# Big, Bigger, Biggest!

Calculus Level 5

Let $$x=10^{100}, y=10^{x}, z=10^{y}$$ and let

$$a_{1}=x!, a_{2}=x^{y}, a_{3}=y^{x}, a_{4}=z^{x}, a_{5}=e^{xyz}, a_{6}=z^{\frac{1}{y}}, a_{7}= y^{\frac{z}{x}}$$.

You might want to use the Stirling's approximation of $$n! \approx \sqrt{2\pi}n^{(n+\frac{1}{2})}e^{-n}$$ for large $$n$$.

Arrange $$a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}$$ in increasing order and catenate the index number of your sequence as the answer.

For example, if you think $$a_{1}<a_{2}<a_{3}<a_{4}<a_{5}<a_{6}<a_{7}$$, then input $$1234567$$ as the answer.

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