Problem:
Score : 200 points

Problem Statement

Takahashi wants to gain muscle, and decides to work out at AtCoder Gym.

The exercise machine at the gym has N buttons, and exactly one of the buttons is lighten up.
These buttons are numbered 1 through N.
When Button i is lighten up and you press it, the light is turned off, and then Button a_i will be lighten up. It is possible that i=a_i.
When Button i is not lighten up, nothing will happen by pressing it.

Initially, Button 1 is lighten up. Takahashi wants to quit pressing buttons when Button 2 is lighten up.

Determine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N

Input

Input is given from Standard Input in the following format:

N
a_1
a_2
:
a_N

Output

Print -1 if it is impossible to lighten up Button 2.
Otherwise, print the minimum number of times we need to press buttons in order to lighten up Button 2.

Sample Input 1

3
3
1
2

Sample Output 1

2

Press Button 1, then Button 3.

Sample Input 2

4
3
4
1
2

Sample Output 2

-1

Pressing Button 1 lightens up Button 3, and vice versa, so Button 2 will never be lighten up.

Sample Input 3

5
3
3
4
2
4

Sample Output 3

3

Solution in PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php

fscanf(STDIN, "%d", $n);

$a = array();

for($i = 0; $i < $n; $i++){
       fscanf(STDIN, "%d", $a[]);
}

for($i = 0; $i < $n; $i++){
       if($a[$i] == 2){
       		 $flag = True;
		 break;
       }
}

if(!$flag){
	echo "-1\n";
	return;
}

$count = 1;
$button = $a[0];

while($button != 2){
  $before = $button;
  $button = $a[$button-1];
  $count++;
  if($before == $a[$button-1]){
    echo "-1\n";
    return;
  }
}
echo $count."\n";

?>