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>
using namespace std;

typedef long long ll;
const ll mod = 1e9 + 7;
const ll inf = 184467440737095516;

ll n, m, x, y, dp[100005];
bool visited[100005];
vector<vector<ll> > v;
vector<ll> hub;

void dfs(ll a){
	visited[a] = 1;
	for (ll i = 0; i < v[a].size(); i++){
		dp[v[a][i]] = max(dp[v[a][i]], dp[a] + 1);
		hub[v[a][i]]--;
		if (hub[v[a][i]] == 0){
			dfs(v[a][i]);
		}
	}
}

int main(){
	ios_base::sync_with_stdio(0); cin.tie(); cout.tie();

	cin >> n >> m;
	v.resize(n + 1);
	hub.resize(n + 1, 0);
	while(m--){
		cin >> x >> y;
		v[x].push_back(y);
		hub[y]++;
	} 

	for (ll i = 1; i <= n; i++){
		if (!visited[i] && hub[i] == 0){
			dfs(i);
		}
	}

	ll maxi = 0;
	for (ll i = 1; i <= n; i++){
		maxi = max(maxi, dp[i]);
	}
	cout << maxi << '\n';
}