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(int argc, char const *argv[]) {

    int N;
    std::cin >> N;

    std::vector<int> buttons;
    for(int times = 0 ; times < N ; times++ )
    {
        int button_number;
        std::cin >> button_number;
        /** ボタンの数を0スタートにしている **/
        buttons.push_back(button_number - 1);
    }

    std::vector<int> pushed_button_indexs;
    int button_index = 0;
    int push_times = 0;
    bool loop_button = false;

    while(true)
    {
        /** 1番目のボタンは終了の合図なので脱出 **/
        if(button_index == 1)
        {
            break;
        }

        auto button_num = buttons[button_index];

        /** 既に押したことのあるボタンに来たときにはループしているので脱出 **/
        auto find_result = std::find(pushed_button_indexs.begin(),pushed_button_indexs.end(),button_index);
        if(find_result != pushed_button_indexs.end())
        {
            loop_button = true;
            break;
        }

        push_times++;

        pushed_button_indexs.push_back(button_index);
        button_index = button_num;
    }

    if(loop_button)
        std::cout << -1 << '\n';
    else
        std::cout << push_times << '\n';

    return 0;
}