# Source code for sortedcontainers.sorteddict

    """Sorted dictionary implementation.

    """

    from collections import Set, Sequence
    from collections import KeysView as AbstractKeysView
    from collections import ValuesView as AbstractValuesView
    from collections import ItemsView as AbstractItemsView
    from sys import hexversion

    from .sortedlist import SortedList, recursive_repr, SortedListWithKey
    from .sortedset import SortedSet

    NONE = object()

    class _IlocWrapper(object):
        "Positional indexing support for sorted dictionary objects."
        # pylint: disable=protected-access, too-few-public-methods
        def __init__(self, _dict):
            self._dict = _dict
        def __len__(self):
            return len(self._dict)
        def __getitem__(self, index):
            """
            Very efficiently return the key at index *index* in iteration. Supports
            negative indices and slice notation. Raises IndexError on invalid
            *index*.
            """
            return self._dict._list[index]
        def __delitem__(self, index):
            """
            Remove the ``sdict[sdict.iloc[index]]`` from *sdict*. Supports negative
            indices and slice notation. Raises IndexError on invalid *index*.
            """
            _dict = self._dict
            _list = _dict._list
            _delitem = _dict._delitem

            if isinstance(index, slice):
                keys = _list[index]
                del _list[index]
                for key in keys:
                    _delitem(key)
            else:
                key = _list[index]
                del _list[index]
                _delitem(key)

    class SortedDict(dict):
        """SortedDict provides the same methods as a dict.  Additionally, SortedDict
        efficiently maintains its keys in sorted order. Consequently, the keys
        method will return the keys in sorted order, the popitem method will remove
        the item with the highest key, etc.

        """
        def __init__(self, *args, **kwargs):
            """SortedDict provides the same methods as a dict.  Additionally, SortedDict
            efficiently maintains its keys in sorted order. Consequently, the keys
            method will return the keys in sorted order, the popitem method will
            remove the item with the highest key, etc.

            An optional *key* argument defines a callable that, like the `key`
            argument to Python's `sorted` function, extracts a comparison key from
            each dict key. If no function is specified, the default compares the
            dict keys directly. The `key` argument must be provided as a positional
            argument and must come before all other arguments.

            An optional *load* argument defines the load factor of the internal list
            used to maintain sort order. If present, this argument must come before
            an iterable. The default load factor of '1000' works well for lists from
            tens to tens of millions of elements.  Good practice is to use a value
            that is the cube root of the list size.  With billions of elements, the
            best load factor depends on your usage.  It's best to leave the load
            factor at the default until you start benchmarking.

            An optional *iterable* argument provides an initial series of items to
            populate the SortedDict.  Each item in the series must itself contain
            two items.  The first is used as a key in the new dictionary, and the
            second as the key's value. If a given key is seen more than once, the
            last value associated with it is retained in the new dictionary.

            If keyword arguments are given, the keywords themselves with their
            associated values are added as items to the dictionary. If a key is
            specified both in the positional argument and as a keyword argument, the
            value associated with the keyword is retained in the dictionary. For
            example, these all return a dictionary equal to ``{"one": 2, "two":
            3}``:

            * ``SortedDict(one=2, two=3)``
            * ``SortedDict({'one': 2, 'two': 3})``
            * ``SortedDict(zip(('one', 'two'), (2, 3)))``
            * ``SortedDict([['two', 3], ['one', 2]])``

            The first example only works for keys that are valid Python
            identifiers; the others work with any valid keys.

            """
            # pylint: disable=super-init-not-called, redefined-variable-type
            if len(args) > 0 and (args[0] is None or callable(args[0])):
                self._key = args[0]
                args = args[1:]
            else:
                self._key = None

            if len(args) > 0 and isinstance(args[0], int):
                self._load = args[0]
                args = args[1:]
            else:
                self._load = 1000

            if self._key is None:
                self._list = SortedList(load=self._load)
            else:
                self._list = SortedListWithKey(key=self._key, load=self._load)

            # Cache function pointers to dict methods.

            _dict = super(SortedDict, self)
            self._dict = _dict
            self._clear = _dict.clear
            self._delitem = _dict.__delitem__
            self._iter = _dict.__iter__
            self._pop = _dict.pop
            self._setdefault = _dict.setdefault
            self._setitem = _dict.__setitem__
            self._dict_update = _dict.update

            # Cache function pointers to SortedList methods.

            _list = self._list
            self._list_add = _list.add
            self.bisect_left = _list.bisect_left
            self.bisect = _list.bisect_right
            self.bisect_right = _list.bisect_right
            self._list_clear = _list.clear
            self.index = _list.index
            self._list_pop = _list.pop
            self._list_remove = _list.remove
            self._list_update = _list.update
            self.irange = _list.irange
            self.islice = _list.islice

            if self._key is not None:
                self.bisect_key_left = _list.bisect_key_left
                self.bisect_key_right = _list.bisect_key_right
                self.bisect_key = _list.bisect_key
                self.irange_key = _list.irange_key

            self.iloc = _IlocWrapper(self)

            self._update(*args, **kwargs)

        def clear(self):
            """Remove all elements from the dictionary."""
            self._clear()
            self._list_clear()

        def __delitem__(self, key):
            """
            Remove ``d[key]`` from *d*.  Raises a KeyError if *key* is not in the
            dictionary.
            """
            self._delitem(key)
            self._list_remove(key)

        def __iter__(self):
            """
            Return an iterator over the sorted keys of the dictionary.

            Iterating the Mapping while adding or deleting keys may raise a
            `RuntimeError` or fail to iterate over all entries.
            """
            return iter(self._list)

        def __reversed__(self):
            """
            Return a reversed iterator over the sorted keys of the dictionary.

            Iterating the Mapping while adding or deleting keys may raise a
            `RuntimeError` or fail to iterate over all entries.
            """
            return reversed(self._list)

        def __setitem__(self, key, value):
            """Set `d[key]` to *value*."""
            if key not in self:
                self._list_add(key)
            self._setitem(key, value)

        def copy(self):
            """Return a shallow copy of the sorted dictionary."""
            return self.__class__(self._key, self._load, self._iteritems())

        __copy__ = copy

        @classmethod
        def fromkeys(cls, seq, value=None):
            """
            Create a new dictionary with keys from *seq* and values set to *value*.
            """
            return cls((key, value) for key in seq)

        if hexversion < 0x03000000:
            def items(self):
                """
                Return a list of the dictionary's items (``(key, value)`` pairs).
                """
                return list(self._iteritems())
        else:
            def items(self):
                """
                Return a new ItemsView of the dictionary's items.  In addition to
                the methods provided by the built-in `view` the ItemsView is
                indexable (e.g. ``d.items()[5]``).
                """
                return ItemsView(self)

        def iteritems(self):
            """
            Return an iterator over the items (``(key, value)`` pairs).

            Iterating the Mapping while adding or deleting keys may raise a
            `RuntimeError` or fail to iterate over all entries.
            """
            return iter((key, self[key]) for key in self._list)

        _iteritems = iteritems

        if hexversion < 0x03000000:
            def keys(self):
                """Return a SortedSet of the dictionary's keys."""
                return SortedSet(self._list, key=self._key, load=self._load)
        else:
            def keys(self):
                """
                Return a new KeysView of the dictionary's keys.  In addition to the
                methods provided by the built-in `view` the KeysView is indexable
                (e.g. ``d.keys()[5]``).
                """
                return KeysView(self)

        def iterkeys(self):
            """
            Return an iterator over the sorted keys of the Mapping.

            Iterating the Mapping while adding or deleting keys may raise a
            `RuntimeError` or fail to iterate over all entries.
            """
            return iter(self._list)

        if hexversion < 0x03000000:
            def values(self):
                """Return a list of the dictionary's values."""
                return list(self._itervalues())
        else:
            def values(self):
                """
                Return a new :class:`ValuesView` of the dictionary's values.
                In addition to the methods provided by the built-in `view` the
                ValuesView is indexable (e.g., ``d.values()[5]``).
                """
                return ValuesView(self)

        def itervalues(self):
            """
            Return an iterator over the values of the Mapping.

            Iterating the Mapping while adding or deleting keys may raise a
            `RuntimeError` or fail to iterate over all entries.
            """
            return iter(self[key] for key in self._list)

        _itervalues = itervalues

        def pop(self, key, default=NONE):
            """
            If *key* is in the dictionary, remove it and return its value,
            else return *default*. If *default* is not given and *key* is not in
            the dictionary, a KeyError is raised.
            """
            if key in self:
                self._list_remove(key)
                return self._pop(key)
            else:
                if default is NONE:
                    raise KeyError(key)
                else:
                    return default

        def popitem(self, last=True):
            """
            Remove and return a ``(key, value)`` pair from the dictionary. If
            last=True (default) then remove the *greatest* `key` from the
            diciontary. Else, remove the *least* key from the dictionary.

            If the dictionary is empty, calling `popitem` raises a
            KeyError`.
            """
            if not len(self):
                raise KeyError('popitem(): dictionary is empty')

            key = self._list_pop(-1 if last else 0)
            value = self._pop(key)

            return (key, value)

        def peekitem(self, index=-1):
            """Return (key, value) item pair at index.

            Unlike ``popitem``, the sorted dictionary is not modified. Index
            defaults to -1, the last/greatest key in the dictionary. Specify
            ``index=0`` to lookup the first/least key in the dictiony.

            If index is out of range, raise IndexError.

            """
            key = self._list[index]
            return key, self[key]

        def setdefault(self, key, default=None):
            """
            If *key* is in the dictionary, return its value.  If not, insert *key*
            with a value of *default* and return *default*.  *default* defaults to
            ``None``.
            """
            if key in self:
                return self[key]
            else:
                self._setitem(key, default)
                self._list_add(key)
                return default

        def update(self, *args, **kwargs):
            """
            Update the dictionary with the key/value pairs from *other*, overwriting
            existing keys.

            *update* accepts either another dictionary object or an iterable of
            key/value pairs (as a tuple or other iterable of length two).  If
            keyword arguments are specified, the dictionary is then updated with
            those key/value pairs: ``d.update(red=1, blue=2)``.
            """
            if not len(self):
                self._dict_update(*args, **kwargs)
                self._list_update(self._iter())
                return

            if len(kwargs) == 0 and len(args) == 1 and isinstance(args[0], dict):
                pairs = args[0]
            else:
                pairs = dict(*args, **kwargs)

            if (10 * len(pairs)) > len(self):
                self._dict_update(pairs)
                self._list_clear()
                self._list_update(self._iter())
            else:
                for key in pairs:
                    self[key] = pairs[key]

        _update = update

        if hexversion >= 0x02070000:
            def viewkeys(self):
                "Return ``KeysView`` of dictionary keys."
                return KeysView(self)

            def viewvalues(self):
                "Return ``ValuesView`` of dictionary values."
                return ValuesView(self)

            def viewitems(self):
                "Return ``ItemsView`` of dictionary (key, value) item pairs."
                return ItemsView(self)

        def __reduce__(self):
            return (self.__class__, (self._key, self._load, list(self._iteritems())))

        @recursive_repr
        def __repr__(self):
            temp = '{0}({1}, {2}, {{{3}}})'
            items = ', '.join('{0}: {1}'.format(repr(key), repr(self[key]))
                              for key in self._list)
            return temp.format(
                self.__class__.__name__,
                repr(self._key),
                repr(self._load),
                items
            )

        def _check(self):
            # pylint: disable=protected-access
            self._list._check()
            assert len(self) == len(self._list)
            assert all(key in self for key in self._list)

    class KeysView(AbstractKeysView, Set, Sequence):
        """
        A KeysView object is a dynamic view of the dictionary's keys, which
        means that when the dictionary's keys change, the view reflects
        those changes.

        The KeysView class implements the Set and Sequence Abstract Base Classes.
        """
        if hexversion < 0x03000000:
            def __init__(self, sorted_dict):
                """
                Initialize a KeysView from a SortedDict container as *sorted_dict*.
                """
                # pylint: disable=super-init-not-called, protected-access
                self._list = sorted_dict._list
                self._view = sorted_dict._dict.viewkeys()
        else:
            def __init__(self, sorted_dict):
                """
                Initialize a KeysView from a SortedDict container as *sorted_dict*.
                """
                # pylint: disable=super-init-not-called, protected-access
                self._list = sorted_dict._list
                self._view = sorted_dict._dict.keys()
        def __len__(self):
            """Return the number of entries in the dictionary."""
            return len(self._view)
        def __contains__(self, key):
            """
            Return True if and only if *key* is one of the underlying dictionary's
            keys.
            """
            return key in self._view
        def __iter__(self):
            """
            Return an iterable over the keys in the dictionary. Keys are iterated
            over in their sorted order.

            Iterating views while adding or deleting entries in the dictionary may
            raise a `RuntimeError` or fail to iterate over all entries.
            """
            return iter(self._list)
        def __getitem__(self, index):
            """Return the key at position *index*."""
            return self._list[index]
        def __reversed__(self):
            """
            Return a reversed iterable over the keys in the dictionary. Keys are
            iterated over in their reverse sort order.

            Iterating views while adding or deleting entries in the dictionary may
            raise a RuntimeError or fail to iterate over all entries.
            """
            return reversed(self._list)
        def index(self, value, start=None, stop=None):
            """
            Return the smallest *k* such that `keysview[k] == value` and `start <= k
            < end`.  Raises `KeyError` if *value* is not present.  *stop* defaults
            to the end of the set.  *start* defaults to the beginning.  Negative
            indexes are supported, as for slice indices.
            """
            # pylint: disable=arguments-differ
            return self._list.index(value, start, stop)
        def count(self, value):
            """Return the number of occurrences of *value* in the set."""
            return 1 if value in self._view else 0
        def __eq__(self, that):
            """Test set-like equality with *that*."""
            return self._view == that
        def __ne__(self, that):
            """Test set-like inequality with *that*."""
            return self._view != that
        def __lt__(self, that):
            """Test whether self is a proper subset of *that*."""
            return self._view < that
        def __gt__(self, that):
            """Test whether self is a proper superset of *that*."""
            return self._view > that
        def __le__(self, that):
            """Test whether self is contained within *that*."""
            return self._view <= that
        def __ge__(self, that):
            """Test whether *that* is contained within self."""
            return self._view >= that
        def __and__(self, that):
            """Return a SortedSet of the intersection of self and *that*."""
            return SortedSet(self._view & that)
        def __or__(self, that):
            """Return a SortedSet of the union of self and *that*."""
            return SortedSet(self._view | that)
        def __sub__(self, that):
            """Return a SortedSet of the difference of self and *that*."""
            return SortedSet(self._view - that)
        def __xor__(self, that):
            """Return a SortedSet of the symmetric difference of self and *that*."""
            return SortedSet(self._view ^ that)
        if hexversion < 0x03000000:
            def isdisjoint(self, that):
                """Return True if and only if *that* is disjoint with self."""
                return not any(key in self._list for key in that)
        else:
            def isdisjoint(self, that):
                """Return True if and only if *that* is disjoint with self."""
                return self._view.isdisjoint(that)
        @recursive_repr
        def __repr__(self):
            return 'SortedDict_keys({0})'.format(repr(list(self)))

    class ValuesView(AbstractValuesView, Sequence):
        """
        A ValuesView object is a dynamic view of the dictionary's values, which
        means that when the dictionary's values change, the view reflects those
        changes.

        The ValuesView class implements the Sequence Abstract Base Class.
        """
        if hexversion < 0x03000000:
            def __init__(self, sorted_dict):
                """
                Initialize a ValuesView from a SortedDict container as
                *sorted_dict*.
                """
                # pylint: disable=super-init-not-called, protected-access
                self._dict = sorted_dict
                self._list = sorted_dict._list
                self._view = sorted_dict._dict.viewvalues()
        else:
            def __init__(self, sorted_dict):
                """
                Initialize a ValuesView from a SortedDict container as
                *sorted_dict*.
                """
                # pylint: disable=super-init-not-called, protected-access
                self._dict = sorted_dict
                self._list = sorted_dict._list
                self._view = sorted_dict._dict.values()
        def __len__(self):
            """Return the number of entries in the dictionary."""
            return len(self._dict)
        def __contains__(self, value):
            """
            Return True if and only if *value* is in the underlying Mapping's
            values.
            """
            return value in self._view
        def __iter__(self):
            """
            Return an iterator over the values in the dictionary.  Values are
            iterated over in sorted order of the keys.

            Iterating views while adding or deleting entries in the dictionary may
            raise a `RuntimeError` or fail to iterate over all entries.
            """
            _dict = self._dict
            return iter(_dict[key] for key in self._list)
        def __getitem__(self, index):
            """
            Efficiently return value at *index* in iteration.

            Supports slice notation and negative indexes.
            """
            _dict, _list = self._dict, self._list
            if isinstance(index, slice):
                return [_dict[key] for key in _list[index]]
            else:
                return _dict[_list[index]]
        def __reversed__(self):
            """
            Return a reverse iterator over the values in the dictionary.  Values are
            iterated over in reverse sort order of the keys.

            Iterating views while adding or deleting entries in the dictionary may
            raise a `RuntimeError` or fail to iterate over all entries.
            """
            _dict = self._dict
            return iter(_dict[key] for key in reversed(self._list))
        def index(self, value):
            """
            Return index of *value* in self.

            Raises ValueError if *value* is not found.
            """
            for idx, val in enumerate(self):
                if value == val:
                    return idx
            raise ValueError('{0} is not in dict'.format(repr(value)))
        if hexversion < 0x03000000:
            def count(self, value):
                """Return the number of occurrences of *value* in self."""
                return sum(1 for val in self._dict.itervalues() if val == value)
        else:
            def count(self, value):
                """Return the number of occurrences of *value* in self."""
                return sum(1 for val in self._dict.values() if val == value)
        def __lt__(self, that):
            raise TypeError
        def __gt__(self, that):
            raise TypeError
        def __le__(self, that):
            raise TypeError
        def __ge__(self, that):
            raise TypeError
        def __and__(self, that):
            raise TypeError
        def __or__(self, that):
            raise TypeError
        def __sub__(self, that):
            raise TypeError
        def __xor__(self, that):
            raise TypeError
        @recursive_repr
        def __repr__(self):
            return 'SortedDict_values({0})'.format(repr(list(self)))

    class ItemsView(AbstractItemsView, Set, Sequence):
        """
        An ItemsView object is a dynamic view of the dictionary's ``(key,
        value)`` pairs, which means that when the dictionary changes, the
        view reflects those changes.

        The ItemsView class implements the Set and Sequence Abstract Base Classes.
        However, the set-like operations (``&``, ``|``, ``-``, ``^``) will only
        operate correctly if all of the dictionary's values are hashable.
        """
        if hexversion < 0x03000000:
            def __init__(self, sorted_dict):
                """
                Initialize an ItemsView from a SortedDict container as
                *sorted_dict*.
                """
                # pylint: disable=super-init-not-called, protected-access
                self._dict = sorted_dict
                self._list = sorted_dict._list
                self._view = sorted_dict._dict.viewitems()
        else:
            def __init__(self, sorted_dict):
                """
                Initialize an ItemsView from a SortedDict container as
                *sorted_dict*.
                """
                # pylint: disable=super-init-not-called, protected-access
                self._dict = sorted_dict
                self._list = sorted_dict._list
                self._view = sorted_dict._dict.items()
        def __len__(self):
            """Return the number of entries in the dictionary."""
            return len(self._view)
        def __contains__(self, key):
            """
            Return True if and only if *key* is one of the underlying dictionary's
            items.
            """
            return key in self._view
        def __iter__(self):
            """
            Return an iterable over the items in the dictionary. Items are iterated
            over in their sorted order.

            Iterating views while adding or deleting entries in the dictionary may
            raise a `RuntimeError` or fail to iterate over all entries.
            """
            _dict = self._dict
            return iter((key, _dict[key]) for key in self._list)
        def __getitem__(self, index):
            """Return the item as position *index*."""
            _dict, _list = self._dict, self._list
            if isinstance(index, slice):
                return [(key, _dict[key]) for key in _list[index]]
            else:
                key = _list[index]
                return (key, _dict[key])
        def __reversed__(self):
            """
            Return a reversed iterable over the items in the dictionary. Items are
            iterated over in their reverse sort order.

            Iterating views while adding or deleting entries in the dictionary may
            raise a RuntimeError or fail to iterate over all entries.
            """
            _dict = self._dict
            return iter((key, _dict[key]) for key in reversed(self._list))
        def index(self, key, start=None, stop=None):
            """
            Return the smallest *k* such that `itemssview[k] == key` and `start <= k
            < end`.  Raises `KeyError` if *key* is not present.  *stop* defaults
            to the end of the set.  *start* defaults to the beginning.  Negative
            indexes are supported, as for slice indices.
            """
            # pylint: disable=arguments-differ
            temp, value = key
            pos = self._list.index(temp, start, stop)
            if value == self._dict[temp]:
                return pos
            else:
                raise ValueError('{0} is not in dict'.format(repr(key)))
        def count(self, item):
            """Return the number of occurrences of *item* in the set."""
            key, value = item
            return 1 if key in self._dict and self._dict[key] == value else 0
        def __eq__(self, that):
            """Test set-like equality with *that*."""
            return self._view == that
        def __ne__(self, that):
            """Test set-like inequality with *that*."""
            return self._view != that
        def __lt__(self, that):
            """Test whether self is a proper subset of *that*."""
            return self._view < that
        def __gt__(self, that):
            """Test whether self is a proper superset of *that*."""
            return self._view > that
        def __le__(self, that):
            """Test whether self is contained within *that*."""
            return self._view <= that
        def __ge__(self, that):
            """Test whether *that* is contained within self."""
            return self._view >= that
        def __and__(self, that):
            """Return a SortedSet of the intersection of self and *that*."""
            return SortedSet(self._view & that)
        def __or__(self, that):
            """Return a SortedSet of the union of self and *that*."""
            return SortedSet(self._view | that)
        def __sub__(self, that):
            """Return a SortedSet of the difference of self and *that*."""
            return SortedSet(self._view - that)
        def __xor__(self, that):
            """Return a SortedSet of the symmetric difference of self and *that*."""
            return SortedSet(self._view ^ that)
        if hexversion < 0x03000000:
            def isdisjoint(self, that):
                """Return True if and only if *that* is disjoint with self."""
                _dict = self._dict
                for key, value in that:
                    if key in _dict and _dict[key] == value:
                        return False
                return True
        else:
            def isdisjoint(self, that):
                """Return True if and only if *that* is disjoint with self."""
                return self._view.isdisjoint(that)
        @recursive_repr
        def __repr__(self):
            return 'SortedDict_items({0})'.format(repr(list(self)))