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 10.0.0) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#pragma warning(disable : 4996)

int main()
{
    long N;
    int i,p;
    long a[100001] = {0};
    long count = 0;
    long pp[100001] = {1};

    scanf("%ld", &N);

    for (i = 1; i <= N; i++) {
        scanf("%ld", &a[i]);
    }

    i = 1;
    pp[i++] = p = a[1];
    count++;

    if (p == 2) {
        printf("%ld", count);
        return 0;
    }

    while (1) {
        
       pp[i++] = p = a[p];
       count++;

       if (p == 2)
           break;

       for (int j = 0; j < i - 1; j++) {
           if (p == pp[j]) {
               printf("-1");
               return 0;
           }
       }
       


    }

    printf("%ld", count);

    return 0;

}