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: Accepted)

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

vector<int> gr[100001];
int res = 0, dp[100001];

void dfs(int src, bool *visited, int len) {
    if(dp[src] != 0) {
        res = max(res, len + dp[src]);
        return ;
    }
    visited[src] = true;
    for(auto x: gr[src]) {
        if(!visited[x]) {
            len++;
            dfs(x, visited, len);
            dp[src] = max(dp[src], 1+dp[x]);
            len--;
        }
    }
    res = max(res, len);
    visited[src] = false;
}

void solve(int N) {
    bool visited[N+1];
    memset(visited, false, sizeof visited);
    memset(dp, 0, sizeof dp);
    for(int i=1;i<=N;i++) dfs(i, visited, 0);
}

int main() {
    int N, M; cin>>N>>M;
    for(int i=0; i<M; i++) {
        int x, y; cin>>x>>y;
        gr[x].push_back(y);
    }

    solve(N);
    cout<<res<<endl;
    return 0;
}