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 dp[100010];
vector <int> adj[100010];

void dfs(int x){
	
	dp[x]=0;
	
	for(int i:adj[x])
	{
		if(dp[i]==-1)
			dfs(i);
		dp[x]=max(dp[i]+1,dp[x]);	
		
	}
}

int main() {
	 int n,m,u,v;
	 cin>>n>>m;
	 fill(dp,dp+n,-1);
	 while(m--){
	 	cin>>u>>v;
	 	u--;v--;
	 	adj[u].push_back(v);
	 }
	 
	 for(int i=0;i<n;i++)
		if(dp[i]==-1) dfs(i);
		
	cout<<*max_element(dp,dp+n);	
	 
	return 0;
}