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)

@N = gets.to_i
@B = gets.split.map(&:to_i)
@b = @B.join

r = Hash.new(0)
@N.times do |i|
  r[@B[i]] += 1
end

def b(p, b, r)
  if p.size == @N
    if @b == b.join
      p.each do |pp|
        puts pp
      end
      return true
    end

    return false
  end

  result = false

  r.each do |i, n|
    next if i > p.size + 1
    next if n == 0

    rd = r.dup
    rd[i] -= 1
    bd = b.dup

    pd = p.dup
    pd << i

    result = b(pd, bd.insert(i - 1, i), rd) || result
  end

  result
end


if r[1] == 0
  puts '-1'
else
  rd = r.dup
  rd[1] -= 1
  unless b([1], [1], rd)
    puts '-1'
  end
end