csharp, 142 bytes

Result

WA

Code [DL]

using System;class M{static void Main(){for(int i=50;i--;)Console.Write((1==Math.Sqrt(Convert.ToInt32(Console.In.ReadLine(),2)*8+1)%2)?1:0);}}

stdin

00111111
01111100
10011011
11000110
00000001
11111101
01110110
10111110
10101011
10111101
00100100
00110111
11101010
10001100
10001011
10101000
11111101
00100111
00000011
10011010
01111011
10011001
00110110
01111110
10100011
11001111
01001111
00110011
10001000
11100111
00001010
01000010
00000000
00010101
01001110
00000000
01101001
00110000
00000010
11010010
00000110
00001111
01111000
00011100
10100111
01011011
11010000
10000011
01010101
00101101

stdout

Compilation failed: 1 error(s), 0 warnings

stderr

/tmp/code.cs(1,55): 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