Ancient Messages

Input

The input consists of several test cases, each of which describes an image containing one or more hieroglyphs chosen from those shown in Figure $\mathrm{C}.1$. The image is given as a sequence of horizontal scan lines consisting of black pixels (represented by $1$) and white pixels (represented by $0$). In the input data, each scan line is encoded in hexadecimal notation. For example, the sequence of pixels $10011100$ (one black pixel, followed by two white pixels, and so on) is represented in hexadecimal as $9c$. Only digits and lowercase letters $a$ through $f$ are used in the hexadecimal encoding. The first line of each test case contains two integers $H$ and $W$. Here $H$ (0 < H \leq 200) is the number of scan lines in the image, and $W$ (0 < W \leq 50) is the number of hexadecimal characters in each line. The following $H$ lines contain the hexadecimal characters of the image, from top to bottom. Input images satisfy the following requirements:

• The image contains only hieroglyphs shown in Figure $\mathrm{C}.1$.

• Each image contains at least one hieroglyph.

• Each black pixel is part of a hieroglyph.

• Each hieroglyph consists of a connected set of black pixels, each of which has at least one adjacent black pixel above, below, to the left, or to the right.

• Hieroglyphs do not touch each other, and no hieroglyph is inside another.

• If two black pixels are diagonally adjacent, there is also a black pixel that is adjacent to both.

• The hieroglyphs may be distorted, but each is topologically equivalent to one of the characters in Figure $\mathrm{C}.1$ (two figures are topologically equivalent if one can be transformed into the other by stretching without tearing).

The last test case is followed by a line containing two zeros.

Output

For each test case, print its case number followed by a string containing a single letter for each recognized hieroglyph in the image, using the following codes:

Ankh: A Wedjat: J Djed: D Scarab: S Was: W Akhet: K

In each output string, print the codes in alphabetical order. Follow the format of the sample output.

The sample input contains test cases shown in Figures $\mathrm{C}.2$ and $\mathrm{C}.3$. Due to space constraints, not all sample input is provided here.

Examples