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 in = new Scanner(System.in);
	String[] temp = in.nextLine().split(" ");
	int N = Integer.parseInt(temp[0]);
	int M = Integer.parseInt(temp[1]);
	ArrayList<Integer>[] graph = new ArrayList[N+1];
	for (int i = 0; i <= N; i++) graph[i] = new ArrayList<>();
	for (int i = 0; i < M; i++) {
	    temp = in.nextLine().split(" ");
	    int from = Integer.parseInt(temp[0]);
	    int to = Integer.parseInt(temp[1]);
	    graph[to].add(from);
	}
	in.close();
	int[] mem = new int[N+1];
	Arrays.fill(mem, -1);
	int res = 0;
	for (int i = 1; i <= N; i++) {
	    res = Math.max(res, longest(i, mem, graph));
	}
	System.out.println(res);
	
    }

    public static int longest(int i, int[] mem, ArrayList<Integer>[] graph) {
	if (mem[i] == -1) {
	    int res = 0;
	    for (int j : graph[i]) {
		res = Math.max(res, longest(j, mem, graph)+1);
	    }
	    mem[i] = res;
	}
	return mem[i];
    }
}