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:
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?
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.
Print a single integer denoting the minimum number of groups that will be formed in the party.
5
-1
1
2
1
-1
3
For the first example, three groups are sufficient, for example: