Deciphering Characters

A syndicate of unknown origin left image data behind, and you have to analyze it. Its members wrote with characters they invented themselves. One binary image holds one character written in black ink on white paper.

Images that look different often stand for the same character. The surrounding relation between connected components decides whether two images stand for the same character. The definitions follow. Assume that white pixels fill the whole plane outside the given image.

• White connected component: a set of white pixels connected to each other horizontally or vertically.
• Black connected component: a set of black pixels connected to each other horizontally, vertically, or diagonally.
• Connected component: a white connected component or a black connected component.
• Background component: the connected component that holds the pixels outside the image. Every white pixel on the border of the image therefore belongs to the background component.

connected	disconnected

Connectedness of white pixels.

connected	connected

Connectedness of black pixels.

Let $C_1$ be a connected component of an image, and let $C_2$ be another connected component of the same image with the opposite color. Build a modified image in which every pixel that lies in neither $C_1$ nor $C_2$ takes the color of $C_2$. If neither $C_1$ nor $C_2$ is the background component, the pixels outside the image also take the color of $C_2$. When no pixel of $C_2$ belongs to the background component of the modified image, $C_1$ surrounds $C_2$ in the original image.

Two images stand for the same character when both of the following conditions hold.

• The two images have the same number of connected components.
• Let $S$ and $S'$ be the sets of connected components of the two images. A bijection $f : S \to S'$ exists that satisfies the following conditions.
  • For each connected component $C$ in $S$, $f(C)$ has the same color as $C$.
  • For each $C_1$ and $C_2$ in $S$, $f(C_1)$ surrounds $f(C_2)$ if and only if $C_1$ surrounds $C_2$.

The connected components of the two images in the figure below have the following surrounding relations.

• $C_1$ surrounds $C_2$.
• $C_2$ surrounds $C_3$.
• $C_2$ surrounds $C_4$.
• $C'_1$ surrounds $C'_2$.
• $C'_2$ surrounds $C'_3$.
• $C'_2$ surrounds $C'_4$.

The bijection $f(C_i) = C'_i$ satisfies both conditions, so the two images stand for the same character.

Write a program that decides whether two given images stand for the same character.

The input holds at most 200 datasets. A line with two zeros ends the input. Each dataset has this form.

image 1
image 2

Each image has this form.

h w
p(1,1) ... p(1,w)
...
p(h,1) ... p(h,w)

$h$ and $w$ are the height and the width of the image in pixels, and $1 \le h \le 100$ and $1 \le w \le 100$ hold. Each of the $h$ lines that follow holds exactly $w$ characters with no separator between them. $p(y,x)$ is the color of the pixel in row $y$ from the top and column $x$ from the left. A period (".") means white and a sharp sign ("#") means black.

For each dataset, print yes on one line when the two images stand for the same character, and print no otherwise. Print nothing else.