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: Time Limit Exceeded)

if !ENV['RUBY_THREAD_VM_STACK_SIZE']
  exec({'RUBY_THREAD_VM_STACK_SIZE'=>'1000000000'}, '/usr/bin/ruby', $0)
end


n = gets.chomp.to_i
$button = []
n.times do |i|
  $button << {id:i+1, next:gets.chomp.to_i}
end

$dp = []
$count = 1
def f(n)
  if $dp.include?(n[:next])
    puts "-1"
    exit
  else
    if n[:next] == 2
      puts $count
      exit
    end
    $dp << n[:id]
    $count+=1
    f($button[n[:next]-1])
  end
end

f($button.first)