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 (1.6) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

func main() {
	var n int
	fmt.Scan(&n)
	arr, flags := make([]int, n + 1), make([]bool, n + 1)
	for i := 1; i <= n; i++ {
		var tmp int
		fmt.Scan(&tmp)
		arr[i] = tmp
	}
	flags[1] = true
	now := 1
	count := 1
	for true {
		next := arr[now]
		if next == 2 {
			fmt.Println(count)
			break
		} else if flags[next] {
			fmt.Println(-1)
			break
		}
		now = next
		count++
	}
}