OpenKattis
Increasing CP5 Lower Bound (Day 2)

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2020-12-07 18:00 AKST

## Increasing CP5 Lower Bound (Day 2)

#### End

2020-12-07 23:00 AKST
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# Problem CMeltdown

A polygon is lowered at a constant speed of $v$ metres per minute from the air into a liquid that dissolves it at a constant speed of $c$ metres per minute from all sides. Given a point $(x,y)$ inside the polygon that moves with the polygon, determine when the liquid reaches the point.

The border between air and liquid always has y-coordinate 0, and the liquid only eats away from the sides of the polygon in 2 dimensions. The polygon does not rotate as it is lowered into the liquid, and at time 0, it is not touching the liquid.

Unlike the polygon, which is flat (2-dimensional), the liquid exists in three dimensions. Therefore, the liquid seeps into cavities in the polygon. For example, if the polygon is “cup-shaped”, the liquid can get “inside” the cup, as in the diagram below.

## Input

The input consists of several test cases.

The first line of each test case contains the five integers $N$, $x$, $y$, $v$, and $c$, where $3 \leq N \leq 30$, $-100 \leq x \leq 100$, $1 \leq y \leq 100$, and $1 \leq c < v \leq 10$.

The following $N$ lines of the test case each contain one vertex of the polygon. The $i$-th line contains the two integers $x$, $y$, where $-100 \leq x \leq 100$, $1 \leq y \leq 100$.

The vertices of the polygon are given in counter-clockwise order. The border of the polygon does not intersect or touch itself, and the point $(x,y)$ lies strictly inside the polygon—it does not lie on the border of the polygon.

Input is terminated by a line containing 0 0 0 0 0. These zeros are not a test case and should not be processed.

## Output

For each test case, output the first time in minutes that the liquid reaches the specified point, rounded to four decimal places.

Sample Input 1 Sample Output 1
4 0 50 2 1
-1 10
1 10
1 90
-1 90
0 0 0 0 0

25.8660