Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:


N
b_1 \dots b_N


Output

If there is no sequence of N operations after which a would be equal to b, print `-1`. If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Examples

Input

3
1 2 1


Output

1
1
2


Input

2
2 2


Output

-1


Input

9
1 1 1 2 2 1 2 3 2


Output

1
2
2
3
1
2
2
1
1
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main(){
	ll n;
	cin >> n;
	vector <ll> arr(n);
	for (int z=0;z<n;z++){
		cin >> arr[z];
	}
	vector <ll> aaa;
	ll count = n;
	while (arr.size() > 0){
		if (count < 0 ){
			cout << -1 << endl;
			return 0;
		}
		for (int z=n-1;z>-1;z--){
			if (arr[z] == z+1 && arr[z] <= count){
				aaa.push_back(z+1);
				arr.erase(arr.begin()+z);
				break;
			}
		}
		count--;
	}
	for (int z=n-1;z>-1;z--){
		cout << aaa[z] << endl;
	}
	cin >> n;
}
