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

class In {

	private $buf = [];
	private $count = 0;
	private $pointer = 0;

	public function nextLine() {
		$ret = '';
		if($this->hasNext()){
			while($this->hasNext()){
				$ret .= $this->next();
			}
		}else{
			$ret = trim(fgets(STDIN));
		}

		return $ret;
	}

	public function next() {
		if(!$this->hasNext()) {
			$str = trim(fgets(STDIN));
			$this->buf = explode(' ',$str);
			$this->count = count($this->buf);
			$this->pointer = 0;
		}

		return $this->buf[$this->pointer++];
	}

	public function hasNext() {
		return $this->pointer < $this->count;
	}

	public function nextInt() {
		return (int)$this->next();
	}

	public function nextDouble() {
		return (double)$this->next();
	}
}

class Out {
	public function println($str = '') {
		echo $str . PHP_EOL;
	}
}

$in = new In();
$out = new Out();

$N = $in->nextInt();
$a = [];
$used = [];
for ($i = 0;$i < $N;$i++) {
	$a[] = $in->nextInt()-1;
	$used[] = false;
}

$cur = 0;
$cnt = 0;
while($used[$cur] === false) {
	$used[$cur] = true;

	if ($cur === 1) {
		$out->println($cnt);
		return;
	}
	$cur = $a[$cur];
	$cnt++;
}

$out->println('-1');

?>