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<iostream>
using namespace std;
#include<vector>
#include<climits>
#include<stack>

vector<int> graph[100005];
vector<int> topo_sort;
int idk[100005];
int dp[100005];
int n,m;

void topological_sort(){
    
    stack<int> s;
    for(int i=0 ; i<n ; i++){
        if(idk[i]==0){
            s.push(i);
        }
    }

    while(!s.empty()){
        int top = s.top();
        // cout<<top<<endl;
        topo_sort.push_back(top);
        s.pop();
        for(int i=0 ; i<graph[top].size() ; i++){
            idk[graph[top][i]]--;
            if(idk[graph[top][i]]==0){
                s.push(graph[top][i]);
            }
        }
    }

for(int i=0 ; i<n ; i++){
    cout<<topo_sort[i]<<" ";
}
cout<<endl;


}


int solution(){

    for(int i=0 ; i<n ; i++){
        dp[i] = INT_MIN;
    }

    topological_sort();

    dp[topo_sort[0]] = 0;
    int ans = 0;

    for(int i=0 ; i<n ; i++){
        for(int j=0 ; j < graph[topo_sort[i]].size() ; j++){
            int dest = graph[topo_sort[i]][j];
            dp[dest] = max(dp[dest] , dp[topo_sort[i]]+1);
            ans = max(ans , dp[dest]);
        }
    }
    
    return ans;

}



int main(){
    cin>>n>>m;
    
    for(int i=0; i<m ; i++){
        int s,d;
        cin>>s>>d;
        graph[s-1].push_back(d-1);
        idk[d-1]++; 
    }

    cout<<solution()<<endl;

}

// 6 6
// 6 3
// 6 1
// 5 1
// 5 2
// 3 4
// 4 2