Parenthesis Matching Problem

Recall the stack$-$based algorithm $($where an opening brace or a parenthesis is pushed into the stack, and on encountering closing braces or parentheses, a pop is performed on the stack$)$ for determining whether a sequence of parentheses is well formed or not $($balanced$).$

If the given string is:

$((()\{\}\{(\}))$

Then what is the maximum number of brackets that would appear in the stack at any instant?

A bracket in this context can be any one of the following four types: $\text{'}(\text{'},\text{'}\{\text{'},\text{'}\}\text{'}$ and $\text{'})\text{'}.$

The sequence can be either well formed or ill formed.

$2$

$3$

$4$

$5$