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 Ruby (2.3.3) (judge verdict: Accepted)

# coding: utf-8
class Case02

  def initialize
  end

  def show
    p self.instance_variables
        .map{ |sym| [sym, self.instance_variable_get(sym)] }
        .to_h
  end
  
  # 実行する
  def execute
    read
    solve
    output
  end

  # 読込
  def read
    @n = gets.chomp.to_i
    @a = []
    @n.times do
      @a << gets.chomp.to_i
    end
  end

  # 回答
  def solve
    @b = 1
    @s = 0
    while @b != 2 and @s < @n do
      @b = @a[@b-1]
      @s += 1
    end
  end
  
  # 出力
  def output
    puts (@b == 2) ? @s : -1;
  end

end

Case02.new.execute if $0 == __FILE__