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>
#define maxn 500009
using namespace std;
int n;
int a[maxn];
int ans[maxn];
int cnt[maxn];
bool mark[maxn];
deque<int>Q;
bool solve(){
	for(int i=1;i<=n*n;i++){
		if(ans[i]){
			for(int j = 0;j<n-ans[i];j++)
				Q.push_back(ans[i]);
			continue;
		}
		else{
			if(Q.empty())
				return 0;
			int u = Q.front();
			Q.pop_front();
			ans[i]=u;
		}
	}
	for(int i=1;i<=n*n;i++){
		cnt[ans[i]]++;
		if(mark[i] && cnt[ans[i]] != ans[i])
			return 0;
	}
	return 1;
}
int main(){
	cin >> n;
	for(int i=1;i<=n;i++){
		cin>>a[i];
	}
	for(int i=1;i<=n;i++){
		ans[a[i]]=i;
		mark[a[i]]=1;
	}
	
	for(int i = 1;i <= n*n;i++){
		if(ans[i] == 0)
			continue;
		for(int j = 0; j< ans[i]-1;j++)
			Q.push_back(ans[i]);
	}

	if(!solve())
		puts("No");
	else{
		puts("Yes");
		for(int i=1;i<=n*n;i++)
			printf("%d ",ans[i]);
	}
	//system("pause");
	return 0;
}