Sky is the limit

Calculus Level 2

Solve this limit \[\displaystyle\lim \limits_{x\to \infty }\left( \frac{x + e^{3}}{x + \pi ^{3}} \right) ^{\left( \frac{x^{2}+ \pi ^{2}}{x^{2}+ e^{2}} \right) ^{\left( \frac{x^{3}+ e}{x^{3}+ \pi } \right) }} =? \] If your answer is \(\infty \), put your answer as 777

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