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.*;
import java.lang.*;


public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();

            while(isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if(c<'0'||c>'9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }

    static long gcd(long a,long b){ if(b==0)return a;return gcd(b,a%b); }
    static long modPow(long a,long p,long m){ if(a==1)return 1;long ans=1;while (p>0){ if(p%2==1)ans=(ans*a)%m;a=(a*a)%m;p>>=1; }return ans; }
    static long modInv(long a,long m){return modPow(a,m-2,m);}
    static long sol_x,sol_y,gcd_a_b;
    static void extendedEuclid(long a,long b){ if(b==0){gcd_a_b=a;sol_x=1;sol_y=0; } else{ extendedEuclid(b,a%b);long temp = sol_x;sol_x=sol_y;sol_y = temp - (a/b)*sol_y; } }
    static class Bhavansort{ Random random;Bhavansort(int a[]){ randomArray(a); sort(a);}Bhavansort(long a[]){ randomArray(a); sort(a);}static int[] sort(int a[]){ Arrays.sort(a);return a;}static long[] sort(long a[]){ Arrays.sort(a);return a; }void randomArray(long a[]){ int n=a.length;for(int i=0;i<n;i++){ int p=random.nextInt(n)%n;long tm=a[i];a[i]=a[p];a[p]=tm; } }void randomArray(int a[]){ int n=a.length;for(int i=0;i<n;i++){ int p=random.nextInt(n)%n;int tm=a[i];a[i]=a[p];a[p]=tm; } }}

    int n,m,visited[],dp[];
    ArrayList<Integer> l[];

    void dfs(int u,int par){
        dp[u]=0;
        for(int v:l[u]){
            if(v!=par){
                if(dp[v]!=-1){
                    dp[u]=Math.max(dp[v]+1,dp[u]);
                }
                else{
                    dfs(v,u);
                    dp[u]=Math.max(dp[v]+1,dp[u]);
                }
            }
        }
    }

    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);


        n=sc.nextInt();
        m=sc.nextInt();
        l=new ArrayList[n];
        for (int i = 0; i <n ; i++) {
            l[i]=new ArrayList<>();
        }
        visited=new int[n];
        dp=new int[n];
        Arrays.fill(dp,-1);
        while (m-->0){
            int u=sc.nextInt()-1;
            int v=sc.nextInt()-1;
            l[u].add(v);
        }
        long ans=0;
        for (int i = 0; i <n ; i++) {
            if(visited[i]==0){
                dfs(i,-1);
            }
        }
        for (int i = 0; i <n ; i++) {
            ans=Math.max(ans,dp[i]);
        }
        out.println(ans);


        out.close();
    }


}