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A. Party

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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?

Input

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.

Output

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

Examples

Input

5

-1

1

2

1

-1

Output

3

Note

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

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

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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