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"
#define readInt(x) scanf("%d", &x)
#define readStr(x) scanf("%s", x)
#define rep(i, n) for(int i=0; i<(n); ++i)
#define write(x) cout << (x) << endl
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int INF = 1 << 28;
const int MAX = 1e5 + 10;

int N;
int a[MAX];

int main()
{
    cin >> N;
    rep(i, N) cin >> a[i];
    int cnt = 0;
    for (int i = 0, cnt = 0; cnt < N; cnt++) {
        if (i == 2 - 1) {
            write(cnt);
            return 0;
        }
        i = a[i] - 1;
    }
    write(-1);
}