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: Accepted)

#include <iostream>
using namespace std;

const int MAX_N = 100000;
int path[MAX_N];
bool arrived[MAX_N];

int main() {
  int N;
  cin >> N;
  fill(arrived, arrived+N, false);
  int ans = 0;
  int pos = 0;
  for (int i = 0; i < N; ++i) {
    cin >> path[i];
    path[i]--;
  }
  for (int i = 0; i < N; ++i) {
    arrived[pos] = true;
    if (arrived[path[pos]]) {
      ans = -1;
      break;
    }
    pos = path[pos];
    ans++;
    if (pos == 1) break;
  }
  cout << ans << endl;
}