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>
#include <array>
using namespace std;

#define rep(i, n) for(int i = 0; i < (n); i++)
using LL = long long;
using ULL = unsigned long long;


void solve() {
	int n; cin >> n;
	pair<int, int> x[500]; rep(i, n) { x[i].second = i + 1; cin >> x[i].first; }
	sort(x, x + n);

	vector<int> buf;
	buf.resize(n*n);
	size_t p = 0;
	rep(i, n) {
		int k = x[i].second;
		size_t kp = x[i].first - 1;
		for (int j = 0; j < k - 1; j++) {
			for (; buf[p] != 0; p++) {
				if (p == kp) {
					cout << "No" << endl; return;
				}
			}
			buf[p] = k;
		}
		buf[kp] = k;
	}
	rep(i, n) {
		int k = x[i].second;
		size_t kp = x[i].first - 1;
		for (int j = 0; j < n - k; j++) {
			for (; buf[p] != 0; p++) {}
			if (p < kp) {
				cout << "No" << endl; return;
			}
			buf[p] = k;
		}
	}

	cout << "Yes" << endl;
	rep(i, buf.size()) {
		if (i != 0) cout << " ";
		cout << buf[i];
	}
}

int main() {

	solve();

	return 0;
}