Work out a family's health-plan cost sharing across embedded deductibles, copays, adjustments and out-of-pocket caps

# Work out a family's health-plan cost sharing across embedded deductibles, copays, adjustments and out-of-pocket caps Inputs: `plan.json`, `members.json` and `claims.csv` (claim_id, member, service_date, received_date, service_type, billed_amount, allowed_amount, status, adjusts). Everything is synthetic and in dollars. `plan.json` and these rules are the record; where `benefits-desk-note.txt` disagrees, the rules win. Rules: - Process claims in service_date order, ties by the number in claim_id; file order and received_date don't matter. Only allowed_amount is shared; billed_amount is ignored. - A claim with status denied costs the member nothing and counts toward nothing. A claim with status adjustment replaces the claim named in adjusts: the original is processed at its own place in the order but with the adjustment's allowed_amount, and the adjustment row is not processed on its own. - Accumulators reset at plan_year_start: claims before it belong to the prior plan year, which has its own deductibles and caps. - preventive costs the member 0. A service_type listed in copays costs the member the copay (or the allowed amount if lower); copays never count toward a deductible but do count toward the out-of-pocket caps. - For any other claim the member first pays toward the deductible, up to the smaller of what is left of their individual deductible and of the family deductible (embedded: a member's deductible is done once either is used up). Then the member pays coinsurance_pct of the rest of the allowed amount, rounded half-up to the cent per claim. - A member's share on any claim is capped so that neither their individual out-of-pocket total nor the family's goes above its oop_max; deductible and coinsurance both count toward the caps. When a cap cuts a share, the part that counts toward the deductible is the smaller of the deductible part and the capped share. The plan pays allowed_amount minus the member's share. - Write `out/costshare.json`: `{"claims": {"<claim_id>": {"member": <dollars>, "plan": <dollars>}, ...} (every processed claim, not adjustment rows; denied claims as 0 and 0), "members": {"<member>": {"deductible_paid": <dollars>, "oop_paid": <dollars>}, ...} (current plan year only), "family_deductible_met_on": "<service_date of the claim that used up the family deductible in the current plan year>" or null}`. ## 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.