Let $P$ be a group of $n$ points in a plane. For a point $S(p,d),$ the parallel square to the axes

with its center at $p$ and side length $d$ is defined.

Describe an efficient algorithm for the following decision problem.

Input $-$ a positive real number $d$

Output $-$ "Yes" if there exist two points $p$ and $q$ in $P$ such that PsubeS$(p,d)S(q,d),$ and

$"$No$"$ otherwise.

The desired runtime is $O(n).$