For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which $\{(a_1)^1 imes (a_2)^2 imes \ldots imes (a_{20})^{20}\} $

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For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which $\{(a_1)^1 imes (a_2)^2 imes \ldots imes (a_{20})^{20}\} $ < $ \{a_{21} imes a_{22} imes \ldots imes a_{(20+m)}\}$ is.

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