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: Accepted)

#include<stack>
#include<cstdio>
inline int in();
inline void wr(int);
const int N=(int)1e5+5;
int ju[N][N/100],_in[N],sum[N];
inline int dfs(int);
inline int mx(int,int);
int main(int argc,char**argv){
	register int n=in(),m=in();
	for(register int i=1;i<=m;++i){
		register int u=in(),v=in();
		ju[u][++ju[u][0]]=v,++_in[v];
	}
	register int ans=0;
	for(register int i=1;i<=n;++i)
		ans=mx(ans,dfs(i));
	wr(ans);
}
inline int dfs(int u){
	if(sum[u])return sum[u];
	for(register int i=1;i<=ju[u][0];++i)
		sum[u]=mx(sum[u],dfs(ju[u][i])+1);
	return sum[u];
}
inline int mx(int x,int y){
	return x>y?x:y;
}
inline int in(){
	register char c=getchar();
	register int x=0,f=1;
	for(;c<'0'||c>'9';c=getchar())
		if(c=='-')f=-1;
	for(;c>='0'&&c<='9';c=getchar())
		x=(x<<1)+(x<<3)+(c&15);
	return x*f;
}
inline void wr(int x){
	if(x<0)putchar('-'),x=-x;
	if(x/10)wr(x/10);
	putchar(x%10+'0');
}