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>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define ll              long long
#define pb              push_back
#define ppb             pop_back
#define endl            '\n'
#define mii             map<ll,ll>
#define pii             pair<ll,ll>
#define vi              vector<ll>
#define vs              vector<string>
#define all(a)          (a).begin(),(a).end()
#define F               first
#define S               second
#define sz(x)           (ll)x.size()
#define hell            1000000007
#define inf             (ll)1e18 + 5
#define PI              3.14159265358979323844
#define rep(i,a,b)      for (ll i=a;i<b;i++)
#define repr(i,a,b)     for (ll i=a-1;i>=b;i--)
#define lbnd            lower_bound
#define ubnd            upper_bound
#define mp              make_pair
#define ios             ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define ordered_set     tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>
#define trace(...)      __f(#__VA_ARGS__, __VA_ARGS__)

template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    std::cerr << name << " : " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');std::cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}

using namespace std;
using namespace __gnu_pbds;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//primes for hashing 937,991,1013,1409,1741

ll n,m,vis[100005];
vi a[100005];
ll dp[100005];

ll find(ll node){
	vis[node]=1;
	if (sz(a[node])==0)return 0;
	if (dp[node]!=-1)return dp[node];
	ll temp=0;
	for (auto i:a[node]){
		if (!vis[i])
			temp=max(temp,find(i));
		else temp=max(temp,dp[i]);
	}
	dp[node]=1+temp;
	return dp[node];
}

void solve() {
    cin>>n>>m;
    rep(i,0,m){
    	ll x,y;
    	cin>>x>>y;
    	a[x].pb(y);
    }
    ll ans=0;
    memset(dp,-1,sizeof dp);
    rep(i,1,n+1){
    	ans=max(find(i),ans);
    }
    cout<<ans<<endl;
}

signed main() {
    ios
    ll test=1;
    //cin>>test;
    while (test--) solve();
    return 0;
}