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: Accepted)

#include<bits/stdc++.h>

#define X first
#define Y second
#define ll long long
#define MP make_pair
#define PB push_back

using namespace std;

const int MAXN=1e5;

ll n,m;
ll br[MAXN+5];
ll dp[MAXN+5];
vector <ll> djc[MAXN+5];
ll rj;
queue <ll> q;
ll trn,dijete,a,b;

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

	cin>>n>>m;
	for(int i=0; i<m; i++){
		cin>>a>>b;
		br[b]++;
		djc[a].PB(b);
	}
	for(int i=1; i<=n; i++){
		if(br[i]==0){
			q.push(i);
		}
	}
	while(q.size()>0){
		trn=q.front();
		q.pop();
		rj=max(rj,dp[trn]);
		for(int i=0; i<djc[trn].size(); i++){
			dijete=djc[trn][i];
			br[dijete]--;
			dp[dijete]=max(dp[dijete],dp[trn]+1);
			if(br[dijete]==0){
				q.push(dijete);
			}
		}
	}
	cout<<rj;
	
	return 0;
}