[0 carbon]

N or S having a solid 6+ suit:
solidN =(top4(north, clubs) + clubs(north)>5) or (top3(north, clubs)and clubs(north)>6) or
(top4(north, diamonds) + diamonds(north)>5) or (top3(north, diamonds)and diamonds(north)>6)
or(top4(north, hearts) + hearts(north)>5) or (top3(north, hearts)and hearts(north)>6)
or(top4(north, spades) + spades(north)>5) or (top3(north, spades)and spades(north)>6)
#
solidS =(top4(south, clubs) + clubs(south)>5) or (top3(south, clubs)and clubs(south)>6)
or(top4(south, diamonds) + diamonds(south)>5) or (top3(south, diamonds)and diamonds(south)>6)
or(top4(south, hearts) + hearts(south)>5) or (top3(south, hearts)and hearts(south)>6)
or(top4(south, spades) + spades(south)>5) or (top3(south, spades)and spades(south)>6)
#
bigN = shape(north, any 6xxx + any 7xxx + any 8xxx + any 9xxx+ any 00xx
+ any 01xx + any 11xx + any 02xx + any 12xx + any 03xx )
bigS = shape(south, any 6xxx + any 7xxx + any 8xxx + any 9xxx+ any 00xx
+ any 01xx + any 11xx + any 02xx + any 12xx + any 03xx )
bigE = shape(east, any 6xxx + any 7xxx + any 8xxx + any 9xxx+ any 00xx
+ any 01xx + any 11xx + any 02xx + any 12xx + any 03xx )
bigW = shape(west, any 6xxx + any 7xxx + any 8xxx + any 9xxx+ any 00xx
+ any 01xx + any 11xx + any 02xx + any 12xx + any 03xx )
#
BigE and BigW and ((SolidN and BigS) or (SolidS and BigN))