Define a sequence $\{a_{i}\}$ by $a_{1}=3$ and $a_{i+1}=3^{a_{i}}$ for $i \geq 1.$ Which integers between $0$ and $99$ inclusive occur as the last two digits in the decimal expansion of infinitely many $a_{i}$?

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