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 REP(i, n) for(int i = 0; i < (int)n; i++)
#define REPvec(itr, mp) for(auto itr = mp.begin();itr != mp.end(); itr ++)
#define all(x) x.begin(), x.end()
#define MOD 1000000007//1e9+7
using namespace std;
typedef long long ll;
typedef vector<int >    vecint;
typedef vector<string > vecstr;
int main()
{
  int n;
  cin >> n;
  vecint a(n,0);
  REP(i,n){
    cin >> a[i];
  }
  map<int, int> check;
  check[0]++;
  int i = 0;
  int count = 0;
  while(true){
    // cout << count << " " << i << " " << a[i] - 1 << endl;
    if(check.count(1) == 1){
      cout << count << endl;
      return 0;
    }
    check[a[i] - 1]++;
    i = a[i] - 1;
    count ++;
    // if(check.count(i) == 1){
    //   cout << -1 << endl;
    //   return 0;
    // }
    if(count == n){
      cout << -1 << endl;
      return 0;
    }
  }
}