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: Time Limit Exceeded)

#include <bits/stdc++.h>

#define ff first
#define ss second
#define mp make_pair

using namespace std;

typedef long long ll;

vector<int> G[100005];
int dp[100005];
bool mark[100005];

int f(int v) {
	if(G[v].size() == 0) return 0;
	int ret = 0;
	mark[v] = 1;
	for(int x : G[v])
		ret = max(ret, f(x)+1);
	return dp[v] = ret;
}

int main() {
	int n,m;
	scanf("%d%d", &n, &m);

	while(m--) {
		int a,b;
		scanf("%d%d", &a, &b);
		G[a].push_back(b);
	}

	int ans = 0;
	for(int i = 1; i <= n; i++)
		ans = max(ans, f(i));

	printf("%d\n", ans);
	
    return 0;
}