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.*;

/**
 * Created by Harry on 4/1/20.
 */
public class Main {
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        List<Integer>[] graph = new ArrayList[n+1];
        int[] in = new int[n+1];
        for(int i=0; i<m; i++){
            int from = scanner.nextInt();
            int to = scanner.nextInt();
            if(graph[from]==null){
                graph[from] = new ArrayList<>();
            }
            graph[from].add(to);
            in[to]++;
        }

        Queue<Integer> q = new LinkedList<>();
        for(int node=1; node<=n; node++){
            if(in[node]==0){
                q.offer(node);
            }
        }

        int res = 0;
        int[] len = new int[n+1];
        while(!q.isEmpty()){
            int node = q.poll();
            if(graph[node]==null) continue;
            for(int next : graph[node]){
                len[next] = Math.max(len[next], len[node]+1);
                res = Math.max(res, len[next]);
                if(--in[next]==0){
                    q.offer(next);
                }
            }
        }
        System.out.print(res);
    }
}