Facebook Hacker Cup 2015 Round 2

In the game Theatrhythm Final Fantasy, you poke a screen with a stick to the beat of various songs. The goal is to poke the screen as accurately as possible. If you hit a note at just the right time, you're awarded a critical. Every song is broken into ~20~ sections, and if you get a critical on every note in a section, then you get that section's golden critical bar.

You would like to collect all ~20~ critical bars for every song.
Songs vary in difficulty, but each song has a fixed probability ~p~, which is the chance that you manage to secure any one critical bar on a single playthrough. The chances are independent, so for any given pair of sections, the probability of getting both critical bars in a single playthrough is ~p^2~, and so on. Critical bars are saved between playthroughs, so you don't have to win all of the critical bars in a single play of the song. You might win the first ~10~ on one play, and then the last ~10~ on another.

On average, how many times will you have to play a song to win all ~20~ critical bars?

Input

Input begins with an integer ~T~, the number of songs you'll play. For each song, there is a line containing a floating point number, ~p~, the probability of winning any particular critical bar on a single play of the song.

Output

For each song, output the expected number of times you need to play the song before acquiring all ~20~ critical bars, rounded to five decimal points.

Absolute errors of up to ~10^{-5}~ will be ignored.

Constraints

~1 \le T \le 20~
~0.01 \le p \le 1.0~

Sample Input

5
0.1
0.12
0.123
0.1234
0.12345

Sample Output

Case #1: 34.64694
Case #2: 28.64398
Case #3: 27.91171
Case #4: 27.81676
Case #5: 27.80493