Computing the Value of π

Problem Background

Special for beginners, ^_^

Problem Description

Based on the formula

$$\arctanx(x) = x-{x^3\over 3}+{x^5\over 5}-{x^7\over 7}+\cdots$$

and

$$\pi=6\cdot arctanx({1\over \sqrt 3})$$

define a function $\arctanx(x)$ and compute the value of $\pi$ when the last term of the series becomes smaller than $10^{-6}$.

Input Format

This problem has no input.

Output Format

Output the value of $\pi$, kept to 10 decimal places.

Sample Input

(no input)

Sample Output

(no input)

Constraints

1s, 1024KiB for each test case.