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>

using namespace std;

#define ll long long 
#define IOS ios_base :: sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define endl "\n"
#define SIZE 100005

vector<int>v[100005];
bool vis[100005];
int dp[100005];

int func(int node)
{
	vis[node] = 1;
	int len = v[node].size();
	int ans = 0;
	
	for(int i = 0;i <len ;i++)
	{
		int child = v[node][i];
		if(!vis[child])
		{
			int curr = 1 + func(child);
			ans = max(ans,curr);
		}
		else
		{
			ans = max(ans,1+dp[child]);
		}
	}
	return dp[node] = ans;
}

int main()
{
	int n,m;
	
	scanf("%d %d", &n, &m);
	for(int i =1 ;i <= m; i++)
	{
		int a, b;
		scanf("%d %d", &a, &b);
		v[a].push_back(b);
	}
	int mx = 0;
	for(int i =1 ; i <= n; i++)
	{
		if(!vis[i])
		{
			int ans = func(i);
			mx = max(mx,ans);
		}
	}
	printf("%d\n",mx);
	return 0;
}