FAVDICE - Favorite Dice

一个n面的骰子，求期望掷几次能使得每一面都被掷到。

BuggyD loves to carry his favorite die around. Perhaps you wonder why it's his favorite? Well, his die is magical and can be transformed into an N-sided unbiased die with the push of a button. Now BuggyD wants to learn more about his die, so he raises a question: What is the expected number of throws of his die while it has **N** sides so that each number is rolled at least once?

The first line of the input contains an integer **t**, the number of test cases. **t** test cases follow. Each test case consists of a single line containing a single integer **N** (1 <= **N** <= 1000) - the number of sides on BuggyD's die.

For each test case, print one line containing the expected number of times BuggyD needs to throw his **N**-sided die so that each number appears at least once. The expected number must be accurate to 2 decimal digits.

2
1
12

1.00
37.24