题目描述

Now everything seems to be done, solving the Reimu's problem, geting the spring. Now Youmu just needs to go back.

But all of a sudden, here comes a witch with blond hair. The stranger stopped Youmu and wants Youmu to help her.

After some introductions, Youmu knows the stranger in front of her called Marisa, and she has some problems with the power of her Master spark

Though there's no common sense in Gensoukyo, the Master spark has a function of it which is below:

At first, we define a function $f(x)$:

Then the power of the Master spark is

With the positive integer number of magic power used as $N$

Marisa is poor at the math, so she comes to Youmu, Youmu, as a gardener is not strange to be good at math right?(as there's no common sense in Gensoukyo). She solves the problem quickly, so can you solve the problem, too?

picture: the stranger Marisa

输入格式

The first line of the input contains one positive integer $T (1\\le T\\le 100000)$ indicating the number of the test cases.

Then follows $T$ lines, each line contains one positive integer $N (1\\le N\\le10^9)$ indicating the number of magic power used at all.

输出格式

For each test case, print $T$ lines. Each line contains one float number the power of Marisa's Master spark.

Your answer will be considered correct, if its absolute or relative error isn't greater than $10^{-8}$. Formally, let your answer be a, while jury's answer be b. Your answer will be considered correct if $\\frac{|a-b|}{max(a,b)}\\le10^{-8}$holds.

样例

3 
123456 
654321 
20210213

2540054047.1300259298 
71355059110.5635324046 
68075422671557.7966003418