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: Wrong Answer)

<?php
fscanf(STDIN, "%d", $n);
for ($k = 1; $k <= $n; $k++) {
    fscanf(STDIN, "%d", $a[$k]);
}

$sumi = [];
$b = [];


$sumi[1] = true;
$next = $a[1];
for ($k = 2; $k <= $n; $k++) {
    $sumi[$a[$next]] = true;
    $next = $a[$next];
    if ($next == 2) {
        $result = $k;
        break;
    }
    if (isset($sumi[$a[$next]])) {
        $result = -1;
        break;
    }
    if ($k == $n) {
        if ($next != 2) {
            $result = -1;
            break;
    
        }
    }
}

echo $result . "\n";