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 (GCC 5.4.1) (judge verdict: Wrong Answer)

    #include <stdio.h>
    #include <stdlib.h>
    int main(void){
      int N;
      int i;
      int b, c;
     
      scanf("%d", &N);
     
      int a[N+1];
      int x[N+1];
     
      for(i=1; i<=N; i++){
        scanf("%d", &a[i]);
      }
     
      i=1;
      c=a[i];
      b=1;
      x[1]=1;
     
      while(1){
        if(x[c]==1){
          printf("-1\n");
          return 0;
        }
        if(c==2)
          break;
        x[c]=1;
        c=a[c];
        b++;
      }
      printf("%d\n", b);
     
      return 0;
    }