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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {

	static int dp[] = new int[100100];
	static ArrayList<ArrayList<Integer>> edge = new ArrayList<>();
	static boolean used[];

	static ArrayList<Integer> ans = new ArrayList<>();

	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String str[] = br.readLine().split(" ");

		int N = Integer.parseInt(str[0]);
		int M = Integer.parseInt(str[1]);

		used = new boolean[N];

		for (int i = 0; i < N; i++) {
			edge.add(new ArrayList<>());
		}

		for (int i = 0; i < M; i++) {
			str = br.readLine().split(" ");
			int x = Integer.parseInt(str[0]) - 1;
			int y = Integer.parseInt(str[1]) - 1;
			edge.get(x).add(y);
		}

		int ans = 0;
		for (int i = 0; i < N; i++) {
			visit(i);
			ans = Math.max(dp[i], ans);
		}
		System.out.println(ans);
	}

	static void visit(int now) {
		if (!used[now]) {
			used[now] = true;
			for (int i : edge.get(now)) {
				visit(i);
				dp[now] = Math.max(dp[now], dp[i] + 1);
			}
		}
	}
}