Factorial and String-Length Sorting

Walmart Global Tech services may need to calculate a numeric value and organize product labels for display. Implement one function that computes the factorial of a non-negative integer and sorts an array of strings by increasing string length.

Formal Specification

Implement factorial_and_sort(n, words):

1. Compute n!, where n! = 1 * 2 * ... * n and 0! = 1.
2. Return the sorted strings in nondecreasing order of length.
3. Preserve the original relative order of strings with equal lengths. Python's built-in sorting is stable, but the ordering requirement must still be satisfied.
4. Return a dictionary with keys factorial and sorted_words.

Examples

Example 1

Input: n = 5, words = ["milk", "egg", "water", "tea"]
Output: {"factorial": 120, "sorted_words": ["egg", "tea", "milk", "water"]}

5! is 120. The strings are ordered by lengths 3, 3, 4, and 5, with egg remaining before tea because they have equal length.

Example 2

Input: n = 0, words = ["apple", "kiwi", "pear"]
Output: {"factorial": 1, "sorted_words": ["kiwi", "pear", "apple"]}

0! is 1, and the two four-letter strings retain their original order.