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Find the largest possible value of nnn, such that there exists nnn real numbers x1,...,xnx_1,...,x_nx1,...,xn which satisfy ∣xi−xj∣>1100(1+xixj)|x_i-x_j|> \frac{1}{100}(1+x_ix_j)∣xi−xj∣>1001(1+xixj) for all values of i≠j i \neq ji=j.
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