Soccer coach Joe has invented a new fitness game that he
thinks will help his players’ agility and fitness. The center
circle of the soccer pitch has a diameter of $60$ feet. He marks $28$ evenlyspaced points on the
circumference of the circle. On the first point (arbitrarily
chosen) he places a pile of tokens all inscribed with the
letter ’A’. On the second point he places a pile of ’B’ tokens,
and so on, covering $26$
of the $28$ points. He
places a pile of blanks (or spacecharacters) on the
$27^{\rm th}$ point and a
pile of disks imprinted with single quotation marks, on the
last point.
He gives each player a slip of paper containing an aphorism,
such as “WINNING ISN’T EVERYTHING IT’S THE ONLY THING” Notice
that the only punctuation marks allowed are spaces and single
quotation marks. Each player gets a different aphorism.
A player starts outside the circle next to the first letter
of his aphorism and, on Joe’s “GO” signal, the player picks up
his first disk and then takes off running around the outside of
the circle, picking up the remaining disks in the order that
the corresponding letters appear in the aphorism. A smart
player will take the shortest route, possibly changing
direction, between consecutive letters of his aphorism.
One of the assistant coaches makes a note of the player’s
time. Although Joe initially envisioned all of his $20$ players running around the circle
simultaneously, this idea was scrapped due to contusions and
fractures.
Joe wants you to write a program to estimate the expected
time for one smart player to complete each of
the aphorisms. Assume for simplicity that the player runs at
$15$ feet per second
between stops for pickups and that each pickup takes
$1$ second.
Input
The input begins with a number $N$, $(1
\leq N \leq 20)$ giving the number of aphorisms to
follow. $N$ lines follow,
each one containing an aphorism made up of uppercase letters,
single quotation marks, and spaces. Each aphorism will be
between $8$ and
$120$ characters
inclusive.
Output
For each aphorism give the time for a smart player to
complete the task. Your answer should be accurate to within
$10^{6}$ seconds.
Sample Input 1 
Sample Output 1 
3
WINNING ISN'T EVERYTHING IT'S THE ONLY THING
WINNERS DON'T WAIT FOR CHANCES THEY TAKE THEM
PAIN IS ONLY TEMPORARY BUT VICTORY IS FOREVER

187.6156641641
190.4108599662
193.1036536692
