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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

typedef struct List {
	struct List *next;
	int data, dist;
} Queue;

int main()
{
	int i, N, a[100001];
	scanf("%d", &N);
	for (i = 1; i <= N; i++) scanf("%d", &(a[i]));
	
	int flag[100001] = {};
	Queue q[100001], *p, *tail = &(q[1]);
	tail->next = NULL;
	tail->data = a[1];
	tail->dist = 0;
	for (p = tail; p != NULL; p = p->next) {
		if (flag[p->data] == 0) {
			flag[p->data] = 1;
			q[p->data].next = NULL;
			q[p->data].data = a[p->data];
			q[p->data].dist = p->dist + 1;
			tail->next = &(q[p->data]);
			tail = tail->next;
			if (p->data == 2) break;
		}
	}
		
	if (p != NULL) printf("%d\n", tail->dist);
	else printf("-1\n");
	fflush(stdout);
	return 0;
}