Given a non-empty array of integers, some numbers might appear multiple times. Return the maximum number of times that any number appears in the array. For example, given the array {7, 1, 3, 1, 7, 2, 3, 7}, the number 1 appears 2 times, the number 3 appears 2 times, and the number 7 appears 3 times. So, the maximum number of times a number appears is 3. Solve this without modifying the given array or creating a new array.