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: Time Limit Exceeded)

$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|
      return 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)
func(bs, [])
puts "-1" unless $flag
# puts "count: #{$count}" if $debug