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

$memo = [];

$back = function($b) use (&$back, $memo) {
    if (isset($memo[implode('', $b)])) {
        return $memo[implode('', $b)];
    }
    if (count($b) === 1) {
        if ($b[0] === 1) {
            return [[1], true];
        } else {
            return [[], false];
        }
    }
    $dame_flag = true;
    for ($i = 0; $i < count($b); $i++) {
        if ($b[$i] === $i + 1) {
            $dame_flag = false;
        }
    }
    if ($dame_flag) {
        $memo[implode('', $b)] = [[], false];
        return [[], false];
    }
    for ($i = count($b) - 1; $i >= 0; $i--) {
        if ($b[$i] === $i + 1) {
            $b_clone = $b;
            array_splice($b_clone, $i, 1);
            list($procedure, $is_able) = $back($b_clone);
            if ($is_able) {
                $memo[implode('', $b)] = [array_merge($procedure, [$i + 1]), true];
                return [array_merge($procedure, [$i + 1]), true];
            }
        }
    }
    $memo[implode('', $b)] = [[], false];
    return [[], false];
};

$N = (int)trim(fgets(STDIN));
$b = array_map(function($str) {
    return (int)$str;
}, explode(' ', trim(fgets(STDIN))));
list($procedure, $is_able) = $back($b);
if ($is_able) {
    for ($i = 0; $i < count($procedure); $i++) {
        echo "{$procedure[$i]}\n";
    }
} else {
    echo "-1\n";
}