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)

Var N,i,Dem:Longint;
    A:Array[1..100000] Of Longint;
    B:Array[1..100000] Of Boolean;
Begin
        //Assign(Input,'TRAINED.INP'); Reset(Input);
        //Assign(Output,'TRAINED.OUT'); Rewrite(Output);
        Readln(N);
        Fillchar(B,SizeOf(B),False);
        For i:=1 to N Do
                Begin
                Readln(A[i]);
                End;
        Dem:=0;
        i:=1;
        B[1]:=True;
        While i<>2 Do
                Begin
                B[i]:=False;
                B[A[i]]:=True;
                i:=A[i];
                Inc(Dem);
                If Dem>N Then Break;
                End;
        If Dem>N Then Write('-1') Else Write(Dem);
        //Close(Input);
        //Close(Output);
End.