Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
    //static String probName = "template";
    static Comparator<int[]> comp = new Comparator<int[]>() {
        public int compare(int[] a, int[] b) {
            for (int i=0; i<a.length; i++) {
                if (a[i] < b[i])       return -1;
                else if (a[i] > b[i])  return 1;
            }
            return 0;
        }
    };
    static final long LARGE_LONG = 1000000000000000000L;
    static final int LARGE_INT = 1000000007;
    static final int[] dx = new int[] {1, -1, 0, 0};
    static final int[] dy = new int[] {0, 0, 1, -1};
    static int n;
    static int m;
    static int[] vals; //vals[i] is the length of the longest directed path starting at i;
    static ArrayList<ArrayList<Integer>> al;

    public static void main(String[] argst) throws IOException {
        FastReader in = new FastReader();
        // FastReader in = new FastReader(probName + ".in");
        // Scanner in = new Scanner(System.in);

        // PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter(probName + ".out")));
        PrintWriter out = new PrintWriter(System.out);
        n = in.nextInt();
        m = in.nextInt();
        vals = new int[n+1];
        for (int i = 0; i <= n; i++) {
            vals[i] = -1;
        }
        al = new ArrayList<ArrayList<Integer>>();
        for (int i = 0; i <= n; i++) {
            al.add(new ArrayList<Integer>());
        }
        for (int i = 0; i < m; i++) {
            al.get(in.nextInt()).add(in.nextInt());
        }
        int mxs = -1;
        for (int i = 1; i <= n; i++) {
            mxs = Math.max(mxs, gv(i));
        }
        out.println(mxs-1);
        out.close();
    }

    static int gv (int node) {
        if (vals[node] != -1) {
            return vals[node];
        }
        else {
            int mx = 0;
            for (int i : al.get(node)) {
                mx = Math.max(mx, gv(i));
            }
            vals[node] = mx + 1;
            return (mx + 1);
        }
    }

    /* FastReader code from  https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
       nextLine modified, and added next(), and hasNext()
    */
    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        final private int MAX_LINE_SIZE = 1 << 20;
        private DataInputStream din;
        private byte[] buffer, lineBuf;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public boolean hasNext() throws IOException {
            byte c;
            while ((c = read()) != -1) {
                if (c > ' ') {
                    bufferPointer--;
                    return true;
                }
            }
            return false;
        }
        public String nextLine() throws IOException {
            if (lineBuf == null)	lineBuf = new byte[MAX_LINE_SIZE];
            int ctr = 0;
            byte c;
            while ((c = read()) != -1) {
                if (c == '\r')        continue;
                if (c == '\n')        break;
                lineBuf[ctr++] = c;
            }
            return new String(lineBuf, 0, ctr);
        }
        public String next() throws IOException {
            if (lineBuf == null)	lineBuf = new byte[MAX_LINE_SIZE];
            int ctr = 0;
            byte c = read();
            while (c <= ' ')  	c = read();
            while (c > ' ') {
                lineBuf[ctr++] = c;
                c = read();
            }
            return new String(lineBuf, 0, ctr);
        }
        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')   c = read();
            boolean neg = (c == '-');
            if (neg)           c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)           return -ret;
            return ret;
        }
        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')    c = read();
            boolean neg = (c == '-');
            if (neg)            c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)            return -ret;
            return ret;
        }
        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)  	c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg)     return -ret;
            return ret;
        }
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
        private byte read() throws IOException {
            if (bufferPointer == bytesRead)     fillBuffer();
            return buffer[bufferPointer++];
        }
        public void close() throws IOException {
            if (din == null) 	   return;
            din.close();
        }
    }
}