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: Accepted)

$debug = false
$flag = false
$count = 0

def func(array, answer)
  $count += 1
  # p array if $debug
  # p answer if $debug

  return if $flag

  if array.empty?
    # arrayが空になった = 操作手順が完成した
    puts "Yay!" if $debug
    puts answer.reverse
    $flag = true
  else
    # arrayが空ではない = 操作を探す
    (array.size-1).step(0, -1) do |k|
      break if $flag
      # 大きい方から見ていって、適合するポイントがあれば再起で放り投げる
      if array[k] == k+1
        next_array = array.dup
        next_array.delete_at(k)
        func(next_array, answer+[k+1])
      end
    end
  end
end

_N = gets.to_i
bs = gets.split.map(&:to_i)

# 先にチェック。n番目にnよりも大きな数字があったら成立せず。
0.step(bs.size - 1, 1) do |n|
  if bs[n] > n + 1
    puts "-1"
    $flag = true
    break
  end
end

# メイン処理。前のチェックでNGで終了フラグが立ってる場合には実行せず。
func(bs, []) unless $flag

# メイン処理を行っても終了フラグが立っていないならダメだったってこと。
puts "-1" unless $flag

puts "count: #{$count}" if $debug