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2220+2221+2222+2223+⋯ \sqrt{ \frac{2}{2^{2^0}} + \sqrt{ \frac{2}{2^{2^1}} + \sqrt{ \frac{2}{2^{2^2}} + \sqrt{ \frac{2}{2^{2^3}} +\cdots }}}} 2202+2212+2222+2232+⋯
If the value of above expression is in the form A\sqrt{A}A, find the value of AAA.
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