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 long double ld;

int dist[100005];
int u[100005];

int main(){
    ios_base::sync_with_stdio(false);
    cout.precision(10);
    cout<<fixed;

    int n;
    cin >> n;
    for(int i=1; i<=n; i++){
        cin >> u[i];
    }
    queue <int> q;
    q.push(1);
    for(int i=2; i<=n; i++) dist[i] = 100000000;
    while(!q.empty()){
        int v = q.front();
        q.pop();
        if(v == 2){
            cout << dist[v] << "\n";
            return 0;
        }
        if(dist[u[v]] > dist[v] + 1){
            dist[u[v]] = dist[v] + 1;
            q.push(u[v]);
        }
    }
    cout << "-1\n";
    return 0;
}