Kata

Description

A chord divides a circle into two arches with an area ratio of 1:X. Please find the central angle of this chord.

Implementation Details

You should implement the following functions:

double circle(double X); // (1)

(1) The argument X is the ratio. It should return the central angle in radians. Note that a chord has two central angles. Return the smaller one. See sample test 2 for more info.

Constraints

1 <= X <= 10^3

Examples

(1) The argument X is the ratio. It should return the central angle in radians.

Test Cases:

3*10^6 random tests.

Sample Explanation

The ratio of the area of arch BCB' to the area of another arch is approximately equal to 265.2504701351.

Since the angle BAB' is pi/6 in radians, the answer is pi/6.