In Java, implement a natural merge sort for linked lists. This sorting method is preferred for linked lists as it requires no additional space and has a guaranteed linearithmic complexity.

During each iteration, the natural merge sort algorithm scans the list from left to right, identifying naturally sorted sub-lists and merging them. This process continues, scanning further to identify and merge sub-lists until reaching the end of the list. The algorithm repeats this process until the entire list is sorted.

Example:

Unsorted list: M → E → R → G → E → S → O → R → T → E → X → A → M → P → L → E

Sorted list: A → E → E → E → E → G → L → M → M → O → P → R → R → S → T → X