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.Scanner;

public class Main {
	public static int[] dp;
	public static path[] a;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int max = 0;
		dp = new int[n];
		a = new path[n];
		for (int i = 0; i < n; i++) dp[i] = -1;
		for (int i = 0; i < n; i++) a[i] = new path();
		int x, y;
		for (int i = 0; i < m; i++) {
			x = sc.nextInt()-1;
			y = sc.nextInt()-1;
			a[x].list.add(y);
		}
		for (int i = 0; i < n; i++) dfs(i);
		for (int i = 0; i < n; i++) {
			max = Math.max(dp[i], max);
		}
		System.out.println(max);
		sc.close();
	}

	public static class path{
		public ArrayList<Integer> list;
		public path() {
			this.list = new ArrayList<Integer>();
		}
	}

	public static int dfs(int x) {
		if(dp[x] != -1) return dp[x];
		int max = 0;
		if(a[x].list.size()>0) {
			for (int i = 0; i < a[x].list.size(); i++) {
				max = Math.max(max, dfs(a[x].list.get(i)));
			}
			dp[x] = max+1;
		}else {
			dp[x] = 0;
		}
		return dp[x];
	}
}