Problem: 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.

Examples

Input

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


Output

3


Input

6 3
2 3
4 5
5 6


Output

2


Input

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


Output

3

Solution (in JAVA):

Solution:
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        ArrayList<Integer>[] adj = (ArrayList<Integer>[]) new ArrayList[n];
        int ans[] = new int[n];

        for (int i = 0; i < n; i++) {
            adj[i] = new ArrayList<Integer>();
            ans[i] = -1;
        }
        for (int i = 0; i < m; i++) {
            int x, y;
            x = scanner.nextInt();
            y = scanner.nextInt();
            adj[x - 1].add(y - 1);
            // adj[y - 1].add(x - 1);
        }
        boolean visited[] = new boolean[n];
        int maxPath = Integer.MIN_VALUE;
        for (int i = 0; i < visited.length; i++) {
            if (!visited[i]) {
                maxPath = Math.max(getPath(adj, visited, i, ans), maxPath);
            }
        }

        System.out.println(maxPath - 1);

    }

    public static int getPath(ArrayList<Integer> graph[], boolean visited[], int vertex, int ans[]) {
        if (ans[vertex] != -1) {
            return ans[vertex];
        }
        int path = Integer.MIN_VALUE;
        for (int i = 0; i < graph[vertex].size(); i++) {

            visited[graph[vertex].get(i)] = true;
            path = Math.max(1 + getPath(graph, visited, graph[vertex].get(i), ans), path);
        }

        if (path == Integer.MIN_VALUE) {
            path = 1;
        }
        ans[vertex] = path;
        return ans[vertex];

    }

}