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.PrintWriter;
public class Main{
	static ArrayList<Integer>[] edge;
	static int[] dp;
	static boolean[] visited;
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		edge=new ArrayList[n];
		dp=new int[n];
		visited=new boolean[n];
		for(int i=0; i<n; i++){
			edge[i]=new ArrayList<>();
		}
		for(int i=0; i<m; i++){
			int x=sc.nextInt()-1;
			int y=sc.nextInt()-1;
			edge[x].add(y);
		}
		int ans=0;
		for(int i=0; i<n; i++){
			if(!visited[i]){
				dfs(i);
				ans=Math.max(ans,dp[i]);
			}
		}
		System.out.println(ans);
	}
	static void dfs(int now){
		visited[now]=true;
		for(int i:edge[now]){
			if(!visited[i]){
				dfs(i);
			}
			dp[now]=Math.max(dp[now],dp[i]+1);
		}
	}
}