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;
map<int,vector<int> > m;
int arr[100005];

int dfs(int root,int depth)
{
	if(arr[root]!=-1)
		return arr[root];
	vector<int> v=m[root];
	//if(v.size()==0)return 1;
	int ans=1;
	for(int i=0;i<v.size();i++)
	{
		int d=dfs(v[i],1);
		ans=max(d+depth,ans);
	}
	arr[root]=ans;
	return ans;
}

int main()
{
	int n,M;
	cin>>n>>M;
	
	
	for(int i=0;i<M;i++)
	{
		int u,v;
		cin>>u>>v;
		m[u].push_back(v);
	}
	
	
	memset(arr,-1,sizeof(arr));
	
	for(int i=1;i<=n;i++)
	{
		if(arr[i]==-1)
			dfs(i,1);
	}
	int ans=0;
	for(int i=1;i<=n;i++)
		ans=max(ans,arr[i]);
	cout<<max(0,ans-1)<<endl;
	
}