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.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;

public class Main {
    private static Scanner in;
    private static int n, m;
    private static HashMap<Integer, ArrayList<Integer>> g;
    private static int[] mem;

	public static void main(String[] args) {
        in = new Scanner(System.in);
        n = in.nextInt();
        m = in.nextInt();
        g = new HashMap<>();
        mem = new int[n];

        Arrays.fill(mem, -1);

        for(int i=0; i<n; i++) {
            g.put(i, new ArrayList<Integer>());
        }

        for(int i=0; i<m; i++) {
            int p = in.nextInt()-1;
            int q = in.nextInt()-1;
            g.get(p).add(q);
        }

        int ans = 0;
        for(int i=0; i<n; i++) {
            ans = Math.max(ans, solve(i));
        }

        System.out.println(ans);
	}

    private static int solve(int u) {
        if (mem[u]!=-1) return mem[u];

        int ans = 0;

        for(int v: g.get(u)) {
            ans = Math.max(ans, 1+solve(v));
        }

        return mem[u] = ans;
    }

}