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=505,M=250005;
int n,m,l,r,x[N],a[M],id[N],num[N];
inline bool comp(const int&a,const int&b){return x[a]<x[b];}
inline void Assert(bool f){if(!f)puts("No"),exit(0);}

int main(){
	scanf("%d",&n),m=n*n;
	for(int i=1;i<=n;i++)scanf("%d",&x[i]),a[x[i]]=i,id[i]=i;
	for(l=1;a[l];l++);for(r=m;a[r];r--);sort(id+1,id+n+1,comp);
	for(int i=1;i<=n;i++){
		int k=id[i];
		for(int j=1;j<k;j++){
			Assert(l<x[k]);
			for(a[l]=k;a[l];l++);
		}
	}
	for(int i=n;i>=1;i--){
		int k=id[i];
		for(int j=k+1;j<=n;j++){
			Assert(r>x[k]);
			for(a[r]=k;a[r];r--);
		}
	}
	puts("Yes");
	for(int i=1;i<=m;i++)printf("%d%c",a[i]," \n"[i==m]);
	return 0;
}