TopCoder Statistics - Problem Statement

Problem Statement

NOTE: This problem statement contains images that may not display properly if viewed outside of the applet.

An N-segment display is a set of N on/off display elements (segments), positioned in such a way that certain arrangements of elements being on and off lead to symbols being represented in the display. Common examples of these types of display are 7-segment displays, which can display arabic numeral digits and 14- or 16-segment displays which can display alphanumeric symbols. See the diagram below for an example of a 7-segment display and its representation of the digits from 0 to 9.

You suspect that certain segments in a particular N-segment display are broken and it is therefore not displaying symbols properly. If a segment is broken, then it remains permanently in an off state, even if the symbol being displayed requires that it turn on. Otherwise, if the segment is working, it will be on when the symbol being displayed requires it to be on and off otherwise. You want to know which segments are broken, so you observe the display for a period of time and note the patterns it displays. The display is set up to only ever show symbols from a known set, but you don't know what symbols from that set might be displayed or in what order they might be appear. Your task is to identify which segments of the display are working and which of them are broken.

You are given the set of symbols that the display shows as a String[], where each element describes a single symbol. Character j in element i will be '1' if segment j of the display should be on when symbol i is being displayed and '0' if it should be off. You are given the patterns that you observed being displayed in a String[] patterns, where each element describes a single pattern that you observe in the display. Character j of element i is '1' if segment j of the display is on for pattern i and '0' if it is off. Return a String containing exactly N elements. Character j of the return should be 'Y' if segment j of the display is definitely working, 'N' if segment j is definitely broken and '?' if there is no way of determining whether or not it is broken from the given data. If there is no way of interpreting the data consistent with some subset of the segments being broken, return "INCONSISTENT" (quotes for clarity) instead.

Definition

Class:: NSegmentDisplay
Method:: brokenSegments
Parameters:: String[], String[]
Returns:: String
Method signature:: String brokenSegments(String[] symbols, String[] patterns)
(be sure your method is public)

Notes

A segment can be considered definitely to be working, if no configuration exists, consistent with the described behavior, in which it is broken.
A segment can be considered definitely to be broken, if no configuration exists, consistent with the described behavior, in which it is working.
If neither of the above conditions is true for a segment, there is no way of being sure whether it is broken or not.

Constraints

patterns and symbols will each contain between 1 and 50 elements, inclusive.
Each element of patterns and symbols will contain between 1 and 50 characters, inclusive.
Each element of patterns and symbols will contain the same number of characters.
Each character in patterns and symbols will be '1' (one) or '0' (zero).

Examples

{"1011111","0000011","1110110","1110011","0101011" ,"1111001","1111101","1000011","1111111","1111011"}

{"1011111"}

Returns: "Y?YYYYY"

This test case represents the 7-segment display shown in the problem statement. The display shows only the numeric symbols given in the statement. The only symbol observed in the display is This could be either '0' or '8', so there is no way of telling whether segment 1 is broken or not.
{"1011111","0000011","1110110","1110011","0101011" ,"1111001","1111101","1000011","1111111","1111011"}

{"0111111"}

Returns: "NYYYYYY"

Now the symbol being shown is This can only be '8', so segment 0 must be broken.
{"1011111","0000011","1110110","1110011","0101011" ,"1111001","1111101","1000011","1111111","1111011"}

{"1000000","0010000"}

Returns: "INCONSISTENT"

There is no way that the observed symbols can be consistent with the set that the display can show.
{"1011111","0000011","1110110","1110011","0101011" ,"1111001","1111101","1000011","1111111","1111011"}

{"0010110","0010010","0010000"}

Returns: "NNYNYYN"

We can deduce that segments 0, 1, 3 and 6 are broken.
{"01111001010","10000001010","00011101110","10110011000","10101000000"}

{"00001100100","00001100100","10101000000","00001100100","10101000000"}

Returns: "Y?YNYY?NYN?"
{"01101001000","00001111110","11010100011","01100111001","00110000111","10001111010","00010111000","11110011011","00100111110","00010010111","10010001011","01111001001","11110101001","11111111011","00101110100","01101111111","01010100001"}

{"00101001001","10100001001","10001011010","00001011010","10000001011"}

Returns: "YNYNYNYYNYY"
{"0101101100100","0001011100101","1000100001000","1100010100001","0000001101001","1110000101001","0111000110010","0111111111110","1110001100000"}

{"0000010000001","0000100001000","0000010000001","0000000001001","0000010000001","0000000000000"}

Returns: "NNN?YY?N?Y??Y"
{"1100110101","1011101110","0000000111","0000010101","1011001000","0010100111","0001101100"}

{"0000000111","0000010101","0100110101","0000101110","0000001000","0000101110","0100110101"}

Returns: "NYNNYYYYYY"
{"110000111001","100000101000","000001010000" ,"101100010011","111111111101"}

{"010000000000","010000000000","000000000000" ,"000000000000","000000000000"}

Returns: "NY????NNN??N"
{"01100101101110001101","01100010011010011111","00101100001011000001","01110000010100100111","11010110100011000110"}

{"00100000000010000001","00100000000010001001","00100000000010000001","10000000000010000000","00100000010000000001","10000000000010000000","00100000010000000001","00100000000010001001","00100000010010011001","00100000000010001001","10000000000010000000","00100000010010011001","00100000000010001001","10000000000010000000","00100000010000000001"}

Returns: "YNYNNNNNNYNNYNNYYNNY"
{"00001101010000011001","11110101101110001100","01000001100010000110","01111110100010100010","11100101100000011010","11001110110101011101","01010000101010001011","00110010011101001100","10000000010001011100","11001001001100010101"}

{"00000000000001001000","01001100000001001000","01000001000000000010","00110000001001001000","00001101000000001000","01010000001000001010","00001101000000001000","01111100000000100010","00000000000001001000","00110000001001001000","01110101001000001000","01110101001000001000","00110000001001001000","00000000000001001000","00110000001001001000"}

Returns: "NYYYYYNYNNYNNYYNYNYN"
{"11011101101000010011","11111111011000110110","00011010000011100111","10010110000100100111","11010010010101001011","01111011001001010000"}

{"11000010000001000000","11001000000000010000","00001010000011100000","01001010000001010000","01001010000001010000","01001010000001010000","11000010000001000000","11001000000000010000","11001010000000110000","11001000000000010000","10000010000000100000","11000010000001000000","11001010000000110000","00001010000011100000","00001010000011100000"}

Returns: "YYNNYNYNNNNNYYYYNNNN"
{"00100111110111001011","01000110001111110010","01010010001011100010","11000011000000110000","01110100111001000000","01101010011100101110","10101010101111110001"}

{"00000000101101110001","00000000001001100010","00000000101001000000","00000000001100100010","00000001000000110000","00000001000000110000","00000001000000110000","00000000001100100010","00000000001101110010","00000000001100100010","00000001100101000011","00000000001101110010","00000000101001000000","00000000101001000000","00000000001101110010"}

Returns: "NNNNNNNYYNYYNYYYNNYY"
{"11101001000010001110","00110001010011010010","10000111010000011011","01011010000010001110","10011101101101101111","01001010100000100111","00000000101100111100","10110111100010010111","00100001011100111000","11010111111000001000"}

{"01000010100000100010","00110000010010010010","10010100100100101010","11010110110000001000","10010100100100101010","01000010100000100010","10110110100010010010","11010110110000001000","10000110010000011010","01010010000010001010","11100000000010001010","10010100100100101010","01000010100000100010","00110000010010010010","10110110100010010010"}

Returns: "YYYYNYYNYYNYYNYYYNYN"
{"11000110000001110011","01111001011101011010","10001101011010100111","00100100101110110001","00101100100100101001","01001111101101001110","00101110000110011111","11110110110101100001","11001001110011110111"}

{"00110000010100000000","00110100110100100001","00110000010100000000","00000100100100000100","00000100010010100101","00000100010010100101","00000000110010100101","00000000110010100101","00100100000110000101","00100100100100100001"}

Returns: "NNYYNYNNYYNYYNYNNYNY"
{"11101101111101000010","01110111100101110000","00010001010011110001","01111111111001111010","11011110111001110010","10001111100110100110","01111011101001110000"}

{"01101000110000011000","01101000100000010000","01001000110000010000","01101000110100000000","01001000110000010000","01100000100100010000","01100000100100010000","00001000100100000100","00000000010000010001","01001000110000010000"}

Returns: "NYYNYNNNYYNYNNNYYYNY"
{"00000000001000000010","01010000001011101110" ,"01010101110110011010","00111001111001000100" ,"10010111010110110000","11011011001000110001"}

{"00011000010000000000","10010110010000100000" ,"00010100010000001000","00010100010000001000" ,"00010000000000101000","00000000000000000000" ,"00010100010000001000","00011000010000000000" ,"00011000010000000000","00000000000000000000"}

Returns: "YNNYYYYNNYNNNNYNYNN?"
{"10011001010110010011","00101100110101111101","01000100011101010101","01100011111010110000","00111000011111001101","00001011000110000011","00101110011110000100","01101000111000011110","11100101111111100100"}

{"01000000001000010110","00010000001011000100","00000001000010000010","01000001001010110000","00000000001010000100","00010001000010010010","01000000001000010110","01000001001010110000","01000000001000010110","00000001000010000010"}

Returns: "NYNYNNNYNNYNYYYYNYYN"
{"01000101011100110101","10111010110100111001","01011000001000001111","00001010000010101010","01000000011101000000","01000111101100110110"}

{"00000000001100010100","00010000001000001101","00010000001000001101","00000000001101000000","00010000001000001101","00000000000010001000","00000000000010001000","00000000001100010101","10010000000100011001","00000000001101000000"}

Returns: "YNNYNNNNNNYYYYNYYYNY"
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Returns: "NNYNNYYYNNNYNYYNNN??????????????NNYNNYYYNNNYNYYNNN"
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Returns: "NNYNYNYNYYNYYYYNNY??????????????NNYNYNYNYYNYYYYNNY"
{"11000110001100001000000000000000110001100011000010","01101101100011010000000000000000011011011000110100","10010100001100000000000000000000100101000011000000","10000100111110110100000000000000100001001111101101","01010000001100011100000000000000010100000011000111","11001100010110001000000000000000110011000101100010","10110010100111010000000000000000101100101001110100","10101111110011101100000000000000101011111100111011","01101101010011111100000000000000011011010100111111","11000011010011001000000000000000110000110100110010","01001111011101001100000000000000010011110111010011","11101100001101100000000000000000111011000011011000","11010000011001111000000000000000110100000110011110","00100100010111011000000000000000001001000101110110","00101011101101100000000000000000001010111011011000","11011110010111111100000000000000110111100101111111","00111010100111001100000000000000001110101001110011","10100010010100010000000000000000101000100101000100","01111010110101111100000000000000011110101101011111","01010001110101100000000000000000010100011101011000","01110101110101011000000000000000011101011101010110","11100010011000100100000000000000111000100110001001","00110101111101010000000000000000001101011111010100","00111010001011010100000000000000001110100010110101","11001101101001101000000000000000110011011010011010","10011110000100111100000000000000100111100001001111","01010001110011011000000000000000010100011100110110","01101000000000101100000000000000011010000000001011","11110011111011010000000000000000111100111110110100","01011010000010100100000000000000010110100000101001","10001110011111110000000000000000100011100111111100","01001000011111101000000000000000010010000111111010","11101000000110010000000000000000111010000001100100","11011001000011111100000000000000110110010000111111","00001001001000011100000000000000000010010010000111","11101011111101001000000000000000111010111111010010","11010010000001101000000000000000110100100000011010","01011000101111001100000000000000010110001011110011","00000011001000111000000000000000000000110010001110","11011000111011111100000000000000110110001110111111","01000111110100100000000000000000010001111101001000","01100111000111011100000000000000011001110001110111","01110001011001011100000000000000011100010110010111","00010011110001001100000000000000000100111100010011","10111111101011011000000000000000101111111010110110","10000010001000001000000000000000100000100010000010","00101100000110010000000000000000001011000001100100","00101111100000100100000000000000001011111000001001","10001110111010010100000000000000100011101110100101","11101001010100101000000000000000111010010101001010"}

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Returns: "YYYYYNNYNNYYNYYNYY??????????????YYYYYNNYNNYYNYYNYY"
{"01000000011111001000000000000000010000000111110010","11111100110101001100000000000000111111001101010011","01111010001010000100000000000000011110100010100001","11010010011101001000000000000000110100100111010010","11010010001011010000000000000000110100100010110100","00110100010010000100000000000000001101000100100001","10110100001110000100000000000000101101000011100001","01100111100001011000000000000000011001111000010110","11000101001010000000000000000000110001010010100000","01110001001111001000000000000000011100010011110010","10011111010010100000000000000000100111110100101000","01111100110100001000000000000000011111001101000010","10001001011110111100000000000000100010010111101111","10100000010010011100000000000000101000000100100111","00111010100101001100000000000000001110101001010011","11110011110100000000000000000000111100111101000000","10100010110100101000000000000000101000101101001010","11111010100000000000000000000000111110101000000000","01000101000010101100000000000000010001010000101011","11011100110100000100000000000000110111001101000001","10100101110100000000000000000000101001011101000000","00111001011101001100000000000000001110010111010011","11100011000110100100000000000000111000110001101001","10111010101000101100000000000000101110101010001011","01000010011000111000000000000000010000100110001110","10110111000001100100000000000000101101110000011001","11101110011100001100000000000000111011100111000011","00111100000110000000000000000000001111000001100000","01000110101010101000000000000000010001101010101010","11110101000011011000000000000000111101010000110110","00110000100110001000000000000000001100001001100010","11110000010010010000000000000000111100000100100100","11101111001000110000000000000000111011110010001100","00101110101011101100000000000000001011101010111011","11001001000110101100000000000000110010010001101011","10111100111111000000000000000000101111001111110000","01100101000010001100000000000000011001010000100011","01011111110011111100000000000000010111111100111111","01100011110000001100000000000000011000111100000011","11111010000111000000000000000000111110100001110000","01000011100001000100000000000000010000111000010001","01001100001100101100000000000000010011000011001011","01001000011000011000000000000000010010000110000110","11011100000011110100000000000000110111000000111101","00110010101100010100000000000000001100101011000101","01011100111001011100000000000000010111001110010111","10001001101110010000000000000000100010011011100100","01010011100000100100000000000000010100111000001001","11011111100010001000000000000000110111111000100010","10000110101001011100000000000000100001101010010111"}

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Returns: "NNNNYNNNYNNYYYNNNY??????????????NNNNYNNNYNNYYYNNNY"
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Returns: "YNYNYYYYYYYNYNNYYY??????????????YNYNYYYYYYYNYNNYYY"
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Returns: "NNNNNYYYYNYYNYNNYNNYYNNYNNYNYYNYNYNYNNYNNYNNYNYNNY"
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Returns: "YNYYNNYYYYNNYNNYYNNYYNNNNNYYYNNYNYYYYYYNNNYNYNYNNN"
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Returns: "NNYYNNYNYNNNNYYNYYNNYYNNNNNNYNNYYNNYNYNNYYYNYYNYYY"
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Returns: "NYYNNNYNYYNNYYNYYNNNNNYNYNYNNNNNYYNNNNNNYYNNYYYYNY"
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Returns: "NYYNNNYNYYNYNNYNYNNYYNYNYYNNNYNYNYNYYYNYNNYYYYYYNN"
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Returns: "INCONSISTENT"
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Returns: "INCONSISTENT"
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Returns: "INCONSISTENT"
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Returns: "INCONSISTENT"
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Returns: "INCONSISTENT"
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{"00000111110000000010100100000100000000000100010001","00100011010000100010100011000001000010001110010001","00100010100010000010100010000000000010000000010000","00001110000001110000100010000000001010001010010000","00001110000001110000100010000000001010001010010000","10100100000011000010000001000000001010001010011100","00101001110011110010100101000001000000001110001001","00000111110000000010100100000100000000000100010001","10001011100000000000000110000100001000000100011101","00101001110011110010100101000001000000001110001001"}

Returns: "YNYNYYYYYYNNYYYYNNYNYNNYYYNNNYNYNNYNYNNNYYYNNYYYNY"
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{"00001000001100000000010100010100100101010000000010","00000000001100000010010100110100100001010000010110","00000000001000000101011010000100101101010000100000","00000000000100000000001000010100001001000000000100","00001000001100000101011010000100000000010000010100","00000000000000000110011010110100000100000000110100","00000000001000000110001010001100000000000000000110","00001000000100000011001100111100000000000000010010","00000000000100000110000010010100101100000000110000","00000000000100000111011010111000001100010000110100"}

Returns: "NNNNYNNNNNYYNNNNNYYYNYYYYNYYYYNNYNYYNYNYNNNNYYNYYN"
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{"01001101110000000100000100000010001000010010001010","00000111100010000100000100000000001000010001000000","01000000011000001000000100001010000001000011000000","00000001010000000000010000001010000000000000001000","01000110110000001100000100001000001001000001001000","01000010011010000100000000000010001000000001000000","00000000101010000100000000000010001001000010000000","00000111100010000100000100000000001000010001000000","01000001010010001100000000001010000000010000001000","01001111001000000100000100000010001000010010001010"}

Returns: "NYNNYYYYYYYNYNNNYYNNNYNYNNNNYNYNNNYNNYNYNNYYNNYNYN"
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{"01011110011010000000110000101000000001001010000001","01100100110010000001101000101000000000100010000100","01000100010011000000111000101000000001001010000001","00010010101011000001011000100000000001001010000100","00100010111001000000111000100000000001100000000000","00010010101001000100110000001000000001001000000100","00111010011000000101001000100000000000001000000001","00000100011000000101000000101000000000100010000001","00011100110000000000001000000000000000001010000001","01011110011010000000110000101000000001001010000001"}

Returns: "?YYYYYYNYYYNYYNNNYNYYYYNNNYNYNNNNNNNNYYNYNYNNNNYNY"
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{"00001011100000101000010100001010000100010001011000","00001000000000000100000010000000000100000001000000","00001011100000101000010100001010000100010001011000","00000001000001101100010111010010000000110000001000","00001000100001101100010100010000000100000001001000","00001011100000101000010100001010000100010001011000","00001010000000001000000011001000000100010001000001","00001011000000001100000110011010000000110000000001","00001010000000000000000000011010000000100001000011","00001001000000100100010000000000000000110001011001"}

Returns: "NNNNYNYYYNNNNYYNYYNN?YNYYYNYYNYNNNNYNNYYNNNYNYYNYY"
{"10011101110111011010001101010101110000100111001001","00100110010110010001000000101011100011100011100000","00110010101001011010010110000010101010100000000000","10100110000101100110000000101110110111010100110110","00000011111100000110001011011100111010101101111100","01101001011001101000100010110010110011101101010111","00100111111101110100110011101001101101010001100100","00101111001011000100100000001101110110011001111111","10000101110110101001101001110011000111011010100100","00001011110100101101011111010011110011110101001100","00010111010011111000111011010101110011001001101111","00010111001101111101110111000100110101001001011111","00010011100000110100001110000111110010011000100110","00111110100010110110100101101111011111101011111010","01011110000000101100000111100010010010001100100000","00110001101011111000101101001011001000001100010001","00011111011100101110110110001011010001001000010100","10111000011001001111010000101000111101011010011010","00111100010111111000010101100100000111010011011101","10001100011100100101011101010100010000100001100101","00001011111001110111001100011001101000000101010111","01111010001101000100010001001011000010111110111001","10010010011111010011010001011111000010011100001111","01101010011000010101100111011100010010000011100000","00011001101000111001000111001101010100101001010101","01000100011011000101010111100000000011100000101111","00001101011101110111000101011111010101110100111101","01000010010001000110011001110100010010100110100001","00001001111100100100001000100011000100010100111011","00101101001001110100111100110111000001000101100010","10011001011001111111010010010011001101101001110001","10101011000010100100011100001111011010101000100011","00000101000111100111101001011100011000001111110001","11010011001101100010010110111001111011101111011011","11110000011001111011011010111111000011111010001101","01001110111001111100110111011010110100111110100011","11000011100101110100111100110001110011111001101010","00101100110101001001101111011100111011000000011000","01001111100110101010111011001110010110010111011011","01111001010100001001001001111011011001001100101111","00000100100101111001100110111110011110000010100100","11100001011010110101011001001111111000111110110000","00101110100010110010000100001110101001110111001010","00111000011110010011111110111010001010110101101010","00101110011100010010101011100001010011001100101110","00010110000011001011011000101111111000010101111001","11000101110100111100111000000001000101100011100011","10100100101011110110110111000010001111100100011101","00001111011001100100010101100101000000010000110000","11000111101100010100000001110000011010011010011111"}

{"00000010000000110011001100001001001000000001010110","11000100000000111000001000000001000000000001100010","00100100000010111000000100100000000000010001011100","00000100000010100011001000001000011000001001110000","00100110000010110010000100101001011000001001111010"}

Returns: "YYYNNYYNNNNNYNYYYNYYNNYY?NYNYNNYNYYNNNNYYNNYYYYYYN"
{"01000010000011000110001111001001001110011101000000","01010110100000100001100000100101101000100010111010","00001001100011100110010011100001111001010001110000","11111000101000010011011010110101000101000111011110","00100111110101110101111100000011011100001001101011","01101001001000001101000000111010110110110110010111","00110101011011110101010011010101100101100100000110","00000101111011001100101000000001011011101000010010","00110001100101001000101101100001000101001010000110","10000110011110010011001101101011000100010010101010","00111001111011101100101110011000001010000011110011","00000010001110111010011111000111100011111101101001","11101001101101010001110001010000001000011100010000","00000011101111100000011100100000100000001010001010","00010110101000111001011011111111111111010010111001","00010010101101001011011011001000100000001110100010","11011001100110101100100000011111000011000111001000","00001110100101101101110010101111111011001101011010","11011001100001001001101010011000101011100101101001","10010111000011101111101100011110010101110010001001","00100011101111011011000001010011110000110000001011","11001000010010010101111001101101010011100000111011","00000101111110110101000000111010101010111111100001","01110111100010100011010100000011100111011011010010","00000111001110010111110101101001011110100101010111","00011001111110101011101000001111110100000100001011","01001100001011011100000011101111001001000010101000","00111110101110010101110101111111101101011100101001","00100101000100101110010001011101011111001101000001","01010111011111000001110011100011010000101001110010","00111111011011100100110000101010110011100010000000","10100000010010111011111001101111101010101111100011","01100000011110011110010110001111111000010001001001","01011100100000111010010111101000000011000011010000","00000001000010111000110110111101111010010001110011","00100001001101011101010011100000110100110001000111","00000010000000100101100110111110001101100001100001","01001000000010100011001110111100111011000110110001","01110110000100000001110100001010010100001010100000","11000101011101111110101010111001100110110001101011","00000000110010101010110101110001001000010010000000","01111011100111000110100000101010010101100100011110","11110010000110101011111101100001011101010111110010","01110101000100100101100111111110100100001101010100","00011111001100111111000011011011110100100001001110","11111011010100001010110010000100001111111110111101","11001111000000001110001000000111011110110001001110","00111000110110010000100010011010011011000010100111","10001101001101010000010111000100110011100111101100","11111000101000010010000111001011010011000010110011"}

{"10011000100000100100000000001000000010000001001000","10101000101001000001010000000000000000010000010000","00100010101001000011000000000000110000110000001010","00011000101000100011000000001000110000000000001010","10011000100000100100000000001000000010000001001000"}

Returns: "YNYYY?YNYNYNNYYNNYYYNYN??N?NYNNNYYNNYNYYNNNY?YY?YN"
{"00000101000010001101011011111011101001111000110111","11011110001110101010101011000111010001100000110101","01101100110111110000101110000010000110010110100000","10001010011111111001101001111111010110010001101010","00000111100101101100011101000110001010101100000010","00010111000011010111010101011101010000010110110011","00010001001010101000010100010011100100100011101001","01001010010000100110000000001001100010001111111011","00001111000110000101111101001101111000110100110011","00110100001101010010011101001101001101001011101010","10011001111011101101101110000010110101101110111010","10100111110111010101110001010101110100011011110010","01111001001110110000011111001000101001001100011111","01000010100011111101010101111011010011100010100100","00011001011000111100010101010000110001110111111100","01011100001001101000010101100001100111000111110111","00101110111101010010001110011101111111001011010010","00100001110110011101110100111110001010101010100101","11100000111101001000101100111101101110111101100001","00011110010100111010111111110011101010010001010000","01111001110111000111000110000011101101110010111100","00001110001000000011010011000101101110001000110001","00001110100101101001011101110110111110110100001010","10011111010110000100000100100011011001111011011111","00010011100111101000010010100001011011000111110101","00110101001111100000011110010010110010100011101110","11110100010110101001100000011010011111011000000100","10101100000010111101101111101010010010010100001100","00100111011110011111001101001101001100111010010111","01010011000110101000101100111011100101111100100100","00000000011110001001101110000010100010100000011001","11000011111010011011010011010110110110100010000101","01000001110101110111101110111101111001110001110010","11100111001111011001111011010110011110000111010111","01110101100001111001110101010110110010101011100000","01111101011101111000110011100001100010000010110101","10110011011100011001111100111110111000110000100100","01111001101000100101011100011111100110111000011110","01110000011001110001011010101000001111000010101100","10100011100100100001100010011111011001100101010110","00110011000000101011110001000110100101111110100001","10000010100100110001001000010001010000011100100101","00101010111100100001100000100101100011001000110000","01101000110000110011101001011010110000101101111101","11110110010110111100010000000111011111110001000111","00101011100110010011010010101001101101110011001000","00000001111011010110111001110111100010011000100000","00000111100000010000110111010000000100110100001100","01110101011001000001110010010001111101010111111101","10001100100000000010101110111000110001110100000001"}

{"00000000000010001100011001110000100000100000100000","00000000000010001100011001110000100000100000100000","00100000000010011100101001100000000010000100000000","00000000010101010110101000110100100000100000100000","00100010011110011110001001000100000100100000000000"}

Returns: "NNY?NNYNNYYYYYNYYYYNYYYNNYYYNYNNYNNYYNYNNYNNYNNNNN"
{"11010111010000010100000001001010110110100110110010","10101001100010010011101011011011111000001010111010","01100111011000011110111000011100111111110111110111","11011011110011001001010001000100001111000110111010","01001110100001111110011101101100000110000100000010","01101011011110001000110000001110010100001010001001","10010011110101001101010111111000000001111000100111","00100110100101000000000110101011100000111010110110","00001010100000011001110011101011110111000110110011","00011011111011011010110111111110010010000110101001","00011010110001011100110110100110100011101101010011","00100100001010110100000101101111111101110000101011","01101001100000010111011010011101000110101110101110","00101110111100011011111101000101111100110110010101","00101101100111001111110110011110101101010010101001","11110100101000010111010001110101110101010001110111","00000001110100010110111110100000111111001111000101","01011110110101001011101110011001010101001010010101","00011110010110101010010001111000010111011111000100","00000101111000000001110111111110111011100001100101","01011110001000010100000011100111111110110111001111","00011101001100101101001001011111000011001001101110","00001101001011010100100101010010111011001101000101","11101111101111000101010000111011001100011000100101","00010000000111100110110011011100111111111110100100","00101101100010011010100101001101110000011011010000","01011010011111110001100100011110010100001001110010","00010000110010111100001111100111101010010111001110","00011110110111000100010000001000110010101011011100","10011100011000111111111010101010111000110111100110","11111011111011001110100011011100100001111000010000","00000000000101011011010101011000011011000101010101","01110011000011101101000010000001110101000001111001","01101100011011010011010111000001010101010010001101","00101011001111111100110011101001111001011010011101","00010010100101001111101011110000011100010001100010","11100011000010000011010110111010101010100110110000","00011100101011000001101111001000010111001101010001","01100111010001010111000101100010001000010011101110","01110011010110000010110111100000110110111110100101","00011111110110000110001110111000101111001010101001","00111011100100111000111111111001100001101111001001","00001001011010100011110100000000110110101111110100","00101101111001100111011101100100010001001101111111","01011000011100101110110100001100001110001010100000","10100001101100110010110100111111011110010100101111","00010110111111000100011000110010000000000110010101","00000100011110010010101100001001101100001001100001","00000111101111000010011000111001100011001101101100","01011001010001011001000110011110000001101111011010"}

{"00000111000000010100000000000010010000000010010010","00100111001000010100000000000100010000010011010010","00000000000111100100000010000100010000011010000000","00101011001110000000000000000110010000001010000000","00100001101100110000000100100111010000010000000010"}

Returns: "NNYNYYYYYNYYYYYYNYN?NNNYYNYNNYYYNYNNNNNYYNYYNYNNYN"
{"10001010001100000111010011111001010011111101001101","01101011100011111010101100101111111101001000000011","00010110010001000011000111001000110100010110011100","00111011010011110011111101011001010000000010001100","10101100001100111000100010110100011111100000101010","01010110111111000001100100010101101110100100100010","01001011000101101010011110010011111001010111001111","00011101111101101100111001101100011000110000100011","11000111000000101100010110111111011011101000001000","11111010111110101111001001010011111001110101000001","01011010011111100111100111001100111011110101010100","10110110011000001001001110001001010110110110000001","00110101000100010011001000001011010111000100100101","00111011000101111010100010100010000010110101111011","01000011100111010100001101011101111101101011000000","11000001110011110111000101001011011110110100101101","00000000101110010101101011000111011101000101001110","00100001100011011000100111011110110111101011111100","00000110011000001100001000111111110011110010100001","00010100001110001010110000110111100111011010011001","01010001111101011100010011100001100110111110011000","01001001110011111000010010100010010010110110111000","01000100110001000101010110110100101111101100000100","01110110001111110000100010111101011000101110000100","11011110011110101111101001011100011111101010011101","11100010101101000001000010001000110010101001100111","11000100001000010111011101110000000101010111111010","11101000100001110101001101111011101001100001010001","10100001000001010100011110111100100101011101001110","00000100010000100010011011111101100010100001011100","01101101000011100010111001000011001101110101011010","01110010100010111001001000011101101100011001010000","11110100101010010100110000101111010111010111000101","10000000110100111101001101110100011111011000111111","11010001001111000110110011101101100001110001010110","00000100111010011100010100001100000100101100010101","00110000010100101101111100100000110000000111011100","10010111111010111100111100001100110000111111110010","10101011010000100110010001010101010001010011101100","00110101111110000100001000011010100100100110001101","10110100110101100010100111000101111010111000011111","00110111010010001111010011111111101100011110100010","00001001001101011010011010011001101100011011011011","11010001010001000111000111000011001110000010000100","00101100101101111010001101111100101011101101100000","00001011100010100001111100010011101110011001100100","11000100011111011001111100010101000101011110111100","11001101000001001011111000100011011010010111001111","00110000100101111000010011001011111110110010100001","00011001010111001010110000111010000111101011111011"}

{"00000100010000100010010001111101000010100000011000","00000000100100111000010001001011000010100010000000","00000001000100011010010000011001000000000010011000","01000001110100011000010001100001000010100010011000","00000001000000010000010100111100000000000000001000"}

Returns: "NYNNNY?YYYNY?NYYYNY??YNYNYYYYYYYNNNNYNYNNNYNNYYNNN"
{"11110111010101001001011111110010110010101110011011","01100000101000111100100010001011110000101111000010","00100100110000011010101001000110110000010000111111","11000111000000101011001111110011110100001100010110","01111110100111100010100111010110100101111011001010","00011000001101111101101101111111010101001101001011","00000000110000011000000010100001110000010011111111","00111100001001100000011101110110011010010011100000","10110010100101101011110101111000111110101011011111","00000011010011101001111110010101001100000111001001","00000111110011100111001111111000001000010110001110","00101011100000011001101000000111001001011110011101","00000100111000010000000100010111011110010000111110","00011000000111010111011000100101010110101000011011","01010111010010100110011011110001010001101100110111","00100000011101111001100100111001110001010011110011","01011010101100100111000101110001010111010001011101","00100100101111100100100110010100010000011110001010","00000001111100100010100110011110011000110100101100","11011011110001110110110011001111101011001111011011","00010101001110000110111001110101001100110001110011","00010101100001101111100001100111111010011110101001","11010110001011101001010010110101001101111101101111","01111100011100110000010111110100111011010100111010","10100000100110010011011111000110001110110101000101","00000101011100101111101000100010111111011111001011","11001001000100000011000110010110111110010101110010","01100100111010000110000010110100000010010010000111","00001001001001001001101111010110111010000000010000","10110101001011110111100000010110111000011101001101","00000001110001011111011010110111011001111101010011","00001100010111110110000111110100011010110101010000","00101111001110011111000001101000000011000011010010","01100111110100101001011010100000110010000011110010","00100000110010010111111011000100101001100011100001","00011101011110011011000010010000111011111110110101","01101000100001111010100111100001011110001000111110","10101100101000110100111000110100101110001110010101","11110011001011110111010010101101010100111011110110","11010001011000101101010110111010000110111000111111","01110100001100100011110111111100101011101101010000","00000000101111001100011110001101101110011111010001","00101110000111101100100101001111011100110110010111","11110100000101010101101010000000010001110111100100","00110111000110101001000000011101011100011011101111","01111100110001000001110011000010000010010111101101","01100110110001011101111011000000111001010111100111","10101100000000001001111101100101101100111001110011","00110010001010111010011011100111010011110001110111","01010001011010110011101000001011110001111001111011"}

{"00010000001100000000010000110100000100100001010011","01010000001000101001010100110010000110100000011111","01010010000000100000010000110000000000100000010111","00101010000101101000000100000110000100100000010111","00000010000001101001010100010100000100000001001001"}

Returns: "NYYYYNYN?NYYNYY?YNNYNYNYNNYYNYYN?NNYYNYNNNNYNYYYYY"
{"01100100001010001111000101111100111100000110000100","10011111000100101000010110011010110000011011111100","00000100111000001011101101101111010010101000011101","10001001010010111111001101010010001111011001001111","00101101100100001010111100111111100011111011110010","01010011001101101100100010101101110000110010000111","00110111001011100110010010001011000010011001000100","01100001001110010110111111001011111001110100111101","00101011110000111001001011111111100001110100111100","01010010101011100111110001000100100001111000001010","00000000101100101110101110100001111001101111111001","00011100100111101010100000101101101101010111000100","01110111000000011001001110000101010011011001000001","00000000110010000111001100001101111001011011101101","10101111001101011111100111000100010001011001011011","00010111001111111101000111101011101110010000010000","01000100000101110000000010000001110101001001110110","00001000100110001100010010111110100000010001100000","00010001000101010100111000001101111110111001101001","10110110110110010001011001010101011110011011110111","11111000110100100011100111101110011111001101011000","00110001010111111100011000000001000101010101001111","10110010110110000110100011110100110100111101101111","11100110001001011100011111100110111111000100010001","00100001011110000110101011110010111001110001101111","01100111010100000000111110011100000111010101001101","01001000111110110001001010000110101001101110111101","01001111001000101000100011001101010101000010010001","00101110101101010001011110101111000100011010001000","01010000011000110011000011100101011001110000110011","00110100110101100010011111101111100011010011101001","00001010011001001101000110001111101010111011111110","00101111100011010011011111100101110100111000010110","00011000011011011110010101001100001000100010100011","00011110010110010000011100010100000100001000010000","01100111110110101010010101110000010110111111011110","00110000110001000000011011100010010000010001011111","00000000101010110110000101001110101100110000110110","00010000000010001111100010100000011101011011111110","00110100110111001100101001001100101101110000111111","00000111110101101010001001101111110101111110100110","01010101101101001001010111001110101010010101101001","00000010000110011111101010110011010001101101000101","10001110001110100010000100101100010101101100010110","00010110001010000011111000010110001000111011101111","01010001111110110001101101100010010100110001100001","00011110100111010011001100010111110011011100001011","11111111100101101001111011001011010110110001111110","01100011000011011101011011010100010000000110111110","00000011101001111110111010111011101010011100011001"}

{"01100100000000011001001010000101010000000001000000","11100000000000000001100011000100010100000001010000","00000100001010000001101000000100000000000011100000","00000000001000001100101010000001010000000011110000","01000000001010010001101001000000010100000001100000"}

Returns: "YYYNNYNNNNYNY?NYYYNYYNYNYYNNNYNYNYNYNNNNNNYYYYNNNN"
{"10010010011101111000110011110100111011000100111011","01100000100100101010111011011100000000001010111100","10101000100010101110000101011011001100010111011111","00010011001110100011110000010100111101100110000010","01111001101110001000110000001001001100100101010011","00010010111111011010010010110001010101000011110110","01111101100110101101100010101100111111101001010101","01101011110110001011111101010101001110000000001010","11001111100101101100001001000010011011110001000001","00100111001111110111101111010111000010101101001010","00010000010100101000101000011000011010101110110011","10110101000111100111110010010111000011111101011101","01100111001011000100000101101011010111001101101010","11001101111010100101011101000011101001000100101110","00111100010000100001011001000101011111000111001101","00000010011001101100001011100011011001110000111110","01010010100001101001111011011001001110101110100100","00000000001000100101010011101001110011001001010000","10000010010110011101111110110011000101100100000010","01110000001010011001100001001011101010011000000101","00110101111001101110010101000100110001011110000100","01101010101011010011101000100101110000110101001101","00011101111100011010010010010111101110010110010111","00010100010101101011000010110110111010011000010101","10110110110000101001110100000111111110111001101101","11100110000100000001111110001111001011000110000000","10011001011110000111101111111010011011110001001111","00000100010101110101000001000010000100000010010001","10011110111010011001111011001000000111000101011010","00111111111110001000000110001000001111011001110100","10101011100000010010100101010010100011011111000000","00111011110001110000110111010000110011010000000011","01110111000010111000001010010001001011111110011111","00010010100001110010110110111001011000010000101011","00110111001010000110101010111000000001011010110111","11011000101011011010001000011011110000110100010011","11001101101001011100111011111011010011111010010111","11111110001000101111001000001111000010100011110011","00101101110100000101010000100010000000111001111000","00000010101101000011000101100001100100001011110100","00101001010010011011010100000100100000000011111001","10111001001011111110100011111110011100001110110000","01001111011001000011001001111011000001011000110100","11100000100011111110001101100100000110001001001000","10101101100101101010011010011000001000011110000101","00100010111101010110110011001001010101011101100111","00001001000101111011010001101101011010110011110100","00001011011011010100100101001011011110100001011011","10111010000001000110110010100001100110000010100100","01110111011100011110110110000101011100110001101111"}

{"10000100100001001000000011101000010010110000010000","10000000000001000010000010100000000010000000000000","10000100100101101010000010001000000000010000000000","00000100010000100000000001000000010010000000000000","00000100110100001010000010000000000010010000010000"}

Returns: "YNNNNYNNYYNY?YYNYNYNNNN?YYYNYNNNNYNNYNYYNNNNNYNNNN"
{"00011111101101010010111111101110100100100000111111","01010011111011001111010010110101111010000110000001","00111000111100101001010000101100101100101100100110","00111111010010001101101000011011111010101110000100","01101010000011011111110011001011010101010011111010","00001101100011000011011111010101001110011100111010","01100110000111011110111101001110101100101000111101","00000010110010101111101001111001001000101111100001","01110011111010010100000001100100111000001100011001","00101011101101000110100001101011100100111100110000","01010111000010000001101100111010100101111000110101","00110101000001011101101010000111001111111111111110","00101000000111110111011111010010100101001110101110","01010111100110111000101101101010010000010101011110","10011011101010101010110001011000100100010100100010","10100011010110011111011100101100100010000101100101","11011100011110100101011001111101100001100001000111","00011001111101010010101101110110101011101110001110","00100010001011001100000011110100000100011100011001","00100110110111110010001000001100100000111101110110","11110000000110111001001000011100110001001100110010","00000011001010010011110001110101101001010010110010","10010000001011001011001101001110001101111101110010","01000111011011110111011001001000110101110111011010","01000011010000101100101101001011101011111100001000","10011101101000001001111010111000110011000001011000","00001101001001010010111110100100100101010111100101","00010001100111011110010000101001101011101001000110","11100101101011101111000100000010110011101111111101","01101000011010001110011000111111100010100010000011","01010011100010111010101110000010000110110110001111","01010111101000000100111111010100010101010110101000","00000000111100111010110111101110111101000110111110","01101110111111000010010011110111111001101101111010","00000001001011010010011101100111111000100111000111","10000001010001010011111100001100000110000111101111","00111111011000000011101111110100001111111011100101","01010011010010111100010001011100111000011111000111","01000101011000111011100110000010010011110011111000","11100111001100101110110101111001011111001011110001","00001011100111010101110111110010010100011001100001","00011110110001100010101000101110011110110100010111","00011001011000001010100110111111100010011010110101","11011001111111000011111100110010011010001111111110","01000110111110000010000001011001001000001110110010","10010000111110011000000001010011101111011011011100","10101010101100100101110000111100101011101101011100","10110101001010110011110011101000100011010111101000","00000010111011011000111000100000111011000001110100","11000110011010000000100000110011000111011000000010"}

{"00010100000010000000001000011010100001001000110101","00001100000010000000001001010100000010001100111010","00000100010000001000000000000010010011000000111000","00010000000010001000001000000010000010000100001111","00000000000010001100000001010100000000001100011001"}

Returns: "?NNYYYNNNYN?YNNNYYNNNNYNNYNYYYYNYYNNYYNNYYNNYYYYYY"
{"11000111011001010001110101111000001001011000100010","00101010000110000000011100100111011001010111100111","11000111100000000010000010001000001101000010001000","00001110000011001010001000001101110111100110101010","10010000110011100101101110010111000111011100010001","01101000011010000010110010100111001011010001111101","01000011011011001011000110001111110111000011101011","00010100100100111011011011101101000011011110011110","01110001000100111100001000010110111011000110010001","00100001011010101001001010110011110110110111101001","00011000011111010000100111001100010011001111001101","01110110111011100100001100001001110101010000110011","11010100100101011000010011101010000101010011111100","01010111011001100100010110010000100011100011000001","01000100010001010011001000100111010011101100001100","01000101111010011110000001000010001110110011000100","01000100011101110000100010110100111011000000110000","00000010101000001011011110110101100001011000000010","10110111100100111011000100011000101100111011101010","00100011111001010110111000101011000010111011110000","00000100111001010110000100100011010000011111010101","00001111000000010111010101100110001011111011101011","10010000101001010100111111100000111101101010111000","00000000001000101001101011001101110111111011110011","00000100011011101000000100011001101000100100001110","10001010110101100111101100100000101111000110101011","01101011000000010001010110101111000101110011000111","00011011111100001111011100101000001001000110011101","00010101101111010010011010011000111100011100100001","00011010111001001110110001011011011011010101111110","11111111111100101101111111001110010111111110101001","00110011101000011010110011011111100001100111010110","10010111001101000011001011100010000101100111011000","11000000010011000111011011101001111001010001100111","00001010010101011010010000111100101001001101111110","01110001100101010111100011101101110101101101010011","11111100110000011111000110110110010001100100101110","00100010101101110100100111001110011000001000101100","01011100011110101000010100001000011101111000100111","00011110010010110011011101100100100101100000001100","11011111101111110011111110101110100111001011110010","01111110001011011110011110100100001011111011100100","00101000000011010001010011110010010000001000010010","00000011010111011111101001100111000100011011111010","00000000110011100001000001011011000001001001011100","00000110100000111110001011101111110110000001111110","01011110100010011110011110111001110110001110000011","00001001011110110010110100101000011011011110011110","10101111111100010011011011111010000010000101101111","11100111110000001000101011100011110001000101000100"}

{"00000000100000000010000000000000000100000000001000","00000000100000110011000000000000100100110000001010","00000000101011110011010000000100100110000000000010","00000000100000110011000000000000100100110000001010","00000000011001110000000000000100100010000000000000"}

Returns: "NNNNNNNNYYYNYYYYN?YYNYNNN?NNNYN?YNNYYNYYN?NNNNY?Y?"
{"011100110011100","000101010111000","000010100000010","010101001111111","111011100111000","110000101111010","001011100000101","001100011100000","001011101000111","101010011001011"}

{"001000000000101","001110000011100","000100001001111","001000001001000","001000001010111"}

Returns: "INCONSISTENT"
{"011010011010000","001001010011111","110101100010110","100011100101111","000010100110011","000010110100011","011101111001101","110101110000011","000000010101110","011100000010110"}

{"101100000010100","100000110000100","001000010001100","000100110000000","000100100000100"}

Returns: "INCONSISTENT"
{"000110100010100","001110011111001","001111011100010","000111011010010","000110110000001","111000000001010","011100011010010","000100001101011","000111101001110","011000111000101"}

{"000001001010010","000000000010000","000001000000000","010001100000100","000000100100000"}

Returns: "INCONSISTENT"
{"100011111010110","011110110111001","000101110011010","001100101001010","011000100001001","100011011011110","000000000011111","000011010011101","001100001001000","101111000101100"}

{"001000101001001","001010110001001","001010110001001","011000100011001","000010111000000"}

Returns: "INCONSISTENT"
{"000110111000111","011100001110111","001001001000010","010101011110110","010001101001110","011100101101001","011110110001010","110001001001000","000110010010000","010101101010111"}

{"000001000000010","000100000000000","000100000000010","010100001000010","001001001000010"}

Returns: "INCONSISTENT"
{"011111101011011","000000111101010","001111011110000","000000110111110","000011011111011","001110011011010","000101010011101","000000101000101","000110000011010","011001010011100"}

{"000001010101001","000001100001001","000001101001001","010000010001000","000001010101001"}

Returns: "INCONSISTENT"
{"000001001000010","010110001111101","000010101110000","011010010010110","011101111010001","000110110010000","010001111111001","001000001101010","001110111010011","000001010101010"}

{"010001000010000","010110000101101","000110110000000","000001000000000","000010100100000"}

Returns: "INCONSISTENT"
{"001000111101000","000001111011001" ,"010010100100010","111000100010011" ,"011011011010001","010011111101000" ,"000101011110011","010000011111000" ,"000001100100011","000000111110000"}

{"001000110001000","000101110000011" ,"000101010000011","001000110101000" ,"010001100000111"}

Returns: "INCONSISTENT"
{"1111111111111111111111111111111111111111" }

{"0011001100110011001100110011001100110011" }

Returns: "NNYYNNYYNNYYNNYYNNYYNNYYNNYYNNYYNNYYNNYY"
{"0" }

{"1" }

Returns: "INCONSISTENT"
{"110", "101", "010", "001" }

{"100", "010", "001" }

Returns: "INCONSISTENT"
{"10001010110101100010110111010101111011101011101100", "10011111010111111011010111111110110101111101010111", "11110111011010111101010111100101011111010111111010", "01000010100010111101010111100001101010000101101111", "01111010101111010111110001010110101011001111101010", "01110101011111010111101001010100010101010111011011", "01011101011011101010110101011110110101011110110110", "11110111101010111101011101011011011110110111101101", "01101011010111010111011101010111011011101010101111", "01111010111111011010101010011111111010111111111101", "11111111111111111111111111111111111111111111111111", "10111101011111111101010101011100000010101100000111", "01011111110111110111111011111111010101011010101101", "10111111110101011101100101101010011110101110101101", "01111010110111111010110101100110101010111110100001", "01110101110100001010101110110000000111011001011010", "11101111111101011111110101011101111111110101010101", "01010001111010111111101010000000011010101101010111", "01110111111110101101010111111010101010101111111101", "01111110101101000000000001100000000101010100000011", "11000000000000001100110011111111101010000000001010", "00001111010000000000101010100000000101010011110101", "11111111101010000000110101111010100000001010110101", "11111111111110111111111010101011001011010110101011", "01111011111111111101010111110111111111110101010101", "01010101010000001111111101010101010101010101111100", "01000010100010111101010111100001101010000101101111", "01111010101111010111110001010110101011001111101010", "01110101011111010111101001010100010101010111011011", "01011101011011101010110101011110110101011110110110", "11110111101010111101011101011011011110110111101101", "01101011010111010111011101010111011011101010101111", "01111010111111011010101010011111111010111111111101", "11111111111111111111111111111111111111111111111111", "10111101011111111101010101011100000010101100000111", "01011111110111110111111011111111010101011010101101", "10111111110101011101100101101010011110101110101101", "01111010110111111010110101100110101010111110100001", "01110101110100001010101110110000000111011001011010", "11101111111101011111110101011101111111110101010101", "01010001111010111111101010000000011010101101010111", "01110111111110101101010111111010101010101111111101", "01111110101101000000000001100000000101010100000011", "11000000000000001100110011111111101010000000001010", "00001111010000000000101010100000000101010011110101", "11111111101010000000110101111010100000001010110101" }

{"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000" }

Returns: "??????????????????????????????????????????????????"
{"1111" }

{"0000", "1111" }

Returns: "INCONSISTENT"
{"11000000000000000000111111111111111100000000" }

{"11000000000000000000111111111111111100000000" }

Returns: "YY??????????????????YYYYYYYYYYYYYYYY????????"
{"10100000000000000000000000000000000000000000000101" }

{"00100000000000000000000000000000000000000000000001" }

Returns: "N?Y????????????????????????????????????????????N?Y"
{"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000" }

{"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000" }

Returns: "??????????????????????????????????????????????????"
{"10001010100000000000000000000000000000100000100101" }

{"10001010100000000000000000000000000000100000100101" }

Returns: "Y???Y?Y?Y?????????????????????????????Y?????Y??Y?Y"
{"11011111100010000101111010001111011010000000110010", "11101110010011000011101110000100010011100110111011", "11100000110100000000101110001011101111000111100111", "01000011100000100011101110101111010101111000101011", "00011110001100010010001110111110100111100111101110", "01000111000011100010010001010111111010101001100010", "00110110001101110001110010010010011110110011000110", "00100011100111101111100101101001111110001111101100", "10000110011111101101011010010011100000011100011011", "00101011000000000001010010010111001100110001000011", "11000000110011110001101000010001101100000010111011", "01100011100101000011101000001000001001000011001111", "00011010001111111010100110100010110000101110010100", "01010001001100000000101001110000011000000100111010", "11000010010101010111101100011010011001001101110100", "10110011010110101011111011100000000100100001111110", "01110011010101111100100010001110111001010100111001", "10100010011101011111101011111011001011110111000101", "11110011010100011011011111100011001100110101101010", "10001111111111000010100011010100010010010100111101", "00110010101010110111101111101111111010110010001100", "00001000111110011110000100011000000110000011101001", "10111101100000011110110011100111111000101111101011", "01010010110011110100010000100001110110111110000000", "01100000110101110101100101111101111011000000101010", "00110001100100111001100001010011010101111100111011", "11000111101011110000110110010111110111111101101010", "11010111010000110000011101001111010000010001101000", "00101000011100010001010001011011111110110110000001", "10101101111000010000011011111010111010011010001000", "10011010110010110110110000010000000010000010110100", "10111101111000011011101111111001001110110101111101", "11110010111000101010100010011010000111010101001001", "00010101010110011001110111011100000001100001111011", "11100100011111001110101010001111011110101100000111", "00000010100101110110100010001001000110111110111010", "11111110111001011111101000100001001011000111011110", "00011100010101101101001101000100011001101011001101", "00100000001101010011011111110100111110000110011111", "11111100011100111001010101000100100001001001010011", "10101100000010010110111111000001011000001111101010", "10110010110111101011101000001101011110100000110100", "11110000011011111000011010100111010100001011110110", "00100001001111001000101100010111010100011011111101", "00000011011111111111001101001101010100101101100110", "00011101000000110011111100111000011011000010111011", "11101010011000010100111000010111111111010000101011", "10100100000111100000111001101111111100000110000000", "01111001011101101001010100101100000000110110011011", "11011001111111001000100001100011111111111010010010" }

{"00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000000" }

Returns: "??????????????????????????????????????????????????"
{"1", "1" }

{"0", "1" }

Returns: "INCONSISTENT"
{"10", "01" }

{"11" }

Returns: "INCONSISTENT"
{"1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111", "1111111111111111111111111111111111111111111111111" }

{"1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010", "1011101111110111111000011100111111000111110011010" }

Returns: "YNYYYNYYYYYYNYYYYYYNNNNYYYNNYYYYYYNNNYYYYYNNYYNYN"
{"10110", "10011", "10100" }

{"10010", "10100" }

Returns: "Y?YYN"
{"110" }

{"000" }

Returns: "NN?"
{"001", "001", "110", "110", "111", "110" }

{"100", "000", "010" }

Returns: "INCONSISTENT"
{"11111111111111111111111111111111111111111111111100" }

{"11111111111111111111111111111111111111111111101100" }

Returns: "YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYNYY??"

Statistics

Problem Statement for "NSegmentDisplay"

Problem Statement

Definition

Notes

Constraints

Examples