Description

You have just taken over a window system project. The window system is fairly simple, and fortunately, you do not have to display the actual windows. There are $5$ basic operations:

• Create a new window.
• Bring a window to the top.
• Send a window to the bottom.
• Delete a window.
• Output the percentage of the window that is visible (i.e., not covered by other windows).

Input Format

In the input file, operations (no more than $600$ of them) appear one per line in the following formats:

• Create a new window: w(I,x,y,X,Y).
• Bring a window to the top: t(I).
• Send a window to the bottom: b(I).
• Delete a window: d(I).
• Output the percentage of the window that is visible: s(I).

$I$ is the unique identifier of each window. An identifier is a letter (uppercase or lowercase) or a single digit. There are no extra spaces in the input file.

$(x,y)$ and $(X,Y)$ are opposite corners of the window. When you create a window, it is automatically placed on the top. You cannot create a window using an existing identifier, but after deleting a window you may reuse its identifier. Coordinates are positive integers, and every window has nonzero area (i.e., $x \ne X$ and $y \ne Y$). The $x$- and $y$-coordinates are in the range $[1,2^{15}-1]$.

Stop processing at end of file.

Output Format

Produce output only for the s(I) commands. There may be many s(I) commands (no more than $500$). Output a sequence of percentages, one per line, each being the percentage of the window that is visible. Percentages must be rounded to three decimal places (do not print the percent sign %).

w(a,10,132,20,12)
w(b,8,76,124,15)
s(a)

49.167

Hint

Translation from NOCOW.

USACO Training Section 5.3.

Translated by ChatGPT 5