[[], [3], [3,3], [2], [2,2], [3,2], [3,3,2], [3,2,2], [3,3,2,2], [2,3,3], [2,3,3,2], [2,3,3,2,2], [1,2,3], [1,2,3,3], [1,2,3,3,3], [1,2,3,2], [1,2,3,2,2], [1,2,3,3,2], [1,2,3,3,3,2], [1,2,3,3,2,2], [1,2,3,3,3,2,2], [1,2,3,2,-3], [1,2,3,2,-3,2], [1,2,3,2,-3,2,2], [1,2,3,1,2,3], [1,2,3,1,2,3,3], [1,2,3,1,2,3,3,3], [1,2,3,1,2,3,2], [1,2,3,1,2,3,2,2], [1,2,3,1,2,3,3,2], [1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,3,3,2,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2], [1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,2,-3,2,2],