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.io.*;
import java.util.ArrayList;

public class Main {
	static ArrayList<Integer>[] arr = null;
	static int longestPath[] = null;
	static boolean vis[]  = null;
	
	private static int dfs(int node) {
		if(vis[node]) return longestPath[node];
		int maxLen = 0;
		for(int i=0; i<arr[node].size(); i++) {
			maxLen = Math.max(maxLen, dfs(arr[node].get(i))+1);
		}
		vis[node] = true;
		return longestPath[node] = maxLen;
	}
	
	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] str;
		str = br.readLine().split(" ");
		int n = Integer.parseInt(str[0]);
		int m = Integer.parseInt(str[1]);
		int len = (int)1e5+1;
		arr = new ArrayList[len];
		for(int i=0; i<len; i++) arr[i] = new ArrayList<>();
		for(int i=0; i<m; i++) {
			str = br.readLine().split(" ");
			int x = Integer.parseInt(str[0]);
			int y = Integer.parseInt(str[1]);
			arr[x].add(y);
		}
		longestPath = new int[len];
		vis = new boolean[len];
		for(int i=0; i<len; i++) dfs(i);
		int ans = -1;
		for(int i=0; i<len; i++) ans = Math.max(ans, longestPath[i]);
		System.out.println(ans);
	}
}