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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define max(a, b) ((a)>(b) ? (a) : (b))

int main(){
  int n, m;  scanf("%d %d", &n, &m);
  int to[100002] = {0};
  int **graph;
  graph = (int **)malloc(sizeof(int*)*(n+5));
  for(int i=0; i<=n+1; i++)  graph[i] = (int *)malloc(sizeof(int)*(n+5));
  for(int i=0; i<m; i++){
    int f, t;
    scanf("%d %d", &f, &t);
    graph[f][++graph[f][0]] = t;
    to[t]++;
  }
  int s[100002] = {0};
  int topo[100002] = {0};
  for(int i=1; i<=n; i++)
    if(to[i] == 0)
      s[++s[0]] = i;

  while(s[0] > 0){
    int tmp = s[s[0]--];
    for(int i=1; i<=graph[tmp][0]; i++){
      if(--to[graph[tmp][i]] == 0)
	s[++s[0]] = graph[tmp][i];
    }
    topo[++topo[0]] = tmp;
  }

  int dp[100003] = {0};
  int ans = 0;
  for(int i=1; i<=topo[0]; i++){
    for(int j=1; j<=graph[topo[i]][0]; j++){
      dp[graph[topo[i]][j]] = max(dp[graph[topo[i]][j]], dp[topo[i]] + 1);
      ans = max(ans, dp[graph[topo[i]][j]]);
    }
  }

  printf("%d\n", ans);
  
  return 0;
}