choose(0,0,1).
choose(1,0,1).
choose(1,1,1).
choose(2,0,1).
choose(2,1,2).
choose(2,2,1).
choose(3,0,1).
choose(3,1,3).
choose(3,2,3).
choose(3,3,1).
choose(3,4,0).
choose(4,0,1).
choose(4,1,4).
choose(4,2,6).
choose(4,3,4).
choose(4,4,1).
choose(5,0,1).
choose(5,1,5).
choose(5,2,10).
choose(5,3,10).
choose(5,4,5).
choose(5,5,1).
choose(6,0,1).
choose(6,1,6).
% choose(6,2,15).
% choose(6,3,20).
% choose(6,4,15).
% choose(6,5,6).
% choose(6,6,1).
