This Is Halloween: Saving Money

The Mayor of Halloween Town is forever trying to save money. When the Pumpkin King, Jack Skellington, decides to try his hand at stealing Christmas again, the Mayor scrambles to cut every corner he can — it is a recession, after all. So when Jack orders enough wrapping paper for all the presents, the Mayor wants to use the absolute minimum. He has asked you, the local computer ghoul, to compute how much wrapping paper each kind of gift will take.

Luckily, every gift fits inside a rectangular box. Each present is described by a name together with the three box dimensions a, b, and c (with 0 < a <= b <= c), measured in frightometers.

A gift is wrapped like this. First, a large sheet of wrapping paper is laid on a flat surface. The box is set on the paper with one of its bc faces resting on it. The paper is folded up around the four c edges and the excess is trimmed away, leaving a 3-frightometer-wide overlap on one of the ac faces. The paper now forms a long rectangular tube of length c whose cross-section wraps once around the box's a-by-b outline.

Next, paper is removed at the two open ends of the tube. There it is cut flush along the a edges, while rectangular flaps are left along the b edges. Each flap is sized so that, when the two flaps are folded in along their b edges, they together cover an ab face with a 3-frightometer-wide overlap where they meet. Any leftover paper is recycled and does not count.

Compute the total area of paper, in square frightometers, needed to wrap each box.

The first line contains a single integer n > 0, the number of box types to process.

Each of the next n lines describes one box: the product name enclosed in single quotes, then three integers a, b, and c giving the box dimensions, and finally one integer giving how many significant digits to report in the answer. That count is never greater than the number of digits in the exact answer. No dimension exceeds 10000.

For each box, print one line in the form:

<Present Name> requires <total paper area> square frightometers of paper to wrap

The present name is printed without its surrounding quotes. <total paper area> is the exact area truncated (cut off, not rounded) to the requested number of significant digits — for instance, an exact area of 29527 reported to 1 significant digit is 20000.