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: Accepted)

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

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, m;
    cin >> n >> m;
    vector<int> g[n];
    vector<int> back[n];
    for(int i = 0; i < m; i++){
        int u, v;
        cin >> u >> v;
        u--; v--;
        g[u].push_back(v);
        back[v].push_back(u);
    }
    vector<bool> mark(n, false);
    vector<int> topo;
    function<void(int)> dfs = [&](int v){
        mark[v] = true;
        for(int x : g[v]){
            if(!mark[x]) dfs(x);
        }
        topo.push_back(v);
    };

    for(int i = 0; i < n; i++){
        if(!mark[i]) dfs(i);        
    }
    reverse(topo.begin(), topo.end());
    vector<int> dp(n, 0);
    for(int v: topo){
        for(int u : g[v]) dp[u] = max(dp[u], dp[v]+1);
    }
    int mx = 0;
    for(int i = 0; i < n; i++) mx = max(mx, dp[i]);
    cout << mx << endl;
    return 0;
}