append([], X, [X]).
append([H|L], X, [H | L1]) :- append(L, X, L1).
 
reverse([], []).
reverse([H|L], R) :- reverse(L, L1), append(L1, H, R).

insertitem(X, [], [X]).
insertitem(X, [H|L], [X, H | L]) :- X =< H.
insertitem(X, [H|L], [H |R]) :- X>H, insertitem(X, L, R).

distance1([],[], 0).
distance1([H1|L1], [H2|L2], X):- 
  Y is (H1-H2)*(H1-H2), 
  distance1(L1, L2, Z), 
  X is Y+Z.
distance(V1, V2, D):- distance1(V1, V2, D1), D is sqrt(D1).