| 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**? |
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|
| ### Input |
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|
| 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 |
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|
| 1 ≤ **T** ≤ 20 |
| 0.01 ≤ **p** ≤ 1.0 |
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