tough one , ain't it

Algebra Level 5

Find the value of

12443+21503283+244212443+21503283+2442. \sqrt{12443+2\sqrt{1503283+2442\sqrt{12443+2\sqrt{1503283+2442\sqrt{\cdots}}}}}.

Details and assumptions: Knowing that 12443 is the sum of 3 squares might be useful.

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