Correcting Parenthesization

Given a string consisting of parentheses, your task is to obtain a well-formed string by changing the minimum number of characters. Deleting or inserting characters is not allowed.

There are three types of parentheses: round $()$, square $[]$, and curly $\{\}$. Each pair consists of an opening parenthesis ($($, $[$, $\{$) and a closing parenthesis ($)$, $]$, $\}$).

A well-formed string is defined by the following rules:

• The empty string is well-formed.

• If $s$ is a well-formed string, then $(s)$, $[s]$, and $\{s\}$ are also well-formed.

• If $s$ and $t$ are well-formed strings, then their concatenation $st$ is also well-formed.

As examples, the strings "([{}])", "", and "(){}[]" are well-formed, while "([}])", "([)]", and "{" are not. For the given string, find the minimum number of changes required to obtain a well-formed string.