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,D[100100],R[100100],x,y,ans;
vector<int> G[100100],Q;
int main()
{
	cin>>N>>M;
	for (int i=0;i<M;i++)
	{
		cin>>x>>y;
		G[x].push_back(y);
		R[y]++;
	}
	for (int i=1;i<=N;i++) if (R[i]==0) Q.push_back(i);
	while (!Q.empty())
	{
		int x=Q.back(); Q.pop_back();
		if (ans<D[x]) ans=D[x];
		for (auto &y : G[x])
		{
			if (D[y]<D[x]+1) D[y]=D[x]+1;
			if (--R[y]==0) Q.push_back(y);
		}
	}
	cout<<ans;
	return 0;
}