Is It a Number Literal

Hard

You are given a string text. Decide whether it is a well-formed number. The rules are: - **Digits**: one or more of the digits 0–9. - **Sign**: an optional + or -. - **Mantissa**: a sign followed by one of: digits (42); digits and a dot (42.); digits, a dot and digits (4.2); a dot and digits (.42). - **Exponent**: the letter e or E, then a sign and digits (e7, E-3). - **Number**: a mantissa, optionally followed by an exponent. For example, "0", "007", "-3.", "+.25", "6e5" and "1.5E-2" are numbers, while "e9", "9e", "1-2", "++1", "1.2.3" and "x1" are not. Return True if text is a number and False otherwise.

Example 1

text='-.5E+12' → True

A sign, a fraction with no integer part (.5) and the exponent E+12: everything follows the rules.

Example 2

text='7e1.5' → False

The exponent after e must be an integer, and 1.5 is not.

Example 3

text='+.' → False

A dot without a single digit is not a number.

Constraints

1 ≤ len(text) ≤ 100
text consists of English letters (upper and lower case), digits, +, - and .

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Topics

String

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Input

text='-.5E+12'

Expected

True

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