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 in=new Scanner(System.in);
		int n=in.nextInt();
		int m=in.nextInt();
		int[] deg=new int[n];
		int[] dp=new int[n];
		ArrayList<Integer>[] G=new ArrayList[n];
		for (int i=0;i<n;++i)
			G[i]=new ArrayList<Integer>();
		while (m-->0) {
			int u=in.nextInt();
			int v=in.nextInt();
			--u;
			--v;
			G[u].add(v);
			++deg[v];
		}
		Queue<Integer> que=new LinkedList<Integer>();
		int res=0;
		for (int i=0;i<n;++i) if (deg[i]==0)
			que.add(i);
		while (!que.isEmpty()) {
			int u=que.peek();
			que.poll();
			for (int i=0;i<G[u].size();++i) {
				int v=G[u].get(i);
				dp[v]=Math.max(dp[v],dp[u]+1);
				res=Math.max(res,dp[v]);
				--deg[v];
				if (deg[v]==0) que.add(v);
			}
		}
		System.out.println(res);
	}
}