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 ll long long int
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define all(a) a.begin(),a.end()
using namespace std;
vector<ll> v[100001];
ll dp[100001], b[100001];
ll calc(ll x)
{
	b[x] = 1;
	if(v[x].empty())
		return dp[x] = 0;
	if(dp[x] >=0)
		return dp[x];
	for(auto u: v[x])
		dp[x] = max(dp[x], 1 + calc(u));
	return dp[x];
}
int main(void)
{
	ll n, m, t1, t2, i, m1;
	for(i=0; i<100001; i++)
		dp[i] = -1;
	cin>>n>>m;
	while(m--)
	{
		cin>>t1>>t2;
		v[t1].pb(t2);
	}
	for(i=1; i<=n; i++)
		if(!b[i])
			calc(i);
	m1 = dp[1];
	for(i=1; i<=n; i++)
		m1 = max(m1, dp[i]);
	cout<<m1<<"\n";
}