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: Time Limit Exceeded)

#include<stdio.h>
#include<stdbool.h>

int main(void){

	int n;
	int a[100001];
	int ans = 0;
	int b = 1;
	int m[100001] = {0};
	bool f = false;

	scanf("%d", &n);

	for(int i= 0; i < n; i++){
		scanf("%d", &a[i]);
	}

	for(int i = 0; i < n; i++){
		m[i] = b;
		b = a[b-1];
		ans++;

		if(b==2){
			break;
		}

		for(int j = 0; j < n; j++){
			if(m[j] == b){
				f = true;
			}
		}

		if(f){
			ans = -1;
			break;
		}


	}

	printf("%d", ans);

	return 0;
}