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 $\text{[math]}$ and $\text{[math]}$ is acute (i.e. strictly less than $\text{[math]}$ ). Otherwise, the point is called good.

The angle between vectors $\text{[math]}$ and $\text{[math]}$ in 5-dimensional space is defined as $\text{[math]}$ , where $\text{[math]}$ is the scalar product and $\text{[math]}$ is length of $\text{[math]}$ .

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

Input

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 a_i, b_i, c_i, d_i, e_i (|a_i|, |b_i|, |c_i|, |d_i|, |e_i| ≤ 10³) — the coordinates of the i-th point. All points are distinct.

Output

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 $\text{[math]}$ 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:

$\text{[math]}$

We can see that all angles here are acute, so no points are good.

Five Dimensional Points

Examples