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>
using namespace std;
#define ll long long int
#define all(x) x.begin(), x.end()
#define MOD 1000000007
#define vi vector < int >
#define pii pair < int, int >
#define INF (int)1e9
#define pb push_back
#define fastIO ios::sync_with_stdio(0); cin.tie(0);

vector < vector < int > > arr;
int cache[100010];

int dfs(int i)
{
    int &res = cache[i];
    if(res != -1)
        return res;
    
    int maxele = 0;
    for(int it : arr[i])
        maxele = max(maxele, dfs(it) + 1);
        
    return res = maxele;
}

int main()
{
    fastIO
    int n, m;
    cin >> n >> m;
    
    memset(cache, -1, sizeof(cache));
    
    arr = vector < vector < int > >(n + 1);
    for(int i = 0; i < m; ++i)
    {
        int u, v;
        cin >> u >> v;
        
        arr[u].push_back(v);
    }
    
    int maxele = 0;
    for(int i = 1; i <= n; ++i)
        maxele = max(maxele, dfs(i));
    
    cout << maxele;

    return 0;
}