[ovs-dev,v2] Add multi-column index support for the Python IDL

Message ID 1523579067-19457-1-git-send-email-twilson@redhat.com
State Accepted
Headers show
Series
  • [ovs-dev,v2] Add multi-column index support for the Python IDL
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Commit Message

Terry Wilson April 13, 2018, 12:24 a.m.
From: Terry Wilson <twilson@redhat.com>

This adds multi-column index support for the Python IDL that is
similar to the feature in the C IDL. Since it adds sortedcontainers
as a dependency and some distros don't yet package it, the library
is copied in-tree and used if sortedcontainers is not installed.

Signed-off-by: Terry Wilson <twilson@redhat.com>
---
 python/automake.mk                               |    8 +-
 python/ovs/compat/__init__.py                    |    0
 python/ovs/compat/sortedcontainers/LICENSE       |   13 +
 python/ovs/compat/sortedcontainers/__init__.py   |   52 +
 python/ovs/compat/sortedcontainers/sorteddict.py |  741 +++++++
 python/ovs/compat/sortedcontainers/sortedlist.py | 2508 ++++++++++++++++++++++
 python/ovs/compat/sortedcontainers/sortedset.py  |  327 +++
 python/ovs/db/custom_index.py                    |  154 ++
 python/ovs/db/idl.py                             |   55 +-
 python/setup.py                                  |    1 +
 tests/test-ovsdb.py                              |    7 +-
 11 files changed, 3850 insertions(+), 16 deletions(-)
 create mode 100644 python/ovs/compat/__init__.py
 create mode 100644 python/ovs/compat/sortedcontainers/LICENSE
 create mode 100644 python/ovs/compat/sortedcontainers/__init__.py
 create mode 100644 python/ovs/compat/sortedcontainers/sorteddict.py
 create mode 100644 python/ovs/compat/sortedcontainers/sortedlist.py
 create mode 100644 python/ovs/compat/sortedcontainers/sortedset.py
 create mode 100644 python/ovs/db/custom_index.py

Comments

Terry Wilson April 13, 2018, 3:27 p.m. | #1
One could argue that if if distro packaging is the issue, then distros
could patch in the simple try/except ImportError and add the
sortedcontainer code like I did above. But, if this works for the ovs
team and distro folks, I'm happy with it.

Terry
Ben Pfaff April 13, 2018, 5:52 p.m. | #2
On Fri, Apr 13, 2018 at 10:27:03AM -0500, Terry Wilson wrote:
> One could argue that if if distro packaging is the issue, then distros
> could patch in the simple try/except ImportError and add the
> sortedcontainer code like I did above. 

I'm quite sympathetic to that viewpoint--I think that OVS currently has
far too much distro-specific stuff in it.  In the long run I'd like to
drop the Debian and Red Hat and XenServer packaging from the tree.  As a
Debian developer myself, I know that it's not actually helpful for
upstream to provide packaging.

> But, if this works for the ovs team and distro folks, I'm happy with
> it.

Seems OK for now.
Raymond Burkholder April 14, 2018, 3:19 p.m. | #3
On 04/13/2018 02:52 PM, Ben Pfaff wrote:
> On Fri, Apr 13, 2018 at 10:27:03AM -0500, Terry Wilson wrote:
>> One could argue that if if distro packaging is the issue, then distros
>> could patch in the simple try/except ImportError and add the
>> sortedcontainer code like I did above.
> 
> I'm quite sympathetic to that viewpoint--I think that OVS currently has
> far too much distro-specific stuff in it.  In the long run I'd like to
> drop the Debian and Red Hat and XenServer packaging from the tree.  As a

How would it work then, if, ..  I enjoy the fact that I can run Master, 
use the tools in the tree to build my Debian packages, and then install 
those packages on the machines where they need to be?

> Debian developer myself, I know that it's not actually helpful for
> upstream to provide packaging.

And if by upstream, you mean the distribution?  They can be quite behind 
at times.  Debian Stretch has 2.6, and nothing in Stretch-Backports. 
Buster does have 2.8 at the moment, but Buster can be very unstable for 
consistently building environments on demand.

>
Ben Pfaff April 17, 2018, 9:19 p.m. | #4
On Sat, Apr 14, 2018 at 12:19:02PM -0300, Raymond Burkholder wrote:
> On 04/13/2018 02:52 PM, Ben Pfaff wrote:
> >On Fri, Apr 13, 2018 at 10:27:03AM -0500, Terry Wilson wrote:
> >>One could argue that if if distro packaging is the issue, then distros
> >>could patch in the simple try/except ImportError and add the
> >>sortedcontainer code like I did above.
> >
> >I'm quite sympathetic to that viewpoint--I think that OVS currently has
> >far too much distro-specific stuff in it.  In the long run I'd like to
> >drop the Debian and Red Hat and XenServer packaging from the tree.  As a
> 
> How would it work then, if, ..  I enjoy the fact that I can run Master, use
> the tools in the tree to build my Debian packages, and then install those
> packages on the machines where they need to be?
> 
> >Debian developer myself, I know that it's not actually helpful for
> >upstream to provide packaging.
> 
> And if by upstream, you mean the distribution?  They can be quite behind at
> times.  Debian Stretch has 2.6, and nothing in Stretch-Backports. Buster
> does have 2.8 at the moment, but Buster can be very unstable for
> consistently building environments on demand.

In this case, by "upstream" I mean OVS developers and by "downstream" I
mean a distribution such as Debian or Red Hat.

There's a couple of things going on here.

One is that I think there is much less pressure than usual on downstream
to keep OVS packaging up-to-date because we maintain packaging
upstream.  I think that if OVS upstream stopped shipping packaging,
downstreams would eventually adapt by updating packaging more
frequently.

Also, I suspect that most users run from a release or at least a release
branch.  On a release branch, usually the packaging changes little, or
at least the packaging changes due to OVS changes are minimal, since OVS
itself doesn't change much on release branches.

I currently have a selfish reason to keep packaging in the tree, which
is that VMware internally uses both the .deb and .rpm packaging as part
of its internal processes (and releases to customers).  We're working on
getting together and contributing to OVS a container build and making
that what we use internally and provide to customers.  So I have
motivation to make sure that the containerization is good quality too,
since otherwise customers will be unhappy.  (At that point, I'll be
happy to transition to emeritus status as a Debian developer, since
being able to directly contribute to OVS downstream packaging--which I
do badly--is about the only reason I stick around there after 20+
years.)

So, if we do manage to get rid of packaging, it'll only be because
there's an acceptable alternative.  Your options will basically be:

* Use the containers, for any branch or master.  We might even publish
  binaries, dunno yet.  You can be sure they'll be pretty good since
  we'll actually use them too.

* Use packaging from your favored distro, for some release branch.

* Help out downstream with keeping the packaging up-to-date with master
  (or be patient and wait for other downstream folks to do the same).
Ben Pfaff April 17, 2018, 9:54 p.m. | #5
On Thu, Apr 12, 2018 at 07:24:27PM -0500, twilson@redhat.com wrote:
> From: Terry Wilson <twilson@redhat.com>
> 
> This adds multi-column index support for the Python IDL that is
> similar to the feature in the C IDL. Since it adds sortedcontainers
> as a dependency and some distros don't yet package it, the library
> is copied in-tree and used if sortedcontainers is not installed.
> 
> Signed-off-by: Terry Wilson <twilson@redhat.com>

Thank you!

flake8 complained bitterly about some of the new files, so I folded in
the following, and applied this to master.

Thanks again,

Ben.

--8<--------------------------cut here-------------------------->8--

diff --git a/python/automake.mk b/python/automake.mk
index 458a2c3d20b4..5a1e1da8a79a 100644
--- a/python/automake.mk
+++ b/python/automake.mk
@@ -63,7 +63,7 @@ EXTRA_DIST += $(PYFILES)
 PYCOV_CLEAN_FILES += $(PYFILES:.py=.py,cover)
 
 FLAKE8_PYFILES += \
-	$(filter-out python/ovs/dirs.py,$(PYFILES)) \
+	$(filter-out python/ovs/compat/% python/ovs/dirs.py,$(PYFILES)) \
 	python/setup.py \
 	python/build/__init__.py \
 	python/build/nroff.py \
Raymond Burkholder April 19, 2018, 12:18 a.m. | #6
On 04/17/2018 06:19 PM, Ben Pfaff wrote:
> On Sat, Apr 14, 2018 at 12:19:02PM -0300, Raymond Burkholder wrote:
>> On 04/13/2018 02:52 PM, Ben Pfaff wrote:
>>>
>>> I'm quite sympathetic to that viewpoint--I think that OVS currently has
>>> far too much distro-specific stuff in it.  In the long run I'd like to
>>> drop the Debian and Red Hat and XenServer packaging from the tree.  As a
>>
>> How would it work then, if, ..  I enjoy the fact that I can run Master, use
>> the tools in the tree to build my Debian packages, and then install those
>> packages on the machines where they need to be?
>>
>>> Debian developer myself, I know that it's not actually helpful for
>>> upstream to provide packaging.

Ok, I got things backwards in my older comments, based upon your 
upstream/downstream definitions further down.

Are you saying that Debian maintainers for the actual distribution 
maintenance 'throw out' your packaging, and have their own packaging? 
Wouldn't they use the tooling your provide?

>>
>> And if by upstream, you mean the distribution?  They can be quite behind at
>> times.  Debian Stretch has 2.6, and nothing in Stretch-Backports. Buster
>> does have 2.8 at the moment, but Buster can be very unstable for
>> consistently building environments on demand.
> 
> In this case, by "upstream" I mean OVS developers and by "downstream" I
> mean a distribution such as Debian or Red Hat.

ok, got it.

> 
> There's a couple of things going on here.
> 
> One is that I think there is much less pressure than usual on downstream
> to keep OVS packaging up-to-date because we maintain packaging
> upstream.  I think that if OVS upstream stopped shipping packaging,
> downstreams would eventually adapt by updating packaging more
> frequently.

But wouldn't your packaging provide good hints on what needs to be 
performed downstream?  open vswitch does have a complicated built based 
upon the dkms modules, et.al.

> 
> Also, I suspect that most users run from a release or at least a release
> branch.  On a release branch, usually the packaging changes little, or
> at least the packaging changes due to OVS changes are minimal, since OVS
> itself doesn't change much on release branches.

I guess I couldn't be counted in the 'most' category.  Have you had 
private feedback?  I don't think I've seen any other feedback messages 
for this topic on this mailing list.

> 
> I currently have a selfish reason to keep packaging in the tree, which
> is that VMware internally uses both the .deb and .rpm packaging as part
> of its internal processes (and releases to customers).  We're working on

I thank you for that, and I whole-heartedly hope you continue to offer 
the debian packaging in the tree.

> getting together and contributing to OVS a container build and making
> that what we use internally and provide to customers.  So I have
> motivation to make sure that the containerization is good quality too,
> since otherwise customers will be unhappy.  (At that point, I'll be
> happy to transition to emeritus status as a Debian developer, since
> being able to directly contribute to OVS downstream packaging--which I
> do badly--is about the only reason I stick around there after 20+

one person's 'badly' is still way-much better than not having it all, 
'specially with the complicated build.

Sorry, if I am laying it on too thick.

> years.)
> 
> So, if we do manage to get rid of packaging, it'll only be because
> there's an acceptable alternative.  Your options will basically be:
> 
> * Use the containers, for any branch or master.  We might even publish
>    binaries, dunno yet.  You can be sure they'll be pretty good since
>    we'll actually use them too.

containers wouldn't really do for me.  Wouldn't they be more complex to 
build anyway?  and are you talking docker, lxc, core, .... ?

My builds, at minimum, incorporate openvswitch, frr, .. plus a bunch of 
other choice packages to build an appropriate platform.  shoe-horning my 
additional stuff into a container doesn't seem quite right.

If it matters at all, I use SaltStack to build assemble the packages and 
configurations for the varied appliances (physical, virtual, and 
containerized) I customize.  So packages are a perfect fit.

And your Master branch seems to be relatively stable, knock on wood, so 
running that seems to work out.

> 
> * Use packaging from your favored distro, for some release branch.

is possible, but as I mentioned earlier, they could be a number of 
versions behind, even in 'testing' flavours

> 
> * Help out downstream with keeping the packaging up-to-date with master

Yes!!

>    (or be patient and wait for other downstream folks to do the same).
>

Patch

diff --git a/python/automake.mk b/python/automake.mk
index 9b5d3d8..458a2c3 100644
--- a/python/automake.mk
+++ b/python/automake.mk
@@ -10,9 +10,15 @@  ovstest_pyfiles = \
 
 ovs_pyfiles = \
 	python/ovs/__init__.py \
+	python/ovs/compat/__init__.py \
+	python/ovs/compat/sortedcontainers/__init__.py \
+	python/ovs/compat/sortedcontainers/sortedlist.py \
+	python/ovs/compat/sortedcontainers/sorteddict.py \
+	python/ovs/compat/sortedcontainers/sortedset.py \
 	python/ovs/daemon.py \
 	python/ovs/fcntl_win.py \
 	python/ovs/db/__init__.py \
+	python/ovs/db/custom_index.py \
 	python/ovs/db/data.py \
 	python/ovs/db/error.py \
 	python/ovs/db/idl.py \
@@ -36,7 +42,6 @@  ovs_pyfiles = \
 	python/ovs/version.py \
 	python/ovs/vlog.py \
 	python/ovs/winutils.py
-
 # These python files are used at build time but not runtime,
 # so they are not installed.
 EXTRA_DIST += \
@@ -46,6 +51,7 @@  EXTRA_DIST += \
 
 # PyPI support.
 EXTRA_DIST += \
+	python/ovs/compat/sortedcontainers/LICENSE \
 	python/README.rst \
 	python/setup.py
 
diff --git a/python/ovs/compat/__init__.py b/python/ovs/compat/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/python/ovs/compat/sortedcontainers/LICENSE b/python/ovs/compat/sortedcontainers/LICENSE
new file mode 100644
index 0000000..8794014
--- /dev/null
+++ b/python/ovs/compat/sortedcontainers/LICENSE
@@ -0,0 +1,13 @@ 
+Copyright 2014-2016 Grant Jenks
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
diff --git a/python/ovs/compat/sortedcontainers/__init__.py b/python/ovs/compat/sortedcontainers/__init__.py
new file mode 100644
index 0000000..392adfa
--- /dev/null
+++ b/python/ovs/compat/sortedcontainers/__init__.py
@@ -0,0 +1,52 @@ 
+"""Sorted Container Types: SortedList, SortedDict, SortedSet
+
+SortedContainers is an Apache2 licensed containers library, written in
+pure-Python, and fast as C-extensions.
+
+
+Python's standard library is great until you need a sorted collections
+type. Many will attest that you can get really far without one, but the moment
+you **really need** a sorted list, dict, or set, you're faced with a dozen
+different implementations, most using C-extensions without great documentation
+and benchmarking.
+
+In Python, we can do better. And we can do it in pure-Python!
+
+::
+
+    >>> from sortedcontainers import SortedList, SortedDict, SortedSet
+    >>> sl = SortedList(xrange(10000000))
+    >>> 1234567 in sl
+    True
+    >>> sl[7654321]
+    7654321
+    >>> sl.add(1234567)
+    >>> sl.count(1234567)
+    2
+    >>> sl *= 3
+    >>> len(sl)
+    30000003
+
+SortedContainers takes all of the work out of Python sorted types - making your
+deployment and use of Python easy. There's no need to install a C compiler or
+pre-build and distribute custom extensions. Performance is a feature and
+testing has 100% coverage with unit tests and hours of stress.
+
+:copyright: (c) 2016 by Grant Jenks.
+:license: Apache 2.0, see LICENSE for more details.
+
+"""
+
+
+from .sortedlist import SortedList, SortedListWithKey
+from .sortedset import SortedSet
+from .sorteddict import SortedDict
+
+__all__ = ['SortedList', 'SortedSet', 'SortedDict', 'SortedListWithKey']
+
+__title__ = 'sortedcontainers'
+__version__ = '1.5.9'
+__build__ = 0x010509
+__author__ = 'Grant Jenks'
+__license__ = 'Apache 2.0'
+__copyright__ = 'Copyright 2016 Grant Jenks'
diff --git a/python/ovs/compat/sortedcontainers/sorteddict.py b/python/ovs/compat/sortedcontainers/sorteddict.py
new file mode 100644
index 0000000..5d425fe
--- /dev/null
+++ b/python/ovs/compat/sortedcontainers/sorteddict.py
@@ -0,0 +1,741 @@ 
+"""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 *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
+        if args and (args[0] is None or callable(args[0])):
+            self._key = args[0]
+            args = args[1:]
+        else:
+            self._key = None
+
+        if self._key is None:
+            self._list = SortedList()
+        else:
+            self._list = SortedListWithKey(key=self._key)
+
+        # 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
+        self._reset = _list._reset  # pylint: disable=protected-access
+
+        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)
+
+    @property
+    def key(self):
+        """Key function used to extract comparison key for sorting."""
+        return self._key
+
+    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._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)
+    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 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]
+
+        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 self:
+            self._dict_update(*args, **kwargs)
+            self._list_update(self._iter())
+            return
+
+        if not kwargs 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, list(self._iteritems())))
+
+    @recursive_repr
+    def __repr__(self):
+        _key = self._key
+        name = type(self).__name__
+        key = '' if _key is None else '{0!r}, '.format(_key)
+        func = '{0!r}: {1!r}'.format
+        items = ', '.join(func(key, self[key]) for key in self._list)
+        return '{0}({1}{{{2}}})'.format(name, key, 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.
+    """
+    # pylint: disable=too-many-ancestors
+    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."""
+            # pylint: disable=arguments-differ
+            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."""
+            # pylint: disable=arguments-differ
+            return self._view.isdisjoint(that)
+    @recursive_repr
+    def __repr__(self):
+        return 'SortedDict_keys({0!r})'.format(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.
+    """
+    # pylint: disable=too-many-ancestors
+    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]]
+        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.
+        """
+        # pylint: disable=arguments-differ
+        for idx, val in enumerate(self):
+            if value == val:
+                return idx
+        raise ValueError('{0!r} is not in dict'.format(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!r})'.format(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.
+    """
+    # pylint: disable=too-many-ancestors
+    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]]
+        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!r} is not in dict'.format(key))
+    def count(self, item):
+        """Return the number of occurrences of *item* in the set."""
+        # pylint: disable=arguments-differ
+        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."""
+            # pylint: disable=arguments-differ
+            _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."""
+            # pylint: disable=arguments-differ
+            return self._view.isdisjoint(that)
+    @recursive_repr
+    def __repr__(self):
+        return 'SortedDict_items({0!r})'.format(list(self))
diff --git a/python/ovs/compat/sortedcontainers/sortedlist.py b/python/ovs/compat/sortedcontainers/sortedlist.py
new file mode 100644
index 0000000..8aec6bb
--- /dev/null
+++ b/python/ovs/compat/sortedcontainers/sortedlist.py
@@ -0,0 +1,2508 @@ 
+"""Sorted list implementation.
+
+"""
+# pylint: disable=redefined-builtin, ungrouped-imports
+
+from __future__ import print_function
+
+from bisect import bisect_left, bisect_right, insort
+from collections import Sequence, MutableSequence
+from functools import wraps
+from itertools import chain, repeat, starmap
+from math import log as log_e
+import operator as op
+from operator import iadd, add
+from sys import hexversion
+
+if hexversion < 0x03000000:
+    from itertools import izip as zip  # pylint: disable=no-name-in-module
+    from itertools import imap as map  # pylint: disable=no-name-in-module
+    try:
+        from thread import get_ident
+    except ImportError:
+        from dummy_thread import get_ident
+else:
+    from functools import reduce
+    try:
+        from _thread import get_ident
+    except ImportError:
+        from _dummy_thread import get_ident # pylint: disable=import-error
+
+LOAD = 1000
+
+def recursive_repr(func):
+    """Decorator to prevent infinite repr recursion."""
+    repr_running = set()
+
+    @wraps(func)
+    def wrapper(self):
+        "Return ellipsis on recursive re-entry to function."
+        key = id(self), get_ident()
+
+        if key in repr_running:
+            return '...'
+
+        repr_running.add(key)
+
+        try:
+            return func(self)
+        finally:
+            repr_running.discard(key)
+
+    return wrapper
+
+class SortedList(MutableSequence):
+    """
+    SortedList provides most of the same methods as a list but keeps the items
+    in sorted order.
+    """
+    # pylint: disable=too-many-ancestors
+    def __init__(self, iterable=None):
+        """
+        SortedList provides most of the same methods as a list but keeps the
+        items in sorted order.
+
+        An optional *iterable* provides an initial series of items to populate
+        the SortedList.
+        """
+        self._len = 0
+        self._lists = []
+        self._maxes = []
+        self._index = []
+        self._load = LOAD
+        self._half = LOAD >> 1
+        self._dual = LOAD << 1
+        self._offset = 0
+
+        if iterable is not None:
+            self._update(iterable)
+
+    def __new__(cls, iterable=None, key=None):
+        """
+        SortedList provides most of the same methods as a list but keeps the
+        items in sorted order.
+
+        An optional *iterable* provides an initial series of items to populate
+        the SortedList.
+
+        An optional *key* argument will return an instance of subtype
+        SortedListWithKey.
+        """
+        # pylint: disable=unused-argument
+        if key is None:
+            return object.__new__(cls)
+        else:
+            if cls is SortedList:
+                return object.__new__(SortedListWithKey)
+            else:
+                raise TypeError('inherit SortedListWithKey for key argument')
+
+    @property
+    def key(self):
+        """Key function used to extract comparison key for sorting."""
+        return None
+
+    def _reset(self, load):
+        """
+        Reset sorted list load.
+
+        The *load* specifies the load-factor of the list. 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.
+        """
+        values = reduce(iadd, self._lists, [])
+        self._clear()
+        self._load = load
+        self._half = load >> 1
+        self._dual = load << 1
+        self._update(values)
+
+    def clear(self):
+        """Remove all the elements from the list."""
+        self._len = 0
+        del self._lists[:]
+        del self._maxes[:]
+        del self._index[:]
+
+    _clear = clear
+
+    def add(self, val):
+        """Add the element *val* to the list."""
+        _lists = self._lists
+        _maxes = self._maxes
+
+        if _maxes:
+            pos = bisect_right(_maxes, val)
+
+            if pos == len(_maxes):
+                pos -= 1
+                _lists[pos].append(val)
+                _maxes[pos] = val
+            else:
+                insort(_lists[pos], val)
+
+            self._expand(pos)
+        else:
+            _lists.append([val])
+            _maxes.append(val)
+
+        self._len += 1
+
+    def _expand(self, pos):
+        """Splits sublists that are more than double the load level.
+
+        Updates the index when the sublist length is less than double the load
+        level. This requires incrementing the nodes in a traversal from the
+        leaf node to the root. For an example traversal see self._loc.
+
+        """
+        _lists = self._lists
+        _index = self._index
+
+        if len(_lists[pos]) > self._dual:
+            _maxes = self._maxes
+            _load = self._load
+
+            _lists_pos = _lists[pos]
+            half = _lists_pos[_load:]
+            del _lists_pos[_load:]
+            _maxes[pos] = _lists_pos[-1]
+
+            _lists.insert(pos + 1, half)
+            _maxes.insert(pos + 1, half[-1])
+
+            del _index[:]
+        else:
+            if _index:
+                child = self._offset + pos
+                while child:
+                    _index[child] += 1
+                    child = (child - 1) >> 1
+                _index[0] += 1
+
+    def update(self, iterable):
+        """Update the list by adding all elements from *iterable*."""
+        _lists = self._lists
+        _maxes = self._maxes
+        values = sorted(iterable)
+
+        if _maxes:
+            if len(values) * 4 >= self._len:
+                values.extend(chain.from_iterable(_lists))
+                values.sort()
+                self._clear()
+            else:
+                _add = self.add
+                for val in values:
+                    _add(val)
+                return
+
+        _load = self._load
+        _lists.extend(values[pos:(pos + _load)]
+                      for pos in range(0, len(values), _load))
+        _maxes.extend(sublist[-1] for sublist in _lists)
+        self._len = len(values)
+        del self._index[:]
+
+    _update = update
+
+    def __contains__(self, val):
+        """Return True if and only if *val* is an element in the list."""
+        _maxes = self._maxes
+
+        if not _maxes:
+            return False
+
+        pos = bisect_left(_maxes, val)
+
+        if pos == len(_maxes):
+            return False
+
+        _lists = self._lists
+        idx = bisect_left(_lists[pos], val)
+
+        return _lists[pos][idx] == val
+
+    def discard(self, val):
+        """
+        Remove the first occurrence of *val*.
+
+        If *val* is not a member, does nothing.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return
+
+        pos = bisect_left(_maxes, val)
+
+        if pos == len(_maxes):
+            return
+
+        _lists = self._lists
+        idx = bisect_left(_lists[pos], val)
+
+        if _lists[pos][idx] == val:
+            self._delete(pos, idx)
+
+    def remove(self, val):
+        """
+        Remove first occurrence of *val*.
+
+        Raises ValueError if *val* is not present.
+        """
+        # pylint: disable=arguments-differ
+        _maxes = self._maxes
+
+        if not _maxes:
+            raise ValueError('{0!r} not in list'.format(val))
+
+        pos = bisect_left(_maxes, val)
+
+        if pos == len(_maxes):
+            raise ValueError('{0!r} not in list'.format(val))
+
+        _lists = self._lists
+        idx = bisect_left(_lists[pos], val)
+
+        if _lists[pos][idx] == val:
+            self._delete(pos, idx)
+        else:
+            raise ValueError('{0!r} not in list'.format(val))
+
+    def _delete(self, pos, idx):
+        """Delete the item at the given (pos, idx).
+
+        Combines lists that are less than half the load level.
+
+        Updates the index when the sublist length is more than half the load
+        level. This requires decrementing the nodes in a traversal from the leaf
+        node to the root. For an example traversal see self._loc.
+        """
+        _lists = self._lists
+        _maxes = self._maxes
+        _index = self._index
+
+        _lists_pos = _lists[pos]
+
+        del _lists_pos[idx]
+        self._len -= 1
+
+        len_lists_pos = len(_lists_pos)
+
+        if len_lists_pos > self._half:
+
+            _maxes[pos] = _lists_pos[-1]
+
+            if _index:
+                child = self._offset + pos
+                while child > 0:
+                    _index[child] -= 1
+                    child = (child - 1) >> 1
+                _index[0] -= 1
+
+        elif len(_lists) > 1:
+
+            if not pos:
+                pos += 1
+
+            prev = pos - 1
+            _lists[prev].extend(_lists[pos])
+            _maxes[prev] = _lists[prev][-1]
+
+            del _lists[pos]
+            del _maxes[pos]
+            del _index[:]
+
+            self._expand(prev)
+
+        elif len_lists_pos:
+
+            _maxes[pos] = _lists_pos[-1]
+
+        else:
+
+            del _lists[pos]
+            del _maxes[pos]
+            del _index[:]
+
+    def _loc(self, pos, idx):
+        """Convert an index pair (alpha, beta) into a single index that corresponds to
+        the position of the value in the sorted list.
+
+        Most queries require the index be built. Details of the index are
+        described in self._build_index.
+
+        Indexing requires traversing the tree from a leaf node to the root. The
+        parent of each node is easily computable at (pos - 1) // 2.
+
+        Left-child nodes are always at odd indices and right-child nodes are
+        always at even indices.
+
+        When traversing up from a right-child node, increment the total by the
+        left-child node.
+
+        The final index is the sum from traversal and the index in the sublist.
+
+        For example, using the index from self._build_index:
+
+        _index = 14 5 9 3 2 4 5
+        _offset = 3
+
+        Tree:
+
+                 14
+              5      9
+            3   2  4   5
+
+        Converting index pair (2, 3) into a single index involves iterating like
+        so:
+
+        1. Starting at the leaf node: offset + alpha = 3 + 2 = 5. We identify
+           the node as a left-child node. At such nodes, we simply traverse to
+           the parent.
+
+        2. At node 9, position 2, we recognize the node as a right-child node
+           and accumulate the left-child in our total. Total is now 5 and we
+           traverse to the parent at position 0.
+
+        3. Iteration ends at the root.
+
+        Computing the index is the sum of the total and beta: 5 + 3 = 8.
+        """
+        if not pos:
+            return idx
+
+        _index = self._index
+
+        if not _index:
+            self._build_index()
+
+        total = 0
+
+        # Increment pos to point in the index to len(self._lists[pos]).
+
+        pos += self._offset
+
+        # Iterate until reaching the root of the index tree at pos = 0.
+
+        while pos:
+
+            # Right-child nodes are at odd indices. At such indices
+            # account the total below the left child node.
+
+            if not pos & 1:
+                total += _index[pos - 1]
+
+            # Advance pos to the parent node.
+
+            pos = (pos - 1) >> 1
+
+        return total + idx
+
+    def _pos(self, idx):
+        """Convert an index into a pair (alpha, beta) that can be used to access
+        the corresponding _lists[alpha][beta] position.
+
+        Most queries require the index be built. Details of the index are
+        described in self._build_index.
+
+        Indexing requires traversing the tree to a leaf node. Each node has
+        two children which are easily computable. Given an index, pos, the
+        left-child is at pos * 2 + 1 and the right-child is at pos * 2 + 2.
+
+        When the index is less than the left-child, traversal moves to the
+        left sub-tree. Otherwise, the index is decremented by the left-child
+        and traversal moves to the right sub-tree.
+
+        At a child node, the indexing pair is computed from the relative
+        position of the child node as compared with the offset and the remaining
+        index.
+
+        For example, using the index from self._build_index:
+
+        _index = 14 5 9 3 2 4 5
+        _offset = 3
+
+        Tree:
+
+                 14
+              5      9
+            3   2  4   5
+
+        Indexing position 8 involves iterating like so:
+
+        1. Starting at the root, position 0, 8 is compared with the left-child
+           node (5) which it is greater than. When greater the index is
+           decremented and the position is updated to the right child node.
+
+        2. At node 9 with index 3, we again compare the index to the left-child
+           node with value 4. Because the index is the less than the left-child
+           node, we simply traverse to the left.
+
+        3. At node 4 with index 3, we recognize that we are at a leaf node and
+           stop iterating.
+
+        4. To compute the sublist index, we subtract the offset from the index
+           of the leaf node: 5 - 3 = 2. To compute the index in the sublist, we
+           simply use the index remaining from iteration. In this case, 3.
+
+        The final index pair from our example is (2, 3) which corresponds to
+        index 8 in the sorted list.
+        """
+        if idx < 0:
+            last_len = len(self._lists[-1])
+
+            if (-idx) <= last_len:
+                return len(self._lists) - 1, last_len + idx
+
+            idx += self._len
+
+            if idx < 0:
+                raise IndexError('list index out of range')
+        elif idx >= self._len:
+            raise IndexError('list index out of range')
+
+        if idx < len(self._lists[0]):
+            return 0, idx
+
+        _index = self._index
+
+        if not _index:
+            self._build_index()
+
+        pos = 0
+        child = 1
+        len_index = len(_index)
+
+        while child < len_index:
+            index_child = _index[child]
+
+            if idx < index_child:
+                pos = child
+            else:
+                idx -= index_child
+                pos = child + 1
+
+            child = (pos << 1) + 1
+
+        return (pos - self._offset, idx)
+
+    def _build_index(self):
+        """Build an index for indexing the sorted list.
+
+        Indexes are represented as binary trees in a dense array notation
+        similar to a binary heap.
+
+        For example, given a _lists representation storing integers:
+
+        [0]: 1 2 3
+        [1]: 4 5
+        [2]: 6 7 8 9
+        [3]: 10 11 12 13 14
+
+        The first transformation maps the sub-lists by their length. The
+        first row of the index is the length of the sub-lists.
+
+        [0]: 3 2 4 5
+
+        Each row after that is the sum of consecutive pairs of the previous row:
+
+        [1]: 5 9
+        [2]: 14
+
+        Finally, the index is built by concatenating these lists together:
+
+        _index = 14 5 9 3 2 4 5
+
+        An offset storing the start of the first row is also stored:
+
+        _offset = 3
+
+        When built, the index can be used for efficient indexing into the list.
+        See the comment and notes on self._pos for details.
+        """
+        row0 = list(map(len, self._lists))
+
+        if len(row0) == 1:
+            self._index[:] = row0
+            self._offset = 0
+            return
+
+        head = iter(row0)
+        tail = iter(head)
+        row1 = list(starmap(add, zip(head, tail)))
+
+        if len(row0) & 1:
+            row1.append(row0[-1])
+
+        if len(row1) == 1:
+            self._index[:] = row1 + row0
+            self._offset = 1
+            return
+
+        size = 2 ** (int(log_e(len(row1) - 1, 2)) + 1)
+        row1.extend(repeat(0, size - len(row1)))
+        tree = [row0, row1]
+
+        while len(tree[-1]) > 1:
+            head = iter(tree[-1])
+            tail = iter(head)
+            row = list(starmap(add, zip(head, tail)))
+            tree.append(row)
+
+        reduce(iadd, reversed(tree), self._index)
+        self._offset = size * 2 - 1
+
+    def __delitem__(self, idx):
+        """Remove the element at *idx*. Supports slicing."""
+        if isinstance(idx, slice):
+            start, stop, step = idx.indices(self._len)
+
+            if step == 1 and start < stop:
+                if start == 0 and stop == self._len:
+                    return self._clear()
+                elif self._len <= 8 * (stop - start):
+                    values = self._getitem(slice(None, start))
+                    if stop < self._len:
+                        values += self._getitem(slice(stop, None))
+                    self._clear()
+                    return self._update(values)
+
+            indices = range(start, stop, step)
+
+            # Delete items from greatest index to least so
+            # that the indices remain valid throughout iteration.
+
+            if step > 0:
+                indices = reversed(indices)
+
+            _pos, _delete = self._pos, self._delete
+
+            for index in indices:
+                pos, idx = _pos(index)
+                _delete(pos, idx)
+        else:
+            pos, idx = self._pos(idx)
+            self._delete(pos, idx)
+
+    _delitem = __delitem__
+
+    def __getitem__(self, idx):
+        """Return the element at *idx*. Supports slicing."""
+        _lists = self._lists
+
+        if isinstance(idx, slice):
+            start, stop, step = idx.indices(self._len)
+
+            if step == 1 and start < stop:
+                if start == 0 and stop == self._len:
+                    return reduce(iadd, self._lists, [])
+
+                start_pos, start_idx = self._pos(start)
+
+                if stop == self._len:
+                    stop_pos = len(_lists) - 1
+                    stop_idx = len(_lists[stop_pos])
+                else:
+                    stop_pos, stop_idx = self._pos(stop)
+
+                if start_pos == stop_pos:
+                    return _lists[start_pos][start_idx:stop_idx]
+
+                prefix = _lists[start_pos][start_idx:]
+                middle = _lists[(start_pos + 1):stop_pos]
+                result = reduce(iadd, middle, prefix)
+                result += _lists[stop_pos][:stop_idx]
+
+                return result
+
+            if step == -1 and start > stop:
+                result = self._getitem(slice(stop + 1, start + 1))
+                result.reverse()
+                return result
+
+            # Return a list because a negative step could
+            # reverse the order of the items and this could
+            # be the desired behavior.
+
+            indices = range(start, stop, step)
+            return list(self._getitem(index) for index in indices)
+        else:
+            if self._len:
+                if idx == 0:
+                    return _lists[0][0]
+                elif idx == -1:
+                    return _lists[-1][-1]
+            else:
+                raise IndexError('list index out of range')
+
+            if 0 <= idx < len(_lists[0]):
+                return _lists[0][idx]
+
+            len_last = len(_lists[-1])
+
+            if -len_last < idx < 0:
+                return _lists[-1][len_last + idx]
+
+            pos, idx = self._pos(idx)
+            return _lists[pos][idx]
+
+    _getitem = __getitem__
+
+    def _check_order(self, idx, val):
+        _len = self._len
+        _lists = self._lists
+
+        pos, loc = self._pos(idx)
+
+        if idx < 0:
+            idx += _len
+
+        # Check that the inserted value is not less than the
+        # previous value.
+
+        if idx > 0:
+            idx_prev = loc - 1
+            pos_prev = pos
+
+            if idx_prev < 0:
+                pos_prev -= 1
+                idx_prev = len(_lists[pos_prev]) - 1
+
+            if _lists[pos_prev][idx_prev] > val:
+                msg = '{0!r} not in sort order at index {1}'.format(val, idx)
+                raise ValueError(msg)
+
+        # Check that the inserted value is not greater than
+        # the previous value.
+
+        if idx < (_len - 1):
+            idx_next = loc + 1
+            pos_next = pos
+
+            if idx_next == len(_lists[pos_next]):
+                pos_next += 1
+                idx_next = 0
+
+            if _lists[pos_next][idx_next] < val:
+                msg = '{0!r} not in sort order at index {1}'.format(val, idx)
+                raise ValueError(msg)
+
+    def __setitem__(self, index, value):
+        """Replace item at position *index* with *value*.
+
+        Supports slice notation. Raises :exc:`ValueError` if the sort order
+        would be violated. When used with a slice and iterable, the
+        :exc:`ValueError` is raised before the list is mutated if the sort
+        order would be violated by the operation.
+
+        """
+        _lists = self._lists
+        _maxes = self._maxes
+        _check_order = self._check_order
+        _pos = self._pos
+
+        if isinstance(index, slice):
+            _len = self._len
+            start, stop, step = index.indices(_len)
+            indices = range(start, stop, step)
+
+            # Copy value to avoid aliasing issues with self and cases where an
+            # iterator is given.
+
+            values = tuple(value)
+
+            if step != 1:
+                if len(values) != len(indices):
+                    raise ValueError(
+                        'attempt to assign sequence of size %s'
+                        ' to extended slice of size %s'
+                        % (len(values), len(indices)))
+
+                # Keep a log of values that are set so that we can
+                # roll back changes if ordering is violated.
+
+                log = []
+                _append = log.append
+
+                for idx, val in zip(indices, values):
+                    pos, loc = _pos(idx)
+                    _append((idx, _lists[pos][loc], val))
+                    _lists[pos][loc] = val
+                    if len(_lists[pos]) == (loc + 1):
+                        _maxes[pos] = val
+
+                try:
+                    # Validate ordering of new values.
+
+                    for idx, _, newval in log:
+                        _check_order(idx, newval)
+
+                except ValueError:
+
+                    # Roll back changes from log.
+
+                    for idx, oldval, _ in log:
+                        pos, loc = _pos(idx)
+                        _lists[pos][loc] = oldval
+                        if len(_lists[pos]) == (loc + 1):
+                            _maxes[pos] = oldval
+
+                    raise
+            else:
+                if start == 0 and stop == _len:
+                    self._clear()
+                    return self._update(values)
+
+                if stop < start:
+                    # When calculating indices, stop may be less than start.
+                    # For example: ...[5:3:1] results in slice(5, 3, 1) which
+                    # is a valid but not useful stop index.
+                    stop = start
+
+                if values:
+
+                    # Check that given values are ordered properly.
+
+                    alphas = iter(values)
+                    betas = iter(values)
+                    next(betas)
+                    pairs = zip(alphas, betas)
+
+                    if not all(alpha <= beta for alpha, beta in pairs):
+                        raise ValueError('given values not in sort order')
+
+                    # Check ordering in context of sorted list.
+
+                    if start and self._getitem(start - 1) > values[0]:
+                        message = '{0!r} not in sort order at index {1}'.format(
+                            values[0], start)
+                        raise ValueError(message)
+
+                    if stop != _len and self._getitem(stop) < values[-1]:
+                        message = '{0!r} not in sort order at index {1}'.format(
+                            values[-1], stop)
+                        raise ValueError(message)
+
+                # Delete the existing values.
+
+                self._delitem(index)
+
+                # Insert the new values.
+
+                _insert = self.insert
+                for idx, val in enumerate(values):
+                    _insert(start + idx, val)
+        else:
+            pos, loc = _pos(index)
+            _check_order(index, value)
+            _lists[pos][loc] = value
+            if len(_lists[pos]) == (loc + 1):
+                _maxes[pos] = value
+
+    def __iter__(self):
+        """
+        Return an iterator over the Sequence.
+
+        Iterating the Sequence while adding or deleting values may raise a
+        `RuntimeError` or fail to iterate over all entries.
+        """
+        return chain.from_iterable(self._lists)
+
+    def __reversed__(self):
+        """
+        Return an iterator to traverse the Sequence in reverse.
+
+        Iterating the Sequence while adding or deleting values may raise a
+        `RuntimeError` or fail to iterate over all entries.
+        """
+        return chain.from_iterable(map(reversed, reversed(self._lists)))
+
+    def reverse(self):
+        """Raise NotImplementedError
+
+        SortedList maintains values in ascending sort order. Values may not be
+        reversed in-place.
+
+        Use ``reversed(sorted_list)`` for a reverse iterator over values in
+        descending sort order.
+
+        Implemented to override MutableSequence.reverse which provides an
+        erroneous default implementation.
+
+        """
+        raise NotImplementedError('.reverse() not defined')
+
+    def islice(self, start=None, stop=None, reverse=False):
+
+        """
+        Returns an iterator that slices `self` from `start` to `stop` index,
+        inclusive and exclusive respectively.
+
+        When `reverse` is `True`, values are yielded from the iterator in
+        reverse order.
+
+        Both `start` and `stop` default to `None` which is automatically
+        inclusive of the beginning and end.
+        """
+        _len = self._len
+
+        if not _len:
+            return iter(())
+
+        start, stop, _ = slice(start, stop).indices(self._len)
+
+        if start >= stop:
+            return iter(())
+
+        _pos = self._pos
+
+        min_pos, min_idx = _pos(start)
+
+        if stop == _len:
+            max_pos = len(self._lists) - 1
+            max_idx = len(self._lists[-1])
+        else:
+            max_pos, max_idx = _pos(stop)
+
+        return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)
+
+    def _islice(self, min_pos, min_idx, max_pos, max_idx, reverse):
+        """
+        Returns an iterator that slices `self` using two index pairs,
+        `(min_pos, min_idx)` and `(max_pos, max_idx)`; the first inclusive
+        and the latter exclusive. See `_pos` for details on how an index
+        is converted to an index pair.
+
+        When `reverse` is `True`, values are yielded from the iterator in
+        reverse order.
+        """
+        _lists = self._lists
+
+        if min_pos > max_pos:
+            return iter(())
+        elif min_pos == max_pos and not reverse:
+            return iter(_lists[min_pos][min_idx:max_idx])
+        elif min_pos == max_pos and reverse:
+            return reversed(_lists[min_pos][min_idx:max_idx])
+        elif min_pos + 1 == max_pos and not reverse:
+            return chain(_lists[min_pos][min_idx:], _lists[max_pos][:max_idx])
+        elif min_pos + 1 == max_pos and reverse:
+            return chain(
+                reversed(_lists[max_pos][:max_idx]),
+                reversed(_lists[min_pos][min_idx:]),
+            )
+        elif not reverse:
+            return chain(
+                _lists[min_pos][min_idx:],
+                chain.from_iterable(_lists[(min_pos + 1):max_pos]),
+                _lists[max_pos][:max_idx],
+            )
+
+        temp = map(reversed, reversed(_lists[(min_pos + 1):max_pos]))
+        return chain(
+            reversed(_lists[max_pos][:max_idx]),
+            chain.from_iterable(temp),
+            reversed(_lists[min_pos][min_idx:]),
+        )
+
+    def irange(self, minimum=None, maximum=None, inclusive=(True, True),
+               reverse=False):
+        """
+        Create an iterator of values between `minimum` and `maximum`.
+
+        `inclusive` is a pair of booleans that indicates whether the minimum
+        and maximum ought to be included in the range, respectively. The
+        default is (True, True) such that the range is inclusive of both
+        minimum and maximum.
+
+        Both `minimum` and `maximum` default to `None` which is automatically
+        inclusive of the start and end of the list, respectively.
+
+        When `reverse` is `True` the values are yielded from the iterator in
+        reverse order; `reverse` defaults to `False`.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return iter(())
+
+        _lists = self._lists
+
+        # Calculate the minimum (pos, idx) pair. By default this location
+        # will be inclusive in our calculation.
+
+        if minimum is None:
+            min_pos = 0
+            min_idx = 0
+        else:
+            if inclusive[0]:
+                min_pos = bisect_left(_maxes, minimum)
+
+                if min_pos == len(_maxes):
+                    return iter(())
+
+                min_idx = bisect_left(_lists[min_pos], minimum)
+            else:
+                min_pos = bisect_right(_maxes, minimum)
+
+                if min_pos == len(_maxes):
+                    return iter(())
+
+                min_idx = bisect_right(_lists[min_pos], minimum)
+
+        # Calculate the maximum (pos, idx) pair. By default this location
+        # will be exclusive in our calculation.
+
+        if maximum is None:
+            max_pos = len(_maxes) - 1
+            max_idx = len(_lists[max_pos])
+        else:
+            if inclusive[1]:
+                max_pos = bisect_right(_maxes, maximum)
+
+                if max_pos == len(_maxes):
+                    max_pos -= 1
+                    max_idx = len(_lists[max_pos])
+                else:
+                    max_idx = bisect_right(_lists[max_pos], maximum)
+            else:
+                max_pos = bisect_left(_maxes, maximum)
+
+                if max_pos == len(_maxes):
+                    max_pos -= 1
+                    max_idx = len(_lists[max_pos])
+                else:
+                    max_idx = bisect_left(_lists[max_pos], maximum)
+
+        return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)
+
+    def __len__(self):
+        """Return the number of elements in the list."""
+        return self._len
+
+    def bisect_left(self, val):
+        """
+        Similar to the *bisect* module in the standard library, this returns an
+        appropriate index to insert *val*. If *val* is already present, the
+        insertion point will be before (to the left of) any existing entries.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return 0
+
+        pos = bisect_left(_maxes, val)
+
+        if pos == len(_maxes):
+            return self._len
+
+        idx = bisect_left(self._lists[pos], val)
+
+        return self._loc(pos, idx)
+
+    def bisect_right(self, val):
+        """
+        Same as *bisect_left*, but if *val* is already present, the insertion
+        point will be after (to the right of) any existing entries.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return 0
+
+        pos = bisect_right(_maxes, val)
+
+        if pos == len(_maxes):
+            return self._len
+
+        idx = bisect_right(self._lists[pos], val)
+
+        return self._loc(pos, idx)
+
+    bisect = bisect_right
+    _bisect_right = bisect_right
+
+    def count(self, val):
+        """Return the number of occurrences of *val* in the list."""
+        # pylint: disable=arguments-differ
+        _maxes = self._maxes
+
+        if not _maxes:
+            return 0
+
+        pos_left = bisect_left(_maxes, val)
+
+        if pos_left == len(_maxes):
+            return 0
+
+        _lists = self._lists
+        idx_left = bisect_left(_lists[pos_left], val)
+        pos_right = bisect_right(_maxes, val)
+
+        if pos_right == len(_maxes):
+            return self._len - self._loc(pos_left, idx_left)
+
+        idx_right = bisect_right(_lists[pos_right], val)
+
+        if pos_left == pos_right:
+            return idx_right - idx_left
+
+        right = self._loc(pos_right, idx_right)
+        left = self._loc(pos_left, idx_left)
+
+        return right - left
+
+    def copy(self):
+        """Return a shallow copy of the sorted list."""
+        return self.__class__(self)
+
+    __copy__ = copy
+
+    def append(self, val):
+        """
+        Append the element *val* to the list. Raises a ValueError if the *val*
+        would violate the sort order.
+        """
+        # pylint: disable=arguments-differ
+        _lists = self._lists
+        _maxes = self._maxes
+
+        if not _maxes:
+            _maxes.append(val)
+            _lists.append([val])
+            self._len = 1
+            return
+
+        pos = len(_lists) - 1
+
+        if val < _lists[pos][-1]:
+            msg = '{0!r} not in sort order at index {1}'.format(val, self._len)
+            raise ValueError(msg)
+
+        _maxes[pos] = val
+        _lists[pos].append(val)
+        self._len += 1
+        self._expand(pos)
+
+    def extend(self, values):
+        """
+        Extend the list by appending all elements from the *values*. Raises a
+        ValueError if the sort order would be violated.
+        """
+        _lists = self._lists
+        _maxes = self._maxes
+        _load = self._load
+
+        if not isinstance(values, list):
+            values = list(values)
+
+        if not values:
+            return
+
+        if any(values[pos - 1] > values[pos]
+               for pos in range(1, len(values))):
+            raise ValueError('given sequence not in sort order')
+
+        offset = 0
+
+        if _maxes:
+            if values[0] < _lists[-1][-1]:
+                msg = '{0!r} not in sort order at index {1}'.format(values[0], self._len)
+                raise ValueError(msg)
+
+            if len(_lists[-1]) < self._half:
+                _lists[-1].extend(values[:_load])
+                _maxes[-1] = _lists[-1][-1]
+                offset = _load
+
+        len_lists = len(_lists)
+
+        for idx in range(offset, len(values), _load):
+            _lists.append(values[idx:(idx + _load)])
+            _maxes.append(_lists[-1][-1])
+
+        _index = self._index
+
+        if len_lists == len(_lists):
+            len_index = len(_index)
+            if len_index > 0:
+                len_values = len(values)
+                child = len_index - 1
+                while child:
+                    _index[child] += len_values
+                    child = (child - 1) >> 1
+                _index[0] += len_values
+        else:
+            del _index[:]
+
+        self._len += len(values)
+
+    def insert(self, idx, val):
+        """
+        Insert the element *val* into the list at *idx*. Raises a ValueError if
+        the *val* at *idx* would violate the sort order.
+        """
+        # pylint: disable=arguments-differ
+        _len = self._len
+        _lists = self._lists
+        _maxes = self._maxes
+
+        if idx < 0:
+            idx += _len
+        if idx < 0:
+            idx = 0
+        if idx > _len:
+            idx = _len
+
+        if not _maxes:
+            # The idx must be zero by the inequalities above.
+            _maxes.append(val)
+            _lists.append([val])
+            self._len = 1
+            return
+
+        if not idx:
+            if val > _lists[0][0]:
+                msg = '{0!r} not in sort order at index {1}'.format(val, 0)
+                raise ValueError(msg)
+            else:
+                _lists[0].insert(0, val)
+                self._expand(0)
+                self._len += 1
+                return
+
+        if idx == _len:
+            pos = len(_lists) - 1
+            if _lists[pos][-1] > val:
+                msg = '{0!r} not in sort order at index {1}'.format(val, _len)
+                raise ValueError(msg)
+            else:
+                _lists[pos].append(val)
+                _maxes[pos] = _lists[pos][-1]
+                self._expand(pos)
+                self._len += 1
+                return
+
+        pos, idx = self._pos(idx)
+        idx_before = idx - 1
+        if idx_before < 0:
+            pos_before = pos - 1
+            idx_before = len(_lists[pos_before]) - 1
+        else:
+            pos_before = pos
+
+        before = _lists[pos_before][idx_before]
+        if before <= val <= _lists[pos][idx]:
+            _lists[pos].insert(idx, val)
+            self._expand(pos)
+            self._len += 1
+        else:
+            msg = '{0!r} not in sort order at index {1}'.format(val, idx)
+            raise ValueError(msg)
+
+    def pop(self, idx=-1):
+        """
+        Remove and return item at *idx* (default last).  Raises IndexError if
+        list is empty or index is out of range.  Negative indices are supported,
+        as for slice indices.
+        """
+        # pylint: disable=arguments-differ
+        if not self._len:
+            raise IndexError('pop index out of range')
+
+        _lists = self._lists
+
+        if idx == 0:
+            val = _lists[0][0]
+            self._delete(0, 0)
+            return val
+
+        if idx == -1:
+            pos = len(_lists) - 1
+            loc = len(_lists[pos]) - 1
+            val = _lists[pos][loc]
+            self._delete(pos, loc)
+            return val
+
+        if 0 <= idx < len(_lists[0]):
+            val = _lists[0][idx]
+            self._delete(0, idx)
+            return val
+
+        len_last = len(_lists[-1])
+
+        if -len_last < idx < 0:
+            pos = len(_lists) - 1
+            loc = len_last + idx
+            val = _lists[pos][loc]
+            self._delete(pos, loc)
+            return val
+
+        pos, idx = self._pos(idx)
+        val = _lists[pos][idx]
+        self._delete(pos, idx)
+
+        return val
+
+    def index(self, val, start=None, stop=None):
+        """
+        Return the smallest *k* such that L[k] == val and i <= k < j`.  Raises
+        ValueError if *val* is not present.  *stop* defaults to the end of the
+        list. *start* defaults to the beginning. Negative indices are supported,
+        as for slice indices.
+        """
+        # pylint: disable=arguments-differ
+        _len = self._len
+
+        if not _len:
+            raise ValueError('{0!r} is not in list'.format(val))
+
+        if start is None:
+            start = 0
+        if start < 0:
+            start += _len
+        if start < 0:
+            start = 0
+
+        if stop is None:
+            stop = _len
+        if stop < 0:
+            stop += _len
+        if stop > _len:
+            stop = _len
+
+        if stop <= start:
+            raise ValueError('{0!r} is not in list'.format(val))
+
+        _maxes = self._maxes
+        pos_left = bisect_left(_maxes, val)
+
+        if pos_left == len(_maxes):
+            raise ValueError('{0!r} is not in list'.format(val))
+
+        _lists = self._lists
+        idx_left = bisect_left(_lists[pos_left], val)
+
+        if _lists[pos_left][idx_left] != val:
+            raise ValueError('{0!r} is not in list'.format(val))
+
+        stop -= 1
+        left = self._loc(pos_left, idx_left)
+
+        if start <= left:
+            if left <= stop:
+                return left
+        else:
+            right = self._bisect_right(val) - 1
+
+            if start <= right:
+                return start
+
+        raise ValueError('{0!r} is not in list'.format(val))
+
+    def __add__(self, that):
+        """
+        Return a new sorted list containing all the elements in *self* and
+        *that*. Elements in *that* do not need to be properly ordered with
+        respect to *self*.
+        """
+        values = reduce(iadd, self._lists, [])
+        values.extend(that)
+        return self.__class__(values)
+
+    def __iadd__(self, that):
+        """
+        Update *self* to include all values in *that*. Elements in *that* do not
+        need to be properly ordered with respect to *self*.
+        """
+        self._update(that)
+        return self
+
+    def __mul__(self, that):
+        """
+        Return a new sorted list containing *that* shallow copies of each item
+        in SortedList.
+        """
+        values = reduce(iadd, self._lists, []) * that
+        return self.__class__(values)
+
+    def __imul__(self, that):
+        """
+        Increase the length of the list by appending *that* shallow copies of
+        each item.
+        """
+        values = reduce(iadd, self._lists, []) * that
+        self._clear()
+        self._update(values)
+        return self
+
+    def _make_cmp(self, seq_op, doc):
+        "Make comparator method."
+        def comparer(self, that):
+            "Compare method for sorted list and sequence."
+            # pylint: disable=protected-access
+            if not isinstance(that, Sequence):
+                return NotImplemented
+
+            self_len = self._len
+            len_that = len(that)
+
+            if self_len != len_that:
+                if seq_op is op.eq:
+                    return False
+                if seq_op is op.ne:
+                    return True
+
+            for alpha, beta in zip(self, that):
+                if alpha != beta:
+                    return seq_op(alpha, beta)
+
+            return seq_op(self_len, len_that)
+
+        comparer.__name__ = '__{0}__'.format(seq_op.__name__)
+        doc_str = 'Return `True` if and only if Sequence is {0} `that`.'
+        comparer.__doc__ = doc_str.format(doc)
+
+        return comparer
+
+    __eq__ = _make_cmp(None, op.eq, 'equal to')
+    __ne__ = _make_cmp(None, op.ne, 'not equal to')
+    __lt__ = _make_cmp(None, op.lt, 'less than')
+    __gt__ = _make_cmp(None, op.gt, 'greater than')
+    __le__ = _make_cmp(None, op.le, 'less than or equal to')
+    __ge__ = _make_cmp(None, op.ge, 'greater than or equal to')
+
+    @recursive_repr
+    def __repr__(self):
+        """Return string representation of sequence."""
+        return '{0}({1!r})'.format(type(self).__name__, list(self))
+
+    def _check(self):
+        try:
+            # Check load parameters.
+
+            assert self._load >= 4
+            assert self._half == (self._load >> 1)
+            assert self._dual == (self._load << 1)
+
+            # Check empty sorted list case.
+
+            if self._maxes == []:
+                assert self._lists == []
+                return
+
+            assert self._maxes and self._lists
+
+            # Check all sublists are sorted.
+
+            assert all(sublist[pos - 1] <= sublist[pos]
+                       for sublist in self._lists
+                       for pos in range(1, len(sublist)))
+
+            # Check beginning/end of sublists are sorted.
+
+            for pos in range(1, len(self._lists)):
+                assert self._lists[pos - 1][-1] <= self._lists[pos][0]
+
+            # Check length of _maxes and _lists match.
+
+            assert len(self._maxes) == len(self._lists)
+
+            # Check _maxes is a map of _lists.
+
+            assert all(self._maxes[pos] == self._lists[pos][-1]
+                       for pos in range(len(self._maxes)))
+
+            # Check load level is less than _dual.
+
+            assert all(len(sublist) <= self._dual for sublist in self._lists)
+
+            # Check load level is greater than _half for all
+            # but the last sublist.
+
+            assert all(len(self._lists[pos]) >= self._half
+                       for pos in range(0, len(self._lists) - 1))
+
+            # Check length.
+
+            assert self._len == sum(len(sublist) for sublist in self._lists)
+
+            # Check index.
+
+            if self._index:
+                assert len(self._index) == self._offset + len(self._lists)
+                assert self._len == self._index[0]
+
+                def test_offset_pos(pos):
+                    "Test positional indexing offset."
+                    from_index = self._index[self._offset + pos]
+                    return from_index == len(self._lists[pos])
+
+                assert all(test_offset_pos(pos)
+                           for pos in range(len(self._lists)))
+
+                for pos in range(self._offset):
+                    child = (pos << 1) + 1
+                    if child >= len(self._index):
+                        assert self._index[pos] == 0
+                    elif child + 1 == len(self._index):
+                        assert self._index[pos] == self._index[child]
+                    else:
+                        child_sum = self._index[child] + self._index[child + 1]
+                        assert self._index[pos] == child_sum
+
+        except:
+            import sys
+            import traceback
+
+            traceback.print_exc(file=sys.stdout)
+
+            print('len', self._len)
+            print('load', self._load, self._half, self._dual)
+            print('offset', self._offset)
+            print('len_index', len(self._index))
+            print('index', self._index)
+            print('len_maxes', len(self._maxes))
+            print('maxes', self._maxes)
+            print('len_lists', len(self._lists))
+            print('lists', self._lists)
+
+            raise
+
+def identity(value):
+    "Identity function."
+    return value
+
+class SortedListWithKey(SortedList):
+    """
+    SortedListWithKey provides most of the same methods as a list but keeps
+    the items in sorted order.
+    """
+    # pylint: disable=too-many-ancestors,abstract-method
+    def __init__(self, iterable=None, key=identity):
+        """SortedListWithKey provides most of the same methods as list but keeps the
+        items in sorted order.
+
+        An optional *iterable* provides an initial series of items to populate
+        the SortedListWithKey.
+
+        An optional *key* argument defines a callable that, like the `key`
+        argument to Python's `sorted` function, extracts a comparison key from
+        each element. The default is the identity function.
+        """
+        # pylint: disable=super-init-not-called
+        self._len = 0
+        self._lists = []
+        self._keys = []
+        self._maxes = []
+        self._index = []
+        self._key = key
+        self._load = LOAD
+        self._half = LOAD >> 1
+        self._dual = LOAD << 1
+        self._offset = 0
+
+        if iterable is not None:
+            self._update(iterable)
+
+    def __new__(cls, iterable=None, key=identity):
+        return object.__new__(cls)
+
+    @property
+    def key(self):
+        """Key function used to extract comparison key for sorting."""
+        return self._key
+
+    def clear(self):
+        """Remove all the elements from the list."""
+        self._len = 0
+        del self._lists[:]
+        del self._keys[:]
+        del self._maxes[:]
+        del self._index[:]
+
+    _clear = clear
+
+    def add(self, val):
+        """Add the element *val* to the list."""
+        _lists = self._lists
+        _keys = self._keys
+        _maxes = self._maxes
+
+        key = self._key(val)
+
+        if _maxes:
+            pos = bisect_right(_maxes, key)
+
+            if pos == len(_maxes):
+                pos -= 1
+                _lists[pos].append(val)
+                _keys[pos].append(key)
+                _maxes[pos] = key
+            else:
+                idx = bisect_right(_keys[pos], key)
+                _lists[pos].insert(idx, val)
+                _keys[pos].insert(idx, key)
+
+            self._expand(pos)
+        else:
+            _lists.append([val])
+            _keys.append([key])
+            _maxes.append(key)
+
+        self._len += 1
+
+    def _expand(self, pos):
+        """Splits sublists that are more than double the load level.
+
+        Updates the index when the sublist length is less than double the load
+        level. This requires incrementing the nodes in a traversal from the
+        leaf node to the root. For an example traversal see self._loc.
+
+        """
+        _lists = self._lists
+        _keys = self._keys
+        _index = self._index
+
+        if len(_keys[pos]) > self._dual:
+            _maxes = self._maxes
+            _load = self._load
+
+            _lists_pos = _lists[pos]
+            _keys_pos = _keys[pos]
+            half = _lists_pos[_load:]
+            half_keys = _keys_pos[_load:]
+            del _lists_pos[_load:]
+            del _keys_pos[_load:]
+            _maxes[pos] = _keys_pos[-1]
+
+            _lists.insert(pos + 1, half)
+            _keys.insert(pos + 1, half_keys)
+            _maxes.insert(pos + 1, half_keys[-1])
+
+            del _index[:]
+        else:
+            if _index:
+                child = self._offset + pos
+                while child:
+                    _index[child] += 1
+                    child = (child - 1) >> 1
+                _index[0] += 1
+
+    def update(self, iterable):
+        """Update the list by adding all elements from *iterable*."""
+        _lists = self._lists
+        _keys = self._keys
+        _maxes = self._maxes
+        values = sorted(iterable, key=self._key)
+
+        if _maxes:
+            if len(values) * 4 >= self._len:
+                values.extend(chain.from_iterable(_lists))
+                values.sort(key=self._key)
+                self._clear()
+            else:
+                _add = self.add
+                for val in values:
+                    _add(val)
+                return
+
+        _load = self._load
+        _lists.extend(values[pos:(pos + _load)]
+                      for pos in range(0, len(values), _load))
+        _keys.extend(list(map(self._key, _list)) for _list in _lists)
+        _maxes.extend(sublist[-1] for sublist in _keys)
+        self._len = len(values)
+        del self._index[:]
+
+    _update = update
+
+    def __contains__(self, val):
+        """Return True if and only if *val* is an element in the list."""
+        _maxes = self._maxes
+
+        if not _maxes:
+            return False
+
+        key = self._key(val)
+        pos = bisect_left(_maxes, key)
+
+        if pos == len(_maxes):
+            return False
+
+        _lists = self._lists
+        _keys = self._keys
+
+        idx = bisect_left(_keys[pos], key)
+
+        len_keys = len(_keys)
+        len_sublist = len(_keys[pos])
+
+        while True:
+            if _keys[pos][idx] != key:
+                return False
+            if _lists[pos][idx] == val:
+                return True
+            idx += 1
+            if idx == len_sublist:
+                pos += 1
+                if pos == len_keys:
+                    return False
+                len_sublist = len(_keys[pos])
+                idx = 0
+
+    def discard(self, val):
+        """
+        Remove the first occurrence of *val*.
+
+        If *val* is not a member, does nothing.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return
+
+        key = self._key(val)
+        pos = bisect_left(_maxes, key)
+
+        if pos == len(_maxes):
+            return
+
+        _lists = self._lists
+        _keys = self._keys
+        idx = bisect_left(_keys[pos], key)
+        len_keys = len(_keys)
+        len_sublist = len(_keys[pos])
+
+        while True:
+            if _keys[pos][idx] != key:
+                return
+            if _lists[pos][idx] == val:
+                self._delete(pos, idx)
+                return
+            idx += 1
+            if idx == len_sublist:
+                pos += 1
+                if pos == len_keys:
+                    return
+                len_sublist = len(_keys[pos])
+                idx = 0
+
+    def remove(self, val):
+        """
+        Remove first occurrence of *val*.
+
+        Raises ValueError if *val* is not present.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            raise ValueError('{0!r} not in list'.format(val))
+
+        key = self._key(val)
+        pos = bisect_left(_maxes, key)
+
+        if pos == len(_maxes):
+            raise ValueError('{0!r} not in list'.format(val))
+
+        _lists = self._lists
+        _keys = self._keys
+        idx = bisect_left(_keys[pos], key)
+        len_keys = len(_keys)
+        len_sublist = len(_keys[pos])
+
+        while True:
+            if _keys[pos][idx] != key:
+                raise ValueError('{0!r} not in list'.format(val))
+            if _lists[pos][idx] == val:
+                self._delete(pos, idx)
+                return
+            idx += 1
+            if idx == len_sublist:
+                pos += 1
+                if pos == len_keys:
+                    raise ValueError('{0!r} not in list'.format(val))
+                len_sublist = len(_keys[pos])
+                idx = 0
+
+    def _delete(self, pos, idx):
+        """
+        Delete the item at the given (pos, idx).
+
+        Combines lists that are less than half the load level.
+
+        Updates the index when the sublist length is more than half the load
+        level. This requires decrementing the nodes in a traversal from the leaf
+        node to the root. For an example traversal see self._loc.
+        """
+        _lists = self._lists
+        _keys = self._keys
+        _maxes = self._maxes
+        _index = self._index
+        keys_pos = _keys[pos]
+        lists_pos = _lists[pos]
+
+        del keys_pos[idx]
+        del lists_pos[idx]
+        self._len -= 1
+
+        len_keys_pos = len(keys_pos)
+
+        if len_keys_pos > self._half:
+
+            _maxes[pos] = keys_pos[-1]
+
+            if _index:
+                child = self._offset + pos
+                while child > 0:
+                    _index[child] -= 1
+                    child = (child - 1) >> 1
+                _index[0] -= 1
+
+        elif len(_keys) > 1:
+
+            if not pos:
+                pos += 1
+
+            prev = pos - 1
+            _keys[prev].extend(_keys[pos])
+            _lists[prev].extend(_lists[pos])
+            _maxes[prev] = _keys[prev][-1]
+
+            del _lists[pos]
+            del _keys[pos]
+            del _maxes[pos]
+            del _index[:]
+
+            self._expand(prev)
+
+        elif len_keys_pos:
+
+            _maxes[pos] = keys_pos[-1]
+
+        else:
+
+            del _lists[pos]
+            del _keys[pos]
+            del _maxes[pos]
+            del _index[:]
+
+    def _check_order(self, idx, key, val):
+        # pylint: disable=arguments-differ
+        _len = self._len
+        _keys = self._keys
+
+        pos, loc = self._pos(idx)
+
+        if idx < 0:
+            idx += _len
+
+        # Check that the inserted value is not less than the
+        # previous value.
+
+        if idx > 0:
+            idx_prev = loc - 1
+            pos_prev = pos
+
+            if idx_prev < 0:
+                pos_prev -= 1
+                idx_prev = len(_keys[pos_prev]) - 1
+
+            if _keys[pos_prev][idx_prev] > key:
+                msg = '{0!r} not in sort order at index {1}'.format(val, idx)
+                raise ValueError(msg)
+
+        # Check that the inserted value is not greater than
+        # the previous value.
+
+        if idx < (_len - 1):
+            idx_next = loc + 1
+            pos_next = pos
+
+            if idx_next == len(_keys[pos_next]):
+                pos_next += 1
+                idx_next = 0
+
+            if _keys[pos_next][idx_next] < key:
+                msg = '{0!r} not in sort order at index {1}'.format(val, idx)
+                raise ValueError(msg)
+
+    def __setitem__(self, index, value):
+        """Replace the item at position *index* with *value*.
+
+        Supports slice notation. Raises a :exc:`ValueError` if the sort order
+        would be violated. When used with a slice and iterable, the
+        :exc:`ValueError` is raised before the list is mutated if the sort
+        order would be violated by the operation.
+
+        """
+        # pylint: disable=too-many-locals
+        _lists = self._lists
+        _keys = self._keys
+        _maxes = self._maxes
+        _check_order = self._check_order
+        _pos = self._pos
+
+        if isinstance(index, slice):
+            _len = self._len
+            start, stop, step = index.indices(_len)
+            indices = range(start, stop, step)
+
+            # Copy value to avoid aliasing issues with self and cases where an
+            # iterator is given.
+
+            values = tuple(value)
+
+            if step != 1:
+                if len(values) != len(indices):
+                    raise ValueError(
+                        'attempt to assign sequence of size %s'
+                        ' to extended slice of size %s'
+                        % (len(values), len(indices)))
+
+                # Keep a log of values that are set so that we can
+                # roll back changes if ordering is violated.
+
+                log = []
+                _append = log.append
+
+                for idx, val in zip(indices, values):
+                    pos, loc = _pos(idx)
+                    key = self._key(val)
+                    _append((idx, _keys[pos][loc], key, _lists[pos][loc], val))
+                    _keys[pos][loc] = key
+                    _lists[pos][loc] = val
+                    if len(_keys[pos]) == (loc + 1):
+                        _maxes[pos] = key
+
+                try:
+                    # Validate ordering of new values.
+
+                    for idx, oldkey, newkey, oldval, newval in log:
+                        _check_order(idx, newkey, newval)
+
+                except ValueError:
+
+                    # Roll back changes from log.
+
+                    for idx, oldkey, newkey, oldval, newval in log:
+                        pos, loc = _pos(idx)
+                        _keys[pos][loc] = oldkey
+                        _lists[pos][loc] = oldval
+                        if len(_keys[pos]) == (loc + 1):
+                            _maxes[pos] = oldkey
+
+                    raise
+            else:
+                if start == 0 and stop == self._len:
+                    self._clear()
+                    return self._update(values)
+
+                if stop < start:
+                    # When calculating indices, stop may be less than start.
+                    # For example: ...[5:3:1] results in slice(5, 3, 1) which
+                    # is a valid but not useful stop index.
+                    stop = start
+
+                if values:
+
+                    # Check that given values are ordered properly.
+
+                    keys = tuple(map(self._key, values))
+                    alphas = iter(keys)
+                    betas = iter(keys)
+                    next(betas)
+                    pairs = zip(alphas, betas)
+
+                    if not all(alpha <= beta for alpha, beta in pairs):
+                        raise ValueError('given values not in sort order')
+
+                    # Check ordering in context of sorted list.
+
+                    if start:
+                        pos, loc = _pos(start - 1)
+                        if _keys[pos][loc] > keys[0]:
+                            msg = '{0!r} not in sort order at index {1}'.format(
+                                values[0], start)
+                            raise ValueError(msg)
+
+                    if stop != _len:
+                        pos, loc = _pos(stop)
+                        if _keys[pos][loc] < keys[-1]:
+                            msg = '{0!r} not in sort order at index {1}'.format(
+                                values[-1], stop)
+                            raise ValueError(msg)
+
+                # Delete the existing values.
+
+                self._delitem(index)
+
+                # Insert the new values.
+
+                _insert = self.insert
+                for idx, val in enumerate(values):
+                    _insert(start + idx, val)
+        else:
+            pos, loc = _pos(index)
+            key = self._key(value)
+            _check_order(index, key, value)
+            _lists[pos][loc] = value
+            _keys[pos][loc] = key
+            if len(_lists[pos]) == (loc + 1):
+                _maxes[pos] = key
+
+    def irange(self, minimum=None, maximum=None, inclusive=(True, True),
+               reverse=False):
+        """
+        Create an iterator of values between `minimum` and `maximum`.
+
+        `inclusive` is a pair of booleans that indicates whether the minimum
+        and maximum ought to be included in the range, respectively. The
+        default is (True, True) such that the range is inclusive of both
+        minimum and maximum.
+
+        Both `minimum` and `maximum` default to `None` which is automatically
+        inclusive of the start and end of the list, respectively.
+
+        When `reverse` is `True` the values are yielded from the iterator in
+        reverse order; `reverse` defaults to `False`.
+        """
+        minimum = self._key(minimum) if minimum is not None else None
+        maximum = self._key(maximum) if maximum is not None else None
+        return self._irange_key(
+            min_key=minimum, max_key=maximum,
+            inclusive=inclusive, reverse=reverse,
+        )
+
+    def irange_key(self, min_key=None, max_key=None, inclusive=(True, True),
+                   reverse=False):
+        """
+        Create an iterator of values between `min_key` and `max_key`.
+
+        `inclusive` is a pair of booleans that indicates whether the min_key
+        and max_key ought to be included in the range, respectively. The
+        default is (True, True) such that the range is inclusive of both
+        `min_key` and `max_key`.
+
+        Both `min_key` and `max_key` default to `None` which is automatically
+        inclusive of the start and end of the list, respectively.
+
+        When `reverse` is `True` the values are yielded from the iterator in
+        reverse order; `reverse` defaults to `False`.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return iter(())
+
+        _keys = self._keys
+
+        # Calculate the minimum (pos, idx) pair. By default this location
+        # will be inclusive in our calculation.
+
+        if min_key is None:
+            min_pos = 0
+            min_idx = 0
+        else:
+            if inclusive[0]:
+                min_pos = bisect_left(_maxes, min_key)
+
+                if min_pos == len(_maxes):
+                    return iter(())
+
+                min_idx = bisect_left(_keys[min_pos], min_key)
+            else:
+                min_pos = bisect_right(_maxes, min_key)
+
+                if min_pos == len(_maxes):
+                    return iter(())
+
+                min_idx = bisect_right(_keys[min_pos], min_key)
+
+        # Calculate the maximum (pos, idx) pair. By default this location
+        # will be exclusive in our calculation.
+
+        if max_key is None:
+            max_pos = len(_maxes) - 1
+            max_idx = len(_keys[max_pos])
+        else:
+            if inclusive[1]:
+                max_pos = bisect_right(_maxes, max_key)
+
+                if max_pos == len(_maxes):
+                    max_pos -= 1
+                    max_idx = len(_keys[max_pos])
+                else:
+                    max_idx = bisect_right(_keys[max_pos], max_key)
+            else:
+                max_pos = bisect_left(_maxes, max_key)
+
+                if max_pos == len(_maxes):
+                    max_pos -= 1
+                    max_idx = len(_keys[max_pos])
+                else:
+                    max_idx = bisect_left(_keys[max_pos], max_key)
+
+        return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)
+
+    _irange_key = irange_key
+
+    def bisect_left(self, val):
+        """
+        Similar to the *bisect* module in the standard library, this returns an
+        appropriate index to insert *val*. If *val* is already present, the
+        insertion point will be before (to the left of) any existing entries.
+        """
+        return self._bisect_key_left(self._key(val))
+
+    def bisect_right(self, val):
+        """
+        Same as *bisect_left*, but if *val* is already present, the insertion
+        point will be after (to the right of) any existing entries.
+        """
+        return self._bisect_key_right(self._key(val))
+
+    bisect = bisect_right
+
+    def bisect_key_left(self, key):
+        """
+        Similar to the *bisect* module in the standard library, this returns an
+        appropriate index to insert a value with a given *key*. If values with
+        *key* are already present, the insertion point will be before (to the
+        left of) any existing entries.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return 0
+
+        pos = bisect_left(_maxes, key)
+
+        if pos == len(_maxes):
+            return self._len
+
+        idx = bisect_left(self._keys[pos], key)
+
+        return self._loc(pos, idx)
+
+    _bisect_key_left = bisect_key_left
+
+    def bisect_key_right(self, key):
+        """
+        Same as *bisect_key_left*, but if *key* is already present, the insertion
+        point will be after (to the right of) any existing entries.
+        """
+        _maxes = self._maxes
+
+        if not _maxes:
+            return 0
+
+        pos = bisect_right(_maxes, key)
+
+        if pos == len(_maxes):
+            return self._len
+
+        idx = bisect_right(self._keys[pos], key)
+
+        return self._loc(pos, idx)
+
+    bisect_key = bisect_key_right
+    _bisect_key_right = bisect_key_right
+
+    def count(self, val):
+        """Return the number of occurrences of *val* in the list."""
+        _maxes = self._maxes
+
+        if not _maxes:
+            return 0
+
+        key = self._key(val)
+        pos = bisect_left(_maxes, key)
+
+        if pos == len(_maxes):
+            return 0
+
+        _lists = self._lists
+        _keys = self._keys
+        idx = bisect_left(_keys[pos], key)
+        total = 0
+        len_keys = len(_keys)
+        len_sublist = len(_keys[pos])
+
+        while True:
+            if _keys[pos][idx] != key:
+                return total
+            if _lists[pos][idx] == val:
+                total += 1
+            idx += 1
+            if idx == len_sublist:
+                pos += 1
+                if pos == len_keys:
+                    return total
+                len_sublist = len(_keys[pos])
+                idx = 0
+
+    def copy(self):
+        """Return a shallow copy of the sorted list."""
+        return self.__class__(self, key=self._key)
+
+    __copy__ = copy
+
+    def append(self, val):
+        """
+        Append the element *val* to the list. Raises a ValueError if the *val*
+        would violate the sort order.
+        """
+        # pylint: disable=arguments-differ
+        _lists = self._lists
+        _keys = self._keys
+        _maxes = self._maxes
+        key = self._key(val)
+
+        if not _maxes:
+            _maxes.append(key)
+            _keys.append([key])
+            _lists.append([val])
+            self._len = 1
+            return
+
+        pos = len(_keys) - 1
+
+        if key < _keys[pos][-1]:
+            msg = '{0!r} not in sort order at index {1}'.format(val, self._len)
+            raise ValueError(msg)
+
+        _lists[pos].append(val)
+        _keys[pos].append(key)
+        _maxes[pos] = key
+        self._len += 1
+        self._expand(pos)
+
+    def extend(self, values):
+        """
+        Extend the list by appending all elements from the *values*. Raises a
+        ValueError if the sort order would be violated.
+        """
+        _lists = self._lists
+        _keys = self._keys
+        _maxes = self._maxes
+        _load = self._load
+
+        if not isinstance(values, list):
+            values = list(values)
+
+        keys = list(map(self._key, values))
+
+        if any(keys[pos - 1] > keys[pos]
+               for pos in range(1, len(keys))):
+            raise ValueError('given sequence not in sort order')
+
+        offset = 0
+
+        if _maxes:
+            if keys[0] < _keys[-1][-1]:
+                msg = '{0!r} not in sort order at index {1}'.format(values[0], self._len)
+                raise ValueError(msg)
+
+            if len(_keys[-1]) < self._half:
+                _lists[-1].extend(values[:_load])
+                _keys[-1].extend(keys[:_load])
+                _maxes[-1] = _keys[-1][-1]
+                offset = _load
+
+        len_keys = len(_keys)
+
+        for idx in range(offset, len(keys), _load):
+            _lists.append(values[idx:(idx + _load)])
+            _keys.append(keys[idx:(idx + _load)])
+            _maxes.append(_keys[-1][-1])
+
+        _index = self._index
+
+        if len_keys == len(_keys):
+            len_index = len(_index)
+            if len_index > 0:
+                len_values = len(values)
+                child = len_index - 1
+                while child:
+                    _index[child] += len_values
+                    child = (child - 1) >> 1
+                _index[0] += len_values
+        else:
+            del _index[:]
+
+        self._len += len(values)
+
+    def insert(self, idx, val):
+        """
+        Insert the element *val* into the list at *idx*. Raises a ValueError if
+        the *val* at *idx* would violate the sort order.
+        """
+        _len = self._len
+        _lists = self._lists
+        _keys = self._keys
+        _maxes = self._maxes
+
+        if idx < 0:
+            idx += _len
+        if idx < 0:
+            idx = 0
+        if idx > _len:
+            idx = _len
+
+        key = self._key(val)
+
+        if not _maxes:
+            self._len = 1
+            _lists.append([val])
+            _keys.append([key])
+            _maxes.append(key)
+            return
+
+        if not idx:
+            if key > _keys[0][0]:
+                msg = '{0!r} not in sort order at index {1}'.format(val, 0)
+                raise ValueError(msg)
+            else:
+                self._len += 1
+                _lists[0].insert(0, val)
+                _keys[0].insert(0, key)
+                self._expand(0)
+                return
+
+        if idx == _len:
+            pos = len(_keys) - 1
+            if _keys[pos][-1] > key:
+                msg = '{0!r} not in sort order at index {1}'.format(val, _len)
+                raise ValueError(msg)
+            else:
+                self._len += 1
+                _lists[pos].append(val)
+                _keys[pos].append(key)
+                _maxes[pos] = _keys[pos][-1]
+                self._expand(pos)
+                return
+
+        pos, idx = self._pos(idx)
+        idx_before = idx - 1
+        if idx_before < 0:
+            pos_before = pos - 1
+            idx_before = len(_keys[pos_before]) - 1
+        else:
+            pos_before = pos
+
+        before = _keys[pos_before][idx_before]
+        if before <= key <= _keys[pos][idx]:
+            self._len += 1
+            _lists[pos].insert(idx, val)
+            _keys[pos].insert(idx, key)
+            self._expand(pos)
+        else:
+            msg = '{0!r} not in sort order at index {1}'.format(val, idx)
+            raise ValueError(msg)
+
+    def index(self, val, start=None, stop=None):
+        """
+        Return the smallest *k* such that L[k] == val and i <= k < j`.  Raises
+        ValueError if *val* is not present.  *stop* defaults to the end of the
+        list. *start* defaults to the beginning. Negative indices are supported,
+        as for slice indices.
+        """
+        _len = self._len
+
+        if not _len:
+            raise ValueError('{0!r} is not in list'.format(val))
+
+        if start is None:
+            start = 0
+        if start < 0:
+            start += _len
+        if start < 0:
+            start = 0
+
+        if stop is None:
+            stop = _len
+        if stop < 0:
+            stop += _len
+        if stop > _len:
+            stop = _len
+
+        if stop <= start:
+            raise ValueError('{0!r} is not in list'.format(val))
+
+        _maxes = self._maxes
+        key = self._key(val)
+        pos = bisect_left(_maxes, key)
+
+        if pos == len(_maxes):
+            raise ValueError('{0!r} is not in list'.format(val))
+
+        stop -= 1
+        _lists = self._lists
+        _keys = self._keys
+        idx = bisect_left(_keys[pos], key)
+        len_keys = len(_keys)
+        len_sublist = len(_keys[pos])
+
+        while True:
+            if _keys[pos][idx] != key:
+                raise ValueError('{0!r} is not in list'.format(val))
+            if _lists[pos][idx] == val:
+                loc = self._loc(pos, idx)
+                if start <= loc <= stop:
+                    return loc
+                elif loc > stop:
+                    break
+            idx += 1
+            if idx == len_sublist:
+                pos += 1
+                if pos == len_keys:
+                    raise ValueError('{0!r} is not in list'.format(val))
+                len_sublist = len(_keys[pos])
+                idx = 0
+
+        raise ValueError('{0!r} is not in list'.format(val))
+
+    def __add__(self, that):
+        """
+        Return a new sorted list containing all the elements in *self* and
+        *that*. Elements in *that* do not need to be properly ordered with
+        respect to *self*.
+        """
+        values = reduce(iadd, self._lists, [])
+        values.extend(that)
+        return self.__class__(values, key=self._key)
+
+    def __mul__(self, that):
+        """
+        Return a new sorted list containing *that* shallow copies of each item
+        in SortedListWithKey.
+        """
+        values = reduce(iadd, self._lists, []) * that
+        return self.__class__(values, key=self._key)
+
+    def __imul__(self, that):
+        """
+        Increase the length of the list by appending *that* shallow copies of
+        each item.
+        """
+        values = reduce(iadd, self._lists, []) * that
+        self._clear()
+        self._update(values)
+        return self
+
+    @recursive_repr
+    def __repr__(self):
+        """Return string representation of sequence."""
+        name = type(self).__name__
+        values = list(self)
+        _key = self._key
+        return '{0}({1!r}, key={2!r})'.format(name, values, _key)
+
+    def _check(self):
+        try:
+            # Check load parameters.
+
+            assert self._load >= 4
+            assert self._half == (self._load >> 1)
+            assert self._dual == (self._load << 1)
+
+            # Check empty sorted list case.
+
+            if self._maxes == []:
+                assert self._keys == []
+                assert self._lists == []
+                return
+
+            assert self._maxes and self._keys and self._lists
+
+            # Check all sublists are sorted.
+
+            assert all(sublist[pos - 1] <= sublist[pos]
+                       for sublist in self._keys
+                       for pos in range(1, len(sublist)))
+
+            # Check beginning/end of sublists are sorted.
+
+            for pos in range(1, len(self._keys)):
+                assert self._keys[pos - 1][-1] <= self._keys[pos][0]
+
+            # Check length of _maxes and _lists match.
+
+            assert len(self._maxes) == len(self._lists) == len(self._keys)
+
+            # Check _keys matches _key mapped to _lists.
+
+            assert all(len(val_list) == len(key_list)
+                       for val_list, key_list in zip(self._lists, self._keys))
+            assert all(self._key(val) == key for val, key in
+                       zip((_val for _val_list in self._lists for _val in _val_list),
+                           (_key for _key_list in self._keys for _key in _key_list)))
+
+            # Check _maxes is a map of _keys.
+
+            assert all(self._maxes[pos] == self._keys[pos][-1]
+                       for pos in range(len(self._maxes)))
+
+            # Check load level is less than _dual.
+
+            assert all(len(sublist) <= self._dual for sublist in self._lists)
+
+            # Check load level is greater than _half for all
+            # but the last sublist.
+
+            assert all(len(self._lists[pos]) >= self._half
+                       for pos in range(0, len(self._lists) - 1))
+
+            # Check length.
+
+            assert self._len == sum(len(sublist) for sublist in self._lists)
+
+            # Check index.
+
+            if self._index:
+                assert len(self._index) == self._offset + len(self._lists)
+                assert self._len == self._index[0]
+
+                def test_offset_pos(pos):
+                    "Test positional indexing offset."
+                    from_index = self._index[self._offset + pos]
+                    return from_index == len(self._lists[pos])
+
+                assert all(test_offset_pos(pos)
+                           for pos in range(len(self._lists)))
+
+                for pos in range(self._offset):
+                    child = (pos << 1) + 1
+                    if self._index[pos] == 0:
+                        assert child >= len(self._index)
+                    elif child + 1 == len(self._index):
+                        assert self._index[pos] == self._index[child]
+                    else:
+                        child_sum = self._index[child] + self._index[child + 1]
+                        assert self._index[pos] == child_sum
+
+        except:
+            import sys
+            import traceback
+
+            traceback.print_exc(file=sys.stdout)
+
+            print('len', self._len)
+            print('load', self._load, self._half, self._dual)
+            print('offset', self._offset)
+            print('len_index', len(self._index))
+            print('index', self._index)
+            print('len_maxes', len(self._maxes))
+            print('maxes', self._maxes)
+            print('len_keys', len(self._keys))
+            print('keys', self._keys)
+            print('len_lists', len(self._lists))
+            print('lists', self._lists)
+
+            raise
diff --git a/python/ovs/compat/sortedcontainers/sortedset.py b/python/ovs/compat/sortedcontainers/sortedset.py
new file mode 100644
index 0000000..6d82b38
--- /dev/null
+++ b/python/ovs/compat/sortedcontainers/sortedset.py
@@ -0,0 +1,327 @@ 
+"""Sorted set implementation.
+
+"""
+
+from collections import Set, MutableSet, Sequence
+from itertools import chain
+import operator as op
+
+from .sortedlist import SortedList, recursive_repr, SortedListWithKey
+
+class SortedSet(MutableSet, Sequence):
+    """
+    A `SortedSet` provides the same methods as a `set`.  Additionally, a
+    `SortedSet` maintains its items in sorted order, allowing the `SortedSet` to
+    be indexed.
+
+    Unlike a `set`, a `SortedSet` requires items be hashable and comparable.
+    """
+    # pylint: disable=too-many-ancestors
+    def __init__(self, iterable=None, key=None):
+        """
+        A `SortedSet` provides the same methods as a `set`.  Additionally, a
+        `SortedSet` maintains its items in sorted order, allowing the
+        `SortedSet` to be indexed.
+
+        An optional *iterable* provides an initial series of items to populate
+        the `SortedSet`.
+
+        An optional *key* argument defines a callable that, like the `key`
+        argument to Python's `sorted` function, extracts a comparison key from
+        each set item. If no function is specified, the default compares the
+        set items directly.
+        """
+        self._key = key
+
+        if not hasattr(self, '_set'):
+            self._set = set()
+
+        _set = self._set
+        self.isdisjoint = _set.isdisjoint
+        self.issubset = _set.issubset
+        self.issuperset = _set.issuperset
+
+        if key is None:
+            self._list = SortedList(self._set)
+        else:
+            self._list = SortedListWithKey(self._set, key=key)
+
+        _list = self._list
+        self.bisect_left = _list.bisect_left
+        self.bisect = _list.bisect
+        self.bisect_right = _list.bisect_right
+        self.index = _list.index
+        self.irange = _list.irange
+        self.islice = _list.islice
+        self._reset = _list._reset  # pylint: disable=protected-access
+
+        if 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
+
+        if iterable is not None:
+            self._update(iterable)
+
+    @property
+    def key(self):
+        """Key function used to extract comparison key for sorting."""
+        return self._key
+
+    @classmethod
+    def _fromset(cls, values, key=None):
+        """Initialize sorted set from existing set."""
+        sorted_set = object.__new__(cls)
+        sorted_set._set = values  # pylint: disable=protected-access
+        sorted_set.__init__(key=key)
+        return sorted_set
+
+    def __contains__(self, value):
+        """Return True if and only if *value* is an element in the set."""
+        return value in self._set
+
+    def __getitem__(self, index):
+        """
+        Return the element at position *index*.
+
+        Supports slice notation and negative indexes.
+        """
+        return self._list[index]
+
+    def __delitem__(self, index):
+        """
+        Remove the element at position *index*.
+
+        Supports slice notation and negative indexes.
+        """
+        _set = self._set
+        _list = self._list
+        if isinstance(index, slice):
+            values = _list[index]
+            _set.difference_update(values)
+        else:
+            value = _list[index]
+            _set.remove(value)
+        del _list[index]
+
+    def _make_cmp(self, set_op, doc):
+        "Make comparator method."
+        def comparer(self, that):
+            "Compare method for sorted set and set-like object."
+            # pylint: disable=protected-access
+            if isinstance(that, SortedSet):
+                return set_op(self._set, that._set)
+            elif isinstance(that, Set):
+                return set_op(self._set, that)
+            return NotImplemented
+
+        comparer.__name__ = '__{0}__'.format(set_op.__name__)
+        doc_str = 'Return True if and only if Set is {0} `that`.'
+        comparer.__doc__ = doc_str.format(doc)
+
+        return comparer
+
+    __eq__ = _make_cmp(None, op.eq, 'equal to')
+    __ne__ = _make_cmp(None, op.ne, 'not equal to')
+    __lt__ = _make_cmp(None, op.lt, 'a proper subset of')
+    __gt__ = _make_cmp(None, op.gt, 'a proper superset of')
+    __le__ = _make_cmp(None, op.le, 'a subset of')
+    __ge__ = _make_cmp(None, op.ge, 'a superset of')
+
+    def __len__(self):
+        """Return the number of elements in the set."""
+        return len(self._set)
+
+    def __iter__(self):
+        """
+        Return an iterator over the Set. Elements are iterated in their sorted
+        order.
+
+        Iterating the Set while adding or deleting values may raise a
+        `RuntimeError` or fail to iterate over all entries.
+        """
+        return iter(self._list)
+
+    def __reversed__(self):
+        """
+        Return an iterator over the Set. Elements are iterated in their reverse
+        sorted order.
+
+        Iterating the Set while adding or deleting values may raise a
+        `RuntimeError` or fail to iterate over all entries.
+        """
+        return reversed(self._list)
+
+    def add(self, value):
+        """Add the element *value* to the set."""
+        _set = self._set
+        if value not in _set:
+            _set.add(value)
+            self._list.add(value)
+
+    def clear(self):
+        """Remove all elements from the set."""
+        self._set.clear()
+        self._list.clear()
+
+    def copy(self):
+        """Create a shallow copy of the sorted set."""
+        return self._fromset(set(self._set), key=self._key)
+
+    __copy__ = copy
+
+    def count(self, value):
+        """Return the number of occurrences of *value* in the set."""
+        return 1 if value in self._set else 0
+
+    def discard(self, value):
+        """
+        Remove the first occurrence of *value*.  If *value* is not a member,
+        does nothing.
+        """
+        _set = self._set
+        if value in _set:
+            _set.remove(value)
+            self._list.discard(value)
+
+    def pop(self, index=-1):
+        """
+        Remove and return item at *index* (default last).  Raises IndexError if
+        set is empty or index is out of range.  Negative indexes are supported,
+        as for slice indices.
+        """
+        # pylint: disable=arguments-differ
+        value = self._list.pop(index)
+        self._set.remove(value)
+        return value
+
+    def remove(self, value):
+        """
+        Remove first occurrence of *value*.  Raises ValueError if
+        *value* is not present.
+        """
+        self._set.remove(value)
+        self._list.remove(value)
+
+    def difference(self, *iterables):
+        """
+        Return a new set with elements in the set that are not in the
+        *iterables*.
+        """
+        diff = self._set.difference(*iterables)
+        return self._fromset(diff, key=self._key)
+
+    __sub__ = difference
+    __rsub__ = __sub__
+
+    def difference_update(self, *iterables):
+        """
+        Update the set, removing elements found in keeping only elements
+        found in any of the *iterables*.
+        """
+        _set = self._set
+        values = set(chain(*iterables))
+        if (4 * len(values)) > len(_set):
+            _list = self._list
+            _set.difference_update(values)
+            _list.clear()
+            _list.update(_set)
+        else:
+            _discard = self.discard
+            for value in values:
+                _discard(value)
+        return self
+
+    __isub__ = difference_update
+
+    def intersection(self, *iterables):
+        """
+        Return a new set with elements common to the set and all *iterables*.
+        """
+        comb = self._set.intersection(*iterables)
+        return self._fromset(comb, key=self._key)
+
+    __and__ = intersection
+    __rand__ = __and__
+
+    def intersection_update(self, *iterables):
+        """
+        Update the set, keeping only elements found in it and all *iterables*.
+        """
+        _set = self._set
+        _list = self._list
+        _set.intersection_update(*iterables)
+        _list.clear()
+        _list.update(_set)
+        return self
+
+    __iand__ = intersection_update
+
+    def symmetric_difference(self, that):
+        """
+        Return a new set with elements in either *self* or *that* but not both.
+        """
+        diff = self._set.symmetric_difference(that)
+        return self._fromset(diff, key=self._key)
+
+    __xor__ = symmetric_difference
+    __rxor__ = __xor__
+
+    def symmetric_difference_update(self, that):
+        """
+        Update the set, keeping only elements found in either *self* or *that*,
+        but not in both.
+        """
+        _set = self._set
+        _list = self._list
+        _set.symmetric_difference_update(that)
+        _list.clear()
+        _list.update(_set)
+        return self
+
+    __ixor__ = symmetric_difference_update
+
+    def union(self, *iterables):
+        """
+        Return a new SortedSet with elements from the set and all *iterables*.
+        """
+        return self.__class__(chain(iter(self), *iterables), key=self._key)
+
+    __or__ = union
+    __ror__ = __or__
+
+    def update(self, *iterables):
+        """Update the set, adding elements from all *iterables*."""
+        _set = self._set
+        values = set(chain(*iterables))
+        if (4 * len(values)) > len(_set):
+            _list = self._list
+            _set.update(values)
+            _list.clear()
+            _list.update(_set)
+        else:
+            _add = self.add
+            for value in values:
+                _add(value)
+        return self
+
+    __ior__ = update
+    _update = update
+
+    def __reduce__(self):
+        return (type(self), (self._set, self._key))
+
+    @recursive_repr
+    def __repr__(self):
+        _key = self._key
+        key = '' if _key is None else ', key={0!r}'.format(_key)
+        name = type(self).__name__
+        return '{0}({1!r}{2})'.format(name, list(self), key)
+
+    def _check(self):
+        # pylint: disable=protected-access
+        self._list._check()
+        assert len(self._set) == len(self._list)
+        _set = self._set
+        assert all(val in _set for val in self._list)
diff --git a/python/ovs/db/custom_index.py b/python/ovs/db/custom_index.py
new file mode 100644
index 0000000..587caf5
--- /dev/null
+++ b/python/ovs/db/custom_index.py
@@ -0,0 +1,154 @@ 
+import collections
+import functools
+import operator
+try:
+    from UserDict import IterableUserDict as DictBase
+except ImportError:
+    from collections import UserDict as DictBase
+
+try:
+    import sortedcontainers
+except ImportError:
+    from ovs.compat import sortedcontainers
+
+from ovs.db import data
+
+OVSDB_INDEX_ASC = "ASC"
+OVSDB_INDEX_DESC = "DESC"
+ColumnIndex = collections.namedtuple('ColumnIndex',
+                                     ['column', 'direction', 'key'])
+
+
+class MultiColumnIndex(object):
+    def __init__(self, name):
+        self.name = name
+        self.columns = []
+        self.clear()
+
+    def __repr__(self):
+        return "{}(name={})".format(self.__class__.__name__, self.name)
+
+    def __str__(self):
+        return repr(self) + " columns={} values={}".format(
+            self.columns, [str(v) for v in self.values])
+
+    def add_column(self, column, direction=OVSDB_INDEX_ASC, key=None):
+        self.columns.append(ColumnIndex(column, direction,
+                             key or operator.attrgetter(column)))
+
+    def add_columns(self, *columns):
+        self.columns.extend(ColumnIndex(col, OVSDB_INDEX_ASC,
+                                        operator.attrgetter(col))
+                            for col in columns)
+
+    def _cmp(self, a, b):
+        for col, direction, key in self.columns:
+            aval, bval = key(a), key(b)
+            if aval == bval:
+                continue
+            result = (aval > bval) - (aval < bval)
+            return result if direction == OVSDB_INDEX_ASC else -result
+        return 0
+
+    def index_entry_from_row(self, row):
+        return row._table.rows.IndexEntry(
+            uuid=row.uuid,
+            **{c.column: getattr(row, c.column) for c in self.columns})
+
+    def add(self, row):
+        if not all(hasattr(row, col.column) for col in self.columns):
+            # This is a new row, but it hasn't had the necessary columns set
+            # We'll add it later
+            return
+        self.values.add(self.index_entry_from_row(row))
+
+    def remove(self, row):
+        self.values.remove(self.index_entry_from_row(row))
+
+    def clear(self):
+        self.values = sortedcontainers.SortedListWithKey(
+            key=functools.cmp_to_key(self._cmp))
+
+    def irange(self, start, end):
+        return iter(r._table.rows[r.uuid]
+                    for r in self.values.irange(start, end))
+
+    def __iter__(self):
+        return iter(r._table.rows[r.uuid] for r in self.values)
+
+
+class IndexedRows(DictBase, object):
+    def __init__(self, table, *args, **kwargs):
+        super(IndexedRows, self).__init__(*args, **kwargs)
+        self.table = table
+        self.indexes = {}
+        self.IndexEntry = IndexEntryClass(table)
+
+    def index_create(self, name):
+        if name in self.indexes:
+            raise ValueError("An index named {} already exists".format(name))
+        index = self.indexes[name] = MultiColumnIndex(name)
+        return index
+
+    def __setitem__(self, key, item):
+        self.data[key] = item
+        for index in self.indexes.values():
+            index.add(item)
+
+    def __delitem__(self, key):
+        val = self.data[key]
+        del self.data[key]
+        for index in self.indexes.values():
+            index.remove(val)
+
+    def clear(self):
+        self.data.clear()
+        for index in self.indexes.values():
+            index.clear()
+
+    # Nothing uses the methods below, though they'd be easy to implement
+    def update(self, dict=None, **kwargs):
+        raise NotImplementedError()
+
+    def setdefault(self, key, failobj=None):
+        raise NotImplementedError()
+
+    def pop(self, key, *args):
+        raise NotImplementedError()
+
+    def popitem(self):
+        raise NotImplementedError()
+
+    @classmethod
+    def fromkeys(cls, iterable, value=None):
+        raise NotImplementedError()
+
+
+def IndexEntryClass(table):
+    """Create a class used represent Rows in indexes
+
+    ovs.db.idl.Row, being inherently tied to transaction processing and being
+    initialized with dicts of Datums, is not really useable as an object to
+    pass to and store in indexes. This method will create a class named after
+    the table's name that is initialized with that Table Row's default values.
+    For example:
+
+    Port = IndexEntryClass(idl.tables['Port'])
+
+    will create a Port class. This class can then be used to search custom
+    indexes. For example:
+
+    for port in idx.iranage(Port(name="test1"), Port(name="test9")):
+       ...
+    """
+
+    def defaults_uuid_to_row(atom, base):
+        return atom.value
+
+    columns = ['uuid'] + list(table.columns.keys())
+    cls = collections.namedtuple(table.name, columns)
+    cls._table = table
+    cls.__new__.__defaults__ = (None,) + tuple(
+        data.Datum.default(c.type).to_python(defaults_uuid_to_row)
+        for c in table.columns.values())
+    return cls
diff --git a/python/ovs/db/idl.py b/python/ovs/db/idl.py
index 5a4d129..564977c 100644
--- a/python/ovs/db/idl.py
+++ b/python/ovs/db/idl.py
@@ -22,6 +22,7 @@  import ovs.jsonrpc
 import ovs.ovsuuid
 import ovs.poller
 import ovs.vlog
+from ovs.db import custom_index
 from ovs.db import error
 
 import six
@@ -148,11 +149,23 @@  class Idl(object):
                 if not hasattr(column, 'alert'):
                     column.alert = True
             table.need_table = False
-            table.rows = {}
+            table.rows = custom_index.IndexedRows(table)
             table.idl = self
             table.condition = [True]
             table.cond_changed = False
 
+    def index_create(self, table, name):
+        """Create a named multi-column index on a table"""
+        return self.tables[table].rows.index_create(name)
+
+    def index_irange(self, table, name, start, end):
+        """Return items in a named index between start/end inclusive"""
+        return self.tables[table].rows.indexes[name].irange(start, end)
+
+    def index_equal(self, table, name, value):
+        """Return items in a named index matching a value"""
+        return self.tables[table].rows.indexes[name].irange(value, value)
+
     def close(self):
         """Closes the connection to the database.  The IDL will no longer
         update."""
@@ -359,7 +372,7 @@  class Idl(object):
         for table in six.itervalues(self.tables):
             if table.rows:
                 changed = True
-                table.rows = {}
+                table.rows = custom_index.IndexedRows(table)
 
         if changed:
             self.change_seqno += 1
@@ -511,8 +524,9 @@  class Idl(object):
             else:
                 row_update = row_update['initial']
             self.__add_default(table, row_update)
-            if self.__row_update(table, row, row_update):
-                changed = True
+            changed = self.__row_update(table, row, row_update)
+            table.rows[uuid] = row
+            if changed:
                 self.notify(ROW_CREATE, row)
         elif "modify" in row_update:
             if not row:
@@ -542,15 +556,19 @@  class Idl(object):
                           % (uuid, table.name))
         elif not old:
             # Insert row.
+            op = ROW_CREATE
             if not row:
                 row = self.__create_row(table, uuid)
                 changed = True
             else:
                 # XXX rate-limit
+                op = ROW_UPDATE
                 vlog.warn("cannot add existing row %s to table %s"
                           % (uuid, table.name))
-            if self.__row_update(table, row, new):
-                changed = True
+            changed |= self.__row_update(table, row, new)
+            if op == ROW_CREATE:
+                table.rows[uuid] = row
+            if changed:
                 self.notify(ROW_CREATE, row)
         else:
             op = ROW_UPDATE
@@ -561,8 +579,10 @@  class Idl(object):
                 # XXX rate-limit
                 vlog.warn("cannot modify missing row %s in table %s"
                           % (uuid, table.name))
-            if self.__row_update(table, row, new):
-                changed = True
+            changed |= self.__row_update(table, row, new)
+            if op == ROW_CREATE:
+                table.rows[uuid] = row
+            if changed:
                 self.notify(op, row, Row.from_json(self, table, uuid, old))
         return changed
 
@@ -638,8 +658,7 @@  class Idl(object):
         data = {}
         for column in six.itervalues(table.columns):
             data[column.name] = ovs.db.data.Datum.default(column.type)
-        row = table.rows[uuid] = Row(self, table, uuid, data)
-        return row
+        return Row(self, table, uuid, data)
 
     def __error(self):
         self._session.force_reconnect()
@@ -844,7 +863,17 @@  class Row(object):
             vlog.err("attempting to write bad value to column %s (%s)"
                      % (column_name, e))
             return
+        # Remove prior version of the Row from the index if it has the indexed
+        # column set, and the column changing is an indexed column
+        if hasattr(self, column_name):
+            for idx in self._table.rows.indexes.values():
+                if column_name in (c.column for c in idx.columns):
+                    idx.remove(self)
         self._idl.txn._write(self, column, datum)
+        for idx in self._table.rows.indexes.values():
+            # Only update the index if indexed columns change
+            if column_name in (c.column for c in idx.columns):
+                idx.add(self)
 
     def addvalue(self, column_name, key):
         self._idl.txn._txn_rows[self.uuid] = self
@@ -972,8 +1001,8 @@  class Row(object):
             del self._idl.txn._txn_rows[self.uuid]
         else:
             self._idl.txn._txn_rows[self.uuid] = self
-        self.__dict__["_changes"] = None
         del self._table.rows[self.uuid]
+        self.__dict__["_changes"] = None
 
     def fetch(self, column_name):
         self._idl.txn._fetch(self, column_name)
@@ -1145,6 +1174,10 @@  class Transaction(object):
 
         for row in six.itervalues(self._txn_rows):
             if row._changes is None:
+                # If we add the deleted row back to rows with _changes == None
+                # then __getattr__ will not work for the indexes
+                row.__dict__["_changes"] = {}
+                row.__dict__["_mutations"] = {}
                 row._table.rows[row.uuid] = row
             elif row._data is None:
                 del row._table.rows[row.uuid]
diff --git a/python/setup.py b/python/setup.py
index a5872ab..0e86834 100644
--- a/python/setup.py
+++ b/python/setup.py
@@ -81,6 +81,7 @@  setup_args = dict(
     ext_modules=[setuptools.Extension("ovs._json", sources=["ovs/_json.c"],
                                       libraries=['openvswitch'])],
     cmdclass={'build_ext': try_build_ext},
+    install_requires=['sortedcontainers'],
 )
 
 try:
diff --git a/tests/test-ovsdb.py b/tests/test-ovsdb.py
index fc42a2d..8aca35b 100644
--- a/tests/test-ovsdb.py
+++ b/tests/test-ovsdb.py
@@ -289,10 +289,7 @@  def idltest_find_simple2(idl, i):
 
 
 def idltest_find_simple3(idl, i):
-    for row in six.itervalues(idl.tables["simple3"].rows):
-        if row.name == i:
-            return row
-    return None
+    return next(idl.index_equal("simple3", "simple3_by_name", i), None)
 
 
 def idl_set(idl, commands, step):
@@ -579,6 +576,8 @@  def do_idl(schema_file, remote, *commands):
     else:
         schema_helper.register_all()
     idl = ovs.db.idl.Idl(remote, schema_helper)
+    if "simple3" in idl.tables:
+        idl.index_create("simple3", "simple3_by_name")
 
     if commands:
         error, stream = ovs.stream.Stream.open_block(