| 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 ≤ **T** ≤ 20 | |
| 0.01 ≤ **p** ≤ 1.0 | |