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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define rep(i,b) FOR(i,0,b)
#define INF mugen
#define dump(x) cerr<<#x<<"="<<x<<endl
#define all(a) (a).begin(),(a).end()
typedef vector<int> vi;
typedef vector<vi> vii;
typedef vector<vii> viii;
typedef pair<int,int> P;
template <class T> void chmin(T & a, T const & b) { if (b < a) a = b; }
inline int toInt(string s) { int v; istringstream sin(s); sin >> v; return v; }
using ll = long long;
const ll mod = LLONG_MAX;

int n;
int a[112345];
bool used[112345];
int ans;
int main(){
  cin>>n;
  rep(i,n)cin>>a[i];
  int next=0;
  while(1){
    ans++;
    if(used[next]){
      cout<<"-1"<<endl;
      return 0;
    }
    used[next]=true;

    next=a[next];
    if(next==2){
      cout<<ans<<endl;
      return 0;
    }
  }


}