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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>

int main(){
    long n;
    std::cin >> n;

    std::vector<long> a(n);
    for (long i = 0; i < n; ++i){
        std::cin >> a.at(i);
    }

    bool flg = false;
    int index = 1;
    long count = 0;
    std::vector<long> history;
    while(!flg){
        ++count;

        index = a.at(index - 1);

        if(2 == index){
            flg = true;
            break;
        }else if(history.end() != std::find(history.begin(), history.end(), index)){
            break;
        }
        
        history.push_back(index);
    }

    if(flg){
        std::cout << count << std::endl;
    }else{
        std::cout << -1 << std::endl;
    }

    return 0;
}