Consider a list where every element is a pair$/2$ structure. The first element of each pair is either a $0$ or a $1.$ We will call this the key. The second element of each pair is some integer. We will call this the value. An example input in Prolog is written below. $[$pair$(0,1),$ pair$(1,2),$ pair$(1,3),$ pair$(0,4),$ pair$(0,3)]$ Implement count$\_$by$\_$cat$/3$ in Prolog as a tail$-$recursive predicate. The first parameter is a nested list as above. The second parameter is the sum of the values associated with $0$ keys. T he third parameter is the sum of the values associated $1$ keys. If there is no pair corresponding to a particular key, then the sum is zero. You will need helper predicates.