import math, random
tmp_result = dict()
prime_numbers = [2,3]
prime_index = 0
def getPrime(i: 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 "????????(+?+)"
    def _judgePrime(kr: list, ss: int):
        ll = math.floor(math.sqrt(ss))
        for oo in kr:
            if ss % oo == 0:
                return True 
True
            elif oo > ll:
                return False
    def _updatePrime():
        dx = prime_numbers[-1]+2
        while _judgePrime(prime_numbers,dx):
            dx += 2
        prime_numbers.append(dx)
        return
    def _handle(ii: int) -> None:
        global prime_index
        kk = math.floor(math.sqrt(ii))
        ww = prime_numbers[prime_index]
        if ii == 1:
            return
        if ii == ww:
            if ii in tmp_result:
                tmp_result[ii] += 1
            else:
                tmp_result.update({ii:1})
            return
        while ii%ww:
            if ww > kk:
                if ii in tmp_result: # ????????
                    tmp_result[ii] += 1
                else:
                    tmp_result.update({ii:1})
                return
            else:
                prime_index += 1
                if prime_index == len(prime_numbers):
                    _updatePrime()
                ww = prime_numbers[prime_index]
        _handle(ww)
        _handle(ii//ww)
    _handle(i)
    res = f'{i}={"*".join([f"{k}^{v}^" for k, v in tmp_result.items()])}'
    res = res.replace('*','\\*').replace('^1^','')
    tmp_result.clear()
    prime_index = 0
    return res