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=505,M=N*N;
int n,i,x,j,a[M];
struct arr{int x,k;}d[N];
bool operator < (arr A,arr B){return A.x<B.x;}
void write(int x){if (x>9) write(x/10);putchar(x%10+48);}
int main(){
	for (scanf("%d",&n),i=1;i<=n;i++)
		scanf("%d",&d[i].x),d[i].k=i;
	sort(d+1,d+n+1);x=1;
	for (i=1;i<=n;i++){
		int k=d[i].k,nx=d[i].x;
		for (j=k-1;j&&x<nx;j--){
			for (;a[x];x++);a[x]=k;
		}
		if (a[nx]){puts("No");return 0;}
		a[nx]=k;
	}
	for (x=n*n,i=n;i;i--){
		int k=d[i].k,nx=d[i].x;
		for (j=n-k;j&&x>nx;j--){
			for (;a[x];x--);a[x]=k;
		}
		if (k!=n&&x<=nx){puts("No");return 0;}
	}
	puts("Yes");
	for (i=1;i<=n*n;i++) write(a[i]),putchar(' ');
}