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;

#define N 300000

int n,f[N],ans[N];

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;++i){
		int x; scanf("%d",&x); f[x]=i;
	}
	for (int i=1,j=1;i<=n*n;++i){
		if (f[i]){
			ans[i]=f[i];
			for (int k=1;k<f[i];++k){
				for (;ans[j];++j);
				ans[j]=f[i];
			}
			if (j>i){puts("No"); return 0;}
		}
	}
	for (int i=n*n,j=n*n;i;--i){
		if (f[i]){
			for (int k=f[i]+1;k<=n;++k){
				for (;ans[j];--j);
				ans[j]=f[i];
				if (j<i){puts("No"); return 0;}
			}
		}
	}
	puts("Yes");
	for (int i=1;i<=n*n;++i) printf(i==n*n?"%d\n":"%d ",ans[i]);
	
	return 0;
}