## Maximum Currency Conversion Rate You are given `N` currency exchange rate pairs. Each pair is a triple `(from_currency, to_currency, rate)`, meaning that 1 unit of `from_currency` can be exchanged for `rate` units of `to_currency`. All rates are strictly positive real numbers. Given a `source` currency and a `target` currency, find the **best (maximum) overall conversion rate** achievable by chaining one or more exchanges from `source` to `target`. Chaining exchanges multiplies their rates: converting through the sequence `A -> B -> C` yields an overall rate of `rate(A->B) * rate(B->C)`. Rules and assumptions: - Exchanges are **directional**: a pair `(A, B, r)` lets you convert `A` to `B` at rate `r`, but does **not** by itself allow converting `B` to `A`. A reverse rate is only available if it appears as its own pair in the input. - A conversion path must **not visit the same currency more than once** (simple paths only), so a path's length is bounded by the number of distinct currencies. - If the same directed pair `(from_currency, to_currency)` appears multiple times, use the one with the highest rate. - If `source == target`, the answer is `1.0`. - If `target` is unreachable from `source`, return `-1.0`. ### Input - `pairs`: a list of `N` triples `[from_currency, to_currency, rate]`, where currencies are strings (e.g., `"USD"`, `"EUR"`) and `rate` is a positive float. - `source`: the starting currency (string). - `target`: the desired currency (string). ### Output Return a single float: the maximum achievable conversion rate from `source` to `target`, or `-1.0` if no conversion path exists. Answers within `1e-6` relative or absolute tolerance are accepted. ### Example ``` pairs = [["USD", "EUR", 0.9], ["EUR", "GBP", 0.85], ["USD", "GBP", 0.7], ["GBP", "JPY", 190.0]] source = "USD" target = "JPY" ``` Output: ``` 145.35 ``` Explanation: the path `USD -> EUR -> GBP -> JPY` gives `0.9 * 0.85 * 190.0 = 145.35`, which beats the direct-ish alternative `USD -> GBP -> JPY = 0.7 * 190.0 = 133.0`. ### Constraints - `1 <= N <= 200` - Number of distinct currencies `<= 14` - Currency codes are non-empty strings of up to 10 uppercase letters - `0 < rate <= 10.0` - The final answer is guaranteed to fit in a standard 64-bit floating-point value (it will not exceed `1e9`) - `source` and `target` are guaranteed to appear in at least one pair