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<vector<int>> g;
vector<int> dp;

int func(int idx) {
	if(idx>=n && idx<0)
		return INT_MIN;
	
	if(g[idx].size() == 0)
		return 0;

	if(dp[idx]!=-1)
		return dp[idx];
	

	int maxm = -1;
	for(int i=0; i<g[idx].size(); i++) {
		maxm = max(maxm, func(g[idx][i]) +1);
	}

	return dp[idx] = maxm;
}

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

	g.clear();
	g.resize(n+1);
	dp.resize(n+1,-1);

	int x,y;
	for(int i=0; i<m; i++) {
		cin>>x>>y;
		g[y].push_back(x);
	}

	int maxm = -1;
	for(int i=0; i<=n;i++) {
		if(dp[i]==-1) {
			func(i);
		}
		// cout<<dp[i]<<" ";
		maxm = max(dp[i], maxm);
	}
	// cout<<endl;
	cout<<maxm<<endl;
}