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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int n_max = (int) 1e5 + 5;
vector<int> dp(n_max, 0);
vector<bool> visited(n_max, 0);
vector<vector<int> > edges(n_max);

void dfs(int start) {
	visited[start] = true;
	
	for(int i=0; i<(int) edges[start].size(); i++) {
		if(!visited[edges[start][i]]) dfs(edges[start][i]);
		dp[start] = max(dp[start], dp[edges[start][i]] + 1);
	}
}

int main() {
	int n, m;
	cin>>n>>m;

	for(int i=0; i<m; i++) {
		int u, v;
		cin>>u>>v;
		edges[u].emplace_back(v);
	}
	
	for(int i=1; i<=n; i++) if(!visited[i]) dfs(i);
	cout<<*max_element(dp.begin(), dp.end())<<endl;
	return 0;
}