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 <cstdio>
#include <algorithm>
using namespace std;
 
#define iter(i, n) for (int i = 1; i <= n; ++i)
#define NR 510
 
int n, a[NR], tp[NR], ans[NR * NR];
 
bool cmp(int i, int j) {
	return a[i] < a[j];
}
 
int main() {
	scanf("%d", &n);
	iter(i, n) {
		scanf("%d", &a[i]);
		tp[i] = i;
	}
 
	sort(tp + 1, tp + n + 1, cmp);
 
	int tot = 0;
	int p = 0;
	iter(k, n) {
		int i = tp[k];
		if (tot + i > a[i]) {
			puts("No");
			return 0;
		}
		tot += i;
		iter(j, i - 1) {
			for (++p; ans[p] != 0; ++p);
			ans[p] = i;
		}
		ans[a[i]] = i;
	}
 
	iter(k, n) {
int i = tp[k];
		iter(j, n - i) {
			for (++p; ans[p] != 0; ++p);
			if (p < a[i]) {
				puts("No");
				return 0;
			}
			ans[p] = i;
		}
	}
 
	puts("Yes");
	iter(i, n * n) printf("%d ", ans[i]); puts("");
	return 0;
}