Don't mess up with the e`s!

Calculus Level 4

Find the value of the following limit: \[\lim\limits_{x\to\infty} e^{\displaystyle e^{\displaystyle e^{\displaystyle \left(x + e^{\displaystyle -\left(a + x + e^{x} + e^{\displaystyle \displaystyle e^{\displaystyle x}}\right)}\right)}}} - e^{e^{e^{x}}}.\]

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