Consider a list where every element is a nested list of length 2. The first element of each nested list is either a 0 or a 1. The second element of each nested list is some integer. As an example:

'((0 1) (1 2) (1 3) (0 4) (0 3))

For the purposes of this question, lets call the first element of each nested list thekey,and the second element of the nested lists thevalue. In racket, implement a function, count-by-cat, that takes such a list as input and yields a two element list where

• the first element is the sum of the values of all nested lists with 0 as the key, and
• the second element is the sum of the values of all nested lists with 1 as the key

It may be helpful to create helper functions. Also do not forget about map and filter.