wants to send gifts to all of her friends. All of her gift items can be considered as $2D$ filled

circles of various radii. Gugua went to PackNsend Courier Service to send all of her gifts.

PackNsend company offers $2D$ flexible boxes (you can consider those as flexible envelops) of

various sized square shapes. Each gift requires one box. The gifts must be put in those

square shaped envelops and then the square has to be adjusted to fit the gift in it tightly.

That is, turn a square to a rhombus so that the circle touches all the sides. Length of the sides of the adjusted rhombus should be (obviously!) equal to the initial

square. The company also charges 1unit/area of the enclosed adjusted envelop. Gugua collected $ N $ envelops of various sizes from the company. As Gugua is very little, all of her gifts were also very little. So she found that any of her gifts can be placed in any of those envelops, and then those envelops can be

adjusted to fit the gifts. Gugua has to pay for the total area of all the adjusted rhombuses.

Your job is to help Gugua to find the minimum area that is required to pack all her gifts using

the square envelops and then adjusting them to rhombuses.

INPUT

First line specifies the test case number $ T (T <= 100) $. Then $T $ test cases follow, each case

starts with an integer,$ N (1 <= N <= 100) $, denoting the number of gifts/envelops. Then two

lines follow. The first line contains $N $integers, $G_i (1 <= i <= N) $, each denoting the radius of $i^{th}$

gift. Next line contains N integers, $S_j$, each denoting the length of side of $j^{th}$ square shaped envelops. No value will be greater than 1000. You can safely assume that, $ S_i >= 2*G_j$ (for all $1 <= i,j <= N$).

OUTPUT

For each line, print the case number, starting from 1, and then print the minimum total area

of the adjusted envelops as described above.

SAMPLE INPUT

SAMPLE OUTPUT