CF115A.Party

A company has n employees numbered from 1 to n. Each employee either has no immediate manager or exactly one immediate manager, who is another employee with a different number. An employee A is said to be the superior of another employee B if at least one of the following is true:

• Employee A is the immediate manager of employee B
• Employee B has an immediate manager employee C such that employee A is the superior of employee C.

The company will not have a managerial cycle. That is, there will not exist an employee who is the superior of his/her own immediate manager.

Today the company is going to arrange a party. This involves dividing all n employees into several groups: every employee must belong to exactly one group. Furthermore, within any single group, there must not be two employees A and B such that A is the superior of B.

What is the minimum number of groups that must be formed?

一家公司有 $n$ 名员工，编号从 $1$ 到 $n$。每名员工要么没有直接上级（即无直属经理），要么恰好有一名直接上级，且该直接上级是另一名编号不同的员工。若满足以下任一条件，则称员工 $A$ 是员工 $B$ 的上级：

• 员工 $A$ 是员工 $B$ 的直接上级；
• 员工 $B$ 有一名直接上级 $C$，且员工 $A$ 是员工 $C$ 的上级。

公司中不会出现管理循环，即不存在某名员工，使其成为其自身直接上级的上级。

今天公司将举办一场聚会，需要将全部 $n$ 名员工划分为若干组：每名员工必须且仅属于一个组；此外，在任意一个组内，不能存在两名员工 $A$ 和 $B$，使得 $A$ 是 $B$ 的上级。

问：至少需要划分成多少个组？

The first line contains integer n (1 ≤ n ≤ 2000) — the number of employees.

The next n lines contain the integers p__i (1 ≤ p__i ≤ n or p__i = -1). Every p__i denotes the immediate manager for the i-th employee. If p__i is -1, that means that the i-th employee does not have an immediate manager.

It is guaranteed, that no employee will be the immediate manager of him/herself (p__i ≠ i). Also, there will be no managerial cycles.

第一行包含一个整数 $n$（$1 \leq n \leq 2000$）—— 员工人数。

接下来的 $n$ 行每行包含一个整数 $p_i$（$1 \leq p_i \leq n$ 或 $p_i = -1$）。每个 $p_i$ 表示第 $i$ 位员工的直接上级。若 $p_i = -1$，则表示第 $i$ 位员工没有直接上级。

保证不会出现某位员工是其自身直接上级的情况（即 $p_i \neq i$），且不存在管理循环。

Print a single integer denoting the minimum number of groups that will be formed in the party.

输出一个整数，表示聚会上形成的最少组数。

For the first example, three groups are sufficient, for example:

• Employee 1
• Employees 2 and 4
• Employees 3 and 5

对于第一个例子，三个组就足够了，例如：

• 员工 1
• 员工 2 和 4
• 员工 3 和 5