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;
const int maxi = 100005;

int len [100005];

vector<int>adj[maxi];

int fun(int u)
{
	if(len[u])return len[u];
	
	for(int i =0;i<adj[u].size();i++)
	len[u]=max(1+fun(adj[u][i]),len[u]);
	return len[u];
}

int main()
{
	int n,m;cin>>n>>m;
	for(int i =0;i<m;i++)
	{
		int x,y;cin>>x>>y;
		adj[x].push_back(y);
	}
	
	int maxi =0;
	for(int i =1;i<=n;i++)
	{
		if(len[i]==0)
		{
			maxi = max(maxi,fun(i));
		}
		
	}
	cout<<maxi<<endl;
}