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: Time Limit Exceeded)

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

#define int long long
#define sz(x) (int)(x.size())
#define fi first
#define se second
#define pii pair<int, int>

const int N = 2e5;
int n, m;
vector<int> g[N];
set<int> dp[N];
void read_input(){
    cin >> n >> m;
    for(int i = 0; i < m; i++) {
        int x, y;
        cin >> x >> y;
        g[x].push_back(y);
        dp[1].insert(y);
    }
}

signed main(){
    ios::sync_with_stdio(false);
    read_input();
    for(int i = 1; i <= m + 1; i++){
        if(dp[i].empty()){
            cout << i - 1 << "\n";
            break;
        }
        for(auto el : dp[i]){
            for(auto adj : g[el]){
                dp[i + 1].insert(adj);
            }
        }
    }
}