Problem9792--ABC263 —— B - Ancestor

9792: ABC263 —— B - Ancestor

[Creator : ]
Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

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

-   $2 \le N \le 50$
-   $1 \le P_i &lt; i(2 \le i \le N)$
-   All values in input are integers.

Sample 1 Input

3
1 2

Sample 1 Output

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 2 Input

10
1 2 3 4 5 6 7 8 9

Sample 2 Output

9

Source/Category