Not so trivial problem

In XML, some characters have strictly predefined special meanings. For example, the character "$\text{<}$" is used to begin start-tags and end-tags. XML provides mechanisms to include text with such special characters. The text is transformed as follows: each special character is replaced with a predefined entity "$\text{\&entity\_name;}$". There are five predefined entities: $\text{\&lt;}$ represents "$\text{<}$" (less), $\text{\&gt;}$ represents "$\text{>}$" (greater), $\text{\&amp;}$ represents "$\text{\&}$" (ampersand), $\text{\&apos;}$ represents "$\text{’}$" (single quote), and $\text{\&quot;}$ represents "$\text{"}$" (double quote). Let us call this transformation the function $\text{XMLEncode(S)}$, where $\text{S}$ is the input string. $\text{XMLEncode()}$ can be applied to the input several times.

For example, let $\text{S}$ be "2<3<4". Then $\text{XMLEncode(S)}$ will be "2&lt;3&lt;4", and $\text{XMLEncode(XMLEncode(S))}$ will be "2&amp;lt;3&amp;lt;4".

Write a program that determines the maximum number of XMLEncode-function calls based on the given resulting string $\text{R}$.