Mr$.$ Minion has arrived in an $2$D world, where Mr$.$ Minion is walking from left to right. There

are light sources that are above the line at different heights, and the ith light illuminates a

triangular area where the pick of the triangle is the light source and the base $[$X$[$i$],$ Xr$[$i$]],$

where X$[$i$]<$ Xr$[$i$],$ is the line segment it can illuminate. Mr$.$ Minion is given the arrays

X$$ and Xr$.$ In addition, there is a dictionary L that given X$[$i$],$ returns Xr$[$i$]$ and vice

versa. Fortunately, all these numbers are distinct.

Our goal is to nd a point p in the line that is illuminated by the maximum number of lights.

Write an algorithm to help Mr$.$ Minion by nding the point p$.$ Write an algorithm, an

argument of why the algorithm is correct, and analyze the running time.

HARD CONSTRAINTS: Your algorithm must be described as a sequence of steps.

Pseudocodes are not allowed. Mr$.$ Minion does not like to use unnecessary computer memory.

So your algorithm can use at most O$(1)$ additional memory. This means you cannot create

a new array or binary$-$search$-$tree like data structures. If you want to sort, you can use

HeapSort which uses O$(1)$ additional memory and takes O$($n log n$)$ time.