Problem Statement

There are $N people, called Person 1, Person 2, \ldots, Person N$.
The parent of Person $i (2 \le i \le N)$ is Person P_i. Here, it is guaranteed that P_i < i.
How many generations away from Person N is Person 1?

Input

Input is given from Standard Input in the following format:
N
$P_2 P_3 \dots P_N$

Output

Print the answer as a positive integer.

Constraints

• $2 \le N \le 50$
• $1 \le P_i < i(2 \le i \le N)$
• All values in input are integers.

Sample Input 1

3
1 2

Sample Output 1

2

Person 2 is a parent of Person 3, and thus is one generation away from Person 3.
Person 1 is a parent of Person 2, and thus is two generations away from Person 3.
Therefore, the answer is 2.

Sample Input 2

10
1 2 3 4 5 6 7 8 9

Sample Output 2

9

见题面 Input 部分

见题面 Output 部分