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;
typedef long long ll;
typedef long double ld;

vector<vector<int>> g;
vector<int> deg, dist;

void dfs(int i) {
	// cout << "[" << i << "]\n";
	for (auto x : g[i]) {
		dist[x] = max(dist[x], dist[i] + 1);
		// cout << "{" << x << " " << dist[x] << "}\n";
		if (--deg[x] == 0) {
			dfs(x);
		}
	}
	// cout << "(" << i << " " << dist[i] << ")\n";
}

void solve() {
	int n, m; cin >> n >> m;
	deg.assign(n + 1, 0);
	dist.assign(n + 1, 0);
	g.assign(n + 1, vector<int>());
	for (int i = 0; i < m; ++i) {
		int x, y; cin >> x >> y;
		g[x].emplace_back(y);
		++deg[y];
	}
	vector<int> sN;
	for (int i = 1; i <= n; ++i) {
		if (!deg[i]) {
			sN.emplace_back(i);
		}
	}
	for (auto s : sN) {
		dfs(s);
	}
	cout << *max_element(dist.begin(), dist.end());
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL);
	// #ifndef ONLINE_JUDGE
	//     freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
	// #endif
	solve();
	return 0;
}