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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	static HashMap<Integer,HashMap<Integer,Integer>>gr;
	public static long solve(int i,long []dp,HashMap<Integer,HashMap<Integer,Integer>>gr)
	{
		
		if(dp[i]!=-1)
		return dp[i];
		long ret=0;
		if(gr.containsKey(i))
		{
		for(int y:gr.get(i).keySet())
		{
		//	System.out.println(i+" "+y);
			ret=Math.max(ret,solve(y,dp,gr)+1);
		}
		}
	//	System.out.println(ret+" i hai"+i);
		
		dp[i]=ret;
		return ret;
	}
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner scn=new Scanner(System.in);
		int n=scn.nextInt();
		int m=scn.nextInt();
		gr=new HashMap<>();
		while(m-->0)
		{
			int a,b;
			a=scn.nextInt();
			b=scn.nextInt();
			if(gr.containsKey(a))
			{
				gr.get(a).put(b,1);
			}
			else
			{
				HashMap<Integer,Integer>map=new HashMap<>();
				map.put(b,1);
				gr.put(a,map);
			}
		}
		//System.out.println(gr);
		// StringBuilder sb=new StringBuilder();
		// for(int x:gr.keySet())
		// {
		// 	sb.append(x+"->");
		// 	for(int y:gr.get(x).keySet())
		// 	{
		// 		sb.append(y+",");
		// 	}
		// 	sb.append("\n");
		// }
		// System.out.println(sb);
		long an=-1;
		long []dp=new long[100005];
		for(int i=0;i<=n;i++)
		{
			dp[i]=-1;
		}
		for(int x:gr.keySet())
		{
			an=Math.max(an,solve(x,dp,gr));
		}
		System.out.println(an);
	}
}