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 <iostream>
#include <vector>
#include <cstring>
using namespace std;

// dp[node] = max(dp[node], 1 + max(dp[child1], dp[child2], dp[child3]..))
void addEdge(vector<int> adj[],int u,int v) {
	adj[u].emplace_back(v);
}

void dfs(int node,vector<int> adj[],int dp[], bool vis[]) {
	vis[node]=true;
	for(int i=0; i<adj[node].size(); ++i) {
		if(!vis[adj[node][i]])
			dfs(adj[node][i],adj,dp,vis);
		dp[node] = max(dp[node], 1+dp[adj[node][i]]);
	}
}

int findLongestPath(vector<int> adj[], int v) {
	int dp[v+1];
	memset(dp,0,sizeof(dp));
	bool vis[v+1];
	memset(vis,0,sizeof(vis));

	for(int i=1; i<=v; ++i) {
		if(!vis[i]) 
			dfs(i,adj,dp,vis);
	}
	int ans = 0;
	for(int i=1; i<=v; ++i) {
		ans = max(ans,dp[i]);
	}
	return ans;
}
int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	int v,e;
	cin >> v >> e;
	vector<int> adj[v+1];
	for(int i=0; i<e; ++i) {
		int u,v;
		cin >> u >>v;
		addEdge(adj,u,v);
	}
	cout << findLongestPath(adj,v) << "\n";
	return 0;
}