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 {
    static Map<Integer,List<Integer>> map = new HashMap();
    static int dp[] = new int[100001];
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int edges = sc.nextInt();
        int dp[] = new int[n+1];
        int ans = 0;
        for(int i=0;i<edges;i++){
            int a = sc.nextInt();
            int b = sc.nextInt();
            if(!map.containsKey(a))
                map.put(a,new ArrayList());
            map.get(a).add(b);
        }
        for(int i=1;i<=n;i++){
            ans = Math.max(ans,dfs(i));
        }
        System.out.println(ans);
    }
    static int dfs(int cur){
        int tmp = 0;
        if(dp[cur]!=0){
            return dp[cur];
        }
        if(!map.containsKey(cur))
            return 0;
        for(int next : map.get(cur))
            tmp = Math.max(tmp,dfs(next)+1);
        dp[cur] = tmp;
        return tmp;
    }
}