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{
  static int[] dp;
  static ArrayList<Integer>[] graph;
  public static void dfs(int v){
    if(graph[v].size()==0)return;
    int a = 0;
    for(Integer e:graph[v]){
      if(dp[e]==0)dfs(e);
      a=Math.max(a,dp[e]);
    }
    dp[v] = a+1;
  }
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    dp = new int[n+1];
    graph = new ArrayList[n+1];
    for(int i=1;i<=n;i++)graph[i] = new ArrayList<Integer>();
    boolean[] has = new boolean[n+1];
    Arrays.fill(has,false);
    for(int i=1;i<=m;i++){
      int x = sc.nextInt();
      int y = sc.nextInt();
      graph[x].add(y);
      has[y]=true;
    }
    for(int i=1;i<=n;i++){
      if(!has[i])dfs(i);
    }
    int ans = 0;
    for(int i=1;i<=n;i++)ans=Math.max(ans,dp[i]);
    System.out.println(ans);
  }
}