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.*;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[][] edges = new int[M][2];
        Map<Integer, List<Integer>> map = new HashMap<>();
        Map<Integer, Integer> memo = new HashMap<>();
        for (int i = 1; i <= N; i++) {
            map.put(i, new ArrayList<>());
        }

        for (int i = 0; i < M; i++) {
            int start = sc.nextInt();
            int end = sc.nextInt();
            map.get(start).add(end);
        }

        int res = 0;
        for (int i = 1; i <= N; i++) {
            res = Math.max(res, helper(i, map, memo));
        }

        System.out.println(res);
    }

    public static int helper(int v, Map<Integer, List<Integer>> map, Map<Integer, Integer> memo) {
        if (memo.containsKey(v)) return memo.get(v);
        Queue<Integer> Q = new LinkedList<>();
        Q.offer(v);
        int res = 0;
        for (int next : map.get(v)) {
            res = Math.max(res, 1 + helper(next, map, memo));
        }

        memo.put(v, res);
        return memo.get(v);
    }
}