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 N 509
using namespace std;

int n,m,a[N],ans[N*N],q[N];
void gg(){
	puts("No"); exit(0);
}
bool cmp(int x,int y){ return a[x]<a[y]; }
int main(){
	scanf("%d",&n); m=n*n;
	int i,j,k,l;
	for (i=1; i<=n; i++){
		scanf("%d",&a[i]);
		if (ans[a[i]]) gg(); ans[a[i]]=i;
	}
	for (i=1; i<=n; i++) q[i]=i;
	sort(q+1,q+n+1,cmp);
	for (l=1; l<=n; l++){
		i=q[l];
		for (j=1,k=1; j<a[i] && k<i; j++) if (!ans[j]){
			ans[j]=i; k++;
		}
		if (k<i) gg();
	}
	for (l=n; l; l--){
		i=q[l];
		for (j=m,k=n; j>a[i] && k>i; j--) if (!ans[j]){
			ans[j]=i; k--;
		}
		if (k>i) gg();
	}
	puts("Yes");
	for (i=1; i<=m; i++) printf("%d%c",ans[i],(i<m)?' ':'\n');
	return 0;
}