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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

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

int main() {
  int N;
  cin >> N;
  vector<int> b(N),ans(N,0);
  for (int i=0; i<N; i++) {
    cin >> b[i];
    if (b[i] > i+1) {
      cout << -1 << endl;
      return 0;
    }
  }
  
  
  int num,loc;
  for (int i=N-1; i>=0; i--) {
    num = i - (b[i] - 1) + 1;
    loc = N;
    while (loc >= 0) {
      if (num == 0) {
        ans[loc] = b[i];
        break;
      }
      if(ans[loc-1] == 0) {
        num--;
      }
      loc--;
    }
  }
  for (int i=0; i<N; i++) {
    cout << ans[i] << endl;
  }
  
}