Let $\square_2=\{(x,y): 0\leq x, y\leq1\}$ be the unit square in $\mathbb{R}^2$. Take $n>1$ points $P_1, \dots, P_n\in\square_2$.

Denote the distances $d_j=\min\{\Vert P_k-P_j\Vert: k\neq j\}$, for $j=1,\dots, n$.

QUESTION. Is it true that $d_1^2+\cdots+d_n^2\leq 4$? The bound is tight when $n=2$.