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 scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        ArrayList<Integer>[] graph = new ArrayList[n];
        int[] dp = new int[n];
        Arrays.fill(dp, -1);
        for (int i = 0; i < m; ++i) {
            int x = scanner.nextInt() - 1;
            int y = scanner.nextInt() - 1;
            if (graph[x] == null)
                graph[x] = new ArrayList<>();
            graph[x].add(y);
        }
        int res = 0;
        for (int i = 0; i < n; ++i) {
            res = Math.max(res, solve(i, graph, dp));
        }
        System.out.println(res-1);
    }

    private static int solve(int a, ArrayList<Integer>[] graph, int[] dp) {
        if (dp[a] != -1)
            return dp[a];
        int res = 0;
        if(graph[a]!= null) {
            for (int i = 0; i < graph[a].size(); ++i) {
                res = Math.max(res, solve(graph[a].get(i), graph, dp) + 1);
            }
        }else {
            res = 1;
        }
        return dp[a] = res;
    }
}
/*
 *
 */