Problem:
Score : 500 points

Problem Statement

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:

Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.

Any two of the sets S_1,S_2,...,S_k have exactly one element in common.

If such a tuple exists, construct one such tuple.

Constraints

1 \leq N \leq 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

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.

Sample Input 1

3

Sample Output 1

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.

Sample Input 2

4

Sample Output 2

No

Solution in Python (3.4.3) (judge verdict: Accepted)

#!/usr/bin/env python3
from collections import deque, Counter
from heapq import heappop, heappush
from bisect import bisect_right

def main():
    N = int(input())
    if N == 1:
        print('Yes')
        print(2)
        print(1,1)
        print(1,1)
        exit()
    i = 3
    l = 2
    while i <= 10**5:
        if i == N:
            break
        else:
            l += 1
            i += l
    else:
        print('No')
        exit()

    # 長さl, k = 2N/l個の配列が答え
    ans = [[1,2],[2,3],[3,1]]
    now = 3# 今使ってる最大の数字
    M = 2# 今の長さ
    k = 2*N//l
    while M < l:
        for j in range(M+1):
            ans[j].append(now+1+j)
        ans.append(list(range(now+1,now+2+M)))
        now += M+1
        M += 1
    print('Yes')
    print(k)
    for i in range(k):
        print(l,*ans[i])



if __name__ == "__main__":
    main()