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;
int n,m;
vector<int> adj[100001];
bool visited[100001]={};

vector<int> v;
void dfs(int s){
	visited[s]=true;
	for(int i=0;i<adj[s].size();++i){
		if(visited[adj[s][i]]==false)
		dfs(adj[s][i]);
	}
	v.push_back(s);
}
int main() {
	cin>>n>>m;
	int x,y;
	for(int i=0;i<m;i++){
		cin>>x>>y;
		adj[x].push_back(y);
	}
	for(int i=1;i<=n;i++){
		if(visited[i]==false)
		dfs(i);
	}
	vector<int> dp(n+1,0);
	reverse(v.begin(),v.end());
	for(int i=v.size()-1;i>=0;i--){
		for(int j=0;j<adj[v[i]].size();j++){
			dp[v[i]]=max(dp[v[i]],dp[adj[v[i]][j]]+1);
		}
	}
	int max=0;
	for(int i=1;i<=n;i++){
		if(max<dp[i])
		max=dp[i];
	}
	cout<<max;
	return 0;
}