Question 14
Let $S=\{1,2,\dots,2012\}$. How many functions $f:S\to S$ satisfy both conditions?
(1) $f$ is a bijection.
(2) For every $1\le a\le2012$, $f(a)+f^{-1}(a)=2013$, where $f^{-1}$ is the inverse of $f$.
(1) $f$ is a bijection.
(2) For every $1\le a\le2012$, $f(a)+f^{-1}(a)=2013$, where $f^{-1}$ is the inverse of $f$.