In this challenge, you must implement part of a raster graphics editor that takes the coordinates of a circle and a square as input and draws them as filled-in shapes on a rectangular canvas.

The rectangular canvas consists of uniformly sized square pixels, and is $\boldsymbol{w}$ pixels wide, and $\mbox{h}$ pixels high. Each point on the canvas belongs to a pixel, the intersection of two pixels has zero area, and each pixel is completely contained within the canvas.

The Cartesian coordinate system set up in the following way:

Point $(0,0)$ is the center of the top-left pixel of the canvas.
Point $(w-1,0)$ is the center of the top-right pixel of the canvas.
Point $(0,h-1)$ is the center of the bottom-left pixel of the canvas.
Point $(w-1,h-1)$ is the center of the bottom-right pixel of the canvas.

Thus, all pixel centers have integer coordinates and if the center of a pixel has coordinates $(x_c,y_c)$, then point $(x,y)$ belongs to the pixel if and only if $x\in[x_c-0.5,x_c+0.5]$ and $y\in[y_c-0.5,y_c+0.5]$. The two shapes should be drawn like so:

The circle is centered at the integer coordinates $(x_{circle},y_{circle})$ and has non-negative integer radius $\textbf{r}$. A pixel should be black as a part of the circle if and only if the Euclidean distance from the pixel's center to the center of the circle is not greater than $\textbf{r}$.

The square is defined by the integer coordinates of two of its opposite corners $(x_{1},y_{1})$ and $(x_{3},y_{3})$. A pixel should be black as a part of the square if and only if its center falls within the square or along its border. The coordinates of different corners of the square do not coincide.

Given $\mbox{h}$, $\boldsymbol{w}$, and the definition of the circle and the square, print a raster image of the canvas where each character is either a . (denoting a white pixel outside of both shapes) or a # (denoting a black pixel that's part of a shape).

Note: The first pixel of the first line of output should correspond to the top-left corner of the canvas.

Input Format

The first line contains two space-separated integers describing the respective values of $\boldsymbol{w}$ (canvas width) and $\mbox{h}$ (canvas height).

The second line contains three space-separated integers describing the respective values of $x_{circle}$, $y_{circle}$, and $\textbf{r}$ defining a circle with radius $\textbf{r}$ centered at $(x_{circle},y_{circle})$.

The third line contains four space-separated integers describing the respective values of $x_{1},y_{1},x_{3},y_{3}$ defining a square with opposite corners at $(x_{1},y_{1})$ and $(x_{3},y_{3})$.

Constraints

$10\leq w,h\leq100$
$-100\leq x_{circle},y_{circle},x_1,y_1,x_3,y_3\leq200$
$0\leq r\leq100$

Output Format

Print $\mbox{h}$ lines where each line contains $\boldsymbol{w}$ characters. Each character must be either a . (to denote a white pixel) or a # (to denote a black pixel). The first pixel of the first line of output corresponds to the top-left corner of the canvas.

Sample Input 0
20 16
9 6 5
16 14 8 14

Sample Output 0
....................
.........#..........
......#######.......
.....#########......
.....#########......
.....#########......
....###########.....
.....#########......
.....#########......
.....#########......
......#######.......
.........#.###......
..........#####.....
.........#######....
........#########...
.........#######....

Explanation 0

The canvas has $h=16$ rows and $\boldsymbol{w}={20}$ columns. The circle has radius $r=5$ and is centered at point $(9,6)$. The square has opposite corners located at points $(16,14)$ and $(8,14)$ and, as you can see, is rotated at an angle with its third corner at point $(12,10)$ (note that its fourth corner is outside the canvas boundary). In addition, the circle and the square overlap at point $(12,10)$.

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