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: Time Limit Exceeded)

// CODE © by 𝕌𝕥𝕜𝕒𝕣𝕤𝕙 𝔾𝕒𝕣𝕘
// Copying or sharing of this code without permission of the Author is strictly prohibited!!!
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define endl "\n"
vector<int>v[100001];
int dp[100001];
int f(int sp, set<int> s) {
	s.insert(sp);
	int ans = 0;
	if (dp[sp] != -1)return dp[sp];
	for (int i = 0; i < v[sp].size(); i++)
		if (s.find(v[sp][i]) == s.end())
			ans = max(ans, f(v[sp][i], s));
	return dp[sp] = 1 + ans;
}
signed main() {
#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
#endif
	int a = 0, b = 0, c = 0, d = 0, i = 0, j = 0, k = 0, t = 0, n = 0, q = 0, m;
	cin >> n >> m;
	memset(dp, -1, sizeof(dp));
	for (i = 0; i < m; i++)
	{cin >> a >> b; v[a].pb(b);}
	set<int> s;
	int ans = 0;
	for (i = 1; i <= n; i++) {
		if (dp[i] != -1)continue;
		ans = max(f(i, s), ans);
	}
	cout << ans - 1 << endl;
}