Zulfikar, a brilliant student at the university, loves his batchmate Dishari, who excels in mathematics. One day he dares to propose marriage to Dishari. "Zulfikar, I agree to marry you on one condition. You have to answer one question perfectly", says Dishari. She asks Zulfikar to solve the following problem.

Suppose, a function is defined such that $f(1)=2022$ and $f(n)={\frac{n}{f(n–1)}}$. Let $r$ and $s$ be two such integers so that, $2^r$$×$$s!$$=$$f(1)×f(2)×f(3)...f(2022)$.

What is the value of $(r-s)+2022=$?

Zulfiqar is not so bad at problem-solving, he found out the right answer and convinced the person he wants to marry. Now tell me, what was Zulfikar's answer?