BUG REPORT — repairmoney: the test suite is failing, fix the code so all tests pass

You have an existing Python package `repairmoney` (tiny money helpers over
integer cents). It LOOKS done, but its bundled test suite
(`repairmoney/test_repairmoney.py`) is RED. Run it, find the bugs, and fix the
code in `repairmoney/public.py` so that every test passes. Keep the public API
exactly as it is; do not rewrite the package from scratch and do not edit the
tests.

## Reproduction

    python -m pytest repairmoney/test_repairmoney.py
    # or, with no pytest installed:
    python repairmoney/test_repairmoney.py

Several tests fail. They point at money being rendered with the sign in the
wrong place, cents that are not zero-padded, and an "even" split whose parts do
not add back up to the original total.

## The two helpers

* `format_cents(cents: int) -> str`
  Renders an amount given as a whole number of integer cents (so $12.34 is the
  int `1234`; negative amounts are debts/refunds) as a `$D.DD` string:

      format_cents(1234)   ->  "$12.34"
      format_cents(-1234)  ->  "-$12.34"     # minus IN FRONT of the $
      format_cents(5)      ->  "$0.05"       # cents zero-padded to 2 digits
      format_cents(0)      ->  "$0.00"

* `split_evenly(cents: int, n: int) -> list[int]`
  Splits a total of `cents` into `n` integer-cent parts. The leftover cents
  (the remainder after the even base share) are distributed one per part to the
  earliest parts, so the parts ALWAYS sum back to the original `cents`:

      split_evenly(1000, 3)  ->  [334, 333, 333]   # sums to 1000
      split_evenly(1000, 4)  ->  [250, 250, 250, 250]
      split_evenly(100, 1)   ->  [100]

## Contract (must hold after your fix)

* Package name stays `repairmoney`; import path `repairmoney` /
  `repairmoney.public`. Keep the public names `format_cents` and `split_evenly`
  and their signatures.
* `format_cents`:
  - The minus sign for a negative amount goes IN FRONT of the `$`
    (`"-$12.34"`, never `"$-12.34"`).
  - The cents are ALWAYS two digits, zero-padded (`5` cents -> `".05"`).
  - `0` formats as `"$0.00"`.
* `split_evenly`:
  - Returns a list of exactly `n` integer cents.
  - The parts MUST sum EXACTLY to the input `cents`, for any `n >= 1`, whether
    or not `cents` divides evenly by `n` (no cent may be lost or duplicated).
  - The remainder cents are distributed one each to the earliest parts, so the
    parts differ from one another by at most one cent.

Do not change the package name or the public function names. Do not edit the
test file.
