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 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdbool.h>
#include<string.h>
#include<math.h>
#include<stdlib.h>
#define rep(i,n) for(int i=0; i <(n); i++)

int compint(const void *a,const void *b){
  return *(int *)a-*(int *)b;
}
int main(){
  int n;
  int a[100001];
  scanf("%d",&n);
  rep(i,n){
    scanf("%d",&a[i]);
  }
  int count=0;
  int light=1;
  int cnt[100001]={0};
  do{
    light=a[light-1];
    count++;
    cnt[light]++;
  }while(light!=2&&cnt[light]<2);
  rep(j,n){
    if(cnt[j]>1){
      printf("-1\n");
      return 0;
    }
  }
  printf("%d\n",count);
  return 0;
}