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;

int n;
vector <int> b, rlt;

int main()
{
    scanf("%d", &n);
    b.resize(n);
    for (int i = 0; i < n; i ++) scanf("%d", &b[i]);
    while (n --)
    {
        int k = n;
        while (k >= 0 && b[k] != k + 1) k --;
        if (k < 0) return printf("-1"), 0;
        rlt.push_back(k + 1), b.erase(b.begin() + k);
    }
    reverse(rlt.begin(), rlt.end());
    for (int i = 0; i < rlt.size(); i ++) printf("%d\n", rlt[i]);
}
