js-rhino, 77 bytes

Result

WA

Code [DL]

for(;c=java.lang.System.in.read(9);)print(+!(Math.sqrt(8*parseInt(c,2)+1)%1))

stdin

11110101
10011100
11010010
00101011
01100101
01011011
10111110
10110111
01101001
10101011
00010001
00001111
11110111
10011011
10001000
10000100
00010111
11110010
00110011
01000011
01111000
00001111
01101111
00010101
11101100
00001010
01001000
11100111
01101001
10101100
10101110
00000001
00000000
10011111
00110111
11111011
01001110
00111101
01000010
00011100
10011001
00000011
01001010
01000001
01111101
00000110
00100100
11111101
00101101
00001101

stdout

stderr

js: Can't find method java.io.BufferedInputStream.read(number).

strace