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: Time Limit Exceeded)

#include<bits/stdc++.h>
#define forn(i,a,b) for(long long i=a;i<=b;i++)
#define fork(i,a,b,k) for(long long i=a;i<=b;i+=k)
using namespace std;
typedef long long ll;
vector<int>child[100005],parent[100005];
queue<int>q;
int used[100005],dist[100005];
int n,m,x[100005],y[100005],mx;
void bfs(int s){
	dist[s]=0;
	q.push(s);
	used[s]=1;
	while(!q.empty()){
		int v=q.front();
		q.pop();
		for(int u : parent[v]){
			dist[u]=dist[v]+1;
			mx=max(mx,dist[u]);
			q.push(u);
		}
	}
}
int main(){
	ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n>>m;
	for(ll i=1;i<=m;i++){
		cin>>x[i]>>y[i];
		parent[y[i]].push_back(x[i]);
		child[x[i]].push_back(y[i]);
	}
	for(int i=1;i<=n;i++){
		if(child[y[i]].empty()){
			bfs(y[i]);
		}
	}
	cout<<mx;
}