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: Accepted)

#include <bits/stdc++.h>
using namespace std;



// last submission

typedef long long  int ll;
#define s(n) scanf("%lld",&n)
#define s2(n,m) scanf("%lld%lld",&n,&m)
int ans[1003][1003],con[1003];
int main()
{

    int n;
    cin>>n;
    int z,x,y;
    for(int i=1; i<=n; i++)
    {
        z = (i*(i+1))/2;
        if(z==n)
        {
            x = i;
            y= x+1;
            break;
        }

        if(z>n)
        {
            puts("No");
            return 0;
        }

    }


    for(int i=1; i<=x; i++)
        ans[1][i] = i,ans[i+1][1] = i;

    for(int i=1; i<=y; i++) con[i] = 2;
    int i,j,v = x+1;
    i = 2;
    j = 3;
    while(v<=n)
    {
        ans[i][con[i]++] = ans[j][con[j]++] = v++;
        j++;
        if(con[i]>x) i++,j=i+1;

    }

    printf("Yes\n%d\n",y);

    for(int i=1; i<=y; i++)
    {
        printf("%d",x);

        for(int j = 1; j<=x; j++)
            printf(" %d",ans[i][j]);

        printf("\n");
    }






}