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.io.*;
import java.util.*;

public class Main {
    private static int n, m;
    private static ArrayList[] graph;
    private static int[] max;

    private static int dfs(int i) {
        if (max[i] != -1) {
            return max[i];
        }
        int dist = 0;
        for (Integer neigh : (ArrayList<Integer>) graph[i]) {
            dist = Math.max(dist, 1 + dfs(neigh));
        }
        return max[i] = dist;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        max = new int[n + 1];
        Arrays.fill(max, -1);
        graph = new ArrayList[n + 1];
        for (int i = 0; i <= n; i++) {
            graph[i] = new ArrayList<Integer>();
        }

        for (int i = 1; i <= m; i++) {
            int p = sc.nextInt();
            int q = sc.nextInt();
            graph[p].add(q);
        }

        for (int i = 1; i <= n; i++) {
            dfs(i);
        }
        int ans = 0;
        for (int i = 1; i <= n; i++) {
            ans = Math.max(ans, max[i]);
        }
        System.out.println(ans);
    }
}