why don't we just embed this to a writer

src/Javran/AdventOfCode/Y2023/Day22.hs

@@ -10,6 +10,7 @@ module Javran.AdventOfCode.Y2023.Day22 () where
 
 import Control.Applicative
 import Control.Monad
+import Control.Monad.Writer.CPS
 import Data.Char
 import Data.Function
 import Data.Function.Memoize (memoFix)
@@ -26,7 +27,6 @@ import qualified Data.Vector as V
 import GHC.Generics (Generic)
 import Javran.AdventOfCode.Prelude
 import Text.ParserCombinators.ReadP hiding (count, get, many)
-import Control.Monad.Writer.CPS
 
 data Day22 deriving (Generic)
 
@@ -95,10 +95,9 @@ brickP = do
 
 type Coord = (Int, Int) -- (x, y)
 type St = IM.IntMap (M.Map Coord Int) -- z-index to 2-d coord to brick reference number.
-type St' = (St, IM.IntMap Int) -- additionally tracking final z-index of each block
 
-insertBrick :: Int -> Brick -> St' -> St'
-insertBrick bkId ((x0, y0, z0), (x1, y1, z1)) (s, zs) = (IM.unionWith M.union s extra, IM.insert bkId finalZ zs)
+insertBrick :: Int -> Brick -> St -> (St, IM.IntMap Int)
+insertBrick bkId ((x0, y0, z0), (x1, y1, z1)) s = (IM.unionWith M.union s extra, IM.singleton bkId finalZ)
   where
     -- a slice of the brick (horizontally cut)
     bSlice :: M.Map Coord Int
@@ -159,11 +158,12 @@ instance Solution Day22 where
         . fmap (consumeOrDie brickP)
         . lines
         <$> getInputS
-    let (sFin, zs) = foldl' (\s (i, b) -> insertBrick i b s) mempty (zip [0 ..] xs)
+    let (sFin, zs) = runWriter do
+          foldM (\s (i, b) -> writer (insertBrick i b s)) mempty (zip [0 ..] xs)
         w = execWriter do
           forM_ (IM.toAscList zs) \(curBk, zBase) -> do
             let bSlice = M.filter (== curBk) (sFin IM.! zBase)
-            case sFin IM.!? (zBase -1) of
+            case sFin IM.!? (zBase - 1) of
               Nothing -> pure ()
               Just supp -> do
                 let