> 
> Inspired by [this chat message](https://chat.stackexchange.com/transcript/message/40172973#40172973)
> 
> 
> 

Your task will be to take a word and find the average position of its letters on the keyboard as a letter.

Keyboard Layout
---------------

Since layouts vary from keyboard to keyboard, we will be using a standard based of of my own keyboard in this question.

The keyboard has 3 rows, the top row from left to right contains the keys

```
QWERTYUIOP

```

The second row contains the letters

```
ASDFGHJKL

```

The final row contains

```
ZXCVBNM

```

Each letter is 1 unit horizontal from its neighbor to the left. This means that `W` is 1 away from `Q` and `E` is 1 away from `W` and so on.

The keys at the beginning of each row have the positions:

```
Q : 0,0
A : 1/3,1
Z : 2/3,2

```

This means that the rows are separated one unit vertically and the bottom two rows are shifted by a third from the row above them.

---

You should take a word as input and output the letter that is closest to the average position of the letters in its word. The average of a set of vectors is

```
(average x value, average y value)

```

When two keys are equidistant from the average you may output either as the "closest" key.

This is [code-golf](/questions/tagged/code-golf "show questions tagged 'code-golf'") so answers will be scored in bytes with fewer bytes being better.

Example solution
----------------

Let's calculate the average of `APL`.

We convert each letter to a vector

```
A -> (1/3,1)
P -> (9,0)
L -> (8 1/3,1)

```

We add these up the three vectors to get `(17 2/3, 2)`. We then divide each coordinate by 3 (The number of letters in the word) to get `(5 8/9, 2/3)`.

The closest letter to `(5 8/9, 2/3)` is `J` at `(6 1/3,1)` so our result is `J`.

Test Cases
----------

```
APL  -> J
TEXT -> R
PPCG -> J
QQQQ -> Q
ZZZZ -> Z
PPPP -> P
MMMM -> M
QQSS -> A or W

```