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Algebra Level 3

2+2222+222 \Large \sqrt{2+ \frac{2}{ \sqrt{2- \frac{2}{ \sqrt{2+ \frac{2}{ \sqrt{2- \frac{2}{ \sqrt{ \ldots }}}}}}}}}

If the value of the infinitely nested expression above equals xx, find the value of 1000x1000x.

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