111000111111111111000000111111mmmaaatttrrriiixxx000000000000111000111111000000000111111111111000000000111111111000111000
111000111111111111000000111111mmmaaatttrrriiixxx000000000000111000111111000000000111111111111000000000111111111000111000
111000111111111111000000111111mmmaaatttrrriiixxx000000000000111000111111000000000111111111111000000000111111111000111000
111000111111111111000000111111mmmaaatttrrriiixxx000000000000111000111111000000000111111111111000000000111111111000111000
111000111111111111000000111111mmmaaatttrrriiixxx000000000000111000111111000000000111111111111000000000111111111000111000
111111111111000111000000111000111000111000000111000000000111111111000111000111000111111111000111000111000111000000111000
111111111111000111000000111000111000111000000111000000000111111111000111000111000111111111000111000111000111000000111000
111111111111000111000000111000111000111000000111000000000111111111000111000111000111111111000111000111000111000000111000
111111111111000111000000111000111000111000000111000000000111111111000111000111000111111111000111000111000111000000111000
111111111111000111000000111000111000111000000111000000000111111111000111000111000111111111000111000111000111000000111000
111000000000000000111111000111000000000000111000000000000111111000000000111111111000111000000000111000000111111111000111
111000000000000000111111000111000000000000111000000000000111111000000000111111111000111000000000111000000111111111000111
111000000000000000111111000111000000000000111000000000000111111000000000111111111000111000000000111000000111111111000111
111000000000000000111111000111000000000000111000000000000111111000000000111111111000111000000000111000000111111111000111
111000000000000000111111000111000000000000111000000000000111111000000000111111111000111000000000111000000111111111000111
000111111111111111111111111111111000111111000111000111111000000111000111111111000000000111000111000111000111000111111111
000111111111111111111111111111111000111111000111000111111000000111000111111111000000000111000111000111000111000111111111
000111111111111111111111111111111000111111000111000111111000000111000111111111000000000111000111000111000111000111111111
000111111111111111111111111111111000111111000111000111111000000111000111111111000000000111000111000111000111000111111111
000111111111111111111111111111111000111111000111000111111000000111000111111111000000000111000111000111000111000111111111
111000000000111000111000000000000000111000111111111111111000000111111000111111000111000111111111111111000000111111000111
111000000000111000111000000000000000111000111111111111111000000111111000111111000111000111111111111111000000111111000111
111000000000111000111000000000000000111000111111111111111000000111111000111111000111000111111111111111000000111111000111
111000000000111000111000000000000000111000111111111111111000000111111000111111000111000111111111111111000000111111000111
111000000000111000111000000000000000111000111111111111111000000111111000111111000111000111111111111111000000111111000111
000000111111111000000000000000000000111111111000000111000111000111000111000000111111000000111000000000111111111000000111
000000111111111000000000000000000000111111111000000111000111000111000111000000111111000000111000000000111111111000000111
000000111111111000000000000000000000111111111000000111000111000111000111000000111111000000111000000000111111111000000111
000000111111111000000000000000000000111111111000000111000111000111000111000000111111000000111000000000111111111000000111
000000111111111000000000000000000000111111111000000111000111000111000111000000111111000000111000000000111111111000000111
000000111111000000000000111000111111111000000111000000000000000111000000000000000111000000000000000111111000000111111111
000000111111000000000000111000111111111000000111000000000000000111000000000000000111000000000000000111111000000111111111
000000111111000000000000111000111111111000000111000000000000000111000000000000000111000000000000000111111000000111111111
000000111111000000000000111000111111111000000111000000000000000111000000000000000111000000000000000111111000000111111111
000000111111000000000000111000111111111000000111000000000000000111000000000000000111000000000000000111111000000111111111
111000111000000111111111111000111111111000000111000000000000000000000000000111111000111000111000000000111111000000000111
111000111000000111111111111000111111111000000111000000000000000000000000000111111000111000111000000000111111000000000111
111000111000000111111111111000111111111000000111000000000000000000000000000111111000111000111000000000111111000000000111
111000111000000111111111111000111111111000000111000000000000000000000000000111111000111000111000000000111111000000000111
111000111000000111111111111000111111111000000111000000000000000000000000000111111000111000111000000000111111000000000111
000111111000111111111111111000111111000111111000111000000000000000000111000111000000000000000000111111000111000000000111
000111111000111111111111111000111111000111111000111000000000000000000111000111000000000000000000111111000111000000000111
000111111000111111111111111000111111000111111000111000000000000000000111000111000000000000000000111111000111000000000111
000111111000111111111111111000111111000111111000111000000000000000000111000111000000000000000000111111000111000000000111
000111111000111111111111111000111111000111111000111000000000000000000111000111000000000000000000111111000111000000000111
000000000000111111111000000111000000111111111000000111000000111000111111111111000111111000000111000000000000000111000000
000000000000111111111000000111000000111111111000000111000000111000111111111111000111111000000111000000000000000111000000
000000000000111111111000000111000000111111111000000111000000111000111111111111000111111000000111000000000000000111000000
000000000000111111111000000111000000111111111000000111000000111000111111111111000111111000000111000000000000000111000000
000000000000111111111000000111000000111111111000000111000000111000111111111111000111111000000111000000000000000111000000
000111000000000000000000111000111111111000000000111000000111000000000111111000111111111111111000000111000000111000111111
000111000000000000000000111000111111111000000000111000000111000000000111111000111111111111111000000111000000111000111111
000111000000000000000000111000111111111000000000111000000111000000000111111000111111111111111000000111000000111000111111
000111000000000000000000111000111111111000000000111000000111000000000111111000111111111111111000000111000000111000111111
000111000000000000000000111000111111111000000000111000000111000000000111111000111111111111111000000111000000111000111111
000000000111000000000111000000000000000111111111111000000111000111111000111111111000111000111111000111111000111111111111
000000000111000000000111000000000000000111111111111000000111000111111000111111111000111000111111000111111000111111111111
000000000111000000000111000000000000000111111111111000000111000111111000111111111000111000111111000111111000111111111111
000000000111000000000111000000000000000111111111111000000111000111111000111111111000111000111111000111111000111111111111
000000000111000000000111000000000000000111111111111000000111000111111000111111111000111000111111000111111000111111111111
111000000111111111111000000111111000111000000000111111000000111000000111111111111111000111000111111000000000000111000000
111000000111111111111000000111111000111000000000111111000000111000000111111111111111000111000111111000000000000111000000
111000000111111111111000000111111000111000000000111111000000111000000111111111111111000111000111111000000000000111000000
111000000111111111111000000111111000111000000000111111000000111000000111111111111111000111000111111000000000000111000000
111000000111111111111000000111111000111000000000111111000000111000000111111111111111000111000111111000000000000111000000
111000000000000000000000000000000111000000111000111000111111111111000000000111000000000111000111111000111111000111111000
111000000000000000000000000000000111000000111000111000111111111111000000000111000000000111000111111000111111000111111000
111000000000000000000000000000000111000000111000111000111111111111000000000111000000000111000111111000111111000111111000
111000000000000000000000000000000111000000111000111000111111111111000000000111000000000111000111111000111111000111111000
111000000000000000000000000000000111000000111000111000111111111111000000000111000000000111000111111000111111000111111000
000000000000000111000000111111111111111000111111111000111111111111111000111000111111000111000000111000000111111111111000
000000000000000111000000111111111111111000111111111000111111111111111000111000111111000111000000111000000111111111111000
000000000000000111000000111111111111111000111111111000111111111111111000111000111111000111000000111000000111111111111000
000000000000000111000000111111111111111000111111111000111111111111111000111000111111000111000000111000000111111111111000
000000000000000111000000111111111111111000111111111000111111111111111000111000111111000111000000111000000111111111111000
000111111111111111000000111111111000000000000111111111111111000111111111111111111000000000000111111000000000111111000000
000111111111111111000000111111111000000000000111111111111111000111111111111111111000000000000111111000000000111111000000
000111111111111111000000111111111000000000000111111111111111000111111111111111111000000000000111111000000000111111000000
000111111111111111000000111111111000000000000111111111111111000111111111111111111000000000000111111000000000111111000000
000111111111111111000000111111111000000000000111111111111111000111111111111111111000000000000111111000000000111111000000
000000000111000000000111111111000000000111111111111000111111111000000000000111111111000111111000111111111000111000111000
000000000111000000000111111111000000000111111111111000111111111000000000000111111111000111111000111111111000111000111000
000000000111000000000111111111000000000111111111111000111111111000000000000111111111000111111000111111111000111000111000
000000000111000000000111111111000000000111111111111000111111111000000000000111111111000111111000111111111000111000111000
000000000111000000000111111111000000000111111111111000111111111000000000000111111111000111111000111111111000111000111000
111000000000111000111000000111000111111000000111111111000111000111000000000111000111111111111111111000111111000000111000
111000000000111000111000000111000111111000000111111111000111000111000000000111000111111111111111111000111111000000111000
111000000000111000111000000111000111111000000111111111000111000111000000000111000111111111111111111000111111000000111000
111000000000111000111000000111000111111000000111111111000111000111000000000111000111111111111111111000111111000000111000
111000000000111000111000000111000111111000000111111111000111000111000000000111000111111111111111111000111111000000111000
111111000000000000111111111111111111000111111000000111111000111111111000111000111111000111111000000111000000111000000000
111111000000000000111111111111111111000111111000000111111000111111111000111000111111000111111000000111000000111000000000
111111000000000000111111111111111111000111111000000111111000111111111000111000111111000111111000000111000000111000000000
111111000000000000111111111111111111000111111000000111111000111111111000111000111111000111111000000111000000111000000000
111111000000000000111111111111111111000111111000000111111000111111111000111000111111000111111000000111000000111000000000
111111000000000111000000111000000000111111000000111000111000111000000111000000000111000000000000111000000111111000111000
111111000000000111000000111000000000111111000000111000111000111000000111000000000111000000000000111000000111111000111000
111111000000000111000000111000000000111111000000111000111000111000000111000000000111000000000000111000000111111000111000
111111000000000111000000111000000000111111000000111000111000111000000111000000000111000000000000111000000111111000111000
111111000000000111000000111000000000111111000000111000111000111000000111000000000111000000000000111000000111111000111000
000000000111111111111111111000111000111111111111111111000000111000000000000000111000000111000111111111000000000000111111
000000000111111111111111111000111000111111111111111111000000111000000000000000111000000111000111111111000000000000111111
000000000111111111111111111000111000111111111111111111000000111000000000000000111000000111000111111111000000000000111111
000000000111111111111111111000111000111111111111111111000000111000000000000000111000000111000111111111000000000000111111
000000000111111111111111111000111000111111111111111111000000111000000000000000111000000111000111111111000000000000111111
000000111111111000000111000111111111111111000000111111000111000000000111111111000111111111000111000111111111000111000000
000000111111111000000111000111111111111111000000111111000111000000000111111111000111111111000111000111111111000111000000
000000111111111000000111000111111111111111000000111111000111000000000111111111000111111111000111000111111111000111000000
000000111111111000000111000111111111111111000000111111000111000000000111111111000111111111000111000111111111000111000000
000000111111111000000111000111111111111111000000111111000111000000000111111111000111111111000111000111111111000111000000
000111111000000111000111111000111111000111111000000111111111000000111000111000000111111000111000000111000000000000000111
000111111000000111000111111000111111000111111000000111111111000000111000111000000111111000111000000111000000000000000111
000111111000000111000111111000111111000111111000000111111111000000111000111000000111111000111000000111000000000000000111
000111111000000111000111111000111111000111111000000111111111000000111000111000000111111000111000000111000000000000000111
000111111000000111000111111000111111000111111000000111111111000000111000111000000111111000111000000111000000000000000111
000111111000000000000111111000000111000111000111111000111111000000111000111111111000111111111111000000111000000000111111
000111111000000000000111111000000111000111000111111000111111000000111000111111111000111111111111000000111000000000111111
000111111000000000000111111000000111000111000111111000111111000000111000111111111000111111111111000000111000000000111111
000111111000000000000111111000000111000111000111111000111111000000111000111111111000111111111111000000111000000000111111
000111111000000000000111111000000111000111000111111000111111000000111000111111111000111111111111000000111000000000111111
000000111000111111111111111000000111111111000000000111000111000000000000000111000111111000000111000111111111000111000111
000000111000111111111111111000000111111111000000000111000111000000000000000111000111111000000111000111111111000111000111
000000111000111111111111111000000111111111000000000111000111000000000000000111000111111000000111000111111111000111000111
000000111000111111111111111000000111111111000000000111000111000000000000000111000111111000000111000111111111000111000111
000000111000111111111111111000000111111111000000000111000111000000000000000111000111111000000111000111111111000111000111
111000111000111111111111000111000000111000000000000000111111000111111000111000000111111000111111111000111000111000000111
111000111000111111111111000111000000111000000000000000111111000111111000111000000111111000111111111000111000111000000111
111000111000111111111111000111000000111000000000000000111111000111111000111000000111111000111111111000111000111000000111
111000111000111111111111000111000000111000000000000000111111000111111000111000000111111000111111111000111000111000000111
111000111000111111111111000111000000111000000000000000111111000111111000111000000111111000111111111000111000111000000111
000000111111111111111111111000000000000111000111000000000111111111000000111000000000000000111000111000000000111111111111
000000111111111111111111111000000000000111000111000000000111111111000000111000000000000000111000111000000000111111111111
000000111111111111111111111000000000000111000111000000000111111111000000111000000000000000111000111000000000111111111111
000000111111111111111111111000000000000111000111000000000111111111000000111000000000000000111000111000000000111111111111
000000111111111111111111111000000000000111000111000000000111111111000000111000000000000000111000111000000000111111111111
000111111000111111111111000111000111111111111000111111111111000000000111111000111000111000111111111000111000000000111000
000111111000111111111111000111000111111111111000111111111111000000000111111000111000111000111111111000111000000000111000
000111111000111111111111000111000111111111111000111111111111000000000111111000111000111000111111111000111000000000111000
000111111000111111111111000111000111111111111000111111111111000000000111111000111000111000111111111000111000000000111000
000111111000111111111111000111000111111111111000111111111111000000000111111000111000111000111111111000111000000000111000
000000111111111000111000111000111111111111000000111111000111111000000111000000111000000111000000111111111000111111000111
000000111111111000111000111000111111111111000000111111000111111000000111000000111000000111000000111111111000111111000111
000000111111111000111000111000111111111111000000111111000111111000000111000000111000000111000000111111111000111111000111
000000111111111000111000111000111111111111000000111111000111111000000111000000111000000111000000111111111000111111000111
000000111111111000111000111000111111111111000000111111000111111000000111000000111000000111000000111111111000111111000111
111111000000111111000000000111111000111000111111000000000000111000111000000000000111111000000111000111111111000000111000
111111000000111111000000000111111000111000111111000000000000111000111000000000000111111000000111000111111111000000111000
111111000000111111000000000111111000111000111111000000000000111000111000000000000111111000000111000111111111000000111000
111111000000111111000000000111111000111000111111000000000000111000111000000000000111111000000111000111111111000000111000
111111000000111111000000000111111000111000111111000000000000111000111000000000000111111000000111000111111111000000111000
111111000000111111111111000111111111000000000000111000111000111000111111111111000111111111111000000000000111111111000111
111111000000111111111111000111111111000000000000111000111000111000111111111111000111111111111000000000000111111111000111
111111000000111111111111000111111111000000000000111000111000111000111111111111000111111111111000000000000111111111000111
111111000000111111111111000111111111000000000000111000111000111000111111111111000111111111111000000000000111111111000111
111111000000111111111111000111111111000000000000111000111000111000111111111111000111111111111000000000000111111111000111
111000111111000111111111111000000000000111111111000111000111111000111111000111111111111111111000111000111000111000111000
111000111111000111111111111000000000000111111111000111000111111000111111000111111111111111111000111000111000111000111000
111000111111000111111111111000000000000111111111000111000111111000111111000111111111111111111000111000111000111000111000
111000111111000111111111111000000000000111111111000111000111111000111111000111111111111111111000111000111000111000111000
111000111111000111111111111000000000000111111111000111000111111000111111000111111111111111111000111000111000111000111000
000111111111111000000111000111111111111000000111000111000111111111111000111000000000000000111000111000111000000000000000
000111111111111000000111000111111111111000000111000111000111111111111000111000000000000000111000111000111000000000000000
000111111111111000000111000111111111111000000111000111000111111111111000111000000000000000111000111000111000000000000000
000111111111111000000111000111111111111000000111000111000111111111111000111000000000000000111000111000111000000000000000
000111111111111000000111000111111111111000000111000111000111111111111000111000000000000000111000111000111000000000000000
111111111000111000111111111111000000111111111000111111111111111000000111000111111000111111111000000000000000000111111000
111111111000111000111111111111000000111111111000111111111111111000000111000111111000111111111000000000000000000111111000
111111111000111000111111111111000000111111111000111111111111111000000111000111111000111111111000000000000000000111111000
111111111000111000111111111111000000111111111000111111111111111000000111000111111000111111111000000000000000000111111000
111111111000111000111111111111000000111111111000111111111111111000000111000111111000111111111000000000000000000111111000
111000000000111111000111111111000000111000111111000111000111000111000111111000111000000000000111000000111000000111111111
111000000000111111000111111111000000111000111111000111000111000111000111111000111000000000000111000000111000000111111111
111000000000111111000111111111000000111000111111000111000111000111000111111000111000000000000111000000111000000111111111
111000000000111111000111111111000000111000111111000111000111000111000111111000111000000000000111000000111000000111111111
111000000000111111000111111111000000111000111111000111000111000111000111111000111000000000000111000000111000000111111111
111111111000000111000000000000111000111111111000000000000000111000111111111000111111111000000000000111111000000111000000
111111111000000111000000000000111000111111111000000000000000111000111111111000111111111000000000000111111000000111000000
111111111000000111000000000000111000111111111000000000000000111000111111111000111111111000000000000111111000000111000000
111111111000000111000000000000111000111111111000000000000000111000111111111000111111111000000000000111111000000111000000
111111111000000111000000000000111000111111111000000000000000111000111111111000111111111000000000000111111000000111000000
111111111000111000000111111111111000111000111000000111111111111111000111111111111111000111000111111111111000111111111000
111111111000111000000111111111111000111000111000000111111111111111000111111111111111000111000111111111111000111111111000
111111111000111000000111111111111000111000111000000111111111111111000111111111111111000111000111111111111000111111111000
111111111000111000000111111111111000111000111000000111111111111111000111111111111111000111000111111111111000111111111000
111111111000111000000111111111111000111000111000000111111111111111000111111111111111000111000111111111111000111111111000
000000000000000000000000111000111000111111000000000111000000111000111000111000000000000111111000111111000111111111111000
000000000000000000000000111000111000111111000000000111000000111000111000111000000000000111111000111111000111111111111000
000000000000000000000000111000111000111111000000000111000000111000111000111000000000000111111000111111000111111111111000
000000000000000000000000111000111000111111000000000111000000111000111000111000000000000111111000111111000111111111111000
000000000000000000000000111000111000111111000000000111000000111000111000111000000000000111111000111111000111111111111000
111000111000000111111000000111111111111000111000111111000111000111111111111000000000111111111000000000000000111111000111
111000111000000111111000000111111111111000111000111111000111000111111111111000000000111111111000000000000000111111000111
111000111000000111111000000111111111111000111000111111000111000111111111111000000000111111111000000000000000111111000111
111000111000000111111000000111111111111000111000111111000111000111111111111000000000111111111000000000000000111111000111
111000111000000111111000000111111111111000111000111111000111000111111111111000000000111111111000000000000000111111000111
000111111111000000111111000000000000111111000000111000111000000000000000000111000111000000000111000111000000000000111000
000111111111000000111111000000000000111111000000111000111000000000000000000111000111000000000111000111000000000000111000
000111111111000000111111000000000000111111000000111000111000000000000000000111000111000000000111000111000000000000111000
000111111111000000111111000000000000111111000000111000111000000000000000000111000111000000000111000111000000000000111000
000111111111000000111111000000000000111111000000111000111000000000000000000111000111000000000111000111000000000000111000