Company Hierarchy Levels

You are given a company hierarchy represented by n employees and a list of direct reporting relations. Each relation is given as a pair of integers x y, which means that employee y reports directly to employee x.

The company's hierarchy forms a tree with a single top-level employee (the root), who does not report to anyone. Your task is to determine the number of distinct levels in this hierarchy. (Level 1 is the root, level 2 contains the direct subordinates of the root, and so on.)

Note: The employees are numbered from 1 to n. It is guaranteed that the structure forms a valid tree.

inputFormat

The input is read from stdin and has the following format:

• The first line contains an integer n, the number of employees.
• The second line contains an integer m, the number of direct reporting relations.
• Each of the following m lines contains two integers x and y indicating that employee y reports directly to employee x.

outputFormat

Output a single integer to stdout representing the number of distinct levels in the company hierarchy.

7
6
1 2
1 3
2 4
2 5
3 6
3 7

3