Problem: 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.

Examples

Input

4 5
1 2
1 3
3 2
2 4
3 4


Output

3


Input

6 3
2 3
4 5
5 6


Output

2


Input

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3


Output

3

Solution (in CPP):

Solution:
#include<cstdio>
#define max(a,b)((a)>(b)?(a):(b))
const int N=1e5+3;
struct edge{int v,nxt;}g[N];
int n,m,f[N],head[N],k,ans;
inline void Insert(int u,int v){g[++k]=(edge){v,head[u]};head[u]=k;}
int Dfs(int u){
	if(f[u])return f[u];
	for(int i=head[u];i;i=g[i].nxt)
	  f[u]=max(f[u],Dfs(g[i].v)+1);
	return f[u];
}
signed main(){
	int u,v;
	scanf("%d%d",&n,&m);
	for(;m--;)scanf("%d%d",&u,&v),Insert(u,v);
	for(u=1;u<=n;u++)Dfs(u),ans=max(ans,f[u]);
	printf("%d",ans);
	return 0;
}