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>
#include <boost/multiprecision/cpp_int.hpp>

#define repd(i, a, b) for (ll i = (a); i < (b); i++)
#define rep(i, n) repd(i, 0, n)

using namespace std;

namespace mp = boost::multiprecision;
using Bint = mp::cpp_int;

using ll = long long;
ll mod = pow(10, 9) + 7;

template <typename T> void output(T, ll);
ll gcd(ll, ll);
ll lcm(ll, ll);
Bint comb(Bint, Bint);
void prime_map(map<ll, ll> &, ll);

int main() {
    // source
    int n;
    cin >> n;
    int a[n + 1];
    repd(i, 1, n + 1) { cin >> a[i]; }

    bool judge[n + 1] = {};
    int count = 0;
    int point = 1;
    while (true) {
        if (point == 2) {
            break;
        }
        count++;
        if (judge[a[point]]) {
            cout << -1 << endl;
            return 0;
        }
        point = a[point];
        judge[point] = true;
    }

    cout << count << endl;
    return 0;
}

Bint comb(Bint a, Bint b) {
    Bint ans = 1;

    if (a < b) {
        return 0;
    }

    rep(i, b) {
        ans *= a - i;
        ans /= i + 1;
    }

    return ans;
}

template <typename T> void output(T a, int precision) {
    if (precision > 0) {
        cout << setprecision(precision) << a << "\n";
    } else {
        cout << a << "\n";
    }
}

template <typename T> T min(T a, T b) {

    if (a < b) {
        return a;
    } else {
        return b;
    }
}

ll gcd(ll a, ll b) {
    if (b == 0) {
        return a;
    }
    return gcd(b, a % b);
}

ll lcm(ll a, ll b) { return a * b / gcd(a, b); }

void prime_map(map<ll, ll> &m, ll num) {
    ll cache = num;
    repd(i, 2, sqrt(num) + 2) {
        if (num % i == 0) {
            if (m[i] == 0) {
                m[i] = 1;
            } else {
                m[i]++;
            }

            num /= i;
            break;
        }
    }

    if (cache == num) {
        if (m[num] == 0) {
            m[num] = 1;
        } else {
            m[num]++;
        }
        return;
    } else {
        prime_map(m, num);
    }
}