Square and cube must have all digits

numbers =  list()
for i in range(10):
    numbers.append(i)
NUMBERS = [str(number) for number in numbers]
print(NUMBERS)

def checkDigitsStep1(n):
    square = n**2
    cube = n**3
    # *****************************************************************************************************
    # 1. I will make a list that will contain the str(digits) of my square and cube
    DIGITS = list()
    SQUARE = str(square)
    CUBE = str(cube)
    SQUAREDIGITS = [SQUARE[i] for i in range(len(SQUARE))]
    CUBEDIGITS = [CUBE[i] for i in range(len(CUBE))]
    # Now if n = 6, square = 36, cube = 216 ----> SQUAREDIGITS = ['3', '6'] and CUBEDIGITS = ['2', '1', '6']

    # *****************************************************************************************************
    # 2. Its time to concatenate the 2 lists in the list 'DIGITS'
    for element in SQUAREDIGITS:
        DIGITS.append(element)
    for element in CUBEDIGITS:
        DIGITS.append(element)

    # *****************************************************************************************************
    # 3. Create a map that counts its digit appearance
    counters = [0 for _ in range(10)]
    # Check every element of my list 'DIGITS'. I will increase the 'counter' in counters list
    for DIGIT in DIGITS:
        for i in range(len(NUMBERS)):
            if DIGIT == NUMBERS[i]:
                counters[i] += 1
                break

    # *****************************************************************************************************
    # 4. Now, my list 'counters' is ready. In my example we should have:
    # counters = [0, 1, 1, 1, 0, 0, 2, 0, 0, 0], because i have 1 '1's, 1 '2's, 1 '3's and 2 '6's
    return counters

def checkDigits(n):
    counters = checkDigitsStep1(n)
    print(n, n**2, n**3, counters)
    # Now, I want all my counters to be 1
    flag = False
    hits = 0
    for i in range(len(counters)):
        if counters[i] == 1:
            hits += 1
    # If hits = len(counters) = 10, that means all the digits from 0 to 9 are once in my square or cube
    if hits == 10:
        flag = True
    return flag


# MAIN FUNCTION
limit1 = 10
limit2 = 100
for n in range(limit1, limit2):
    if checkDigits(n) == True:
        print()
        print("Solution = " + str(n))
        print("n = " + str(n) + ", n^2 = " + str(n**2) + ", n^3 = " + str(n**3))
        break