Fizzbuzz in typescript (types)

fizzbuzz.ts

// based on https://dev.to/gypsydave5/fizz-buzz-in-typescript-7ip (with some corrections)

type Z = 0;
type S<N> = [N];

type N1 = S<Z>;
type N2 = S<N1>;
type N3 = S<N2>;
type N4 = S<N3>;
type N5 = S<N4>;
type N6 = S<N5>;
type N7 = S<N6>;
type N8 = S<N7>;
type N9 = S<N8>;
type N10 = S<N9>;
type N11 = S<N10>;
type N12 = S<N11>;
type N13 = S<N12>;
type N14 = S<N13>;
type N15 = S<N14>;

type Equal<Na, Nb> = {
  0: Nb extends Z ? true : false;
  1: {
    0: false;
    1: Na extends S<infer Pa> ? (Nb extends S<infer Pb> ? Equal<Pa, Pb> : never) : never;
  }[Nb extends Z ? 0 : 1];
}[Na extends Z ? 0 : 1];

type LessThan<Na, Nb> = {
  0: false;
  1: Na extends Z
    ? true
    : Na extends S<infer Pa>
    ? Nb extends S<infer Pb>
      ? LessThan<Pa, Pb>
      : never
    : never;
}[Nb extends Z ? 0 : 1];

type IsMultipleOfThree<T> = {
  1: true;
  0: Ternary<LessThan<T, N3>, false, T extends S<S<S<infer P>>> ? IsMultipleOfThree<P> : false>;
}[Equal<T, N3> extends true ? 1 : 0];

type IsMultipleOfFive<T> = {
  1: true;
  0: Ternary<
    LessThan<T, N3>,
    false,
    T extends S<S<S<S<S<infer P>>>>> ? IsMultipleOfFive<P> : false
  >;
}[Equal<T, N5> extends true ? 1 : 0];

type Ternary<B, P, Q> = {
  1: P;
  0: Q;
}[B extends true ? 1 : 0];

type FIZZ = "fizz";
type BUZZ = "buzz";
type FIZZBUZZ = "fizzbuzz";

type FB<N> = Ternary<
  IsMultipleOfThree<N>,
  Ternary<IsMultipleOfFive<N>, FIZZBUZZ, FIZZ>,
  Ternary<IsMultipleOfFive<N>, BUZZ, N>
>;

type Should1 = FB<N1>;
type ShouldFizz = FB<N3>;
type Should4 = FB<N4>;
type ShouldBuzz = FB<N5>;
type ShouldFizzBuzz = FB<N15>;