Description:
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 $${ \vec { a } } { \vec { b } }$$ and $${ \vec { a } } { \vec { c } }$$ is acute (i.e. strictly less than $$90^\circ$$). Otherwise, the point is called good.
The angle between vectors $$\overrightarrow{\tau}$$ and $${ \overrightarrow { y } }$$ in 5-dimensional space is defined as $$\arccos\left(\frac{\vec{x} \cdot \vec{y}}{|\vec{x}||\vec{y}|}\right)$$, where $$\vec{x} \cdot \vec{y} = x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} + x_{4} y_{4} + x_{5} y_{5}$$ is the scalar product and $$|\vec{x}| = \sqrt{\vec{x} \cdot \vec{x}}$$ is length of $$\overrightarrow{\tau}$$.
Given the list of points, print the indices of the good points in ascending order.
Input Format:
The first line of input contains a single integer n (1 ≤ n ≤ 103) — the number of points.
The next n lines of input contain five integers ai, bi, ci, di, ei (|ai|, |bi|, |ci|, |di|, |ei| ≤ 103) — the coordinates of the i-th point. All points are distinct.
Output Format:
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.
Note:
In the first sample, the first point forms exactly a $$90^\circ$$ 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.