For some positive reals satisfying $\displaystyle{ \sum_{i=1}^{24} x_i=1}$, determine the maximum possible value of $\displaystyle{ \left (\sum_{i=1}^{24}\sqrt{x_i} \right ) \left (\sum_{i=1}^{24} \frac{1}{\sqrt{1+x_i}} \right )}.$

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