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: Accepted)

#include <bits/stdc++.h>
//#include <atcoder/all>
using namespace std;
//using namespace atcoder;
#define ll long long
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rep1(i, n) FOR(i, 1, n+1)
#define rrep(i, n) for (int i = ((int)(n)-1); i >= 0; --i)
#define whole(x) (x).begin(),(x).end()
#define rwhole(x) (x).rbegin(), (x).rend()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define P pair<int, int>
#define debug(var) cerr << "[" << #var << "] " << var << '\n'
template<typename T1, typename T2>
bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
template<typename T1, typename T2>
bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
#define vi vector<int>
#define vl vector<ll>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define pr(s) cout << (s) << '\n'
const ll mod = 1000000007;
const int dx[] = {-1,0,1,0};
const int dy[] = {0,-1,0,1};
const int INF = 1001001001;
const ll INFll = 1E+18;


int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int n;
    cin >> n;
    int now = 0;
    bool ok = false;
    int k = 1;
    while (now<n) {
        now += k;
        k++;
        if (now==n) {
            ok = true;
            break;
        }
    }
    if (!ok) {
        pr("No");
        return 0;
    }
    pr("Yes");
    pr(k);
    vector<vector<int>> ans(k);
    int x = 0;
    int y = 1;
    for (int i=1; i<=n; i++) {
        ans[x].pb(i);
        ans[y].pb(i);
        if (y+1<k) y++;
        else {
            x++;
            y = x + 1;
        }
    }
    rep(i, k) {
        cout << 2*n/k << " ";
        rep(j, 2*n/k) {
            cout << ans[i][j] << " ";
        }
        cout << endl;
    }
    return 0;
}