def __init__(self, data=None, files=None, auto_id='id_%s', prefix=None,
             initial=None, error_class=ErrorList, label_suffix=None,
             empty_permitted=False):
    self.is_bound = data is not None or files is not None
    self.data = data or {}
    self.files = files or {}
    self.auto_id = auto_id
    self.prefix = prefix
    self.initial = initial or {}
    self.error_class = error_class
    # Translators: This is the default suffix added to form field labels
    self.label_suffix = label_suffix if label_suffix is not None else _(':')
    self.empty_permitted = empty_permitted
    self._errors = None # Stores the errors after clean() has been called.
    self._changed_data = None
    # The base_fields class attribute is the *class-wide* definition of
    # fields. Because a particular *instance* of the class might want to
    # alter self.fields, we create self.fields here by copying base_fields.
    # Instances should always modify self.fields; they should not modify
    # self.base_fields.
    self.fields = copy.deepcopy(self.base_fields)

def add_initial_prefix(self, field_name):
    """
    Add a 'initial' prefix for checking dynamic initial values
    """
    return 'initial-%s' % self.add_prefix(field_name)

def add_prefix(self, field_name):
    """
    Returns the field name with a prefix appended, if this Form has a
    prefix set.
    Subclasses may wish to override.
    """
    return '%s-%s' % (self.prefix, field_name) if self.prefix else field_name

def as_p(self):
    "Returns this form rendered as HTML <p>s."
    return self._html_output(
        normal_row = '<p%(html_class_attr)s>%(label)s %(field)s%(help_text)s</p>',
        error_row = '%s',
        row_ender = '</p>',
        help_text_html = ' <span class="helptext">%s</span>',
        errors_on_separate_row = True)

def as_table(self):
    "Returns this form rendered as HTML <tr>s -- excluding the <table></table>."
    return self._html_output(
        normal_row = '<tr%(html_class_attr)s><th>%(label)s</th><td>%(errors)s%(field)s%(help_text)s</td></tr>',
        error_row = '<tr><td colspan="2">%s</td></tr>',
        row_ender = '</td></tr>',
        help_text_html = '<br /><span class="helptext">%s</span>',
        errors_on_separate_row = False)

def as_ul(self):
    "Returns this form rendered as HTML <li>s -- excluding the <ul></ul>."
    return self._html_output(
        normal_row = '<li%(html_class_attr)s>%(errors)s%(label)s %(field)s%(help_text)s</li>',
        error_row = '<li>%s</li>',
        row_ender = '</li>',
        help_text_html = ' <span class="helptext">%s</span>',
        errors_on_separate_row = False)

def clean(self):
    """
    Hook for doing any extra form-wide cleaning after Field.clean() been
    called on every field. Any ValidationError raised by this method will
    not be associated with a particular field; it will have a special-case
    association with the field named '__all__'.
    """
    return self.cleaned_data

def full_clean(self):
    """
    Cleans all of self.data and populates self._errors and
    self.cleaned_data.
    """
    self._errors = ErrorDict()
    if not self.is_bound: # Stop further processing.
        return
    self.cleaned_data = {}
    # If the form is permitted to be empty, and none of the form data has
    # changed from the initial data, short circuit any validation.
    if self.empty_permitted and not self.has_changed():
        return
    self._clean_fields()
    self._clean_form()
    self._post_clean()

def get_brackets(dir):
    list = []
    for i in range(4):
        brackets = ""
        for j in range(i):
            if dir=="left":
                brackets+="( "
            elif dir=="right":
                brackets+=") "
        list.append((brackets,brackets))
    return list

def has_changed(self):
    """
    Returns True if data differs from initial.
    """
    return bool(self.changed_data)

def hidden_fields(self):
    """
    Returns a list of all the BoundField objects that are hidden fields.
    Useful for manual form layout in templates.
    """
    return [field for field in self if field.is_hidden]

def is_multipart(self):
    """
    Returns True if the form needs to be multipart-encoded, i.e. it has
    FileInput. Otherwise, False.
    """
    for field in self.fields.values():
        if field.widget.needs_multipart_form:
            return True
    return False

def is_valid(self):
    """
    Returns True if the form has no errors. Otherwise, False. If errors are
    being ignored, returns False.
    """
    return self.is_bound and not bool(self.errors)

def non_field_errors(self):
    """
    Returns an ErrorList of errors that aren't associated with a particular
    field -- i.e., from Form.clean(). Returns an empty ErrorList if there
    are none.
    """
    return self.errors.get(NON_FIELD_ERRORS, self.error_class())

def visible_fields(self):
    """
    Returns a list of BoundField objects that aren't hidden fields.
    The opposite of the hidden_fields() method.
    """
    return [field for field in self if not field.is_hidden]