Score : 500 points
You are given an integer N. Determine if there exists a tuple of subsets of \{1,2,...N\}, (S_1,S_2,...,S_k), that satisfies the following conditions:
If such a tuple exists, construct one such tuple.
Input is given from Standard Input in the following format:
N
If a tuple of subsets of \{1,2,...N\} that satisfies the conditions does not exist, print No
.
If such a tuple exists, print Yes
first, then print such subsets in the following format:
k |S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|} : |S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}
where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.
If there are multiple such tuples, any of them will be accepted.
3
Yes 3 2 1 2 2 3 1 2 2 3
It can be seen that (S_1,S_2,S_3)=(\{1,2\},\{3,1\},\{2,3\}) satisfies the conditions.
4
No