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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
unordered_map<int,list<int> > adj;
int dfs(vector<bool> &visited, int len, int vertex, vector<int> &dp)
{
    visited[vertex] = 1;
    if(dp[vertex] != -1)
        return dp[vertex];
    for(auto itr : adj[vertex])
    {
        if(visited[itr] == false)
            len = dfs(visited, len + 1, itr,dp);
    }
    return len;
}
void dfsUtil(int vertices)
{
    int max_length = INT_MIN;
    vector<int> dp(vertices + 1, -1);
    
    for(int i = 1; i <= vertices; i++)
    {
        vector<bool> visited(vertices + 1, 0);
        max_length = max(dfs(visited, 0, i,dp ), max_length);
        dp[i] = max_length;
    }
    cout << max_length ;
}
int main() {
    int vertices,edges;
    cin >> vertices >> edges;
    
    for(int i = 0; i < edges; i++)
    {
        int st, end;
        cin >> st >> end;
        adj[st].push_back(end);
    }
    
    dfsUtil(vertices);
    return 0;
}