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 rep(i, N) for(int i=0;i<int(N);++i)
#define rep1(i, N) for(int i=1;i<int(N);++i)
#define all(a) (a).begin(),(a).end()
#define print(v) { cerr<<#v<<": [ "; for(auto _ : v) cerr<<_<<", "; cerr<<"]"<<endl; }
#define printpair(v) { cerr<<#v<<": [ "; for(auto _ : v) cerr<<"{"<<_.first<<","<<_.second<<"}"<<", "; cerr<<"]"<<endl; }
#define dump(x) cerr<<#x<<": "<<x<<endl;
#define bit(k) (1LL<<(k))
typedef long long ll;
typedef pair<int, int> i_i;
typedef pair<ll, ll> l_l;
template<class T> using vec = vector<T>;
template<class T> using vvec = vector<vec<T>>;

template<typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
    os << "{" << p.first << ", " << p.second << "}";
    return os;
}

template<class T>
inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

const int INF = (ll) 1e9;
const ll INFLL = (ll) 1e18 + 1;
const ll MOD = (ll) 1e9 + 7;
const double PI = acos(-1.0);

/*
const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
const string dir = "DRUL";
*/
ll a[1000][1000];

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    rep(i,1000)rep(j,1000)a[i][j] = -1;
    ll N;
    cin >> N;
    bool ok = false;
    ll cnt;
    for (ll x = 1; x * (x - 1) / 2 <= 2*N; x++) {
        if (x * (x - 1) / 2 == N) {
            ok = true;
            cnt = x;
            break;
        }
    }
    if (!ok) {
        cout << "No" << endl;
        return 0;
    }
    cout << "Yes" << endl;
    cout << cnt << endl;
    int c = 1;
    rep1(i, cnt + 1)
        rep1(j, cnt + 1) {
            if (i >= j)continue;
            a[i][j] = c;
            c++;
        }
    rep1(i, cnt + 1)
        rep1(j, cnt + 1) {
            chmax(a[i][j], a[j][i]);
        }
    rep1(i, cnt + 1) {
        cout << cnt - 1 << " ";
        rep1(j, cnt + 1) {
            if (i == j)continue;
            cout << a[i][j] << " ";
        }
        cout << endl;
    }
}