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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fi first
#define se second
#define pi pair<ll,ll>
#define pii pair<ll,pi>
#define pb push_back
#define mk make_pair
const int siz = 1e5 + 7;
vector<int>adj[siz];
int dis[siz];
int n, m;
bool vis[siz];
void dfs(int v) {
	vis[v] = true;
	for (auto k : adj[v]) {
		if (!vis[k]) {
			dfs(k);
		}
		dis[v] = max(dis[v], dis[k] + 1);

	}

}
int main() {

	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cin >> n >> m;
	vector<int>u(n);
	for (int i = 0; i < m; i++) {
		int v;
		cin >> u[i] >> v;
		adj[u[i]].pb(v);
	}
	for (int i = 0; i < m; i++) {
		if (!vis[u[i]])
			dfs(u[i]);
	}
	int nax = 0;
	for (int i = 1; i <= n; i++)nax = max(nax, dis[i]);
	cout << nax << endl;
}