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++ (GCC 9.2.1) (judge verdict: Accepted)

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

const int N = 1e5+1;
int n,m;
vector<vector<int>> adj(N);
vector<int> dist(N);
vector<int> nbPere(N);
deque<int> q;

void bfs(){
	for (int start:q){
		dist[start] = 0;
	}
	while (!q.empty()){
		int f = q.front();
		q.pop_front();
		for (int i:adj[f]){
			dist[i] = max(dist[i],dist[f]+1);
			nbPere[i]--;
			if (nbPere[i] == 0) q.emplace_back(i);
		}
	}
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n >> m;
	for (int i=0; i<m; ++i){
		int a,b;
		cin >> a >> b;
		a--; b--;
		adj[a].emplace_back(b);
		nbPere[b]++;
	}
	for (int i=0; i<n; ++i){
		if (nbPere[i] == 0) q.emplace_back(i);
	}
	bfs();
	cout << *max_element(dist.begin(),dist.end());
	return 0;
}