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;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vll>;
using vc = vector<char>;
using vvc = vector<vc>;
using pll = pair<ll, ll>;
using stkll = vector<pll>;
const ll INF = 1LL << 60;
const ll MOD = 1e9 + 7;
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define debug(x) cerr << #x << ": " << x << endl;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

int main() {
    ll N;
    cin >> N;

    ll tmp = sqrt(2 * N);
    ll k;
    if (2 * N == tmp * (tmp - 1)) k = tmp;
    else if (2 * N == tmp * (tmp + 1)) k = tmp + 1;
    else {
        cout << "No" << endl;
        return 0;
    }

    ll a = 1;
    vvll ans(k);
    for(ll i = 0; i < k; i++) {
        for(ll j = i + 1; j < k; j++) {
            ans[i].push_back(a);
            ans[j].push_back(a);
            a++;
        }
    }

    cout << "Yes" << endl;
    cout << k << endl;
    rep(i, k) {
        cout << k-1;
        rep(j, k-1) {
            cout << " " << ans[i][j];
        }
        cout << endl;
    }
}