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;
  list<int>B;for(int i=0;i<N;i++){int b;cin>>b;B.push_back(b);}
  vector<int>ans;
  while(B.size()){
    int i=B.size();bool OK=false;
    auto itr=B.end();itr--;
    while(1){
      if(*itr==i){ans.push_back(i);B.erase(itr);OK=true;break;}
      i--;
      if(itr==B.begin())break;
      itr--;
    }
    if(OK==false){cout<<-1;return 0;}
  }
  for(int i=N-1;i>=0;i--)cout<<ans[i]<<endl;
}