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 C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int result=0;

void search(vector<int> vec,vector<int> loop, int lit){
    loop.push_back(lit);
    if(lit == 2 ){
        result = loop.size()-1;
        return;
    }else{
        lit = vec.at(lit-1);
        // loop detection
        for(int j=0; j< loop.size();j++){
            if (loop.at(j)== lit){
                result = -1;
                return;
            }
        }
        search(vec,loop,lit);
    }
}

int main(){
    int n;
    cin >> n ;
    vector<int> vec(n);
    for (int i=0;i<n;i++){
        cin >> vec.at(i);
    }
    vector<int> loop;
    int lit=1;
    search(vec,loop,lit);
    cout << result << endl;
}