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.ArrayList;
import java.util.Scanner;

class Main{
	static int[][] dp;




	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int n = sc.nextInt();
		int m = sc.nextInt();
		ArrayList<ArrayList<Integer>> list = new ArrayList<ArrayList<Integer>>();
		int[] p = new int[n];

		for(int i = 0;i < n;i++){
			list.add(new ArrayList<Integer>());
		}
		for(int i = 0;i < m;i++){
			int x = sc.nextInt()-1;
			int y = sc.nextInt()-1;
			list.get(x).add(y);
			p[y]++;
		}
		ArrayList<Integer> q = new ArrayList<Integer>();
		for(int i = 0;i < n;i++){				//誰からも繋がり先でない町(親ノード)を見つける
			if(p[i] == 0){
				q.add(i);
			}
		}
		int[] dp = new int[n];
		for(int i = 0;i < q.size();i++){
			int parent = q.get(i);
			for(int child : list.get(parent)){		//親ノードから繋がっている町を探す
				dp[child] = Math.max(dp[child], dp[parent]+1);
				p[child]--;					//親ノードからの矢印をなくす
				if(p[child] == 0){			//どこからも繋がり先出なくなったら親ノードになる
					q.add(child);			
				}
			}
		}
		int ans = 0;
		for(int i = 0;i < n;i++){
			ans = Math.max(ans,dp[i]);
		}
		System.out.println(ans);
		
		
		
		
		//		for(int i = 0;i < m;i++){
		//			int x = sc.nextInt();
		//			int y  = sc.nextInt();
		//			dp[x+1][y+1]++;
		//		}



	}

	//	static int dfs(int x, int y){
	//		
	//		
	//		
	//		
	//	}
}







class Pair implements Comparable{
	int from;		//p
	int end;		//y
	int num;
	int bango;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return end - otherpair.end;
	}
}