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<bits/stdc++.h>
using namespace std;
int n,m,k,u,v,fix[100005],length[100005],ans;
vector<int>V[100005];
int go(int u){
	
	if(fix[u]) return length[u];
	fix[u]=1;
	for(int i=0;i<V[u].size();i++){
		length[u]=max(length[u],go(V[u][i])+1);
	}
	return length[u];
}
int main(){
	cin>>n>>m;
	for(k=1;k<=m;k++){
		cin>>u>>v;
		V[v].push_back(u);
	}
	
	for(k=1;k<=n;k++){
		if(fix[k]==0){
			go(k);
		}
		ans=max(ans,length[k]);
	}
	cout<<ans;
	
}