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  rep(i,a,b)for(int i=a;i<b;++i)
#define  rrep(i,a,b)for(int i=a;i>=b;--i)
#define  yesno(flag)if(flag)cout<<"Yes"<<endl; else cout<<"No"<<endl;
using namespace std;
typedef long long ll;
const ll INF=10000000000LL;
const ll r197=1000000007;
typedef pair<int,int>P;

typedef pair<int,P>Pa;
vector<int> v[100001];
int n,m;
int x[100005],y[100005];
int C[100005]={};
int main() {
	cin>>n>>m;
	rep(i,0,m){
		cin>>x[i]>>y[i];
		v[x[i]-1].push_back(y[i]-1);
	}
	queue<int> que;
	rep(i,0,n)que.push(i);
	while(!que.empty()){
		int num=que.front();que.pop();
		for(int num2:v[num]){
			if(C[num2]<C[num]+1){
				C[num2]=C[num]+1;
				que.push(num2);
			}
		}
	}
	int ans=0;
	rep(i,0,n){
		ans=max(ans,C[i]);
	}
	cout<<ans<<endl;
	return 0;
}