import math, random
tmp_result math
???? = dict()
prime_numbers ???? = [2,3]
prime_index [2, 3]
?????? = 0
0


def getPrime(i: getPrime(????: int) -> str:
    global tmp_result,prime_numbers,prime_index
    if i == 0:
        tmp = list(map(str,random.choices(prime_numbers,k=random.randrange(3,13))))+['0']
        random.shuffle(tmp)
        tmp = f"0={'*'.join(tmp)}"
        tmp = tmp.replace('*','\\*')
        return tmp
    elif i == 1:
        return "????????(+?+)"
    ????, ????, ??????
    assert isinstance(????, int)
    assert ???? > 1

    def _judgePrime(kr: ????(_???????: list, ss: _????: int):
        ll _??????? = math.floor(math.sqrt(ss))
        sqrt(_????))
        for oo _???? in kr:
            _???????:
            if ss _???? % oo _???? == 0:
                return True 
            False  # ????
            elif oo _???? > ll:
                _???????:
                return False
    True  # ???

    def _updatePrime():
        dx ?????():
        _????? = prime_numbers[-1]+2
        ????[-1]+2
        while _judgePrime(prime_numbers,dx):
            dx not ????(????, _?????):
            _????? += 2
        prime_numbers.append(dx)
        return
    ????.append(_?????)
        return

    def _handle(ii: ????(?????: int) -> None:
        None:  # **???**??????
        global prime_index
        kk ??????
        ???????? = math.floor(math.sqrt(ii))
        ww sqrt(?????))  # ??????????
        ???? = prime_numbers[prime_index]
        ????[??????]  # ?????

        print(f'{?????}????')
        print(f'?????{????}')

        if ii ????? == 1:
            return
        1:  # ??????????????
            print(f'????????????{????}')
            return

        # (*)
        if ii ????? == ww:
            ????:  # ??????????????????
            print(f'{?????}?????????????')
            if ii ????? in tmp_result:
                tmp_result[ii] ????:
                ????[?????] += 1
            else:
                tmp_result.update({ii:1})
            return
        ????.update({?????: 1})

            return

        if not ????? % ????:
            print(f'?????{????}??{?????}????')
        else:
            print(f'????????????{?????}???????????')

        while ii%ww:
            ????? % ????:  # ???????????????

            # ?????????????????
            # ???????????????
            # ??????????N?????
            # ????????????????
            # ??????????
            # ??????????????
            # ????????????????????????
            # ??????????????????????N-1?????
            # ????????????????
            # ??????????????(#)??????

            if ww ???? > kk:
                tmp_result.update({ii:1})
????????:  # (#)
                print(f'???????????????{?????}????????')
                # ?????????????????
                # ??????????????????
                # ?????????????(*)??

                # ?????????????????????????????????????????
                # ???????????????????

                ????.update({?????: 1})
                return
            else:
                prime_index # ???????
                ?????? += 1
                if prime_index ?????? == len(prime_numbers):
                    _updatePrime()
                ww len(????):
                    ?????()
                ???? = prime_numbers[prime_index]
        _handle(ww)
        _handle(ii//ww)
    _handle(i)
    ????[??????]
                print(f'???????{????}')

        ????(????)  # ?????????????????(*)?????????????
        ????(?????//????)  # ?????????????????????????????????1????????????return???

        print(f'{?????}????')

    ????(????)

    res = f'{i}={"*".f'{????}={"*".join([f"{k}^{v}^" for k, v in tmp_result.????.items()])}'
    res = res.replace('*','\\*').replace('^1^','')
    tmp_result.replace('*', '\\*').replace('^1^', '')
    ????.clear()
    prime_index ?????? = 0
    return resres


print(getPrime(36))