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>

int main() {
	int N;
    scanf("%d\n",&N);
	int j = 0;
	int size, number;
	for (int i = 0;i <= N;i++)
		if (2 * N == i * (i - 1)) {
			j = 1;
			number = i;
			size = (2 * N) / number;
			break;
		}
	if (j == 0)
		 printf("No") ;
	else {
		printf("Yes\n");
		int set[number][size];

		

		int i = 1;
		for (int l = 0;l < number;l++) {
                       int n=0;
			for (int k = 0;k < size;k++) {
				while(n<l) {
					set[l][k++] = set[n++][l - 1];
				}
				set[l][k] = i;
				i++;
			}
			printf("%d ", size);
			for (int m = 0;m < size;m++)
				printf("%d ", set[l][m]);
			printf("\n");
		}
	}
}