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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int maxLevel;
vector<int> dp;
int dfs(int i,vector<vector<int>> &graph,vector<bool> &vis){
    if(dp[i]!=-1)return dp[i];
    vis[i]=true;
    dp[i]=0;
    for(int node:graph[i]){
        if(!vis[node]){
            dp[i]= max(dp[i],dfs(node,graph,vis)+1);
        }
    }
    return dp[i];
    
}

int main(){
    int n,e;
    cin>>n>>e;
    vector<vector<int>> graph(n);
    dp.clear();
     dp.resize(n,-1);
    int a,b;
    for(int i=0;i<e;i++){
        cin>>a>>b;
        a--,b--;
        graph[a].push_back(b);
    }
    vector<bool> vis(n);
    maxLevel=0;
    for(int i=0;i<n;i++){
        if(!vis[i]){
            maxLevel=max(maxLevel,dfs(i,graph,vis)+1);
        }
    }
    cout<<maxLevel<<endl;
}