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],c[maxn],a[maxn*maxn];

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&x[i]);
	bool ER = 0;
	for(int i=1;i<=n*n;i++){
		for(int j=1;j<=n;j++) if(x[j] == i){
			c[j] ++;
			if(c[j] != j){
				ER = 1;
			}
			a[i] = j;
			break;
		}
		if(!a[i]){
			int p=0 , lc = n*n+2;
			for(int j=1;j<=n;j++) if(c[j] < j-1 && x[j] > i){
				if(x[j] < lc){
					lc = x[j];
					p = j;
				}
			}
			if(p){
				a[i] = p ,
				c[p] ++;
			}
		}
	}
	for(int i=n*n;i>=1;i--)if(!a[i]){
		if(!a[i]){
			int p=0 , lc = 0;
			for(int j=1;j<=n;j++) if(c[j] < n && x[j] < i){
				if(x[j] > lc){
					lc = x[j];
					p = j;
				}
			}
			if(p){
				a[i] = p ,
				c[p] ++;
			}
			else{
				ER = 1;
			}
		}
	}
	
	if(ER){
		puts("No");
	}
	else{
		puts("Yes");
		for(int i=1;i<=n*n;i++) printf("%d%c",a[i]," \n"[i==n*n]);
	}
}