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>

const int N=505;
int n,a[N],b[N],c[N*N];

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",a+i),c[a[i]]=b[i]=i;
	std::sort(b+1,b+n+1,[](int x,int y){return a[x]<a[y];});
	for(int i=1,p=1;i<=n;++i)
	{
		for(int j=1;j<b[i];c[p]=b[i],++j)while(c[p])++p;
		if(p>a[b[i]])return puts("No"),0;
	}
	for(int i=n,p=n*n;i>=1;--i)
	{
		for(int j=b[i]+1;j<=n;c[p]=b[i],++j)while(c[p])--p;
		if(p<a[b[i]])return puts("No"),0;
	}
	puts("Yes");
	for(int i=1;i<=n*n;++i)printf("%d%c",c[i],i==n*n?'\n':' ');
	return 0;
}