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>

using namespace std;

vector<int> adj[100007];
int in[100007] = {};
int dp[100007] = {};

int main() {
	
	int i,j;
	int N,M;
	
	scanf("%d %d", &N, &M);
	for( i=1; i<=M; i++) {
		int x,y;
		scanf("%d %d", &x, &y);
		adj[x].push_back(y);
		in[y]++;
	}
	
	queue<int> que;
	for( i=1; i<=N; i++) {
		if( in[i] == 0)
			que.push(i);
	}
	while( !que.empty()) {
		int x = que.front();
		que.pop();
		for( auto y:adj[x]) {
			if( --in[y] == 0)
				que.push(y);
			dp[y] = max( dp[y], dp[x]+1);
		}
	}
	int ans = 0;
	for( i=1; i<=N; i++)
		ans = max( ans, dp[i]);
	printf("%d\n", ans);
	return 0;
}