from math import sqrt                                 # needed for computing distances

class Point:
  
    def __init__(self, dimension, coords=None):
        if coords is None:
            self._coords = [0] * dimension     # all zeros
        else:
            self._coords = list(coords)

    def __getitem__(self, index):
        return self._coords[index]

    def __setitem__(self, index, value):
        self._coords[index] = value
      
    def __len__(self):
        return len(self._coords)
      
    def distance(self, other):
        total = 0
        for k in range(len(self._coords)):
            d = self._coords[k] - other._coords[k]
            total += d*d
        return sqrt(total)

    def normalize(self):
        mag = self.distance( Point(len(self._coords)) )
        if mag > 0:
            self.scale(1/mag)

    def __str__(self):
        return '< ' + ','.join([str(c) for c in self._coords]) + ' >'

    def __mul__(self, operand):
        dim = len(self._coords)
        if isinstance(operand, (int,float)):                      # multiply by constant
            duplicate = Point(dim, self._coords)
            duplicate.scale(operand)
            return duplicate
        elif isinstance(operand, Point):                          # dot product
            return sum([self._coords[k] * operand._coords[k] for k in range(dim)])

    def __rmul__(self, operand):
        return self * operand

    #----------- your part follows ------------

    def scale(self, factor):
        # not yet implemented...
        pass

    def __add__(self, other):
        # not yet implemented
        pass