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<bits/stdc++.h>
using namespace std;
#define fs first
#define sc second
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long ll;
typedef pair<ll,ll> P;
const ll mod=1000000007;
const ll LINF=1LL<<60;
const int INF=1<<30;

int main(){
	int n,l;
	cin >> n;
	vector<int> v(n);
	vector<int> x(n,0);
	for (int i = 0; i < n; i++){
		cin >> l;
		v[i] = l;
	}
	x[0] = 1;
	int next =v[0];
	int counter = 1;
	int flag = 0;
	while(next != 2){
		x[next - 1] ++;
		if (x[next - 1] <2){
			next = v[next - 1];
			counter++;
		}
		else{
			flag = 1;
			break;
		}
	}
	if (flag == 0){
		cout << counter << endl;
	}
	else{
		cout << -1 << endl;
	}

	return 0;
}