## Educational DP Contest AtCoder G - Longest Path

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Points: 10
Time limit: 1.0s
Memory limit: 1G

Problem types

There is a directed graph with vertices and edges. The vertices are numbered , and for each , the -th directed edge goes from Vertex to . does not contain directed cycles.

Find the length of the longest directed path in . Here, the length of a directed path is the number of edges in it.

#### Constraints

• All values in input are integers.
• All pairs are distinct.
• does not contain directed cycles.

#### Input Specification

The first line will contain 2 space separated integers .

The next lines will contain 2 space separated integers, .

#### Output Specification

Print the length of the longest directed path in .

#### Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

#### Sample Output 1

3

#### Explanation For Sample 1

The red directed path in the following figure is the longest:

#### Sample Input 2

6 3
2 3
4 5
5 6

#### Sample Output 2

2

#### Explanation For Sample 2

The red directed path in the following figure is the longest:

#### Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

#### Sample Output 3

3

#### Explanation For Sample 3

The red directed path in the following figure is one of the longest: