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.*;

public class Main {
    public static void main(String[] args)  {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        graff graph = new graff(n);
        for(int i=0;i<m;i++)    {
            int x = in.nextInt();
            int y = in.nextInt();
            graph.adj[x].add(y);
        }
        int max = 0;
        for(int i=1;i<=n;i++)   {
            max = Math.max(max, graph.solve(i));
        }
        System.out.println(max);
        in.close();
    }
}

class graff {
    int n;
    int[] dp;
    boolean[] visited;
    List<Integer>[] adj;

    @SuppressWarnings("unchecked")
    graff(int size) {
        n = size;
        dp = new int[n+1];
        visited = new boolean[size+1];
        adj = new ArrayList[size+1];
        for (int i=1;i<=size;i++)    {
            adj[i] = new ArrayList<Integer>();
        }
    }

    int solve(int i)    {
        if(visited[i])  return dp[i];
        visited[i] = true;
        int best = 0;
        for(int u:adj[i])   {
            best = Math.max(best, solve(u)+1);
        }
        return dp[i] = best;
    }
}