diff --git a/11.hs b/11.hs
index 3a33312..2419a49 100644
--- a/11.hs
+++ b/11.hs
@@ -2,9 +2,10 @@ import Data.List.Split (splitOn)
 import Data.Foldable (fold)
 
 data Coordinates = Coordinates Int Int Int deriving Show
+instance Semigroup Coordinates where
+    Coordinates x y z <> Coordinates x' y' z' = Coordinates (x + x') (y + y') (z + z')
 instance Monoid Coordinates where
     mempty = Coordinates 0 0 0
-    Coordinates x y z `mappend` Coordinates x' y' z' = Coordinates (x + x') (y + y') (z + z')
 
 getCoordinates :: String -> Coordinates
 getCoordinates direction = case direction of
diff --git a/20.hs b/20.hs
index 42befad..dbd490a 100644
--- a/20.hs
+++ b/20.hs
@@ -2,30 +2,41 @@ import Data.List.Split (splitOn)
 import Data.List (elemIndex, sortOn, groupBy)
 import Data.Monoid ((<>))
 import Data.Function (on)
-import Data.Vector.Class
-import Data.Vector.V3
 
-data Particle = Particle {
-    position     :: Vector3,
-    velocity     :: Vector3,
-    acceleration :: Vector3
-}
+data Vector3 s = Vector3 s s s deriving Eq
 
-instance Ord Vector3 where
+instance Functor Vector3 where
+    fmap f (Vector3 x y z) = Vector3 (f x) (f y) (f z)
+
+instance Num s => Semigroup (Vector3 s) where
+    Vector3 x1 y1 z1 <> Vector3 x2 y2 z2 = Vector3 (x1 + x2) (y1 + y2) (z1 + z2)
+
+instance Ord s => Ord (Vector3 s) where
     Vector3 x1 y1 z1 `compare` Vector3 x2 y2 z2 = compare x1 x2 <> compare y1 y2 <> compare z1 z2
 
-norm :: Vector3 -> Double
+type Property = Vector3 Double
+
+data Particle = Particle {
+    position     :: Property,
+    velocity     :: Property,
+    acceleration :: Property
+}
+
+(*|) :: Double -> Property -> Property
+(*|) s = fmap (s *)
+
+norm :: Property -> Double
 norm (Vector3 x y z) = abs x + abs y + abs z
 
 updateParticle :: Double -> Particle -> Particle
 updateParticle t (Particle p v a) =
-    Particle (p + t *| v + (t * (t + 1) / 2) *| a) (v + t *| a) a
+    Particle (p <> t *| v <> (t * (t + 1) / 2) *| a) (v <> t *| a) a
 
 stepParticles :: [Particle] -> [Particle]
 stepParticles particles =
     concat . filter ((== 1) . length) . groupBy ((==) `on` position) . sortOn position . map (updateParticle 1) $ particles
 
-parseProperty :: String -> Vector3
+parseProperty :: String -> Property
 parseProperty str = 
     let x : y : z : [] = map read . splitOn "," . drop 3 . init $ str
     in Vector3 x y z
diff --git a/README.md b/README.md
index 6ef98b4..889f906 100644
--- a/README.md
+++ b/README.md
@@ -40,3 +40,14 @@ These are the runtimes of only one trial but the variances are fairly small and
 Problems that could use some work: 05, 22, 24, 25, 14, 15, 21, 17
 
 Problems that are good enough with optimizations: 13
+
+## Dependencies
+
+I haven't gotten Stack set up with this project (I'll do it next year!), so here's a list of the extra dependencies needed by various files.
+
+* hashmap
+* matrix
+* split
+* tuple
+* unordered-containers
+* vector