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: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
const int MAX=100010;
using namespace std;
int cntc[MAX],dp[MAX],index[MAX][2];
vector <vector<int>> a;
int n,m,a1,a2,ans=0;

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

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

int main(){
  cin >>n>>m;
  for (int i=1;i<=n;i++){
    index[i][0]=-1;
    cntc[i]=0;
  }
  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=0;i<m;i++){
    if (index[a[i][0]][0]==-1)
      index[a[i][0]][0]=i;
    index[a[i][0]][1]=i;
  }

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

}