Required minimum distributions from a supplied divisor table, with and without delaying the first one

# Required minimum distributions from a supplied divisor table, with and without delaying the first one `input.json` describes retirement accounts, yearly growth, a **fictional** life-expectancy divisor table and fictional tax brackets. Write `solve.py` (Python 3 standard library only) so that `python solve.py input.json answer.json` builds the year-by-year distribution schedule for two choices and compares the tax. Use only the rules below and the input. We re-run it on fresh inputs, so do not hard-code anything. ## Input `birth_year`, `start_age` (first age with a required distribution), `first_year` (first calendar year to simulate), `accounts` (each with `balance` = balance on Dec 31 of the year before `first_year`), `growth` (one yearly return per simulated year; the number of years simulated is its length), `other_income`, `brackets` (`[lower_bound, rate]` list as in a progressive tax), `divisor_table` (age as string -> divisor). ## Rules 1. All accounts are pooled: the balance is the sum of the account balances. 2. For calendar year Y (index j, Y = first_year + j) the age is Y - birth_year. If age >= start_age, the required amount is rmd = (balance on Dec 31 of the previous year) / divisor(age), else 0. For ages above the table's largest age use the largest age's divisor. 3. Withdrawals happen at the start of the year, then the balance grows: end balance = (previous balance - withdrawal) * (1 + growth[j]). 4. **no_delay**: withdrawal = min(balance, rmd) every year. 5. **delay_first**: the first year with rmd > 0 withdraws 0 and that rmd is carried to the next year, which withdraws min(balance, its own rmd + the carried amount). The next year's own rmd still uses its previous Dec 31 balance (which was not reduced by the carried amount). After that, same as no_delay. 6. Tax for a year = tax(other_income + withdrawal) - tax(other_income), using the progressive brackets: rate j applies to income above bound j up to bound j+1. 7. `lower_tax` = "no_delay" or "delay_first" (smaller total tax), or "same" if the totals differ by less than 0.005. 8. Round money to 2 decimals only when writing. ## Output `answer.json`: `{"no_delay": S, "delay_first": S, "lower_tax": ...}` where S = `{"rows": [{"year", "age", "rmd", "withdrawal", "tax", "end_balance"}, ... one per simulated year], "total_withdrawn", "total_tax", "final_balance"}`. ## Scoring Hidden checks (partial credit = fraction passed; all must pass), money within 0.011, years/ages/labels exact: `rmd_amounts_no_delay`, `totals_no_delay`, `delay_first_schedule`, `delay_first_totals_and_choice` on the given input; `fresh_run_1`, `fresh_run_2`: the whole answer on fresh inputs. Each run has a 60-second limit.