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 Go (1.14.1) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var n int
	fmt.Scanf("%d\n", &n)
	a := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scanf("%d\n", &a[i])
	}

	key, count := 1, 0
	buttons := map[int]bool{key: true}
	for {
		count++
		key = a[key-1]
		if buttons[key] {
			fmt.Println(-1)
			break
		} else if key == 2 {
			fmt.Println(count)
			break
		} else {
			buttons[key] = true
		}
	}

}