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;
int x[510],a[250010],go[250010];
int main()
{
	int n,now=1;scanf("%d",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%d",&x[i]);
		if (go[x[i]]) {puts("No");return 0;}go[x[i]]=i;
	}
	sort(x+1,x+n+1);
	for (int i=1;i<=n;i++)
	{
		if (a[x[i]]) {puts("No");return 0;}a[x[i]]=i;while (a[now]) now++;
		int w=go[x[i]]-1;
		while (w)
		{
			if (now>x[i]) {puts("No");return 0;}
			a[now]=i;w--;
			now++;while (a[now]) now++;
		}
	}
	now=1;while (a[now]) now++;
	for (int i=1;i<=n;i++)
	{
		now=max(now,x[i]+1);while (a[now]) now++;
		int w=n-go[x[i]];
		while (w)
		{
			if (now>n*n) {puts("No");return 0;}
			a[now]=i;w--;
			now++;while (a[now]) now++;
		}
	}
	puts("Yes");
	for (int i=1;i<=n*n;i++) printf("%d ",go[x[a[i]]]);
}