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 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int dp[100010] = {0};
int M;
int l[100010][2];

int maxNum(int a,int b){
	if(a>b) return a;
	else return b;
}

int f(int a){
	if(dp[a]>=0) return dp[a];
	int max = 0;
	for(int i=0;i<M;i++){
		if(a==l[i][0]) max = maxNum(f(l[i][1])+1,max);
	}
	dp[a] = max;
	return dp[a];
}

int main(void) {
	int N;
	scanf("%d%d",&N,&M);
	for(int i=0;i<M;i++) scanf("%d%d",&l[i][0],&l[i][1]);
	for(int i=0;i<=N;i++) dp[i] = -1;
	int ans=0;
	for(int i=1;i<=N;i++){
		ans = maxNum(f(i),ans);
	}
	printf("%d",ans);
	/*for(int i=1;i<=N;i++){
		printf("%d\n",dp[i]);
	}*/
	return 0;
}