js-rhino, 98 bytes

Result

WA

Code [DL]

s = new Scanner(System.in);
for(;c.hasNext();)print(+!(Math.sqrt(8*parseInt(c.nextLine(),2)+1)%1))

stdin

11101001
11100111
11110001
11001111
10001000
01101001
11010010
01011011
01010111
10111110
10001000
01011010
00111000
01001110
00000011
11001000
10111001
10100110
10011010
00000110
00100100
01001010
00000001
00010101
00000000
01111000
10101011
10000110
10010011
11100000
00001111
10100111
10000000
00010000
01110010
10011001
01110000
00010111
10101001
01000010
00110111
00011100
00001010
00010001
11000001
10000100
00100100
11111101
01100011
00101101

stdout

stderr

js: uncaught JavaScript runtime exception: ReferenceError: "Scanner" is not defined.

strace