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[100001]={};
bool node[100001]={};

void load(int i,vector<int> e[],int n)
{
	int m=0;
	for(auto j:e[i])
	{
		if(!node[j]) load(j,e,n);
		m=max(m,1+dp[j]);
	}
	node[i]=true;
	dp[i]=m;
}

int main()
{
	int n,m;
	cin>>n>>m;
	vector<int> e[n+1];
	int x,y;
	for(int i=0;i<m;++i)
	cin>>x>>y,e[x].push_back(y);
	
	int mi=0;
	for(int i=1;i<=n;++i)
	{
		if(!node[i]) load(i,e,n);
		mi=max(mi,dp[i]);
	}
	cout<<mi;
}