Making a Box

Kkung wants to make a gift box for his future girlfriend out of a square panel of size $a \times a$. The box must have a square base and an open top. It is made in two steps:

1. Cut a square piece of side $b$ from each of the four corners of the panel.
2. Fold the four remaining rectangular flaps straight up to form the walls.

The resulting box has a square base of side $a - 2b$ and height $b$, so its volume is $V(b) = b\,(a - 2b)^2$.

Find the height $b$ that maximizes the volume $V(b)$.

The first line contains the number of test cases $n$ ($1 \le n \le 10$). Each of the next $n$ lines contains one real number $a$ ($1 \le a \le 1024$), the side length of a panel.

For each test case, print the value of $b$ that maximizes the volume, rounded to $10$ digits after the decimal point, one per line.

If you still have time after solving this, please help Kkung find a girlfriend too.