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.*; 
public class Main {
    static ArrayList<Integer> adj_lst[];
    static boolean vis[];
    static int dp[];
    public static void main(String args[]){
        Scanner input=new Scanner(System.in);
        int n=input.nextInt();
        int m=input.nextInt();
        adj_lst=new ArrayList[n];
        vis=new boolean[n];
        dp=new int[n];
        for(int i=0;i<adj_lst.length;i++) {
            adj_lst[i]=new ArrayList<Integer>();
            dp[i]=-1;
        }
        for(int i=0;i<m;i++) {
            int u=input.nextInt()-1;
            int v=input.nextInt()-1;
            adj_lst[u].add(v);
        }
//        for(int i=0;i<adj_lst.length;i++) {
//            System.out.print(i+"->");
//            for(int j=0;j<adj_lst[i].size();j++) {
//                System.out.print(adj_lst[i].get(j)+" ");
//            }
//            System.out.println();
//        }
        for(int i=0;i<n;i++) {
            if(!vis[i]) {
                solve(i);
            }
        }
        int max=Integer.MIN_VALUE;
        for(int i=0;i<n;i++) {
            max=Math.max(max,dp[i]);
        }
        System.out.println(max);
    }
    public static void solve(int root) {
        vis[root]=true;
        if(adj_lst[root].size()==0) {
            dp[root]=0;
            return;
        }
        dp[root]=Integer.MIN_VALUE;
        for(int i=0;i<adj_lst[root].size();i++) {
            if(dp[adj_lst[root].get(i)]==-1) {
                solve(adj_lst[root].get(i));
            }
            dp[root]=Math.max(dp[root],1+dp[adj_lst[root].get(i)]);
        }
    }
}