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.List;
import java.util.Scanner;

public class Main {

	public static void main(String args[]) {
		Scanner scan = new Scanner(System.in);
		List<List<Integer>> adj = new ArrayList<>();
		int n = scan.nextInt();
		int m = scan.nextInt();

		for (int i = 0; i <= n; i++) {
			adj.add(i, new ArrayList<>());
		}

		for (int i = 1; i <= m; i++) {
			adj.get(scan.nextInt()).add(scan.nextInt());
		}

		int[] dp = new int[n + 1];
		int path = Integer.MIN_VALUE;
		
		for (int i = 1; i <= n; i++) {
			path = Math.max(path, findLongestPath(adj, i, dp));
		}
		System.out.println(path);

	}

	public static int findLongestPath(List<List<Integer>> adj, int node, int dp[]) {
		if (adj.get(node).size() == 0) {
			return 0;
		}

		if (dp[node] != 0) {
			return dp[node];
		}
		List<Integer> nbrs = adj.get(node);
		int path = Integer.MIN_VALUE;
		for (int nbr : nbrs) {
			path = Math.max(path, findLongestPath(adj, nbr, dp));
		}

		dp[node] = path + 1;
		return dp[node];

	}
}