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 {

    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    List<Integer>[] lists = new ArrayList[n];
    int[] dp = new int[n];

    public static void main(String[] args) {
        new Main().run();
    }

    void run() {

        for (int i=0; i<n; i++) lists[i] = new ArrayList<>();

        for (int i=0; i<m; i++) {
            int s = sc.nextInt() - 1;
            int t = sc.nextInt() - 1;
            lists[s].add(t);
        }

        Arrays.fill(dp, -1);

        int ret = 0;

        for (int i=0; i<n; i++) {
            ret = Math.max(ret, rec(i));
        }

        System.out.println(ret);

    }

    int rec(int v) {
        if (dp[v] != -1) return dp[v];

        int ret = 0;

        for (int u: lists[v]) {
            if (dp[u] == -1) rec(u);
            ret = Math.max(ret, dp[u] + 1);
        }

        return dp[v] = ret;
    }
}