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 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main()
{
	int N;
	scanf("%d", &N);

	int i, j, k, n, p[1000] = {};
	for (n = 1; n * (n + 1) / 2 < N; n++);
	if (n * (n + 1) / 2 > N) printf("No\n");
	else {
		printf("%d\n%d", n + 1, n);
		for (j = 1; j <= n; j++) printf(" %d", j);
		for (i = 1, k = n + 1; i <= n; i++) {
			printf("\n%d %d", n, i);
			for (j = 2; j <= n - i + 1; j++) printf(" %d", k++);
			p[i] = k - 1;
			for (j = 1; j < i; j++) printf(" %d", p[j]--);
		}
		printf("\n");
	}
	fflush(stdout);
	return 0;
}