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 <bits/stdc++.h>
using namespace std;
#define finish(x) return cout << x << endl, 0
#define ll long long

int n;
vector <int> ans[2000];

int s(int x){
    return x * (x - 1) / 2;
}
int f(int n){
    int sq = sqrt(n) - 5;
    sq = max(sq, 0);
    for(int i = sq ; ; i++){
        if(s(i) > n) break;
        if(s(i) == n) return i;
    }
    cout << "No" << endl;
    exit(0);
}
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cin >> n;
    int k = f(n);
    int cur = 1;
    for(int i = 1 ; i <= k ; i++){
        for(int j = i + 1 ; j <= k ; j++){
            ans[i].push_back(cur);
            ans[j].push_back(cur);
            cur++;
        }
    }
    cout << "Yes" << endl << k << endl;
    for(int i = 1 ; i <= k ; i++){
        cout << ans[i].size() << " ";
        for(auto &j : ans[i]) cout << j << " ";
        cout << endl;
    }
}