Longest Delegation Chain in a Company

A company has N employees, numbered 1 through N, where employee 1 is the CEO and has no manager. Every other employee i (2 <= i <= N) reports directly to exactly one manager, given as p_i, and an employee may have any number of direct reports, including zero. A management chain starting at the CEO is a path that begins at employee 1 and repeatedly moves to a direct report, ending at some employee who has no direct reports of their own; its length is the number of employees on that path, counting both the CEO and the final employee. Determine the length of the longest such management chain in the company.

Input format

• Line 1: a single integer N -- the number of employees.
• Line 2 (present only when N > 1): N-1 integers p_2, p_3, ..., p_N, where p_i is the direct manager of employee i. It is guaranteed that p_i < i for every i, so the input always describes a valid tree rooted at employee 1.

Output format

Print a single integer: the number of employees on the longest management chain starting at the CEO.

Constraints

• 1 <= N <= 10000
• for every i with 2 <= i <= N: 1 <= p_i < i

7
1 1 3 3 4 4

4

5
1 1 1 1

2