Problem: 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.

Examples

Input

3


Output

Yes
3
2 1 2
2 3 1
2 2 3


Input

4


Output

No

Solution (in PYTHON3):

Solution:
import math
N=int(input())
kf = (math.sqrt(8*N+1)+1)/2
k = int(kf)
if k!=kf:
    print("No")
else:
    print("Yes")
    print(k)
    for i in range(1,k+1):
        print(k-1, end=' ')
        elements = []
        for j in range((i-1)*(i-2)//2+1,i*(i-1)//2+1):
            elements.append(j)
        for q in range(i+1,k+1):
            elements.append(i + (q-1)*(q-2)//2)
        last = elements.pop()
        for e in elements:
            print(e, end=' ')
        print(last)