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 javax.swing.*;
import java.io.*;
import java.sql.Struct;
import java.util.*;

public class Main {


    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();

        ArrayList<Integer>[] graph = new ArrayList[n];
        int[] arr = new int[n];

        for (int i = 0; i < n; i++) {
            graph[i] = new ArrayList<Integer>();
            arr[i] = -1;
        }

        for (int i = 0; i < m; i++) {
            int start = sc.nextInt();
            int end = sc.nextInt();
            graph[start - 1].add(end - 1);
        }

        int length = 0;
        for (int i = 0; i < n; i++) {
           int curLength = calculate(i, graph, arr);
           if (curLength > length) {
               length = curLength;
            }
        }
        System.out.println(length);
    }

    static int calculate(int vertex,  ArrayList<Integer>[] graph, int[] arr) {
        if (arr[vertex] != -1) {
            return arr[vertex];
        }
        int length = 0;
        for(int i = 0; i < graph[vertex].size(); i++) {
            int neghbourLength = calculate(graph[vertex].get(i), graph, arr);
            if (neghbourLength + 1 > length) {
                length = neghbourLength + 1;
            }
        }
        arr[vertex] = length;
        return length;
    }
}