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++ (Clang 10.0.0) (judge verdict: Accepted)

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

int main() {
  int N;
  cin >> N;
  
  int a[N];
  for(int i = 0; i < N; i++) {
    cin >> a[i];
  }
  int x[N];
  for(int i = 0; i < N; i++) {
    x[i] = 0;
  }
  
  int now = 0;
  int i = 0;
  while(x[now] == 0) {
    i++;
    x[now] = 1;
    now = a[now] - 1;
    if(now == 1) {
      cout << i << endl;
      break;
    }
  }
  if(now != 1) {
    cout << -1 << endl;
  }
}