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: Runtime Error)

N=gets.to_i
BS=gets.split.map(&:to_i)
A=[]
C=[]
D=[]

ans = "No"

BS.each_with_index do |b, i|
  break if b > i+1
  ans = "Yes"
end

if ans == "No"
  puts "-1"
else
  BS.each do |b|
    A[b-1, 0] = b
  end
  
  A.each do |a|
    C[a-1, 0] = a
  end
  
  C.each do |c|
    D[c-1, 0] = c
  end
  if BS==D
    A.each do |a|
      p a
    end
  else
    BS.each do |b|
      p b
    end
  end
end