(*Question 2 FINAL FINAL*)
local
	fun min var1 var2 = if var1<var2 then var1 else var2
	fun makeMinFirst var [] = [] |
	makeMinFirst var (x::xs) = (min var x):: (makeMinFirst var xs)
in
	fun max_city  [] _ = [] |
	max_city (west::xs) north = makeMinFirst west north :: max_city xs north

end;

local
	fun transpo ([]::_) = []
	|transpo rows =
	(map hd rows) :: transpo (map tl rows);

	fun initList 0 = [] | initList size = (~1):: (initList (size-1));

	fun correctLine [] _ _ _= [] |
		correctLine (north::xs)   var numOfRepeats maxRepatNorth =

			if((var=north) andalso (numOfRepeats=1) andalso (maxRepatNorth >= 1)) then var::(initList (length xs))
			else if ((var=north) andalso (numOfRepeats >1 ) andalso (maxRepatNorth = 1)) then var::correctLine xs var (numOfRepeats-1) maxRepatNorth
			else if ((var=north) andalso numOfRepeats >1) then (~1)::correctLine xs var (numOfRepeats-1) (maxRepatNorth-1)
			else if ((north > var) andalso (maxRepatNorth = 0)) then var::(initList (length xs))
			else (~1)::correctLine xs var numOfRepeats maxRepatNorth ;


	fun maxRepeat x [] repeats = repeats |
		maxRepeat x (y::ys) repeats = if(x=y) then maxRepeat x ys (repeats+1) else maxRepeat x ys repeats ;


	fun apearannceTillIndexOfWest _ 0 _ repeatance = repeatance |
		apearannceTillIndexOfWest [] _ _ repeatance = repeatance|
		apearannceTillIndexOfWest (west::xs) lineNum var repeatance= if(var=west) then (apearannceTillIndexOfWest xs (lineNum-1) var (repeatance+1))
		else apearannceTillIndexOfWest xs (lineNum-1) var repeatance ;

	fun buildLine x west north lineNum =  correctLine north x (apearannceTillIndexOfWest west lineNum x 0) (maxRepeat x north 0) ;

	fun buildMat [] _ _  _ = [] |
		buildMat (x::xs) west north lineNum= (buildLine x west north  lineNum)::(buildMat xs west north (lineNum+1));

	fun unionLine [] [] = [] |
		unionLine (x::xs) (y::ys) = if(x=(~1)) then y::unionLine  xs ys else x::unionLine  xs ys;

	fun unionmMat [] [] = [] |
		unionmMat (x::xs) (y::ys) = (unionLine x y)::(unionmMat xs ys);

	fun buildUnionMat west north = unionmMat (buildMat west west north  1) (transpo (buildMat north north west  1));

	fun replaceZero [] = [] |
		replaceZero (x::xs) = if(x=(~1)) then (0 :: replaceZero xs)   else x::replaceZero  xs ;
	fun makeZero [] = [] |
		makeZero (x::xs) =  replaceZero x:: makeZero xs;

in
		fun min_city west north = makeZero (buildUnionMat west north)


end;