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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef pair<ll,ll> mp;
#define inf 1e9


int main(){
	int n;
	cin>>n;
	int k = 1;
	for(k=1;k<=n;k++){
		if(k*(k-1)/2 == n) break;
	}
	if(n == k*(k-1)/2 ){
		cout<<"Yes"<<endl;
		vector<vector<int> > s(k);
		int st = 1;
		cout<<k<<endl;
		for(int i=0;i<k-1;i++){
			for(int  j=0;j<k-1-i;j++){
				s[i].push_back(st);
				s[i+j+1].push_back(st);
				st++;
			}
		}
		for(int i=0;i<k;i++){
			cout<<s[i].size();
			for(int j=0;j<s[i].size();j++){
				cout<<' '<<s[i][j];
			}
			cout<<endl;
		}
	}else{
		cout<<"No"<<endl;
	}


	return 0;
}