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,b[505*505];
struct note{
	int x,i;
}a[505];
bool cmp(note x,note y){
	return x.x<y.x;
}
void ex(){
	puts("No");
	exit(0);
}
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i].x),a[i].i=i;
	int N=n*n;
	std::sort(a+1,a+n+1,cmp); 
	for (int i=1;i<=n;i++){
		int now=1;
		for (int j=1;j<a[i].x && now<a[i].i;j++)
			if (!b[j]) b[j]=a[i].i,now++;
		b[a[i].x]=a[i].i;
		if (now<a[i].i) ex();
	}
	for (int i=n;i>=1;i--){
		int now=n;
		for (int j=N;j>=a[i].x && now>a[i].i;j--)
			if (!b[j]) b[j]=a[i].i,now--;
		if (now>a[i].i) ex();
	}
	puts("Yes"); 
	for (int i=1;i<=N;i++) printf("%d ",b[i]);
}