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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef  long long ll;
#define FIO                ios_base::sync_with_stdio(false);cin.tie(NULL);
vector<ll>g[100005];
vector<ll>dp(100000,-1);

ll dfs(ll n)
{
    if(dp[n]!=-1)
        return dp[n];
    ll ans=0;
    for(auto k:g[n])
    {
        ans=max(ans,dfs(k)+1);
    }
    return dp[n]=ans;
}

int main()
{
    FIO;
    ll n,m;
    cin>>n>>m;
    for(ll i=0;i<m;i++)
    {
        ll x,y;
        cin>>x>>y;
        x--;
        y--;
        g[x].push_back(y);
    }
    ll ret=0;
    for(ll i=0;i<n;i++)
    {
        ret=max(ret,dfs(i));
    }
    cout<<ret<<endl;
    return 0;
    
}