There is a river which flows horizontally through a country. There are $N$ cities

on the north side of the river and $M$ cities on the south side of the river. The $x$

coordinates of the $N$ cities on the north side of the river are $n_1,n_2,dots{n}_N,$ and the $x$

coordinates of the $M$ cities on the south side of the river are $s_1,s_2,dots{s}_M.$ Assume

that we can only build bridges between cities with the same number from north

and south sides. In this problem, you have to determine the maximum number of

bridges we can build without any bridges crossing with each other. Note that, both

$n_1$ through $n_N$ and $s_1$ through $s_M$ are not sorted. Design an algorithm for this

problem, that falls into any of the design methods you have studied, and illustrate

with an example sequence of length at least $8.$