Problem Statement

Today is Yuyu's birthday. As a birthday present, Yuyu received a toy that, for an input positive integer $N$, displays the value of the definite integral $\displaystyle \int_0^{\frac{1}{e\pi^2}} e^{\cos \frac{x}{N}}\ dx$. However, the screen was damaged for some reason, so part of the value could not be seen. Therefore, please find the value of the above definite integral in place of the toy. Solve $T$ test cases per $1$ input file.

Input

$T$
$N_1$
$\vdots$
$N_T$

• $T,N_1,\ldots,N_T$ are integers
• $1\leq T \leq 2\cdot 10^5$
• $1 \leq N_i \leq 10^8$ for each $1\leq i \leq T$

Output

First, a positive integer $T$ is given. For the $T$ positive integers $N_i$, output the value of the definite integral $\displaystyle \int_0^{\frac{1}{e\pi^2}} e^{\cos \frac{x}{N_i}}\ dx$. Also, print a newline after each test case.
Floating-point errors are tolerated: the absolute error or relative error must be at most $10^{-8}$. However, due to judge limitations, please output fewer than 500 digits.

Sample

2
1
100000000

0.1012977284
0.1013211836