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 <iostream>
#include <vector>

using namespace std;

int main() {
    int n;
    cin >> n;
    vector<int> v;
    for(int i=0;i<n;i++) {
        int b;
        cin >> b;
        if (b > (i+1)) {
            cout << -1 << endl;
            return 0;
        }
        // (b-1)番目にbを挿入
        auto it = v.begin();
        for(int j=0;j<(b-1);j++) {
            it++;
        }
        v.insert(it, b);
    }
    for(auto i: v) {
        cout << i << endl;
    }
    return 0;
}