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>
int n,as[300007];
struct pos{
	int w,p;
	bool operator<(const pos&w)const{return p<w.p;}
}ps[555];
int main(){
	scanf("%d",&n);
	for(int i=1,x;i<=n;++i){
		scanf("%d",&x);
		as[x]=i;
		ps[i]=(pos){i,x};
	}
	std::sort(ps+1,ps+n+1);
	int L=1,R=n*n;
	for(int i=1;i<=n;++i){
		for(int j=ps[i].w-1,p=ps[i].p;j;--j){
			while(L<=p&&as[L])++L;
			if(L>p)return puts("No"),0;
			as[L]=ps[i].w;
		}
	}
	for(int i=n;i;--i){
		for(int j=n-ps[i].w,p=ps[i].p;j;--j){
			while(R>=p&&as[R])--R;
			if(R<p)return puts("No"),0;
			as[R]=ps[i].w;
		}
	}
	puts("Yes");
	for(int i=1;i<=n*n;++i)printf("%d ",as[i]);
	return 0;
}