SP1026 FAVDICE - Favorite Dice

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 $N$ ($1 \le N \le 1000$) - 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.