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 {
  public static void main(String args[]) {
    Scanner scan = new Scanner(System.in);
    int N = scan.nextInt();
    int M = scan.nextInt();

    Map<Integer, List<Integer>> graph = new HashMap<>();
    for (int i = 1; i <= N; i++)
      graph.put(i, new LinkedList<Integer>());

    for (int i = 0; i < M; i++)
      graph.get(scan.nextInt()).add(scan.nextInt());

    scan.close();

    System.out.println(longestPath(graph, N));
  }

  private static int longestPath(Map<Integer, List<Integer>> graph, int n) {
    if (n == 0) return 0;

    int[] cache = new int[n + 1];
    Arrays.fill(cache, -1);
    int max = 0;
    for (int i = 1; i <= n; i++)
      max = Math.max(max, dfs(graph, i, cache));
    return max;
  }

  private static int dfs(Map<Integer, List<Integer>> graph, int idx, int[] cache) {
    if (cache[idx] >= 0) return cache[idx];

    int maxPath = 0;
    for (int con : graph.get(idx))
      maxPath = Math.max(maxPath, dfs(graph, con, cache) + 1);

    return cache[idx] = maxPath;
  }

}