Solution to the first problem of the Prologin 2012 selections in Spoon
0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0