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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define rep(i, n) REP(i, 0, n)
#define REP(i,k,n) for(int i = k; i < n; i++)
#define mmax(start, end) *max_element(start, end)
#define mmin(start, end) *min_element(start, end)
#define argmax max_element
#define argmin min_element
#define ALL(x) (x).begin(), (x).end()

typedef long long ll;
typedef pair<int, int> prii;

int dx[4] = {1, -1, 0, 0};
int dy[4] = {0, 0, 1, -1};
int dx8[8] = {-1, -1, -1, 0, 0, 1, 1, 1};
int dy8[8] = {-1, 0, 1, -1, 1, -1, 0, 1};

template<class T = ll> T in() {
    T _in;
    cin >> _in;
    return _in;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    cin >> N;
    int a[100001];
    bool closed[100000] = {false};
    a[0] = N;
    REP(i, 1, N+1) {
        cin >> a[i];
    }

    int cur = 1;
    int ans = 0;
    while(true) {
        if(closed[cur]) {
            cout << -1 << endl;
            exit(0);
        }

        closed[cur] = true;
        cur = a[cur];
        ans++;
        if(cur == 2)
            break;
    }

    cout << ans << endl;

    return 0;
}