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.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = in.nextInt();
        int m = in.nextInt();
        Map<Integer, List<Integer>> paths = new HashMap<>();
        int[] dp = new int[n];
        for (int i = 0; i < m; i++) {
            int from = in.nextInt();
            int to = in.nextInt();
            paths.compute(from - 1, (integer, integers) -> {
                if (integers == null) {
                    integers = new ArrayList<>();
                }
                integers.add(to - 1);
                return integers;
            });
        }
        boolean[] visited = new boolean[n];
        for (int i = 0; i < n; i++) {
            if (!visited[i]) {
                dfs(i, visited, paths, dp);
            }
        }

        int result = Integer.MIN_VALUE;
        for (int j = 0; j < n; j++) {
            result = Math.max(result, dp[j]);
        }
        System.out.println(result);
    }

    private static void dfs(int from, boolean[] visited, Map<Integer, List<Integer>> paths, int[] dp) {
        final List<Integer> tos = paths.getOrDefault(from, Collections.emptyList());
        for (Integer to : tos) {
            if (!visited[to]) {
                dfs(to, visited, paths, dp);
            }
        }
        for (Integer to : tos) {
            dp[from] = Math.max(dp[from], dp[to] + 1);
        }
        visited[from] = true;
    }
}