Question 145
How many functions $f$ from $\{-1005, \ldots, 1005\}$ to $\{-2010, \ldots, 2010\}$ are there such that the following two conditions are satisfied?
- If $a\lt b$ then $f(a)\lt f(b)$.
- There is no $n$ in $\{-1005, \ldots, 1005\}$ such that $|f(n)|=|n|$.
- If $a\lt b$ then $f(a)\lt f(b)$.
- There is no $n$ in $\{-1005, \ldots, 1005\}$ such that $|f(n)|=|n|$.