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{
	public static void main(String args[]) {
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		ArrayList<ArrayList<Integer>> al = new ArrayList<ArrayList<Integer>>();
		for(int i=0;i<=n;i++) {
			al.add(new ArrayList<Integer>());
		}
		int m = input.nextInt();
		for(int i=0;i<m;i++) {
			int x1 = input.nextInt();
			int y1 = input.nextInt();
			al.get(x1).add(y1);
		}
		System.out.println(func(al,n,m));
	}
	static int func(ArrayList<ArrayList<Integer>> al,int n,int m) {
		int dp[] = new int[n+1];
		boolean vis[] = new boolean[n+1];
		for(int i=1;i<=n;i++) {
			if(vis[i]==false) {
				dfs(i,al,dp,vis);
			}
		}
		int res = Integer.MIN_VALUE;
		for(int i=0;i<=n;i++) {
			res = Math.max(res, dp[i]);
		}
		return res;
	}
	static void dfs(int k,ArrayList<ArrayList<Integer>> al,int dp[],boolean vis[]) {
		vis[k] = true;
		for(Integer j:al.get(k)) {
			if(vis[j]==false) {
				dfs(j,al,dp,vis);
			}
			dp[k] = Math.max(dp[k], dp[j]+1);
		}
	}
}