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;

const int maxn=250010;

int n,a[maxn],a0[maxn];

int main()
{
#ifdef h10
	freopen("D.in","r",stdin);
	freopen("D.out","w",stdout);
#endif
	int i,j,x,p;
	scanf("%d",&n);
	for (i=1;i<=n;i++)
		scanf("%d",&x),a0[x]=a[x]=i;

	for (i=p=1;i<=n*n;i++)
		if (a0[i])
		{
			int val=a0[i];
			for (j=1;j<val;j++)
			{
				while (a[p]) p++;
				a[p]=val;
			}
			if (p>i) {puts("No"); return 0;}
		}

	for (i=p=n*n;i>=1;i--)
		if (a0[i])
		{
			int val=a0[i];
			for (j=val;j<n;j++)
			{
				while (a[p]) p--;
				a[p]=val;
			}
			if (p<i) {puts("No"); return 0;}
		}

	puts("Yes");
	for (i=1;i<=n*n;i++)
		printf("%d ",a[i]);
}