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.*;
import java.io.*;

public class Main {

	public static int n, m;
	public static Map<Integer, LinkedList<Integer>> graph = new HashMap<>();
	public static int[] dp;

	public static int TopologicalSort() {
		Queue<Integer> qu = new LinkedList<>();
		for (int i = 1; i <= n; i++)
			if (dp[i] == 0)
				qu.add(i);

		int count = 0;
		while (!qu.isEmpty()) {
			int size = qu.size();
			for (int k = 0; k < size; k++) {
				LinkedList<Integer> temp = graph.get(qu.poll());
				if (temp == null)
					continue;
				for (int t : temp) {
					dp[t]--;
					if (dp[t] == 0)
						qu.add(t);
				}
			}
			count++;
		}
		return count - 1;
	}

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] s = br.readLine().split(" ");
		n = Integer.parseInt(s[0]);
		m = Integer.parseInt(s[1]);
		dp = new int[n + 1];

		for (int i = 0; i < m; i++) {
			s = br.readLine().split(" ");
			int x = Integer.parseInt(s[0]);
			int y = Integer.parseInt(s[1]);
			if (!graph.containsKey(x))
				graph.put(x, new LinkedList<Integer>());
			graph.get(x).add(y);
			dp[y]++;
		}

		System.out.println(TopologicalSort());

	}

}