How many different ordered pairs of positive integers are there each of whose squares sum to 9797 ? For example, for this ordered pair of positive integers, $$\(\$(10,11) \$\)$$, its squares sum to $$\(10^{2}+11^{2}=221\)$$. [Hint: The identity $$\(\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)=(a c+b d)^{2}+(a d-b c)^{2}\)$$ can help.]

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