There is a stair with $n$ stages, and on each stage there is a coupon to your favorite restau$-$

rant. Each coupon has an associated value which may be different. You can climb up $1,2,$

or $3$ stages in a step. Since you are in a hurry, you need to reach the top of the stair in at

most $L$ steps, where $Ln.$ When you visit a particular stage, you can collect the coupon

on that stage. Find a way to climb the stair within $L$ steps so that you can collect coupons

with maximum total value. Your algorithm should run in $O(n^2)$ time.