Solve string transform and min-move sorting

## Problem 1: "Goat Latin"-style string transformation You are given a sentence `s` consisting of words separated by single spaces. Transform it into a new sentence using these rules: 1. For each word: - If it begins with a vowel (`a,e,i,o,u` or `A,E,I,O,U`), keep the word as-is. - Otherwise, move its first character to the end of the word. 2. Append the string `"ma"` to the end of the word. 3. Append the letter `'a'` repeated `i` times, where `i` is the 1-based index of the word in the sentence. 4. Join the transformed words with single spaces. **Input:** a string `s` **Output:** the transformed string --- ## Problem 2: Minimum total moving distance to sort an array You are given an integer array `arr` (may contain duplicates), e.g. `[5, 2, 2, 4, 3]`. You want to reorder the array into **nondecreasing** order. - An element can be moved by swapping with adjacent elements. - The **cost** of moving an element is the number of adjacent positions it shifts (equivalently, each adjacent swap costs 1). Return the **minimum total cost** required to transform `arr` into sorted order. **Input:** integer array `arr` **Output:** minimum total moving distance (an integer) **Notes/constraints (typical interview scale):** - Aim for better than `O(n^2)` time for large `n`. - Be careful with duplicates (multiple valid sorted arrangements exist).