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<cstdio>
#include<algorithm>
using namespace std;
int n,x[505],a[250005],st[250005],top,now;
bool check[250005];
struct sd{int w,pos;bool operator < (const sd &fu) const {return pos<fu.pos;};}in[505];
int main() {
	scanf("%d",&n);for(int i=1;i<=n;++i) {scanf("%d",&x[i]);a[x[i]]=i;in[i]=(sd){i,x[i]};check[x[i]]=true;}
	sort(in+1,in+1+n);for(int i=1;i<=n*n;++i) if(!check[i]) st[++top]=i;
	for(int i=1;i<=n;++i) {
		for(int j=1;j<in[i].w;++j) a[st[++now]]=in[i].w;
		if(st[now]>in[i].pos) {printf("No");return 0;}
	}st[++top]=2147483647;
	for(int i=n;i;--i) {
		for(int j=n;j>in[i].w;--j) a[st[--top]]=in[i].w;
		if(st[top]<in[i].pos) {printf("No");return 0;}
	}
	puts("Yes");
	for(int i=1;i<=n*n;++i) printf("%d ",a[i]);
	return 0;
}