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>
const long long MOD = 1000000007;
const int INF = INT_MAX / 2;
const long double PI = 3.1415926;
#define FOR(i, r, n) for(int i=(ll)(r); i<(ll)(n); i++) 
#define REP(i, n) FOR(i, (0), n)
#define ALL(r) r.begin(), r.end()
#define ll long long int
#define vi vector<ll>
#define vs vector<string>
#define vp vector<pair<ll, ll>>
#define vt vector<tuple<ll, ll, ll>>
using namespace std;
vector<vector<ll>> vv(110, vector<ll>(50, 0));
map<ll, ll> mp;

typedef int Weight;
struct Edge
{
	int from, to; Weight cost;
	bool operator < (const Edge& e) const { return cost < e.cost; }
	bool operator > (const Edge& e) const { return cost > e.cost; }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &g, int from, int to, Weight cost)
{
	g[from].push_back(Edge{ from, to, cost });
}

vi v;

ll parent(ll num) {
	if (v[num] == num) return num;
	else {
		ll res = parent(v[num]);
		v[num] = res;
		return res;
	}
}

ll same(ll v01, ll v02) {
	if (parent(v01) == parent(v02)) return 1;
	else return 0;
}

void unionn(ll v01, ll v02) {
	v[parent(v02)] = parent(v01);
}

int main()
{
	ll n;
	cin >> n;
	v.resize(n);
	REP(i,n)
	{
		ll m;
		cin >> m;
		unionn(i, m - 1);
	}
	cout << (same(0, 1) ? "yes" : "no") << endl;
}