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: Time Limit Exceeded)

#pragma GCC optimize("O3")
#include <bits/stdc++.h>

using namespace std;

typedef long long int ll;

int a[100005];

void DFS(vector<int> adj[] , int s)
{
    for(int i=0 ; i<adj[s].size() ;i++)
    {
        if(a[s]+1 > a[adj[s][i]])
        {
          a[adj[s][i]] = a[s]+1;
          DFS(adj,adj[s][i]);
        }
    }
}

int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int n,m;
    cin >> n >> m;
    vector<int> adj[n+1];
    bool in[n+1]={0};
    for(int i=0 ; i<m ; i++)
    {
        int u,v;
        cin >> u >> v;
        adj[u].push_back(v);
        in[v] = 1;
    }
    for(int i=1 ; i<=n ; i++)
    {
        if(!in[i])
        {
            DFS(adj,i);
        }
    }
    int ans = 0;
    for(int i=1;  i<=n ; i++)
        ans = max(ans,a[i]);
    cout << ans;
    return 0;
}