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.*;
import java.io.*;
class Main {
    static void dfs(int src, ArrayList<Integer>[] graph, boolean[] visited, int[] dist) {
        visited[src] = true;
        for(int i: graph[src]) {
            if(!visited[i])
                dfs(i, graph, visited, dist);
            dist[src] = Math.max(dist[src], dist[i]+1);
        }
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        ArrayList<Integer>[] graph = new ArrayList[n];
        for(int i = 0; i<n; i++)
            graph[i] = new ArrayList<>();
        for(int i = 0; i<m; i++) {
            int u = sc.nextInt()-1;
            int v = sc.nextInt()-1;
            graph[u].add(v);
        }
        int[] dist = new int[n];
        boolean[] visited = new boolean[n];
        for(int i = 0; i<n; i++) 
            if(!visited[i])
                dfs(i, graph, visited, dist);
        System.out.println(Arrays.stream(dist).max().getAsInt());
    }
}