USAMO 1994 Problem 2

The sequence $a_{1}, a_{2}, \ldots, a_{99}$ has $a_{1}=a_{3}=a_{5}=\ldots=a_{97}=1, a_{2}=a_{4}=a_{6}=\ldots=a_{98}=2$, and $a_{99}=3$. We interpret subscripts greater than 99 by subtracting 99 , so that $\mathbf{a}_{100}$ means $\mathrm{a}_{1}$ etc. An allowed move is to change the value of any one of the $a_{n}$ to another member of $\{1,2,3\}$ different from its two neighbors, $a_{n-1}$ and $a_{n+1}$. Is there a sequence of allowed moves which results in $\mathrm{a}_{\mathrm{m}}=\mathrm{a}_{\mathrm{m}+2}=\ldots=\mathrm{a}_{\mathrm{m}+96}=1, \mathrm{a}_{\mathrm{m}+1}=\mathrm{a}_{\mathrm{m}+3}=\ldots=\mathrm{a}_{\mathrm{m}+95}=2$, $\mathrm{a}_{\mathrm{m}+97}=3, \mathrm{a}_{\mathrm{n}+98}=2$ for some $\mathrm{m}$ ? [So if $\mathrm{m}=1$, we have just interchanged the values of $\mathrm{a}_{98}$ and $\mathrm{a}_{99}$.]