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 {
    private static Map<Integer, Integer> memo = new HashMap<>();
    private static List<List<Integer>> graph = new ArrayList<>();

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(), m = sc.nextInt();
        for (int i = 0; i <= n; i++) {
            graph.add(new ArrayList<>());
        }

        for (int i = 0; i < m; i++) {
            graph.get(sc.nextInt()).add(sc.nextInt());
        }

        int result = 0;
        for (int i = 1; i <= n; i++) {
            result = Math.max(result, rec(i));
        }

        System.out.println(result);
    }

    private static int rec(int n) {
        if (memo.containsKey(n)) {
            return memo.get(n);
        }
        if (graph.get(n).size() == 0) {
            memo.put(n, 0);
            return 0;
        }
        int length = 0;
        for (Integer i : graph.get(n)) {
            length = Math.max(length, rec(i) + 1);
        }
        memo.put(n, length);
        return length;
    }
}