js-rhino, 89 bytes

Result

WA

Code [DL]

for(;;)print(+!(Math.sqrt(8*new java.util.Scanner(java.lang.System.in).nextInt(2)+1)%1))

stdin

11101001
11110011
01101001
10111001
11100111
00001010
01000010
11101010
01111000
10110001
00011100
10001000
00010101
00100100
11000110
11010011
11011110
10111110
00000110
00011111
10011001
01100011
00101011
00000000
00001111
11111101
00100110
10000010
10111011
00000001
10101011
11001100
00110111
11101111
01100100
10100000
10100011
01000110
01001110
10010010
00101100
11011000
00000000
01011011
00101101
11100111
00000011
11110100
11010010
01011101

stdout

0

stderr

org.mozilla.javascript.WrappedException: Wrapped java.util.NoSuchElementException
	at org.mozilla.javascript.Context.throwAsScriptRuntimeEx(Context.java:1893)
	at org.mozilla.javascript.MemberBox.invoke(MemberBox.java:148)
	at org.mozilla.javascript.NativeJavaMethod.call(NativeJavaMethod.java:225)
	at org.mozilla.javascript.optimizer.OptRuntime.call1(OptRuntime.java:32)
	at org.mozilla.javascript.gen._volume_CODE_1._c_script_0(Unknown Source)
	at org.mozilla.javascript.gen._volume_CODE_1.call(Unknown Source)
	at org.mozilla.javascript.ContextFactory.doTopCall(ContextFactory.java:393)
	at org.mozilla.javascript.ScriptRuntime.doTopCall(ScriptRuntime.java:3282)
	at org.mozilla.javascript.gen._volume_CODE_1.call(Unknown Source)
	at org.mozilla.javascript.gen._volume_CODE_1.exec(Unknown Source)
	at org.mozilla.javascript.tools.shell.Main.processFileSecure(Main.java:601)
	at org.mozilla.javascript.tools.shell.Main.processFile(Main.java:560)
	at org.mozilla.javascript.tools.shell.Main.processSource(Main.java:531)
	at org.mozilla.javascript.tools.shell.Main.processFiles(Main.java:179)
	at org.mozilla.javascript.tools.shell.Main$IProxy.run(Main.java:100)
	at org.mozilla.javascript.Context.call(Context.java:501)
	at org.mozilla.javascript.ContextFactory.call(ContextFactory.java:503)
	at org.mozilla.javascript.tools.shell.Main.exec(Main.java:161)
	at org.mozilla.javascript.tools.shell.Main.main(Main.java:136)
Caused by: java.util.NoSuchElementException
	at java.util.Scanner.throwFor(Scanner.java:862)
	at java.util.Scanner.next(Scanner.java:1485)
	at java.util.Scanner.nextInt(Scanner.java:2117)
	at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
	at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
	at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
	at java.lang.reflect.Method.invoke(Method.java:498)
	at org.mozilla.javascript.MemberBox.invoke(MemberBox.java:126)
	... 17 more

strace