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 C (Clang 3.8.0) (judge verdict: Accepted)

// ABC065 B - Trained?
#include <stdio.h>

int main(void) {
    int N;  // 10^5
    scanf("%d", &N);
    int a[N + 1];
    int flag[100001] = { 0 };
    for (int i = 1; i <= N; i++) {
        scanf("%d", &a[i]);
    }
    int i = 1;
    int count = 0;
    while(1) {
        count++;
        int onButton = a[i];
        if (onButton == 2) {
            printf("%d\n", count);
            return 0;
        }
        if (flag[onButton] == 1) {
            printf("%d\n", -1);
            return 0;
        } else {
            flag[onButton] = 1;
        }
        i = onButton;
    }
}