Score : $200$ points

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 $1$?

Constraints

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

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.

3
1 2

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 $2$.

10
1 2 3 4 5 6 7 8 9

9