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)

#pragma GCC optimize ("-O3")
#include <bits/stdc++.h>  
#include <complex>
#include <queue>
#include <set>
#include <unordered_set>
#include <list>
#include <chrono>
#include <random>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <map>
#include <unordered_map>
#include <stack>
#include <iomanip>
#include <fstream>
 
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> p32;
typedef pair<ll,ll> p64;
typedef pair<double,double> pdd;
typedef vector<ll> v64;
typedef vector<ll> v32;
typedef vector<vector<ll> > vv32;
typedef vector<vector<ll> > vv64;
typedef vector<vector<p64> > vvp64;
typedef vector<p64> vp64;
typedef vector<p32> vp32;
ll MOD = 998244353;
#define forn(i,e) for(ll i = 0; i < e; i++)
#define forsn(i,s,e) for(ll i = s; i < e; i++)
#define rforn(i,s) for(ll i = s; i >= 0; i--)
#define rforsn(i,s,e) for(ll i = s; i >= e; i--)
#define ln "\n"
#define dbg(x) cout<<#x<<" = "<<x<<ln
#define mp make_pair
#define pb push_back
#define fi first
#define se second
// #define INF 1e18
#define fast_cin() ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define sz(x) ((ll)(x).size())
int LIM=2e5+100;
vv64 adj(LIM); 
ll func(int n,v64 &dp)
{
	if (dp[n]!=-1)
		return dp[n];
	dp[n]=0;
	for (int i=0; i<adj[n].size(); i++)
	{
		dp[n]=max(dp[n],func(adj[n][i],dp)+1);
	}
	return dp[n];
}
void solve()
{
	int n,m;
	cin>>n>>m;
	for (int i=1; i<=m; i++)
	{
		int a,b;
		cin>>a>>b;
		adj[a].push_back(b);
	}
	v64 dp(n+1,-1);
	ll ans=0;
	for (int i=1; i<=n; i++)
	{
		dp[i]=func(i,dp);
		ans=max(ans,dp[i]);
	}
	cout<<ans<<endl;


}
int main() 
{ 
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
 
    int t=1;
    while (t--)
    {
        solve();
    }
    return 0;   
}