% Author: Sergey Kopeliovich
% Source: SPBU Championship, October 2013

\gdef\thisproblemauthor{Sergey Kopeliovich}
\gdef\thisproblemdeveloper{Sergey Kopeliovich}

\begin{problem}{Dependent Subsets}
{subset.in}{subset.out}
{2 seconds (\textsl{3 seconds for Java})}{256 mebibytes}{}

You are given $n$ vectors in $d$-dimensional space.
You have to choose a set of vectors $A$ of maximal size in such a way that:
$$\forall a, b, c \in A \quad \exists x, y, z \in \mathbb{Z} \colon
\begin{cases} ax + by + cz = 0 \\ x^2 + y^2 + z^2 > 0 \end{cases}$$

\InputFile

The first line contains integers $n$ and $d$
($1 \le n \le 1000$, $1 \le d \le 10$).
Each of the following $n$ lines contains $d$ integers
$a_{i,1}, \dots, a_{i,d}$: the vectors themselves.
It is guaranteed that \mbox{$|a_{i,j}| \le 10^4$} and
\mbox{$\forall i \sum\limits_{j=1}^{d} a_{i,j}^2 > 0$}.
The vectors are numbered by integers from $1$ to $n$ in the order
they are given.

\OutputFile

On the first line, print $k$: the number of vectors in the set you found.
On the second line, print $k$ different integers from $1$ to $n$:
the numbers of vectors in the initial set.
If there are several optimal answers, output any one.

\Example

\begin{example}
\exmp{
6 3
3 -2 0
9 0 0
0 9 0
0 0 9
3 3 0
0 1 1
}{
4
2 3 1 5
}%
\end{example}

\end{problem}
