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<iostream>
#include<algorithm>
using namespace std;
const int MAX=505;
int result[MAX*MAX];
int n;
pair<int,int> a[MAX];
int main()
{
	cin>>n;
	for(int i=1;i<=n;++i){
		cin>>a[i].first;
		a[i].second=i;
	}
	sort(a+1,a+n+1);
//	for(int i=1;i<=n;++i) cout<<a[i].second<<endl;
	for(int i=1;i<=n;++i){
		result[a[i].first]=a[i].second;
	}
	int curr=n*n;
	for(int i=n;i>=1;--i){
		int temp=n-a[i].second;
		while(temp>0){
			if(result[curr]==0){
				result[curr]=a[i].second;
				temp--;
				curr--;
			}
			else if(result[curr]==a[i].second){
				cout<<"No"<<endl;
				return 0;
			}
			else{
				curr--;
				continue;
			}
		}
	}
	curr=1;
	for(int i=1;i<=n;++i){
		int temp=a[i].second-1;
		while(temp>0){
			if(result[curr]==0){
				result[curr]=a[i].second;
				temp--;
				curr++;
			}
			else if(result[curr]==a[i].second){
				cout<<"No"<<endl;
				return 0;
			}
			else{
				curr++;
				continue;
			}
		}
	}
	cout<<"Yes"<<endl;
	for(int i=1;i<=n*n;++i) cout<<result[i]<<" ";
	return 0;
}