import math

def considerHex(letter):
    if letter == "A" or letter == "a":
        return 10
    if letter == "B" or letter == "b":
        return 11
    if letter == "C" or letter == "c":
        return 12
    if letter == "D" or letter == "d":
        return 13
    if letter == "E" or letter == "e":
        return 14
    if letter == "F" or letter == "f":
        return 15
    else:
        return int(letter)

def main():
    # retrieve an input from the user
    # if type isnt number output error and get input again
    # if type is number then store it and retrieve input again for the base of the number supplied
    # store the number for the base of the number supplied
    # ask the user for the base of the desired  output nuymber
    # calculate the conversion and return it

    originalNumber = input("Please input a number: ")
    originalBase = int(input("Please input the base of your number in numerical form: "))
    outputBase = int(input("Please input the base of the desired conversion: "))
    baseTen = 0
    maxExponent = 30
    outputNumber = 0
    for index, digit in enumerate(originalNumber):
        # add consideration for bases higher than 10
        digit = considerHex(digit)
        currentPlace = (len(originalNumber) - index - 1)
        baseTen += digit * (originalBase ** (len(originalNumber) - index - 1))
    print("your number in base 10 is %s" % baseTen)
    # now convert to output base
    while baseTen >= 0 and maxExponent >= 0:
        currentDigit = baseTen / (outputBase ** maxExponent)
        if 1 <= currentDigit < baseTen:
            multiplier = math.floor((baseTen / (outputBase ** maxExponent)))
            if multiplier == 0:
                multiplier = 1
            outputNumber += multiplier * (10 ** maxExponent)
            baseTen -= multiplier * (outputBase ** maxExponent)
        maxExponent -= 1
    # add the last trailing remainder of baseTen
    outputNumber += baseTen
    baseTen -= baseTen
    print("your number in base %s is %s" % (outputBase, outputNumber))


if __name__ == '__main__':
    main()