The occupants and the coterminous owners of lands enclosed with fences are mutually and equally bound to maintain the partition fences between their own and the next adjoining enclosures unless one of such owners chooses to let that owner’s land lie open. If one of such occupants or owners shall require a partition fence which shall exceed the requirements for a legal fence, the occupant or owner who shall require such a fence shall bear the entire cost of erecting and maintaining such a fence unless both such occupants or owners shall otherwise agree.