csharp, 135 bytes

Result

WA

Code [DL]

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

stdin

10110100
00000011
10011100
10111111
11100111
01010001
00010111
01101001
11001100
00100111
00000110
00000001
10101011
10111010
00110111
01100101
01001110
10111110
11110010
01111000
11000001
01111000
11100011
01000110
00011100
00001111
00100100
10001000
10000110
00010010
00000011
10000000
01000010
00101101
01011011
10001100
11010010
00001010
00010101
00010110
10011001
11000110
00010000
01001100
01001000
11111101
00000000
01111001
10001110
10001011

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