In this challenge, you have to create a class to deal with Big Integers. It will use just a single static method called max, used to find the Big Integer with the highest value among the given data.

You'll have to also manage a series of exceptions, establishing if the given input is valid:

• A given Big Integer will always be valid.
• A given integer lower or equal than the JS MAX_SAFE_INTEGER will be converted into a Big Integer (before calculating the max value).
• A given string containing an integer lower or equal than the JS MAX_SAFE_INTEGER will be converted into a Big Integer (before calculating the max value).
• If no input is given, the function must return null.
• If none of the previous conditions are satisfied, the given input is not valid.

The max method applied to the input has to return:

• If the input is valid, the highest given value as a Big Integer.
• null if no input is given.
• A string "Big Error" if the input contains invalid data.

Examples

Big.max(1n, 10n, 5n) ➞ 10n

Big.max("10", 5n, 1) ➞ 10n

Big.max() ➞ null

Big.max(2 ** 53 - 1) ➞ 9007199254740991n

Big.max(2 ** 53) ➞ "Big Error"

Big.max("10" / 3) ➞ "Big Error"

Big.max("10" / 2) ➞ 5n

Big.max(10 - 12, 10 - 10, 10 - 11) ➞ 0n

Big.max(0n) ➞ 0n

Big.max("") ➞ "Big Error"

Note

• Reading the specific link about BigInt behaviors (look at the Resources tab) is highly recommended.
• Inputs and values will be given in various ways trying to represent a real scenario. For coding easiness, tests are grouped separately.