type MaxDay = {
  "01": 31,
  "02": 28,
  "03": 31,
  "04": 30,
  "05": 31,
  "06": 30,
  "07": 31,
  "08": 31,
  "09": 30,
  "10": 31,
  "11": 30,
  "12": 31,
}

type TNumOf<N extends number, _A extends 0[] = []> = _A["length"] extends N ? _A : TNumOf<N, [..._A, 0]>;
type Gte<Left extends number, Right extends number> = TNumOf<Left> extends [...TNumOf<Right>, ...infer Rest] ? true : false;
type Lte<Left extends number, Right extends number> = TNumOf<Right> extends [...TNumOf<Left>, ...infer _] ? true : false;

type ValidDate_Impl<Month extends string, Day extends string> =
  Month extends keyof MaxDay
  ? Day extends `${infer DayN extends number}`
  ? DayN extends 0
  ? false
  : Gte<DayN, 0> extends true
  ? Lte<DayN, MaxDay[Month]> extends true
  ? true
  : false
  : false
  : false
  : false;

type ValidDate<T extends string> =
  T extends `${infer M1 extends number}${infer M2 extends number}${infer D1 extends number}${infer D2 extends number}${infer R}`
  ? R extends ""
  ? ValidDate_Impl<`${M1}${M2}`, `${D1 extends 0 ? "" : D1}${D2}`>
  : false
  : false;

import type { Equal, Expect } from '@type-challenges/utils'

type cases = [
  Expect<Equal<ValidDate<'0102'>, true>>,
  Expect<Equal<ValidDate<'0131'>, true>>,
  Expect<Equal<ValidDate<'1231'>, true>>,
  Expect<Equal<ValidDate<'0229'>, false>>,
  Expect<Equal<ValidDate<'0100'>, false>>,
  Expect<Equal<ValidDate<'0132'>, false>>,
  Expect<Equal<ValidDate<'1301'>, false>>,
]