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();
        HashMap<Integer, ArrayList<Integer>> map = new HashMap<>();
        for (int i = 0; i < m; i++) {
            int v = scanner.nextInt();
            int e = scanner.nextInt();
            map.putIfAbsent(v,new ArrayList<>());
            map.get(v).add(e);
        }
        int[] dp = new int[n+1];
        Arrays.fill(dp,-1);
        for(int i : map.keySet()){
            path(map,i,dp);
        }
        int longestPath=0;
        for(int i : dp)
            longestPath = Math.max(longestPath,i);
        System.out.println(longestPath);

    }
    private static int path(HashMap<Integer, ArrayList<Integer>> map ,int n ,int[] dp){
        if(!map.containsKey(n)) {
            dp[n]=0;
            return 0;
        }
        if(dp[n] !=-1)
            return dp[n];
        int longestPath=0;
        for(int i : map.get(n)){
            longestPath = Math.max(longestPath,path(map,i,dp));
        }
        return dp[n]=longestPath+1;
    }
}