Problem: 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.

Examples

Input

3


Output

Yes
3
2 1 2
2 3 1
2 2 3


Input

4


Output

No

Solution (in CPP):

Solution:
#include <iostream>
#include <cmath>

using namespace std;

int main() {
  int N; cin >> N;
  int k = (1 + sqrt(1 + 8 * N)) / 2;
  if (2 * N != k * (k - 1)) {
    cout << "No" << endl;
    return 0;
  }
  cout << "Yes" << endl;
  cout << k << endl;
  cout << k - 1;
  for (int i = N - k + 2; i <= N; i++) cout << " " << i;
  cout << endl;

  for (int i = 1; i < k; i++) {
    cout << k - 1;
    int j = i * (i - 1) / 2 + 1;
    int l = i;
    bool downward = true;
    while (j != (k - i) * (k - i + 1) / 2) {
      cout << " " << j;
      if (j >= N - k + 2 && j <= N) downward = false;
      if (downward) {
        j += l + 1;
        l++;
      } else {
        j -= l - 1;
        l--;
      }
    }
    cout << " " << j << endl;
  }
}