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 int solve(int n, int m, int[] x, int[] y) {
        Map<Integer, List<Integer>> graph = new HashMap<>();
      	for (int i = 0; i < n; i++) {
          graph.put(i, new LinkedList<Integer>());
        }
      
        for (int i = 0; i < m; i++) {
          graph.get(x[i] - 1).add(y[i] - 1);
        }

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

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

      int maxPath = 0;
      for (int to : graph.get(from)) {
        maxPath = Math.max(maxPath, dfs(graph, to, memo) + 1);
      }
      memo[from] = maxPath;
      return maxPath;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();

        int[] from, to;
        from = new int[m];
        to = new int[m];
        for (int i = 0; i < m; i++) {
          from[i] = scanner.nextInt();
          to[i] = scanner.nextInt();
        }
        
        int result = solve(n, m, from, to);
        System.out.println(result);
    }
}