CN-TST 2016 Problem 8

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