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)

"後ろからたどる必要はなかった...
普通に前からたどればOK"

#a→bに到達可能か？
# def isAccessible(a, s, t)
#   (a[s-1] == t) ? true : false
# end 

N = gets.to_i
a = []
N.times.map{a << gets.to_i}


start = 1
target = 2
1.upto N do |i|
  start = a[start-1]
  if start == target
    puts i
    exit
  end
end
puts -1

#下、TLEくらいました
# 1.upto N do |e|
#   1.upto N do |i|
#     if isAccessible(a, i, target)
#       target = i
#       if target == 1
#         puts e
#         exit
#       end
#       break
#     end
#   end
# end
# puts -1