csharp, 136 bytes

Result

WA

Code [DL]

using System;class E{static void Main(){for(int i=51;--i;)Console.Write(Math.Sqrt(8*Convert.ToByte(Console.ReadLine(),2)+1)%2==1?1:0);}}

stdin

01000010
11111001
01101001
11100111
10100000
01111000
01001110
00111101
00000001
00010101
01101011
11111101
00011100
00011001
11011000
00100100
11010010
10101111
01001001
00110010
10111111
00000110
11001110
00110111
00101101
01110110
01001110
01100000
11000000
01010000
00100100
01011011
01101000
00001010
00000011
10000001
00101110
01010100
00000000
10001000
00010000
00001000
00001110
10101011
00001111
11101110
10011001
10111110
11111100
01111101

stdout

Compilation failed: 1 error(s), 0 warnings

stderr

/tmp/code.cs(1,54): error CS0029: Cannot implicitly convert type `int' to `bool'
Cannot open assembly '/tmp/code.exe': No such file or directory.
rm: cannot remove '/tmp/code.exe': No such file or directory

strace