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 G with N vertices and M edges. The vertices are numbered 1, 2, \dots, N, and for each i (1 \le i \le M), the i-th directed edge goes from Vertex x_i to y_i. G does not contain directed cycles.

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

Constraints

  • All values in input are integers.
  • 2 \le N \le 10^5
  • 1 \le M \le 10^5
  • 1 \le x_i, y_i \le N
  • All pairs (x_i, y_i) are distinct.
  • G does not contain directed cycles.

Input Specification

The first line will contain 2 space separated integers N, M.

The next M lines will contain 2 space separated integers, x_i, y_i.

Output Specification

Print the length of the longest directed path in G.

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:


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