Moon
Beginner astronomer Dasha has finally acquired a digital camera. Capturing the starry sky with just a click and then conducting research is now much more convenient.
The camera's sensor resolution is not very high, so the photographs of the night sky only distinguish between two colors: black and white. However, this has its advantages: Dasha has already taken numerous pictures, and the memory is still not full. Now, Dasha is interested in identifying the position of the Moon in each picture.
Let's assume the Moon in the picture appears as a circle with a center at point C and an integer non-negative radius r. This means it consists of white points, where the distance from their centers to point C is no more than r. The Moon is entirely contained within the picture.
Additionally, some sufficiently bright stars may appear in the picture as separate white points. There are no more than 25 such points. The picture contains no objects other than the Moon and stars.
Write a program to determine the largest possible radius of the circle representing the Moon, as well as its possible position.
Input
The first line of input contains the integers w and h — the horizontal and vertical resolution of the picture, respectively (1 ≤ w, h ≤ 50). The next h lines contain w characters: "." (black point) or "*" (white point).
Output
In the first line, output a natural number representing the maximum radius of the Moon's image. In the second line, output the coordinates (column, then row) of the center of the Moon's image with the given radius. Columns and rows are numbered starting from one, from left to right and top to bottom, respectively.
If there are multiple possible centers, output any one. It is guaranteed that a correct answer exists.