Find the largest possible positive integer $n$, such that there exists $n$ distinct positive real numbers $x_1, x_2, \cdots, x_n $ satisfying the following inequality:
for any $ 1 \le i, j \le n$
$ (3x_i - x_j) (x_i - 3x_j) \ge (1 - x_ix_j) ^2$
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