1   0   2   0   0   0   0   1   0   0   0   0   1       34   0   0   1   0   2   1   0   0   0   1   0   0   0   1   0       35   0   0   1   0   2   2   0   0   0   1   0   0   0   1   1       36   0   0   1   1   0   0   0   0   0   1   0   0   1   0   0       37   0   0   1   1   0   1   0   0   0   1   0   0   1   0   1       38   0   0   1   1   0   2   0   0   0   1   0   0   1   1   0       39   0   0   1   1   1   0   0   0   0   1   0   0   1   1   1       40   0   0   1   1   1   1   0   0   0   1   0   1   0   0   0       41   0   0   1   1   1   2   0   0   0   1   0   1   0   0   1       42   0   0   1   1   2   0   0   0   0   1   0   1   0   1   0       43   0   0   1   1   2   1   0   0   0   1   0   1   0   1   1       44   0   0   1   1   2   2   0   0   0   1   0   1   1   0   0       45   0   0   1   2   0   0   0   0   0   1   0   1   1   0   1       46   0   0   1   2   0   1   0   0   0   1   0   1   1   1   0       47   0   0   1   2   0   2   0   0   0   1   0   1   1   1   1       48   0   0   1   2   1   0   0   0   0   1   1   0   0   0   0       49   0   0   1   2   1   1   0   0   0   1   1   0   0   0   1       50   0   0   1   2   1   2   0   0   0   1   1   0   0   1   0       51   0   0   1   2   2   0   0   0   0   1   1   0   0   1   1       52   0   0   1   2   2   1   0   0   0   1   1   0   1   0   0       53   0   0   1   2   2   2   0   0   0   1   1   0   1   0   1       54   0   0   2   0   0   0   0   0   0   1   1   0   1   1   0       55   0   0   2   0   0   1   0   0   0   1   1   0   1   1   1       56   0   0   2   0   0   2   0   0   0   1   1   1   0   0   0       57   0   0   2   0   1   0   0   0   0   1   1   1   0   0   1       58   0   0   2   0   1   1   0   0   0   1   1   1   0   1   0       59   0   0   2   0   1   2   0   0   0   1   1   1   0   1   1       60   0   0   2   0   2   0   0   0   0   1   1   1   1   0   0       61   0   0   2   0   2   1   0   0   0   1   1   1   1   0   1       62   0   0   2   0   2   2   0   0   0   1   1   1   1   1   0       63   0   0   2   1   0   0   0   0   0   1   1   1   1   1   1       64   0   0   2   1   0   1   0   0   1   0   0   0   0   0   0       65   0   0   2   1   0   2   0   0   1   0   0   0   0   0   1       66   0   0   2   1   1   0   0   0   1   0   0   0   0   1   0       67   0   0   2   1   1   1   0   0   1   0   0   0   0   1   1       68   0   0   2   1   1   2   0   0   1   0   0   0   1   0   0       69   0   0   2   1   2   0   0   0   1   0   0   0   1   0   1       70   0   0   2   1   2   1   0   0   1   0   0   0   1   1   0       71   0   0   2   1   2   2   0   0   1   0   0   0   1   1   1       72   0   0   2   2   0   0   0   0   1   0   0   1   0   0   0       73   0   0   2   2   0   1   0   0   1   0   0   1   0   0   1       74   0   0   2   2   0   2   0   0   1   0   0   1   0   1   0       75   0   0   2   2   1   0   0   0   1   0   0   1   0   1   1       76   0   0   2   2   1   1   0   0   1   0   0   1   1   0   0       77   0   0   2   2   1   2   0   0   1   0   0   1   1   0   1       78   0   0   2   2   2   0   0   0   1   0   0   1   1   1   0       79   0   0   2   2   2   1   0   0   1   0   0   1   1   1   1       80   0   0   2   2   2   2   0   0   1   0   1   0   0   0   0       81   0   1   0   0   0   0   0   0   1   0   1   0   0   0   1       82   0   1   0   0   0   1   0   0   1   0   1   0   0   1   0       83   0   1   0   0   0   2   0   0   1   0   1   0   0   1   1       84   0   1   0   0   1   0   0   0   1   0   1   0   1   0   0       85   0   1   0   0   1   1   0   0   1   0   1   0   1   0   1       86   0   1   0   0   1   2   0   0   1   0   1   0   1   1   0       87   0   1   0   0   2   0   0   0   1   0   1   0   1   1   1       88   0   1   0   0   2   1   0   0   1   0   1   1   0   0   0       89   0   1   0   0   2   2   0   0   1   0   1   1   0   0   1       90   0   1   0   1   0   0   0   0   1   0   1   1   0   1   0       91   0   1   0   1   0   1   0   0   1   0   1   1   0   1   1       92   0   1   0   1   0   2   0   0   1   0   1   1   1   0   0       93   0   1   0   1   1   0   0   0   1   0   1   1   1   0   1       94   0   1   0   1   1   1   0   0   1   0   1   1   1   1   0       95   0   1   0   1   1   2   0   0   1   0   1   1   1   1   1       96   0   1   0   1   2   0   0   0   1   1   0   0   0   0   0       97   0   1   0   1   2   1   0   0   1   1   0   0   0   0   1       98   0   1   0   1   2   2   0   0   1   1   0   0   0   1   0       99   0   1   0   2   0   0   0   0   1   1   0   0   0   1   1       100   0   1   0   2   0   1   0   0   1   1   0   0   1   0   0       101   0   1   0   2   0   2   0   0   1   1   0   0   1   0   1       102   0   1   0   2   1   0   0   0   1   1   0   0   1   1   0       103   0   1   0   2   1   1   0   0   1   1   0   0   1   1   1       104   0   1   0   2   1   2   0   0   1   1   0   1   0   0   0       105   0   1   0   2   2   0   0   0   1   1   0   1   0   0   1       106   0   1   0   2   2   1   0   0   1   1   0   1   0   1   0       107   0   1   0   2   2   2   0   0   1   1   0   1   0   1   1       108   0   1   1   0   0   0   0   0   1   1   0   1   1   0   0       109   0   1   1   0   0   1   0   0   1   1   0   1   1   0   1       110   0   1   1   0   0   2   0   0   1   1   0   1   1   1   0       111   0   1   1   0   1   0   0   0   1   1   0   1   1   1   1       112   0   1   1   0   1   1   0   0   1   1   1   0   0   0   0       113   0   1   1   0   1   2   0   0   1   1   1   0   0   0   1       114   0   1   1   0   2   0   0   0   1   1   1   0   0   1   0       115   0   1   1   0   2   1   0   0   1   1   1   0   0   1   1       116   0   1   1   0   2   2   0   0   1   1   1   0   1   0   0       117   0   1   1   1   0   0   0   0   1   1   1   0   1   0   1       118   0   1   1   1   0   1   0   0   1   1   1   0   1   1   0       119   0   1   1   1   0   2   0   0   1   1   1   0   1   1   1       120   0   1   1   1   1   0   0   0   1   1   1   1   0   0   0       121   0   1   1   1   1   1   0   0   1   1   1   1   0   0   1       122   0   1   1   1   1   2   0   0   1   1   1   1   0   1   0       123   0   1   1   1   2   0   0   0   1   1   1   1   0   1   1       124   0   1   1   1   2   1   0   0   1   1   1   1   1   0   0       125   0   1   1   1   2   2   0   0   1   1   1   1   1   0   1       156   0   1   1   2   0   0   0   0   1   1   1   1   1   1   0       127   0   1   1   2   0   1   0   0   1   1   1   1   1   1   1       128   0   1   1   2   0   2   0   1   0   0   0   0   0   0   0       129   0   1   1   2   1   0   0   1   0   0   0   0   0   0   1       130   0   1   1   2   1   1   0   1   0   0   0   0   0   1   0       131   0   1   1   2   1   2   0   1   0   0   0   0   0   1   1       132   0   1   1   2   2   0   0   1   0   0   0   0   1   0   0       133   0   1   1   2   2   1   0   1   0   0   0   0   1   0   1       134   0   1   1   2   2   2   0   1   0   0   0   0   1   1   0       135   0   1   2   0   0   0   0   1   0   0   0   0   1   1   1       136   0   1   2   0   0   1   0   1   0   0   0   1   0   0   0       137   0   1   2   0   0   2   0   1   0   0   0   1   0   0   1       138   0   1   2   0   1   0   0   1   0   0   0   1   0   1   0       139   0   1   2   0   1   1   0   1   0   0   0   1   0   1   1       140   0   1   2   0   1   2   0   1   0   0   0   1   1   0   0       141   0   1   2   0   2   0   0   1   0   0   0   1   1   0   1       142   0   1   2   0   2   1   0   1   0   0   0   1   1   1   0       143   0   1   2   0   2   2   0   1   0   0   0   1   1   1   1       144   0   1   2   1   0   0   0   1   0   0   1   0   0   0   0       145   0   1   2   1   0   1   0   1   0   0   1   0   0   0   1       146   0   1   2   1   0   2   0   1   0   0   1   0   0   1   0       147   0   1   2   1   1   0   0   1   0   0   1   0   0   1   1       148   0   1   2   1   1   1   0   1   0   0   1   0   1   0   0       149   0   1   2   1   1   2   0   1   0   0   1   0   1   0   1       150   0   1   2   1   2   0   0   1   0   0   1   0   1   1   0       151   0   1   2   1   2   1   0   1   0   0   1   0   1   1   1       152   0   1   2   1   2   2   0   1   0   0   1   1   0   0   0       153   0   1   2   2   0   0   0   1   0   0   1   1   0   0   1       154   0   1   2   2   0   1   0   1   0   0   1   1   0   1   0       155   0   1   2   2   0   2   0   1   0   0   1   1   0   1   1       156   0   1   2   2   1   0   0   1   0   0   1   1   1   0   0       157   0   1   2   2   1   1   0   1   0   0   1   1   1   0   1       158   0   1   2   2   1   2   0   1   0   0   1   1   1   1   0       159   0   1   2   2   2   0   0   1   0   0   1   1   1   1   1       160   0   1   2   2   2   1   0   1   0   1   0   0   0   0   0       161   0   1   2   2   2   2   0   1   0   1   0   0   0   0   1       162   0   2   0   0   0   0   0   1   0   1   0   0   0   1   0       163   0   2   0   0   0   1   0   1   0   1   0   0   0   1   1       164   0   2   0   0   0   2   0   1   0   1   0   0   1   0   0       165   0   2   0   0   1   0   0   1   0   1   0   0   1   0   1       166   0   2   0   0   1   1   0   1   0   1   0   0   1   1   0       167   0   2   0   0   1   2   0   1   0   1   0   0   1   1   1       168   0   2   0   0   2   0   0   1   0   1   0   1   0   0   0       169   0   2   0   0   2   1   0   1   0   1   0   1   0   0   1       170   0   2   0   0   2   2   0   1   0   1   0   1   0   1   0       171   0   2   0   1   0   0   0   1   0   1   0   1   0   1   1       172   0   2   0   1   0   1   0   1   0   1   0   1   1   0   0       173   0   2   0   1   0   2   0   1   0   1   0   1   1   0   1       174   0   2   0   1   1   0   0   1   0   1   0   1   1   1   0       175   0   2   0   1   1   1   0   1   0   1   0   1   1   1   1       176   0   2   0   1   1   2   0   1   0   1   1   0   0   0   0       177   0   2   0   1   2   0   0   1   0   1   1   0   0   0   1       178   0   2   0   1   2   1   0   1   0   1   1   0   0   1   0       179   0   2   0   1   2   2   0   1   0   1   1   0   0   1   1       180   0   2   0   2   0   0   0   1   0   1   1   0   1   0   0       181   0   2   0   2   0   1   0   1   0   1   1   0   1   0   1       182   0   2   0   2   0   2   0   1   0   1   1   0   1   1   0       183   0   2   0   2   1   0   0   1   0   1   1   0   1   1   1       184   0   2   0   2   1   1   0   1   0   1   1   1   0   0   0       185   0   2   0   2   1   2   0   1   0   1   1   1   0   0   1       186   0   2   0   2   2   0   0   1   0   1   1   1   0   1   0       187   0   2   0   2   2   1   0   1   0   1   1   1   0   1   1       188   0   2   0   2   2   2   0   1   0   1   1   1   1   0   0       189   0   2   1   0   0   0   0   1   0   1   1   1   1   0   1       190   0   2   1   0   0   1   0   1   0   1   1   1   1   1   0       191   0   2   1   0   0   2   0   1   0   1   1   1   1   1   1       192   0   2   1   0   1   0   0   1   1   0   0   0   0   0   0       193   0   2   1   0   1   1   0   1   1   0   0   0   0   0   1       194   0   2   1   0   1   2   0   1   1   0   0   0   0   1   0       195   0   2   1   0   2   0   0   1   1   0   0   0   0   1   1       196   0   2   1   0   2   1   0   1   1   0   0   0   1   0   0       197   0   2   1   0   2   2   0   1   1   0   0   0   1   0   1       198   0   2   1   1   0   0   0   1   1   0   0   0   1   1   0       199   0   2   1   1   0   1   0   1   1   0   0   0   1   1   1       200   0   2   1   1   0   2   0   1   1   0   0   1   0   0   0       201   0   2   1   1   1   0   0   1   1   0   0   1   0   0   1       202   0   2   1   1   1   1   0   1   1   0   0   1   0   1   0       203   0   2   1   1   1   2   0   1   1   0   0   1   0   1   1       204   0   2   1   1   2   0   0   1   1   0   0   1   1   0   0       205   0   2   1   1   2   1   0   1   1   0   0   1   1   0   1       206   0   2   1   1   2   2   0   1   1   0   0   1   1   1   0       207   0   2   1   2   0   0   0   1   1   0   0   1   1   1   1       208   0   2   1   2   0   1   0   1   1   0   1   0   0   0   0       209   0   2   1   2   0   2   0   1   1   0   1   0   0   0   1       210   0   2   1   2   1   0   0   1   1   0   1   0   0   1   0       211   0   2   1   2   1   1   0   1   1   0   1   0   0   1   1       212   0   2   1   2   1   2   0   1   1   0   1   0   1   0   0       213   0   2   1   2   2   0   0   1   1   0   1   0   1   0   1       214   0   2   1   2   2   1   0   1   1   0   1   0   1   1   0       215   0   2   1   2   2   2   0   1   1   0   1   0   1   1   1       216   0   2   2   0   0   0   0   1   1   0   1   1   0   0   0       217   0   2   2   0   0   1   0   1   1   0   1   1   0   0   1       218   0   2   2   0   0   2   0   1   1   0   1   1   0   1   0       219   0   2   2   0   1   0   0   1   1   0   1   1   0   1   1       220   0   2   2   0   1   1   0   1   1   0   1   1   1   0   0       221   0   2   2   0   1   2   0   1   1   0   1   1   1   0   1       222   0   2   2   0   2   0   0   1   1   0   1   1   1   1   0       223   0   2   2   0   2   1   0   1   1   0   1   1   1   1   1       224   0   2   2   0   2   2   0   1   1   1   0   0   0   0   0       225   0   2   2   1   0   0   0   1   1   1   0   0   0   0   1       226   0   2   2   1   0   1   0   1   1   1   0   0   0   1   0       227   0   2   2   1   0   2   0   1   1   1   0   0   0   1   1       228   0   2   2   1   1   0   0   1   1   1   0   0   1   0   0       229   0   2   2   1   1   1   0   1   1   1   0   0   1   0   1       230   0   2   2   1   1   2   0   1   1   1   0   0   1   1   0       231   0   2   2   1   2   0   0   1   1   1   0   0   1   1   1       232   0   2   2   1   2   1   0   1   1   1   0   1   0   0   0       233   0   2   2   1   2   2   0   1   1   1   0   1   0   0   1       234   0   2   2   2   0   0   0   1   1   1   0   1   0   1   0       235   0   2   2   2   0   1   0   1   1   1   0   1   0   1   1       236   0   2   2   2   0   2   0   1   1   1   0   1   1   0   0       237   0   2   2   2   1   0   0   1   1   1   0   1   1   0   1       238   0   2   2   2   1   1   0   1   1   1   0   1   1   1   0       239   0   2   2   2   1   2   0   1   1   1   0   1   1   1   1       240   0   2   2   2   2   0   0   1   1   1   1   0   0   0   0       241   0   2   2   2   2   1   0   1   1   1   1   0   0   0   1       242   0   2   2   2   2   2   0   1   1   1   1   0   0   1   0       243   1   0   0   0   0   0   0   1   1   1   1   0   0   1   1       244   1   0   0   0   0   1   0   1   1   1   1   0   1   0   0       245   1   0   0   0   0   2   0   1   1   1   1   0   1   0   1       246   1   0   0   0   1   0   0   1   1   1   1   0   1   1   0       247   1   0   0   0   1   1   0   1   1   1   1   0   1   1   1       248   1   0   0   0   1   2   0   1   1   1   1   1   0   0   0       249   1   0   0   0   2   0   0   1   1   1   1   1   0   0   1       250   1   0   0   0   2   1   0   1   1   1   1   1   0   1   0       251   1   0   0   0   2   2   0   1   1   1   1   1   0   1   1       252   1   0   0   1   0   0   0   1   1   1   1   1   1   0   0       253   1   0   0   1   0   1   0   1   1   1   1   1   1   0   1       254   1   0   0   1   0   2   0   1   1   1   1   1   1   1   0       255   1   0   0   1   1   0   0   1   1   1   1   1   1   1   1       256   1   0   0   1   1   1   1   0   0   0   0   0   0   0   0       257   1   0   0   1   1   2   1   0   0   0   0   0   0   0   1       258   1   0   0   1   2   0   1   0   0   0   0   0   0   1   0       259   1   0   0   1   2   1   1   0   0   0   0   0   0   1   1       260   1   0   0   1   2   2   1   0   0   0   0   0   1   0   0       261   1   0   0   2   0   0   1   0   0   0   0   0   1   0   1       262   1   0   0   2   0   1   1   0   0   0   0   0   1   1   0       263   1   0   0   2   0   2   1   0   0   0   0   0   1   1   1       264   1   0   0   2   1   0   1   0   0   0   0   1   0   0   0       265   1   0   0   2   1   1   1   0   0   0   0   1   0   0   1       266   1   0   0   2   1   2   1   0   0   0   0   1   0   1   0       267   1   0   0   2   2   0   1   0   0   0   0   1   0   1   1       268   1   0   0   2   2   1   1   0   0   0   0   1   1   0   0       269   1   0   0   2   2   2   1   0   0   0   0   1   1   0   1       270   1   0   1   0   0   0   1   0   0   0   0   1   1   1   0       271   1   0   1   0   0   1   1   0   0   0   0   1   1   1   1       272   1   0   1   0   0   2   1   0   0   0   1   0   0   0   0       273   1   0   1   0   1   0   1   0   0   0   1   0   0   0   1       274   1   0   1   0   1   1   1   0   0   0   1   0   0   1   0       275   1   0   1   0   1   2   1   0   0   0   1   0   0   1   1       276   1   0   1   0   2   0   1   0   0   0   1   0   1   0   0       277   1   0   1   0   2   1   1   0   0   0   1   0   1   0   1       278   1   0   1   0   2   2   1   0   0   0   1   0   1   1   0       279   1   0   1   1   0   0   1   0   0   0   1   0   1   1   1       280   1   0   1   1   0   1   1   0   0   0   1   1   0   0   0       281   1   0   1   1   0   2   1   0   0   0   1   1   0   0   1       282   1   0   1   1   1   0   1   0   0   0   1   1   0   1   0       283   1   0   1   1   1   1   1   0   0   0   1   1   0   1   1       284   1   0   1   1   1   2   1   0   0   0   1   1   1   0   0       285   1   0   1   1   2   0   1   0   0   0   1   1   1   0   1       286   1   0   1   1   2   1   1   0   0   0   1   1   1   1   0       287   1   0   1   1   2   2   1   0   0   0   1   1   1   1   1       288   1   0   1   2   0   0   1   0   0   1   0   0   0   0   0       289   1   0   1   2   0   1   1   0   0   1   0   0   0   0   1       290   1   0   1   2   0   2   1   0   0   1   0   0   0   1   0       291   1   0   1   2   1   0   1   0   0   1   0   0   0   1   1       292   1   0   1   2   1   1   1   0   0   1   0   0   1   0   0       293   1   0   1   2   1   2   1   0   0   1   0   0   1   0   1       294   1   0   1   2   2   0   1   0   0   1   0   0   1   1   0       295   1   0   1   2   2   1   1   0   0   1   0   0   1   1   1       296   1   0   1   2   2   2   1   0   0   1   0   1   0   0   0       297   1   0   2   0   0   0   1   0   0   1   0   1   0   0   1       298   1   0   2   0   0   1   1   0   0   1   0   1   0   1   0       299   1   0   2   0   0   2   1   0   0   1   0   1   0   1   1       300   1   0   2   0   1   0   1   0   0   1   0   1   1   0   0       301   1   0   2   0   1   1   1   0   0   1   0   1   1   0   1       302   1   0   2   0   1   2   1   0   0   1   0   1   1   1   0       303   1   0   2   0   2   0   1   0   0   1   0   1   1   1   1       304   1   0   2   0   2   1   1   0   0   1   1   0   0   0   0       305   1   0   2   0   2   2   1   0   0   1   1   0   0   0   1       306   1   0   2   1   0   0   1   0   0   1   1   0   0   1   0       307   1   0   2   1   0   1   1   0   0   1   1   0   0   1   1       308   1   0   2   1   0   2   1   0   0   1   1   0   1   0   0       309   1   0   2   1   1   0   1   0   0   1   1   0   1   0   1       310   1   0   2   1   1   1   1   0   0   1   1   0   1   1   0       311   1   0   2   1   1   2   1   0   0   1   1   0   1   1   1       312   1   0   2   1   2   0   1   0   0   1   1   1   0   0   0       313   1   0   2   1   2   1   1   0   0   1   1   1   0   0   1       314   1   0   2   1   2   2   1   0   0   1   1   1   0   1   0       315   1   0   2   2   0   0   1   0   0   1   1   1   0   1   1       316   1   0   2   2   0   1   1   0   0   1   1   1   1   0   0       317   1   0   2   2   0   2   1   0   0   1   1   1   1   0   1       318   1   0   2   2   1   0   1   0   0   1   1   1   1   1   0       319   1   0   2   2   1   1   1   0   0   1   1   1   1   1   1       320   1   0   2   2   1   2   1   0   1   0   0   0   0   0   0       321   1   0   2   2   2   0   1   0   1   0   0   0   0   0   1       322   1   0   2   2   2   1   1   0   1   0   0   0   0   1   0       323   1   0   2   2   2   2   1   0   1   0   0   0   0   1   1       324   1   1   0   0   0   0   1   0   1   0   0   0   1   0   0       325   1   1   0   0   0   1   1   0   1   0   0   0   1   0   1       326   1   1   0   0   0   2   1   0   1   0   0   0   1   1   0       327   1   1   0   0   1   0   1   0   1   0   0   0   1   1   1       328   1   1   0   0   1   1   1   0   1   0   0   1   0   0   0       329   1   1   0   0   1   2   1   0   1   0   0   1   0   0   1       330   1   1   0   0   2   0   1   0   1   0   0   1   0   1   0       331   1   1   0   0   2   1   1   0   1   0   0   1   0   1   1       332   1   1   0   0   2   2   1   0   1   0   0   1   1   0   0       333   1   1   0   1   0   0   1   0   1   0   0   1   1   0   1       334   1   1   0   1   0   1   1   0   1   0   0   1   1   1   0       335   1   1   0   1   0   2   1   0   1   0   0   1   1   1   1       336   1   1   0   1   1   0   1   0   1   0   1   0   0   0   0       337   1   1   0   1   1   1   1   0   1   0   1   0   0   0   1       338   1   1   0   1   1   2   1   0   1   0   1   0   0   1   0       339   1   1   0   1   2   0   1   0   1   0   1   0   0   1   1       340   1   1   0   1   2   1   1   0   1   0   1   0   1   0   0       341   1   1   0   1   2   2   1   0   1   0   1   0   1   0   1       342   1   1   0   2   0   0   1   0   1   0   1   0   1   1   0       343   1   1   0   2   0   1   1   0   1   0   1   0   1   1   1       344   1   1   0   2   0   2   1   0   1   0   1   1   0   0   0       345   1   1   0   2   1   0   1   0   1   0   1   1   0   0   1       346   1   1   0   2   1   1   1   0   1   0   1   1   0   1   0       347   1   1   0   2   1   2   1   0   1   0   1   1   0   1   1       348   1   1   0   2   2   0   1   0   1   0   1   1   1   0   0       349   1   1   0   2   2   1   1   0   1   0   1   1   1   0   1       350   1   1   0   2   2   2   1   0   1   0   1   1   1   1   0       351   1   1   1   0   0   0   1   0   1   0   1   1   1   1   1       352   1   1   1   0   0   1   1   0   1   1   0   0   0   0   0       353   1   1   1   0   0   2   1   0   1   1   0   0   0   0   1       354   1   1   1   0   1   0   1   0   1   1   0   0   0   1   0       355   1   1   1   0   1   1   1   0   1   1   0   0   0   1   1       356   1   1   1   0   1   2   1   0   1   1   0   0   1   0   0       357   1   1   1   0   2   0   1   0   1   1   0   0   1   0   1       358   1   1   1   0   2   1   1   0   1   1   0   0   1   1   0       359   1   1   1   0   2   2   1   0   1   1   0   0   1   1   1       360   1   1   1   1   0   0   1   0   1   1   0   1   0   0   0       361   1   1   1   1   0   1   1   0   1   1   0   1   0   0   1       362   1   1   1   1   0   2   1   0   1   1   0   1   0   1   0       363   1   1   1   1   1   0   1   0   1   1   0   1   0   1   1       364   1   1   1   1   1   1   1   0   1   1   0   1   1   0   0       365   1   1   1   1   1   2   1   0   1   1   0   1   1   0   1       366   1   1   1   1   2   0   1   0   1   1   0   1   1   1   0       367   1   1   1   1   2   1   1   0   1   1   0   1   1   1   1       368   1   1   1   1   2   2   1   0   1   1   1   0   0   0   0       369   1   1   1   2   0   0   1   0   1   1   1   0   0   0   1       370   1   1   1   2   0   1   1   0   1   1   1   0   0   1   0       371   1   1   1   2   0   2   1   0   1   1   1   0   0   1   1       372   1   1   1   2   1   0   1   0   1   1   1   0   1   0   0       373   1   1   1   2   1   1   1   0   1   1   1   0   1   0   1       374   1   1   1   2   1   2   1   0   1   1   1   0   1   1   0       375   1   1   1   2   2   0   1   0   1   1   1   0   1   1   1       376   1   1   1   2   2   1   1   0   1   1   1   1   0   0   0       377   1   1   1   2   2   2   1   0   1   1   1   1   0   0   1       378   1   1   2   0   0   0   1   0   1   1   1   1   0   1   0       379   1   1   2   0   0   1   1   0   1   1   1   1   0   1   1       380   1   1   2   0   0   2   1   0   1   1   1   1   1   0   0       381   1   1   2   0   1   0   1   0   1   1   1   1   1   0   1       382   1   1   2   0   1   1   1   0   1   1   1   1   1   1   0       383   1   1   2   0   1   2   1   0   1   1   1   1   1   1   1       384   1   1   2   0   2   0   1   1   0   0   0   0   0   0   0       385   1   1   2   0   2   1   1   1   0   0   0   0   0   0   1       386   1   1   2   0   2   2   1   1   0   0   0   0   0   1   0       387   1   1   2   1   0   0   1   1   0   0   0   0   0   1   1       388   1   1   2   1   0   1   1   1   0   0   0   0   1   0   0       389   1   1   2   1   0   2   1   1   0   0   0   0   1   0   1       390   1   1   2   1   1   0   1   1   0   0   0   0   1   1   0       391   1   1   2   1   1   1   1   1   0   0   0   0   1   1   1       392   1   1   2   1   1   2   1   1   0   0   0   1   0   0   0       393   1   1   2   1   2   0   1   1   0   0   0   1   0   0   1       394   1   1   2   1   2   1   1   1   0   0   0   1   0   1   0       395   1   1   2   1   2   2   1   1   0   0   0   1   0   1   1       396   1   1   2   2   0   0   1   1   0   0   0   1   1   0   0       397   1   1   2   2   0   1   1   1   0   0   0   1   1   0   1       398   1   1   2   2   0   2   1   1   0   0   0   1   1   1   0       399   1   1   2   2   1   0   1   1   0   0   0   1   1   1   1       400   1   1   2   2   1   1   1   1   0   0   1   0   0   0   0       401   1   1   2   2   1   2   1   1   0   0   1   0   0   0   1       402   1   1   2   2   2   0   1   1   0   0   1   0   0   1   0       403   1   1   2   2   2   1   1   1   0   0   1   0   0   1   1       404   1   1   2   2   2   2   1   1   0   0   1   0   1   0   0       405   1   2   0   0   0   0   1   1   0   0   1   0   1   0   1       406   1   2   0   0   0   1   1   1   0   0   1   0   1   1   0       407   1   2   0   0   0   2   1   1   0   0   1   0   1   1   1       408   1   2   0   0   1   0   1   1   0   0   1   1   0   0   0       409   1   2   0   0   1   1   1   1   0   0   1   1   0   0   1       410   1   2   0   0   1   2   1   1   0   0   1   1   0   1   0       411   1   2   0   0   2   0   1   1   0   0   1   1   0   1   1       412   1   2   0   0   2   1   1   1   0   0   1   1   1   0   0       413   1   2   0   0   2   2   1   1   0   0   1   1   1   0   1       414   1   2   0   1   0   0   1   1   0   0   1   1   1   1   0       415   1   2   0   1   0   1   1   1   0   0   1   1   1   1   1       416   1   2   0   1   0   2   1   1   0   1   0   0   0   0   0       417   1   2   0   1   1   0   1   1   0   1   0   0   0   0   1       418   1   2   0   1   1   1   1   1   0   1   0   0   0   1   0       419   1   2   0   1   1   2   1   1   0   1   0   0   0   1   1       420   1   2   0   1   2   0   1   1   0   1   0   0   1   0   0       421   1   2   0   1   2   1   1   1   0   1   0   0   1   0   1       422   1   2   0   1   2   2   1   1   0   1   0   0   1   1   0       423   1   2   0   2   0   0   1   1   0   1   0   0   1   1   1       424   1   2   0   2   0   1   1   1   0   1   0   1   0   0   0       425   1   2   0   2   0   2   1   1   0   1   0   1   0   0   1       426   1   2   0   2   1   0   1   1   0   1   0   1   0   1   0       427   1   2   0   2   1   1   1   1   0   1   0   1   0   1   1       428   1   2   0   2   1   2   1   1   0   1   0   1   1   0   0       429   1   2   0   2   2   0   1   1   0   1   0   1   1   0   1       430   1   2   0   2   2   1   1   1   0   1   0   1   1   1   0       431   1   2   0   2   2   2   1   1   0   1   0   1   1   1   1       432   1   2   1   0   0   0   1   1   0   1   1   0   0   0   0       433   1   2   1   0   0   1   1   1   0   1   1   0   0   0   1       434   1   2   1   0   0   2   1   1   0   1   1   0   0   1   0       435   1   2   1   0   1   0   1   1   0   1   1   0   0   1   1       436   1   2   1   0   1   1   1   1   0   1   1   0   1   0   0       437   1   2   1   0   1   2   1   1   0   1   1   0   1   0   1       438   1   2   1   0   2   0   1   1   0   1   1   0   1   1   0       439   1   2   1   0   2   1   1   1   0   1   1   0   1   1   1       440   1   2   1   0   2   2   1   1   0   1   1   1   0   0   0       441   1   2   1   1   0   0   1   1   0   1   1   1   0   0   1       442   1   2   1   1   0   1   1   1   0   1   1   1   0   1   0       443   1   2   1   1   0   2   1   1   0   1   1   1   0   1   1       444   1   2   1   1   1   0   1   1   0   1   1   1   1   0   0       445   1   2   1   1   1   1   1   1   0   1   1   1   1   0   1       446   1   2   1   1   1   2   1   1   0   1   1   1   1   1   0       447   1   2   1   1   2   0   1   1   0   1   1   1   1   1   1       448   1   2   1   1   2   1   1   1   1   0   0   0   0   0   0       449   1   2   1   1   2   2   1   1   1   0   0   0   0   0   1       450   1   2   1   2   0   0   1   1   1   0   0   0   0   1   0       451   1   2   1   2   0   1   1   1   1   0   0   0   0   1   1       452   1   2   1   2   0   2   1   1   1   0   0   0   1   0   0       453   1   2   1   2   1   0   1   1   1   0   0   0   1   0   1       454   1   2   1   2   1   1   1   1   1   0   0   0   1   1   0       455   1   2   1   2   1   2   1   1   1   0   0   0   1   1   1       456   1   2   1   2   2   0   1   1   1   0   0   1   0   0   0       457   1   2   1   2   2   1   1   1   1   0   0   1   0   0   1       458   1   2   1   2   2   2   1   1   1   0   0   1   0   1   0       459   1   2   2   0   0   0   1   1   1   0   0   1   0   1   1       460   1   2   2   0   0   1   1   1   1   0   0   1   1   0   0       461   1   2   2   0   0   2   1   1   1   0   0   1   1   0   1       462   1   2   2   0   1   0   1   1   1   0   0   1   1   1   0       463   1   2   2   0   1   1   1   1   1   0   0   1   1   1   1       464   1   2   2   0   1   2   1   1   1   0   1   0   0   0   0       465   1   2   2   0   2   0   1   1   1   0   1   0   0   0   1       466   1   2   2   0   2   1   1   1   1   0   1   0   0   1   0       467   1   2   2   0   2   2   1   1   1   0   1   0   0   1   1       468   1   2   2   1   0   0   1   1   1   0   1   0   1   0   0       469   1   2   2   1   0   1   1   1   1   0   1   0   1   0   1       470   1   2   2   1   0   2   1   1   1   0   1   0   1   1   0       471   1   2   2   1   1   0   1   1   1   0   1   0   1   1   1       472   1   2   2   1   1   1   1   1   1   0   1   1   0   0   0       473   1   2   2   1   1   2   1   1   1   0   1   1   0   0   1       474   1   2   2   1   2   0   1   1   1   0   1   1   0   1   0       475   1   2   2   1   2   1   1   1   1   0   1   1   0   1   1       476   1   2   2   1   2   2   1   1   1   0   1   1   1   0   0       477   1   2   2   2   0   0   1   1   1   0   1   1   1   0   1       478   1   2   2   2   0   1   1   1   1   0   1   1   1   1   0       479   1   2   2   2   0   2   1   1   1   0   1   1   1   1   1       480   1   2   2   2   1   0   1   1   1   1   0   0   0   0   0       481   1   2   2   2   1   1   1   1   1   1   0   0   0   0   1       482   1   2   2   2   1   2   1   1   1   1   0   0   0   1   0       483   1   2   2   2   2   0   1   1   1   1   0   0   0   1   1       484   1   2   2   2   2   1   1   1   1   1   0   0   1   0   0       485   1   2   2   2   2   2   1   1   1   1   0   0   1   0   1       486   2   0   0   0   0   0   1   1   1   1   0   0   1   1   0       487   2   0   0   0   0   1   1   1   1   1   0   0   1   1   1       488   2   0   0   0   0   2   1   1   1   1   0   1   0   0   0       489   2   0   0   0   1   0   1   1   1   1   0   1   0   0   1       490   2   0   0   0   1   1   1   1   1   1   0   1   0   1   0       491   2   0   0   0   1   2   1   1   1   1   0   1   0   1   1       492   2   0   0   0   2   0   1   1   1   1   0   1   1   0   0       493   2   0   0   0   2   1   1   1   1   1   0   1   1   0   1       494   2   0   0   0   2   2   1   1   1   1   0   1   1   1   0       495   2   0   0   1   0   0   1   1   1   1   0   1   1   1   1       496   2   0   0   1   0   1   1   1   1   1   1   0   0   0   0       497   2   0   0   1   0   2   1   1   1   1   1   0   0   0   1       498   2   0   0   1   1   0   1   1   1   1   1   0   0   1   0       499   2   0   0   1   1   1   1   1   1   1   1   0   0   1   1       500   2   0   0   1   1   2   1   1   1   1   1   0   1   0   0       501   2   0   0   1   2   0   1   1   1   1   1   0   1   0   1       502   2   0   0   1   2   1   1   1   1   1   1   0   1   1   0       503   2   0   0   1   2   2   1   1   1   1   1   0   1   1   1       504   2   0   0   2   0   0   1   1   1   1   1   1   0   0   0       505   2   0   0   2   0   1   1   1   1   1   1   1   0   0   1       506   2   0   0   2   0   2   1   1   1   1   1   1   0   1   0       507   2   0   0   2   1   0   1   1   1   1   1   1   0   1   1       508   2   0   0   2   1   1   1   1   1   1   1   1   1   0   0       509   2   0   0   2   1   2   1   1   1   1   1   1   1   0   1       510   2   0   0   2   2   0   1   1   1   1   1   1   1   1   0       511   2   0   0   2   2   1   1   1   1   1   1   1   1   1   1       512   2   0   0   2   2   2   X   X   X   X   X   X   X   X   X       513   2   0   1   0   0   0   X   X   X   X   X   X   X   X   X       514   2   0   1   0   0   1   X   X   X   X   X   X   X   X   X       515   2   0   1   0   0   2   X   X   X   X   X   X   X   X   X       516   2   0   1   0   1   0   X   X   X   X   X   X   X   X   X       517   2   0   1   0   1   1   X   X   X   X   X   X   X   X   X       518   2   0   1   0   1   2   X   X   X   X   X   X   X   X   X       519   2   0   1   0   2   0   X   X   X   X   X   X   X   X   X       520   2   0   1   0   2   1   X   X   X   X   X   X   X   X   X       521   2   0   1   0   2   2   X   X   X   X   X   X   X   X   X       522   2   0   1   1   0   0   X   X   X   X   X   X   X   X   X       523   2   0   1   1   0   1   X   X   X   X   X   X   X   X   X       524   2   0   1   1   0   2   X   X   X   X   X   X   X   X   X       525   2   0   1   1   1   0   X   X   X   X   X   X   X   X   X       526   2   0   1   1   1   1   X   X   X   X   X   X   X   X   X       527   2   0   1   1   1   2   X   X   X   X   X   X   X   X   X       528   2   0   1   1   2   0   X   X   X   X   X   X   X   X   X       529   2   0   1   1   2   1   X   X   X   X   X   X   X   X   X       530   2   0   1   1   2   2   X   X   X   X   X   X   X   X   X       531   2   0   1   2   0   0   X   X   X   X   X   X   X   X   X       532   2   0   1   2   0   1   X   X   X   X   X   X   X   X   X       533   2   0   1   2   0   2   X   X   X   X   X   X   X   X   X       534   2   0   1   2   1   0   X   X   X   X   X   X   X   X   X       535   2   0   1   2   1   1   X   X   X   X   X   X   X   X   X       536   2   0   1   2   1   2   X   X   X   X   X   X   X   X   X       537   2   0   1   2   2   0   X   X   X   X   X   X   X   X   X       538   2   0   1   2   2   1   X   X   X   X   X   X   X   X   X       539   2   0   1   2   2   2   X   X   X   X   X   X   X   X   X       540   2   0   2   0   0   0   X   X   X   X   X   X   X   X   X       541   2   0   2   0   0   1   X   X   X   X   X   X   X   X   X       542   2   0   2   0   0   2   X   X   X   X   X   X   X   X   X       543   2   0   2   0   1   0   X   X   X   X   X   X   X   X   X       544   2   0   2   0   1   1   X   X   X   X   X   X   X   X   X       545   2   0   2   0   1   2   X   X   X   X   X   X   X   X   X       546   2   0   2   0   2   0   X   X   X   X   X   X   X   X   X       547   2   0   2   0   2   1   X   X   X   X   X   X   X   X   X       548   2   0   2   0   2   2   X   X   X   X   X   X   X   X   X       549   2   0   2   1   0   0   X   X   X   X   X   X   X   X   X       550   2   0   2   1   0   1   X   X   X   X   X   X   X   X   X       551   2   0   2   1   0   2   X   X   X   X   X   X   X   X   X       552   2   0   2   1   1   0   X   X   X   X   X   X   X   X   X       553   2   0   2   1   1   1   X   X   X   X   X   X   X   X   X       554   2   0   2   1   1   2   X   X   X   X   X   X   X   X   X       555   2   0   2   1   2   0   X   X   X   X   X   X   X   X   X       556   2   0   2   1   2   1   X   X   X   X   X   X   X   X   X       557   2   0   2   1   2   2   X   X   X   X   X   X   X   X   X       558   2   0   2   2   0   0   X   X   X   X   X   X   X   X   X       559   2   0   2   2   0   1   X   X   X   X   X   X   X   X   X       560   2   0   2   2   0   2   X   X   X   X   X   X   X   X   X       561   2   0   2   2   1   0   X   X   X   X   X   X   X   X   X       562   2   0   2   2   1   1   X   X   X   X   X   X   X   X   X       563   2   0   2   2   1   2   X   X   X   X   X   X   X   X   X       564   2   0   2   2   2   0   X   X   X   X   X   X   X   X   X       565   2   0   2   2   2   1   X   X   X   X   X   X   X   X   X       566   2   0   2   2   2   2   X   X   X   X   X   X   X   X   X       567   2   1   0   0   0   0   X   X   X   X   X   X   X   X   X       568   2   1   0   0   0   1   X   X   X   X   X   X   X   X   X       569   2   1   0   0   0   2   X   X   X   X   X   X   X   X   X       570   2   1   0   0   1   0   X   X   X   X   X   X   X   X   X       571   2   1   0   0   1   1   X   X   X   X   X   X   X   X   X       572   2   1   0   0   1   2   X   X   X   X   X   X   X   X   X       573   2   1   0   0   2   0   X   X   X   X   X   X   X   X   X       574   2   1   0   0   2   1   X   X   X   X   X   X   X   X   X       575   2   1   0   0   2   2   X   X   X   X   X   X   X   X   X       576   2   1   0   1   0   0   X   X   X   X   X   X   X   X   X       577   2   1   0   1   0   1   X   X   X   X   X   X   X   X   X       578   2   1   0   1   0   2   X   X   X   X   X   X   X   X   X       579   2   1   0   1   1   0   X   X   X   X   X   X   X   X   X       580   2   1   0   1   1   1   X   X   X   X   X   X   X   X   X       581   2   1   0   1   1   2   X   X   X   X   X   X   X   X   X       582   2   1   0   1   2   0   X   X   X   X   X   X   X   X   X       583   2   1   0   1   2   1   X   X   X   X   X   X   X   X   X       584   2   1   0   1   2   2   X   X   X   X   X   X   X   X   X       585   2   1   0   2   0   0   X   X   X   X   X   X   X   X   X       586   2   1   0   2   0   1   X   X   X   X   X   X   X   X   X       587   2   1   0   2   0   2   X   X   X   X   X   X   X   X   X       588   2   1   0   2   1   0   X   X   X   X   X   X   X   X   X       589   2   1   0   2   1   1   X   X   X   X   X   X   X   X   X       590   2   1   0   2   1   2   X   X   X   X   X   X   X   X   X       591   2   1   0   2   2   0   X   X   X   X   X   X   X   X   X       592   2   1   0   2   2   1   X   X   X   X   X   X   X   X   X       593   2   1   0   2   2   2   X   X   X   X   X   X   X   X   X       594   2   1   1   0   0   0   X   X   X   X   X   X   X   X   X       595   2   1   1   0   0   1   X   X   X   X   X   X   X   X   X       596   2   1   1   0   0   2   X   X   X   X   X   X   X   X   X       597   2   1   1   0   1   0   X   X   X   X   X   X   X   X   X       598   2   1   1   0   1   1   X   X   X   X   X   X   X   X   X       599   2   1   1   0   1   2   X   X   X   X   X   X   X   X   X       600   2   1   1   0   2   0   X   X   X   X   X   X   X   X   X       601   2   1   1   0   2   1   X   X   X   X   X   X   X   X   X       602   2   1   1   0   2   2   X   X   X   X   X   X   X   X   X       603   2   1   1   1   0   0   X   X   X   X   X   X   X   X   X       604   2   1   1   1   0   1   X   X   X   X   X   X   X   X   X       605   2   1   1   1   0   2   X   X   X   X   X   X   X   X   X       606   2   1   1   1   1   0   X   X   X   X   X   X   X   X   X       607   2   1   1   1   1   1   X   X   X   X   X   X   X   X   X       608   2   1   1   1   1   2   X   X   X   X   X   X   X   X   X       609   2   1   1   1   2   0   X   X   X   X   X   X   X   X   X       610   2   1   1   1   2   1   X   X   X   X   X   X   X   X   X       611   2   1   1   1   2   2   X   X   X   X   X   X   X   X   X       612   2   1   1   2   0   0   X   X   X   X   X   X   X   X   X       613   2   1   1   2   0   1   X   X   X   X   X   X   X   X   X       614   2   1   1   2   0   2   X   X   X   X   X   X   X   X   X       615   2   1   1   2   1   0   X   X   X   X   X   X   X   X   X       616   2   1   1   2   1   1   X   X   X   X   X   X   X   X   X       617   2   1   1   2   1   2   X   X   X   X   X   X   X   X   X       618   2   1   1   2   2   0   X   X   X   X   X   X   X   X   X       619   2   1   1   2   2   1   X   X   X   X   X   X   X   X   X       620   2   1   1   2   2   2   X   X   X   X   X   X   X   X   X       621   2   1   2   0   0   0   X   X   X   X   X   X   X   X   X       622   2   1   2   0   0   1   X   X   X   X   X   X   X   X   X       623   2   1   2   0   0   2   X   X   X   X   X   X   X   X   X       624   2   1   2   0   1   0   X   X   X   X   X   X   X   X   X       625   2   1   2   0   1   1   X   X   X   X   X   X   X   X   X       626   2   1   2   0   1   2   X   X   X   X   X   X   X   X   X       627   2   1   2   0   2   0   X   X   X   X   X   X   X   X   X       628   2   1   2   0   2   1   X   X   X   X   X   X   X   X   X       629   2   1   2   0   2   2   X   X   X   X   X   X   X   X   X       630   2   1   2   1   0   0   X   X   X   X   X   X   X   X   X       631   2   1   2   1   0   1   X   X   X   X   X   X   X   X   X       632   2   1   2   1   0   2   X   X   X   X   X   X   X   X   X       633   2   1   2   1   1   0   X   X   X   X   X   X   X   X   X       634   2   1   2   1   1   1   X   X   X   X   X   X   X   X   X       635   2   1   2   1   1   2   X   X   X   X   X   X   X   X   X       636   2   1   2   1   2   0   X   X   X   X   X   X   X   X   X       637   2   1   2   1   2   1   X   X   X   X   X   X   X   X   X       638   2   1   2   1   2   2   X   X   X   X   X   X   X   X   X       639   2   1   2   2   0   0   X   X   X   X   X   X   X   X   X       640   2   1   2   2   0   1   X   X   X   X   X   X   X   X   X       641   2   1   2   2   0   2   X   X   X   X   X   X   X   X   X       642   2   1   2   2   1   0   X   X   X   X   X   X   X   X   X       643   2   1   2   2   1   1   X   X   X   X   X   X   X   X   X       644   2   1   2   2   1   2   X   X   X   X   X   X   X   X   X       645   2   1   2   2   2   0   X   X   X   X   X   X   X   X   X       646   2   1   2   2   2   1   X   X   X   X   X   X   X   X   X       647   2   1   2   2   2   2   X   X   X   X   X   X   X   X   X       648   2   2   0   0   0   0   X   X   X   X   X   X   X   X   X       649   2   2   0   0   0   1   X   X   X   X   X   X   X   X   X       650   2   2   0   0   0   2   X   X   X   X   X   X   X   X   X       651   2   2   0   0   1   0   X   X   X   X   X   X   X   X   X       652   2   2   0   0   1   1   X   X   X   X   X   X   X   X   X       653   2   2   0   0   1   2   X   X   X   X   X   X   X   X   X       654   2   2   0   0   2   0   X   X   X   X   X   X   X   X   X       655   2   2   0   0   2   1   X   X   X   X   X   X   X   X   X       656   2   2   0   0   2   2   X   X   X   X   X   X   X   X   X       657   2   2   0   1   0   0   X   X   X   X   X   X   X   X   X       658   2   2   0   1   0   1   X   X   X   X   X   X   X   X   X       659   2   2   0   1   0   2   X   X   X   X   X   X   X   X   X       660   2   2   0   1   1   0   X   X   X   X   X   X   X   X   X       661   2   2   0   1   1   1   X   X   X   X   X   X   X   X   X       662   2   2   0   1   1   2   X   X   X   X   X   X   X   X   X       663   2   2   0   1   2   0   X   X   X   X   X   X   X   X   X       664   2   2   0   1   2   1   X   X   X   X   X   X   X   X   X       665   2   2   0   1   2   2   X   X   X   X   X   X   X   X   X       666   2   2   0   2   0   0   X   X   X   X   X   X   X   X   X       667   2   2   0   2   0   1   X   X   X   X   X   X   X   X   X       668   2   2   0   2   0   2   X   X   X   X   X   X   X   X   X       669   2   2   0   2   1   0   X   X   X   X   X   X   X   X   X       670   2   2   0   2   1   1   X   X   X   X   X   X   X   X   X       671   2   2   0   2   1   2   X   X   X   X   X   X   X   X   X       672   2   2   0   2   2   0   X   X   X   X   X   X   X   X   X       673   2   2   0   2   2   1   X   X   X   X   X   X   X   X   X       674   2   2   0   2   2   2   X   X   X   X   X   X   X   X   X       675   2   2   1   0   0   0   X   X   X   X   X   X   X   X   X       676   2   2   1   0   0   1   X   X   X   X   X   X   X   X   X       677   2   2   1   0   0   2   X   X   X   X   X   X   X   X   X       678   2   2   1   0   1   0   X   X   X   X   X   X   X   X   X       679   2   2   1   0   1   1   X   X   X   X   X   X   X   X   X       680   2   2   1   0   1   2   X   X   X   X   X   X   X   X   X       681   2   2   1   0   2   0   X   X   X   X   X   X   X   X   X       682   2   2   1   0   2   1   X   X   X   X   X   X   X   X   X       683   2   2   1   0   2   2   X   X   X   X   X   X   X   X   X       684   2   2   1   1   0   0   X   X   X   X   X   X   X   X   X       685   2   2   1   1   0   1   X   X   X   X   X   X   X   X   X       686   2   2   1   1   0   2   X   X   X   X   X   X   X   X   X       687   2   2   1   1   1   0   X   X   X   X   X   X   X   X   X       688   2   2   1   1   1   1   X   X   X   X   X   X   X   X   X       689   2   2   1   1   1   2   X   X   X   X   X   X   X   X   X       690   2   2   1   1   2   0   X   X   X   X   X   X   X   X   X       691   2   2   1   1   2   1   X   X   X   X   X   X   X   X   X       692   2   2   1   1   2   2   X   X   X   X   X   X   X   X   X       693   2   2   1   2   0   0   X   X   X   X   X   X   X   X   X       694   2   2   1   2   0   1   X   X   X   X   X   X   X   X   X       695   2   2   1   2   0   2   X   X   X   X   X   X   X   X   X       696   2   2   1   2   1   0   X   X   X   X   X   X   X   X   X       697   2   2   1   2   1   1   X   X   X   X   X   X   X   X   X       698   2   2   1   2   1   2   X   X   X   X   X   X   X   X   X       699   2   2   1   2   2   0   X   X   X   X   X   X   X   X   X       700   2   2   1   2   2   1   X   X   X   X   X   X   X   X   X       701   2   2   1   2   2   2   X   X   X   X   X   X   X   X   X       702   2   2   2   0   0   0   X   X   X   X   X   X   X   X   X       703   2   2   2   0   0   1   X   X   X   X   X   X   X   X   X       704   2   2   2   0   0   2   X   X   X   X   X   X   X   X   X       705   2   2   2   0   1   0   X   X   X   X   X   X   X   X   X       706   2   2   2   0   1   1   X   X   X   X   X   X   X   X   X       707   2   2   2   0   1   2   X   X   X   X   X   X   X   X   X       708   2   2   2   0   2   0   X   X   X   X   X   X   X   X   X       709   2   2   2   0   2   1   X   X   X   X   X   X   X   X   X       710   2   2   2   0   2   2   X   X   X   X   X   X   X   X   X       711   2   2   2   1   0   0   X   X   X   X   X   X   X   X   X       712   2   2   2   1   0   1   X   X   X   X   X   X   X   X   X       713   2   2   2   1   0   2   X   X   X   X   X   X   X   X   X       714   2   2   2   1   1   0   X   X   X   X   X   X   X   X   X       715   2   2   2   1   1   1   X   X   X   X   X   X   X   X   X       716   2   2   2   1   1   2   X   X   X   X   X   X   X   X   X       717   2   2   2   1   2   0   X   X   X   X   X   X   X   X   X       718   2   2   2   1   2   1   X   X   X   X   X   X   X   X   X       719   2   2   2   1   2   2   X   X   X   X   X   X   X   X   X       720   2   2   2   2   0   0   X   X   X   X   X   X   X   X   X       721   2   2   2   2   0   1   X   X   X   X   X   X   X   X   X       722   2   2   2   2   0   2   X   X   X   X   X   X   X   X   X       723   2   2   2   2   1   0   X   X   X   X   X   X   X   X   X       724   2   2   2   2   1   1   X   X   X   X   X   X   X   X   X       725   2   2   2   2   1   2   X   X   X   X   X   X   X   X   X       726   2   2   2   2   2   0   X   X   X   X   X   X   X   X   X       727   2   2   2   2   2   1   X   X   X   X   X   X   X   X   X       728   2   2   2   2   2   2   X   X   X   X   X   X   X   X   X                  
 
         [0041]    Although this invention has been described with reference to particular embodiments, the invention is not limited to these described embodiments. Rather, the invention is limited only by the appended claims, which include within their scope all equivalent devices or methods that operate according to the principles of the invention as described herein.