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: Wrong Answer)

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

int main() {
  //入力値取得
  int N;	cin >> N;
  vector<int> toNumber(N+1);	//0番目は使用しない
  for(int i=1; i<N+1; i++){
    cin >> toNumber.at(i);
  }
  
  //入力確認
  //cout << N << endl;
  //for(int i=1; i<N+1; i++){
  //  cout << i << ':' << toNumber.at(i) << endl;
  //}
  
  //フラグ宣言
  vector<int> hasPush(N+1, false);
  int now = 1;
  
  while(1){
    if(toNumber.at(now) == 2){
      cout << toNumber.at(now) << endl;
      return 0;
    }
    
    if(hasPush.at(toNumber.at(now))){
      cout << -1 << endl;
      return 0;
    }
    else {
      hasPush.at(now) = 1;
      now = toNumber.at(now);
    }
  }
  
  
  //hasPush.at(now) = 1;
  //now = toNumber.at(now);
  
  //cout << "      ";
  //for(int i=1; i<N+1; i++){
  //  cout << "btn" << i << ' ';
  //} 
  //cout << endl;
  
  //フラグ初期値確認
  //cout << "now:" << now;
  //for(int i=1; i<N+1; i++){
  //  cout << "    " << hasPush.at(i);
  //}
  //cout << endl;
  
  
  //while(1){
  //  //cout << now << endl;
  //  
  //  if(now == 2){
  //    return 88888;
  //  }
  //  
  //  if(hasPush.at(now) == 0){
  //    hasPush.at(now) = 1;
  //    now = toNumber.at(now);
  //  }
  //  else{
  //    cout << -1 << endl;
  //    return 0;
  //  }
  //}
}