js-rhino, 60 bytes

Result

WA

Code [DL]

for(c=readline();;)print(+!(Math.sqrt(8*parseInt(c,2)+1)%1))

stdin

10100010
11101110
01101001
11010010
01011011
11111101
10011001
00001010
11000110
11000010
10100101
00000011
01010100
01111000
10000110
00000001
00010101
00100010
00000001
00000000
00001111
00000001
01001011
10110100
11100111
01001110
10010111
00110111
11011000
01100001
11001001
11011001
00011100
00000110
11100110
10101011
10001000
01010101
11000111
01000010
10111100
00000111
10010101
01010000
10111110
01110001
00101101
00100100
11110111
10011100

stdout

stderr

org.mozilla.javascript.WrappedException: Wrapped java.lang.NullPointerException
	at org.mozilla.javascript.Context.throwAsScriptRuntimeEx(Context.java:1893)
	at org.mozilla.javascript.MemberBox.invoke(MemberBox.java:148)
	at org.mozilla.javascript.FunctionObject.call(FunctionObject.java:387)
	at org.mozilla.javascript.optimizer.OptRuntime.callName0(OptRuntime.java:74)
	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.lang.NullPointerException
	at org.mozilla.javascript.tools.shell.Global.readline(Global.java:1149)
	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