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 ll long long
#define ull unsigned long long
#define FOR(i,a,b) for (int i=(a);i<(b);++i)
#define REP(i,n) for(int i=0;i<(n);++i)
#define debug(x) cerr<<#x<<": "<<x<<'\n'
#define all(x) (x).begin(),(x).end()
#define SZ(x) ((int)(x).size())
#define pb push_back
#define mp make_pair

using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;

int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

template<class T=int>
T in(){T x;cin>>x;return (x);}
template<class T>
void print(T& x){cout<<x<<'\n';}

const int MOD =(int)1e9+7;
const int MAX =510000;

ll fac[MAX],finv[MAX],inv[MAX];
void COMint(){
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    for(int i=2;i<MAX;i++){
        fac[i]=fac[i-1]*i%MOD;
        inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
        finv[i]=finv[i-1]*inv[i]%MOD;
    }
}
ll COM(int n,int k){
    if(n<k) return 0;
    if(n<0||k<0)return 0;
    return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

ll gcd(ll a,ll b){
    if(b==0)return a;
    if(a>b){
        swap(a,b);
    }
    return gcd(a,b%a);
}
ll lcm(ll a,ll b){
    ll g;g=gcd(a,b);
    return a*b/g;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int N=in();
    int a[N+1];
    bool checked[N+1];
    REP(i,N){
        cin>>a[i+1];
        checked[i+1]=false;
    }
    int cnt;cnt=0;
    int next;next=1;
    while(checked[next]==false){
        cnt++;
        checked[next]=true;
        next=a[next];
        //debug(next);
        if(next==2){
            cout<<cnt<<endl;
            return 0;
        }
    }
    cout<<-1<<endl;
    return 0;

}