Rancher`s Gift#3557

Rancher`s Gift

1 second

64 megabytes

Very easy

Rancher Joel has a tract of land in the shape of a convex quadrilateral that he wants to divide among his sons Al, Bob, Chas, and Dave, who wish to continue ranching on their portions, and his daughter Emily, who wants to grow vegetables on her portion.

The center of the tract is most suitable for vegetable farming, so Joel decides to divide the land by drawing lines from each corner ( $A$ , $B$ , $C$ , $D$ in counterclockwise order) to the center of the opposing side (respectively $A^{'}$ A', $B^{'}$ B', $C^{'}$ C', and $D^{'}$ D'). Each son will receive one of the triangular sections, and Emily will receive the central quadrilateral section. As shown in the figure, Al's tract is bounded by the line from $A$ to $B$ , the line from $A$ to the midpoint of $B C$ , and the line from $B$ to the midpoint of $C D^{'}$ CD'. Bob's tract is bounded by the line from $B$ to $C$ , the line from $B$ to the midpoint of $C D$ , and the line from $C$ to the midpoint of $D A$ , and so on.

Your task is to write a program that will help Rancher Joel determine the area of each child's tract and the length of the fence he will have to put around Emily's parcel to keep her brothers' cows out of her crops.

For this problem, $A$ will always be at $(0, 0)$ and $B$ will always be at $(x, 0)$ . Coordinates will be in rods (one rod is $16.5$ feet). The returned areas should be in acres to $3$ decimal places (an acre is $160$ square rods), and the length of the fence should be in feet, rounded up to the next foot.

Input

The first line of input contains a single integer $P$ ( $1 \leq P \leq 1000$ 1 \leq P \leq 1000), which is the number of data sets that follow. Each data set is a single line that consists of a decimal integer followed by five ( $5$ ) space-separated floating-point values. The first (integer) value is the data set number, $N$ . The floating-point values are $B . x$ , $C . x$ , $C . y$ , $D . x$ , and $D . y$ in that order (where $V . x$ indicates the $x$ coordinate of $V$ and $V . y$ indicates the $y$ coordinate of $V$ ). Recall that the $y$ coordinate of $B$ is always zero ( $0$ ). The supplied coordinates will always specify a valid convex quadrilateral.

Output

For each data set, there is a single line of output. It contains the data set number, $N$ , followed by a single space, followed by five ( $5$ ) space-separated floating-point values to three ( $3$ ) decimal places, followed by a single space and a decimal integer. The floating-point values are the areas in acres of the properties of Al, Bob, Chas, Dave, and Emily, respectively. The final integer is the length of the fence in feet required to enclose Emily's property (rounded up to the next foot).

Examples

Example 1