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>

int N;
int a[114514];

char visited[114514];

int main(void) {
	int i;
	int count = 0;
	int current = 1;
	if (scanf("%d", &N) != 1) return 1;
	for (i = 1; i <= N; i++) {
		if (scanf("%d", &a[i]) != 1) return 1;
	}
	for (;;) {
		if (visited[current]) {
			puts("-1");
			return 0;
		}
		if (current == 2) {
			printf("%d\n", count);
			return 0;
		}
		visited[current] = 1;
		current = a[current];
		count++;
	}
}