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 main(){
  int N;
  cin >> N;
  
  vector<int> b(N);
  
  for(int i=0;i<N;i++){
    cin >> b.at(i);
  }
  
  vector<int> a;
  
  for(int i=0;i<N;i++){
    for(int j=b.size()-1;j>=0;j--){
      if(b.at(j)==j+1){
        a.push_back(j+1);
        b.erase(b.begin()+j);
        break;
      }
    }
  }
  
  reverse(a.begin(),a.end());
  
  if(a.size()==N){
    for(int k=0;k<N;k++){
      cout << a.at(k) << endl;
    }
  }else{
    cout << -1 << endl;
  }
}