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[] ,N ,M;
	static List<ArrayList<Integer>> G; 
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt(); M = sc.nextInt();
		G = new ArrayList<ArrayList<Integer>>();
		for(int i=0;i<N;i++)G.add(new ArrayList<Integer>());
		for(int i=0;i<M;i++) {
			G.get(sc.nextInt()-1).add(sc.nextInt()-1);
		}
		sc.close();
		dp = new int[N];//nを頂点とする時の最長経路の長さ
		Arrays.fill(dp, -1);
		
		int ans = 0;
		//全頂点を始点にする場合を調べる。
		for(int i=0;i<N;i++) {
			ans = Math.max(ans,rec(i));
		}
		System.out.println(ans);
	}
	//　頂点vを始点とした時の最長経路の長さを返す。
	static int rec(int v) {
		if(dp[v]!=-1)return dp[v];
		int ret = 0;
		for(int to:G.get(v)) {
			ret = Math.max(ret, rec(to)+1); //DAGなので、次のノードを始点とした時の最長に、+1する事で自分始点の最長経路の長さが分かる。
		}
		return dp[v] = ret;
	}
}