Find the smallest positive number $\lambda$, such that for any 12 points on the plane $P_1, P_2, \ldots, P_{12}$ (points can overlap), if the distance between any two of them does not exceed 1, then the inequality \( \sum_{1 \le i < j \le 12} |P_iP_j|^2 \le \lambda \) holds.

Let's think step by step and output the final answer within \boxed{}.
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