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: Wrong Answer)

import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int vertexCount = scanner.nextInt();
        int edgeCount = scanner.nextInt();

        int[][] edges = new int[edgeCount][2];
        for (int i = 0; i < edgeCount; ++i) {
            edges[i][0] = scanner.nextInt();
            edges[i][1] = scanner.nextInt();
        }

        Arrays.sort(edges, Comparator.comparingInt(edge -> edge[0]));

        int[] dp = new int[vertexCount];
        for (int step = 0; step < 2; ++step) {
            for (int i = 0; i < edgeCount; ++i) {
                dp[edges[i][1] - 1] = Math.max(dp[edges[i][1] - 1], dp[edges[i][0] - 1] + 1);
            }
        }

        int res = 0;
        for (int i = 0; i < vertexCount; ++i) {
            res = Math.max(res, dp[i]);
        }

        System.out.println(res);
    }
}