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.lang.*;
import java.io.*;
public class Main{
	static int[]dp=new int[100001];
	static ArrayList<ArrayList<Integer>>al=new ArrayList<ArrayList<Integer>>();
	static int solve(int src){
		if(dp[src]!=0)
			return dp[src];

		boolean leaf=true;
		int bestChild=0;
		for(int child:al.get(src)){
			leaf=false;
			bestChild=Math.max(bestChild,solve(child));
		}
		return dp[src]= leaf?0:1+bestChild;
	}
	public static void main(String[] args)throws IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String s=br.readLine();
		String[]s1=s.split(" ");
		int n=Integer.parseInt(s1[0]);
		int m=Integer.parseInt(s1[1]);
		for (int i = 0; i <=n; i++) 
            al.add(new ArrayList<Integer>());
		for(int i=0;i<m;i++){
			String d=br.readLine();
			String[]s2=d.split(" ");
			int x=Integer.parseInt(s2[0]);
			int y=Integer.parseInt(s2[1]);
			al.get(x).add(y);
		}
		int ans=0;
		for(int i=1;i<=n;i++){
			ans=Math.max(ans,solve(i));
		}
		System.out.println(ans);
	}
}