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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
#define N 505
int pos[N],id[N],ans[N*N];
bool cmp(int x,int y){return pos[x]<pos[y];}
int main()
{
	int n,i,j,k,x;
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		scanf("%d",&pos[i]);
		id[i]=i;ans[pos[i]]=i;
	}
	sort(id+1,id+n+1,cmp);
	k=1;
	for(i=1;i<=n;i++){
		x=id[i];
		for(j=1;j<x;j++){
			while(ans[k])k++;
			if(k>pos[x]){printf("No\n");return 0;}
			ans[k]=x;
		}
	}
	for(i=1;i<=n;i++){
		x=id[i];
		for(j=x+1;j<=n;j++){
			while(ans[k])k++;
			if(k<pos[x]){printf("No\n");return 0;}
			ans[k]=x;
		}
	}
	printf("Yes\n%d",ans[1]);
	for(i=2;i<=n*n;i++)
		printf(" %d",ans[i]);
}