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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	static List<Integer>[] es;
	static int[] dp;

	private static void dfs(int v) {
		if (es[v].size() == 0) return;
		int a = 0;
		for (Integer e : es[v]) {
			if (dp[e] == 0) {
				dfs(e);
			}
			a = Math.max(a, dp[e]);
		}
		dp[v] = a + 1;
	}

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

		dp = new int[n];
		es = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			es[i] = new ArrayList<>();
		}
		boolean[] hasIn = new boolean[n];
		for (int i = 0; i < m; i++) {
			int x = sc.nextInt() - 1;
			int y = sc.nextInt() - 1;
			es[x].add(y);
			hasIn[y] = true;
		}

		for (int i = 0; i < n; i++) {
			if (!hasIn[i]) dfs(i);
		}

		int answer = 0;
		for (int i = 0; i < n; i++) {
			answer = Math.max(answer, dp[i]);
		}

		System.out.println(answer);
	}
}