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?

The first line contains integer $ n $ ( $ 1

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

For the first example, three groups are sufficient, for example: - Employee 1 - Employees 2 and 4 - Employees 3 and 5