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 {// Main
	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) throws Exception {
		int n =sc.nextInt();
		int m = sc.nextInt();
		
		map = directed(n, m);
		int[] dp = new int[n+1];
		boolean[] vis = new boolean[n+1];
		for(int i = 1 ;i <= n;i++) {
			find(i , vis , dp);
		}
		int ans = 0 ;
		for(int val : dp)ans = Math.max(ans , val);
		
		
		
		
		
  System.out.println(ans);
	}
	
	private static int find(int i, boolean[] vis , int[] dp) {
		if(vis[i])return dp[i];
		int max = -1 ;
		for(int nbr : map.get(i)) {
			max = Math.max(max , find(nbr, vis , dp) );
		}
		vis[i]=true;
		dp[i] = max+1;
		return dp[i];
	}

	static TreeMap<Integer , ArrayList<Integer> > map ;

	public static TreeMap<Integer , ArrayList<Integer> > directed(int n , int m  ) throws Exception{
		TreeMap<Integer , ArrayList<Integer> > map = new TreeMap<>();
		for(int i = 1 ;i<=n ;i++)map.put(i, new ArrayList<Integer>());
		for(int i = 1 ;i <= m ;i++) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			map.get(a).add(b);
		}
		return map;
	}
}