We have $12 \times 23 = 276$. If we reverse the numbers, we get $672 = 32 \times 21$, which is still a true statement.

Does there exist non-palindromes $\overline{abc}$ and $\overline{def}$ such that

$\overline{abc} \times \overline{def} = \overline{ghijk}$ and $\overline{kjihg} = \overline{fed} \times \overline{cba}$?

Note: The letters do not represent distinct digits.

The first digit is non-zero.

Non-palindromes mean that $a \neq c$ and $d \neq f$.

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