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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function Main(input) {
    // 1行目がinput[0], 2行目がinput[1], …に入る
    // 上下左右が全て"."である"#"が存在するかどうかを探す
    N = Number(input.split("\n")[0]);
    a=new Array;
    //b;j番目のボタンに訪れたことがあるかどうか
    b=new Array;
    answer = 0;
    for(i=0;i<N;i++){
        a[i]=Number(input.split("\n")[i+1])-1;
    }
    j=0


    while(true){
        //j：ボタンを押すと、次はj番目のボタンが光る
        j=a[j];
        answer++;
        
        
        if(j==1){
            //j==1なら、終わり
            break;
        }else{
            if(b[j]==1){
                //j番目のボタンを押したことあるなら、ループしてるのでbreak
                answer = -1;
                break;
            }else{
                //j番目のボタンを押したことを記録
                b[j]=1;
            }
        }
        
    }

    console.log(answer);
    
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));