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)

//If there is no outward edge then ,length of longest path=0
#include<bits/stdc++.h>
#define ll long long
using namespace std;
map<ll,list<ll>> graph;
ll dp[100003];
ll solve(ll y)
{
	if(dp[y]!=-1)
		return dp[y];
	if(graph[y].size()==0)
	{
		return 0;
	}
	ll ans=0;
	for(auto it:graph[y])
	{
		ans=max(ans,solve(it));
	}
	return dp[y]=1+ans;
}
int main()
{
	ll n,m;
	cin>>n>>m;
	for(ll p=0;p<m;p++)
	{
		ll x,y;
		cin>>x>>y;
		graph[x].push_back(y);
	}
	ll ans=0;
	for(ll p=1;p<=n;p++)
		dp[p]=-1;
	for(ll r=1;r<=n;r++)
	{
		ans=max(ans,solve(r));
	}
	cout<<ans<<endl;
}