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.*;
public class Main{
   

  public static int longestPath(ArrayList<ArrayList<Integer>> graph,int sv,int dp[])
  {
	  
	  ArrayList<Integer> edges=graph.get(sv);
	 
	  int ans=0;
	  if(edges.size()==0)
		  return 0;
	  if(dp[sv]!=0)
		  return dp[sv];
	  for(int i=0;i<edges.size();i++)
	  {
		  
		  ans=Math.max(ans,1+longestPath(graph,edges.get(i),dp));
	  }
	  dp[sv]=ans;
	  return ans;
  }
	
  public static void main(String[] args)
  {
     
  Scanner s=new Scanner(System.in);
  int nVert=s.nextInt();
  int nEdges=s.nextInt();
  ArrayList<ArrayList<Integer>> graph=new ArrayList<>();
  for(int i=0;i<=nVert;i++)
  {
	  graph.add(i,new ArrayList<Integer>());
  }
  
  for(int i=1;i<=nEdges;i++)
  {
	  int sVert=s.nextInt();
	  int eVert=s.nextInt();
	
	  graph.get(sVert).add(eVert);
	  
  }
  
int dp[]=new int[nVert+1];
  int ans=Integer.MIN_VALUE;
  for(int i=1;i<=nVert;i++) {
	
  ans=Math.max(ans,longestPath(graph,i,dp));
  }
 System.out.println(ans);
  s.close();
    
  }
}