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<algorithm>
#include<iostream>
#include<vector>
#include<string>
#include<cstring>
#include<utility>
#include<queue>
#include<cmath>
using namespace std;
#define REP(i, a,b) for(i=a;i<b;i++) 
#define REP1(i,b,a) for(i=b-1;i>=a;i--)
#define output(x) cout<<x<<endl;
#define pb(x) push_back(x);
typedef long long int ll;
const int MAX = 510000;
const int MOD = 1000000007;


int main()
{
	ll i, j, k, l, m, sum, flag, N, M;
	sum = 0;
	flag = 0;
	cin >> N;
	ll s[40][40];
	REP(i, 1, N*2) {
		if (i*(i - 1) == 2*N) {
			flag = 1;
			break;
		}
	}
	k = i;
	if (flag == 0) {
		output("No");
	}
	else {
		output("Yes");
		output(k);
		ll z;
		z = 1;
		REP(i, 1, k + 1) {
			REP(j, 0, k - i) {
				s[i][j + i] = z;
				s[i + j+1][i] = z;
				z++;
			}
		}
		
		REP(i, 1, k + 1) {
			cout << k - 1 << " ";
			REP(j, 1, k) {
				cout << s[i][j] << " ";
			}
			cout << endl;
		}
	}
    return 0;
}