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.

Input

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.

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 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.