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;
typedef long long ll;

int cnt[1005];
int x[1005];
int huix[1005];
int a[1000000];

int main()
{
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++)
    {
        cin >> x[i];
        huix[i] = x[i];
        a[x[i]] = i;
    }

    sort(x + 1, x + n + 1);

    int it = 1;
    for (int i = 1; i <= n; i++)
    {
        int k = a[x[i]];
        for (int j = 1; j < k; j++)
        {
            while(a[it] != 0) it++;
            a[it] = k;
        }
    }

    it = 1;
    for (int i = 1; i <= n; i++)
    {
        int k = a[x[i]];
        for (int j = n; j > k; j--)
        {
            while(a[it] != 0) it++;
            a[it] = k;
        }
    }

    for (int i = 1; i <= n*n; i++)
    {
        int k = a[i];
        cnt[k]++;
        if (cnt[k] == k && i != huix[k])
        {
            cout << "No";
            return 0;
        }
    }

    cout << "Yes" << endl;
    for (int i = 1; i <= n*n; i++) cout << a[i] << " ";

    return 0;
}