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Rounded Buttons

Most styles of graphical user interface make use of lots of rectangles. Buttons are rectangular, menus are rectangular and windows are rectangular. Some styles of user interface exhibit a softer appearance by using rounded rectangles for some components. As illustrated below, a rounded rectangle replaces the sharp corners of an ordinary rectangle with a smooth quarter circles.

\includegraphics[width=0.5\textwidth ]{rect}

Using a coordinate system with the $X$ axis pointing to the right and the $Y$ axis pointing down, a rounded rectangle is described by giving the $x, y$ locations of the left and top edges. The width, $w$, describes the distance between the left and right edges, and the height, $h$, describes the distance between the top and the bottom edges. The radius used for the quarter-circle rounded corners is given by the $r$ parameter.

Input

Input begins with a line containing an integer $1 \le n \le 100$. The next $n$ lines each contain one test case. A test case has a rounded rectangle description and mouse click locations. The rectangle is given by $5$ real numbers for the parameters $x$ $y$ $w$ $h$ and $r$. These parameters always describe a legal rounded rectangle. In particular, it is guaranteed that $0 \le x, y \le 1\, 000$, $0 < w, h \le 1\, 000$, and $0 \leq 2r \leq \min (w,h)$. After the rectangle description is an integer $0 \le m \le 1\, 000$. Following this on the same line are $m$ pairs of real numbers, each pair representing the $x$ and $y$ coordinates of a mouse click. All mouse clicks are in the range $0 \leq x, y \leq 2\, 000$. All real numbers given as input have at most $3$ digits after the decimal point.

Output

For each mouse click location, output inside if the location is inside the rounded rectangle, or outside otherwise. A mouse click right on the edge of a rounded rectangle should be classified as inside.

Sample Input 1 Sample Output 1
3
1 8 14 13 3 5 8 6 15 8 12 11 14 21 2.5 20
2 2 13 14 4 5 4 4 4 16 13 14 3 3 3 9
85.7 114.7 3.2 6.0 1.2 3 86.3 114.8 88.1 118.2 85.9 120.7
outside
outside
inside
outside
inside

inside
outside
inside
outside
inside

outside
inside
outside

CPU Time limit 1 second
Memory limit 1024 MB
Difficulty 2.8medium
Statistics Show
License Creative Commons License (cc by-sa)

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