Question 145
Numbers $1$, $2$, ..., $n$ are placed in a row in a certain order. We are allowed to do the following operation: take any two pairs of consecutive elements, that have no common elements, and exchange their positions. Is it possible to get a monotone sequence of elements after a finite number of steps if:
a) $n = 2009$;
b) $n = 2010$?
a) $n = 2009$;
b) $n = 2010$?