Given a string s, return true if s is a valid number, or false otherwise.

A valid number is defined as either a decimal number or an integer, optionally followed by an exponent.

An integer is defined as:

• An optional sign character, either '+' or '-'.

• At least $1$ digit.

A decimal number is defined as:

• An optional sign character, either '+' or '-'.

• One of the following patterns:

  • At least $1$ digit followed by a dot '.'.

  • At least $1$ digit followed by a dot '.' and at least $1$ digit.

  • A dot '.' followed by at least $1$ digit.

An exponent is defined as:

• An exponent character, either 'e' or 'E'.

• Followed by an integer.

Constraints:

• $1 \leq$ s.length $\leq 20$

• s consists of only English letters (both uppercase and lowercase), digits ($0$ through $9$), plus '+', minus '-', or dot '.'.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.