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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program name
    implicit none
    integer(4):: n,i,cnt
    integer(4),allocatable:: a(:)
    logical,allocatable:: pulled(:)

    read*, n
    allocate(a(n),pulled(n))

    do i=1,n
        read*, a(i)
    end do

    pulled(:) = .false.
    i=1
    cnt = 0
    do while(.not.(pulled(2)))
        i = a(i)
        if (pulled(i)) then
            print*, -1
            stop
        end if
        pulled(i) = .true.
        cnt=cnt+1
    end do

    print*, cnt

end program name