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 scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        int E = scanner.nextInt();
        List<List<Integer>> graph = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            graph.add(new ArrayList<>());
        }
        for (int i = 0; i < E; i++) {
            int start = scanner.nextInt()-1;
            int end = scanner.nextInt()-1;
            graph.get(start).add(end);
        }

        int dp[] = new int[N];
        int result = 0;
        for (int i = 0; i < N; i++) {
            result = Math.max(result, logesntPath(i, dp, graph));
        }
        System.out.println(result-1);
    }

    public static int logesntPath(int vertex, int[] dp, List<List<Integer>> graph) {
        if (dp[vertex] != 0) {
            return dp[vertex];
        }
        int result = 0;
        for (int  end : graph.get(vertex)) {
            result = Math.max(result, logesntPath(end, dp, graph));
        }
        dp[vertex] = result + 1;
        return dp[vertex];
    }
}