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 vector<ll> V;
#define rep(cnt,e) for(ll cnt=0;cnt<e;cnt++ )
typedef pair<ll,ll> P;
const ll mod = 1e9+7;
const ll INF = INT64_MAX;
typedef tuple<ll,ll,ll,ll> T;

ll i,j,k;


int main(){
   ll N;
   cin>>N;
   V a(N);
   rep(i,N)cin>>a[i];
   vector<bool> jud(N,true);
   ll ans=0;
   ll current=0;
   jud[0]=false;
   while(true){
      ans++;
      if(jud[a[current]-1]){
          if(a[current]-1==1){
              cout<<ans<<endl;
              break;
          }
          else{
              jud[a[current]-1]=false;
              current=a[current]-1;
              
          }

      }
      else{
          cout<<-1<<endl;
          break;
      }
   }
}