What is the correct order of these expressions, from smallest to largest?

\(\large 3^{3^4}\)

\(\large 3^{4^3}\)

\(\large 3^{4^4}\)

\(\large 4^{3^3}\)

\(\large 4^{3^4}\)

Give your answer as the number of the smallest, followed by second smallest, and so on until the largest.

e.g. If you think they are already in order, then your answer should be 12345.

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