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 dp[];
  public static int dfs(List<Integer>[] g,
  int u)
  {
      if(dp[u]!=-1)
      return dp[u];
      int ans=0;
      for(int child:g[u])
      {
        ans=Math.max(ans,1+dfs(g,child));
      }
      return dp[u]=ans;
  }
  public static void main(String[] args)
  {
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    int m=sc.nextInt();
    List<Integer>[] g=
      new ArrayList[n];
    for(int i=0;i<n;i++)
    g[i]=new ArrayList<>();
    for(int i=0;i<m;i++)
    {
      int x=sc.nextInt();
      int y=sc.nextInt();
      x--; y--;
      g[x].add(y);
    }
    int max=0;
    dp=new int[n];
    for(int i=0;i<n;i++)
    dp[i]=-1;
    for(int i=0;i<n;i++)
    {
        int cnt=dfs(g,i);
        max=Math.max(max,cnt);
    }
    System.out.println(max);
  }
}