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?

• 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 "};".

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.