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.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws IOException {
        init();

        int V = nextInt(), E = nextInt();

        adjacency = new HashMap<>();

        for (int i = 0; i < V; i++) adjacency.put(i + 1, new ArrayList<>());

        for (int i = 0; i < E; i++) adjacency.get(nextInt()).add(nextInt());

        seen = new boolean[V + 1];

        longestPathFrom = new int[V + 1];

        for (int i = 1; i <= V; i++) if (!seen[i]) calcLongestPathFrom(i);

        System.out.println(Arrays.stream(longestPathFrom).max().getAsInt());
    }

    private static Map<Integer, ArrayList<Integer>> adjacency;
    private static boolean[] seen;
    private static int[] longestPathFrom;

    private static int calcLongestPathFrom(int v) {
        if (seen[v]) return longestPathFrom[v];
        seen[v] = true;
        if (adjacency.get(v).isEmpty()) return 0;
        int longestPath = 0;
        for (int adj: adjacency.get(v)) longestPath = Math.max(longestPath, 1 + calcLongestPathFrom(adj));

        longestPathFrom[v] = longestPath;
        return longestPath;
    }

    //Input Reader
    private static BufferedReader reader;
    private static StringTokenizer tokenizer;

    private static void init() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    private static String next() throws IOException {
        String read;
        while (!tokenizer.hasMoreTokens()) {
            read = reader.readLine();
            if (read == null || read.equals(""))
                return "-1";
            tokenizer = new StringTokenizer(read);
        }

        return tokenizer.nextToken();
    }

    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
}