Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3
1 2 1

Sample Output 1

1
1
2

In this sequence of operations, the sequence a changes as follows:

After the first operation: (1)

After the second operation: (1,1)

After the third operation: (1,2,1)

Sample Input 2

2
2 2

Sample Output 2

-1

2 cannot be inserted at the beginning of the sequence, so this is impossible.

Sample Input 3

9
1 1 1 2 2 1 2 3 2

Sample Output 3

1
2
2
3
1
2
2
1
1

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int main(){
  int N;
  cin >>N;
  int S=N;
  vector<int> a(N);
  int b[N+1]={0};
  bool flag=0;
  for (int i=0;i<N;i++) cin>>a[i];
  do{
    
    for (int i=N-1;i>=0;i--){
      if(a[i]==i+1){
        b[N]=i+1;
        //cout<<b[N]<<"#"<<N<<endl;
        a.erase(a.begin()+i);
        flag=0;
        N--;
        if(N==0){
          for(int k=1;k<=S;k++){
            cout<<b[k]<<endl;
          }
            return 0;
        }
        break;
      }
    }
    if(flag){
      cout<<"-1"<<endl;
      return 0;
    }
    flag=1;
      
  }
  while (N>-1);
  return 0;
}