Migrated from Lutece 708 Improper Integral

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Description

In advanced mathematics, Improper integral is a problem that is so hard to solve!But thanks to computer programming, we can solve these problems in the given precision easily. Today, Small Qiang is facing a simple and common improper integral problem, which asks him to determine the cumulative distribution function of normal distribution defined below:

$\phi(x)=F(x;0,1)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{x}e^{-\frac{x^2}{2}}\mathrm dx$

But Small Qiang is busy playing basketball, so he is asking you for help!Please determine $\phi(x)$ with a given $x$.

Input

In the first line, there is one integer $T$($T<500$).

In the following $T$ lines, each contains one real number $x$ ($0.0\le x\le 5.0$).

Output

For each $x$, output a real number $\phi(x)$ which keeps to five decimal places.

Samples

1
0.0

0.50000

Resources

The 7th BUPT Collegiate Programming Contest