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;

#define WA {puts("No");return 0;}
#define MAXN 501

struct Data
{
	int id,v;
	bool operator<(const Data &d)const
	{
		return v<d.v;
	}
}data[MAXN];

int num[MAXN*MAXN],pos=1,n;

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
	{
		scanf("%d",&data[i].v);
		num[data[i].v]=i;
		data[i].id=i;
	}
	sort(data+1,data+n+1);
	for(int i=1;i<=n;++i)
	{
		int cnt=1;
		while(cnt<data[i].id)
		{
			while(num[pos]!=0)++pos;
			num[pos]=data[i].id;
			++cnt;
		}
		if(pos>data[i].v)WA
	}
	pos=n*n;
	for(int i=n;i>=1;--i)
	{
		int cnt=0;
		while(cnt<n-data[i].id)
		{
			while(num[pos]!=0)--pos;
			num[pos]=data[i].id;
			++cnt;
		}
		if(pos<data[i].v)WA
	}
	puts("Yes");
	for(int i=1;i<=n*n;++i)printf("%d ",num[i]);
	puts("");
}