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)

#include<bits/stdc++.h>
#define INF 1e5 + 1
using namespace std ;
vector<int>in_degree(1e5+1,0) ;
vector<vector<int> >v(1e5+1) ;
bool arr[(int)1e5+1] ;
vector<int>dp(1e5+1,0) ;
int max(int a, int b)
{
	if(a>b)
	{
		return(a) ;
	}
	return(b) ;
}
void dfs(int j)
{
	arr[j] = true ;
	//cout<<j<<" " ;
	for(int i=0 ; i<v[j].size() ; i=i+1)
	{
		int a = v[j][i] ;
		dp[a] = max(dp[a],1+dp[j]) ;
		--in_degree[a];
		if(in_degree[a]==0)
		{
			dfs(a) ;
		}
	}
}
int main()
{
	int a,b,c,d,i,n,j,m ;
	cin>>n>>m ;
	
	for(i=0 ; i<m ; i=i+1)
	{
		cin>>a>>b;
		++in_degree[b] ;
		v[a].push_back(b) ;
	}
	for(i=1 ; i<=n ; i=i+1)
	{
		arr[i] = false ;
	}
	arr[0] = true ;
	
	for(i=1 ; i<n+1 ; i=i+1)
	{
		if(arr[i]==false && in_degree[i]==0)
		{
			//cout<<i<<" " ;
			dfs(i) ;
		}
	}
	dp[0] = 0 ;
	cout<<*max_element(dp.begin(),dp.begin()+n+2) ;
}