Let $X,Y$ be independent standard uniform random variables. How do we compute the joint density $$P(a\leq X\leq 1-a, a \leq Y \leq 1-a, |X-Y|\geq a) $$

for some positive value $a$. I can split the absolute value into two separate conditions $X-Y\geq a$ and $-(X-Y) \geq a$. Now, I have way too many conditions. Any leads is appreciated.

Many thanks.