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<iostream>
#include<vector>
using namespace std;

int n,m;
vector<int> g[100005];
int dp[100005];
int visited[100005];
int mx=0;

void dfs(int node){

	if(visited[node])
		return;	

	visited[node]=1;	
	dp[node]=0;
	for(auto child:g[node]){
		dfs(child);
		dp[node]=max(dp[node],dp[child]+1);
	}
	mx=max(mx,dp[node]);
}

int main(){
	cin>>n>>m;
	for(int i=1;i<=m;++i){
		int from,to;
		cin>>from>>to;
		g[from].push_back(to);
	}
	for(int i=1;i<=n;++i)
		if(!visited[i])
			dfs(i);
	cout<<mx<<endl;
	return 0;
}