LOGICAL = "logical"
PHYSICAL = "physical"

class Point:
    def __init__(self, x=0, y=0, t=None):
        assert t is None or \
               t == LOGICAL or \
               t == PHYSICAL
        self.x = x
        self.y = y
        self.type = t

    def offset(self, x, y, t=None):
        return Point(self.x + x, self.y + y, t)

    def copy(self):
        return Point(self.x, self.y, self.type)

    def __cmp__(self, other):
        assert self.type == other.type or \
               self.type is None or \
               other.type is None
        c = cmp(self.y, other.y)
        if c == 0:
            return cmp(self.x, other.x)
        else:
            return c

    def __add__(self, other):
        assert self.type == other.type or \
               self.type is None or \
               other.type is None
        return Point(self.x + other.x,
                     self.y + other.y)
    def __iadd__(self, other):
        assert self.type == other.type or \
               self.type is None or \
               other.type is None
        x = other.x
        y = other.y
        self.x += x
        self.y += y

    def __sub__(self, other):
        assert self.type == other.type or \
               self.type is None or \
               other.type is None
        return Point(self.x - other.x,
                     self.y - other.y)
    def __isub__(self, other):
        assert self.type == other.type or \
               self.type is None or \
               other.type is None
        x = other.x
        y = other.y
        self.x -= x
        self.y -= y

    def __abs__(self):
        return Point(abs(self.x), abs(self.y))

    def __repr__(self):
        if self.type is None:
            return "Point(%d, %d)" % (self.x, self.y)
        else:
            return "Point(%s:%d, %d)" % (self.type[0], self.x, self.y)