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 <stdio.h>

typedef struct List {
	struct List *next;
	int v;
} list;

int main()
{
	int i, N, M, u, w, deg[100001] = {};
	list *adj[100001] = {}, e[100001], *p;
	scanf("%d %d", &N, &M);
	for (i = 0; i < M; i++) {
		scanf("%d %d", &u, &w);
		e[i].v = w;
		e[i].next = adj[u];
		adj[u] = &(e[i]);
		deg[w]++;
	}
	
	int dist[100001] = {}, q[100001], head, tail;
	for (i = 1, tail = 0; i <= N; i++) if (deg[i] == 0) q[tail++] = i;
	for (head = 0; head < tail; head++) {
		u = q[head];
		for (p = adj[u]; p != NULL; p = p->next) {
			w = p->v;
			if (dist[u] + 1 > dist[w]) dist[w] = dist[u] + 1;
			deg[w]--;
			if (deg[w] == 0) q[tail++] = w;
		}			
	}
	
	int max = 0;
	for (i = 1; i <= N; i++) if (dist[i] > max) max = dist[i];
	printf("%d\n", max);
	fflush(stdout);
	return 0;
}