Brackets

Let $\text{S}$ be a proper bracketing sequence if it consists only of the characters $\text{{}$, $\text{}}$, $\text{[}$, $\text{]}$, $\text{(}$, $\text{)}$ and satisfies at least one of the following three conditions:

1. $\text{S}$ is an empty string;

2. $\text{S}$ can be represented as \textbf{S} = S_1 + S_2 + S_3 + \ldots + S_n (n > 1), where S_i are non-empty proper bracketing sequences, and the "$+$" sign denotes string concatenation;

3. $\text{S}$ can be represented as \textbf{S} = \textbf{\{} + C + \textbf{\}}, \textbf{S} = \textbf{[} + C + \textbf{]}, or \textbf{S} = \textbf{(} + C + \textbf{)}, where $C$ is a proper bracketing sequence.

A string is given, consisting only of the characters $\text{{}$, $\text{}}$, $\text{[}$, $\text{]}$, $\text{(}$, $\text{)}$. Determine the minimum number of characters that need to be inserted to make it a proper bracketing sequence.