CF850A 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.

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In the first sample, the first point forms exactly a  angle with all other pairs of points, so it is good. In the second sample, along the cd plane, we can see the points look as follows:  We can see that all angles here are acute, so no points are good.