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)

#!/usr/bin/env ruby
STDIN.readline()
as = []
while (lines = STDIN.gets) do
  as << lines.strip.to_i
end
def make_tree(as, n)
  index = (0...as.size).bsearch{|i| as[i] >=  n} || as.size
  as.insert(index, n)
end
def trained?(as)
  # puts "as: #{as}"
  s = []
  l = 1
  while true
    make_tree(s, l)
    l = as[l-1]
    # puts "#{s}, #{l}"
    return s.length if l == 2
    return nil if s.bsearch{|n| n == l}
  end
end

n = trained?(as)
puts "#{n ? n : -1}"