there is not an initial position it is a circle , after position D you return again to position A and so on.
I do work twice , first change it from position A to position B , moving it horizontally , without horizontal resistance . also another horizontal motion from position C to D .
second changing it from position B to C , doing little work, because the magnetic force will be less, the critical point is , the magnetic force at position C will be less than it in position D , right? if so then the input work is much less than the output work.
for the output work it will be in changing from position D to A again , so the output work is much more the input work.
I mean I lifted it with small force to counter small magnetic force from stage B to stage C, and it came back with huge magnetic force from stage D to stage A again, the horizontal work can be neglected .