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);
		int k = in.nextInt();
		int n = in.nextInt();
		List<List<Integer>> list = new ArrayList<>();
		for (int i = 0; i <= k; i++) list.add(new ArrayList<>());
		int[] degrees = new int[k+1];
		for (int i = 0; i < n; i++) {
			int a = in.nextInt();
			int b = in.nextInt();
			list.get(a).add(b);
			degrees[b]++;
		}
		Queue<Integer> queue = new LinkedList<>();
		for (int i = 1; i <= k; i++) {
			if(degrees[i] == 0) queue.add(i);
		}
		int depth = -1;
		while(!queue.isEmpty()){
			depth++;
			int size = queue.size();
			for (int i = 0; i < size; i++) {
				int tmp = queue.poll();
				for(int node : list.get(tmp)){
					if(--degrees[node] == 0) queue.add(node);
				}
			}
		}
		System.out.println(depth);
	}
}