Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in C (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include<math.h>
#include<stdlib.h>

int N,M,x[100001],y[100001],a[100001];

int num(int n)
{
  int k,temp;
  
  if(a[n]>=0)
  {
    temp=a[n];
  }
  else 
  {
    temp=0;

    for(k=1;k<M+1;k++)
    {
    if(n==x[k])
    {
      temp=fmax(temp,num(y[k])+1);
    }
    }
  }
  a[n]=temp;
  
  return temp;
  
}

int main()
{
  
  int i,j;
  scanf("%d %d",&N,&M);
  
  for(i=1;i<M+1;i++)
  {
    scanf("%d %d",&x[i],&y[i]);
  }
  
  for(i=1;i<N+1;i++)
  {
    a[i]=-1;
  }
  j=0;
  for(i=1;i<N+1;i++)
  {
    j=fmax(j,num(i));
  }
  
  printf("%d",j);
  
  return 0;
}