bee 1725 - Quadtree II

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 "};".

Note: The comments on the input sample (enclosed by /* and */) are not part of the input. They should help to explain the XBM format.

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	Sample Output
#define quadtree_width 16 #define quadtree_height 16 static char quadtree_bits[] = { 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 */ };	16 QQWBBWQWBBWQWBBWQWBBW

Sample Input

Sample Output

#define quadtree_width 16

#define quadtree_height 16

static char quadtree_bits[] = {

0xf0,0xf0, /* WWWWBBBB WWWWBBBB */

0x0f,0x0f, /* BBBBWWWW BBBBWWWW */

0xf0,0xf0, /* WWWWBBBB WWWWBBBB */

0x0f,0x0f, /* BBBBWWWW BBBBWWWW */

};

QQWBBWQWBBWQWBBWQWBBW