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)

program Project1;

{$APPTYPE CONSOLE}

uses
  SysUtils,Classes;
var
  h,w,i,j,count,x,y,sw,m,n,b,c,soeji:Integer;
  a:array of Integer;
  s123,s1,s2,s3:string;
  tf:Boolean;
  nyu:TStringList;
begin
  try
    { TODO -oUser -cConsole Main : ここにコードを記述してください }
    Readln(n);
    SetLength(a,n+1);
    for i := 1 to n do
      Readln(a[i]);

    soeji:=1;
    for i := 1 to n do begin
      if a[soeji]=2 then begin
        Writeln(i);
        Readln;
        exit;
      end;
      soeji:=a[soeji];
    end;

    Writeln('-1');
    Readln;
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
end.