def total_ordering(cls):
    """Class decorator that fills in missing ordering methods"""
    convert = {'__lt__': [('__gt__', lambda self, other: not (self < other or
        self == other)), ('__le__', lambda self, other: self < other or 
        self == other), ('__ge__', lambda self, other: not self < other)],
        '__le__': [('__ge__', lambda self, other: not self <= other or self ==
        other), ('__lt__', lambda self, other: self <= other and not self ==
        other), ('__gt__', lambda self, other: not self <= other)],
        '__gt__': [('__lt__', lambda self, other: not (self > other or self ==
        other)), ('__ge__', lambda self, other: self > other or self ==
        other), ('__le__', lambda self, other: not self > other)], '__ge__':
        [('__le__', lambda self, other: not self >= other or self == other),
        ('__gt__', lambda self, other: self >= other and not self == other),
        ('__lt__', lambda self, other: not self >= other)]}
    roots = set(dir(cls)) & set(convert)
    if not roots:
        raise ValueError(
            'must define at least one ordering operation: < > <= >=')
    root = max(roots)
    for opname, opfunc in convert[root]:
        if opname not in roots:
            opfunc.__name__ = opname
            opfunc.__doc__ = getattr(int, opname).__doc__
            setattr(cls, opname, opfunc)
    return cls
