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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>
#include<math.h>
#include<stdlib.h>
 
int N,M,x,y;
int **G,*aa,*z;

int num(int n)
{
  int k,temp;
  
  if(aa[n]!=-1)
  {
    return aa[n];
  }
  else 
  {
    temp=1;
 
    for(k=0;k<z[n];k++)
    {
      if(z[G[n][k]]>0)
      {
        temp=fmax(temp,num(G[n][k])+1);
      }
    }           
    aa[n]=temp;
  }
  
    return aa[n];
}
 
int main()
{
  
  int i,j,s,t;
  scanf("%d %d",&N,&M);

  aa=(int *)malloc(sizeof(int)*N);
  z=(int *)malloc(sizeof(int)*N);

  for(i=0;i<N;i++)
  {
    aa[i]=-1;
    z[i]=0;
  }
  
  G=(int **)malloc(sizeof(int)*N);
  for(i=0;i<N;i++)
  {
    G[i]=(int *)malloc(sizeof(int)*M);
  }

  
  for(i=0;i<M;i++)
  {
    scanf("%d %d",&x,&y);
    x--;
    y--;
    G[x][z[x]]=y;
    z[x]++;
  }
  
  j=0;
  for(i=0;i<N;i++)
  {
    if(z[i]>0)
    {
      for(s=0;s<z[i];s++)
      { 
        j=fmax(j,num(G[i][s]));
      }
    }
  }
  j++;
  printf("%d",j);
  
  return 0;
}