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ZOJ Problem Set - 1959
Quadtree II

Time Limit: 2 Seconds      Memory Limit: 65536 KB

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.

#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 */
};


Sample Output

16
QQWBBWQWBBWQWBBWQWBBW


Source: University of Ulm Local Contest 1999
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