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>
inline int Get() {
	char ch;
	while ((ch = getchar()) < '0' || ch > '9');
	int Num = ch - '0';
	while ((ch = getchar()) >= '0' && ch <= '9')
		Num = (Num << 3) + (Num << 1) + ch - '0';
	return Num;
}
const int N = 505;
int n, a[N], g[N * N], id[N], cur;
inline bool cmp(const int &x, const int &y) {
	return a[x] < a[y];
}
int main() {
	n = Get();
	for (int i = 1; i <= n; ++i) a[i] = Get(), id[i] = i;
	
	std :: sort(id + 1, id + n + 1, cmp);
	cur = 1;
	for (int i = 1, k; k = id[i], i <= n; ++i) {
		for (int j = 1; j < k; ++j) {
			while (g[cur]) ++cur;
			g[cur] = k;
		}
		
		if (cur > a[k] || g[a[k]]) {
			puts("No");
			return 0;
		}
		
		g[a[k]] = k;
	}
	
	for (int i = 1, k; k = id[i], i <= n; ++i) {
		for (int j = 1; j <= n - k; ++j) {	
			while (g[cur]) ++cur;
			if (cur < a[k]) {
				puts("No");
				return 0;
			}
			g[cur] = k;
		}
	}
	
	puts("Yes");
	for (int i = 1; i <= n * n; ++i) printf("%d ", g[i]);
}