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 PHP (5.6.30) (judge verdict: Accepted)

<?php

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

for ($i=0; $i < $n; $i++) {
    fscanf(STDIN,"%d",$botton[$i]);
    $isDone[$i] = False;
}
$isDone[1] = True;

if(in_array(2,$botton)){
    $i = 0;
    $ans=0;
    while($isDone[$i] == False){
        $isDone[$i] = True;
        $i = $botton[$i] - 1;
        $ans++;
    }
    if($i == 1){
        echo $ans.PHP_EOL;
        return;

    }
}
echo (-1).PHP_EOL;