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;

typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pi;

#define F first
#define S second
#define PB push_back
#define MP make_pair

#define FOR_EX(i, a, b) for (int i = a; i < b; i++)
#define FOR_IN(i, a, b) for (int i = a; i <= b; i++)

#define ALL(a) a.begin(), a.end()

// g++ -std=c++17 -O2 -Wall template.cpp -o template
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    // cout << fixed << setprecision(10);
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
    // Solution

    int n;
    cin >> n;
    unordered_map<int, int> b;
    FOR_IN(i, 1, n) {
        cin >> b[i];
    }
    unordered_set<int> pressed;
    int times = 0;
    int cur = 1;
    while (cur != 2) {
        if (b.find(cur) == b.end() || pressed.find(cur) != pressed.end()) {
            cout << -1 << endl;
            return 0;
        }
        times++;
        pressed.insert(cur);
        cur = b[cur];
    }
    cout << times << endl;
}