For how many numbers $$𝑛$$ in the set $$\left\{1,2,3,....,37\right\}$$ can we split the $$2𝑛$$ numbers $$1, 2, … , 2𝑛$$ into $$𝑛$$ pairs $$\left\{a_{i},b_{i}\right\},1 \le i \le n$$, such that $$\prod_{i=1}^{n}(a_{i}+b_{i})$$ is a square?

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