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 s=new Scanner(System.in);
    int n=s.nextInt();
    int m=s.nextInt();
    ArrayList<Integer>[] graph=new ArrayList[n];
    for(int i=0;i<n;i++)
      graph[i]=new ArrayList<Integer>();
    for(int i=0;i<m;i++){
      int x=s.nextInt();
      int y=s.nextInt();
      graph[x-1].add(y-1);
    }
    int[] dp=new int[n];
    for(int i=0;i<n;i++){
      dfs(i,graph,dp);
    }
    int max=Integer.MIN_VALUE;
    for(int i=0;i<n;i++){
      max=Math.max(dp[i],max);
    }
    
    System.out.println(max);
  }
  public static int dfs(int i, ArrayList<Integer>[] graph, int[] dp){
    if(graph[i].size()==0){
      return 0;
    }
    if(dp[i]!=0)
      return dp[i];
    dp[i]=Integer.MIN_VALUE;
    for(int j=0;j<graph[i].size();j++){
      dp[i]=Math.max(dp[i],dfs(graph[i].get(j),graph,dp)+1);
                     }
                   return   dp[i];
                     }
}