[Graphs generated by this script: setBorder(60,30,60,30);initPicture(0,10,0,5); fontsize=14;fontstyle='none';marker=null;line([0,0],[0,5]);line([0,0],[5,0]);line([0,5],[5,0]);line([0,5],[5,5]);line([5,0],[5,5]);line([5,0],[10,0]);line([5,5],[10,0]);line([5,5],[10,5]);line([10,0],[10,5]);fontbackground='white';fontfill='blue';text([0,0],'A','belowleft');dot([0,0]);fontfill='red';text([0,2.5],'8');fontfill='red';text([2.5,0],'19');fontfill='blue';text([0,5],'B','aboveleft');dot([0,5]);fontfill='red';text([2.5,2.5],'5');fontfill='red';text([2.5,5],'20');fontfill='blue';text([5,0],'C','belowleft');dot([5,0]);fontfill='red';text([5,2.5],'14');fontfill='red';text([7.5,0],'18');fontfill='blue';text([5,5],'D','aboveleft');dot([5,5]);fontfill='red';text([7.5,2.5],'1');fontfill='red';text([7.5,5],'10');fontfill='blue';text([10,0],'E','belowright');dot([10,0]);fontfill='red';text([10,2.5],'7');fontfill='blue';text([10,5],'F','aboveright');dot([10,5]);]

Eulerize the graph above in the most efficient way possible. The weights on the edges represent the cost to duplicate that edge. Which path of vertices did you duplicate to eulerize the graph? If two paths worth equally well, select both.