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>
using namespace std;
const int MAX = 501;

int n, cnt[MAX], res[MAX*MAX];
pair<int,int> x[MAX];
set<int> pos;
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin >> n;
	for(int i = 1; i <= n*n; i++) pos.insert(i);
	for(int i = 1; i <= n; i++) cnt[i] = n;
	for(int i = 1; i <= n; i++) {
		cin >> x[i].first;
		x[i].second = i;
	}
	sort(x+1, x+n+1);
	for(int i = 1; i <= n; i++) {
		if(x[i].first == x[i-1].first) cout << "No", exit(0);
		for(int j = 0; j < x[i].second-1; j++) {
			if(pos.empty() || *pos.begin() >= x[i].first) cout << "No", exit(0);
			res[*pos.begin()] = x[i].second;
			--cnt[x[i].second];
			pos.erase(pos.begin());
		}
		res[x[i].first] = x[i].second;
		--cnt[x[i].second];
		pos.erase(x[i].first);
	}
	for(int i = 1, j = 1; i <= n*n; i++) if(!res[i]) {
		while(j <= n && !cnt[x[j].second]) ++j;
		if(i <= x[j].first) cout << "No", exit(0);
		res[i] = x[j].second;
		--cnt[x[j].second];
	}
	cout << "Yes\n";
	for(int i = 1; i <= n*n; i++) cout << res[i] << ' ';
}