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: Accepted)

#include <iostream>
#include <vector>
#include <string>
#define FOR(i,a,b) for(int i=a; i<b; i++)
#define rep(i,N) FOR(i,0,N)
using namespace std;


int main() {
	int N;
	cin >> N;
	vector<int> botton(N);


	rep(i,N){
		cin >> botton.at(i);
	}

	int count=1;
	int number=1;
	bool judge=false;
	while (count < N) {
		if (botton.at(number-1) == number) {
			judge=false;
			break;
		}
		else if (botton.at(number-1)==2) {
			judge = true;
			break;
		}
		else {
			number = botton.at(number-1);
			count++;
			
		}
	}

	if (judge == true) {
		cout << count;
	}
	else {
		cout << -1;
	}

	return 0;
}