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.*;
class Main{
  static Map<Integer,List<Integer>> graph=new HashMap<>();
  static Map<Integer,Integer> dist=new HashMap<>();
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    int e=sc.nextInt();
    for(int i=0;i<e;i++){
      populate(sc.nextInt(),sc.nextInt());
    }
    Set<Integer> visited=new HashSet<>();
    int ans=0;
    for(int i:graph.keySet()){
      if(!visited.contains(i)) {
        ans=Math.max(ans,dfs(i,visited));
      }
    }
    System.out.println(ans-1);
  }
  public static int dfs(int src,Set<Integer> visited){
        if(dist.containsKey(src)) return dist.get(src);
        visited.add(src);
        int current=0;
        for(int nei:graph.getOrDefault(src,new ArrayList<>())){
            if(!visited.contains(nei)) current=Math.max(current,dfs(nei,visited));
            current=Math.max(current,dist.get(nei));
        }
    	dist.put(src,1+current);
        return 1+current;
    }
    public static void populate(int i,int j){
            graph.putIfAbsent(i,new ArrayList<>());
            graph.get(i).add(j); 
    }
}