Find the greatest positive integer \(n\) such that there are \(n\) different real numbers \(x_1, x_2, \cdots, x_n\) which satisfy the following inequality for any \(1 \leq i \leq j \leq n\):

\[100(1+x_i x_j)^2 \leq 99(1+x_i^2)(1+x_j^2).\]

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