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>
#define maxn 505
using namespace std;
int n,x[maxn],a[maxn*maxn],c[maxn];
bool solve(){
	for(int i=1;i<=n*n;i++){
		for(int j=1;j<=n;j++) if(x[j]==i){
			if(++c[j]<j) return 0;
			a[i]=j; break;
		}
		if(a[i]) continue;
		int k=0;
		for(int j=1;j<=n;j++) if(x[j]>i&&c[j]<j-1&&x[j]<x[k]) k=j;
		if(k) {c[a[i]=k]++;continue;}
		for(int j=1;j<=n;j++) if(x[j]<i&&c[j]<n) {k=j;break;}
		if(k) c[a[i]=k]++;
		else return 0;
	}
	return 1;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&x[i]); x[0]=n*n+1;
	if(!solve()) return puts("No"),0;
	puts("Yes");
	for(int i=1;i<=n*n;i++) printf("%d%c",a[i],i==n*n?10:32);
}