Time Limit: 1000 ms Memory Limit: 65536 KiB

#### Problem Description

Having realized that the quadtree-encoded treasure map was a fake, Florida Jones maliciously plans to also play a prank for the next treasure hunter after him. But for that, he needs your help once again:

Can you write a program that takes a picture in the XBM format and encodes it with the quadtree scheme?

#### Input

• The first line will be "#define quadtree_width n" where n is the picture size in pixels. (The picture is quadratic: n*n pixels)
• The second line will be "#define quadtree_height n" accordingly.
• The third line will be "static char quadtree_bits[] = {".
• Then, n lines will follow, each one encoding one pixel row of the picture. There will be n/8 hexadecimal numbers per line.
Each hexadecimal number is composed of 8 bits that encode 8 pixels from left to right (where the leftmost bit has the value 1 and the rightmost bit has the value 128). The hexadecimal numbers are printed in the form 0xdd where d is one character of the set { 0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f }.
Example: The 8 pixels WBBBBWWB are written as 0x9e. (2+4+8+16+128 = 158 = 0x9e)
After each hexadecimal number, a comma follows.
• The last line will be "};".

#### Output

First, print the integer n (8 <= n <= 512) on a line by itself.
Then, print a string consisting of the letters B, W and Q that correctly encodes the picture with the quadtree scheme.
Finally, terminate the string with a newline character.

#### Sample Input

Note: The comments (enclosed by /* and */) are not part of the input. They should help to explain the XBM format.
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0xf0,0xf0,                       /* WWWWBBBB WWWWBBBB */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
0x0f,0x0f,                       /* BBBBWWWW BBBBWWWW */
};

#### Sample Output

16
QQWBBWQWBBWQWBBWQWBBW

#### Hint

Since the problems "Quadtree" and "Quadtree II" are inverse to each other, you can double check your programs by converting back and forth between the respective input and output files.

#### Source

1999/2000 University of Ulm Local Contest