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 Python (3.8.2) (judge verdict: Accepted)

#
# abc065 b
#
import sys
from io import StringIO
import unittest


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例_1(self):
        input = """3
3
1
2"""
        output = """2"""
        self.assertIO(input, output)

    def test_入力例_2(self):
        input = """4
3
4
1
2"""
        output = """-1"""
        self.assertIO(input, output)

    def test_入力例_3(self):
        input = """5
3
3
4
2
4"""
        output = """3"""
        self.assertIO(input, output)


def resolve():
    N = int(input())
    a = [0] + [int(input()) for _ in range(N)]
    A = [0] * (N+1)

    p = 1
    ans = 0
    while True:
        A[p] += 1
        if A[p] == 2:
            ans = "-1"
            break
        ans += 1
        p = a[p]
        if p == 2:
            break

    print(ans)


if __name__ == "__main__":
    # unittest.main()
    resolve()