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>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
using namespace std;

// #define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
#define ll long long int
#define ld long double
#define pb push_back
#define mp make_pair
#define pll pair<ll,ll>

vector <ll> v,adj[100005];
ll pr[100005],d[100005];

ll fep(ll x, ll y, ll mod)
{ll res=1;while(y>0){if(y&1)res=(res*x)%mod;
    y=y>>1;x=(x*x)%mod;}return res%mod;}

ll dfs(ll node)
{
	pr[node]=1;
	ll m=0,i;
	for(i=0;i<adj[node].size();i++)
		m=max(m,dfs(adj[node][i]));
	d[node]=1+m;
	return d[node];
}

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);cout.tie(0);

	ll n,i,m,j,k,x,y,a,b;
	string s;
	
	cin >> n >> m;
	for(i=0;i<m;i++)
	{
		cin >> x >> y;
		adj[x].pb(y);
	}
	m=0;
	for(i=1;i<=n;i++)
	{
		if(!pr[i])
			x=dfs(i);
		m=max(m,d[i]);
	}
	cout << m-1;
	return 0;
}