A11079 | Five Dimensional Points

You are given set of $n$ points in 5-dimensional space. The points are labeled from $1$ to $n$ . No two points coincide.

We will call point $a$ bad if there are different points $b$ and $c$ , not equal to $a$ , from the given set such that angle between vectors  and  is acute (i.e. strictly less than ). Otherwise, the point is called good.

The angle between vectors  and  in 5-dimensional space is defined as , where  is the scalar product and  is length of .

Given the list of points, print the indices of the good points in ascending order.

The first line of input contains a single integer $n$ ( $1<=n<=10^{3}$ ) — the number of points.

The next $n$ lines of input contain five integers $a_{i},b_{i},c_{i},d_{i},e_{i}$ ( $|a_{i}|,|b_{i}|,|c_{i}|,|d_{i}|,|e_{i}|<=10^{3}$ ) — the coordinates of the i-th point. All points are distinct.

First, print a single integer $k$ — the number of good points.

Then, print $k$ integers, each on their own line — the indices of the good points in ascending order.