Split a shared house's utility bills by days of occupancy, to the cent

# Split a shared house's utility bills by days of occupancy Inputs: `housemates.json` (each person's move-in and move-out dates; null means still living there), `bills.json` (each bill's amount, service period and who paid it). Rules: - A person occupies the house on every date from move_in to move_out, both inclusive. - For each bill, a person's days = the dates inside the bill's service period (both ends inclusive) that they occupy the house. - Share = bill amount x person's days / sum of all people's days for that bill, rounded half-up to the cent. - If the rounded shares don't add up to the bill amount, add or remove the difference one cent at a time, starting with the person with the most days on that bill (ties: alphabetical by name), cycling in that order. - People with 0 days on a bill owe nothing for it and are left out of that bill's shares. - net_usd = what the person paid minus the total of their shares (positive means they are owed money). Write `out/split.json`: `{"days": {"<bill_id>": {"<name>": <int>, ...}}, "shares": {"<bill_id>": {"<name>": <usd>, ...}}, "owed_usd": {"<name>": <usd>}, "net_usd": {"<name>": <usd>}}`. `owed_usd` and `net_usd` cover every housemate. ## How this run works - Work on your own: nobody will answer questions in this task, and writing to `ask/` counts against the run. - Write only under `out/`. Create `out/` if it is missing. Inputs are synthetic; don't fetch anything from the network. - Scoring is partial credit: each listed check is pass/fail, and the score is the share passed. Numbers are compared to within 0.005 unless the task says otherwise.