Prolog, how should I construct a list of list to a single list?

Question

I want to construct a list of list to interleave each other to a single list like: coon([[1,4],[2,5],[3,6]], X) should return X=1,2,3,4,5,6. and there is a condition that each sublist should only have the same length, otherwise, it should fail such as [[q,r,y],[a,e],[c,g,t],X] shouid fail, and coon([A,B,C],[q,w,e,r,t,y]) should only return one solution, that is A=[q,r],B=[w,t],C=[e,y]. my recent approach is.

  conns([],[]).
  conns([[Head|Tail]|X],[Head|Y]):-
    append(X,[Tail],X2),
    conns(X2,Y).                                                

conns([[]|T],A):-
    conns(T,A).

It gives me multiple solutions when I try coon([A,B,C],[q,w,e,r,t,y]). I have been trying hours to figure it out but all failed. How should I return the single list to each sub-lists that contain the same length? Thank you so much!

Answer 1

:- use_module(library(clpfd),[transpose/2]).

connsx(Xss, Xs) :-
   transpose(Xss, XssT),
   append(XssT, Xs).