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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    static int ANS = 0;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.nextLine());
        int[] an = new int[N];
        boolean[] hasPushed = new boolean[N];
        for (int i = 0; i < N; i++) {
            an[i] = Integer.parseInt(sc.next());
        }

        boolean canComp = true;
        int next = 0;
        for (int i = 0; i < N; i++) {
            if (hasPushed[next]) {
                // 既に押したボタンの場合はループしているので終了する
                canComp = false;
                break;
            }
            next = push(an, next, hasPushed);

            if (next == 1) {
                // ボタン2に到達したので終わる
                break;
            }
        }
        System.out.println(canComp ? ANS : -1);
    }

    private static int push(int[] an, int next, boolean[] hasPushed) {
        ANS++;
        hasPushed[next] = true;
        return an[next] - 1;
    }
}