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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>

main() {
	long long int n, i;
	long long int memo;
	long long int s[500][501] = {};
	int fir = 1, sec = 2, check = 1, check2 = 1;
	int not[1000] = {};
	scanf("%d", &n);
	for (int i = 1; i < 500; i++) {
		if (i*(i + 1) == n * 2) {
			memo = i;
			goto next;
		}
	}
	printf("No");
	return 0;


	next:

	
	for (int i = 1; i <= memo + 1; i++) {
		if (i >= 2) {
			s[i][i - 1] = s[i - 1][i - 1];
			not[check] = s[i - 1][i - 1];
			check++;
		
		}
	

		for (int j = i; j <= memo; j++) {
			s[i][j] = fir;
			fir++;
		}
		for (int j = 1; j <= i - 2;j++) {
			if (sec == not[check2]) {
				sec++;
				check2++;
			}
			s[i][j] = sec;
          sec++;
		}

	}
	printf("Yes\n");
   printf("%d\n", memo+1);
	for (int i = 1; i <= memo + 1; i++) {
		printf("%d ", memo);
		for (int j = 1; j <= memo; j++) {
			printf("%d ", s[i][j]);
		}
		printf("\n");
	}
	return 0;
}