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: Runtime Error)

<?php

$N  = fget(STDIN);
$bStr = fget(STDIN);
$nums = explode(" ", $bStr);

$run = 0;
$result = [];
$findResult = true;
while ($run < $N) {
    $found = false;
    for ($i = count($nums) - 1; $i >=0; $i--) {
        if ($nums[$i] == $i + 1) {
            $result[] = $nums[$i];
            unset($nums[$i]);
            $nums = array_values($nums);
            $found = true;
            break;
        }
    }
    if (false == $found) {
        $findResult = false;
        break;
    }

    $run++;
}

if ($findResult) {
    foreach ($result as $output) {
        echo $output . "\n";
    }
} else {
    echo "-1\n";
}