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: Accepted)

<?php
/*
    Problem URL : https://beta.atcoder.jp/contests/abc065/tasks/abc065_b

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

// define('DEBUG', true);
define('DEBUG', false);

ini_set('error_reporting', E_ALL & ~E_NOTICE);

fscanf(STDIN, "%d", $N);
$m = array();
$cursor = 1;
$ans = 0;

for ($i = 1; $i <= $N; $i++) {
    fscanf(STDIN, "%d", $a[$i]);
}

while(true) {
    $ans++;
    $cursor = $a[$cursor];
    if ($m[$cursor] == 1) {
        echo "-1\n";
        exit;
    }
    $m[$cursor] = 1;
    if ($cursor == 2) {
        echo $ans . PHP_EOL;
        exit;
    }
}