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>
#define sz(x) ((int)x.size())
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
int n,m,dp[100010];
bool vis[100010];
vector<int> adj[100010],topo;
void f(int u) {
	if(vis[u]) return;
	vis[u]=1;
	for(auto& it:adj[u])f(it);
	topo.push_back(u);
}
int main() {
	scanf("%d%d",&n,&m);
	int i;
	for(i=0;i<m;i++) {
		int x,y;
		scanf("%d%d",&x,&y);
		adj[x].push_back(y);
	}
	for(i=1;i<=n;i++) f(i);
	int res=0;
	for(i=0;i<sz(topo);i++) {
		dp[topo[i]]=0;
		for(auto& it:adj[topo[i]]) {
			dp[topo[i]]=max(dp[topo[i]],dp[it]+1);
		}
		res=max(res,dp[topo[i]]);
	}
	printf("%d",res);
	return 0;
}