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Quadtree II or: Florida Jones strikes back
 Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 421 Accepted: 199

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 "};".
Note: The comments (enclosed by /* and */) in the sample input 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

```#define quadtree_width 16
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

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