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 scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        List<List<Integer>> graph = new ArrayList<>();
        int[] degree = new int[n+1];
        int[] dp = new int[n+1];
        for(int i = 0; i <= n; i++){
            graph.add(new ArrayList<>());
        }
        for(int i = 0; i < m; i++){
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            degree[y]++;
            graph.get(x).add(y);
        }
        Deque<Integer> stack = new LinkedList<>();
        for(int i = 1; i <= n; i++){
            if(degree[i] == 0){
                stack.push(i);
            }
        }
        List<Integer> list = new ArrayList<>();
        while(!stack.isEmpty()){
            int j = stack.pop();
            list.add(j);
            for(int k : graph.get(j)){
                degree[k]--;
                if(degree[k] == 0)
                    stack.push(k);
            }
        }
        for(int i : list){
            for(int j : graph.get(i)){
                dp[j] = Math.max(dp[j], dp[i] + 1);
            }
        }
        int ans = 0;
        for(int i = 1; i <= n; i++){
            ans = Math.max(ans, dp[i]);
        }
        System.out.println(ans);
    }
}