Let $n$ be a positive integer. In the $\mathit{philand}$ language, words are all finite sequences formed by the letters "$P$", "$H$" and "$I$". Philipe, who speaks only the $\mathit{philand}$ language, writes the word $PHIPHI\ldots PHI$ on a piece of paper, where $PHI$ is repeated $n$ times. He can do the following operations: • Erase two identical letters and write in their place two different letters from the original and from each other; (Ex: $PP\rightarrow HI$) • Erase two distinct letters and rewrite them changing the order in which they appear; (Ex: $PI\rightarrow IP$) • Erase two distinct letters and write the letter distinct from the two he erased. (Ex: $PH\rightarrow I$) Find the largest integer $C$ such that any Philandese word of up to $C$ letters can be written by Philip through the above operations. Note: Operations are taken on adjacent letters.