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: Time Limit Exceeded)

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

int main (){
  int N;
  cin >> N;
  vector<int> X (N);
  for (int i=0; i<N ; i++){
    cin >> X.at(i);
  }
  int a=1;
  vector<int> Y (1,1);
  for (int i=0; i<N ; i++){
    Y.push_back ( X.at(a-1));
    a = X.at(a-1);
    if ( a == 2 ){
      cout << i + 1 << endl;
      break;
    }
    int b=0;
    for (int k=0; k < i+1; k++){
      if ( Y.at(k) == a )
        b=1;
      if (b == 1) 
        break;
    }
    if (b == 1 ){
      cout<< -1 <<endl;
      break;
    }
  }
}