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>
int MAX(int a,int b){return a<b?b:a;}
int main(){
  int n,m,i,t,r,a,q[100010];
  int ta[100010],to[100010],nt[100010],c[100010]={};
  int d[100010]={};
  scanf("%d %d",&n,&m);
  for(i=0;i<n;i++)ta[i+1]=-1;
  for(i=0;i<m;i++){
    scanf("%d %d",&a,&to[i]);
    nt[i]=ta[a];
    ta[a]=i;
    c[to[i]]++;
  }
  for(i=r=0;i<n;i++){
    if(c[i+1]==0)q[r++]=i+1;
  }
  for(t=a=0;r-t;t++){//printf("!%d %d\n",q[t],d[q[t]]);
    a=MAX(d[q[t]],a);
    for(i=ta[q[t]];i+1;i=nt[i]){
      d[to[i]]=MAX(d[to[i]],d[q[t]]+1);
      c[to[i]]--;
      if(c[to[i]]==0)q[r++]=to[i];
    }
  }
  printf("%d\n",a);
  return 0;
}