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 mxN=1e5+10;

//vector< vector< int > > adj(mxN,vector<int> ());
vector <int> adj[mxN];
int vis[mxN],a[mxN],dp[mxN];

int dfs(int v)
{
	if(vis[v]) return dp[v];

	vis[v]=1;
	int mx=0;
	for(int u:adj[v])
	{
		mx=max(mx,dfs(u)+1);
	}

	return dp[v]=mx;
}

int main()
{
	int n,m;
	cin>>n>>m;

	for(int i=0;i<m;i++)
	{
		int u,v;
		cin>>u>>v;

		adj[u].push_back(v);
		
	}
	int best=0;
	for(int i=1;i<=n;i++)
	{
		best=max(best,dfs(i));
	}

	cout<<best<<"\n";
}