The Queen's Journey 2
Given a sequence of squares on an 8×8 chessboard, represented by consecutive coordinates of a queen in chess notation, determine how many squares were visited the maximum number of times during the queen's journey.
A square is considered visited if it lies on any straight-line path between two consecutive positions of the queen, even if it is not explicitly listed in the sequence.
Input
The input consists of a single line containing the sequence of squares where the queen was positioned during her journey. The input data is guaranteed to be correct.
Output
Output a single line with 2 numbers separated by a space: the first number is the count of squares visited the maximum number of times, and the second number is the maximum number of times any square was visited (refer to examples for clarity).