John is a successful farmer and he would like to expand his business. For this reason he is going to buy a new plot of land to grow even more crops (and earn even more money). Currently there are _T_ (0 ≤ T ≤ 1000) plots on sale and John wants to find the best deal. He considers deal the best if the price per area unit is the lowest. Can you help him by coding a solution that computes price per area unit?
First line contains the number of plots _T_ (0 ≤ T ≤ 1000). Each plot defined is as a quadrilateral by 4 integer points on the 2D plane (in clockwise or counterclockwise order), meaning there are 8 integers (32-bit) in total which describe geometry and location of the plot. Last number on the line represents the price of plot.
For each plot output a line “_Case #tc: x_”, where _tc_ is plot’s sequence number (starting from 1) and _x_ is price per unit for the _tc_-th plot rounded to two decimal places.
## Input
First line contains the number of plots _T_ (0 ≤ T ≤ 1000). Each plot defined is as a quadrilateral by 4 integer points on the 2D plane (in clockwise or counterclockwise order), meaning there are 8 integers (32-bit) in total which describe geometry and location of the plot. Last number on the line represents the price of plot.
## Output
For each plot output a line “_Case #tc: x_”, where _tc_ is plot’s sequence number (starting from 1) and _x_ is price per unit for the _tc_-th plot rounded to two decimal places.
[samples]
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of plots, with $ 0 \leq T \leq 1000 $.
For each plot $ k \in \{1, \dots, T\} $:
- Let $ P_k = \{(x_{k,1}, y_{k,1}), (x_{k,2}, y_{k,2}), (x_{k,3}, y_{k,3}), (x_{k,4}, y_{k,4})\} $ be the four vertices of a quadrilateral in order (clockwise or counterclockwise), where $ x_{k,i}, y_{k,i} \in \mathbb{Z} $.
- Let $ p_k \in \mathbb{R} $ be the price of plot $ k $.
**Constraints**
1. $ 0 \leq T \leq 1000 $
2. For each $ k \in \{1, \dots, T\} $:
- $ x_{k,i}, y_{k,i} \in \mathbb{Z} $, representable as 32-bit integers.
- $ p_k \geq 0 $
**Objective**
For each plot $ k $, compute the area $ A_k $ of the quadrilateral $ P_k $ using the shoelace formula:
$$
A_k = \frac{1}{2} \left| \sum_{i=1}^{4} (x_{k,i} y_{k,i+1} - x_{k,i+1} y_{k,i}) \right|, \quad \text{where } (x_{k,5}, y_{k,5}) = (x_{k,1}, y_{k,1})
$$
Then compute the price per unit area:
$$
r_k = \frac{p_k}{A_k}, \quad \text{if } A_k > 0
$$
Output $ r_k $ rounded to two decimal places for each plot $ k $ as "Case #k: r_k".