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 int dp[];
  static List<Integer> list[];
  static int solve(int i){
    int ret = 0;
    if (dp[i] != - 1) return dp[i];
    else{
      for (int j = 0; j < list[i].size(); j++) {
        ret = Math.max(ret, solve(list[i].get(j)) + 1);
//        System.out.println(ret + " ret inside");
      }
    }
    return dp[i] = ret;
  }
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    list = new LinkedList[n + 1];
    for (int i = 0; i <= n; i++)
      list[i] = new LinkedList<>();
    for (int i = 0; i < m; i++) {
      list[sc.nextInt()].add(sc.nextInt());
    }
    int ret = 0;
    dp = new int[n + 1];
    Arrays.fill(dp, -1);
    for (int i = 1; i <= n; i++){
      ret = Math.max(ret, solve(i));
//      System.out.println(ret + " ret");
    }
    System.out.println(ret);
  }
}