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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

int main()
{
	//freopen("input14.txt","r",stdin);freopen("output14.txt","w",stdout);
	int n,m,f,t,i,j,k;
	cin>>n>>m;
	vector<int> a(n,0);
	vector<vector<int>> g(n);
	for (i=0;i<m;i++){
		cin>>f>>t;
		f--,t--;
		g[f].push_back(t);
	}
	for (i=0;i<10;i++){
		for (j=0;j<g.size();j++){
			for (k=0;k<g[j].size();k++){
				a[g[j][k]]=max(a[g[j][k]],a[j]+1);
			}
		}
	}
	t=0;
	for (i=0;i<a.size();i++){
		t=max(t,a[i]);
	}
	cout<<t;
	return 0;
}