Is it possible to split the total population in 501 polygons, each polygon with a different number of inhabitants into two North/South sub-areas with roughly the same number of inhabitants in each sub-area?

The split line, trending east-west should be along administrative boundaries of the polygons (it is called geographic median).i.e. no polygon divided/shared between sub-areas.

The picture shows the region with 501 villages (polygons) with different numbers of inhabitants each.