12. Let $a_{1}, a_{2}, \cdots, a_{m n+1}$ be $m n+1$ positive integers and $a_{1}<a_{2}<\cdots<a_{m n+1}$, prove: the sequence $a_{1}, a_{2}, \cdots, a_{m n+1}$ must contain a subsequence of $m+1$ terms, in which no term divides another; or it contains a subsequence of $n+1$ terms, in which each term from the second onward is divisible by the preceding term.