Recommend a vendor on three-year total cost when the cheapest first month is the wrong choice

# Recommend a vendor on three-year total cost Inputs: `offers.json` (each vendor's setup fee, monthly base fee, tiered per-unit prices, tier type and annual escalator), `forecast.json` (monthly volume for the next 36 months) and `status-quo.json` (what we pay today per month, fixed). Rules: - Tier type "all_units": every unit in the month is charged at the price of the tier the month's total volume falls in. "incremental": each unit is charged at the price of the tier it falls in (like tax brackets). A tier's `up_to` is inclusive; null means no upper limit. - The escalator raises the base fee and every unit price by that percentage at the start of month 13 and again at the start of month 25 (compounding). - Monthly cost = base fee + unit charges, rounded half-up to the cent each month. The setup fee is paid in month 1 on top of the monthly cost. - TCO = sum of the 36 monthly costs plus the setup fee. - recommended = the vendor with the lowest TCO. cheapest_first_month = the vendor with the lowest month-1 cost excluding the setup fee. - breakeven_month = the first month in which cumulative savings of the recommended vendor against the status quo (status-quo cost minus vendor cost, including setup in month 1) reach 0 or more; null if never within 36 months. - claims: `first_month_price_misleads` = true when cheapest_first_month is not recommended; `saves_vs_status_quo` = true when the recommended vendor's TCO is below 36 x the status-quo monthly cost. Write `out/memo.json`: `{"tco": {"<vendor>": <usd>, ...}, "recommended": "<vendor>", "cheapest_first_month": "<vendor>", "breakeven_month": <int|null>, "claims": {"first_month_price_misleads": <bool>, "saves_vs_status_quo": <bool>}}`. ## 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.