Rebalance to target weights with whole shares and highest-cost-first tax lots

# Rebalance to target weights with whole shares and highest-cost-first tax lots `input.json` is a **synthetic** portfolio: cash, prices, target weights and the tax lots held. Write `solve.py` (Python 3 standard library only) so that `python solve.py input.json answer.json` plans the rebalancing trades and their tax effect. Nothing is traded; this only computes a plan. We re-run it on fresh inputs, so do not hard-code anything. ## Input `as_of` (ISO date), `cash`, `prices` (symbol -> price), `targets` (symbol -> weight; weights sum to 1; a held symbol missing from `targets` has target 0; a target symbol may have no lots), `lots` (each `{"id", "symbol", "shares", "cost_per_share", "acquired"}`), `short_term_rate`, `long_term_rate`. ## Rules 1. Use `decimal.Decimal` for money (convert numbers with `Decimal(str(x))`); round with ROUND_HALF_UP to cents when writing. 2. total_value = cash + sum over symbols of (shares held * price). Current value and target value (= weight * total_value) of each symbol are computed once, before any trade. 3. Work through symbols in alphabetical order. **Sells first:** if current > target, sell floor((current - target) / price) shares (never more than held). Then **buys**, again alphabetically: if target > current, buy floor(min(target - current, cash available now) / price) shares, where cash available includes all sale proceeds and decreases with each buy. No fees. 4. Lots for a sale are used highest `cost_per_share` first, ties by earlier `acquired`, then by `id`; a lot can be partly sold. 5. A lot slice's gain = (price - cost_per_share) * shares sold. It is long-term if (as_of - acquired) in days is greater than 365, otherwise short-term. 6. realized_short_term and realized_long_term are the sums of gains (can be negative). estimated_tax = max(realized_short_term, 0) * short_term_rate + max(realized_long_term, 0) * long_term_rate (no netting between the two). 7. weights_after[symbol] = shares held after trades * price / total_value (6 decimals), for every symbol that is held or targeted. ## Output `answer.json`: ``` {"total_value": ..., "trades": [{"symbol", "side": "sell"|"buy", "shares"}, ...] sorted by symbol then side, "lot_sales": [{"lot_id", "shares", "gain", "term": "short"|"long"}, ...] in the order lots are used (symbols alphabetically), "realized_short_term": ..., "realized_long_term": ..., "estimated_tax": ..., "cash_after": ..., "weights_after": {symbol: weight}} ``` Only trades with at least 1 share are listed. ## Scoring Hidden checks (partial credit = fraction passed; all must pass), money within 0.011, weights within 0.000001, shares and labels exact: `trades` (with total_value), `lot_selection`, `gains_and_tax`, `cash_and_weights` on the given input; `fresh_run_1` and `fresh_run_2_sell_out` (a symbol with target 0 must be sold out; lots held exactly 365 and 366 days appear) on fresh inputs. Each run has a 60-second limit.