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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
$n = fgets(STDIN);
$array = explode(" ", trim(fgets(STDIN)));

for($i = 0; $i < $n; $i++){
 	@$map[$array[$i]]++; 
}
$result = n([], $map, $array, []);
echo -1;
function n($path, $map, $array, $cmd){
  if(!$map){
    if(implode("-", $path) == implode("-", $array)){
        echo implode("\n", $cmd);
        exit; 
    }else{
        return;
    }
  }
  for($i = 1; $i <= count($path) + 1; $i++){
    if(@$map[$i]){
      //echo implode(" ", $map)."\n";
      $m = $map;
      $m[$i]--;
      $p = $path;
      $c = $cmd;
      $c[] = $i;
      array_splice($p, $i - 1, 0, $i);
      if($m[$i] == 0){
        unset($m[$i]);
      }
      n($p, $m, $array, $c);
    }
  }  
}