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 Perl (v5.18.2) (judge verdict: Accepted)

#!/usr/bin/perl
my ($n) = map { $_ - 0 } split(/\s+/,<STDIN>);
my @b = map { $_ - 0 } split(/\s+/,<STDIN>);

my %cnt = ();
foreach my $b (@b){
  $cnt{$b} ++;
}

foreach my $c (keys %cnt){
  if( $cnt{$c} > $n + 1 - ( $c - 0 ) ){
    print "-1\n"; exit(0);
  }
}

my @bb = @b;
my @op = ();
my $cl = $n;
for(my $i=0;$i<$n;$i++){
  my $j;
  for($j=$cl;$j>0;$j--){
    last if $bb[$j - 1] == $j;
  }
  if( $j<=0 ){
    print "-1\n"; exit(0);
  }
  unshift(@op,$j);
  my @newbb = ();
  push(@newbb,@bb[0..($j-2)]) if $j>1;
  push(@newbb,@bb[$j..($cl-1)]) if $j<$cl;
  @bb = (@newbb);
  $cl--;
}
for(my $i=0;$i<$n;$i++){
  print "$op[$i]\n";
}

exit(0);