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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main(){
  int N,M; cin>>N>>M;
  vector<vector<int>> G(N);
  vector<pair<int,int>> P(N,{0,0}); //{入る数,頂点番号}
  for(int i=0;i<N;i++){
    P[i].second=i;
  }
  vector<int> path(N,0);
  int x,y;
  for(int i=0;i<M;i++){
    cin>>x>>y;
    x--; y--;
    P[y].first++;
    G[x].push_back(y);
  }
  sort(P.begin(),P.end());
  for(int i=0;i<N;i++){
    x=P[i].second;
    for(int j=0;j<G[x].size();j++){
      path[G[x][j]]=max(path[G[x][j]],path[x]+1);
    }
  }
  sort(path.begin(),path.end());
  cout<<path[N-1]<<endl;
}