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.

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