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>
using namespace std;
# define pb push_back
# define FOR(i,a,n) for(int i=a;i<n;i++)
# define mp make_pair
# define RFOR(i,a,n) for(int i=n;i>a;i--)
# define pii pair<long long int,long long int>
#define ub upper_bound
#define lb lower_bound
typedef long long int ll;
vector<ll> g[100009];
ll level[100009];
ll mark[100009];
vector<ll> v;
void dfs(int u)
{
	ll k;
	for(int i=0;i<g[u].size();i++)
	{
		k=g[u][i];
		if((level[u]+1)>level[k])
		level[k]=level[u]+1;
		dfs(k);
	}
}
int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	ll n,m;
	cin>>n>>m;
	ll u,v;
	FOR(i,0,m)
	{
		cin>>u>>v;
		g[u].pb(v);
		mark[v]=1;
	}
	for(int i=1;i<=n;i++)
	{
		if(mark[i]==0)
		dfs(i);
	}
	ll max=0;
	for(int  i=1;i<=n;i++)
	{
		if(level[i]>max)
		max=level[i];
	}
	cout<<max<<endl;
}