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;

struct node { int id,x; }h[510];

int a[250010],num[510],n;
bool bo[250010];

inline int rd()
{
	int x=0;char ch=getchar();
	for (;ch<'0'||ch>'9';ch=getchar());
	for (;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x;
}

inline bool cmp(node x,node y) { return x.id<y.id; }

int main()
{
	n=rd();
	for (int i=1;i<=n;i++) num[i]=rd();
	for (int i=1;i<=n;i++) h[i]=(node){num[i],i},bo[num[i]]=true,a[num[i]]=i;
	sort(h+1,h+n+1,cmp);
	int now=1;
	for (int i=1;i<=n;i++)
	{
		int hh=h[i].x-1;
		for (int j=1;j<=hh;j++)
		{
			while (bo[now]) now++;
			bo[now]=true;a[now]=h[i].x;now++;
		}
	}
	now=n*n;
	for (int i=n;i;i--)
	{
		int hh=n-h[i].x;
		for (int j=1;j<=hh;j++)
		{
			while (bo[now]) now--;
			bo[now]=true;a[now]=h[i].x;now--;
		}
	}
	for (int i=1;i<=n;i++)
	{
		int hh=0;
		for (int j=1;j<num[i];j++) if (a[j]==i) hh++;
		if (hh!=i-1) { puts("No");return 0; }
	}
	puts("Yes");
	for (int i=1;i<=n*n;i++) printf("%d ",a[i]);
	puts("");
	return 0;
}