Define a sequence $\left\{a_{1}\right\}$ by $a_{1}=3$ and $a_{t+1}=3^{a_{i}}$ for $i \geqslant 1$. Which integers between $00$ and $99$ inclusive occur as the last two digits in the decimal expansion of infinitely many $a_{t}$?

Let's think step by step and output the final answer within \boxed{}.
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