Min and Max Regular Tetrahedral Shadows

Problem #53

Tags: geometry puzzle

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This problem is intended to follow Tetrahedral Shadows.

Now let's imagine an opaque regular tetrahedron, having all edges of equal length.
This tetrahedron may rotate along any axis, and as it does the shape and size of the shadow cast onto the ground changes.

Problem Statement

Input data will contain the number of testcases T in the first line.
The following T lines will each contain one decimal value L.

Answer
Should be a string of T space-separated values corresponding to the minimum and maximum possible areas of a shadow cast by a regular tetrahedron with edge length L.
Round all answers to the nearest integer.

Example

input data:
2
2.345678
123.456789

answer:
2 3 5389 7621
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