Problem:
Score : 800 points

Problem Statement

Niwango has N cards, numbered 1,2,\ldots,N.
He will now arrange these cards in a row.

Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below.
To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.

To the immediate right of Card 1 (if any) is NOT Card a_1.

To the immediate right of Card 2 (if any) is NOT Card a_2.

\vdots

To the immediate right of Card N (if any) is NOT Card a_N.

Constraints

2 \leq N \leq 10^{5}

1 \leq a_i \leq N

a_i \neq i

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

If no arrangements satisfy the conditions, print -1. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:

b_1 b_2 \ldots b_N

Here, b_i represents the i-th card from the left.

Sample Input 1

4
2 3 4 1

Sample Output 1

1 3 2 4

The arrangement (1,2,3,4) is lexicographically smaller than (1,3,2,4), but is invalid, since it violates the condition "to the immediate right of Card 1 is not Card 2."

Sample Input 2

2
2 1

Sample Output 2

-1

If no arrangements satisfy the conditions, print -1.

Sample Input 3

13
2 3 4 5 6 7 8 9 10 11 12 13 12

Sample Output 3

1 3 2 4 6 5 7 9 8 10 12 11 13

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$n=trim(fgets(STDIN));
if($n==2){
  echo -1;
  exit;
}
$a=explode(" ",trim(fgets(STDIN)));
$r=0;
$ans[0]=1;
$c=0;
$i=1;
while($i<$n){
  if($r!=0){
    if($r+2==$n && $a[$c]==$r+2){
      $ans[$i]=$r+2;
      $ans[$i+1]=$r;
      $i=$n;
      break;
    }else{
      $ans[$i]=$r;
      $c=$r-1;
      $r=0;
    }
  }elseif($a[$c]!=$i+1){
    $ans[$i]=$i+1;
    $c=$i;
  }else{
    $ans[$i]=$i+2;
    $r=$i+1;
    $c=$i;
  }
  ++$i;
}
echo join(" ",$ans);