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 <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define all(x) (x).begin(), (x).end()
using ll = long long;
using namespace std;

int N, M;
vector<vector<int>> G;
vector<int> dp;

int f(int now){
  if(dp[now] != 1e9) return dp[now];
  else if(G[now].size() == 0){
    dp[now] = 0;
    return 0;
  }else {
    int mxcount = 0;
    for(auto e:G[now]) mxcount = max(mxcount,f(e)+1);
    dp[now] = max(dp[now],mxcount);
    return mxcount;
  }
}

int main() {
    cin >> N >> M;
    G.resize(N);
    dp.resize(N,1e9);
    rep(i,M){
      int x,y;
      cin >> x >> y;
      x--;y--;
      G[x].push_back(y);
    }

    int ans = 0;
    rep(i,N){
      ans = max(ans,f(i));
    }
    cout << ans << endl;
}