What is $i^{i^{\,{}^{.\,^{.\,^{.\,^i}}}}}$ equal to?

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How to compute the infinite tower of the complex number $i$, that is$ ^{\infty}i$

Define $a_0 = i$, and $a_n = i^{a_{n-1}}$.

What is

$$\lim_{n \rightarrow \infty}{a_n} = i^{i^{\,{}^{.\,^{.\,^{.\,^i}}}}} = ~~~? $$