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;

int main() {
  int n; cin>>n;
  
  int k=-1;
  for (int i=1; i<=n; i++) {
    if ((i*(i+1))==2*n) {
      k=i;
      break;
    }
  }
  if (k==-1) cout<<"No"<<endl;
  else {
    vector<vector<int>> res(k+1, vector<int>(k, 0));
    int cnt=1;
    for (int i=0; i<k; i++) {
      for (int j=i; j<k; j++) {
        res[i][j]=cnt;
        res[j+1][i]=cnt;
        cnt++;
      }
    }
    cout<<"Yes"<<endl;
    cout<<k+1<<endl;
    for (int i=0; i<=k; i++) {
      cout<<k<<" ";
      for (int j=0; j<k; j++) {
        if (j) cout<<" ";
        cout<<res[i][j];
      }
      cout<<endl;
    }
  }
}