Problem: You are given an integer sequence x of length N. Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.

* a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.
* For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.

Constraints

* 1 ≤ N ≤ 500
* 1 ≤ x_i ≤ N^2
* All x_i are distinct.

Input

The input is given from Standard Input in the following format:


N
x_1 x_2 ... x_N


Output

If there does not exist an integer sequence a that satisfies all the conditions, print `No`. If there does exist such an sequence a, print `Yes` in the first line, then print an instance of a in the second line, with spaces inbetween.

Examples

Input

3
1 5 9


Output

Yes
1 1 1 2 2 2 3 3 3


Input

2
4 1


Output

No

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

using namespace std;

void fail()
{
  cout << "No" << endl;
  exit(0);
}

int main()
{
  int N, X[500];
  int Z[250000], ev[250000];
  memset(Z, -1, sizeof(Z));
  memset(ev, -1, sizeof(ev));

  cin >> N;
  for(int i = 0; i < N; i++) {
    cin >> X[i];
    --X[i];
    ev[X[i]] = i + 1;
  }

  queue< int > unhappy, happy;

  for(int i = 0; i < N * N; i++) {
    if(~ev[i]) {
      if(ev[i] - 1 > unhappy.size()) fail();
      for(int j = 0; j < ev[i] - 1; j++) {
        Z[unhappy.front()] = ev[i];
        unhappy.pop();
      }
      Z[i] = ev[i];
    } else unhappy.push(i);
  }
  
  for(int i = N * N - 1; i >= 0; i--) {
    if(~ev[i]) {
      if(N - ev[i] > happy.size()) fail();
      for(int j = 0; j < N - ev[i]; j++) {
        Z[happy.front()] = ev[i];
        happy.pop();
      }
    } else if(Z[i] == -1) happy.push(i);
  }

  cout << "Yes" << endl;
  for(int i = 0; i < N * N; i++) {
    cout << Z[i] << " ";
  }
  cout << endl;

}