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?

Input

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

The next n lines contain the integers pi (1 ≤ pi ≤ n or pi = -1). Every pi denotes the immediate manager for the i-th employee. If pi 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 (pi ≠ 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 
def search_depth(employee_mapping, number):
    if number not in employee_mapping:
        return 1
    max_depth = 0
    for employee in employee_mapping[number]:
        depth = search_depth(employee_mapping, employee)
        if depth > max_depth:
            max_depth = depth

    return max_depth + 1


def func():
    employee_mapping = {}
    n = int(input())
    for i in range(n):
        manager_number = int(input())
        if manager_number not in employee_mapping:
            employee_mapping[manager_number] = []
        employee_mapping[manager_number].append(i + 1)
    depth = search_depth(employee_mapping, -1)
    print(depth - 1)


if __name__ == '__main__':
    func()
