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>
#pragma GCC optimize ("Ofast")
#define int long long 
#define ld long double
#define pb push_back
#define vi vector<int>
#define pii pair<int,int>
#define ff first
#define ss second
#define endl '\n'
#define all(v) v.begin(),v.end()
#define sz(v) (int)v.size()
#define rep(i,n) for(int i=0;i<n;i++)
#define rrep(i,n) for(int i=n;i>=0;i--)
#define loop(i,l,r) for(int i=l;i<r;i++)
#define rloop(i,r,l) for(int i=r;i>=l;i--)
#define watch(x) cerr<<(#x)<<"= "<<(x)<<endl;
#define watcharr(a) cerr<<(#a)<<"("<<sz(a)<<")= ";rep(i,sz(a))cerr<<a[i]<<",";cerr<<'\n';
#define inf 2000000000000000000LL
#define mod 1000000007
#define mod1 998244353
#define FASTIO std::ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
using namespace std;

int n,m;
vector<int> g[100005];
int vis[100005];
int len[100005];
int ans=0;

void dfs(int x){
    vis[x]=1;
    for(auto i:g[x]){
        if(!vis[i]) 
            dfs(i);
        len[x]=max(len[x],1+len[i]);
    }
}

signed main() {
    FASTIO;
    // #ifndef ONLINE_JUDGE
    //     freopen("input.txt", "r", stdin);
    //     freopen("output.txt", "w", stdout);
    //     freopen("stderr.txt", "w", stderr);
    // #endif

    // int tt=1;
    // cin>>tt;
    // while(tt--){
        cin>>n>>m;
        int u,v;
        rep(i,m){
            cin>>u>>v;
            g[u].pb(v);
        }
        loop(i,1,n+1) dfs(i);
        loop(i,1,n+1) ans=max(ans,len[i]);
        cout<<ans<<endl;
        
        
    // }
    cerr<<"Time Elapsed: "<<1.0*clock()/CLOCKS_PER_SEC<<" sec";
    return 0;
}