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 void main(String args[])
  {
    Scanner sc= new Scanner(System.in);
    int n=sc.nextInt();
    int m=sc.nextInt();
    ArrayList<Integer> g[]= new ArrayList[n+1];
    for(int i=0;i<=n;i++)
      g[i]=new ArrayList<Integer>();
    for(int i=0;i<m;i++)
    {
      int x=sc.nextInt();
      int y=sc.nextInt();
      g[x].add(y);
    }
    boolean vis[]= new boolean[n+1];
    int dp[]=new int[n+1];
    for(int i=1;i<=n;i++)
    {
      if(!vis[i])
        dfs(vis,dp,g,i);
    }
    int max=0;
    for(int i=1;i<=n;i++)
		max=Math.max(max,dp[i]);
    System.out.println(max);
  }
  static void dfs(boolean vis[],int dp[],ArrayList<Integer> g[],int i)
  {
    vis[i]=true;
    for(int j=0;j<g[i].size();j++)
    {
      if(!vis[g[i].get(j)])
        dfs(vis,dp,g,g[i].get(j));
      dp[i]=Math.max(dp[i],1+dp[g[i].get(j)]);
    }
  }
}