You are in charge of distributing chairs to children at a recreational event. You have a stock

of $n$ chairs available for $n$ children. Each child and each chair has a size, which is an integer

between $1$ and $k,$ inclusive. Ideally, a size i chair should be used by a size i child. However,

any child can use any available chair, although a bit uncomfortably.

You are given two size$-n$ arrays: chair$[]$ and child$[].$ chair$[$i$]$ is the size of the $i^{th}$ chair, and

child$[i$ is the size of the $i^{th}$ child. The discomfort a child experiences is the absolute value of

the difference between the size of the child and the size of the chair that is paired with the

child. The total discomfort is the sum of the discomfort experienced by each of the children.

Provide an efficient algorithm to minimize the total discomfort between all children and their

paired chairs. Prove that your algorithm is correct.