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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <algorithm>
const int MAX=110000;
using namespace std;
int cntc[MAX],longest[MAX];
vector <vector<int>> a;
int n,m,a1,a2,ans=0;

bool compare(vector<int> x,vector<int> y){
  return x[0]<=y[0];
}


int fmax(int i){
  if (longest[i]){
  } else if (!cntc[i]){
    longest[i]=1;
  } else {
    int maxv=0;
    for (int j=0;j<m;j++){
      if (i==a[j][0])
        maxv=max(maxv,fmax(a[j][1]));
    }
    longest[i]=maxv+1;
  }
  return longest[i];
}

int main(){
  cin >>n>>m;
  for (int i=0;i<m;i++){
    cin >>a1>>a2;
    vector<int> tmp={a1,a2};
    a.push_back(tmp);
    cntc[a1]++;
  }
//sort(a.begin(),a.end(),compare);

  for (int i=1;i<=n;i++){
    ans=max(fmax(i),ans);
  }
cout << ans-1<<endl;
return 0;

}