commit 9017c4379c9035917d4b588b72a26cf339211151
Author: Alexander Gehrke <github@qwertyuiop.de>
Date:   Thu Dec 2 23:34:40 2021 +0100

    Add base structure and library stuff from last year

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..047aaca
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,6 @@
+.bloop
+.bsp
+target/
+project/project
+project/bloop.sbt
+project/metals.sbt
diff --git a/build.sbt b/build.sbt
new file mode 100644
index 0000000..b5d109f
--- /dev/null
+++ b/build.sbt
@@ -0,0 +1,20 @@
+lazy val root = project
+  .in(file("."))
+  .settings(
+    name := "aoc2021",
+    version := "0.1.0",
+
+    scalaVersion := "3.1.0",
+    scalacOptions ++= Seq(
+      "-Yexplicit-nulls",
+      "-language:strict-equality",
+      "-deprecation",
+    ),
+    libraryDependencies ++= Seq(
+      "org.typelevel" %% "cats-core" % "2.6.1",
+      "org.typelevel" %% "cats-effect" % "3.1.1",
+      "org.typelevel" %% "kittens" % "3.0.0-M1",
+      )
+  )
+
+Runtime / unmanagedSources += baseDirectory.value / "input"
diff --git a/project/build.properties b/project/build.properties
new file mode 100644
index 0000000..67d27a1
--- /dev/null
+++ b/project/build.properties
@@ -0,0 +1 @@
+sbt.version=1.5.3
diff --git a/project/plugins.sbt b/project/plugins.sbt
new file mode 100644
index 0000000..32c4ba8
--- /dev/null
+++ b/project/plugins.sbt
@@ -0,0 +1,2 @@
+//addSbtPlugin("ch.epfl.scala" % "sbt-scalafix" % "0.9.29")
+addSbtPlugin("org.scalameta" % "sbt-scalafmt" % "2.4.3")
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day1.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day1.scala
new file mode 100644
index 0000000..cd58684
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day1.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day1(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day10.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day10.scala
new file mode 100644
index 0000000..7125092
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day10.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day10(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day11.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day11.scala
new file mode 100644
index 0000000..be34951
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day11.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day11(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day12.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day12.scala
new file mode 100644
index 0000000..3c98a57
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day12.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day12(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day13.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day13.scala
new file mode 100644
index 0000000..230a145
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day13.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day13(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day14.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day14.scala
new file mode 100644
index 0000000..506abd4
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day14.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day14(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day15.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day15.scala
new file mode 100644
index 0000000..982ffe5
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day15.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day15(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day16.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day16.scala
new file mode 100644
index 0000000..053d9ba
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day16.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day16(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day17.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day17.scala
new file mode 100644
index 0000000..6cf7c46
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day17.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day17(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day18.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day18.scala
new file mode 100644
index 0000000..a4c0eb2
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day18.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day18(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day19.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day19.scala
new file mode 100644
index 0000000..b79c880
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day19.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day19(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day2.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day2.scala
new file mode 100644
index 0000000..2d71836
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day2.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day2(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day20.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day20.scala
new file mode 100644
index 0000000..9f42879
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day20.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day20(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day21.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day21.scala
new file mode 100644
index 0000000..59b5659
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day21.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day21(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day22.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day22.scala
new file mode 100644
index 0000000..22d782f
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day22.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day22(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day23.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day23.scala
new file mode 100644
index 0000000..ce8468f
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day23.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day23(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day24.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day24.scala
new file mode 100644
index 0000000..8350506
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day24.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day24(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day25.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day25.scala
new file mode 100644
index 0000000..a283fd9
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day25.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day25(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day3.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day3.scala
new file mode 100644
index 0000000..ab7b569
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day3.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day3(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day4.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day4.scala
new file mode 100644
index 0000000..8141f42
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day4.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day4(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day5.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day5.scala
new file mode 100644
index 0000000..62021b7
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day5.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day5(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day6.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day6.scala
new file mode 100644
index 0000000..e86d217
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day6.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day6(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day7.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day7.scala
new file mode 100644
index 0000000..ebeaab1
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day7.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day7(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day8.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day8.scala
new file mode 100644
index 0000000..dc892b4
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day8.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day8(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/2021/day9.scala b/src/main/scala/de.qwertyuiop.aoc/2021/day9.scala
new file mode 100644
index 0000000..710c992
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/2021/day9.scala
@@ -0,0 +1,6 @@
+package de.qwertyuiop.aoc.`2021`
+
+import de.qwertyuiop.aoc.lib.*
+import cats.*, cats.implicits.given
+
+def day9(using InputSource): Unit = ???
diff --git a/src/main/scala/de.qwertyuiop.aoc/Main.scala b/src/main/scala/de.qwertyuiop.aoc/Main.scala
new file mode 100644
index 0000000..772d9d1
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/Main.scala
@@ -0,0 +1,37 @@
+package de.qwertyuiop.aoc
+import de.qwertyuiop.aoc.lib._
+import de.qwertyuiop.aoc.`2021`._
+@main def runDay(inputDir: String, day: Int, sample: Int*): Unit =
+  given InputSource = inputSource(inputDir, day, sample.headOption)
+  day match {
+    case 1 => day1
+    case 2 => day2
+    case 3 => day3
+    case 4 => day4
+    case 5 => day5
+    case 6 => day6
+    case 7 => day7
+    case 8 => day8
+    case 9 => day9
+    case 10 => day10
+    case 11 => day11
+    case 12 => day12
+    case 13 => day13
+    case 14 => day14
+    case 15 => day15
+    case 16 => day16
+    case 17 => day17
+    case 18 => day18
+    case 19 => day19
+    case 20 => day20
+    case 21 => day21
+    case 22 => day22
+    case 23 => day23
+    case 24 => day24
+    case 25 => day25
+    case _ => println("No such day implemented")
+  }
+
+def inputSource(inputDir:String, day: Int, sample: Option[Int]) =
+  sample.map(InputSource.SampleLocation(inputDir, day, _))
+    .getOrElse(InputSource.Location(inputDir, day))
diff --git a/src/main/scala/de.qwertyuiop.aoc/lib/RingBuffer.scala b/src/main/scala/de.qwertyuiop.aoc/lib/RingBuffer.scala
new file mode 100644
index 0000000..024fe78
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/lib/RingBuffer.scala
@@ -0,0 +1,28 @@
+package de.qwertyuiop.aoc.lib
+
+import scala.annotation.targetName
+
+/* Wrap a vector to create a limited size ring buffer */
+
+case class RingBuffer[A](underlying: Vector[A], maxSize: Int):
+  /* pass through any methods to the underlying vector, except appending and
+   * prepending single elements */
+  export underlying.{ :+ => _, appended => _, +: => _, prepended => _, _ }
+
+  inline def full: Boolean = underlying.size == maxSize
+
+  @targetName("appended") def :+[B >: A](b: B): RingBuffer[B] =
+    val appendedVec = (if full then underlying.tail else underlying) :+ b
+    new RingBuffer(appendedVec, maxSize)
+
+  @targetName("prepended") def +:[B >: A](b: B): RingBuffer[B] =
+    val prependedVec = b +: (if full then underlying.init else underlying)
+    new RingBuffer(prependedVec, maxSize)
+
+object RingBuffer:
+  def apply[A](underlying: Vector[A], maxSize: Int): RingBuffer[A] =
+    new RingBuffer(
+      if underlying.size > maxSize then underlying.view.slice(0, maxSize).toVector 
+      else underlying,
+      maxSize
+    )
diff --git a/src/main/scala/de.qwertyuiop.aoc/lib/extensions.scala b/src/main/scala/de.qwertyuiop.aoc/lib/extensions.scala
new file mode 100644
index 0000000..0bada30
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/lib/extensions.scala
@@ -0,0 +1,23 @@
+package de.qwertyuiop.aoc.lib
+
+/* for splitting input with separator lines */
+extension [A](input: List[A])(using CanEqual[A,A])
+  def split(separator: A, keepSeparator: Boolean = false): LazyList[List[A]] =
+    input.span(_ != separator) match
+        case (Nil, Nil)              => LazyList()
+        case (h,   Nil)              => LazyList(h)
+        case (h,   tail @ (_ :: t)) =>
+          h #:: (if keepSeparator then tail else t).split(separator)
+
+
+/* Using -Yexplicit-nulls isn't really ready for use with the java standard
+ * library. e.g. String doesn't have `@NotNull` annotations for its methods
+ */
+extension (s: String)
+  def splitOnce(regex: String): Option[(String, String)] =
+    s.split(regex, 2) match
+      case Array(a, b) => Some((a.nn, b.nn))
+      case _ => None
+
+extension [K,V,W](map: Map[K,V])
+  def mapValuesS(f: V => W): Map[K, W] = map.view.mapValues(f).toMap
diff --git a/src/main/scala/de.qwertyuiop.aoc/lib/inputs.scala b/src/main/scala/de.qwertyuiop.aoc/lib/inputs.scala
new file mode 100644
index 0000000..c7986c5
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/lib/inputs.scala
@@ -0,0 +1,31 @@
+package de.qwertyuiop.aoc.lib
+
+import scala.io.Source
+
+enum InputSource:
+  case Location(inputDir: String, day: Int)
+  case Fixed(lines: List[String])
+  case SampleLocation(inputDir: String, day: Int, sample: Int)
+
+def inputLines(using src: InputSource): Iterator[String] = 
+  src match
+    case InputSource.Location(inputDir, day) => scala.io.Source.fromFile(s"${inputDir}/day${day}.txt").getLines
+    case InputSource.Fixed(input) => input.iterator
+    case InputSource.SampleLocation(inputDir, day, sample) => scala.io.Source.fromFile(s"${inputDir}/day${day}-sample${sample}.txt").getLines
+
+
+def simpleInput(using l: InputSource): String = inputLines.mkString
+
+def input[A](format: String => A = identity)(using l: InputSource): List[A] =
+  inputF(format)(List)
+
+def inputF[A, C[_]](format: String => A = identity)(coll: collection.Factory[A, C[A]])(using l: InputSource): C[A] =
+  inputLines.map(format).to(coll)
+
+def flatInput[A](format: String => List[A] = List.apply)(using l: InputSource): List[A] =
+  flatInputF(format)(List)
+
+def flatInputF[A, C[_]](format: String => IterableOnce[A] = identity)(coll: collection.Factory[A, C[A]])(using l: InputSource): C[A] =
+  inputLines.flatMap(format).to(coll)
+
+def boolChar(trueChar: Char): String => Vector[Boolean] = _.map(_ == trueChar).toVector
diff --git a/src/main/scala/de.qwertyuiop.aoc/lib/misc.scala b/src/main/scala/de.qwertyuiop.aoc/lib/misc.scala
new file mode 100644
index 0000000..9507073
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/lib/misc.scala
@@ -0,0 +1,9 @@
+package de.qwertyuiop.aoc.lib
+
+import scala.collection.mutable
+
+def memoize[I, O](f: I => O): I => O = new mutable.HashMap[I, O]() {self =>
+  override def apply(key: I) = self.synchronized(getOrElseUpdate(key, f(key)))
+}
+
+def repeat[T](n: Int)(f: T => T): T => T = Function.chain(Seq.fill(n)(f))
diff --git a/src/main/scala/de.qwertyuiop.aoc/lib/vectors.scala b/src/main/scala/de.qwertyuiop.aoc/lib/vectors.scala
new file mode 100644
index 0000000..708688a
--- /dev/null
+++ b/src/main/scala/de.qwertyuiop.aoc/lib/vectors.scala
@@ -0,0 +1,145 @@
+package de.qwertyuiop.aoc.lib
+
+import cats.*, cats.implicits.given
+import cats.derived.semiauto
+
+object Vectors: 
+  import scala.Numeric.Implicits.given
+  import scala.compiletime.ops.int.*
+  import Directions.*
+
+  opaque type Vec2D[T] = (T, T)
+  opaque type Vec3D[T] = (T, T, T)
+  opaque type Vec4D[T] = (T, T, T, T)
+
+  def Vec2D[T](x: T, y: T): Vec2D[T] = (x,y)
+  def Vec3D[T](x: T, y: T, z: T): Vec3D[T] = (x,y,z)
+  def Vec4D[T](x: T, y: T, z: T, w: T): Vec4D[T] = (x,y,z,w)
+
+  trait Vec[T]:
+    extension (v: T)
+      def +(w: T): T
+      def neighbours: List[T]
+
+  given [T : Show]: Show[Vec2D[T]] with
+    def show(v: Vec2D[T]): String = show"Vec2D(${v._1}, ${v._2})"
+  given [T : Show]: Show[Vec3D[T]] with
+    def show(v: Vec3D[T]): String = show"Vec3D(${v._1}, ${v._2}, ${v._3})"
+  given [T : Show]: Show[Vec4D[T]] with
+    def show(v: Vec4D[T]): String = show"Vec4D(${v._1}, ${v._2}, ${v._3}, ${v._4})"
+
+  given [T: Numeric]: Vec[Vec2D[T]] with
+    extension (v: Vec2D[T])
+      def +(w: Vec2D[T]): Vec2D[T] = (v._1 + w._1, v._2 + w._2)
+      def -(w: Vec2D[T]): Vec2D[T] = (v._1 - w._1, v._2 - w._2)
+      def *(x: T): Vec2D[T] = (v._1 * x, v._2 * x)
+
+      def x: T = v._1
+      def y: T = v._2
+
+      def rot(deg: Dir): Vec2D[T] = deg match
+        case North => (-v._2, v._1)
+        case West => (-v._1, -v._2)
+        case South => (v._2, -v._1)
+        case East => v
+
+      def left(deg: Int): Vec2D[T] = repeat[Vec2D[T]](deg / 90)(_.rotLeft)(v)
+      def right(deg: Int): Vec2D[T] = repeat[Vec2D[T]](deg / 90)(_.rotRight)(v)
+
+      def rotLeft: Vec2D[T] = (-v._2, v._1)
+      def rotRight: Vec2D[T] = (v._2, -v._1)
+
+      def move(dir: Dir, dist: T): Vec2D[T] = dir match
+        case North => (v._1, v._2 + dist)
+        case South => (v._1, v._2 - dist)
+        case East => (v._1 + dist, v._2)
+        case West => (v._1 - dist, v._2)
+
+      def manhattan: T = v._1.abs + v._2.abs
+      def neighbours: List[Vec2D[T]] =
+        neighbourCoords(2).map(n => v + (n(0), n(1)))
+
+  given [T: Monoid]: Monoid[Vec2D[T]] = semiauto.monoid
+  given [T: Monoid]: Monoid[Vec3D[T]] = semiauto.monoid
+  given [T: Monoid]: Monoid[Vec4D[T]] = semiauto.monoid
+
+
+  given [T: Numeric]: Vec[Vec3D[T]] with
+    extension (v: Vec3D[T])
+      def +(w: Vec3D[T]): Vec3D[T] = (v._1 + w._1, v._2 + w._2, v._3 + w._3)
+      def neighbours: List[Vec3D[T]] =
+        neighbourCoords(3).map(n => v + (n(0), n(1), n(2)))
+
+      def x: T = v._1
+      def y: T = v._2
+      def z: T = v._3
+
+  given [T: Numeric]: Vec[Vec4D[T]] with
+    extension (v: Vec4D[T])
+      def +(u: Vec4D[T]): Vec4D[T] = (v._1 + u._1, v._2 + u._2, v._3 + u._3, v._4 + u._4)
+      def neighbours: List[Vec4D[T]] =
+        neighbourCoords(4).map(n => v + (n(0), n(1), n(2), n(3)))
+
+      def x: T = v._1
+      def y: T = v._2
+      def z: T = v._3
+      def w: T = v._4
+
+
+  /* compute these only once per type and dimension*/
+  import scala.collection.mutable
+  private var _neighbourCache = mutable.Map[(Numeric[_], Int), List[List[_]]]()
+  def neighbourCoords[T](dim: Int)(using n: Numeric[T]): List[List[T]] =
+    _neighbourCache.get((n, dim)) match
+      case None =>
+        val self = List.fill(dim)(n.zero)
+        val neighs = List.fill(dim)(List(-n.one, n.zero, n.one)).sequence[List, T]
+          .filter(_ != self)
+        _neighbourCache.put((n, dim), neighs)
+        neighs
+      case Some(neighs) => neighs.asInstanceOf[List[List[T]]]
+
+object Directions:
+  opaque type Dir = Int
+  val East: Dir = 0
+  val North: Dir = 90
+  val West: Dir = 180
+  val South: Dir = 270
+
+  extension (c: Char)
+    def cardinal: Dir = c match
+      case 'E' => East
+      case 'N' => North
+      case 'W' => West
+      case 'S' => South
+
+  def Dir(deg: Int): Dir = (deg % 360 + 360) % 360
+
+  private val rotationOrder = Vector(North, West, South, East, North, West)
+
+  extension (dir: Dir)
+    def +(deg: Int|Dir): Dir = (dir + deg) % 360
+    def -(deg: Int|Dir): Dir = ((dir - deg) % 360 + 360) % 360
+    def unary_- : Dir = 360 - dir
+    def str: String = dir match
+      case East  => "East"
+      case North => "North"
+      case West  => "West"
+      case South => "South"
+
+    def rotLeft: Dir = rotationOrder(rotationOrder.indexOf(dir) + 1)
+    def rotRight: Dir = rotationOrder(rotationOrder.lastIndexOf(dir) - 1)
+    def flip: Dir = rotationOrder(rotationOrder.indexOf(dir) + 2)
+
+    def flipHor: Dir = dir match
+      case West => East
+      case East => West
+      case o => o
+
+    def flipVert: Dir = dir match
+      case North => South
+      case South => North
+      case o => o
+
+  given Show[Dir] with
+    def show(d: Dir): String = d.str