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diff --git a/2023/10-Pipe_Maze/second.hs b/2023/10-Pipe_Maze/second.hs
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+-- requires cabal install --lib megaparsec parser-combinators
+module Main (main) where
+
+import Control.Applicative.Permutations
+import Control.Monad (void, when)
+import Data.Char qualified as C
+import Data.Either
+import Data.Functor
+import Data.List qualified as L
+import Data.Map qualified as M
+import Data.Maybe
+import Data.Set qualified as S
+import Data.Vector qualified as V
+import Data.Void (Void)
+import Text.Megaparsec
+import Text.Megaparsec.Char
+
+import Debug.Trace
+
+exampleExpectedOutput = 4
+
+data Direction = N | S | E | W deriving (Eq, Show)
+data Tile = NS | NE | NW | EW | ES | WS | Floor | Start | Loop deriving (Eq, Show)
+type Line = V.Vector Tile
+type Input = V.Vector Line
+
+type Parser = Parsec Void String
+
+parseTile :: Parser Tile
+parseTile = char '|' $> NS
+        <|> char 'L' $> NE
+        <|> char 'J' $> NW
+        <|> char '-' $> EW
+        <|> char 'F' $> ES
+        <|> char '7' $> WS
+        <|> char '.' $> Floor
+        <|> char 'S' $> Start
+
+parseLine :: Parser Line
+parseLine = do
+  line <- some parseTile <* eol
+  return $ V.generate (length line) (line !!)
+
+parseInput' :: Parser Input
+parseInput' = do
+  line <- some parseLine <* eof
+  return $ V.generate (length line) (line !!)
+
+parseInput :: String -> IO Input
+parseInput filename = do
+  input <- readFile filename
+  case runParser parseInput' filename input of
+    Left bundle -> error $ errorBundlePretty bundle
+    Right input' -> return input'
+
+compatible :: Tile -> Direction -> Bool
+compatible NS N = True
+compatible NS S = True
+compatible NE S = True
+compatible NE W = True
+compatible NW S = True
+compatible NW E = True
+compatible EW E = True
+compatible EW W = True
+compatible ES W = True
+compatible ES N = True
+compatible WS E = True
+compatible WS N = True
+compatible _ _ = False
+
+type Position = (Int, Int)
+type Heading = (Position, Direction)
+data Where = Outside | Inside
+
+compute :: Input -> Int
+compute input = V.sum $ V.zipWith (count 0 False) inputWithStartReplaced inputLooped
+  where
+    count :: Int -> Bool -> Line -> Line -> Int
+    count i w line line' | V.length line == 0 = i
+                         | u /= Loop = count (if w then i+1 else i) w r s
+                         | t == NS = count i (not w) r s
+                         | (t == NE && t'== NW) || (t == ES && t' == WS) = count i w r'' s'
+                         | otherwise = count i (not w) r'' s'
+      where
+        (t, u) = (line V.! 0, line' V.!0)
+        (r, s) = (V.tail line, V.tail line')
+        r' = V.dropWhile (== EW) r
+        s' = V.drop (1 + V.length s - V.length r') s
+        t' = r' V.! 0
+        r'' = V.tail r'
+    inputWithStartReplaced = input V.// [(sy, (input V.! sy) V.// [(sx, startingPipe startn starte starts startw)])]
+    startingPipe Nothing Nothing _ _ = WS
+    startingPipe Nothing _ Nothing _ = EW
+    startingPipe Nothing _ _ Nothing = ES
+    startingPipe _ Nothing Nothing _ = NW
+    startingPipe _ Nothing _ Nothing = NS
+    startingPipe _ _ Nothing Nothing = NE
+    inputLooped = walk start input
+    walk :: Heading -> Input -> Input -- walk the loop, marking each point in the loop to a Loop tile
+    walk h@((x, y), _) i | tile (fst h) == Just Start = i'
+                         | otherwise = walk h' i'
+      where
+        h' = step h
+        i' = i V.// [(y, (i V.! y) V.// [(x, Loop)])]
+    step :: Heading -> Heading
+    step (p@(x, y), N) | tile p == Just NS = ((x, y-1), N)
+                       | tile p == Just ES = ((x+1, y), E)
+                       | tile p == Just WS = ((x-1, y), W)
+    step (p@(x, y), S) | tile p == Just NS = ((x, y+1), S)
+                       | tile p == Just NE = ((x+1, y), E)
+                       | tile p == Just NW = ((x-1, y), W)
+    step (p@(x, y), E) | tile p == Just NW = ((x, y-1), N)
+                       | tile p == Just EW = ((x+1, y), E)
+                       | tile p == Just WS = ((x, y+1), S)
+    step (p@(x, y), W) | tile p == Just NE = ((x, y-1), N)
+                       | tile p == Just EW = ((x-1, y), W)
+                       | tile p == Just ES = ((x, y+1), S)
+    start = head $ catMaybes [startn, starte, starts, startw]
+    startn = nearStart (sx, sy-1) N
+    starts = nearStart (sx, sy+1) S
+    starte = nearStart (sx+1, sy) E
+    startw = nearStart (sx-1, sy) W
+    nearStart :: Position -> Direction -> Maybe Heading
+    nearStart p d = case tile p of
+      Just t -> if compatible t d then Just (p, d) else Nothing
+      Nothing -> Nothing
+    (sx, sy) = (x, y) -- start
+      where
+        hasNoStart :: Line -> Bool
+        hasNoStart = V.all (/= Start)
+        y = length $ V.takeWhile hasNoStart input
+        x = length $ V.takeWhile (/= Start) (input V.! y)
+    tile :: Position -> Maybe Tile
+    tile (x, y) = case input V.!? y of
+      Just line -> line V.!? x
+      Nothing -> Nothing
+
+main :: IO ()
+main = do
+  example <- parseInput "example3"
+  let exampleOutput = compute example
+  when  (exampleOutput /= exampleExpectedOutput)  (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
+  example4 <- parseInput "example4"
+  let exampleOutput4 = compute example4
+  when  (exampleOutput4 /= 8)  (error $ "example failed: got " ++ show exampleOutput4 ++ " instead of " ++ show 8)
+  example5 <- parseInput "example5"
+  let exampleOutput5 = compute example5
+  when  (exampleOutput5 /= 10)  (error $ "example failed: got " ++ show exampleOutput5 ++ " instead of " ++ show 10)
+  input <- parseInput "input"
+  print $ compute input