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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <cmath>
#include <climits>
#include <string>
#include <numeric>
#include <vector>
#include <queue>
#include <map>
#include <algorithm>
#include <functional>

using namespace std;
using ll = long long;

int main() {
  
	int N;
	cin >> N;
	vector<int> vec(N + 1);

	for (int i = 1; i < N+1; i++) {

		cin >> vec.at(i);

 }
	int count=0;
	int x = 1;/*ボタン*/
	int y;/*次のボタン*/

	for (int i = 1; i < N+1; i++) {

		y = vec.at(x);
		x = y;
		count++;

		if (x == 2) {
			cout << count << endl;
			return 0;
		}

		else if (i == N) {

			cout << -1 << endl;
			return 0;
		}

	}


	return 0;

}