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;
int main() {
	int N;
	cin >> N;
	vector<int> X(N);
	for (auto& x : X) cin >> x;
	vector<int> ans(N*N);
	bool ok = true;
	vector<pair<int,int>> a;
	for (int i = 0; i < N; ++ i) a.push_back({X[i], i+1});
	sort(a.begin(), a.end());
	for (auto p : a) {
		int xi = p.first;
		int i = p.second;
		ans[xi-1] = i;
		int k = 0;
		for (int j = 1; j < i; ++ j) {
			for (;;) {
				if (k >= xi-1) {
					ok = false;
					goto out;
				}
				if (ans[k] == 0) break;
				++ k;
			}
			ans[k] = i;
		}
	}
	for (auto p : a) {
		int xi = p.first;
		int i = p.second;
		int k = xi;
		for (int j = i; j < N; ++ j) {
			for (;;) {
				if (k >= ans.size()) {
					ok = false;
					goto out;
				}
				if (ans[k] == 0) break;
				++ k;
			}
			ans[k] = i;
		}
	}
	out:;
	if (ok) {
		cout << "Yes" << endl;
		for (int i = 0; i < ans.size(); ++ i) {
			if (i) cout << " ";
			cout << ans[i];
		}
		cout << endl;
	} else {
		cout << "No" << endl;
	}
}