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# Problem IRounded 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. 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