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.*;
import java.util.*;

public class Main {

	static ArrayList<ArrayList<Integer> >ve ; 
	static int dp[] ; 
	static void dfs(int i)
	{
		ArrayList<Integer> u = ve.get(i) ; 
		if(u.size()!=0)
		{
			int y = 0 ;
			for(int ele : u)
			{
				if(dp[ele]==0)
				{
					dfs(ele) ; 	
				}
				int va = dp[ele] ; 
				y = Integer.max(y, va) ; 
				
			}
	        dp[i]= y+1 ; 
		}
				
	}
	public static void main(String[] args) throws Exception{
		BufferedReader  jk =  new BufferedReader(new InputStreamReader( System.in))  ; 
		PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)) ; 
		StringTokenizer ana = new StringTokenizer(jk.readLine()) ;
		int n =Integer.parseInt(ana.nextToken()) ; 
		int m = Integer.parseInt(ana.nextToken()) ;
		dp = new int[n] ;  
		ve = new ArrayList<>() ; 
		boolean v[] = new boolean[n] ; 
		for(int i=0 ; i<n ;i++) ve.add(new ArrayList<>()) ; 
		for(int i=0 ; i<m ;i++)
		{
			ana = new StringTokenizer(jk.readLine()) ;
			int x= Integer.parseInt(ana.nextToken())-1 ; int y= Integer.parseInt(ana.nextToken())-1 ; 
			ve.get(x).add(y) ; 
			v[y]=true ;

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



		int y = 0 ;
		for(int i=0 ; i<n ;i++)
		{
			if(dp[i]>y) y=dp[i] ; 
		}

		out.println(y);



		out.flush();
	}
}