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 N;
    static int M;
    static ArrayList<ArrayList<Integer>> edge;
    static int[] ans;

    static int path(int i) {
        if (ans[i]!=-1) return ans[i];
        int tmp = 0;
        for (Integer j : edge.get(i)) {
            tmp = Math.max(tmp, path(j)+1);
        }
        ans[i] = tmp;
        return tmp;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = Integer.parseInt(sc.next());
        M = Integer.parseInt(sc.next());
        edge = new ArrayList<ArrayList<Integer>>();
        for (int i=0;i<N;i++) {
            ArrayList<Integer> add = new ArrayList<Integer>();
            edge.add(add);
        }
        for (int i=0;i<M;i++) {
            int x = Integer.parseInt(sc.next())-1;
            int y = Integer.parseInt(sc.next())-1;
            edge.get(x).add(y);
        }

        ans = new int[N];
        Arrays.fill(ans, -1);
        int max = 0;
        for (int i=0;i<N;i++) {
            max = Math.max(max, path(i));
        }
        System.out.println(max);
    }
}