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>
char c;
int f;
int nextInt();

int N, n, i, t;
int A[100001];
int main(){
	N=nextInt();
	for(i=1; i<=N; i++){
		A[i]=nextInt();
	}
	i=0;
	n=1;
	do{
		t = A[n];
		A[n] = 1;
		n = t;
		i++;
	}while(n!=1 && n!=2);
	if(n==2){
		printf("%d\n", i);
	}else{
		printf("-1\n");
	}
}

int nextInt(){
	f=0; c=getchar();
	while((c<'0')||('9'<c)){c=getchar();}
	while((c>='0')&&(c<='9')){f=f*10+(c-'0'); c=getchar();}
	return f;
}