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: Runtime Error)

#include <bits/stdc++.h>
using namespace std ;
#define ll long long

inline int D(){
    int t ;
    scanf( "%d" , &t ) ;
    return t ;
}
inline ll LLD(){
    ll t ;
    scanf( "%lld" , &t ) ;
    return t ;
}
//const int INF = 0x3f3f3f3f;
//const int mod=1e9+7;
//###################################################################
const int N=100009;
int n,m;
vector<vector<int>>g(N);

int mem[N];
int solve(int num){
    if(mem[num]!=-1)return mem[num];
    if(g[num].size()) {
        for (auto i:g[num]) {
            return mem[i]= 1+solve(i);
        }
    }

}

int main(){
    n=D(),m=D();
    for(int i=0;i<m;i++){
        int u=D(),v=D();
        g[u].push_back(v);
    }
    int mx=0;
    memset(mem,-1,sizeof(mem));
    for(int i=1;i<=n;i++){
        mx=max(mx,solve(i));
    }
    cout<<mx;
}