class Currency:
    """ allows calculations with a currency where the main unit
        is divided into hundredths. """
    symbol = 'US$'
    def __init__(self, dollars, cents):
        if dollars >= 0:
            self.value = dollars*100+cents
        else:
            self.value = dollars*100-cents
    def __str__(self):
        if self.value > 0:
            return "{:s}{:d}.{:02d}".format(Currency.symbol,self.value//100, self.value%100)
        else:
            val = -self.value
            return "-{:s}{:d}.{:02d}".format(Currency.symbol,val//100, val%100)
    def __eq__(self, other):
        return self.value == other.value
    def __lt__(self, other):
        return self.value < other.value
    def __rmul__(self, factor):
        """we assume that factor is a floating point number """
        value = round(self.value*factor)
        return Currency(value//100, value%100)
    def change_symbol(new_symbol):
        Currency.symbol = new_symbol