Shiritori question

I was curious how many words in the English language fit the following patterns:
Q_______X
Q_______Q
X_______Q
X_______X

In other words, how many words begin with a Q or an X and also end with a Q or an X?

Relevancy: you play a game where the first letter of the last word has to be the same as the last letter of the previous word. If your enemies divert the game onto a Q or an X, you can throw it right back at them by using one of these words. For example:

DOG
GOOD
DODGE
EVERYMAN
NEOPHYTE
ELIXIR
RELINQUISH
HEX
XYLOPHONE

This person was handed an X but failed to throw it back in his opponent's face. However ...

RELINQUISH
HEX
XEROX
XYLOPHONE

You force the opponent to divert us back into normal territory. And so even better is when you also know ~every word which ends in Q or X, regardless of what letter it starts with. Such that ...

RELINQUISH
HEX
XEROX
XYLOPHONE
ESSEX
X.....X.....XERODERMA
AJAX
X...X...XENO
ONYX
Damn you!
:D