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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int N,M;
int place;

vector<vector<int>> adj_list;
vector<int> t,visited;


void dfs(int i) {
	visited[i]=true;
	for (int u:adj_list[i])
	{
		if(!visited[u])
			dfs(u);
	}
	t[place] = i;
	place--;
}

void top_sort() {
	t.resize(N+1);
	visited.assign(N+1,0);

	place = N;
	for(int i=1;i<=N;++i) {
		if(!visited[i]) 
			dfs(i);
	}
}


int main() {

	cin>>N>>M;
	adj_list.resize(N+1);
	for (int i = 0; i < M; ++i)
	{
		int x,y;
		cin>>x>>y;
		adj_list[x].push_back(y);
	}

	top_sort();

	vector<int> path(N+1);

	for(int i:t) {
		cout<<i<<" ";
	}
	cout<<endl;

	for (int i = N; i >= 0; --i)
	{
		int node = t[i];
		if(adj_list[node].empty()) {
			path[node] =0;
		}
		else {
			for(int u:adj_list[node]) {
				path[node] = max(path[node],path[u]+1);
			}
		}
	}

	cout<<*max_element(path.begin(),path.end());




	return 0;
}