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 <bits/stdc++.h>
#define ll long long int
#define FASTIO std::ios::sync_with_stdio(false);
#define pb push_back
#define mp make_pair
#define ld long double
#define F first
#define S second
#define input_from_file  freopen("input.txt", "r", stdin);
#define inf 1000000000000000
using namespace std;

vector<int> v[100003];
bool vis[100003];
int dp[100003];

void dfs(int s){
  vis[s] = 1;
  if(v[s].size() == 0){
    dp[s] = 0;
  }
  for(auto it: v[s]){
    if(!vis[it]){
      dfs(it);
    }
    dp[s] = max(dp[s], dp[it] + 1);
  }

}

int main()
{
FASTIO
//input_from_file

int n, m;
cin >> n >> m;

for(int i = 0; i < m; i++){
  int x, y;
  cin >> x >> y;
  x--; y--;
  v[x].pb(y);
}

int ans = 0;

for(int i = 0; i < n; ++i){
  if(!vis[i]){
    dfs(i);
  }
  ans = max(ans, dp[i]);
}

cout << ans;
}