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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    private int findLongestPath(int[][] edges, int n) {
      List<Integer>[] adjList = new List[n + 1];
      int[] dist = new int[n + 1];
      boolean[] visited = new boolean[n + 1];
      for (int i = 1; i <= n; i++) {
        adjList[i] = new ArrayList<>();
      }
      for (int[] e: edges) {
        adjList[e[0]].add(e[1]);
      }
      for (int i = 1; i <= n; i++) {
        if (!visited[i]) {
          dfs(i, adjList, dist, visited);
        }
      }
      int result = 0;
      for (int i = 1; i <= n; i++) {
        if (dist[i] > result) {
          result = dist[i];
        }
      }
      return result;
    }
    private void dfs(int i, List<Integer>[] adjList, int[] dist, boolean[] visited) {
      visited[i] = true;
      for (int u: adjList[i]) {
        if (!visited[u]) {
          dfs(u, adjList, dist, visited);
        }
        dist[i] = Math.max(dist[i], 1 + dist[u]);
      }
    }
    public static void main(String[] args)  {
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
            String[] split = br.readLine().split(" ");
            int n = Integer.parseInt(split[0]);
            int m = Integer.parseInt(split[1]);
            int[][] edges = new int[m][2];
            for (int i = 0; i < m; i++) {
              split = br.readLine().split(" ");
              edges[i][0] = Integer.parseInt(split[0]);
              edges[i][1] = Integer.parseInt(split[1]);
            }
            Main app = new Main();
            int result = app.findLongestPath(edges, n);
            System.out.println(result);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}