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.split.map {|e| e.to_i }.first
$bs = gets.split.map {|e| e.to_i }
cs = $bs # .sort.reverse

def f(as, xs, ys)
  # p [as, xs, ys]
  if as.size == 0
    if ys == $bs
      puts xs
      exit
    end
  else
    as.size.times { |i|
      x = as[i]
      if x <= xs.size + 1
        f(as[0...i] + as[i+1..-1], xs + [x], ys[0...x-1] + [x] + ys[x-1..-1])
      end
    }
  end
end

f(cs, [], [])
puts -1