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: Wrong Answer)

N = (gets).to_i
bs = (gets).split(" ").map {|i| i.to_i}

# check
def condition_chk(arr)
  #p arr
  arr.each.with_index do |b,i|
    if (b > i+1) then
        return false
    end
  end
  return true
end

# 作ってみる
# １で分割すると良い気がする
arr = []
an = 0
bs.each_with_index do |b,i|
    an = an + 1 if (b==1 && i>0)
    arr[an] = [] if arr[an].nil?
    arr[an] << b
end

A = an
isOK = true
res = []
an.downto(0) do |n|
    if not condition_chk(arr[n]) then
        isOK = false
        break
    end
    (arr[n].sort).each do |a|
        res << a
    end
end

if isOK then
    puts res
else
    puts "-1"
end