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: Accepted)

#include <cstdio>
#include <iostream>
#include <string>
#include <algorithm>
#include <cstring>
#include <utility>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <cmath>
#include <deque>

using namespace std;
typedef long long LL;
typedef pair<int, int> pii;
const int MAXN = 123456;
vector<int> ans[MAXN];

int main() {
    int n;
    scanf("%d", &n);
    int tmp = n * 2;
    int k = sqrt(tmp);
    if (k * (k + 1) != tmp) return !printf("No\n");
    printf("Yes\n%d\n", k + 1);
    int cur = 1;
    for (int i = 1; i <= k + 1; i++) {
        printf("%d ", k);
        int cnt = 0;
        for (int j = 1; j < i; j++) {
            printf("%d ", ans[j].back());
            ans[j].pop_back();
            cnt++;
        }
        for (int j = 0; j < k - cnt; j++) {
            printf("%d ", cur);
            ans[i].push_back(cur++);
        }
        puts("");
    }

    return 0;
}