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For positive integers $A,B,C,D$ , we have

$\large \displaystyle \lim_{x \to 2} \frac {x^{x^{x^x}} - 2^{16}}{x^{x^x} - 16}$

equals to

$\frac {2^A}{1 + B ( \ln 2)^2 + C \cdot ( \ln 2) } + 2^D \cdot \ln 2$

What is the value of $A + B + C - D$?

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