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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(n);i++)

bool ok[100150];
int ans[600][600];
using namespace std;

int main(void){
	cin.tie(0);
	ios::sync_with_stdio(false);
	int N,k=2,big=0;
	cin >> N;
	int cnt=1;
	int g = 2;
	vector<int> test;
	while(cnt+g<=N){
		ok[cnt+g] = 1;
		test.push_back(cnt+g);
		cnt = cnt+g;
		g++;
		k++;
		big= cnt + g;
	}
	ans[0][0] = 1;
	ans[0][1] = 2;
	ans[1][0] = 2;
	ans[1][1] = 3;
	ans[2][0] = 3;
	ans[2][1] = 1;
	int a = 4;
	for(int i=3;i<600;i++){
		for(int j=0;j<i;j++){
			ans[i][j] = a;
			a++;
		}
	}
	a = 4;
	for(int i=2;i<600;i++){
		for(int j=0;j<i+1;j++){
			ans[j][i] = a;
			a++;
		}
	}
	if(ok[N]){
		cout << "Yes" << endl;
		cout << k << endl;
		for(int i=0;i<k;i++){
			cout << k-1 << " ";
			for(int j=0;j<k-1;j++){
				cout << ans[i][j] <<" ";
			}
			cout << endl;
		}
	}else{
		cout << "No" << endl;
	}
}