Image and Shadow#2553
In order to make machine recognition of characters more difficult in the "CAPTCHA" (Completely Automated Public Turing test to tell Computers and Humans Apart) system, various transformations are used. One such transformation is the "fall of the shadow"—the symbol is shifted and superimposed on itself. For example, the picture below shows the process of applying a shadow to the letter "S" for an 8 \times 8 image.
Now consider an image of size 16 \times 16. We take the upper left corner as the origin and measure the horizontal coordinate axis from left to right, and the vertical coordinate axis from top to bottom. The vector (, ) by which the image is shifted is called the shift vector. In the picture above, the shift vector is (, )—the image is shifted by points to the right and point down. The original image without any imposed shadow is called the image, while the modified image is called the image with shadow. It is also assumed that the shift vector is such that no shaded (black) point of the image falls outside the 16 \times 16 square.
Your task is to write a program that performs the inverse operation: given the image with a shadow, find the original image and the shift vector with the minimal number of shaded (black) points. If there are several such images, any of them may be given as the answer.
Limits. The shift vector is restricted so that black points of the image do not extend beyond the 16 \times 16 square. -15 \le x, y \le 15.
The input file contains the image with shadow, consisting of lines, each containing exactly characters. A blank (white) point is denoted by a "." (ASCII = 2Eh), and a shaded point is denoted by a "#" (ASCII = 23h).
The first line of the output file should contain two integers and (the shift vector), separated by a space. Then lines of characters each should follow—the image encoded exactly as in the input file.
Example 1