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;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;

vector<int> v[1001];
int main(){
    int n;
    cin>>n;
    int k=-1;
    FOR(i,1,1001){
        if(i*(i-1)/2==n){
            k=i;
            break;
        }
    }
    if(k==-1){
        cout<<"No"<<endl;
        return 0;
    }
    cout<<"Yes"<<endl;
    cout<<k<<endl;
    int cur=0;
    FOR(i,1,k+1){
        FOR(j,i+1,k+1){
            v[i].pb(++cur);
            v[j].pb(cur);
        }
    }
    FOR(i,1,k+1){
        cout<<v[i].size()<<" ";
        rep(j,v[i].size()) cout<<v[i][j]<<" ";
        cout<<endl;
    }
    return 0;
}