##### 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 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 **critical bars** for every song.

Songs vary in difficulty, but each song has a fixed probability , 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 , 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 on one play, and then the last on another.

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

### Input

Input begins with an integer , the number of songs you'll play. For each song, there is a line containing a floating point number, , 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 **critical bars**, rounded to five decimal points.

Absolute errors of up to will be ignored.

### Constraints

### 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
```

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

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