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 <stdio.h>
#include <algorithm>
#define N 500
using namespace std;

int a[N + 5], p[N + 5], b[N * N + 5] = {0};

void write(int x)
{
	if(x < 10){
		putchar(x + 48);
		return;
	}
	write(x / 10);
	putchar(x % 10 + 48);
}

int cmp(int x, int y)
{
	return a[x] < a[y];
}

int next(int i)
{
	for(i++; b[i]; i++);
	return i;
}

int main()
{		
	int n, i, head = 1, j, x, t;
	
	scanf("%d", &n);
	for(i = 1; i <= n; i++){
		scanf("%d", a + i);
		p[i] = i;
	}
	sort(p + 1, p + n + 1, cmp);
	
	for(i = 1; i <= n; i++){
		x = p[i], t = a[x];
		for(j = 1; j < x; j++){
			if(head >= t){
				puts("No");
				return 0;
			}
			b[head] = x;
			head = next(head);
		}
		if(head == t) head = next(head);
		b[t] = x;
	}
	for(i = 1; i <= n; i++){
		x = p[i], t = a[x];
		for(j = x + 1; j <= n; j++){
			if(head > t) b[head] = x;
			else{
				puts("No");
				return 0;
			}
			head = next(head);
		}
	}
	puts("Yes");
	write(b[1]);
	for(i = 2, t = n * n; i <= t; i++){
		putchar(32), write(b[i]);
	}
	puts("");
			
	return 0;
}