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;
const int N=550,M=250250;
int i,j,k,n,m;
int a[N],ans[M],l[M],r[M];
struct cc {
	int x,p;
	bool operator < (const cc &n) const {
		return p<n.p;
	}
} A[N];
int main() {
	scanf("%d",&n);
	m=n*n;
	for (i=1;i<=n;i++) {
		scanf("%d",&a[i]);
		A[i].x=i;
		A[i].p=a[i];
	}
	sort(A+1,A+n+1);
	for (i=1;i<=m;i++) r[i]=i+1,l[i]=i-1;
	r[0]=1;l[m+1]=m;
	for (i=1;i<=n;i++) {
		for (j=r[0],k=1;k<A[i].x;k++,j=r[j]) {
			ans[j]=A[i].x;
			r[l[j]]=r[j];
			l[r[j]]=l[j];
			if (j>=A[i].p) return puts("No"),0;
		}
		ans[A[i].p]=A[i].x;
		r[l[A[i].p]]=r[A[i].p];
		l[r[A[i].p]]=l[A[i].p];
	}
	for (i=n;i;i--) {
		for (j=l[m+1],k=n;k>A[i].x;k--,j=l[j]) {
			ans[j]=A[i].x;
			r[l[j]]=r[j];
			l[r[j]]=l[j];
			if (j<=A[i].p) return puts("No"),0;
		}
	}
	puts("Yes");
	for (i=1;i<=m;i++) printf("%d ",ans[i]);
	puts("");
}