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[]=new int[100001];
	public static void main(String args[]){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		ArrayList<ArrayList<Integer>> g=new ArrayList<ArrayList<Integer>>();
		for(int i=0;i<n;i++){
			g.add(new ArrayList<Integer>());
		}
		for(int i=0;i<m;i++){
			int x=sc.nextInt();
			int y=sc.nextInt();
			g.get(x-1).add(y-1);
		}
		int ans=0;
		for(int i=0;i<n;i++){
			ans=Math.max(ans,dfs(i,g));
		}
		System.out.println(ans);
	}
	public static int dfs(int i,ArrayList<ArrayList<Integer>> g){
		int temp=0;
		if(dp[i]!=0){
			return dp[i];
		}
		for(int z:g.get(i)){
			temp=Math.max(temp,dfs(z,g)+1);
		}
		dp[i]=temp;
		return temp;
	}
}