diff --git a/Cargo.lock b/Cargo.lock
index a9a0cc7..9adcd0c 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -16,6 +16,8 @@ name = "aoc"
 version = "0.1.0"
 dependencies = [
  "num-traits",
+ "strum",
+ "thiserror",
 ]
 
 [[package]]
@@ -213,6 +215,12 @@ version = "0.12.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8a9ee70c43aaf417c914396645a0fa852624801b24ebb7ae78fe8272889ac888"
 
+[[package]]
+name = "heck"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "2540771e65fc8cb83cd6e8a237f70c319bd5c29f78ed1084ba5d50eeac86f7f9"
+
 [[package]]
 name = "hermit-abi"
 version = "0.1.19"
@@ -611,6 +619,12 @@ dependencies = [
  "aoc",
 ]
 
+[[package]]
+name = "rustversion"
+version = "1.0.11"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5583e89e108996506031660fe09baa5011b9dd0341b89029313006d1fb508d70"
+
 [[package]]
 name = "ryu"
 version = "1.0.11"
@@ -670,6 +684,28 @@ dependencies = [
  "serde",
 ]
 
+[[package]]
+name = "strum"
+version = "0.24.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "063e6045c0e62079840579a7e47a355ae92f60eb74daaf156fb1e84ba164e63f"
+dependencies = [
+ "strum_macros",
+]
+
+[[package]]
+name = "strum_macros"
+version = "0.24.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1e385be0d24f186b4ce2f9982191e7101bb737312ad61c1f2f984f34bcf85d59"
+dependencies = [
+ "heck",
+ "proc-macro2",
+ "quote",
+ "rustversion",
+ "syn",
+]
+
 [[package]]
 name = "syn"
 version = "1.0.105"
@@ -690,6 +726,26 @@ dependencies = [
  "unicode-width",
 ]
 
+[[package]]
+name = "thiserror"
+version = "1.0.38"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "6a9cd18aa97d5c45c6603caea1da6628790b37f7a34b6ca89522331c5180fed0"
+dependencies = [
+ "thiserror-impl",
+]
+
+[[package]]
+name = "thiserror-impl"
+version = "1.0.38"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1fb327af4685e4d03fa8cbcf1716380da910eeb2bb8be417e7f9fd3fb164f36f"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
 [[package]]
 name = "tinytemplate"
 version = "1.2.1"
diff --git a/common/rust/Cargo.toml b/common/rust/Cargo.toml
index 00a20b8..ebe2750 100644
--- a/common/rust/Cargo.toml
+++ b/common/rust/Cargo.toml
@@ -7,3 +7,5 @@ edition = "2021"
 
 [dependencies]
 num-traits = "0.2.15"
+strum = { version = "0.24.1", features = ["derive"] }
+thiserror = "1.0.38"
diff --git a/common/rust/src/lib.rs b/common/rust/src/lib.rs
index c79c26f..aa9633a 100644
--- a/common/rust/src/lib.rs
+++ b/common/rust/src/lib.rs
@@ -2,6 +2,7 @@
 
 mod section_range;
 pub mod vec2;
+pub mod vecn;
 
 use std::{mem, path::Path};
 
diff --git a/common/rust/src/vecn.rs b/common/rust/src/vecn.rs
new file mode 100644
index 0000000..2219986
--- /dev/null
+++ b/common/rust/src/vecn.rs
@@ -0,0 +1,365 @@
+use std::{
+    array,
+    iter::Sum,
+    ops::{Add, AddAssign, Mul, Neg, Sub, SubAssign},
+    str::FromStr,
+};
+
+use num_traits::{one, zero, One, Zero};
+use strum::EnumIter;
+use thiserror::Error;
+
+pub trait Abs {
+    type Output;
+    fn abs(self) -> Self::Output;
+}
+
+macro_rules! impl_abs_signed {
+    ($($t:ty)*) => {
+        $(impl Abs for $t {
+            type Output = $t;
+            fn abs(self) -> Self {
+                self.abs()
+            }
+        })*
+    };
+}
+impl_abs_signed!(i8 i16 i32 i64 i128 f32 f64);
+
+macro_rules! impl_abs_noop {
+    ($($t:ty)*) => {
+        $(impl Abs for $t {
+            type Output = $t;
+            fn abs(self) -> Self {
+                self
+            }
+        })*
+    };
+}
+impl_abs_noop!(u8 u16 u32 u64 u128);
+
+/// A vector in `N`-space.
+///
+/// The coordinate system is canonically left-handed:
+///
+/// Axis | +       | -
+/// -----|---------|------
+/// x    | right   | left
+/// y    | up      | down
+/// z    | forward | back
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub struct VecN<const N: usize, T> {
+    coords: [T; N],
+}
+
+impl<T> VecN<2, T> {
+    #[must_use]
+    pub const fn new(x: T, y: T) -> Self {
+        Self { coords: [x, y] }
+    }
+}
+
+impl<T> VecN<3, T> {
+    #[must_use]
+    pub const fn new(x: T, y: T, z: T) -> Self {
+        Self { coords: [x, y, z] }
+    }
+}
+
+impl<const N: usize, T> VecN<N, T> {
+    #[must_use]
+    pub fn map<U>(self, f: impl FnMut(T) -> U) -> VecN<N, U> {
+        VecN {
+            coords: self.coords.map(f),
+        }
+    }
+
+    pub fn try_map<U, E>(self, mut f: impl FnMut(T) -> Result<U, E>) -> Result<VecN<N, U>, E>
+    where
+        [U; N]: Default,
+    {
+        let mut coords: [U; N] = Default::default();
+        for (coord, x) in coords.iter_mut().zip(self.coords) {
+            *coord = f(x)?;
+        }
+        Ok(VecN { coords })
+    }
+
+    #[must_use]
+    pub fn len(self) -> f64
+    where
+        T: Into<f64>,
+    {
+        self.coords
+            .into_iter()
+            .map(|l| l.into().powi(2))
+            .sum::<f64>()
+            .sqrt()
+    }
+
+    #[must_use]
+    pub fn manhattan_len<U>(self) -> U
+    where
+        T: Abs<Output = U>,
+        U: Sum,
+    {
+        self.coords.into_iter().map(Abs::abs).sum()
+    }
+}
+
+impl<const N: usize, T> Add for VecN<N, T>
+where
+    T: Add<Output = T>,
+{
+    type Output = Self;
+
+    fn add(self, rhs: Self) -> Self::Output {
+        let mut coords = self.coords.into_iter().zip(rhs.coords).map(|(l, r)| l + r);
+        Self {
+            coords: array::from_fn(|_| coords.next().unwrap()),
+        }
+    }
+}
+
+impl<const N: usize, T> AddAssign for VecN<N, T>
+where
+    T: AddAssign,
+{
+    fn add_assign(&mut self, rhs: Self) {
+        for (l, r) in self.coords.iter_mut().zip(rhs.coords) {
+            *l += r;
+        }
+    }
+}
+
+impl<const N: usize, T> Sub for VecN<N, T>
+where
+    T: Sub<Output = T>,
+{
+    type Output = Self;
+
+    fn sub(self, rhs: Self) -> Self::Output {
+        let mut coords = self.coords.into_iter().zip(rhs.coords).map(|(l, r)| l - r);
+        Self {
+            coords: array::from_fn(|_| coords.next().unwrap()),
+        }
+    }
+}
+
+impl<const N: usize, T> SubAssign for VecN<N, T>
+where
+    T: SubAssign,
+{
+    fn sub_assign(&mut self, rhs: Self) {
+        for (l, r) in self.coords.iter_mut().zip(rhs.coords) {
+            *l -= r;
+        }
+    }
+}
+
+impl<const N: usize, T, U> Mul<U> for VecN<N, T>
+where
+    T: Mul<U, Output = T>,
+    U: Copy,
+{
+    type Output = Self;
+
+    fn mul(self, n: U) -> Self::Output {
+        Self {
+            coords: self.coords.map(|c| c * n),
+        }
+    }
+}
+
+/*
+impl<const N: usize, T> Mul<VecN<N, T>> for T
+where
+    T: Mul<Output = T>,
+{
+    type Output = VecN<N, T>;
+
+    fn mul(self, vec: VecN<N, T>) -> Self::Output {
+        VecN {
+            coords: vec.coords.map(|c| c * self),
+        }
+    }
+}
+*/
+
+impl<const N: usize, T> From<[T; N]> for VecN<N, T> {
+    fn from(coords: [T; N]) -> Self {
+        Self { coords }
+    }
+}
+
+impl<const N: usize, T> From<VecN<N, T>> for [T; N] {
+    fn from(v: VecN<N, T>) -> Self {
+        v.coords
+    }
+}
+
+impl<T> From<Direction2> for VecN<2, T>
+where
+    T: Zero + One + Neg<Output = T>,
+{
+    /// Creates a unit vector in the given direction.
+    fn from(dir: Direction2) -> Self {
+        let z = zero();
+        let o = one();
+
+        match dir {
+            Direction2::Right => Self::new(o, z),
+            Direction2::Left => Self::new(-o, z),
+            Direction2::Up => Self::new(z, o),
+            Direction2::Down => Self::new(z, -o),
+        }
+    }
+}
+
+impl<T> From<Direction3> for VecN<3, T>
+where
+    T: Zero + One + Neg<Output = T> + Copy,
+{
+    /// Creates a unit vector in the given direction.
+    fn from(dir: Direction3) -> Self {
+        let z = zero();
+        let o = one();
+
+        match dir {
+            Direction3::Right => Self::new(o, z, z),
+            Direction3::Left => Self::new(-o, z, z),
+            Direction3::Up => Self::new(z, o, z),
+            Direction3::Down => Self::new(z, -o, z),
+            Direction3::Forward => Self::new(z, z, o),
+            Direction3::Back => Self::new(z, z, -o),
+        }
+    }
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Error)]
+pub enum ParseVecError<E> {
+    #[error("failed to parse axis {axis}")]
+    AxisParseError {
+        axis: usize,
+        #[source]
+        source: E,
+    },
+    #[error("not enough dimensions specified, expected {expected}")]
+    NotEnoughDimensions { expected: usize },
+    #[error("too many dimensions specified, expected {expected}")]
+    TooManyDimensions { expected: usize },
+}
+
+impl<const N: usize, T> FromStr for VecN<N, T>
+where
+    [T; N]: Default,
+    T: FromStr,
+{
+    type Err = ParseVecError<T::Err>;
+
+    fn from_str(s: &str) -> Result<Self, Self::Err> {
+        let mut parts = s.split(',');
+
+        let mut coords: [T; N] = Default::default();
+        for (i, axis) in coords.iter_mut().enumerate() {
+            *axis = parts
+                .next()
+                .ok_or(ParseVecError::NotEnoughDimensions { expected: N })?
+                .parse()
+                .map_err(|e| ParseVecError::AxisParseError { axis: i, source: e })?;
+        }
+
+        if parts.next().is_some() {
+            return Err(ParseVecError::TooManyDimensions { expected: N });
+        }
+
+        Ok(Self { coords })
+    }
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, EnumIter)]
+pub enum Direction2 {
+    Right,
+    Left,
+    Up,
+    Down,
+}
+
+impl Neg for Direction2 {
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        match self {
+            Direction2::Right => Direction2::Left,
+            Direction2::Left => Direction2::Right,
+            Direction2::Up => Direction2::Down,
+            Direction2::Down => Direction2::Up,
+        }
+    }
+}
+
+impl FromStr for Direction2 {
+    type Err = ();
+
+    fn from_str(s: &str) -> Result<Self, Self::Err> {
+        match s {
+            "R" => Ok(Direction2::Right),
+            "L" => Ok(Direction2::Left),
+            "U" => Ok(Direction2::Up),
+            "D" => Ok(Direction2::Down),
+            _ => Err(()),
+        }
+    }
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, EnumIter)]
+pub enum Direction3 {
+    Right = 0,
+    Left = 1,
+    Up = 2,
+    Down = 4,
+    Forward = 5,
+    Back = 6,
+}
+
+impl From<Direction2> for Direction3 {
+    fn from(dir: Direction2) -> Self {
+        match dir {
+            Direction2::Right => Direction3::Right,
+            Direction2::Left => Direction3::Left,
+            Direction2::Up => Direction3::Up,
+            Direction2::Down => Direction3::Down,
+        }
+    }
+}
+
+impl Neg for Direction3 {
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        match self {
+            Direction3::Right => Direction3::Left,
+            Direction3::Left => Direction3::Right,
+            Direction3::Up => Direction3::Down,
+            Direction3::Down => Direction3::Up,
+            Direction3::Forward => Direction3::Back,
+            Direction3::Back => Direction3::Forward,
+        }
+    }
+}
+
+impl FromStr for Direction3 {
+    type Err = ();
+
+    fn from_str(s: &str) -> Result<Self, Self::Err> {
+        match s {
+            "R" => Ok(Direction3::Right),
+            "L" => Ok(Direction3::Left),
+            "U" => Ok(Direction3::Up),
+            "D" => Ok(Direction3::Down),
+            "F" => Ok(Direction3::Forward),
+            "B" => Ok(Direction3::Back),
+            _ => Err(()),
+        }
+    }
+}