Problem:
Score : 100 points

Problem Statement

There is a directed graph G with N vertices and M edges.
The vertices are numbered 1, 2, \ldots, N, and for each i (1 \leq i \leq 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 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq x_i, y_i \leq N

All pairs (x_i, y_i) are distinct.

G does not contain directed cycles.

Input

Input is given from Standard Input in the following format:

N M
x_1 y_1
x_2 y_2
:
x_M y_M

Output

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

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

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

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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.stream.IntStream;

public class Main {
    private static java.util.Scanner scanner = new java.util.Scanner(System.in);

    public static void main(String[] args) {
        int n = scanner.nextInt(), m = scanner.nextInt();
        int[] dp = new int[n];
        @SuppressWarnings("unchecked")
        List<Integer>[] sideList = IntStream.range(0, n).mapToObj(i -> new ArrayList()).toArray(List[]::new);
        IntStream.range(0, m).forEach(i -> sideList[scanner.nextInt() - 1].add(scanner.nextInt() - 1));

        int max, max1 = 0;
        boolean hasChanged = true;
        while (hasChanged) {
            hasChanged = false;
            max = max1;
            for (int i = 0; i < n; i++) {
                if (dp[i] == max) {
                    for (int j : sideList[i]) {
                        if (dp[j] <= dp[i]) {
                            max1 = dp[j] = dp[i] + 1;
                            hasChanged = true;
                        }
                    }
                }
            }
        }
        Arrays.stream(dp).max().ifPresent(System.out::println);
    }
}