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)

#pragma GCC optimize ("O3")
#include <bits/stdc++.h>

using namespace std;
typedef long long int ll;
typedef long double lld;

const ll MOD = 1000000007;
vector<vector<int>> adj;
vector<int> path;

void topo(int x) {
	if(path[x] >= 0) return; // already visited.
	path[x] = 0;
	for(int i = 0; i < adj[x].size(); i++) {
		int v = adj[x][i];
		topo(v);
		path[x] = max(path[x], path[v] + 1);
	}
}

int main() {
	ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);

	int n, m; cin >> n >> m;
	path.resize(n, -1); adj.resize(n, vector<int>());

	for(int i = 0; i < m; i++) {
		int u, v; cin >> u >> v; --u; --v;
		adj[u].push_back(v);
	}

	for(int i = 0; i < n; i++) {
		if(path[i] < 0) topo(i);
	}

	int ans = 0;
	for(int i = 0; i < n; i++) {
		ans = max(ans, path[i]);
	}
	cout << ans << endl;
}