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Geometrically, any square has a unique, well-defined centre point. On a grid this is only true if the sides of the square span an odd number of points. Since any odd number can be written in the form 2k+1, we can characterise any such square by specifying k, i.e. we can say that a square whose sides are of length 2k+1 has size k. Now define a pattern of squares as follows.
Hence, given a value of k, we can draw a unique pattern of squares according to the above rules, e.g., if k is 15, then the following pattern would be produced.
Obviously, any point in the grid will be surrounded by zero or more squares. (If the point is on the border of a square, it is considered to be surrounded by that square).
Write a program that will read in a value of k and the coordinates of a point, and will determine how many squares surround the point.
Input will consist of a series of lines containing 3 integers (k and the coordinates of the point) terminated by a line consisting of three zeroes (0 0 0).
Output will consist of a series of lines, one for each line of the input. Each line will consist of the number of squares surrounding the specified point.
500 113 941 0 0 0