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>
#define int long long
#define pb       push_back
#define io    ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define all(a)      (a).begin(),(a).end()
#define endl        '\n'
#define F    first
#define S second
#define mod 1000000007 
#define N 100005
#define pii pair<int,int>
using namespace std;
vector<int> v[N];
stack<int> s;
vector<bool> vis(N,false);
vector<int> dist(N,0);
void dfs(int x)
{
    vis[x]=true;
    for(auto i: v[x])
    {
            dfs(i);
            dist[x]=max(dist[x],1+dist[i]);
    }
}
void solve()
{
    int n,m;
    cin>>n>>m;
    for(int i=0;i<m;i++)
    {
        int a,b;
        cin>>a>>b;
        v[a].pb(b);
    }
    for(int i=1;i<=n;i++)
    {
        if(!vis[i])
        {
            dfs(i);
        }
    }
    cout<<*max_element(all(dist));
}

signed main(){
    io;
    int t=1;
    //cin>>t;
    while(t--){
      solve();
    }
    return 0;
}