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 C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<cstdio>
#include<string>
#include<iostream>
#include<vector>

using namespace std;

int n=0,m=1,c=0,ip;
int q[100][100];

int main(){
    scanf("%d",&ip);
    for(int i=1;c<=10000;i++){
        c+=i;
        if(c==ip)n=i;
    }
    if(n){
        printf("Yes\n");
        printf("%d\n",n+1);
        for(int i=0;i<=n;i++){
            printf("%d ",n);
            for(int e=0;e<n;e++){
                if(e<i){
                    q[i][e]=q[e][i-1]+0;
                }
                else{
                    q[i][e]=m;
                    m+=1;
                }
                printf("%d ",q[i][e]);
            }
            printf("\n");
        }
    }
    else printf("No\n");
}