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 N=3e5+10;
int n,x[N],a[N];
typedef pair<int,int> pii;
priority_queue<pii,vector<pii>,greater<pii> > Q;
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++){
		scanf("%d",&x[i]);
		a[x[i]]=i;
		for (int j=1;j<i;j++) Q.push(pii(x[i],i));
	}
	for (int i=1;i<=n*n;i++)
	if (a[i]){
		int id=a[i];
		for (int j=0;j<n-id;j++) Q.push(pii(1e9,id));
	}
	else{
		if (Q.empty()) return puts("No"),0;
		if (i>Q.top().first) return puts("No"),0;
		a[i]=Q.top().second;
		Q.pop();
	}
	puts("Yes");
	for (int i=1;i<=n*n;i++) printf("%d ",a[i]);
	puts("");
	return 0;
}