Optimal Text Word Wrap

You are given an array of words `wordList` and a line width `lineWidth`. You must arrange all words into lines such that:

1. Words appear in the original order.
2. Words on the same line are separated by exactly one space.
3. No line exceeds `lineWidth` characters (including spaces between words on that line).

Define the **badness** of a line (other than the last line) as the **cube** of the number of unused characters at the end: `(lineWidth - total_chars_on_line)^3`.

The last line always has badness 0 regardless of trailing spaces.

Return the **minimum total badness** over all valid arrangements.

**Example 1:**
```
Input: wordList = ["hello", "world", "fit", "now"], lineWidth = 12
Output: 0
Explanation: Line 1: "hello world" (11 chars, 1 space unused but it's not the last line, badness=1).
Line 2: "fit now" (7 chars, last line, badness=0). Total = 1.
Better: Line 1: "hello world" (11, 1 slack → 1^3=1), Line 2: "fit now" (last, 0). Total=1.
Actually: Line 1 "hello world fit" = 5+1+5+1+3=15 > 12. No.
Line 1 "hello world" (11), Line 2 "fit now" (7). Total badness = 1^3 + 0 = 1.
```

**Example 1 (corrected):**
```
Input: wordList = ["use", "dp", "here"], lineWidth = 7
Output: 0
Explanation: Line 1: "use dp" (6 chars, slack=1, badness=1). Line 2: "here" (last, badness=0). Total=1.
Or Line 1: "use" (3, slack=4, badness=64). Line 2: "dp here" (7, last, badness=0). Total=64.
Minimum is 1.
```

**Example 1:**
```
Input: wordList = ["use", "dp", "here"], lineWidth = 7
Output: 1
Explanation: Best split: Line 1 "use dp" (slack 1, badness 1), Line 2 "here" (last line, badness 0). Total = 1.
```

**Example 2:**
```
Input: wordList = ["ab", "cd", "ef", "gh"], lineWidth = 5
Output: 1
Explanation: Line 1: "ab cd" (5, slack 0, badness 0). Line 2: "ef gh" (5, last line, badness 0). Total = 0.
```

**Example 2:**
```
Input: wordList = ["go", "do", "run", "jump", "fast"], lineWidth = 7
Output: 1
Explanation:
Line 1: "go do" (5 chars, slack=2, badness=8).
Line 2: "run" (3 chars, slack=4, badness=64).
Line 3: "jump" (4 chars, slack=3, badness=27).
Line 4: "fast" (last, badness=0). Not great.
Better: Line 1 "go do" (5, badness=8), Line 2 "run jump" = 8 > 7. No.
Line 1 "go do" (5, badness 8), Line 2 "run" (3, badness 64), Line 3 "jump fast" = 9 > 7.
Hmm. Let me use a simpler example with a known answer.
```