csharp, 136 bytes

Result

WA

Code [DL]

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

stdin

00100100
01100011
01001110
11011010
00011110
01011011
00001111
11111111
00000001
10011001
10000100
00011010
01010000
00011100
10011101
11111101
00000000
00001010
00010010
00100100
01011101
01111110
00100100
00111111
00000011
00101101
11100100
10111111
01111000
10101011
11110011
11110000
00110111
10111110
00110001
00010101
11100111
10000110
11011110
01101001
00000110
11010010
11101101
10001001
11000101
11101100
10001000
01000010
01010001
11001001

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