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;
	static ArrayList<Integer>[] a;
	public static int solve(int i)
	{
		if(dp[i]!=-1)
		{
			return dp[i];
		}
		int ret=0;
		for(int j=0;j<a[i].size();j++)
		{
			ret=Math.max(ret,solve(a[i].get(j))+1);
		}
		dp[i]=ret;
		return dp[i];
	}
	public static void main(String [] Args)
	{
		Scanner in = new Scanner(System.in);
		int n=in.nextInt();
		int m=in.nextInt();
		a=new ArrayList[n];
		dp = new int [n];
		for(int i=0;i<n;i++)
		{
			dp[i]=-1;
			a[i]=new ArrayList<Integer>();
		}
		for(int i=0;i<m;i++)
		{
			int p=in.nextInt();
			int q=in.nextInt();
			a[p-1].add(q-1);
		}
		int ret=0;
		for(int i=0;i<n;i++)
		{
			ret=Math.max(ret,solve(i));
		}
		System.out.println(ret);
	}
}