Chocolate and (not so many) friends

Coco's chocolate machine produces rectangular chocolates whose width $M$ and height $N$ are both multiples of 4. Coco is going to divide it into dominoes of size $1 \times 2$ or $2 \times 1$ and sell them.

Unfortunately, Coco's $K$ friends came to Coco's house and took away one $1 \times 1$ piece each. Calculate the maximum number of dominoes Coco can get by dividing the remaining chocolate.

The first line contains the number of test cases $T$. ($1 \le T \le 1000$)

For each test case, the first line contains the integers $M$, $N$, and $$. (, and are multiples of , )

For each test case, output the maximum number of dominoes Coco can get by dividing the chocolate on its own line.