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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

const fi='abc065_b.inp';
        fo='abc065_b.out';
var n,i:longint;
        a:array[1..100000] of longint;
        d:array[1..100000] of boolean;
function conan:longint;
        var i,kq:longint;
        begin
                i:=1;
                kq:=0;
                while i<n+1 do
                        begin
                                if d[i] then exit(-1);
                                if i=2 then exit(kq);
                                d[i]:=true;
                                i:=a[i];
                                inc(kq);
                        end;
        end;
begin

        readln(n);
        for i:=1 to n do readln(a[i]);
        writeln(conan);
end.