import math
import strformat

type
    Vector* = object
        x*: float
        y*: float
        z*: float

func vector*(x, y, z: float): Vector =
    Vector(x: x, y: y, z: z)

func vector0*: Vector =
    vector(0.0, 0.0, 0.0)

func `+`*(a, b: Vector): Vector =
    Vector(x: a.x + b.x, y: a.y + b.y, z: a.z + b.z)

func `-`*(a: Vector): Vector =
    Vector(x: -a.x, y: -a.y, z: -a.z)

func `-`*(a, b: Vector): Vector =
    a + (-b)

func `*`*(a: Vector, f: float): Vector =
    Vector(x: a.x * f, y: a.y * f, z: a.z * f)

func `*`*(f: float, a: Vector): Vector =
    a * f

func dot*(a, b: Vector): float =
    a.x * b.x + a.y * b.y + a.z * b.z

func len*(a: Vector): float =
    sqrt(dot(a, a))

func `/`*(a: Vector, f: float): Vector =
    a * (1/f)

func normalize*(a: Vector): Vector =
    a / a.len

func `+=`*(a: var Vector, b: Vector) =
    a = a + b

func `-=`*(a: var Vector, b: Vector) =
    a = a - b

func `$`*(a: Vector): string =
    &"{a.x} {a.y} {a.z}"