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 BufferedReader br;
	static int cin() throws Exception
	{
		return Integer.valueOf(br.readLine());
	}
	static int[] split() throws Exception
	{
		String[] cmd=br.readLine().split(" ");
		int[] ans=new int[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Integer.valueOf(cmd[i]);
		}
		return ans;
	}
	static long[] splitL() throws IOException
	{
		String[] cmd=br.readLine().split(" ");
		long[] ans=new long[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Long.valueOf(cmd[i]);
		}
		return ans;
	}
	static int[] dp;
	static ArrayList<Integer>[]gr;
	static int dfs(int node)
	{
		int res=0;
		for(int i=0;i<gr[node].size();i++)
		{
			int y=gr[node].get(i);
			if(dp[y]!=-1)
				res=Math.max(res,1+dp[y]);
			else
				res=Math.max(res,1+dfs(y));
		}
		dp[node]=res;
		return res;
	}
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		br=new BufferedReader(new InputStreamReader(System.in));
		int[]ar=split();
		int n=ar[0];
		int m=ar[1];
		gr=new ArrayList[n+1];
		for(int i=0;i<=n;i++)
		{
			gr[i]=new ArrayList<>();
		}
		for(int i=0;i<m;i++)
		{
			ar=split();
			int x=ar[0];
			int y=ar[1];
			gr[x].add(y);
		}
		dp=new int[n+1];
		Arrays.fill(dp, -1);
		for(int i=1;i<=n;i++)
		{
			if(dp[i]!=-1)
				continue;
			dp[i]=dfs(i);
		}
		int ans=0;
		for(int i=1;i<=n;i++)
		{
			ans=Math.max(ans, dp[i]);
		}
		System.out.println(ans);
	}
}