Tohu wants to enter Moscow State University, and he must pass the math exam. He does not know math, and asks you to help him. The problem is to find the sum of the sequence on condition

Input

First line contains single integer T <= 20000 - the number of test cases.

Each of the next T lines contains single integer 1 <= n <= 10^9.

Output

For each n output the value with 11 digits after decimal point.

Example

Input:
2
2
5

Output:
0.70833333333
0.73809523810