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>

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

using namespace __gnu_pbds;
using namespace std;

#define int long long
#define pb push_back
#define pii pair<int,int>
#define fr(i,n) for(int i=0;i<n;i++)
#define F first
#define S second
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
int dp[int32_t(1e5)+5];
int dfs(int root , map<int , vector<int>>&mp)
{
    if(dp[root] != -1) return dp[root];
    if(mp[root].size() == 0)return 0;
    int cnt=0;
    for(auto x:mp[root])
    {
        //cout<<"For Loop for Root "<<root<<endl;
        cnt=max(1+dfs(x , mp) , cnt);
    }
    return dp[root]=cnt;
}
int32_t main()
{   fastio;
    int n , m;
    cin>>n>>m;
    for(int& i:dp)i=-1;
    map<int , vector<int>>mp;
    for(int i=0; i<m; i++)
    {
        int u , v;
        cin>>u>>v;
        mp[u].pb(v);
    }
    for(int i=1; i <= n; i++)
    {
        dfs(i , mp);
        //cout<<endl;
    }
    /*for(int i=1; i <= n; i++)cout<<dp[i]<<" ";
    cout<<endl;*/
    cout<<*max_element(dp+1 , dp+n+1)<<"\n";
}