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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <math.h>
#define MOD 1000000007
#define ll long long

int cmpfunc(const void *a, const void *b){
    return (*(int*)a - *(int*)b);
}

void swap(int *a, int *b);

int main(int argc, char **argv){
    int n,i;
    scanf("%d",&n);
    int a[n+1];
    for(i=1;i<=n;i++) scanf("%d",&a[i]);
    int j=0;
    int position=1;
    while(j<2*n){
        j++;
        position = a[position];
        if(position==2){
            printf("%d\n",j);
            return 0;
        }
    }
    printf("-1\n");
    return 0;
}

void swap(int *a, int *b){
    int tmp=*a;
    *a = *b;
    *b = tmp;
}