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>
using namespace std;
int main () {
  int N;
  cin >> N;
  int b[102];
  for (int i = 1; i <= N; i ++) {
    cin >> b[i];
    if (b[i] > i) {
      cout << "-1" << endl;
      return 0;
    }
  }
  int ans[101];
  for (int i = N; i > 0; i --) {
    for (int j = i; j > 0; j --) {
      if (b[j] == j) {
        ans[i] = j;
        for (int k = j; k < i; k ++) b[k] = b[k + 1];
        break;
      }
    }
  }
  for (int i = 1; i <= N; i ++) cout << ans[i] << endl;
}
  