Maximize Amount After Two Days of Conversions

You are given a string initialCurrency, and you start with 1.0 of initialCurrency.

You are also given four arrays with currency pairs (strings) and rates (real numbers):

- `pairs1[i] = [startCurrency_i, targetCurrency_i]` denotes that you can convert from `startCurrency_i` to `targetCurrency_i` at a rate of `rates1[i]` on **day 1**.

- `pairs2[i] = [startCurrency_i, targetCurrency_i]` denotes that you can convert from `startCurrency_i` to `targetCurrency_i` at a rate of `rates2[i]` on **day 2**.

- Also, each `targetCurrency` can be converted back to its corresponding `startCurrency` at a rate of `1 / rate`.

You can perform any number of conversions, including zero, using rates1 on day 1, followed by any number of additional conversions, including zero, using rates2 on day 2.

Return the maximum amount of initialCurrency you can have after performing any number of conversions on both days in order.

**Note: **Conversion rates are valid, and there will be no contradictions in the rates for either day. The rates for the days are independent of each other.

Example 1:

Input: initialCurrency = "EUR", pairs1 = [["EUR","USD"],["USD","JPY"]], rates1 = [2.0,3.0], pairs2 = [["JPY","USD"],["USD","CHF"],["CHF","EUR"]], rates2 = [4.0,5.0,6.0]

Output: 720.00000

Explanation:

To get the maximum amount of EUR, starting with 1.0 EUR:

- On Day 1:

	Convert **EUR **to **USD** to get 2.0 **USD**.

	- Convert **USD** to **JPY** to get 6.0 **JPY**.




- On Day 2:

	Convert **JPY** to **USD** to get 24.0 **USD**.

	- Convert **USD** to **CHF** to get 120.0 **CHF**.

	- Finally, convert **CHF** to **EUR** to get 720.0 **EUR**.

Example 2:

Input: initialCurrency = "NGN", pairs1 = [["NGN","EUR"]], rates1 = [9.0], pairs2 = [["NGN","EUR"]], rates2 = [6.0]

Output: 1.50000

Explanation:

Converting NGN to EUR on day 1 and EUR to NGN using the inverse rate on day 2 gives the maximum amount.

Example 3:

Input: initialCurrency = "USD", pairs1 = [["USD","EUR"]], rates1 = [1.0], pairs2 = [["EUR","JPY"]], rates2 = [10.0]

Output: 1.00000

Explanation:

In this example, there is no need to make any conversions on either day.

Constraints:

- `1 

- `pairs2[i] == [startCurrency_i, targetCurrency_i]`

- `1 <= startCurrency_i.length, targetCurrency_i.length <= 3`

- `startCurrency_i` and `targetCurrency_i` consist only of uppercase English letters.

- `rates1.length == n`

- `rates2.length == m`

- `1.0 <= rates1[i], rates2[i] <= 10.0`

- The input is generated such that there are no contradictions or cycles in the conversion graphs for either day.

- The input is generated such that the output is **at most** `5 * 10^10`.