$(22$ pts$)$ Your little sibling needs your help with checking his$/$her solutions of a ton of math expressions, which are made up of single digits $(0,1,$dots,$9),$ arithmetic operators $("+","--","*","/"($integer division$),$ and $"\%"($mod$)),$ and brackets $("({)}^{\text{'}\text{'}},[]",$ and $"\{\}"),$ but you'd like to save more time to have fun. For your cute and helpless sibling's sake, please use what you learned to help him$/$her out!

Note: for all the questions below, you may leverage the code given in class or STL containers.

Your code should expect and produce C$-$style string expressions $($e$.$g$.,$ char $[])$ that terminate with ${10}^{\text{'}}.$

a$)(7$ pts$)$ First, you may want to make sure that the handwritten expressions that your sibling copied from the board in class are valid $($you don't want to get confused by his$/$her silly writing mistakes$).$

$***$ An expression is valid if:

All the brackets are balanced. That is$,$ each left$/$right bracket can be paired with a right$/$left one in the same style. For instance, a left parenthesis $"("$ can be paired with a right one $")",$ and a right square bracket $"]"$ can find a corresponding left one $"[",$ and so on$.$ There is no single bracket left alone. The appearance order of different types of brackets does not matter, that is$,$ say, parentheses can include square brackets $("[[])")$ or be included by square brackets $("($:$[(){]}^{\text{'}\text{'}}\},$ and so on$.$

Within each pair of brackets, there is only one operator for two operands $($e$.$g$.,"(3+5)"),$ but each operand may also be an expression in a pair of parentheses $($e$.$g$.,"[1+(2**3){]}^{\text{'}\text{'}}.$

Let's write a function checkValid to do that. It will return a Boolean value "True" if the expression is valid, or "False" otherwise.

Function signature:

bool checkValid$($char exp$[]$

Example $1$:

$$ Input: exp$=\{1+[(2+3)**(4**5)]\}$

$$ Output: True