$P, Q, R, S, T$, and $U$ are seated around a circular table $R$ is seated two places to the right of $Q. \: P$ is seated three places to the left of $R. \: S$ is seated opposite $U.$ If $P$ and $U$ now switch seats, which of the following must necessarily be true?

$P$ is immediately to the right of $R$

$T$ is immediately to the left of $P$

$T$ is immediately to the left of $P$ or $P$ is immediately to the right of $Q$

$U$ is immediately to the right of $R$ or $P$ is immediately to the left of $T$