diff --git a/.gitattributes b/.gitattributes
index eb29b6d22d365827d93107b94daa93c48b4a6094..6c104ebc609828fe0b3dd12b46022876affd2b7f 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -46,3 +46,4 @@ tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/distl
 tuning-competition-baseline/.venv/lib/python3.11/site-packages/Cython/Utils.cpython-311-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
 tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/__pycache__/typing_extensions.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text
 tuning-competition-baseline/.venv/lib/python3.11/site-packages/Cython/Compiler/__pycache__/Optimize.cpython-311.pyc filter=lfs diff=lfs merge=lfs -text
+tuning-competition-baseline/.venv/lib/python3.11/site-packages/Cython/Tempita/_tempita.cpython-311-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/Cython/Tempita/_tempita.cpython-311-x86_64-linux-gnu.so b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/Cython/Tempita/_tempita.cpython-311-x86_64-linux-gnu.so
new file mode 100644
index 0000000000000000000000000000000000000000..a235ca2f249ce5a43b45d87b82a5571b99b058e8
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/Cython/Tempita/_tempita.cpython-311-x86_64-linux-gnu.so
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:0477f20b0dfa19f79dc484a4a92c0ba4ae204d074ad171452e1d7de8bbd4d6cf
+size 595904
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/conftest.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/conftest.py
new file mode 100644
index 0000000000000000000000000000000000000000..6874a42c4895c3c7b973dc5d63fd4488a4e60b44
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/conftest.py
@@ -0,0 +1,55 @@
+import os
+import shutil
+import subprocess
+import sys
+import time
+
+import pytest
+
+import fsspec
+from fsspec.implementations.cached import CachingFileSystem
+
+
+@pytest.fixture()
+def m():
+    """
+    Fixture providing a memory filesystem.
+    """
+    m = fsspec.filesystem("memory")
+    m.store.clear()
+    m.pseudo_dirs.clear()
+    m.pseudo_dirs.append("")
+    try:
+        yield m
+    finally:
+        m.store.clear()
+        m.pseudo_dirs.clear()
+        m.pseudo_dirs.append("")
+
+
+@pytest.fixture
+def ftp_writable(tmpdir):
+    """
+    Fixture providing a writable FTP filesystem.
+    """
+    pytest.importorskip("pyftpdlib")
+    from fsspec.implementations.ftp import FTPFileSystem
+
+    FTPFileSystem.clear_instance_cache()  # remove lingering connections
+    CachingFileSystem.clear_instance_cache()
+    d = str(tmpdir)
+    with open(os.path.join(d, "out"), "wb") as f:
+        f.write(b"hello" * 10000)
+    P = subprocess.Popen(
+        [sys.executable, "-m", "pyftpdlib", "-d", d, "-u", "user", "-P", "pass", "-w"]
+    )
+    try:
+        time.sleep(1)
+        yield "localhost", 2121, "user", "pass"
+    finally:
+        P.terminate()
+        P.wait()
+        try:
+            shutil.rmtree(tmpdir)
+        except Exception:
+            pass
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diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/implementations/github.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/implementations/github.py
new file mode 100644
index 0000000000000000000000000000000000000000..e8fe7a2f67d7d9648e75b82d5f0b5cf2bf7a4868
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/implementations/github.py
@@ -0,0 +1,227 @@
+import requests
+
+from ..spec import AbstractFileSystem
+from ..utils import infer_storage_options
+from .memory import MemoryFile
+
+# TODO: add GIST backend, would be very similar
+
+
+class GithubFileSystem(AbstractFileSystem):
+    """Interface to files in github
+
+    An instance of this class provides the files residing within a remote github
+    repository. You may specify a point in the repos history, by SHA, branch
+    or tag (default is current master).
+
+    Given that code files tend to be small, and that github does not support
+    retrieving partial content, we always fetch whole files.
+
+    When using fsspec.open, allows URIs of the form:
+
+    - "github://path/file", in which case you must specify org, repo and
+      may specify sha in the extra args
+    - 'github://org:repo@/precip/catalog.yml', where the org and repo are
+      part of the URI
+    - 'github://org:repo@sha/precip/catalog.yml', where the sha is also included
+
+    ``sha`` can be the full or abbreviated hex of the commit you want to fetch
+    from, or a branch or tag name (so long as it doesn't contain special characters
+    like "/", "?", which would have to be HTTP-encoded).
+
+    For authorised access, you must provide username and token, which can be made
+    at https://github.com/settings/tokens
+    """
+
+    url = "https://api.github.com/repos/{org}/{repo}/git/trees/{sha}"
+    rurl = "https://raw.githubusercontent.com/{org}/{repo}/{sha}/{path}"
+    protocol = "github"
+    timeout = (60, 60)  # connect, read timeouts
+
+    def __init__(
+        self, org, repo, sha=None, username=None, token=None, timeout=None, **kwargs
+    ):
+        super().__init__(**kwargs)
+        self.org = org
+        self.repo = repo
+        if (username is None) ^ (token is None):
+            raise ValueError("Auth required both username and token")
+        self.username = username
+        self.token = token
+        if timeout is not None:
+            self.timeout = timeout
+        if sha is None:
+            # look up default branch (not necessarily "master")
+            u = "https://api.github.com/repos/{org}/{repo}"
+            r = requests.get(
+                u.format(org=org, repo=repo), timeout=self.timeout, **self.kw
+            )
+            r.raise_for_status()
+            sha = r.json()["default_branch"]
+
+        self.root = sha
+        self.ls("")
+
+    @property
+    def kw(self):
+        if self.username:
+            return {"auth": (self.username, self.token)}
+        return {}
+
+    @classmethod
+    def repos(cls, org_or_user, is_org=True):
+        """List repo names for given org or user
+
+        This may become the top level of the FS
+
+        Parameters
+        ----------
+        org_or_user: str
+            Name of the github org or user to query
+        is_org: bool (default True)
+            Whether the name is an organisation (True) or user (False)
+
+        Returns
+        -------
+        List of string
+        """
+        r = requests.get(
+            f"https://api.github.com/{['users', 'orgs'][is_org]}/{org_or_user}/repos",
+            timeout=cls.timeout,
+        )
+        r.raise_for_status()
+        return [repo["name"] for repo in r.json()]
+
+    @property
+    def tags(self):
+        """Names of tags in the repo"""
+        r = requests.get(
+            f"https://api.github.com/repos/{self.org}/{self.repo}/tags",
+            timeout=self.timeout,
+            **self.kw,
+        )
+        r.raise_for_status()
+        return [t["name"] for t in r.json()]
+
+    @property
+    def branches(self):
+        """Names of branches in the repo"""
+        r = requests.get(
+            f"https://api.github.com/repos/{self.org}/{self.repo}/branches",
+            timeout=self.timeout,
+            **self.kw,
+        )
+        r.raise_for_status()
+        return [t["name"] for t in r.json()]
+
+    @property
+    def refs(self):
+        """Named references, tags and branches"""
+        return {"tags": self.tags, "branches": self.branches}
+
+    def ls(self, path, detail=False, sha=None, _sha=None, **kwargs):
+        """List files at given path
+
+        Parameters
+        ----------
+        path: str
+            Location to list, relative to repo root
+        detail: bool
+            If True, returns list of dicts, one per file; if False, returns
+            list of full filenames only
+        sha: str (optional)
+            List at the given point in the repo history, branch or tag name or commit
+            SHA
+        _sha: str (optional)
+            List this specific tree object (used internally to descend into trees)
+        """
+        path = self._strip_protocol(path)
+        if path == "":
+            _sha = sha or self.root
+        if _sha is None:
+            parts = path.rstrip("/").split("/")
+            so_far = ""
+            _sha = sha or self.root
+            for part in parts:
+                out = self.ls(so_far, True, sha=sha, _sha=_sha)
+                so_far += "/" + part if so_far else part
+                out = [o for o in out if o["name"] == so_far]
+                if not out:
+                    raise FileNotFoundError(path)
+                out = out[0]
+                if out["type"] == "file":
+                    if detail:
+                        return [out]
+                    else:
+                        return path
+                _sha = out["sha"]
+        if path not in self.dircache or sha not in [self.root, None]:
+            r = requests.get(
+                self.url.format(org=self.org, repo=self.repo, sha=_sha),
+                timeout=self.timeout,
+                **self.kw,
+            )
+            if r.status_code == 404:
+                raise FileNotFoundError(path)
+            r.raise_for_status()
+            types = {"blob": "file", "tree": "directory"}
+            out = [
+                {
+                    "name": path + "/" + f["path"] if path else f["path"],
+                    "mode": f["mode"],
+                    "type": types[f["type"]],
+                    "size": f.get("size", 0),
+                    "sha": f["sha"],
+                }
+                for f in r.json()["tree"]
+                if f["type"] in types
+            ]
+            if sha in [self.root, None]:
+                self.dircache[path] = out
+        else:
+            out = self.dircache[path]
+        if detail:
+            return out
+        else:
+            return sorted([f["name"] for f in out])
+
+    def invalidate_cache(self, path=None):
+        self.dircache.clear()
+
+    @classmethod
+    def _strip_protocol(cls, path):
+        opts = infer_storage_options(path)
+        if "username" not in opts:
+            return super()._strip_protocol(path)
+        return opts["path"].lstrip("/")
+
+    @staticmethod
+    def _get_kwargs_from_urls(path):
+        opts = infer_storage_options(path)
+        if "username" not in opts:
+            return {}
+        out = {"org": opts["username"], "repo": opts["password"]}
+        if opts["host"]:
+            out["sha"] = opts["host"]
+        return out
+
+    def _open(
+        self,
+        path,
+        mode="rb",
+        block_size=None,
+        autocommit=True,
+        cache_options=None,
+        sha=None,
+        **kwargs,
+    ):
+        if mode != "rb":
+            raise NotImplementedError
+        url = self.rurl.format(
+            org=self.org, repo=self.repo, path=path, sha=sha or self.root
+        )
+        r = requests.get(url, timeout=self.timeout, **self.kw)
+        if r.status_code == 404:
+            raise FileNotFoundError(path)
+        r.raise_for_status()
+        return MemoryFile(None, None, r.content)
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/registry.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/registry.py
new file mode 100644
index 0000000000000000000000000000000000000000..db9d3d577e9f9490fdbdc70802b2c9f19ac6c964
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/registry.py
@@ -0,0 +1,299 @@
+from __future__ import annotations
+
+import importlib
+import types
+import warnings
+
+__all__ = ["registry", "get_filesystem_class", "default"]
+
+# internal, mutable
+_registry: dict[str, type] = {}
+
+# external, immutable
+registry = types.MappingProxyType(_registry)
+default = "file"
+
+
+def register_implementation(name, cls, clobber=False, errtxt=None):
+    """Add implementation class to the registry
+
+    Parameters
+    ----------
+    name: str
+        Protocol name to associate with the class
+    cls: class or str
+        if a class: fsspec-compliant implementation class (normally inherits from
+        ``fsspec.AbstractFileSystem``, gets added straight to the registry. If a
+        str, the full path to an implementation class like package.module.class,
+        which gets added to known_implementations,
+        so the import is deferred until the filesystem is actually used.
+    clobber: bool (optional)
+        Whether to overwrite a protocol with the same name; if False, will raise
+        instead.
+    errtxt: str (optional)
+        If given, then a failure to import the given class will result in this
+        text being given.
+    """
+    if isinstance(cls, str):
+        if name in known_implementations and clobber is False:
+            if cls != known_implementations[name]["class"]:
+                raise ValueError(
+                    f"Name ({name}) already in the known_implementations and clobber "
+                    f"is False"
+                )
+        else:
+            known_implementations[name] = {
+                "class": cls,
+                "err": errtxt or f"{cls} import failed for protocol {name}",
+            }
+
+    else:
+        if name in registry and clobber is False:
+            if _registry[name] is not cls:
+                raise ValueError(
+                    f"Name ({name}) already in the registry and clobber is False"
+                )
+        else:
+            _registry[name] = cls
+
+
+# protocols mapped to the class which implements them. This dict can be
+# updated with register_implementation
+known_implementations = {
+    "data": {"class": "fsspec.implementations.data.DataFileSystem"},
+    "file": {"class": "fsspec.implementations.local.LocalFileSystem"},
+    "local": {"class": "fsspec.implementations.local.LocalFileSystem"},
+    "memory": {"class": "fsspec.implementations.memory.MemoryFileSystem"},
+    "dropbox": {
+        "class": "dropboxdrivefs.DropboxDriveFileSystem",
+        "err": (
+            'DropboxFileSystem requires "dropboxdrivefs",'
+            '"requests" and "dropbox" to be installed'
+        ),
+    },
+    "http": {
+        "class": "fsspec.implementations.http.HTTPFileSystem",
+        "err": 'HTTPFileSystem requires "requests" and "aiohttp" to be installed',
+    },
+    "https": {
+        "class": "fsspec.implementations.http.HTTPFileSystem",
+        "err": 'HTTPFileSystem requires "requests" and "aiohttp" to be installed',
+    },
+    "zip": {"class": "fsspec.implementations.zip.ZipFileSystem"},
+    "tar": {"class": "fsspec.implementations.tar.TarFileSystem"},
+    "gcs": {
+        "class": "gcsfs.GCSFileSystem",
+        "err": "Please install gcsfs to access Google Storage",
+    },
+    "gs": {
+        "class": "gcsfs.GCSFileSystem",
+        "err": "Please install gcsfs to access Google Storage",
+    },
+    "gdrive": {
+        "class": "gdrivefs.GoogleDriveFileSystem",
+        "err": "Please install gdrivefs for access to Google Drive",
+    },
+    "sftp": {
+        "class": "fsspec.implementations.sftp.SFTPFileSystem",
+        "err": 'SFTPFileSystem requires "paramiko" to be installed',
+    },
+    "ssh": {
+        "class": "fsspec.implementations.sftp.SFTPFileSystem",
+        "err": 'SFTPFileSystem requires "paramiko" to be installed',
+    },
+    "ftp": {"class": "fsspec.implementations.ftp.FTPFileSystem"},
+    "hdfs": {
+        "class": "fsspec.implementations.arrow.HadoopFileSystem",
+        "err": "pyarrow and local java libraries required for HDFS",
+    },
+    "arrow_hdfs": {
+        "class": "fsspec.implementations.arrow.HadoopFileSystem",
+        "err": "pyarrow and local java libraries required for HDFS",
+    },
+    "webhdfs": {
+        "class": "fsspec.implementations.webhdfs.WebHDFS",
+        "err": 'webHDFS access requires "requests" to be installed',
+    },
+    "s3": {"class": "s3fs.S3FileSystem", "err": "Install s3fs to access S3"},
+    "s3a": {"class": "s3fs.S3FileSystem", "err": "Install s3fs to access S3"},
+    "wandb": {"class": "wandbfs.WandbFS", "err": "Install wandbfs to access wandb"},
+    "oci": {
+        "class": "ocifs.OCIFileSystem",
+        "err": "Install ocifs to access OCI Object Storage",
+    },
+    "ocilake": {
+        "class": "ocifs.OCIFileSystem",
+        "err": "Install ocifs to access OCI Data Lake",
+    },
+    "asynclocal": {
+        "class": "morefs.asyn_local.AsyncLocalFileSystem",
+        "err": "Install 'morefs[asynclocalfs]' to use AsyncLocalFileSystem",
+    },
+    "adl": {
+        "class": "adlfs.AzureDatalakeFileSystem",
+        "err": "Install adlfs to access Azure Datalake Gen1",
+    },
+    "abfs": {
+        "class": "adlfs.AzureBlobFileSystem",
+        "err": "Install adlfs to access Azure Datalake Gen2 and Azure Blob Storage",
+    },
+    "az": {
+        "class": "adlfs.AzureBlobFileSystem",
+        "err": "Install adlfs to access Azure Datalake Gen2 and Azure Blob Storage",
+    },
+    "cached": {"class": "fsspec.implementations.cached.CachingFileSystem"},
+    "blockcache": {"class": "fsspec.implementations.cached.CachingFileSystem"},
+    "filecache": {"class": "fsspec.implementations.cached.WholeFileCacheFileSystem"},
+    "simplecache": {"class": "fsspec.implementations.cached.SimpleCacheFileSystem"},
+    "dask": {
+        "class": "fsspec.implementations.dask.DaskWorkerFileSystem",
+        "err": "Install dask distributed to access worker file system",
+    },
+    "dbfs": {
+        "class": "fsspec.implementations.dbfs.DatabricksFileSystem",
+        "err": "Install the requests package to use the DatabricksFileSystem",
+    },
+    "github": {
+        "class": "fsspec.implementations.github.GithubFileSystem",
+        "err": "Install the requests package to use the github FS",
+    },
+    "git": {
+        "class": "fsspec.implementations.git.GitFileSystem",
+        "err": "Install pygit2 to browse local git repos",
+    },
+    "smb": {
+        "class": "fsspec.implementations.smb.SMBFileSystem",
+        "err": 'SMB requires "smbprotocol" or "smbprotocol[kerberos]" installed',
+    },
+    "jupyter": {
+        "class": "fsspec.implementations.jupyter.JupyterFileSystem",
+        "err": "Jupyter FS requires requests to be installed",
+    },
+    "jlab": {
+        "class": "fsspec.implementations.jupyter.JupyterFileSystem",
+        "err": "Jupyter FS requires requests to be installed",
+    },
+    "libarchive": {
+        "class": "fsspec.implementations.libarchive.LibArchiveFileSystem",
+        "err": "LibArchive requires to be installed",
+    },
+    "reference": {"class": "fsspec.implementations.reference.ReferenceFileSystem"},
+    "generic": {"class": "fsspec.generic.GenericFileSystem"},
+    "oss": {
+        "class": "ossfs.OSSFileSystem",
+        "err": "Install ossfs to access Alibaba Object Storage System",
+    },
+    "webdav": {
+        "class": "webdav4.fsspec.WebdavFileSystem",
+        "err": "Install webdav4 to access WebDAV",
+    },
+    "dvc": {
+        "class": "dvc.api.DVCFileSystem",
+        "err": "Install dvc to access DVCFileSystem",
+    },
+    "hf": {
+        "class": "huggingface_hub.HfFileSystem",
+        "err": "Install huggingface_hub to access HfFileSystem",
+    },
+    "root": {
+        "class": "fsspec_xrootd.XRootDFileSystem",
+        "err": "Install fsspec-xrootd to access xrootd storage system."
+        + " Note: 'root' is the protocol name for xrootd storage systems,"
+        + " not referring to root directories",
+    },
+    "dir": {"class": "fsspec.implementations.dirfs.DirFileSystem"},
+    "box": {
+        "class": "boxfs.BoxFileSystem",
+        "err": "Please install boxfs to access BoxFileSystem",
+    },
+    "lakefs": {
+        "class": "lakefs_spec.LakeFSFileSystem",
+        "err": "Please install lakefs-spec to access LakeFSFileSystem",
+    },
+}
+
+
+def get_filesystem_class(protocol):
+    """Fetch named protocol implementation from the registry
+
+    The dict ``known_implementations`` maps protocol names to the locations
+    of classes implementing the corresponding file-system. When used for the
+    first time, appropriate imports will happen and the class will be placed in
+    the registry. All subsequent calls will fetch directly from the registry.
+
+    Some protocol implementations require additional dependencies, and so the
+    import may fail. In this case, the string in the "err" field of the
+    ``known_implementations`` will be given as the error message.
+    """
+    if not protocol:
+        protocol = default
+
+    if protocol not in registry:
+        if protocol not in known_implementations:
+            raise ValueError(f"Protocol not known: {protocol}")
+        bit = known_implementations[protocol]
+        try:
+            register_implementation(protocol, _import_class(bit["class"]))
+        except ImportError as e:
+            raise ImportError(bit["err"]) from e
+    cls = registry[protocol]
+    if getattr(cls, "protocol", None) in ("abstract", None):
+        cls.protocol = protocol
+
+    return cls
+
+
+s3_msg = """Your installed version of s3fs is very old and known to cause
+severe performance issues, see also https://github.com/dask/dask/issues/10276
+
+To fix, you should specify a lower version bound on s3fs, or
+update the current installation.
+"""
+
+
+def _import_class(cls, minv=None):
+    """Take a string FQP and return the imported class or identifier
+
+    clas is of the form "package.module.klass" or "package.module:subobject.klass"
+    """
+    if ":" in cls:
+        mod, name = cls.rsplit(":", 1)
+        s3 = mod == "s3fs"
+        mod = importlib.import_module(mod)
+        if s3 and mod.__version__.split(".") < ["0", "5"]:
+            warnings.warn(s3_msg)
+        for part in name.split("."):
+            mod = getattr(mod, part)
+        return mod
+    else:
+        mod, name = cls.rsplit(".", 1)
+        s3 = mod == "s3fs"
+        mod = importlib.import_module(mod)
+        if s3 and mod.__version__.split(".") < ["0", "5"]:
+            warnings.warn(s3_msg)
+        return getattr(mod, name)
+
+
+def filesystem(protocol, **storage_options):
+    """Instantiate filesystems for given protocol and arguments
+
+    ``storage_options`` are specific to the protocol being chosen, and are
+    passed directly to the class.
+    """
+    if protocol == "arrow_hdfs":
+        warnings.warn(
+            "The 'arrow_hdfs' protocol has been deprecated and will be "
+            "removed in the future. Specify it as 'hdfs'.",
+            DeprecationWarning,
+        )
+
+    cls = get_filesystem_class(protocol)
+    return cls(**storage_options)
+
+
+def available_protocols():
+    """Return a list of the implemented protocols.
+
+    Note that any given protocol may require extra packages to be importable.
+    """
+    return list(known_implementations)
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/transaction.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/transaction.py
new file mode 100644
index 0000000000000000000000000000000000000000..67584d61e8f5f86b22e19beb609ffe49ce7cc689
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/fsspec/transaction.py
@@ -0,0 +1,85 @@
+from collections import deque
+
+
+class Transaction:
+    """Filesystem transaction write context
+
+    Gathers files for deferred commit or discard, so that several write
+    operations can be finalized semi-atomically. This works by having this
+    instance as the ``.transaction`` attribute of the given filesystem
+    """
+
+    def __init__(self, fs):
+        """
+        Parameters
+        ----------
+        fs: FileSystem instance
+        """
+        self.fs = fs
+        self.files = deque()
+
+    def __enter__(self):
+        self.start()
+        return self
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        """End transaction and commit, if exit is not due to exception"""
+        # only commit if there was no exception
+        self.complete(commit=exc_type is None)
+        self.fs._intrans = False
+        self.fs._transaction = None
+
+    def start(self):
+        """Start a transaction on this FileSystem"""
+        self.files = deque()  # clean up after previous failed completions
+        self.fs._intrans = True
+
+    def complete(self, commit=True):
+        """Finish transaction: commit or discard all deferred files"""
+        while self.files:
+            f = self.files.popleft()
+            if commit:
+                f.commit()
+            else:
+                f.discard()
+        self.fs._intrans = False
+
+
+class FileActor:
+    def __init__(self):
+        self.files = []
+
+    def commit(self):
+        for f in self.files:
+            f.commit()
+        self.files.clear()
+
+    def discard(self):
+        for f in self.files:
+            f.discard()
+        self.files.clear()
+
+    def append(self, f):
+        self.files.append(f)
+
+
+class DaskTransaction(Transaction):
+    def __init__(self, fs):
+        """
+        Parameters
+        ----------
+        fs: FileSystem instance
+        """
+        import distributed
+
+        super().__init__(fs)
+        client = distributed.default_client()
+        self.files = client.submit(FileActor, actor=True).result()
+
+    def complete(self, commit=True):
+        """Finish transaction: commit or discard all deferred files"""
+        if commit:
+            self.files.commit().result()
+        else:
+            self.files.discard().result()
+        self.fs._intrans = False
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/functorch/dim/__init__.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/functorch/dim/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..519a7cb271cdc3eef40ccd76c94c504ed1a325e8
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/functorch/dim/__init__.py
@@ -0,0 +1,179 @@
+import dis
+import inspect
+from typing import Sequence, Union
+
+import torch
+
+import functorch._C
+from functorch._C import dim as _C
+from .tree_map import tree_flatten, tree_map
+from .wrap_type import wrap_type
+
+_C._patch_tensor_class()
+dims, DimList, dimlists = _C.dims, _C.DimList, _C.dimlists
+
+
+class DimensionMismatchError(Exception):
+    pass
+
+
+class DimensionBindError(Exception):
+    pass
+
+
+from . import op_properties
+
+# use dict to avoid writing C++ bindings for set
+pointwise = dict.fromkeys(op_properties.pointwise, True)
+
+use_c = True
+if not use_c:
+    from . import reference
+
+
+class _Tensor:
+    # fast path around slow wrapping/unwrapping logic for simply queries used
+    # by the implementation...
+
+    @property
+    def dims(self):
+        return tuple(d for d in self._levels if isinstance(d, Dim))
+
+    def dim(self):
+        return self.ndim
+
+    if use_c:
+        __torch_function__ = classmethod(_C.__torch_function__)
+        expand = _C._instancemethod(_C.expand)
+    else:
+        __torch_function__ = reference.__torch_function__
+        expand = reference.expand
+
+    index = _C._instancemethod(_C.index)
+
+    def __repr__(self):
+        tensor, levels, ndim = self._tensor, self._levels, self.ndim
+        return f"{tensor}\nwith dims={tuple(l + ndim if isinstance(l, int) else l for l in levels)} sizes={tuple(tensor.size())}"
+
+
+TensorLike = (_Tensor, torch.Tensor)
+
+
+class Dim(_C.Dim, _Tensor):
+    # note that _C.Dim comes before tensor because we want the Dim API for things like size to take precendence.
+    # Tensor defines format, but we want to print Dims with special formatting
+    __format__ = object.__format__
+
+
+class Tensor(_Tensor, _C.Tensor):
+    if not use_c:
+        from_batched = staticmethod(_C.Tensor_from_batched)
+    from_positional = staticmethod(_C.Tensor_from_positional)
+    sum = _C._instancemethod(_C.Tensor_sum)
+
+
+def cat(tensors, dim, new_dim):
+    n = dims()
+    return stack(tensors, n, dim).index([n, dim], new_dim)
+
+
+if use_c:
+    _wrap = _C._wrap
+
+    def _def(name, *args, **kwargs):
+        orig = getattr(torch.Tensor, name)
+        setattr(_Tensor, name, _C._instancemethod(_wrap(orig, *args, **kwargs)))
+
+    t__getitem__ = _C._instancemethod(_C.__getitem__)
+    stack = _C.stack
+    split = _C._instancemethod(_C.split)
+else:
+    _wrap, _def = reference._wrap, reference._def
+    t__getitem__ = reference.t__getitem__
+    stack = reference.stack
+    split = reference.split
+
+# note: there is no python reference
+t__setitem__ = _C._instancemethod(_C.__setitem__)
+# this is patched in the C API because otherwise torch.Tensor will
+# no longer be considered a sequence and things will break
+# torch.Tensor.__getitem__ = t__getitem__
+
+_Tensor.__getitem__ = t__getitem__
+# torch.Tensor.__setitem__ = t__setitem__
+_Tensor.__setitem__ = t__setitem__
+
+torch.Tensor.split = split
+_Tensor.split = split
+torch.Tensor.expand = _C._instancemethod(_C.expand)
+torch.Tensor.index = _C._instancemethod(_C.index)
+wrap_type(use_c, _Tensor, torch.Tensor, _Tensor.__torch_function__)
+del _Tensor.ndim
+
+if use_c:
+    _Tensor.order = _C._instancemethod(_C.order)
+else:
+    _Tensor.order = reference.positional
+
+_def("mean")
+_def("sum")
+_def("all")
+_def("amax")
+_def("amin")
+_def("aminmax")
+_def("any")
+_def("count_nonzero")
+_def("logsumexp")
+_def("nanmean")
+_def("nansum")
+_def("prod")
+_def("std", keepdim_offset=2)
+_def("var", keepdim_offset=2)
+_def("max", single_dim=True)
+_def("min", single_dim=True)
+_def("argmax", single_dim=True)
+_def("argmin", single_dim=True)
+_def("kthvalue", single_dim=True)
+_def("median", single_dim=True)
+_def("nanmedian", single_dim=True)
+_def("mode", single_dim=True)
+_def("sort", reduce=False)
+_def("argsort", reduce=False)
+_def("unbind", single_dim=True)
+_def("chunk", dim_offset=1, reduce=False)
+_def("cummax", single_dim=True, reduce=False)
+_def("cummin", single_dim=True, reduce=False)
+_def("cumprod", single_dim=True, reduce=False)
+_def("cumprod_", single_dim=True, reduce=False)
+_def("cumsum", single_dim=True, reduce=False)
+_def("cumsum_", single_dim=True, reduce=False)
+_def("logcumsumexp", single_dim=True, reduce=False)
+_def("renorm", dim_offset=1, single_dim=True, reduce=False)
+_def("softmax", single_dim=True, reduce=False)
+softmax = _wrap(torch.nn.functional.softmax, single_dim=True, reduce=False)
+
+# stuff to handle in the future, because they require special
+# binding logic for dims
+# cross
+# diag_embed
+# diagonal
+# diagonal_scatter
+# diff
+# nanquantile
+# quantile
+# roll
+# rot90
+# topk (new dimes on output)
+# should these all be subsumed by inplace indexing?
+# index_add_
+# index_add
+# index_copy
+# index_copy_
+# index_fill
+# index_fill_
+# index_select
+# scatter
+# scatter_
+# scatter_add
+# scatter_add_
+# scatter_reduce
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diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/functorch/dim/batch_tensor.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/functorch/dim/batch_tensor.py
new file mode 100644
index 0000000000000000000000000000000000000000..0fc17f2492d5344821071a726a0e3a0e9d5dea95
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/functorch/dim/batch_tensor.py
@@ -0,0 +1,25 @@
+# Copyright (c) Facebook, Inc. and its affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the BSD-style license found in the
+# LICENSE file in the root directory of this source tree.
+from contextlib import contextmanager
+
+from torch._C._functorch import _vmap_add_layers, _vmap_remove_layers
+
+_enabled = False
+
+
+@contextmanager
+def _enable_layers(dims):
+    global _enabled
+    assert not _enabled
+    input = sorted((d._level, d.size) for d in dims if not isinstance(d, int))
+    n = len(input)
+    try:
+        _vmap_add_layers(input)
+        _enabled = True
+        yield
+    finally:
+        _enabled = False
+        _vmap_remove_layers(n)
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_base.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_base.py
new file mode 100644
index 0000000000000000000000000000000000000000..1946f8daf4dbe165b3943be09af361812828aab1
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_base.py
@@ -0,0 +1,494 @@
+from operator import gt, lt
+
+from .libmp.backend import xrange
+
+from .functions.functions import SpecialFunctions
+from .functions.rszeta import RSCache
+from .calculus.quadrature import QuadratureMethods
+from .calculus.inverselaplace import LaplaceTransformInversionMethods
+from .calculus.calculus import CalculusMethods
+from .calculus.optimization import OptimizationMethods
+from .calculus.odes import ODEMethods
+from .matrices.matrices import MatrixMethods
+from .matrices.calculus import MatrixCalculusMethods
+from .matrices.linalg import LinearAlgebraMethods
+from .matrices.eigen import Eigen
+from .identification import IdentificationMethods
+from .visualization import VisualizationMethods
+
+from . import libmp
+
+class Context(object):
+    pass
+
+class StandardBaseContext(Context,
+    SpecialFunctions,
+    RSCache,
+    QuadratureMethods,
+    LaplaceTransformInversionMethods,
+    CalculusMethods,
+    MatrixMethods,
+    MatrixCalculusMethods,
+    LinearAlgebraMethods,
+    Eigen,
+    IdentificationMethods,
+    OptimizationMethods,
+    ODEMethods,
+    VisualizationMethods):
+
+    NoConvergence = libmp.NoConvergence
+    ComplexResult = libmp.ComplexResult
+
+    def __init__(ctx):
+        ctx._aliases = {}
+        # Call those that need preinitialization (e.g. for wrappers)
+        SpecialFunctions.__init__(ctx)
+        RSCache.__init__(ctx)
+        QuadratureMethods.__init__(ctx)
+        LaplaceTransformInversionMethods.__init__(ctx)
+        CalculusMethods.__init__(ctx)
+        MatrixMethods.__init__(ctx)
+
+    def _init_aliases(ctx):
+        for alias, value in ctx._aliases.items():
+            try:
+                setattr(ctx, alias, getattr(ctx, value))
+            except AttributeError:
+                pass
+
+    _fixed_precision = False
+
+    # XXX
+    verbose = False
+
+    def warn(ctx, msg):
+        print("Warning:", msg)
+
+    def bad_domain(ctx, msg):
+        raise ValueError(msg)
+
+    def _re(ctx, x):
+        if hasattr(x, "real"):
+            return x.real
+        return x
+
+    def _im(ctx, x):
+        if hasattr(x, "imag"):
+            return x.imag
+        return ctx.zero
+
+    def _as_points(ctx, x):
+        return x
+
+    def fneg(ctx, x, **kwargs):
+        return -ctx.convert(x)
+
+    def fadd(ctx, x, y, **kwargs):
+        return ctx.convert(x)+ctx.convert(y)
+
+    def fsub(ctx, x, y, **kwargs):
+        return ctx.convert(x)-ctx.convert(y)
+
+    def fmul(ctx, x, y, **kwargs):
+        return ctx.convert(x)*ctx.convert(y)
+
+    def fdiv(ctx, x, y, **kwargs):
+        return ctx.convert(x)/ctx.convert(y)
+
+    def fsum(ctx, args, absolute=False, squared=False):
+        if absolute:
+            if squared:
+                return sum((abs(x)**2 for x in args), ctx.zero)
+            return sum((abs(x) for x in args), ctx.zero)
+        if squared:
+            return sum((x**2 for x in args), ctx.zero)
+        return sum(args, ctx.zero)
+
+    def fdot(ctx, xs, ys=None, conjugate=False):
+        if ys is not None:
+            xs = zip(xs, ys)
+        if conjugate:
+            cf = ctx.conj
+            return sum((x*cf(y) for (x,y) in xs), ctx.zero)
+        else:
+            return sum((x*y for (x,y) in xs), ctx.zero)
+
+    def fprod(ctx, args):
+        prod = ctx.one
+        for arg in args:
+            prod *= arg
+        return prod
+
+    def nprint(ctx, x, n=6, **kwargs):
+        """
+        Equivalent to ``print(nstr(x, n))``.
+        """
+        print(ctx.nstr(x, n, **kwargs))
+
+    def chop(ctx, x, tol=None):
+        """
+        Chops off small real or imaginary parts, or converts
+        numbers close to zero to exact zeros. The input can be a
+        single number or an iterable::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> chop(5+1e-10j, tol=1e-9)
+            mpf('5.0')
+            >>> nprint(chop([1.0, 1e-20, 3+1e-18j, -4, 2]))
+            [1.0, 0.0, 3.0, -4.0, 2.0]
+
+        The tolerance defaults to ``100*eps``.
+        """
+        if tol is None:
+            tol = 100*ctx.eps
+        try:
+            x = ctx.convert(x)
+            absx = abs(x)
+            if abs(x) < tol:
+                return ctx.zero
+            if ctx._is_complex_type(x):
+                #part_tol = min(tol, absx*tol)
+                part_tol = max(tol, absx*tol)
+                if abs(x.imag) < part_tol:
+                    return x.real
+                if abs(x.real) < part_tol:
+                    return ctx.mpc(0, x.imag)
+        except TypeError:
+            if isinstance(x, ctx.matrix):
+                return x.apply(lambda a: ctx.chop(a, tol))
+            if hasattr(x, "__iter__"):
+                return [ctx.chop(a, tol) for a in x]
+        return x
+
+    def almosteq(ctx, s, t, rel_eps=None, abs_eps=None):
+        r"""
+        Determine whether the difference between `s` and `t` is smaller
+        than a given epsilon, either relatively or absolutely.
+
+        Both a maximum relative difference and a maximum difference
+        ('epsilons') may be specified. The absolute difference is
+        defined as `|s-t|` and the relative difference is defined
+        as `|s-t|/\max(|s|, |t|)`.
+
+        If only one epsilon is given, both are set to the same value.
+        If none is given, both epsilons are set to `2^{-p+m}` where
+        `p` is the current working precision and `m` is a small
+        integer. The default setting typically allows :func:`~mpmath.almosteq`
+        to be used to check for mathematical equality
+        in the presence of small rounding errors.
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> almosteq(3.141592653589793, 3.141592653589790)
+            True
+            >>> almosteq(3.141592653589793, 3.141592653589700)
+            False
+            >>> almosteq(3.141592653589793, 3.141592653589700, 1e-10)
+            True
+            >>> almosteq(1e-20, 2e-20)
+            True
+            >>> almosteq(1e-20, 2e-20, rel_eps=0, abs_eps=0)
+            False
+
+        """
+        t = ctx.convert(t)
+        if abs_eps is None and rel_eps is None:
+            rel_eps = abs_eps = ctx.ldexp(1, -ctx.prec+4)
+        if abs_eps is None:
+            abs_eps = rel_eps
+        elif rel_eps is None:
+            rel_eps = abs_eps
+        diff = abs(s-t)
+        if diff <= abs_eps:
+            return True
+        abss = abs(s)
+        abst = abs(t)
+        if abss < abst:
+            err = diff/abst
+        else:
+            err = diff/abss
+        return err <= rel_eps
+
+    def arange(ctx, *args):
+        r"""
+        This is a generalized version of Python's :func:`~mpmath.range` function
+        that accepts fractional endpoints and step sizes and
+        returns a list of ``mpf`` instances. Like :func:`~mpmath.range`,
+        :func:`~mpmath.arange` can be called with 1, 2 or 3 arguments:
+
+        ``arange(b)``
+            `[0, 1, 2, \ldots, x]`
+        ``arange(a, b)``
+            `[a, a+1, a+2, \ldots, x]`
+        ``arange(a, b, h)``
+            `[a, a+h, a+h, \ldots, x]`
+
+        where `b-1 \le x < b` (in the third case, `b-h \le x < b`).
+
+        Like Python's :func:`~mpmath.range`, the endpoint is not included. To
+        produce ranges where the endpoint is included, :func:`~mpmath.linspace`
+        is more convenient.
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> arange(4)
+            [mpf('0.0'), mpf('1.0'), mpf('2.0'), mpf('3.0')]
+            >>> arange(1, 2, 0.25)
+            [mpf('1.0'), mpf('1.25'), mpf('1.5'), mpf('1.75')]
+            >>> arange(1, -1, -0.75)
+            [mpf('1.0'), mpf('0.25'), mpf('-0.5')]
+
+        """
+        if not len(args) <= 3:
+            raise TypeError('arange expected at most 3 arguments, got %i'
+                            % len(args))
+        if not len(args) >= 1:
+            raise TypeError('arange expected at least 1 argument, got %i'
+                            % len(args))
+        # set default
+        a = 0
+        dt = 1
+        # interpret arguments
+        if len(args) == 1:
+            b = args[0]
+        elif len(args) >= 2:
+            a = args[0]
+            b = args[1]
+        if len(args) == 3:
+            dt = args[2]
+        a, b, dt = ctx.mpf(a), ctx.mpf(b), ctx.mpf(dt)
+        assert a + dt != a, 'dt is too small and would cause an infinite loop'
+        # adapt code for sign of dt
+        if a > b:
+            if dt > 0:
+                return []
+            op = gt
+        else:
+            if dt < 0:
+                return []
+            op = lt
+        # create list
+        result = []
+        i = 0
+        t = a
+        while 1:
+            t = a + dt*i
+            i += 1
+            if op(t, b):
+                result.append(t)
+            else:
+                break
+        return result
+
+    def linspace(ctx, *args, **kwargs):
+        """
+        ``linspace(a, b, n)`` returns a list of `n` evenly spaced
+        samples from `a` to `b`. The syntax ``linspace(mpi(a,b), n)``
+        is also valid.
+
+        This function is often more convenient than :func:`~mpmath.arange`
+        for partitioning an interval into subintervals, since
+        the endpoint is included::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> linspace(1, 4, 4)
+            [mpf('1.0'), mpf('2.0'), mpf('3.0'), mpf('4.0')]
+
+        You may also provide the keyword argument ``endpoint=False``::
+
+            >>> linspace(1, 4, 4, endpoint=False)
+            [mpf('1.0'), mpf('1.75'), mpf('2.5'), mpf('3.25')]
+
+        """
+        if len(args) == 3:
+            a = ctx.mpf(args[0])
+            b = ctx.mpf(args[1])
+            n = int(args[2])
+        elif len(args) == 2:
+            assert hasattr(args[0], '_mpi_')
+            a = args[0].a
+            b = args[0].b
+            n = int(args[1])
+        else:
+            raise TypeError('linspace expected 2 or 3 arguments, got %i' \
+                            % len(args))
+        if n < 1:
+            raise ValueError('n must be greater than 0')
+        if not 'endpoint' in kwargs or kwargs['endpoint']:
+            if n == 1:
+                return [ctx.mpf(a)]
+            step = (b - a) / ctx.mpf(n - 1)
+            y = [i*step + a for i in xrange(n)]
+            y[-1] = b
+        else:
+            step = (b - a) / ctx.mpf(n)
+            y = [i*step + a for i in xrange(n)]
+        return y
+
+    def cos_sin(ctx, z, **kwargs):
+        return ctx.cos(z, **kwargs), ctx.sin(z, **kwargs)
+
+    def cospi_sinpi(ctx, z, **kwargs):
+        return ctx.cospi(z, **kwargs), ctx.sinpi(z, **kwargs)
+
+    def _default_hyper_maxprec(ctx, p):
+        return int(1000 * p**0.25 + 4*p)
+
+    _gcd = staticmethod(libmp.gcd)
+    list_primes = staticmethod(libmp.list_primes)
+    isprime = staticmethod(libmp.isprime)
+    bernfrac = staticmethod(libmp.bernfrac)
+    moebius = staticmethod(libmp.moebius)
+    _ifac = staticmethod(libmp.ifac)
+    _eulernum = staticmethod(libmp.eulernum)
+    _stirling1 = staticmethod(libmp.stirling1)
+    _stirling2 = staticmethod(libmp.stirling2)
+
+    def sum_accurately(ctx, terms, check_step=1):
+        prec = ctx.prec
+        try:
+            extraprec = 10
+            while 1:
+                ctx.prec = prec + extraprec + 5
+                max_mag = ctx.ninf
+                s = ctx.zero
+                k = 0
+                for term in terms():
+                    s += term
+                    if (not k % check_step) and term:
+                        term_mag = ctx.mag(term)
+                        max_mag = max(max_mag, term_mag)
+                        sum_mag = ctx.mag(s)
+                        if sum_mag - term_mag > ctx.prec:
+                            break
+                    k += 1
+                cancellation = max_mag - sum_mag
+                if cancellation != cancellation:
+                    break
+                if cancellation < extraprec or ctx._fixed_precision:
+                    break
+                extraprec += min(ctx.prec, cancellation)
+            return s
+        finally:
+            ctx.prec = prec
+
+    def mul_accurately(ctx, factors, check_step=1):
+        prec = ctx.prec
+        try:
+            extraprec = 10
+            while 1:
+                ctx.prec = prec + extraprec + 5
+                max_mag = ctx.ninf
+                one = ctx.one
+                s = one
+                k = 0
+                for factor in factors():
+                    s *= factor
+                    term = factor - one
+                    if (not k % check_step):
+                        term_mag = ctx.mag(term)
+                        max_mag = max(max_mag, term_mag)
+                        sum_mag = ctx.mag(s-one)
+                        #if sum_mag - term_mag > ctx.prec:
+                        #    break
+                        if -term_mag > ctx.prec:
+                            break
+                    k += 1
+                cancellation = max_mag - sum_mag
+                if cancellation != cancellation:
+                    break
+                if cancellation < extraprec or ctx._fixed_precision:
+                    break
+                extraprec += min(ctx.prec, cancellation)
+            return s
+        finally:
+            ctx.prec = prec
+
+    def power(ctx, x, y):
+        r"""Converts `x` and `y` to mpmath numbers and evaluates
+        `x^y = \exp(y \log(x))`::
+
+            >>> from mpmath import *
+            >>> mp.dps = 30; mp.pretty = True
+            >>> power(2, 0.5)
+            1.41421356237309504880168872421
+
+        This shows the leading few digits of a large Mersenne prime
+        (performing the exact calculation ``2**43112609-1`` and
+        displaying the result in Python would be very slow)::
+
+            >>> power(2, 43112609)-1
+            3.16470269330255923143453723949e+12978188
+        """
+        return ctx.convert(x) ** ctx.convert(y)
+
+    def _zeta_int(ctx, n):
+        return ctx.zeta(n)
+
+    def maxcalls(ctx, f, N):
+        """
+        Return a wrapped copy of *f* that raises ``NoConvergence`` when *f*
+        has been called more than *N* times::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> f = maxcalls(sin, 10)
+            >>> print(sum(f(n) for n in range(10)))
+            1.95520948210738
+            >>> f(10) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: maxcalls: function evaluated 10 times
+
+        """
+        counter = [0]
+        def f_maxcalls_wrapped(*args, **kwargs):
+            counter[0] += 1
+            if counter[0] > N:
+                raise ctx.NoConvergence("maxcalls: function evaluated %i times" % N)
+            return f(*args, **kwargs)
+        return f_maxcalls_wrapped
+
+    def memoize(ctx, f):
+        """
+        Return a wrapped copy of *f* that caches computed values, i.e.
+        a memoized copy of *f*. Values are only reused if the cached precision
+        is equal to or higher than the working precision::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = True
+            >>> f = memoize(maxcalls(sin, 1))
+            >>> f(2)
+            0.909297426825682
+            >>> f(2)
+            0.909297426825682
+            >>> mp.dps = 25
+            >>> f(2) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: maxcalls: function evaluated 1 times
+
+        """
+        f_cache = {}
+        def f_cached(*args, **kwargs):
+            if kwargs:
+                key = args, tuple(kwargs.items())
+            else:
+                key = args
+            prec = ctx.prec
+            if key in f_cache:
+                cprec, cvalue = f_cache[key]
+                if cprec >= prec:
+                    return +cvalue
+            value = f(*args, **kwargs)
+            f_cache[key] = (prec, value)
+            return value
+        f_cached.__name__ = f.__name__
+        f_cached.__doc__ = f.__doc__
+        return f_cached
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_fp.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_fp.py
new file mode 100644
index 0000000000000000000000000000000000000000..aa72ea5b03fde4da66b0d8fbf8ffa4012e3f6178
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_fp.py
@@ -0,0 +1,253 @@
+from .ctx_base import StandardBaseContext
+
+import math
+import cmath
+from . import math2
+
+from . import function_docs
+
+from .libmp import mpf_bernoulli, to_float, int_types
+from . import libmp
+
+class FPContext(StandardBaseContext):
+    """
+    Context for fast low-precision arithmetic (53-bit precision, giving at most
+    about 15-digit accuracy), using Python's builtin float and complex.
+    """
+
+    def __init__(ctx):
+        StandardBaseContext.__init__(ctx)
+
+        # Override SpecialFunctions implementation
+        ctx.loggamma = math2.loggamma
+        ctx._bernoulli_cache = {}
+        ctx.pretty = False
+
+        ctx._init_aliases()
+
+    _mpq = lambda cls, x: float(x[0])/x[1]
+
+    NoConvergence = libmp.NoConvergence
+
+    def _get_prec(ctx): return 53
+    def _set_prec(ctx, p): return
+    def _get_dps(ctx): return 15
+    def _set_dps(ctx, p): return
+
+    _fixed_precision = True
+
+    prec = property(_get_prec, _set_prec)
+    dps = property(_get_dps, _set_dps)
+
+    zero = 0.0
+    one = 1.0
+    eps = math2.EPS
+    inf = math2.INF
+    ninf = math2.NINF
+    nan = math2.NAN
+    j = 1j
+
+    # Called by SpecialFunctions.__init__()
+    @classmethod
+    def _wrap_specfun(cls, name, f, wrap):
+        if wrap:
+            def f_wrapped(ctx, *args, **kwargs):
+                convert = ctx.convert
+                args = [convert(a) for a in args]
+                return f(ctx, *args, **kwargs)
+        else:
+            f_wrapped = f
+        f_wrapped.__doc__ = function_docs.__dict__.get(name, f.__doc__)
+        setattr(cls, name, f_wrapped)
+
+    def bernoulli(ctx, n):
+        cache = ctx._bernoulli_cache
+        if n in cache:
+            return cache[n]
+        cache[n] = to_float(mpf_bernoulli(n, 53, 'n'), strict=True)
+        return cache[n]
+
+    pi = math2.pi
+    e = math2.e
+    euler = math2.euler
+    sqrt2 = 1.4142135623730950488
+    sqrt5 = 2.2360679774997896964
+    phi = 1.6180339887498948482
+    ln2 = 0.69314718055994530942
+    ln10 = 2.302585092994045684
+    euler = 0.57721566490153286061
+    catalan = 0.91596559417721901505
+    khinchin = 2.6854520010653064453
+    apery = 1.2020569031595942854
+    glaisher = 1.2824271291006226369
+
+    absmin = absmax = abs
+
+    def is_special(ctx, x):
+        return x - x != 0.0
+
+    def isnan(ctx, x):
+        return x != x
+
+    def isinf(ctx, x):
+        return abs(x) == math2.INF
+
+    def isnormal(ctx, x):
+        if x:
+            return x - x == 0.0
+        return False
+
+    def isnpint(ctx, x):
+        if type(x) is complex:
+            if x.imag:
+                return False
+            x = x.real
+        return x <= 0.0 and round(x) == x
+
+    mpf = float
+    mpc = complex
+
+    def convert(ctx, x):
+        try:
+            return float(x)
+        except:
+            return complex(x)
+
+    power = staticmethod(math2.pow)
+    sqrt = staticmethod(math2.sqrt)
+    exp = staticmethod(math2.exp)
+    ln = log = staticmethod(math2.log)
+    cos = staticmethod(math2.cos)
+    sin = staticmethod(math2.sin)
+    tan = staticmethod(math2.tan)
+    cos_sin = staticmethod(math2.cos_sin)
+    acos = staticmethod(math2.acos)
+    asin = staticmethod(math2.asin)
+    atan = staticmethod(math2.atan)
+    cosh = staticmethod(math2.cosh)
+    sinh = staticmethod(math2.sinh)
+    tanh = staticmethod(math2.tanh)
+    gamma = staticmethod(math2.gamma)
+    rgamma = staticmethod(math2.rgamma)
+    fac = factorial = staticmethod(math2.factorial)
+    floor = staticmethod(math2.floor)
+    ceil = staticmethod(math2.ceil)
+    cospi = staticmethod(math2.cospi)
+    sinpi = staticmethod(math2.sinpi)
+    cbrt = staticmethod(math2.cbrt)
+    _nthroot = staticmethod(math2.nthroot)
+    _ei = staticmethod(math2.ei)
+    _e1 = staticmethod(math2.e1)
+    _zeta = _zeta_int = staticmethod(math2.zeta)
+
+    # XXX: math2
+    def arg(ctx, z):
+        z = complex(z)
+        return math.atan2(z.imag, z.real)
+
+    def expj(ctx, x):
+        return ctx.exp(ctx.j*x)
+
+    def expjpi(ctx, x):
+        return ctx.exp(ctx.j*ctx.pi*x)
+
+    ldexp = math.ldexp
+    frexp = math.frexp
+
+    def mag(ctx, z):
+        if z:
+            return ctx.frexp(abs(z))[1]
+        return ctx.ninf
+
+    def isint(ctx, z):
+        if hasattr(z, "imag"):   # float/int don't have .real/.imag in py2.5
+            if z.imag:
+                return False
+            z = z.real
+        try:
+            return z == int(z)
+        except:
+            return False
+
+    def nint_distance(ctx, z):
+        if hasattr(z, "imag"):   # float/int don't have .real/.imag in py2.5
+            n = round(z.real)
+        else:
+            n = round(z)
+        if n == z:
+            return n, ctx.ninf
+        return n, ctx.mag(abs(z-n))
+
+    def _convert_param(ctx, z):
+        if type(z) is tuple:
+            p, q = z
+            return ctx.mpf(p) / q, 'R'
+        if hasattr(z, "imag"):    # float/int don't have .real/.imag in py2.5
+            intz = int(z.real)
+        else:
+            intz = int(z)
+        if z == intz:
+            return intz, 'Z'
+        return z, 'R'
+
+    def _is_real_type(ctx, z):
+        return isinstance(z, float) or isinstance(z, int_types)
+
+    def _is_complex_type(ctx, z):
+        return isinstance(z, complex)
+
+    def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
+        coeffs = list(coeffs)
+        num = range(p)
+        den = range(p,p+q)
+        tol = ctx.eps
+        s = t = 1.0
+        k = 0
+        while 1:
+            for i in num: t *= (coeffs[i]+k)
+            for i in den: t /= (coeffs[i]+k)
+            k += 1; t /= k; t *= z; s += t
+            if abs(t) < tol:
+                return s
+            if k > maxterms:
+                raise ctx.NoConvergence
+
+    def atan2(ctx, x, y):
+        return math.atan2(x, y)
+
+    def psi(ctx, m, z):
+        m = int(m)
+        if m == 0:
+            return ctx.digamma(z)
+        return (-1)**(m+1) * ctx.fac(m) * ctx.zeta(m+1, z)
+
+    digamma = staticmethod(math2.digamma)
+
+    def harmonic(ctx, x):
+        x = ctx.convert(x)
+        if x == 0 or x == 1:
+            return x
+        return ctx.digamma(x+1) + ctx.euler
+
+    nstr = str
+
+    def to_fixed(ctx, x, prec):
+        return int(math.ldexp(x, prec))
+
+    def rand(ctx):
+        import random
+        return random.random()
+
+    _erf = staticmethod(math2.erf)
+    _erfc = staticmethod(math2.erfc)
+
+    def sum_accurately(ctx, terms, check_step=1):
+        s = ctx.zero
+        k = 0
+        for term in terms():
+            s += term
+            if (not k % check_step) and term:
+                if abs(term) <= 1e-18*abs(s):
+                    break
+            k += 1
+        return s
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_iv.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_iv.py
new file mode 100644
index 0000000000000000000000000000000000000000..c038e00a5677e318d222b63c22d225e3045e1c2b
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_iv.py
@@ -0,0 +1,551 @@
+import operator
+
+from . import libmp
+
+from .libmp.backend import basestring
+
+from .libmp import (
+    int_types, MPZ_ONE,
+    prec_to_dps, dps_to_prec, repr_dps,
+    round_floor, round_ceiling,
+    fzero, finf, fninf, fnan,
+    mpf_le, mpf_neg,
+    from_int, from_float, from_str, from_rational,
+    mpi_mid, mpi_delta, mpi_str,
+    mpi_abs, mpi_pos, mpi_neg, mpi_add, mpi_sub,
+    mpi_mul, mpi_div, mpi_pow_int, mpi_pow,
+    mpi_from_str,
+    mpci_pos, mpci_neg, mpci_add, mpci_sub, mpci_mul, mpci_div, mpci_pow,
+    mpci_abs, mpci_pow, mpci_exp, mpci_log,
+    ComplexResult,
+    mpf_hash, mpc_hash)
+from .matrices.matrices import _matrix
+
+mpi_zero = (fzero, fzero)
+
+from .ctx_base import StandardBaseContext
+
+new = object.__new__
+
+def convert_mpf_(x, prec, rounding):
+    if hasattr(x, "_mpf_"): return x._mpf_
+    if isinstance(x, int_types): return from_int(x, prec, rounding)
+    if isinstance(x, float): return from_float(x, prec, rounding)
+    if isinstance(x, basestring): return from_str(x, prec, rounding)
+    raise NotImplementedError
+
+
+class ivmpf(object):
+    """
+    Interval arithmetic class. Precision is controlled by iv.prec.
+    """
+
+    def __new__(cls, x=0):
+        return cls.ctx.convert(x)
+
+    def cast(self, cls, f_convert):
+        a, b = self._mpi_
+        if a == b:
+            return cls(f_convert(a))
+        raise ValueError
+
+    def __int__(self):
+        return self.cast(int, libmp.to_int)
+
+    def __float__(self):
+        return self.cast(float, libmp.to_float)
+
+    def __complex__(self):
+        return self.cast(complex, libmp.to_float)
+
+    def __hash__(self):
+        a, b = self._mpi_
+        if a == b:
+            return mpf_hash(a)
+        else:
+            return hash(self._mpi_)
+
+    @property
+    def real(self): return self
+
+    @property
+    def imag(self): return self.ctx.zero
+
+    def conjugate(self): return self
+
+    @property
+    def a(self):
+        a, b = self._mpi_
+        return self.ctx.make_mpf((a, a))
+
+    @property
+    def b(self):
+        a, b = self._mpi_
+        return self.ctx.make_mpf((b, b))
+
+    @property
+    def mid(self):
+        ctx = self.ctx
+        v = mpi_mid(self._mpi_, ctx.prec)
+        return ctx.make_mpf((v, v))
+
+    @property
+    def delta(self):
+        ctx = self.ctx
+        v = mpi_delta(self._mpi_, ctx.prec)
+        return ctx.make_mpf((v,v))
+
+    @property
+    def _mpci_(self):
+        return self._mpi_, mpi_zero
+
+    def _compare(*args):
+        raise TypeError("no ordering relation is defined for intervals")
+
+    __gt__ = _compare
+    __le__ = _compare
+    __gt__ = _compare
+    __ge__ = _compare
+
+    def __contains__(self, t):
+        t = self.ctx.mpf(t)
+        return (self.a <= t.a) and (t.b <= self.b)
+
+    def __str__(self):
+        return mpi_str(self._mpi_, self.ctx.prec)
+
+    def __repr__(self):
+        if self.ctx.pretty:
+            return str(self)
+        a, b = self._mpi_
+        n = repr_dps(self.ctx.prec)
+        a = libmp.to_str(a, n)
+        b = libmp.to_str(b, n)
+        return "mpi(%r, %r)" % (a, b)
+
+    def _compare(s, t, cmpfun):
+        if not hasattr(t, "_mpi_"):
+            try:
+                t = s.ctx.convert(t)
+            except:
+                return NotImplemented
+        return cmpfun(s._mpi_, t._mpi_)
+
+    def __eq__(s, t): return s._compare(t, libmp.mpi_eq)
+    def __ne__(s, t): return s._compare(t, libmp.mpi_ne)
+    def __lt__(s, t): return s._compare(t, libmp.mpi_lt)
+    def __le__(s, t): return s._compare(t, libmp.mpi_le)
+    def __gt__(s, t): return s._compare(t, libmp.mpi_gt)
+    def __ge__(s, t): return s._compare(t, libmp.mpi_ge)
+
+    def __abs__(self):
+        return self.ctx.make_mpf(mpi_abs(self._mpi_, self.ctx.prec))
+    def __pos__(self):
+        return self.ctx.make_mpf(mpi_pos(self._mpi_, self.ctx.prec))
+    def __neg__(self):
+        return self.ctx.make_mpf(mpi_neg(self._mpi_, self.ctx.prec))
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.ctx.almosteq(s, t, rel_eps, abs_eps)
+
+class ivmpc(object):
+
+    def __new__(cls, re=0, im=0):
+        re = cls.ctx.convert(re)
+        im = cls.ctx.convert(im)
+        y = new(cls)
+        y._mpci_ = re._mpi_, im._mpi_
+        return y
+
+    def __hash__(self):
+        (a, b), (c,d) = self._mpci_
+        if a == b and c == d:
+            return mpc_hash((a, c))
+        else:
+            return hash(self._mpci_)
+
+    def __repr__(s):
+        if s.ctx.pretty:
+            return str(s)
+        return "iv.mpc(%s, %s)" % (repr(s.real), repr(s.imag))
+
+    def __str__(s):
+        return "(%s + %s*j)" % (str(s.real), str(s.imag))
+
+    @property
+    def a(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((a, a))
+
+    @property
+    def b(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((b, b))
+
+    @property
+    def c(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((c, c))
+
+    @property
+    def d(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((d, d))
+
+    @property
+    def real(s):
+        return s.ctx.make_mpf(s._mpci_[0])
+
+    @property
+    def imag(s):
+        return s.ctx.make_mpf(s._mpci_[1])
+
+    def conjugate(s):
+        a, b = s._mpci_
+        return s.ctx.make_mpc((a, mpf_neg(b)))
+
+    def overlap(s, t):
+        t = s.ctx.convert(t)
+        real_overlap = (s.a <= t.a <= s.b) or (s.a <= t.b <= s.b) or (t.a <= s.a <= t.b) or (t.a <= s.b <= t.b)
+        imag_overlap = (s.c <= t.c <= s.d) or (s.c <= t.d <= s.d) or (t.c <= s.c <= t.d) or (t.c <= s.d <= t.d)
+        return real_overlap and imag_overlap
+
+    def __contains__(s, t):
+        t = s.ctx.convert(t)
+        return t.real in s.real and t.imag in s.imag
+
+    def _compare(s, t, ne=False):
+        if not isinstance(t, s.ctx._types):
+            try:
+                t = s.ctx.convert(t)
+            except:
+                return NotImplemented
+        if hasattr(t, '_mpi_'):
+            tval = t._mpi_, mpi_zero
+        elif hasattr(t, '_mpci_'):
+            tval = t._mpci_
+        if ne:
+            return s._mpci_ != tval
+        return s._mpci_ == tval
+
+    def __eq__(s, t): return s._compare(t)
+    def __ne__(s, t): return s._compare(t, True)
+
+    def __lt__(s, t): raise TypeError("complex intervals cannot be ordered")
+    __le__ = __gt__ = __ge__ = __lt__
+
+    def __neg__(s): return s.ctx.make_mpc(mpci_neg(s._mpci_, s.ctx.prec))
+    def __pos__(s): return s.ctx.make_mpc(mpci_pos(s._mpci_, s.ctx.prec))
+    def __abs__(s): return s.ctx.make_mpf(mpci_abs(s._mpci_, s.ctx.prec))
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.ctx.almosteq(s, t, rel_eps, abs_eps)
+
+def _binary_op(f_real, f_complex):
+    def g_complex(ctx, sval, tval):
+        return ctx.make_mpc(f_complex(sval, tval, ctx.prec))
+    def g_real(ctx, sval, tval):
+        try:
+            return ctx.make_mpf(f_real(sval, tval, ctx.prec))
+        except ComplexResult:
+            sval = (sval, mpi_zero)
+            tval = (tval, mpi_zero)
+            return g_complex(ctx, sval, tval)
+    def lop_real(s, t):
+        if isinstance(t, _matrix): return NotImplemented
+        ctx = s.ctx
+        if not isinstance(t, ctx._types): t = ctx.convert(t)
+        if hasattr(t, "_mpi_"): return g_real(ctx, s._mpi_, t._mpi_)
+        if hasattr(t, "_mpci_"): return g_complex(ctx, (s._mpi_, mpi_zero), t._mpci_)
+        return NotImplemented
+    def rop_real(s, t):
+        ctx = s.ctx
+        if not isinstance(t, ctx._types): t = ctx.convert(t)
+        if hasattr(t, "_mpi_"): return g_real(ctx, t._mpi_, s._mpi_)
+        if hasattr(t, "_mpci_"): return g_complex(ctx, t._mpci_, (s._mpi_, mpi_zero))
+        return NotImplemented
+    def lop_complex(s, t):
+        if isinstance(t, _matrix): return NotImplemented
+        ctx = s.ctx
+        if not isinstance(t, s.ctx._types):
+            try:
+                t = s.ctx.convert(t)
+            except (ValueError, TypeError):
+                return NotImplemented
+        return g_complex(ctx, s._mpci_, t._mpci_)
+    def rop_complex(s, t):
+        ctx = s.ctx
+        if not isinstance(t, s.ctx._types):
+            t = s.ctx.convert(t)
+        return g_complex(ctx, t._mpci_, s._mpci_)
+    return lop_real, rop_real, lop_complex, rop_complex
+
+ivmpf.__add__, ivmpf.__radd__, ivmpc.__add__, ivmpc.__radd__ = _binary_op(mpi_add, mpci_add)
+ivmpf.__sub__, ivmpf.__rsub__, ivmpc.__sub__, ivmpc.__rsub__ = _binary_op(mpi_sub, mpci_sub)
+ivmpf.__mul__, ivmpf.__rmul__, ivmpc.__mul__, ivmpc.__rmul__ = _binary_op(mpi_mul, mpci_mul)
+ivmpf.__div__, ivmpf.__rdiv__, ivmpc.__div__, ivmpc.__rdiv__ = _binary_op(mpi_div, mpci_div)
+ivmpf.__pow__, ivmpf.__rpow__, ivmpc.__pow__, ivmpc.__rpow__ = _binary_op(mpi_pow, mpci_pow)
+
+ivmpf.__truediv__ = ivmpf.__div__; ivmpf.__rtruediv__ = ivmpf.__rdiv__
+ivmpc.__truediv__ = ivmpc.__div__; ivmpc.__rtruediv__ = ivmpc.__rdiv__
+
+class ivmpf_constant(ivmpf):
+    def __new__(cls, f):
+        self = new(cls)
+        self._f = f
+        return self
+    def _get_mpi_(self):
+        prec = self.ctx._prec[0]
+        a = self._f(prec, round_floor)
+        b = self._f(prec, round_ceiling)
+        return a, b
+    _mpi_ = property(_get_mpi_)
+
+class MPIntervalContext(StandardBaseContext):
+
+    def __init__(ctx):
+        ctx.mpf = type('ivmpf', (ivmpf,), {})
+        ctx.mpc = type('ivmpc', (ivmpc,), {})
+        ctx._types = (ctx.mpf, ctx.mpc)
+        ctx._constant = type('ivmpf_constant', (ivmpf_constant,), {})
+        ctx._prec = [53]
+        ctx._set_prec(53)
+        ctx._constant._ctxdata = ctx.mpf._ctxdata = ctx.mpc._ctxdata = [ctx.mpf, new, ctx._prec]
+        ctx._constant.ctx = ctx.mpf.ctx = ctx.mpc.ctx = ctx
+        ctx.pretty = False
+        StandardBaseContext.__init__(ctx)
+        ctx._init_builtins()
+
+    def _mpi(ctx, a, b=None):
+        if b is None:
+            return ctx.mpf(a)
+        return ctx.mpf((a,b))
+
+    def _init_builtins(ctx):
+        ctx.one = ctx.mpf(1)
+        ctx.zero = ctx.mpf(0)
+        ctx.inf = ctx.mpf('inf')
+        ctx.ninf = -ctx.inf
+        ctx.nan = ctx.mpf('nan')
+        ctx.j = ctx.mpc(0,1)
+        ctx.exp = ctx._wrap_mpi_function(libmp.mpi_exp, libmp.mpci_exp)
+        ctx.sqrt = ctx._wrap_mpi_function(libmp.mpi_sqrt)
+        ctx.ln = ctx._wrap_mpi_function(libmp.mpi_log, libmp.mpci_log)
+        ctx.cos = ctx._wrap_mpi_function(libmp.mpi_cos, libmp.mpci_cos)
+        ctx.sin = ctx._wrap_mpi_function(libmp.mpi_sin, libmp.mpci_sin)
+        ctx.tan = ctx._wrap_mpi_function(libmp.mpi_tan)
+        ctx.gamma = ctx._wrap_mpi_function(libmp.mpi_gamma, libmp.mpci_gamma)
+        ctx.loggamma = ctx._wrap_mpi_function(libmp.mpi_loggamma, libmp.mpci_loggamma)
+        ctx.rgamma = ctx._wrap_mpi_function(libmp.mpi_rgamma, libmp.mpci_rgamma)
+        ctx.factorial = ctx._wrap_mpi_function(libmp.mpi_factorial, libmp.mpci_factorial)
+        ctx.fac = ctx.factorial
+
+        ctx.eps = ctx._constant(lambda prec, rnd: (0, MPZ_ONE, 1-prec, 1))
+        ctx.pi = ctx._constant(libmp.mpf_pi)
+        ctx.e = ctx._constant(libmp.mpf_e)
+        ctx.ln2 = ctx._constant(libmp.mpf_ln2)
+        ctx.ln10 = ctx._constant(libmp.mpf_ln10)
+        ctx.phi = ctx._constant(libmp.mpf_phi)
+        ctx.euler = ctx._constant(libmp.mpf_euler)
+        ctx.catalan = ctx._constant(libmp.mpf_catalan)
+        ctx.glaisher = ctx._constant(libmp.mpf_glaisher)
+        ctx.khinchin = ctx._constant(libmp.mpf_khinchin)
+        ctx.twinprime = ctx._constant(libmp.mpf_twinprime)
+
+    def _wrap_mpi_function(ctx, f_real, f_complex=None):
+        def g(x, **kwargs):
+            if kwargs:
+                prec = kwargs.get('prec', ctx._prec[0])
+            else:
+                prec = ctx._prec[0]
+            x = ctx.convert(x)
+            if hasattr(x, "_mpi_"):
+                return ctx.make_mpf(f_real(x._mpi_, prec))
+            if hasattr(x, "_mpci_"):
+                return ctx.make_mpc(f_complex(x._mpci_, prec))
+            raise ValueError
+        return g
+
+    @classmethod
+    def _wrap_specfun(cls, name, f, wrap):
+        if wrap:
+            def f_wrapped(ctx, *args, **kwargs):
+                convert = ctx.convert
+                args = [convert(a) for a in args]
+                prec = ctx.prec
+                try:
+                    ctx.prec += 10
+                    retval = f(ctx, *args, **kwargs)
+                finally:
+                    ctx.prec = prec
+                return +retval
+        else:
+            f_wrapped = f
+        setattr(cls, name, f_wrapped)
+
+    def _set_prec(ctx, n):
+        ctx._prec[0] = max(1, int(n))
+        ctx._dps = prec_to_dps(n)
+
+    def _set_dps(ctx, n):
+        ctx._prec[0] = dps_to_prec(n)
+        ctx._dps = max(1, int(n))
+
+    prec = property(lambda ctx: ctx._prec[0], _set_prec)
+    dps = property(lambda ctx: ctx._dps, _set_dps)
+
+    def make_mpf(ctx, v):
+        a = new(ctx.mpf)
+        a._mpi_ = v
+        return a
+
+    def make_mpc(ctx, v):
+        a = new(ctx.mpc)
+        a._mpci_ = v
+        return a
+
+    def _mpq(ctx, pq):
+        p, q = pq
+        a = libmp.from_rational(p, q, ctx.prec, round_floor)
+        b = libmp.from_rational(p, q, ctx.prec, round_ceiling)
+        return ctx.make_mpf((a, b))
+
+    def convert(ctx, x):
+        if isinstance(x, (ctx.mpf, ctx.mpc)):
+            return x
+        if isinstance(x, ctx._constant):
+            return +x
+        if isinstance(x, complex) or hasattr(x, "_mpc_"):
+            re = ctx.convert(x.real)
+            im = ctx.convert(x.imag)
+            return ctx.mpc(re,im)
+        if isinstance(x, basestring):
+            v = mpi_from_str(x, ctx.prec)
+            return ctx.make_mpf(v)
+        if hasattr(x, "_mpi_"):
+            a, b = x._mpi_
+        else:
+            try:
+                a, b = x
+            except (TypeError, ValueError):
+                a = b = x
+            if hasattr(a, "_mpi_"):
+                a = a._mpi_[0]
+            else:
+                a = convert_mpf_(a, ctx.prec, round_floor)
+            if hasattr(b, "_mpi_"):
+                b = b._mpi_[1]
+            else:
+                b = convert_mpf_(b, ctx.prec, round_ceiling)
+        if a == fnan or b == fnan:
+            a = fninf
+            b = finf
+        assert mpf_le(a, b), "endpoints must be properly ordered"
+        return ctx.make_mpf((a, b))
+
+    def nstr(ctx, x, n=5, **kwargs):
+        x = ctx.convert(x)
+        if hasattr(x, "_mpi_"):
+            return libmp.mpi_to_str(x._mpi_, n, **kwargs)
+        if hasattr(x, "_mpci_"):
+            re = libmp.mpi_to_str(x._mpci_[0], n, **kwargs)
+            im = libmp.mpi_to_str(x._mpci_[1], n, **kwargs)
+            return "(%s + %s*j)" % (re, im)
+
+    def mag(ctx, x):
+        x = ctx.convert(x)
+        if isinstance(x, ctx.mpc):
+            return max(ctx.mag(x.real), ctx.mag(x.imag)) + 1
+        a, b = libmp.mpi_abs(x._mpi_)
+        sign, man, exp, bc = b
+        if man:
+            return exp+bc
+        if b == fzero:
+            return ctx.ninf
+        if b == fnan:
+            return ctx.nan
+        return ctx.inf
+
+    def isnan(ctx, x):
+        return False
+
+    def isinf(ctx, x):
+        return x == ctx.inf
+
+    def isint(ctx, x):
+        x = ctx.convert(x)
+        a, b = x._mpi_
+        if a == b:
+            sign, man, exp, bc = a
+            if man:
+                return exp >= 0
+            return a == fzero
+        return None
+
+    def ldexp(ctx, x, n):
+        a, b = ctx.convert(x)._mpi_
+        a = libmp.mpf_shift(a, n)
+        b = libmp.mpf_shift(b, n)
+        return ctx.make_mpf((a,b))
+
+    def absmin(ctx, x):
+        return abs(ctx.convert(x)).a
+
+    def absmax(ctx, x):
+        return abs(ctx.convert(x)).b
+
+    def atan2(ctx, y, x):
+        y = ctx.convert(y)._mpi_
+        x = ctx.convert(x)._mpi_
+        return ctx.make_mpf(libmp.mpi_atan2(y,x,ctx.prec))
+
+    def _convert_param(ctx, x):
+        if isinstance(x, libmp.int_types):
+            return x, 'Z'
+        if isinstance(x, tuple):
+            p, q = x
+            return (ctx.mpf(p) / ctx.mpf(q), 'R')
+        x = ctx.convert(x)
+        if isinstance(x, ctx.mpf):
+            return x, 'R'
+        if isinstance(x, ctx.mpc):
+            return x, 'C'
+        raise ValueError
+
+    def _is_real_type(ctx, z):
+        return isinstance(z, ctx.mpf) or isinstance(z, int_types)
+
+    def _is_complex_type(ctx, z):
+        return isinstance(z, ctx.mpc)
+
+    def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
+        coeffs = list(coeffs)
+        num = range(p)
+        den = range(p,p+q)
+        #tol = ctx.eps
+        s = t = ctx.one
+        k = 0
+        while 1:
+            for i in num: t *= (coeffs[i]+k)
+            for i in den: t /= (coeffs[i]+k)
+            k += 1; t /= k; t *= z; s += t
+            if t == 0:
+                return s
+            #if abs(t) < tol:
+            #    return s
+            if k > maxterms:
+                raise ctx.NoConvergence
+
+
+# Register with "numbers" ABC
+#     We do not subclass, hence we do not use the @abstractmethod checks. While
+#     this is less invasive it may turn out that we do not actually support
+#     parts of the expected interfaces.  See
+#     http://docs.python.org/2/library/numbers.html for list of abstract
+#     methods.
+try:
+    import numbers
+    numbers.Complex.register(ivmpc)
+    numbers.Real.register(ivmpf)
+except ImportError:
+    pass
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_mp.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_mp.py
new file mode 100644
index 0000000000000000000000000000000000000000..93594dd44474a415c74e4b0beb83bd7012666c9d
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_mp.py
@@ -0,0 +1,1339 @@
+"""
+This module defines the mpf, mpc classes, and standard functions for
+operating with them.
+"""
+__docformat__ = 'plaintext'
+
+import functools
+
+import re
+
+from .ctx_base import StandardBaseContext
+
+from .libmp.backend import basestring, BACKEND
+
+from . import libmp
+
+from .libmp import (MPZ, MPZ_ZERO, MPZ_ONE, int_types, repr_dps,
+    round_floor, round_ceiling, dps_to_prec, round_nearest, prec_to_dps,
+    ComplexResult, to_pickable, from_pickable, normalize,
+    from_int, from_float, from_str, to_int, to_float, to_str,
+    from_rational, from_man_exp,
+    fone, fzero, finf, fninf, fnan,
+    mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
+    mpf_div, mpf_rdiv_int, mpf_pow_int, mpf_mod,
+    mpf_eq, mpf_cmp, mpf_lt, mpf_gt, mpf_le, mpf_ge,
+    mpf_hash, mpf_rand,
+    mpf_sum,
+    bitcount, to_fixed,
+    mpc_to_str,
+    mpc_to_complex, mpc_hash, mpc_pos, mpc_is_nonzero, mpc_neg, mpc_conjugate,
+    mpc_abs, mpc_add, mpc_add_mpf, mpc_sub, mpc_sub_mpf, mpc_mul, mpc_mul_mpf,
+    mpc_mul_int, mpc_div, mpc_div_mpf, mpc_pow, mpc_pow_mpf, mpc_pow_int,
+    mpc_mpf_div,
+    mpf_pow,
+    mpf_pi, mpf_degree, mpf_e, mpf_phi, mpf_ln2, mpf_ln10,
+    mpf_euler, mpf_catalan, mpf_apery, mpf_khinchin,
+    mpf_glaisher, mpf_twinprime, mpf_mertens,
+    int_types)
+
+from . import function_docs
+from . import rational
+
+new = object.__new__
+
+get_complex = re.compile(r'^\(?(?P<re>[\+\-]?\d*(\.\d*)?(e[\+\-]?\d+)?)??'
+                         r'(?P<im>[\+\-]?\d*(\.\d*)?(e[\+\-]?\d+)?j)?\)?$')
+
+if BACKEND == 'sage':
+    from sage.libs.mpmath.ext_main import Context as BaseMPContext
+    # pickle hack
+    import sage.libs.mpmath.ext_main as _mpf_module
+else:
+    from .ctx_mp_python import PythonMPContext as BaseMPContext
+    from . import ctx_mp_python as _mpf_module
+
+from .ctx_mp_python import _mpf, _mpc, mpnumeric
+
+class MPContext(BaseMPContext, StandardBaseContext):
+    """
+    Context for multiprecision arithmetic with a global precision.
+    """
+
+    def __init__(ctx):
+        BaseMPContext.__init__(ctx)
+        ctx.trap_complex = False
+        ctx.pretty = False
+        ctx.types = [ctx.mpf, ctx.mpc, ctx.constant]
+        ctx._mpq = rational.mpq
+        ctx.default()
+        StandardBaseContext.__init__(ctx)
+
+        ctx.mpq = rational.mpq
+        ctx.init_builtins()
+
+        ctx.hyp_summators = {}
+
+        ctx._init_aliases()
+
+        # XXX: automate
+        try:
+            ctx.bernoulli.im_func.func_doc = function_docs.bernoulli
+            ctx.primepi.im_func.func_doc = function_docs.primepi
+            ctx.psi.im_func.func_doc = function_docs.psi
+            ctx.atan2.im_func.func_doc = function_docs.atan2
+        except AttributeError:
+            # python 3
+            ctx.bernoulli.__func__.func_doc = function_docs.bernoulli
+            ctx.primepi.__func__.func_doc = function_docs.primepi
+            ctx.psi.__func__.func_doc = function_docs.psi
+            ctx.atan2.__func__.func_doc = function_docs.atan2
+
+        ctx.digamma.func_doc = function_docs.digamma
+        ctx.cospi.func_doc = function_docs.cospi
+        ctx.sinpi.func_doc = function_docs.sinpi
+
+    def init_builtins(ctx):
+
+        mpf = ctx.mpf
+        mpc = ctx.mpc
+
+        # Exact constants
+        ctx.one = ctx.make_mpf(fone)
+        ctx.zero = ctx.make_mpf(fzero)
+        ctx.j = ctx.make_mpc((fzero,fone))
+        ctx.inf = ctx.make_mpf(finf)
+        ctx.ninf = ctx.make_mpf(fninf)
+        ctx.nan = ctx.make_mpf(fnan)
+
+        eps = ctx.constant(lambda prec, rnd: (0, MPZ_ONE, 1-prec, 1),
+            "epsilon of working precision", "eps")
+        ctx.eps = eps
+
+        # Approximate constants
+        ctx.pi = ctx.constant(mpf_pi, "pi", "pi")
+        ctx.ln2 = ctx.constant(mpf_ln2, "ln(2)", "ln2")
+        ctx.ln10 = ctx.constant(mpf_ln10, "ln(10)", "ln10")
+        ctx.phi = ctx.constant(mpf_phi, "Golden ratio phi", "phi")
+        ctx.e = ctx.constant(mpf_e, "e = exp(1)", "e")
+        ctx.euler = ctx.constant(mpf_euler, "Euler's constant", "euler")
+        ctx.catalan = ctx.constant(mpf_catalan, "Catalan's constant", "catalan")
+        ctx.khinchin = ctx.constant(mpf_khinchin, "Khinchin's constant", "khinchin")
+        ctx.glaisher = ctx.constant(mpf_glaisher, "Glaisher's constant", "glaisher")
+        ctx.apery = ctx.constant(mpf_apery, "Apery's constant", "apery")
+        ctx.degree = ctx.constant(mpf_degree, "1 deg = pi / 180", "degree")
+        ctx.twinprime = ctx.constant(mpf_twinprime, "Twin prime constant", "twinprime")
+        ctx.mertens = ctx.constant(mpf_mertens, "Mertens' constant", "mertens")
+
+        # Standard functions
+        ctx.sqrt = ctx._wrap_libmp_function(libmp.mpf_sqrt, libmp.mpc_sqrt)
+        ctx.cbrt = ctx._wrap_libmp_function(libmp.mpf_cbrt, libmp.mpc_cbrt)
+        ctx.ln = ctx._wrap_libmp_function(libmp.mpf_log, libmp.mpc_log)
+        ctx.atan = ctx._wrap_libmp_function(libmp.mpf_atan, libmp.mpc_atan)
+        ctx.exp = ctx._wrap_libmp_function(libmp.mpf_exp, libmp.mpc_exp)
+        ctx.expj = ctx._wrap_libmp_function(libmp.mpf_expj, libmp.mpc_expj)
+        ctx.expjpi = ctx._wrap_libmp_function(libmp.mpf_expjpi, libmp.mpc_expjpi)
+        ctx.sin = ctx._wrap_libmp_function(libmp.mpf_sin, libmp.mpc_sin)
+        ctx.cos = ctx._wrap_libmp_function(libmp.mpf_cos, libmp.mpc_cos)
+        ctx.tan = ctx._wrap_libmp_function(libmp.mpf_tan, libmp.mpc_tan)
+        ctx.sinh = ctx._wrap_libmp_function(libmp.mpf_sinh, libmp.mpc_sinh)
+        ctx.cosh = ctx._wrap_libmp_function(libmp.mpf_cosh, libmp.mpc_cosh)
+        ctx.tanh = ctx._wrap_libmp_function(libmp.mpf_tanh, libmp.mpc_tanh)
+        ctx.asin = ctx._wrap_libmp_function(libmp.mpf_asin, libmp.mpc_asin)
+        ctx.acos = ctx._wrap_libmp_function(libmp.mpf_acos, libmp.mpc_acos)
+        ctx.atan = ctx._wrap_libmp_function(libmp.mpf_atan, libmp.mpc_atan)
+        ctx.asinh = ctx._wrap_libmp_function(libmp.mpf_asinh, libmp.mpc_asinh)
+        ctx.acosh = ctx._wrap_libmp_function(libmp.mpf_acosh, libmp.mpc_acosh)
+        ctx.atanh = ctx._wrap_libmp_function(libmp.mpf_atanh, libmp.mpc_atanh)
+        ctx.sinpi = ctx._wrap_libmp_function(libmp.mpf_sin_pi, libmp.mpc_sin_pi)
+        ctx.cospi = ctx._wrap_libmp_function(libmp.mpf_cos_pi, libmp.mpc_cos_pi)
+        ctx.floor = ctx._wrap_libmp_function(libmp.mpf_floor, libmp.mpc_floor)
+        ctx.ceil = ctx._wrap_libmp_function(libmp.mpf_ceil, libmp.mpc_ceil)
+        ctx.nint = ctx._wrap_libmp_function(libmp.mpf_nint, libmp.mpc_nint)
+        ctx.frac = ctx._wrap_libmp_function(libmp.mpf_frac, libmp.mpc_frac)
+        ctx.fib = ctx.fibonacci = ctx._wrap_libmp_function(libmp.mpf_fibonacci, libmp.mpc_fibonacci)
+
+        ctx.gamma = ctx._wrap_libmp_function(libmp.mpf_gamma, libmp.mpc_gamma)
+        ctx.rgamma = ctx._wrap_libmp_function(libmp.mpf_rgamma, libmp.mpc_rgamma)
+        ctx.loggamma = ctx._wrap_libmp_function(libmp.mpf_loggamma, libmp.mpc_loggamma)
+        ctx.fac = ctx.factorial = ctx._wrap_libmp_function(libmp.mpf_factorial, libmp.mpc_factorial)
+
+        ctx.digamma = ctx._wrap_libmp_function(libmp.mpf_psi0, libmp.mpc_psi0)
+        ctx.harmonic = ctx._wrap_libmp_function(libmp.mpf_harmonic, libmp.mpc_harmonic)
+        ctx.ei = ctx._wrap_libmp_function(libmp.mpf_ei, libmp.mpc_ei)
+        ctx.e1 = ctx._wrap_libmp_function(libmp.mpf_e1, libmp.mpc_e1)
+        ctx._ci = ctx._wrap_libmp_function(libmp.mpf_ci, libmp.mpc_ci)
+        ctx._si = ctx._wrap_libmp_function(libmp.mpf_si, libmp.mpc_si)
+        ctx.ellipk = ctx._wrap_libmp_function(libmp.mpf_ellipk, libmp.mpc_ellipk)
+        ctx._ellipe = ctx._wrap_libmp_function(libmp.mpf_ellipe, libmp.mpc_ellipe)
+        ctx.agm1 = ctx._wrap_libmp_function(libmp.mpf_agm1, libmp.mpc_agm1)
+        ctx._erf = ctx._wrap_libmp_function(libmp.mpf_erf, None)
+        ctx._erfc = ctx._wrap_libmp_function(libmp.mpf_erfc, None)
+        ctx._zeta = ctx._wrap_libmp_function(libmp.mpf_zeta, libmp.mpc_zeta)
+        ctx._altzeta = ctx._wrap_libmp_function(libmp.mpf_altzeta, libmp.mpc_altzeta)
+
+        # Faster versions
+        ctx.sqrt = getattr(ctx, "_sage_sqrt", ctx.sqrt)
+        ctx.exp = getattr(ctx, "_sage_exp", ctx.exp)
+        ctx.ln = getattr(ctx, "_sage_ln", ctx.ln)
+        ctx.cos = getattr(ctx, "_sage_cos", ctx.cos)
+        ctx.sin = getattr(ctx, "_sage_sin", ctx.sin)
+
+    def to_fixed(ctx, x, prec):
+        return x.to_fixed(prec)
+
+    def hypot(ctx, x, y):
+        r"""
+        Computes the Euclidean norm of the vector `(x, y)`, equal
+        to `\sqrt{x^2 + y^2}`. Both `x` and `y` must be real."""
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        return ctx.make_mpf(libmp.mpf_hypot(x._mpf_, y._mpf_, *ctx._prec_rounding))
+
+    def _gamma_upper_int(ctx, n, z):
+        n = int(ctx._re(n))
+        if n == 0:
+            return ctx.e1(z)
+        if not hasattr(z, '_mpf_'):
+            raise NotImplementedError
+        prec, rounding = ctx._prec_rounding
+        real, imag = libmp.mpf_expint(n, z._mpf_, prec, rounding, gamma=True)
+        if imag is None:
+            return ctx.make_mpf(real)
+        else:
+            return ctx.make_mpc((real, imag))
+
+    def _expint_int(ctx, n, z):
+        n = int(n)
+        if n == 1:
+            return ctx.e1(z)
+        if not hasattr(z, '_mpf_'):
+            raise NotImplementedError
+        prec, rounding = ctx._prec_rounding
+        real, imag = libmp.mpf_expint(n, z._mpf_, prec, rounding)
+        if imag is None:
+            return ctx.make_mpf(real)
+        else:
+            return ctx.make_mpc((real, imag))
+
+    def _nthroot(ctx, x, n):
+        if hasattr(x, '_mpf_'):
+            try:
+                return ctx.make_mpf(libmp.mpf_nthroot(x._mpf_, n, *ctx._prec_rounding))
+            except ComplexResult:
+                if ctx.trap_complex:
+                    raise
+                x = (x._mpf_, libmp.fzero)
+        else:
+            x = x._mpc_
+        return ctx.make_mpc(libmp.mpc_nthroot(x, n, *ctx._prec_rounding))
+
+    def _besselj(ctx, n, z):
+        prec, rounding = ctx._prec_rounding
+        if hasattr(z, '_mpf_'):
+            return ctx.make_mpf(libmp.mpf_besseljn(n, z._mpf_, prec, rounding))
+        elif hasattr(z, '_mpc_'):
+            return ctx.make_mpc(libmp.mpc_besseljn(n, z._mpc_, prec, rounding))
+
+    def _agm(ctx, a, b=1):
+        prec, rounding = ctx._prec_rounding
+        if hasattr(a, '_mpf_') and hasattr(b, '_mpf_'):
+            try:
+                v = libmp.mpf_agm(a._mpf_, b._mpf_, prec, rounding)
+                return ctx.make_mpf(v)
+            except ComplexResult:
+                pass
+        if hasattr(a, '_mpf_'): a = (a._mpf_, libmp.fzero)
+        else: a = a._mpc_
+        if hasattr(b, '_mpf_'): b = (b._mpf_, libmp.fzero)
+        else: b = b._mpc_
+        return ctx.make_mpc(libmp.mpc_agm(a, b, prec, rounding))
+
+    def bernoulli(ctx, n):
+        return ctx.make_mpf(libmp.mpf_bernoulli(int(n), *ctx._prec_rounding))
+
+    def _zeta_int(ctx, n):
+        return ctx.make_mpf(libmp.mpf_zeta_int(int(n), *ctx._prec_rounding))
+
+    def atan2(ctx, y, x):
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        return ctx.make_mpf(libmp.mpf_atan2(y._mpf_, x._mpf_, *ctx._prec_rounding))
+
+    def psi(ctx, m, z):
+        z = ctx.convert(z)
+        m = int(m)
+        if ctx._is_real_type(z):
+            return ctx.make_mpf(libmp.mpf_psi(m, z._mpf_, *ctx._prec_rounding))
+        else:
+            return ctx.make_mpc(libmp.mpc_psi(m, z._mpc_, *ctx._prec_rounding))
+
+    def cos_sin(ctx, x, **kwargs):
+        if type(x) not in ctx.types:
+            x = ctx.convert(x)
+        prec, rounding = ctx._parse_prec(kwargs)
+        if hasattr(x, '_mpf_'):
+            c, s = libmp.mpf_cos_sin(x._mpf_, prec, rounding)
+            return ctx.make_mpf(c), ctx.make_mpf(s)
+        elif hasattr(x, '_mpc_'):
+            c, s = libmp.mpc_cos_sin(x._mpc_, prec, rounding)
+            return ctx.make_mpc(c), ctx.make_mpc(s)
+        else:
+            return ctx.cos(x, **kwargs), ctx.sin(x, **kwargs)
+
+    def cospi_sinpi(ctx, x, **kwargs):
+        if type(x) not in ctx.types:
+            x = ctx.convert(x)
+        prec, rounding = ctx._parse_prec(kwargs)
+        if hasattr(x, '_mpf_'):
+            c, s = libmp.mpf_cos_sin_pi(x._mpf_, prec, rounding)
+            return ctx.make_mpf(c), ctx.make_mpf(s)
+        elif hasattr(x, '_mpc_'):
+            c, s = libmp.mpc_cos_sin_pi(x._mpc_, prec, rounding)
+            return ctx.make_mpc(c), ctx.make_mpc(s)
+        else:
+            return ctx.cos(x, **kwargs), ctx.sin(x, **kwargs)
+
+    def clone(ctx):
+        """
+        Create a copy of the context, with the same working precision.
+        """
+        a = ctx.__class__()
+        a.prec = ctx.prec
+        return a
+
+    # Several helper methods
+    # TODO: add more of these, make consistent, write docstrings, ...
+
+    def _is_real_type(ctx, x):
+        if hasattr(x, '_mpc_') or type(x) is complex:
+            return False
+        return True
+
+    def _is_complex_type(ctx, x):
+        if hasattr(x, '_mpc_') or type(x) is complex:
+            return True
+        return False
+
+    def isnan(ctx, x):
+        """
+        Return *True* if *x* is a NaN (not-a-number), or for a complex
+        number, whether either the real or complex part is NaN;
+        otherwise return *False*::
+
+            >>> from mpmath import *
+            >>> isnan(3.14)
+            False
+            >>> isnan(nan)
+            True
+            >>> isnan(mpc(3.14,2.72))
+            False
+            >>> isnan(mpc(3.14,nan))
+            True
+
+        """
+        if hasattr(x, "_mpf_"):
+            return x._mpf_ == fnan
+        if hasattr(x, "_mpc_"):
+            return fnan in x._mpc_
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return False
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isnan(x)
+        raise TypeError("isnan() needs a number as input")
+
+    def isfinite(ctx, x):
+        """
+        Return *True* if *x* is a finite number, i.e. neither
+        an infinity or a NaN.
+
+            >>> from mpmath import *
+            >>> isfinite(inf)
+            False
+            >>> isfinite(-inf)
+            False
+            >>> isfinite(3)
+            True
+            >>> isfinite(nan)
+            False
+            >>> isfinite(3+4j)
+            True
+            >>> isfinite(mpc(3,inf))
+            False
+            >>> isfinite(mpc(nan,3))
+            False
+
+        """
+        if ctx.isinf(x) or ctx.isnan(x):
+            return False
+        return True
+
+    def isnpint(ctx, x):
+        """
+        Determine if *x* is a nonpositive integer.
+        """
+        if not x:
+            return True
+        if hasattr(x, '_mpf_'):
+            sign, man, exp, bc = x._mpf_
+            return sign and exp >= 0
+        if hasattr(x, '_mpc_'):
+            return not x.imag and ctx.isnpint(x.real)
+        if type(x) in int_types:
+            return x <= 0
+        if isinstance(x, ctx.mpq):
+            p, q = x._mpq_
+            if not p:
+                return True
+            return q == 1 and p <= 0
+        return ctx.isnpint(ctx.convert(x))
+
+    def __str__(ctx):
+        lines = ["Mpmath settings:",
+            ("  mp.prec = %s" % ctx.prec).ljust(30) + "[default: 53]",
+            ("  mp.dps = %s" % ctx.dps).ljust(30) + "[default: 15]",
+            ("  mp.trap_complex = %s" % ctx.trap_complex).ljust(30) + "[default: False]",
+        ]
+        return "\n".join(lines)
+
+    @property
+    def _repr_digits(ctx):
+        return repr_dps(ctx._prec)
+
+    @property
+    def _str_digits(ctx):
+        return ctx._dps
+
+    def extraprec(ctx, n, normalize_output=False):
+        """
+        The block
+
+            with extraprec(n):
+                <code>
+
+        increases the precision n bits, executes <code>, and then
+        restores the precision.
+
+        extraprec(n)(f) returns a decorated version of the function f
+        that increases the working precision by n bits before execution,
+        and restores the parent precision afterwards. With
+        normalize_output=True, it rounds the return value to the parent
+        precision.
+        """
+        return PrecisionManager(ctx, lambda p: p + n, None, normalize_output)
+
+    def extradps(ctx, n, normalize_output=False):
+        """
+        This function is analogous to extraprec (see documentation)
+        but changes the decimal precision instead of the number of bits.
+        """
+        return PrecisionManager(ctx, None, lambda d: d + n, normalize_output)
+
+    def workprec(ctx, n, normalize_output=False):
+        """
+        The block
+
+            with workprec(n):
+                <code>
+
+        sets the precision to n bits, executes <code>, and then restores
+        the precision.
+
+        workprec(n)(f) returns a decorated version of the function f
+        that sets the precision to n bits before execution,
+        and restores the precision afterwards. With normalize_output=True,
+        it rounds the return value to the parent precision.
+        """
+        return PrecisionManager(ctx, lambda p: n, None, normalize_output)
+
+    def workdps(ctx, n, normalize_output=False):
+        """
+        This function is analogous to workprec (see documentation)
+        but changes the decimal precision instead of the number of bits.
+        """
+        return PrecisionManager(ctx, None, lambda d: n, normalize_output)
+
+    def autoprec(ctx, f, maxprec=None, catch=(), verbose=False):
+        r"""
+        Return a wrapped copy of *f* that repeatedly evaluates *f*
+        with increasing precision until the result converges to the
+        full precision used at the point of the call.
+
+        This heuristically protects against rounding errors, at the cost of
+        roughly a 2x slowdown compared to manually setting the optimal
+        precision. This method can, however, easily be fooled if the results
+        from *f* depend "discontinuously" on the precision, for instance
+        if catastrophic cancellation can occur. Therefore, :func:`~mpmath.autoprec`
+        should be used judiciously.
+
+        **Examples**
+
+        Many functions are sensitive to perturbations of the input arguments.
+        If the arguments are decimal numbers, they may have to be converted
+        to binary at a much higher precision. If the amount of required
+        extra precision is unknown, :func:`~mpmath.autoprec` is convenient::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> mp.pretty = True
+            >>> besselj(5, 125 * 10**28)    # Exact input
+            -8.03284785591801e-17
+            >>> besselj(5, '1.25e30')   # Bad
+            7.12954868316652e-16
+            >>> autoprec(besselj)(5, '1.25e30')   # Good
+            -8.03284785591801e-17
+
+        The following fails to converge because `\sin(\pi) = 0` whereas all
+        finite-precision approximations of `\pi` give nonzero values::
+
+            >>> autoprec(sin)(pi) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: autoprec: prec increased to 2910 without convergence
+
+        As the following example shows, :func:`~mpmath.autoprec` can protect against
+        cancellation, but is fooled by too severe cancellation::
+
+            >>> x = 1e-10
+            >>> exp(x)-1; expm1(x); autoprec(lambda t: exp(t)-1)(x)
+            1.00000008274037e-10
+            1.00000000005e-10
+            1.00000000005e-10
+            >>> x = 1e-50
+            >>> exp(x)-1; expm1(x); autoprec(lambda t: exp(t)-1)(x)
+            0.0
+            1.0e-50
+            0.0
+
+        With *catch*, an exception or list of exceptions to intercept
+        may be specified. The raised exception is interpreted
+        as signaling insufficient precision. This permits, for example,
+        evaluating a function where a too low precision results in a
+        division by zero::
+
+            >>> f = lambda x: 1/(exp(x)-1)
+            >>> f(1e-30)
+            Traceback (most recent call last):
+              ...
+            ZeroDivisionError
+            >>> autoprec(f, catch=ZeroDivisionError)(1e-30)
+            1.0e+30
+
+
+        """
+        def f_autoprec_wrapped(*args, **kwargs):
+            prec = ctx.prec
+            if maxprec is None:
+                maxprec2 = ctx._default_hyper_maxprec(prec)
+            else:
+                maxprec2 = maxprec
+            try:
+                ctx.prec = prec + 10
+                try:
+                    v1 = f(*args, **kwargs)
+                except catch:
+                    v1 = ctx.nan
+                prec2 = prec + 20
+                while 1:
+                    ctx.prec = prec2
+                    try:
+                        v2 = f(*args, **kwargs)
+                    except catch:
+                        v2 = ctx.nan
+                    if v1 == v2:
+                        break
+                    err = ctx.mag(v2-v1) - ctx.mag(v2)
+                    if err < (-prec):
+                        break
+                    if verbose:
+                        print("autoprec: target=%s, prec=%s, accuracy=%s" \
+                            % (prec, prec2, -err))
+                    v1 = v2
+                    if prec2 >= maxprec2:
+                        raise ctx.NoConvergence(\
+                        "autoprec: prec increased to %i without convergence"\
+                        % prec2)
+                    prec2 += int(prec2*2)
+                    prec2 = min(prec2, maxprec2)
+            finally:
+                ctx.prec = prec
+            return +v2
+        return f_autoprec_wrapped
+
+    def nstr(ctx, x, n=6, **kwargs):
+        """
+        Convert an ``mpf`` or ``mpc`` to a decimal string literal with *n*
+        significant digits. The small default value for *n* is chosen to
+        make this function useful for printing collections of numbers
+        (lists, matrices, etc).
+
+        If *x* is a list or tuple, :func:`~mpmath.nstr` is applied recursively
+        to each element. For unrecognized classes, :func:`~mpmath.nstr`
+        simply returns ``str(x)``.
+
+        The companion function :func:`~mpmath.nprint` prints the result
+        instead of returning it.
+
+        The keyword arguments *strip_zeros*, *min_fixed*, *max_fixed*
+        and *show_zero_exponent* are forwarded to :func:`~mpmath.libmp.to_str`.
+
+        The number will be printed in fixed-point format if the position
+        of the leading digit is strictly between min_fixed
+        (default = min(-dps/3,-5)) and max_fixed (default = dps).
+
+        To force fixed-point format always, set min_fixed = -inf,
+        max_fixed = +inf. To force floating-point format, set
+        min_fixed >= max_fixed.
+
+            >>> from mpmath import *
+            >>> nstr([+pi, ldexp(1,-500)])
+            '[3.14159, 3.05494e-151]'
+            >>> nprint([+pi, ldexp(1,-500)])
+            [3.14159, 3.05494e-151]
+            >>> nstr(mpf("5e-10"), 5)
+            '5.0e-10'
+            >>> nstr(mpf("5e-10"), 5, strip_zeros=False)
+            '5.0000e-10'
+            >>> nstr(mpf("5e-10"), 5, strip_zeros=False, min_fixed=-11)
+            '0.00000000050000'
+            >>> nstr(mpf(0), 5, show_zero_exponent=True)
+            '0.0e+0'
+
+        """
+        if isinstance(x, list):
+            return "[%s]" % (", ".join(ctx.nstr(c, n, **kwargs) for c in x))
+        if isinstance(x, tuple):
+            return "(%s)" % (", ".join(ctx.nstr(c, n, **kwargs) for c in x))
+        if hasattr(x, '_mpf_'):
+            return to_str(x._mpf_, n, **kwargs)
+        if hasattr(x, '_mpc_'):
+            return "(" + mpc_to_str(x._mpc_, n, **kwargs)  + ")"
+        if isinstance(x, basestring):
+            return repr(x)
+        if isinstance(x, ctx.matrix):
+            return x.__nstr__(n, **kwargs)
+        return str(x)
+
+    def _convert_fallback(ctx, x, strings):
+        if strings and isinstance(x, basestring):
+            if 'j' in x.lower():
+                x = x.lower().replace(' ', '')
+                match = get_complex.match(x)
+                re = match.group('re')
+                if not re:
+                    re = 0
+                im = match.group('im').rstrip('j')
+                return ctx.mpc(ctx.convert(re), ctx.convert(im))
+        if hasattr(x, "_mpi_"):
+            a, b = x._mpi_
+            if a == b:
+                return ctx.make_mpf(a)
+            else:
+                raise ValueError("can only create mpf from zero-width interval")
+        raise TypeError("cannot create mpf from " + repr(x))
+
+    def mpmathify(ctx, *args, **kwargs):
+        return ctx.convert(*args, **kwargs)
+
+    def _parse_prec(ctx, kwargs):
+        if kwargs:
+            if kwargs.get('exact'):
+                return 0, 'f'
+            prec, rounding = ctx._prec_rounding
+            if 'rounding' in kwargs:
+                rounding = kwargs['rounding']
+            if 'prec' in kwargs:
+                prec = kwargs['prec']
+                if prec == ctx.inf:
+                    return 0, 'f'
+                else:
+                    prec = int(prec)
+            elif 'dps' in kwargs:
+                dps = kwargs['dps']
+                if dps == ctx.inf:
+                    return 0, 'f'
+                prec = dps_to_prec(dps)
+            return prec, rounding
+        return ctx._prec_rounding
+
+    _exact_overflow_msg = "the exact result does not fit in memory"
+
+    _hypsum_msg = """hypsum() failed to converge to the requested %i bits of accuracy
+using a working precision of %i bits. Try with a higher maxprec,
+maxterms, or set zeroprec."""
+
+    def hypsum(ctx, p, q, flags, coeffs, z, accurate_small=True, **kwargs):
+        if hasattr(z, "_mpf_"):
+            key = p, q, flags, 'R'
+            v = z._mpf_
+        elif hasattr(z, "_mpc_"):
+            key = p, q, flags, 'C'
+            v = z._mpc_
+        if key not in ctx.hyp_summators:
+            ctx.hyp_summators[key] = libmp.make_hyp_summator(key)[1]
+        summator = ctx.hyp_summators[key]
+        prec = ctx.prec
+        maxprec = kwargs.get('maxprec', ctx._default_hyper_maxprec(prec))
+        extraprec = 50
+        epsshift = 25
+        # Jumps in magnitude occur when parameters are close to negative
+        # integers. We must ensure that these terms are included in
+        # the sum and added accurately
+        magnitude_check = {}
+        max_total_jump = 0
+        for i, c in enumerate(coeffs):
+            if flags[i] == 'Z':
+                if i >= p and c <= 0:
+                    ok = False
+                    for ii, cc in enumerate(coeffs[:p]):
+                        # Note: c <= cc or c < cc, depending on convention
+                        if flags[ii] == 'Z' and cc <= 0 and c <= cc:
+                            ok = True
+                    if not ok:
+                        raise ZeroDivisionError("pole in hypergeometric series")
+                continue
+            n, d = ctx.nint_distance(c)
+            n = -int(n)
+            d = -d
+            if i >= p and n >= 0 and d > 4:
+                if n in magnitude_check:
+                    magnitude_check[n] += d
+                else:
+                    magnitude_check[n] = d
+                extraprec = max(extraprec, d - prec + 60)
+            max_total_jump += abs(d)
+        while 1:
+            if extraprec > maxprec:
+                raise ValueError(ctx._hypsum_msg % (prec, prec+extraprec))
+            wp = prec + extraprec
+            if magnitude_check:
+                mag_dict = dict((n,None) for n in magnitude_check)
+            else:
+                mag_dict = {}
+            zv, have_complex, magnitude = summator(coeffs, v, prec, wp, \
+                epsshift, mag_dict, **kwargs)
+            cancel = -magnitude
+            jumps_resolved = True
+            if extraprec < max_total_jump:
+                for n in mag_dict.values():
+                    if (n is None) or (n < prec):
+                        jumps_resolved = False
+                        break
+            accurate = (cancel < extraprec-25-5 or not accurate_small)
+            if jumps_resolved:
+                if accurate:
+                    break
+                # zero?
+                zeroprec = kwargs.get('zeroprec')
+                if zeroprec is not None:
+                    if cancel > zeroprec:
+                        if have_complex:
+                            return ctx.mpc(0)
+                        else:
+                            return ctx.zero
+
+            # Some near-singularities were not included, so increase
+            # precision and repeat until they are
+            extraprec *= 2
+            # Possible workaround for bad roundoff in fixed-point arithmetic
+            epsshift += 5
+            extraprec += 5
+
+        if type(zv) is tuple:
+            if have_complex:
+                return ctx.make_mpc(zv)
+            else:
+                return ctx.make_mpf(zv)
+        else:
+            return zv
+
+    def ldexp(ctx, x, n):
+        r"""
+        Computes `x 2^n` efficiently. No rounding is performed.
+        The argument `x` must be a real floating-point number (or
+        possible to convert into one) and `n` must be a Python ``int``.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> ldexp(1, 10)
+            mpf('1024.0')
+            >>> ldexp(1, -3)
+            mpf('0.125')
+
+        """
+        x = ctx.convert(x)
+        return ctx.make_mpf(libmp.mpf_shift(x._mpf_, n))
+
+    def frexp(ctx, x):
+        r"""
+        Given a real number `x`, returns `(y, n)` with `y \in [0.5, 1)`,
+        `n` a Python integer, and such that `x = y 2^n`. No rounding is
+        performed.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> frexp(7.5)
+            (mpf('0.9375'), 3)
+
+        """
+        x = ctx.convert(x)
+        y, n = libmp.mpf_frexp(x._mpf_)
+        return ctx.make_mpf(y), n
+
+    def fneg(ctx, x, **kwargs):
+        """
+        Negates the number *x*, giving a floating-point result, optionally
+        using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        An mpmath number is returned::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fneg(2.5)
+            mpf('-2.5')
+            >>> fneg(-5+2j)
+            mpc(real='5.0', imag='-2.0')
+
+        Precise control over rounding is possible::
+
+            >>> x = fadd(2, 1e-100, exact=True)
+            >>> fneg(x)
+            mpf('-2.0')
+            >>> fneg(x, rounding='f')
+            mpf('-2.0000000000000004')
+
+        Negating with and without roundoff::
+
+            >>> n = 200000000000000000000001
+            >>> print(int(-mpf(n)))
+            -200000000000000016777216
+            >>> print(int(fneg(n)))
+            -200000000000000016777216
+            >>> print(int(fneg(n, prec=log(n,2)+1)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, dps=log(n,10)+1)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, prec=inf)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, dps=inf)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, exact=True)))
+            -200000000000000000000001
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_'):
+            return ctx.make_mpf(mpf_neg(x._mpf_, prec, rounding))
+        if hasattr(x, '_mpc_'):
+            return ctx.make_mpc(mpc_neg(x._mpc_, prec, rounding))
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fadd(ctx, x, y, **kwargs):
+        """
+        Adds the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        The default precision is the working precision of the context.
+        You can specify a custom precision in bits by passing the *prec* keyword
+        argument, or by providing an equivalent decimal precision with the *dps*
+        keyword argument. If the precision is set to ``+inf``, or if the flag
+        *exact=True* is passed, an exact addition with no rounding is performed.
+
+        When the precision is finite, the optional *rounding* keyword argument
+        specifies the direction of rounding. Valid options are ``'n'`` for
+        nearest (default), ``'f'`` for floor, ``'c'`` for ceiling, ``'d'``
+        for down, ``'u'`` for up.
+
+        **Examples**
+
+        Using :func:`~mpmath.fadd` with precision and rounding control::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fadd(2, 1e-20)
+            mpf('2.0')
+            >>> fadd(2, 1e-20, rounding='u')
+            mpf('2.0000000000000004')
+            >>> nprint(fadd(2, 1e-20, prec=100), 25)
+            2.00000000000000000001
+            >>> nprint(fadd(2, 1e-20, dps=15), 25)
+            2.0
+            >>> nprint(fadd(2, 1e-20, dps=25), 25)
+            2.00000000000000000001
+            >>> nprint(fadd(2, 1e-20, exact=True), 25)
+            2.00000000000000000001
+
+        Exact addition avoids cancellation errors, enforcing familiar laws
+        of numbers such as `x+y-x = y`, which don't hold in floating-point
+        arithmetic with finite precision::
+
+            >>> x, y = mpf(2), mpf('1e-1000')
+            >>> print(x + y - x)
+            0.0
+            >>> print(fadd(x, y, prec=inf) - x)
+            1.0e-1000
+            >>> print(fadd(x, y, exact=True) - x)
+            1.0e-1000
+
+        Exact addition can be inefficient and may be impossible to perform
+        with large magnitude differences::
+
+            >>> fadd(1, '1e-100000000000000000000', prec=inf)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_add(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_add_mpf(y._mpc_, x._mpf_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_add_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_add(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fsub(ctx, x, y, **kwargs):
+        """
+        Subtracts the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        Using :func:`~mpmath.fsub` with precision and rounding control::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fsub(2, 1e-20)
+            mpf('2.0')
+            >>> fsub(2, 1e-20, rounding='d')
+            mpf('1.9999999999999998')
+            >>> nprint(fsub(2, 1e-20, prec=100), 25)
+            1.99999999999999999999
+            >>> nprint(fsub(2, 1e-20, dps=15), 25)
+            2.0
+            >>> nprint(fsub(2, 1e-20, dps=25), 25)
+            1.99999999999999999999
+            >>> nprint(fsub(2, 1e-20, exact=True), 25)
+            1.99999999999999999999
+
+        Exact subtraction avoids cancellation errors, enforcing familiar laws
+        of numbers such as `x-y+y = x`, which don't hold in floating-point
+        arithmetic with finite precision::
+
+            >>> x, y = mpf(2), mpf('1e1000')
+            >>> print(x - y + y)
+            0.0
+            >>> print(fsub(x, y, prec=inf) + y)
+            2.0
+            >>> print(fsub(x, y, exact=True) + y)
+            2.0
+
+        Exact addition can be inefficient and may be impossible to perform
+        with large magnitude differences::
+
+            >>> fsub(1, '1e-100000000000000000000', prec=inf)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_sub(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_sub((x._mpf_, fzero), y._mpc_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_sub_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_sub(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fmul(ctx, x, y, **kwargs):
+        """
+        Multiplies the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        The result is an mpmath number::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fmul(2, 5.0)
+            mpf('10.0')
+            >>> fmul(0.5j, 0.5)
+            mpc(real='0.0', imag='0.25')
+
+        Avoiding roundoff::
+
+            >>> x, y = 10**10+1, 10**15+1
+            >>> print(x*y)
+            10000000001000010000000001
+            >>> print(mpf(x) * mpf(y))
+            1.0000000001e+25
+            >>> print(int(mpf(x) * mpf(y)))
+            10000000001000011026399232
+            >>> print(int(fmul(x, y)))
+            10000000001000011026399232
+            >>> print(int(fmul(x, y, dps=25)))
+            10000000001000010000000001
+            >>> print(int(fmul(x, y, exact=True)))
+            10000000001000010000000001
+
+        Exact multiplication with complex numbers can be inefficient and may
+        be impossible to perform with large magnitude differences between
+        real and imaginary parts::
+
+            >>> x = 1+2j
+            >>> y = mpc(2, '1e-100000000000000000000')
+            >>> fmul(x, y)
+            mpc(real='2.0', imag='4.0')
+            >>> fmul(x, y, rounding='u')
+            mpc(real='2.0', imag='4.0000000000000009')
+            >>> fmul(x, y, exact=True)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_mul(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_mul_mpf(y._mpc_, x._mpf_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_mul_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_mul(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fdiv(ctx, x, y, **kwargs):
+        """
+        Divides the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        The result is an mpmath number::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fdiv(3, 2)
+            mpf('1.5')
+            >>> fdiv(2, 3)
+            mpf('0.66666666666666663')
+            >>> fdiv(2+4j, 0.5)
+            mpc(real='4.0', imag='8.0')
+
+        The rounding direction and precision can be controlled::
+
+            >>> fdiv(2, 3, dps=3)    # Should be accurate to at least 3 digits
+            mpf('0.6666259765625')
+            >>> fdiv(2, 3, rounding='d')
+            mpf('0.66666666666666663')
+            >>> fdiv(2, 3, prec=60)
+            mpf('0.66666666666666667')
+            >>> fdiv(2, 3, rounding='u')
+            mpf('0.66666666666666674')
+
+        Checking the error of a division by performing it at higher precision::
+
+            >>> fdiv(2, 3) - fdiv(2, 3, prec=100)
+            mpf('-3.7007434154172148e-17')
+
+        Unlike :func:`~mpmath.fadd`, :func:`~mpmath.fmul`, etc., exact division is not
+        allowed since the quotient of two floating-point numbers generally
+        does not have an exact floating-point representation. (In the
+        future this might be changed to allow the case where the division
+        is actually exact.)
+
+            >>> fdiv(2, 3, exact=True)
+            Traceback (most recent call last):
+              ...
+            ValueError: division is not an exact operation
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        if not prec:
+            raise ValueError("division is not an exact operation")
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        if hasattr(x, '_mpf_'):
+            if hasattr(y, '_mpf_'):
+                return ctx.make_mpf(mpf_div(x._mpf_, y._mpf_, prec, rounding))
+            if hasattr(y, '_mpc_'):
+                return ctx.make_mpc(mpc_div((x._mpf_, fzero), y._mpc_, prec, rounding))
+        if hasattr(x, '_mpc_'):
+            if hasattr(y, '_mpf_'):
+                return ctx.make_mpc(mpc_div_mpf(x._mpc_, y._mpf_, prec, rounding))
+            if hasattr(y, '_mpc_'):
+                return ctx.make_mpc(mpc_div(x._mpc_, y._mpc_, prec, rounding))
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def nint_distance(ctx, x):
+        r"""
+        Return `(n,d)` where `n` is the nearest integer to `x` and `d` is
+        an estimate of `\log_2(|x-n|)`. If `d < 0`, `-d` gives the precision
+        (measured in bits) lost to cancellation when computing `x-n`.
+
+            >>> from mpmath import *
+            >>> n, d = nint_distance(5)
+            >>> print(n); print(d)
+            5
+            -inf
+            >>> n, d = nint_distance(mpf(5))
+            >>> print(n); print(d)
+            5
+            -inf
+            >>> n, d = nint_distance(mpf(5.00000001))
+            >>> print(n); print(d)
+            5
+            -26
+            >>> n, d = nint_distance(mpf(4.99999999))
+            >>> print(n); print(d)
+            5
+            -26
+            >>> n, d = nint_distance(mpc(5,10))
+            >>> print(n); print(d)
+            5
+            4
+            >>> n, d = nint_distance(mpc(5,0.000001))
+            >>> print(n); print(d)
+            5
+            -19
+
+        """
+        typx = type(x)
+        if typx in int_types:
+            return int(x), ctx.ninf
+        elif typx is rational.mpq:
+            p, q = x._mpq_
+            n, r = divmod(p, q)
+            if 2*r >= q:
+                n += 1
+            elif not r:
+                return n, ctx.ninf
+            # log(p/q-n) = log((p-nq)/q) = log(p-nq) - log(q)
+            d = bitcount(abs(p-n*q)) - bitcount(q)
+            return n, d
+        if hasattr(x, "_mpf_"):
+            re = x._mpf_
+            im_dist = ctx.ninf
+        elif hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            isign, iman, iexp, ibc = im
+            if iman:
+                im_dist = iexp + ibc
+            elif im == fzero:
+                im_dist = ctx.ninf
+            else:
+                raise ValueError("requires a finite number")
+        else:
+            x = ctx.convert(x)
+            if hasattr(x, "_mpf_") or hasattr(x, "_mpc_"):
+                return ctx.nint_distance(x)
+            else:
+                raise TypeError("requires an mpf/mpc")
+        sign, man, exp, bc = re
+        mag = exp+bc
+        # |x| < 0.5
+        if mag < 0:
+            n = 0
+            re_dist = mag
+        elif man:
+            # exact integer
+            if exp >= 0:
+                n = man << exp
+                re_dist = ctx.ninf
+            # exact half-integer
+            elif exp == -1:
+                n = (man>>1)+1
+                re_dist = 0
+            else:
+                d = (-exp-1)
+                t = man >> d
+                if t & 1:
+                    t += 1
+                    man = (t<<d) - man
+                else:
+                    man -= (t<<d)
+                n = t>>1   # int(t)>>1
+                re_dist = exp+bitcount(man)
+            if sign:
+                n = -n
+        elif re == fzero:
+            re_dist = ctx.ninf
+            n = 0
+        else:
+            raise ValueError("requires a finite number")
+        return n, max(re_dist, im_dist)
+
+    def fprod(ctx, factors):
+        r"""
+        Calculates a product containing a finite number of factors (for
+        infinite products, see :func:`~mpmath.nprod`). The factors will be
+        converted to mpmath numbers.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fprod([1, 2, 0.5, 7])
+            mpf('7.0')
+
+        """
+        orig = ctx.prec
+        try:
+            v = ctx.one
+            for p in factors:
+                v *= p
+        finally:
+            ctx.prec = orig
+        return +v
+
+    def rand(ctx):
+        """
+        Returns an ``mpf`` with value chosen randomly from `[0, 1)`.
+        The number of randomly generated bits in the mantissa is equal
+        to the working precision.
+        """
+        return ctx.make_mpf(mpf_rand(ctx._prec))
+
+    def fraction(ctx, p, q):
+        """
+        Given Python integers `(p, q)`, returns a lazy ``mpf`` representing
+        the fraction `p/q`. The value is updated with the precision.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> a = fraction(1,100)
+            >>> b = mpf(1)/100
+            >>> print(a); print(b)
+            0.01
+            0.01
+            >>> mp.dps = 30
+            >>> print(a); print(b)      # a will be accurate
+            0.01
+            0.0100000000000000002081668171172
+            >>> mp.dps = 15
+        """
+        return ctx.constant(lambda prec, rnd: from_rational(p, q, prec, rnd),
+            '%s/%s' % (p, q))
+
+    def absmin(ctx, x):
+        return abs(ctx.convert(x))
+
+    def absmax(ctx, x):
+        return abs(ctx.convert(x))
+
+    def _as_points(ctx, x):
+        # XXX: remove this?
+        if hasattr(x, '_mpi_'):
+            a, b = x._mpi_
+            return [ctx.make_mpf(a), ctx.make_mpf(b)]
+        return x
+
+    '''
+    def _zetasum(ctx, s, a, b):
+        """
+        Computes sum of k^(-s) for k = a, a+1, ..., b with a, b both small
+        integers.
+        """
+        a = int(a)
+        b = int(b)
+        s = ctx.convert(s)
+        prec, rounding = ctx._prec_rounding
+        if hasattr(s, '_mpf_'):
+            v = ctx.make_mpf(libmp.mpf_zetasum(s._mpf_, a, b, prec))
+        elif hasattr(s, '_mpc_'):
+            v = ctx.make_mpc(libmp.mpc_zetasum(s._mpc_, a, b, prec))
+        return v
+    '''
+
+    def _zetasum_fast(ctx, s, a, n, derivatives=[0], reflect=False):
+        if not (ctx.isint(a) and hasattr(s, "_mpc_")):
+            raise NotImplementedError
+        a = int(a)
+        prec = ctx._prec
+        xs, ys = libmp.mpc_zetasum(s._mpc_, a, n, derivatives, reflect, prec)
+        xs = [ctx.make_mpc(x) for x in xs]
+        ys = [ctx.make_mpc(y) for y in ys]
+        return xs, ys
+
+class PrecisionManager:
+    def __init__(self, ctx, precfun, dpsfun, normalize_output=False):
+        self.ctx = ctx
+        self.precfun = precfun
+        self.dpsfun = dpsfun
+        self.normalize_output = normalize_output
+    def __call__(self, f):
+        @functools.wraps(f)
+        def g(*args, **kwargs):
+            orig = self.ctx.prec
+            try:
+                if self.precfun:
+                    self.ctx.prec = self.precfun(self.ctx.prec)
+                else:
+                    self.ctx.dps = self.dpsfun(self.ctx.dps)
+                if self.normalize_output:
+                    v = f(*args, **kwargs)
+                    if type(v) is tuple:
+                        return tuple([+a for a in v])
+                    return +v
+                else:
+                    return f(*args, **kwargs)
+            finally:
+                self.ctx.prec = orig
+        return g
+    def __enter__(self):
+        self.origp = self.ctx.prec
+        if self.precfun:
+            self.ctx.prec = self.precfun(self.ctx.prec)
+        else:
+            self.ctx.dps = self.dpsfun(self.ctx.dps)
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        self.ctx.prec = self.origp
+        return False
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_mp_python.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_mp_python.py
new file mode 100644
index 0000000000000000000000000000000000000000..cfbd72fb8300bf840069c38529b7b41418d26eeb
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/ctx_mp_python.py
@@ -0,0 +1,1149 @@
+#from ctx_base import StandardBaseContext
+
+from .libmp.backend import basestring, exec_
+
+from .libmp import (MPZ, MPZ_ZERO, MPZ_ONE, int_types, repr_dps,
+    round_floor, round_ceiling, dps_to_prec, round_nearest, prec_to_dps,
+    ComplexResult, to_pickable, from_pickable, normalize,
+    from_int, from_float, from_npfloat, from_Decimal, from_str, to_int, to_float, to_str,
+    from_rational, from_man_exp,
+    fone, fzero, finf, fninf, fnan,
+    mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
+    mpf_div, mpf_rdiv_int, mpf_pow_int, mpf_mod,
+    mpf_eq, mpf_cmp, mpf_lt, mpf_gt, mpf_le, mpf_ge,
+    mpf_hash, mpf_rand,
+    mpf_sum,
+    bitcount, to_fixed,
+    mpc_to_str,
+    mpc_to_complex, mpc_hash, mpc_pos, mpc_is_nonzero, mpc_neg, mpc_conjugate,
+    mpc_abs, mpc_add, mpc_add_mpf, mpc_sub, mpc_sub_mpf, mpc_mul, mpc_mul_mpf,
+    mpc_mul_int, mpc_div, mpc_div_mpf, mpc_pow, mpc_pow_mpf, mpc_pow_int,
+    mpc_mpf_div,
+    mpf_pow,
+    mpf_pi, mpf_degree, mpf_e, mpf_phi, mpf_ln2, mpf_ln10,
+    mpf_euler, mpf_catalan, mpf_apery, mpf_khinchin,
+    mpf_glaisher, mpf_twinprime, mpf_mertens,
+    int_types)
+
+from . import rational
+from . import function_docs
+
+new = object.__new__
+
+class mpnumeric(object):
+    """Base class for mpf and mpc."""
+    __slots__ = []
+    def __new__(cls, val):
+        raise NotImplementedError
+
+class _mpf(mpnumeric):
+    """
+    An mpf instance holds a real-valued floating-point number. mpf:s
+    work analogously to Python floats, but support arbitrary-precision
+    arithmetic.
+    """
+    __slots__ = ['_mpf_']
+
+    def __new__(cls, val=fzero, **kwargs):
+        """A new mpf can be created from a Python float, an int, a
+        or a decimal string representing a number in floating-point
+        format."""
+        prec, rounding = cls.context._prec_rounding
+        if kwargs:
+            prec = kwargs.get('prec', prec)
+            if 'dps' in kwargs:
+                prec = dps_to_prec(kwargs['dps'])
+            rounding = kwargs.get('rounding', rounding)
+        if type(val) is cls:
+            sign, man, exp, bc = val._mpf_
+            if (not man) and exp:
+                return val
+            v = new(cls)
+            v._mpf_ = normalize(sign, man, exp, bc, prec, rounding)
+            return v
+        elif type(val) is tuple:
+            if len(val) == 2:
+                v = new(cls)
+                v._mpf_ = from_man_exp(val[0], val[1], prec, rounding)
+                return v
+            if len(val) == 4:
+                if val not in (finf, fninf, fnan):
+                    sign, man, exp, bc = val
+                    val = normalize(sign, MPZ(man), exp, bc, prec, rounding)
+                v = new(cls)
+                v._mpf_ = val
+                return v
+            raise ValueError
+        else:
+            v = new(cls)
+            v._mpf_ = mpf_pos(cls.mpf_convert_arg(val, prec, rounding), prec, rounding)
+            return v
+
+    @classmethod
+    def mpf_convert_arg(cls, x, prec, rounding):
+        if isinstance(x, int_types): return from_int(x)
+        if isinstance(x, float): return from_float(x)
+        if isinstance(x, basestring): return from_str(x, prec, rounding)
+        if isinstance(x, cls.context.constant): return x.func(prec, rounding)
+        if hasattr(x, '_mpf_'): return x._mpf_
+        if hasattr(x, '_mpmath_'):
+            t = cls.context.convert(x._mpmath_(prec, rounding))
+            if hasattr(t, '_mpf_'):
+                return t._mpf_
+        if hasattr(x, '_mpi_'):
+            a, b = x._mpi_
+            if a == b:
+                return a
+            raise ValueError("can only create mpf from zero-width interval")
+        raise TypeError("cannot create mpf from " + repr(x))
+
+    @classmethod
+    def mpf_convert_rhs(cls, x):
+        if isinstance(x, int_types): return from_int(x)
+        if isinstance(x, float): return from_float(x)
+        if isinstance(x, complex_types): return cls.context.mpc(x)
+        if isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            return from_rational(p, q, cls.context.prec)
+        if hasattr(x, '_mpf_'): return x._mpf_
+        if hasattr(x, '_mpmath_'):
+            t = cls.context.convert(x._mpmath_(*cls.context._prec_rounding))
+            if hasattr(t, '_mpf_'):
+                return t._mpf_
+            return t
+        return NotImplemented
+
+    @classmethod
+    def mpf_convert_lhs(cls, x):
+        x = cls.mpf_convert_rhs(x)
+        if type(x) is tuple:
+            return cls.context.make_mpf(x)
+        return x
+
+    man_exp = property(lambda self: self._mpf_[1:3])
+    man = property(lambda self: self._mpf_[1])
+    exp = property(lambda self: self._mpf_[2])
+    bc = property(lambda self: self._mpf_[3])
+
+    real = property(lambda self: self)
+    imag = property(lambda self: self.context.zero)
+
+    conjugate = lambda self: self
+
+    def __getstate__(self): return to_pickable(self._mpf_)
+    def __setstate__(self, val): self._mpf_ = from_pickable(val)
+
+    def __repr__(s):
+        if s.context.pretty:
+            return str(s)
+        return "mpf('%s')" % to_str(s._mpf_, s.context._repr_digits)
+
+    def __str__(s): return to_str(s._mpf_, s.context._str_digits)
+    def __hash__(s): return mpf_hash(s._mpf_)
+    def __int__(s): return int(to_int(s._mpf_))
+    def __long__(s): return long(to_int(s._mpf_))
+    def __float__(s): return to_float(s._mpf_, rnd=s.context._prec_rounding[1])
+    def __complex__(s): return complex(float(s))
+    def __nonzero__(s): return s._mpf_ != fzero
+
+    __bool__ = __nonzero__
+
+    def __abs__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpf_ = mpf_abs(s._mpf_, prec, rounding)
+        return v
+
+    def __pos__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpf_ = mpf_pos(s._mpf_, prec, rounding)
+        return v
+
+    def __neg__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpf_ = mpf_neg(s._mpf_, prec, rounding)
+        return v
+
+    def _cmp(s, t, func):
+        if hasattr(t, '_mpf_'):
+            t = t._mpf_
+        else:
+            t = s.mpf_convert_rhs(t)
+            if t is NotImplemented:
+                return t
+        return func(s._mpf_, t)
+
+    def __cmp__(s, t): return s._cmp(t, mpf_cmp)
+    def __lt__(s, t): return s._cmp(t, mpf_lt)
+    def __gt__(s, t): return s._cmp(t, mpf_gt)
+    def __le__(s, t): return s._cmp(t, mpf_le)
+    def __ge__(s, t): return s._cmp(t, mpf_ge)
+
+    def __ne__(s, t):
+        v = s.__eq__(t)
+        if v is NotImplemented:
+            return v
+        return not v
+
+    def __rsub__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if type(t) in int_types:
+            v = new(cls)
+            v._mpf_ = mpf_sub(from_int(t), s._mpf_, prec, rounding)
+            return v
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t - s
+
+    def __rdiv__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if isinstance(t, int_types):
+            v = new(cls)
+            v._mpf_ = mpf_rdiv_int(t, s._mpf_, prec, rounding)
+            return v
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t / s
+
+    def __rpow__(s, t):
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t ** s
+
+    def __rmod__(s, t):
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t % s
+
+    def sqrt(s):
+        return s.context.sqrt(s)
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.context.almosteq(s, t, rel_eps, abs_eps)
+
+    def to_fixed(self, prec):
+        return to_fixed(self._mpf_, prec)
+
+    def __round__(self, *args):
+        return round(float(self), *args)
+
+mpf_binary_op = """
+def %NAME%(self, other):
+    mpf, new, (prec, rounding) = self._ctxdata
+    sval = self._mpf_
+    if hasattr(other, '_mpf_'):
+        tval = other._mpf_
+        %WITH_MPF%
+    ttype = type(other)
+    if ttype in int_types:
+        %WITH_INT%
+    elif ttype is float:
+        tval = from_float(other)
+        %WITH_MPF%
+    elif hasattr(other, '_mpc_'):
+        tval = other._mpc_
+        mpc = type(other)
+        %WITH_MPC%
+    elif ttype is complex:
+        tval = from_float(other.real), from_float(other.imag)
+        mpc = self.context.mpc
+        %WITH_MPC%
+    if isinstance(other, mpnumeric):
+        return NotImplemented
+    try:
+        other = mpf.context.convert(other, strings=False)
+    except TypeError:
+        return NotImplemented
+    return self.%NAME%(other)
+"""
+
+return_mpf = "; obj = new(mpf); obj._mpf_ = val; return obj"
+return_mpc = "; obj = new(mpc); obj._mpc_ = val; return obj"
+
+mpf_pow_same = """
+        try:
+            val = mpf_pow(sval, tval, prec, rounding) %s
+        except ComplexResult:
+            if mpf.context.trap_complex:
+                raise
+            mpc = mpf.context.mpc
+            val = mpc_pow((sval, fzero), (tval, fzero), prec, rounding) %s
+""" % (return_mpf, return_mpc)
+
+def binary_op(name, with_mpf='', with_int='', with_mpc=''):
+    code = mpf_binary_op
+    code = code.replace("%WITH_INT%", with_int)
+    code = code.replace("%WITH_MPC%", with_mpc)
+    code = code.replace("%WITH_MPF%", with_mpf)
+    code = code.replace("%NAME%", name)
+    np = {}
+    exec_(code, globals(), np)
+    return np[name]
+
+_mpf.__eq__ = binary_op('__eq__',
+    'return mpf_eq(sval, tval)',
+    'return mpf_eq(sval, from_int(other))',
+    'return (tval[1] == fzero) and mpf_eq(tval[0], sval)')
+
+_mpf.__add__ = binary_op('__add__',
+    'val = mpf_add(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_add(sval, from_int(other), prec, rounding)' + return_mpf,
+    'val = mpc_add_mpf(tval, sval, prec, rounding)' + return_mpc)
+
+_mpf.__sub__ = binary_op('__sub__',
+    'val = mpf_sub(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_sub(sval, from_int(other), prec, rounding)' + return_mpf,
+    'val = mpc_sub((sval, fzero), tval, prec, rounding)' + return_mpc)
+
+_mpf.__mul__ = binary_op('__mul__',
+    'val = mpf_mul(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_mul_int(sval, other, prec, rounding)' + return_mpf,
+    'val = mpc_mul_mpf(tval, sval, prec, rounding)' + return_mpc)
+
+_mpf.__div__ = binary_op('__div__',
+    'val = mpf_div(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_div(sval, from_int(other), prec, rounding)' + return_mpf,
+    'val = mpc_mpf_div(sval, tval, prec, rounding)' + return_mpc)
+
+_mpf.__mod__ = binary_op('__mod__',
+    'val = mpf_mod(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_mod(sval, from_int(other), prec, rounding)' + return_mpf,
+    'raise NotImplementedError("complex modulo")')
+
+_mpf.__pow__ = binary_op('__pow__',
+    mpf_pow_same,
+    'val = mpf_pow_int(sval, other, prec, rounding)' + return_mpf,
+    'val = mpc_pow((sval, fzero), tval, prec, rounding)' + return_mpc)
+
+_mpf.__radd__ = _mpf.__add__
+_mpf.__rmul__ = _mpf.__mul__
+_mpf.__truediv__ = _mpf.__div__
+_mpf.__rtruediv__ = _mpf.__rdiv__
+
+
+class _constant(_mpf):
+    """Represents a mathematical constant with dynamic precision.
+    When printed or used in an arithmetic operation, a constant
+    is converted to a regular mpf at the working precision. A
+    regular mpf can also be obtained using the operation +x."""
+
+    def __new__(cls, func, name, docname=''):
+        a = object.__new__(cls)
+        a.name = name
+        a.func = func
+        a.__doc__ = getattr(function_docs, docname, '')
+        return a
+
+    def __call__(self, prec=None, dps=None, rounding=None):
+        prec2, rounding2 = self.context._prec_rounding
+        if not prec: prec = prec2
+        if not rounding: rounding = rounding2
+        if dps: prec = dps_to_prec(dps)
+        return self.context.make_mpf(self.func(prec, rounding))
+
+    @property
+    def _mpf_(self):
+        prec, rounding = self.context._prec_rounding
+        return self.func(prec, rounding)
+
+    def __repr__(self):
+        return "<%s: %s~>" % (self.name, self.context.nstr(self(dps=15)))
+
+
+class _mpc(mpnumeric):
+    """
+    An mpc represents a complex number using a pair of mpf:s (one
+    for the real part and another for the imaginary part.) The mpc
+    class behaves fairly similarly to Python's complex type.
+    """
+
+    __slots__ = ['_mpc_']
+
+    def __new__(cls, real=0, imag=0):
+        s = object.__new__(cls)
+        if isinstance(real, complex_types):
+            real, imag = real.real, real.imag
+        elif hasattr(real, '_mpc_'):
+            s._mpc_ = real._mpc_
+            return s
+        real = cls.context.mpf(real)
+        imag = cls.context.mpf(imag)
+        s._mpc_ = (real._mpf_, imag._mpf_)
+        return s
+
+    real = property(lambda self: self.context.make_mpf(self._mpc_[0]))
+    imag = property(lambda self: self.context.make_mpf(self._mpc_[1]))
+
+    def __getstate__(self):
+        return to_pickable(self._mpc_[0]), to_pickable(self._mpc_[1])
+
+    def __setstate__(self, val):
+        self._mpc_ = from_pickable(val[0]), from_pickable(val[1])
+
+    def __repr__(s):
+        if s.context.pretty:
+            return str(s)
+        r = repr(s.real)[4:-1]
+        i = repr(s.imag)[4:-1]
+        return "%s(real=%s, imag=%s)" % (type(s).__name__, r, i)
+
+    def __str__(s):
+        return "(%s)" % mpc_to_str(s._mpc_, s.context._str_digits)
+
+    def __complex__(s):
+        return mpc_to_complex(s._mpc_, rnd=s.context._prec_rounding[1])
+
+    def __pos__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpc_ = mpc_pos(s._mpc_, prec, rounding)
+        return v
+
+    def __abs__(s):
+        prec, rounding = s.context._prec_rounding
+        v = new(s.context.mpf)
+        v._mpf_ = mpc_abs(s._mpc_, prec, rounding)
+        return v
+
+    def __neg__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpc_ = mpc_neg(s._mpc_, prec, rounding)
+        return v
+
+    def conjugate(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpc_ = mpc_conjugate(s._mpc_, prec, rounding)
+        return v
+
+    def __nonzero__(s):
+        return mpc_is_nonzero(s._mpc_)
+
+    __bool__ = __nonzero__
+
+    def __hash__(s):
+        return mpc_hash(s._mpc_)
+
+    @classmethod
+    def mpc_convert_lhs(cls, x):
+        try:
+            y = cls.context.convert(x)
+            return y
+        except TypeError:
+            return NotImplemented
+
+    def __eq__(s, t):
+        if not hasattr(t, '_mpc_'):
+            if isinstance(t, str):
+                return False
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+        return s.real == t.real and s.imag == t.imag
+
+    def __ne__(s, t):
+        b = s.__eq__(t)
+        if b is NotImplemented:
+            return b
+        return not b
+
+    def _compare(*args):
+        raise TypeError("no ordering relation is defined for complex numbers")
+
+    __gt__ = _compare
+    __le__ = _compare
+    __gt__ = _compare
+    __ge__ = _compare
+
+    def __add__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_add_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+        v = new(cls)
+        v._mpc_ = mpc_add(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __sub__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_sub_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+        v = new(cls)
+        v._mpc_ = mpc_sub(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __mul__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            if isinstance(t, int_types):
+                v = new(cls)
+                v._mpc_ = mpc_mul_int(s._mpc_, t, prec, rounding)
+                return v
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_mul_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+            t = s.mpc_convert_lhs(t)
+        v = new(cls)
+        v._mpc_ = mpc_mul(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __div__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_div_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+        v = new(cls)
+        v._mpc_ = mpc_div(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __pow__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if isinstance(t, int_types):
+            v = new(cls)
+            v._mpc_ = mpc_pow_int(s._mpc_, t, prec, rounding)
+            return v
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        v = new(cls)
+        if hasattr(t, '_mpf_'):
+            v._mpc_ = mpc_pow_mpf(s._mpc_, t._mpf_, prec, rounding)
+        else:
+            v._mpc_ = mpc_pow(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    __radd__ = __add__
+
+    def __rsub__(s, t):
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t - s
+
+    def __rmul__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if isinstance(t, int_types):
+            v = new(cls)
+            v._mpc_ = mpc_mul_int(s._mpc_, t, prec, rounding)
+            return v
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t * s
+
+    def __rdiv__(s, t):
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t / s
+
+    def __rpow__(s, t):
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t ** s
+
+    __truediv__ = __div__
+    __rtruediv__ = __rdiv__
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.context.almosteq(s, t, rel_eps, abs_eps)
+
+
+complex_types = (complex, _mpc)
+
+
+class PythonMPContext(object):
+
+    def __init__(ctx):
+        ctx._prec_rounding = [53, round_nearest]
+        ctx.mpf = type('mpf', (_mpf,), {})
+        ctx.mpc = type('mpc', (_mpc,), {})
+        ctx.mpf._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
+        ctx.mpc._ctxdata = [ctx.mpc, new, ctx._prec_rounding]
+        ctx.mpf.context = ctx
+        ctx.mpc.context = ctx
+        ctx.constant = type('constant', (_constant,), {})
+        ctx.constant._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
+        ctx.constant.context = ctx
+
+    def make_mpf(ctx, v):
+        a = new(ctx.mpf)
+        a._mpf_ = v
+        return a
+
+    def make_mpc(ctx, v):
+        a = new(ctx.mpc)
+        a._mpc_ = v
+        return a
+
+    def default(ctx):
+        ctx._prec = ctx._prec_rounding[0] = 53
+        ctx._dps = 15
+        ctx.trap_complex = False
+
+    def _set_prec(ctx, n):
+        ctx._prec = ctx._prec_rounding[0] = max(1, int(n))
+        ctx._dps = prec_to_dps(n)
+
+    def _set_dps(ctx, n):
+        ctx._prec = ctx._prec_rounding[0] = dps_to_prec(n)
+        ctx._dps = max(1, int(n))
+
+    prec = property(lambda ctx: ctx._prec, _set_prec)
+    dps = property(lambda ctx: ctx._dps, _set_dps)
+
+    def convert(ctx, x, strings=True):
+        """
+        Converts *x* to an ``mpf`` or ``mpc``. If *x* is of type ``mpf``,
+        ``mpc``, ``int``, ``float``, ``complex``, the conversion
+        will be performed losslessly.
+
+        If *x* is a string, the result will be rounded to the present
+        working precision. Strings representing fractions or complex
+        numbers are permitted.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> mpmathify(3.5)
+            mpf('3.5')
+            >>> mpmathify('2.1')
+            mpf('2.1000000000000001')
+            >>> mpmathify('3/4')
+            mpf('0.75')
+            >>> mpmathify('2+3j')
+            mpc(real='2.0', imag='3.0')
+
+        """
+        if type(x) in ctx.types: return x
+        if isinstance(x, int_types): return ctx.make_mpf(from_int(x))
+        if isinstance(x, float): return ctx.make_mpf(from_float(x))
+        if isinstance(x, complex):
+            return ctx.make_mpc((from_float(x.real), from_float(x.imag)))
+        if type(x).__module__ == 'numpy': return ctx.npconvert(x)
+        if isinstance(x, numbers.Rational): # e.g. Fraction
+            try: x = rational.mpq(int(x.numerator), int(x.denominator))
+            except: pass
+        prec, rounding = ctx._prec_rounding
+        if isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            return ctx.make_mpf(from_rational(p, q, prec))
+        if strings and isinstance(x, basestring):
+            try:
+                _mpf_ = from_str(x, prec, rounding)
+                return ctx.make_mpf(_mpf_)
+            except ValueError:
+                pass
+        if hasattr(x, '_mpf_'): return ctx.make_mpf(x._mpf_)
+        if hasattr(x, '_mpc_'): return ctx.make_mpc(x._mpc_)
+        if hasattr(x, '_mpmath_'):
+            return ctx.convert(x._mpmath_(prec, rounding))
+        if type(x).__module__ == 'decimal':
+            try: return ctx.make_mpf(from_Decimal(x, prec, rounding))
+            except: pass
+        return ctx._convert_fallback(x, strings)
+
+    def npconvert(ctx, x):
+        """
+        Converts *x* to an ``mpf`` or ``mpc``. *x* should be a numpy
+        scalar.
+        """
+        import numpy as np
+        if isinstance(x, np.integer): return ctx.make_mpf(from_int(int(x)))
+        if isinstance(x, np.floating): return ctx.make_mpf(from_npfloat(x))
+        if isinstance(x, np.complexfloating):
+            return ctx.make_mpc((from_npfloat(x.real), from_npfloat(x.imag)))
+        raise TypeError("cannot create mpf from " + repr(x))
+
+    def isnan(ctx, x):
+        """
+        Return *True* if *x* is a NaN (not-a-number), or for a complex
+        number, whether either the real or complex part is NaN;
+        otherwise return *False*::
+
+            >>> from mpmath import *
+            >>> isnan(3.14)
+            False
+            >>> isnan(nan)
+            True
+            >>> isnan(mpc(3.14,2.72))
+            False
+            >>> isnan(mpc(3.14,nan))
+            True
+
+        """
+        if hasattr(x, "_mpf_"):
+            return x._mpf_ == fnan
+        if hasattr(x, "_mpc_"):
+            return fnan in x._mpc_
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return False
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isnan(x)
+        raise TypeError("isnan() needs a number as input")
+
+    def isinf(ctx, x):
+        """
+        Return *True* if the absolute value of *x* is infinite;
+        otherwise return *False*::
+
+            >>> from mpmath import *
+            >>> isinf(inf)
+            True
+            >>> isinf(-inf)
+            True
+            >>> isinf(3)
+            False
+            >>> isinf(3+4j)
+            False
+            >>> isinf(mpc(3,inf))
+            True
+            >>> isinf(mpc(inf,3))
+            True
+
+        """
+        if hasattr(x, "_mpf_"):
+            return x._mpf_ in (finf, fninf)
+        if hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            return re in (finf, fninf) or im in (finf, fninf)
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return False
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isinf(x)
+        raise TypeError("isinf() needs a number as input")
+
+    def isnormal(ctx, x):
+        """
+        Determine whether *x* is "normal" in the sense of floating-point
+        representation; that is, return *False* if *x* is zero, an
+        infinity or NaN; otherwise return *True*. By extension, a
+        complex number *x* is considered "normal" if its magnitude is
+        normal::
+
+            >>> from mpmath import *
+            >>> isnormal(3)
+            True
+            >>> isnormal(0)
+            False
+            >>> isnormal(inf); isnormal(-inf); isnormal(nan)
+            False
+            False
+            False
+            >>> isnormal(0+0j)
+            False
+            >>> isnormal(0+3j)
+            True
+            >>> isnormal(mpc(2,nan))
+            False
+        """
+        if hasattr(x, "_mpf_"):
+            return bool(x._mpf_[1])
+        if hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            re_normal = bool(re[1])
+            im_normal = bool(im[1])
+            if re == fzero: return im_normal
+            if im == fzero: return re_normal
+            return re_normal and im_normal
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return bool(x)
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isnormal(x)
+        raise TypeError("isnormal() needs a number as input")
+
+    def isint(ctx, x, gaussian=False):
+        """
+        Return *True* if *x* is integer-valued; otherwise return
+        *False*::
+
+            >>> from mpmath import *
+            >>> isint(3)
+            True
+            >>> isint(mpf(3))
+            True
+            >>> isint(3.2)
+            False
+            >>> isint(inf)
+            False
+
+        Optionally, Gaussian integers can be checked for::
+
+            >>> isint(3+0j)
+            True
+            >>> isint(3+2j)
+            False
+            >>> isint(3+2j, gaussian=True)
+            True
+
+        """
+        if isinstance(x, int_types):
+            return True
+        if hasattr(x, "_mpf_"):
+            sign, man, exp, bc = xval = x._mpf_
+            return bool((man and exp >= 0) or xval == fzero)
+        if hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            rsign, rman, rexp, rbc = re
+            isign, iman, iexp, ibc = im
+            re_isint = (rman and rexp >= 0) or re == fzero
+            if gaussian:
+                im_isint = (iman and iexp >= 0) or im == fzero
+                return re_isint and im_isint
+            return re_isint and im == fzero
+        if isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            return p % q == 0
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isint(x, gaussian)
+        raise TypeError("isint() needs a number as input")
+
+    def fsum(ctx, terms, absolute=False, squared=False):
+        """
+        Calculates a sum containing a finite number of terms (for infinite
+        series, see :func:`~mpmath.nsum`). The terms will be converted to
+        mpmath numbers. For len(terms) > 2, this function is generally
+        faster and produces more accurate results than the builtin
+        Python function :func:`sum`.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fsum([1, 2, 0.5, 7])
+            mpf('10.5')
+
+        With squared=True each term is squared, and with absolute=True
+        the absolute value of each term is used.
+        """
+        prec, rnd = ctx._prec_rounding
+        real = []
+        imag = []
+        for term in terms:
+            reval = imval = 0
+            if hasattr(term, "_mpf_"):
+                reval = term._mpf_
+            elif hasattr(term, "_mpc_"):
+                reval, imval = term._mpc_
+            else:
+                term = ctx.convert(term)
+                if hasattr(term, "_mpf_"):
+                    reval = term._mpf_
+                elif hasattr(term, "_mpc_"):
+                    reval, imval = term._mpc_
+                else:
+                    raise NotImplementedError
+            if imval:
+                if squared:
+                    if absolute:
+                        real.append(mpf_mul(reval,reval))
+                        real.append(mpf_mul(imval,imval))
+                    else:
+                        reval, imval = mpc_pow_int((reval,imval),2,prec+10)
+                        real.append(reval)
+                        imag.append(imval)
+                elif absolute:
+                    real.append(mpc_abs((reval,imval), prec))
+                else:
+                    real.append(reval)
+                    imag.append(imval)
+            else:
+                if squared:
+                    reval = mpf_mul(reval, reval)
+                elif absolute:
+                    reval = mpf_abs(reval)
+                real.append(reval)
+        s = mpf_sum(real, prec, rnd, absolute)
+        if imag:
+            s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
+        else:
+            s = ctx.make_mpf(s)
+        return s
+
+    def fdot(ctx, A, B=None, conjugate=False):
+        r"""
+        Computes the dot product of the iterables `A` and `B`,
+
+        .. math ::
+
+            \sum_{k=0} A_k B_k.
+
+        Alternatively, :func:`~mpmath.fdot` accepts a single iterable of pairs.
+        In other words, ``fdot(A,B)`` and ``fdot(zip(A,B))`` are equivalent.
+        The elements are automatically converted to mpmath numbers.
+
+        With ``conjugate=True``, the elements in the second vector
+        will be conjugated:
+
+        .. math ::
+
+            \sum_{k=0} A_k \overline{B_k}
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> A = [2, 1.5, 3]
+            >>> B = [1, -1, 2]
+            >>> fdot(A, B)
+            mpf('6.5')
+            >>> list(zip(A, B))
+            [(2, 1), (1.5, -1), (3, 2)]
+            >>> fdot(_)
+            mpf('6.5')
+            >>> A = [2, 1.5, 3j]
+            >>> B = [1+j, 3, -1-j]
+            >>> fdot(A, B)
+            mpc(real='9.5', imag='-1.0')
+            >>> fdot(A, B, conjugate=True)
+            mpc(real='3.5', imag='-5.0')
+
+        """
+        if B is not None:
+            A = zip(A, B)
+        prec, rnd = ctx._prec_rounding
+        real = []
+        imag = []
+        hasattr_ = hasattr
+        types = (ctx.mpf, ctx.mpc)
+        for a, b in A:
+            if type(a) not in types: a = ctx.convert(a)
+            if type(b) not in types: b = ctx.convert(b)
+            a_real = hasattr_(a, "_mpf_")
+            b_real = hasattr_(b, "_mpf_")
+            if a_real and b_real:
+                real.append(mpf_mul(a._mpf_, b._mpf_))
+                continue
+            a_complex = hasattr_(a, "_mpc_")
+            b_complex = hasattr_(b, "_mpc_")
+            if a_real and b_complex:
+                aval = a._mpf_
+                bre, bim = b._mpc_
+                if conjugate:
+                    bim = mpf_neg(bim)
+                real.append(mpf_mul(aval, bre))
+                imag.append(mpf_mul(aval, bim))
+            elif b_real and a_complex:
+                are, aim = a._mpc_
+                bval = b._mpf_
+                real.append(mpf_mul(are, bval))
+                imag.append(mpf_mul(aim, bval))
+            elif a_complex and b_complex:
+                #re, im = mpc_mul(a._mpc_, b._mpc_, prec+20)
+                are, aim = a._mpc_
+                bre, bim = b._mpc_
+                if conjugate:
+                    bim = mpf_neg(bim)
+                real.append(mpf_mul(are, bre))
+                real.append(mpf_neg(mpf_mul(aim, bim)))
+                imag.append(mpf_mul(are, bim))
+                imag.append(mpf_mul(aim, bre))
+            else:
+                raise NotImplementedError
+        s = mpf_sum(real, prec, rnd)
+        if imag:
+            s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
+        else:
+            s = ctx.make_mpf(s)
+        return s
+
+    def _wrap_libmp_function(ctx, mpf_f, mpc_f=None, mpi_f=None, doc="<no doc>"):
+        """
+        Given a low-level mpf_ function, and optionally similar functions
+        for mpc_ and mpi_, defines the function as a context method.
+
+        It is assumed that the return type is the same as that of
+        the input; the exception is that propagation from mpf to mpc is possible
+        by raising ComplexResult.
+
+        """
+        def f(x, **kwargs):
+            if type(x) not in ctx.types:
+                x = ctx.convert(x)
+            prec, rounding = ctx._prec_rounding
+            if kwargs:
+                prec = kwargs.get('prec', prec)
+                if 'dps' in kwargs:
+                    prec = dps_to_prec(kwargs['dps'])
+                rounding = kwargs.get('rounding', rounding)
+            if hasattr(x, '_mpf_'):
+                try:
+                    return ctx.make_mpf(mpf_f(x._mpf_, prec, rounding))
+                except ComplexResult:
+                    # Handle propagation to complex
+                    if ctx.trap_complex:
+                        raise
+                    return ctx.make_mpc(mpc_f((x._mpf_, fzero), prec, rounding))
+            elif hasattr(x, '_mpc_'):
+                return ctx.make_mpc(mpc_f(x._mpc_, prec, rounding))
+            raise NotImplementedError("%s of a %s" % (name, type(x)))
+        name = mpf_f.__name__[4:]
+        f.__doc__ = function_docs.__dict__.get(name, "Computes the %s of x" % doc)
+        return f
+
+    # Called by SpecialFunctions.__init__()
+    @classmethod
+    def _wrap_specfun(cls, name, f, wrap):
+        if wrap:
+            def f_wrapped(ctx, *args, **kwargs):
+                convert = ctx.convert
+                args = [convert(a) for a in args]
+                prec = ctx.prec
+                try:
+                    ctx.prec += 10
+                    retval = f(ctx, *args, **kwargs)
+                finally:
+                    ctx.prec = prec
+                return +retval
+        else:
+            f_wrapped = f
+        f_wrapped.__doc__ = function_docs.__dict__.get(name, f.__doc__)
+        setattr(cls, name, f_wrapped)
+
+    def _convert_param(ctx, x):
+        if hasattr(x, "_mpc_"):
+            v, im = x._mpc_
+            if im != fzero:
+                return x, 'C'
+        elif hasattr(x, "_mpf_"):
+            v = x._mpf_
+        else:
+            if type(x) in int_types:
+                return int(x), 'Z'
+            p = None
+            if isinstance(x, tuple):
+                p, q = x
+            elif hasattr(x, '_mpq_'):
+                p, q = x._mpq_
+            elif isinstance(x, basestring) and '/' in x:
+                p, q = x.split('/')
+                p = int(p)
+                q = int(q)
+            if p is not None:
+                if not p % q:
+                    return p // q, 'Z'
+                return ctx.mpq(p,q), 'Q'
+            x = ctx.convert(x)
+            if hasattr(x, "_mpc_"):
+                v, im = x._mpc_
+                if im != fzero:
+                    return x, 'C'
+            elif hasattr(x, "_mpf_"):
+                v = x._mpf_
+            else:
+                return x, 'U'
+        sign, man, exp, bc = v
+        if man:
+            if exp >= -4:
+                if sign:
+                    man = -man
+                if exp >= 0:
+                    return int(man) << exp, 'Z'
+                if exp >= -4:
+                    p, q = int(man), (1<<(-exp))
+                    return ctx.mpq(p,q), 'Q'
+            x = ctx.make_mpf(v)
+            return x, 'R'
+        elif not exp:
+            return 0, 'Z'
+        else:
+            return x, 'U'
+
+    def _mpf_mag(ctx, x):
+        sign, man, exp, bc = x
+        if man:
+            return exp+bc
+        if x == fzero:
+            return ctx.ninf
+        if x == finf or x == fninf:
+            return ctx.inf
+        return ctx.nan
+
+    def mag(ctx, x):
+        """
+        Quick logarithmic magnitude estimate of a number. Returns an
+        integer or infinity `m` such that `|x| <= 2^m`. It is not
+        guaranteed that `m` is an optimal bound, but it will never
+        be too large by more than 2 (and probably not more than 1).
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.pretty = True
+            >>> mag(10), mag(10.0), mag(mpf(10)), int(ceil(log(10,2)))
+            (4, 4, 4, 4)
+            >>> mag(10j), mag(10+10j)
+            (4, 5)
+            >>> mag(0.01), int(ceil(log(0.01,2)))
+            (-6, -6)
+            >>> mag(0), mag(inf), mag(-inf), mag(nan)
+            (-inf, +inf, +inf, nan)
+
+        """
+        if hasattr(x, "_mpf_"):
+            return ctx._mpf_mag(x._mpf_)
+        elif hasattr(x, "_mpc_"):
+            r, i = x._mpc_
+            if r == fzero:
+                return ctx._mpf_mag(i)
+            if i == fzero:
+                return ctx._mpf_mag(r)
+            return 1+max(ctx._mpf_mag(r), ctx._mpf_mag(i))
+        elif isinstance(x, int_types):
+            if x:
+                return bitcount(abs(x))
+            return ctx.ninf
+        elif isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            if p:
+                return 1 + bitcount(abs(p)) - bitcount(q)
+            return ctx.ninf
+        else:
+            x = ctx.convert(x)
+            if hasattr(x, "_mpf_") or hasattr(x, "_mpc_"):
+                return ctx.mag(x)
+            else:
+                raise TypeError("requires an mpf/mpc")
+
+
+# Register with "numbers" ABC
+#     We do not subclass, hence we do not use the @abstractmethod checks. While
+#     this is less invasive it may turn out that we do not actually support
+#     parts of the expected interfaces.  See
+#     http://docs.python.org/2/library/numbers.html for list of abstract
+#     methods.
+try:
+    import numbers
+    numbers.Complex.register(_mpc)
+    numbers.Real.register(_mpf)
+except ImportError:
+    pass
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/identification.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/identification.py
new file mode 100644
index 0000000000000000000000000000000000000000..226f62d3fe9cacedbd9ba2b1e66ff0ad017fa604
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/identification.py
@@ -0,0 +1,844 @@
+"""
+Implements the PSLQ algorithm for integer relation detection,
+and derivative algorithms for constant recognition.
+"""
+
+from .libmp.backend import xrange
+from .libmp import int_types, sqrt_fixed
+
+# round to nearest integer (can be done more elegantly...)
+def round_fixed(x, prec):
+    return ((x + (1<<(prec-1))) >> prec) << prec
+
+class IdentificationMethods(object):
+    pass
+
+
+def pslq(ctx, x, tol=None, maxcoeff=1000, maxsteps=100, verbose=False):
+    r"""
+    Given a vector of real numbers `x = [x_0, x_1, ..., x_n]`, ``pslq(x)``
+    uses the PSLQ algorithm to find a list of integers
+    `[c_0, c_1, ..., c_n]` such that
+
+    .. math ::
+
+        |c_1 x_1 + c_2 x_2 + ... + c_n x_n| < \mathrm{tol}
+
+    and such that `\max |c_k| < \mathrm{maxcoeff}`. If no such vector
+    exists, :func:`~mpmath.pslq` returns ``None``. The tolerance defaults to
+    3/4 of the working precision.
+
+    **Examples**
+
+    Find rational approximations for `\pi`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 15; mp.pretty = True
+        >>> pslq([-1, pi], tol=0.01)
+        [22, 7]
+        >>> pslq([-1, pi], tol=0.001)
+        [355, 113]
+        >>> mpf(22)/7; mpf(355)/113; +pi
+        3.14285714285714
+        3.14159292035398
+        3.14159265358979
+
+    Pi is not a rational number with denominator less than 1000::
+
+        >>> pslq([-1, pi])
+        >>>
+
+    To within the standard precision, it can however be approximated
+    by at least one rational number with denominator less than `10^{12}`::
+
+        >>> p, q = pslq([-1, pi], maxcoeff=10**12)
+        >>> print(p); print(q)
+        238410049439
+        75888275702
+        >>> mpf(p)/q
+        3.14159265358979
+
+    The PSLQ algorithm can be applied to long vectors. For example,
+    we can investigate the rational (in)dependence of integer square
+    roots::
+
+        >>> mp.dps = 30
+        >>> pslq([sqrt(n) for n in range(2, 5+1)])
+        >>>
+        >>> pslq([sqrt(n) for n in range(2, 6+1)])
+        >>>
+        >>> pslq([sqrt(n) for n in range(2, 8+1)])
+        [2, 0, 0, 0, 0, 0, -1]
+
+    **Machin formulas**
+
+    A famous formula for `\pi` is Machin's,
+
+    .. math ::
+
+        \frac{\pi}{4} = 4 \operatorname{acot} 5 - \operatorname{acot} 239
+
+    There are actually infinitely many formulas of this type. Two
+    others are
+
+    .. math ::
+
+        \frac{\pi}{4} = \operatorname{acot} 1
+
+        \frac{\pi}{4} = 12 \operatorname{acot} 49 + 32 \operatorname{acot} 57
+            + 5 \operatorname{acot} 239 + 12 \operatorname{acot} 110443
+
+    We can easily verify the formulas using the PSLQ algorithm::
+
+        >>> mp.dps = 30
+        >>> pslq([pi/4, acot(1)])
+        [1, -1]
+        >>> pslq([pi/4, acot(5), acot(239)])
+        [1, -4, 1]
+        >>> pslq([pi/4, acot(49), acot(57), acot(239), acot(110443)])
+        [1, -12, -32, 5, -12]
+
+    We could try to generate a custom Machin-like formula by running
+    the PSLQ algorithm with a few inverse cotangent values, for example
+    acot(2), acot(3) ... acot(10). Unfortunately, there is a linear
+    dependence among these values, resulting in only that dependence
+    being detected, with a zero coefficient for `\pi`::
+
+        >>> pslq([pi] + [acot(n) for n in range(2,11)])
+        [0, 1, -1, 0, 0, 0, -1, 0, 0, 0]
+
+    We get better luck by removing linearly dependent terms::
+
+        >>> pslq([pi] + [acot(n) for n in range(2,11) if n not in (3, 5)])
+        [1, -8, 0, 0, 4, 0, 0, 0]
+
+    In other words, we found the following formula::
+
+        >>> 8*acot(2) - 4*acot(7)
+        3.14159265358979323846264338328
+        >>> +pi
+        3.14159265358979323846264338328
+
+    **Algorithm**
+
+    This is a fairly direct translation to Python of the pseudocode given by
+    David Bailey, "The PSLQ Integer Relation Algorithm":
+    http://www.cecm.sfu.ca/organics/papers/bailey/paper/html/node3.html
+
+    The present implementation uses fixed-point instead of floating-point
+    arithmetic, since this is significantly (about 7x) faster.
+    """
+
+    n = len(x)
+    if n < 2:
+        raise ValueError("n cannot be less than 2")
+
+    # At too low precision, the algorithm becomes meaningless
+    prec = ctx.prec
+    if prec < 53:
+        raise ValueError("prec cannot be less than 53")
+
+    if verbose and prec // max(2,n) < 5:
+        print("Warning: precision for PSLQ may be too low")
+
+    target = int(prec * 0.75)
+
+    if tol is None:
+        tol = ctx.mpf(2)**(-target)
+    else:
+        tol = ctx.convert(tol)
+
+    extra = 60
+    prec += extra
+
+    if verbose:
+        print("PSLQ using prec %i and tol %s" % (prec, ctx.nstr(tol)))
+
+    tol = ctx.to_fixed(tol, prec)
+    assert tol
+
+    # Convert to fixed-point numbers. The dummy None is added so we can
+    # use 1-based indexing. (This just allows us to be consistent with
+    # Bailey's indexing. The algorithm is 100 lines long, so debugging
+    # a single wrong index can be painful.)
+    x = [None] + [ctx.to_fixed(ctx.mpf(xk), prec) for xk in x]
+
+    # Sanity check on magnitudes
+    minx = min(abs(xx) for xx in x[1:])
+    if not minx:
+        raise ValueError("PSLQ requires a vector of nonzero numbers")
+    if minx < tol//100:
+        if verbose:
+            print("STOPPING: (one number is too small)")
+        return None
+
+    g = sqrt_fixed((4<<prec)//3, prec)
+    A = {}
+    B = {}
+    H = {}
+    # Initialization
+    # step 1
+    for i in xrange(1, n+1):
+        for j in xrange(1, n+1):
+            A[i,j] = B[i,j] = (i==j) << prec
+            H[i,j] = 0
+    # step 2
+    s = [None] + [0] * n
+    for k in xrange(1, n+1):
+        t = 0
+        for j in xrange(k, n+1):
+            t += (x[j]**2 >> prec)
+        s[k] = sqrt_fixed(t, prec)
+    t = s[1]
+    y = x[:]
+    for k in xrange(1, n+1):
+        y[k] = (x[k] << prec) // t
+        s[k] = (s[k] << prec) // t
+    # step 3
+    for i in xrange(1, n+1):
+        for j in xrange(i+1, n):
+            H[i,j] = 0
+        if i <= n-1:
+            if s[i]:
+                H[i,i] = (s[i+1] << prec) // s[i]
+            else:
+                H[i,i] = 0
+        for j in range(1, i):
+            sjj1 = s[j]*s[j+1]
+            if sjj1:
+                H[i,j] = ((-y[i]*y[j])<<prec)//sjj1
+            else:
+                H[i,j] = 0
+    # step 4
+    for i in xrange(2, n+1):
+        for j in xrange(i-1, 0, -1):
+            #t = floor(H[i,j]/H[j,j] + 0.5)
+            if H[j,j]:
+                t = round_fixed((H[i,j] << prec)//H[j,j], prec)
+            else:
+                #t = 0
+                continue
+            y[j] = y[j] + (t*y[i] >> prec)
+            for k in xrange(1, j+1):
+                H[i,k] = H[i,k] - (t*H[j,k] >> prec)
+            for k in xrange(1, n+1):
+                A[i,k] = A[i,k] - (t*A[j,k] >> prec)
+                B[k,j] = B[k,j] + (t*B[k,i] >> prec)
+    # Main algorithm
+    for REP in range(maxsteps):
+        # Step 1
+        m = -1
+        szmax = -1
+        for i in range(1, n):
+            h = H[i,i]
+            sz = (g**i * abs(h)) >> (prec*(i-1))
+            if sz > szmax:
+                m = i
+                szmax = sz
+        # Step 2
+        y[m], y[m+1] = y[m+1], y[m]
+        for i in xrange(1,n+1): H[m,i], H[m+1,i] = H[m+1,i], H[m,i]
+        for i in xrange(1,n+1): A[m,i], A[m+1,i] = A[m+1,i], A[m,i]
+        for i in xrange(1,n+1): B[i,m], B[i,m+1] = B[i,m+1], B[i,m]
+        # Step 3
+        if m <= n - 2:
+            t0 = sqrt_fixed((H[m,m]**2 + H[m,m+1]**2)>>prec, prec)
+            # A zero element probably indicates that the precision has
+            # been exhausted. XXX: this could be spurious, due to
+            # using fixed-point arithmetic
+            if not t0:
+                break
+            t1 = (H[m,m] << prec) // t0
+            t2 = (H[m,m+1] << prec) // t0
+            for i in xrange(m, n+1):
+                t3 = H[i,m]
+                t4 = H[i,m+1]
+                H[i,m] = (t1*t3+t2*t4) >> prec
+                H[i,m+1] = (-t2*t3+t1*t4) >> prec
+        # Step 4
+        for i in xrange(m+1, n+1):
+            for j in xrange(min(i-1, m+1), 0, -1):
+                try:
+                    t = round_fixed((H[i,j] << prec)//H[j,j], prec)
+                # Precision probably exhausted
+                except ZeroDivisionError:
+                    break
+                y[j] = y[j] + ((t*y[i]) >> prec)
+                for k in xrange(1, j+1):
+                    H[i,k] = H[i,k] - (t*H[j,k] >> prec)
+                for k in xrange(1, n+1):
+                    A[i,k] = A[i,k] - (t*A[j,k] >> prec)
+                    B[k,j] = B[k,j] + (t*B[k,i] >> prec)
+        # Until a relation is found, the error typically decreases
+        # slowly (e.g. a factor 1-10) with each step TODO: we could
+        # compare err from two successive iterations. If there is a
+        # large drop (several orders of magnitude), that indicates a
+        # "high quality" relation was detected. Reporting this to
+        # the user somehow might be useful.
+        best_err = maxcoeff<<prec
+        for i in xrange(1, n+1):
+            err = abs(y[i])
+            # Maybe we are done?
+            if err < tol:
+                # We are done if the coefficients are acceptable
+                vec = [int(round_fixed(B[j,i], prec) >> prec) for j in \
+                range(1,n+1)]
+                if max(abs(v) for v in vec) < maxcoeff:
+                    if verbose:
+                        print("FOUND relation at iter %i/%i, error: %s" % \
+                            (REP, maxsteps, ctx.nstr(err / ctx.mpf(2)**prec, 1)))
+                    return vec
+            best_err = min(err, best_err)
+        # Calculate a lower bound for the norm. We could do this
+        # more exactly (using the Euclidean norm) but there is probably
+        # no practical benefit.
+        recnorm = max(abs(h) for h in H.values())
+        if recnorm:
+            norm = ((1 << (2*prec)) // recnorm) >> prec
+            norm //= 100
+        else:
+            norm = ctx.inf
+        if verbose:
+            print("%i/%i:  Error: %8s   Norm: %s" % \
+                (REP, maxsteps, ctx.nstr(best_err / ctx.mpf(2)**prec, 1), norm))
+        if norm >= maxcoeff:
+            break
+    if verbose:
+        print("CANCELLING after step %i/%i." % (REP, maxsteps))
+        print("Could not find an integer relation. Norm bound: %s" % norm)
+    return None
+
+def findpoly(ctx, x, n=1, **kwargs):
+    r"""
+    ``findpoly(x, n)`` returns the coefficients of an integer
+    polynomial `P` of degree at most `n` such that `P(x) \approx 0`.
+    If no polynomial having `x` as a root can be found,
+    :func:`~mpmath.findpoly` returns ``None``.
+
+    :func:`~mpmath.findpoly` works by successively calling :func:`~mpmath.pslq` with
+    the vectors `[1, x]`, `[1, x, x^2]`, `[1, x, x^2, x^3]`, ...,
+    `[1, x, x^2, .., x^n]` as input. Keyword arguments given to
+    :func:`~mpmath.findpoly` are forwarded verbatim to :func:`~mpmath.pslq`. In
+    particular, you can specify a tolerance for `P(x)` with ``tol``
+    and a maximum permitted coefficient size with ``maxcoeff``.
+
+    For large values of `n`, it is recommended to run :func:`~mpmath.findpoly`
+    at high precision; preferably 50 digits or more.
+
+    **Examples**
+
+    By default (degree `n = 1`), :func:`~mpmath.findpoly` simply finds a linear
+    polynomial with a rational root::
+
+        >>> from mpmath import *
+        >>> mp.dps = 15; mp.pretty = True
+        >>> findpoly(0.7)
+        [-10, 7]
+
+    The generated coefficient list is valid input to ``polyval`` and
+    ``polyroots``::
+
+        >>> nprint(polyval(findpoly(phi, 2), phi), 1)
+        -2.0e-16
+        >>> for r in polyroots(findpoly(phi, 2)):
+        ...     print(r)
+        ...
+        -0.618033988749895
+        1.61803398874989
+
+    Numbers of the form `m + n \sqrt p` for integers `(m, n, p)` are
+    solutions to quadratic equations. As we find here, `1+\sqrt 2`
+    is a root of the polynomial `x^2 - 2x - 1`::
+
+        >>> findpoly(1+sqrt(2), 2)
+        [1, -2, -1]
+        >>> findroot(lambda x: x**2 - 2*x - 1, 1)
+        2.4142135623731
+
+    Despite only containing square roots, the following number results
+    in a polynomial of degree 4::
+
+        >>> findpoly(sqrt(2)+sqrt(3), 4)
+        [1, 0, -10, 0, 1]
+
+    In fact, `x^4 - 10x^2 + 1` is the *minimal polynomial* of
+    `r = \sqrt 2 + \sqrt 3`, meaning that a rational polynomial of
+    lower degree having `r` as a root does not exist. Given sufficient
+    precision, :func:`~mpmath.findpoly` will usually find the correct
+    minimal polynomial of a given algebraic number.
+
+    **Non-algebraic numbers**
+
+    If :func:`~mpmath.findpoly` fails to find a polynomial with given
+    coefficient size and tolerance constraints, that means no such
+    polynomial exists.
+
+    We can verify that `\pi` is not an algebraic number of degree 3 with
+    coefficients less than 1000::
+
+        >>> mp.dps = 15
+        >>> findpoly(pi, 3)
+        >>>
+
+    It is always possible to find an algebraic approximation of a number
+    using one (or several) of the following methods:
+
+        1. Increasing the permitted degree
+        2. Allowing larger coefficients
+        3. Reducing the tolerance
+
+    One example of each method is shown below::
+
+        >>> mp.dps = 15
+        >>> findpoly(pi, 4)
+        [95, -545, 863, -183, -298]
+        >>> findpoly(pi, 3, maxcoeff=10000)
+        [836, -1734, -2658, -457]
+        >>> findpoly(pi, 3, tol=1e-7)
+        [-4, 22, -29, -2]
+
+    It is unknown whether Euler's constant is transcendental (or even
+    irrational). We can use :func:`~mpmath.findpoly` to check that if is
+    an algebraic number, its minimal polynomial must have degree
+    at least 7 and a coefficient of magnitude at least 1000000::
+
+        >>> mp.dps = 200
+        >>> findpoly(euler, 6, maxcoeff=10**6, tol=1e-100, maxsteps=1000)
+        >>>
+
+    Note that the high precision and strict tolerance is necessary
+    for such high-degree runs, since otherwise unwanted low-accuracy
+    approximations will be detected. It may also be necessary to set
+    maxsteps high to prevent a premature exit (before the coefficient
+    bound has been reached). Running with ``verbose=True`` to get an
+    idea what is happening can be useful.
+    """
+    x = ctx.mpf(x)
+    if n < 1:
+        raise ValueError("n cannot be less than 1")
+    if x == 0:
+        return [1, 0]
+    xs = [ctx.mpf(1)]
+    for i in range(1,n+1):
+        xs.append(x**i)
+        a = ctx.pslq(xs, **kwargs)
+        if a is not None:
+            return a[::-1]
+
+def fracgcd(p, q):
+    x, y = p, q
+    while y:
+        x, y = y, x % y
+    if x != 1:
+        p //= x
+        q //= x
+    if q == 1:
+        return p
+    return p, q
+
+def pslqstring(r, constants):
+    q = r[0]
+    r = r[1:]
+    s = []
+    for i in range(len(r)):
+        p = r[i]
+        if p:
+            z = fracgcd(-p,q)
+            cs = constants[i][1]
+            if cs == '1':
+                cs = ''
+            else:
+                cs = '*' + cs
+            if isinstance(z, int_types):
+                if z > 0: term = str(z) + cs
+                else:     term = ("(%s)" % z) + cs
+            else:
+                term = ("(%s/%s)" % z) + cs
+            s.append(term)
+    s = ' + '.join(s)
+    if '+' in s or '*' in s:
+        s = '(' + s + ')'
+    return s or '0'
+
+def prodstring(r, constants):
+    q = r[0]
+    r = r[1:]
+    num = []
+    den = []
+    for i in range(len(r)):
+        p = r[i]
+        if p:
+            z = fracgcd(-p,q)
+            cs = constants[i][1]
+            if isinstance(z, int_types):
+                if abs(z) == 1: t = cs
+                else:           t = '%s**%s' % (cs, abs(z))
+                ([num,den][z<0]).append(t)
+            else:
+                t = '%s**(%s/%s)' % (cs, abs(z[0]), z[1])
+                ([num,den][z[0]<0]).append(t)
+    num = '*'.join(num)
+    den = '*'.join(den)
+    if num and den: return "(%s)/(%s)" % (num, den)
+    if num: return num
+    if den: return "1/(%s)" % den
+
+def quadraticstring(ctx,t,a,b,c):
+    if c < 0:
+        a,b,c = -a,-b,-c
+    u1 = (-b+ctx.sqrt(b**2-4*a*c))/(2*c)
+    u2 = (-b-ctx.sqrt(b**2-4*a*c))/(2*c)
+    if abs(u1-t) < abs(u2-t):
+        if b:  s = '((%s+sqrt(%s))/%s)' % (-b,b**2-4*a*c,2*c)
+        else:  s = '(sqrt(%s)/%s)' % (-4*a*c,2*c)
+    else:
+        if b:  s = '((%s-sqrt(%s))/%s)' % (-b,b**2-4*a*c,2*c)
+        else:  s = '(-sqrt(%s)/%s)' % (-4*a*c,2*c)
+    return s
+
+# Transformation y = f(x,c), with inverse function x = f(y,c)
+# The third entry indicates whether the transformation is
+# redundant when c = 1
+transforms = [
+  (lambda ctx,x,c: x*c, '$y/$c', 0),
+  (lambda ctx,x,c: x/c, '$c*$y', 1),
+  (lambda ctx,x,c: c/x, '$c/$y', 0),
+  (lambda ctx,x,c: (x*c)**2, 'sqrt($y)/$c', 0),
+  (lambda ctx,x,c: (x/c)**2, '$c*sqrt($y)', 1),
+  (lambda ctx,x,c: (c/x)**2, '$c/sqrt($y)', 0),
+  (lambda ctx,x,c: c*x**2, 'sqrt($y)/sqrt($c)', 1),
+  (lambda ctx,x,c: x**2/c, 'sqrt($c)*sqrt($y)', 1),
+  (lambda ctx,x,c: c/x**2, 'sqrt($c)/sqrt($y)', 1),
+  (lambda ctx,x,c: ctx.sqrt(x*c), '$y**2/$c', 0),
+  (lambda ctx,x,c: ctx.sqrt(x/c), '$c*$y**2', 1),
+  (lambda ctx,x,c: ctx.sqrt(c/x), '$c/$y**2', 0),
+  (lambda ctx,x,c: c*ctx.sqrt(x), '$y**2/$c**2', 1),
+  (lambda ctx,x,c: ctx.sqrt(x)/c, '$c**2*$y**2', 1),
+  (lambda ctx,x,c: c/ctx.sqrt(x), '$c**2/$y**2', 1),
+  (lambda ctx,x,c: ctx.exp(x*c), 'log($y)/$c', 0),
+  (lambda ctx,x,c: ctx.exp(x/c), '$c*log($y)', 1),
+  (lambda ctx,x,c: ctx.exp(c/x), '$c/log($y)', 0),
+  (lambda ctx,x,c: c*ctx.exp(x), 'log($y/$c)', 1),
+  (lambda ctx,x,c: ctx.exp(x)/c, 'log($c*$y)', 1),
+  (lambda ctx,x,c: c/ctx.exp(x), 'log($c/$y)', 0),
+  (lambda ctx,x,c: ctx.ln(x*c), 'exp($y)/$c', 0),
+  (lambda ctx,x,c: ctx.ln(x/c), '$c*exp($y)', 1),
+  (lambda ctx,x,c: ctx.ln(c/x), '$c/exp($y)', 0),
+  (lambda ctx,x,c: c*ctx.ln(x), 'exp($y/$c)', 1),
+  (lambda ctx,x,c: ctx.ln(x)/c, 'exp($c*$y)', 1),
+  (lambda ctx,x,c: c/ctx.ln(x), 'exp($c/$y)', 0),
+]
+
+def identify(ctx, x, constants=[], tol=None, maxcoeff=1000, full=False,
+    verbose=False):
+    r"""
+    Given a real number `x`, ``identify(x)`` attempts to find an exact
+    formula for `x`. This formula is returned as a string. If no match
+    is found, ``None`` is returned. With ``full=True``, a list of
+    matching formulas is returned.
+
+    As a simple example, :func:`~mpmath.identify` will find an algebraic
+    formula for the golden ratio::
+
+        >>> from mpmath import *
+        >>> mp.dps = 15; mp.pretty = True
+        >>> identify(phi)
+        '((1+sqrt(5))/2)'
+
+    :func:`~mpmath.identify` can identify simple algebraic numbers and simple
+    combinations of given base constants, as well as certain basic
+    transformations thereof. More specifically, :func:`~mpmath.identify`
+    looks for the following:
+
+        1. Fractions
+        2. Quadratic algebraic numbers
+        3. Rational linear combinations of the base constants
+        4. Any of the above after first transforming `x` into `f(x)` where
+           `f(x)` is `1/x`, `\sqrt x`, `x^2`, `\log x` or `\exp x`, either
+           directly or with `x` or `f(x)` multiplied or divided by one of
+           the base constants
+        5. Products of fractional powers of the base constants and
+           small integers
+
+    Base constants can be given as a list of strings representing mpmath
+    expressions (:func:`~mpmath.identify` will ``eval`` the strings to numerical
+    values and use the original strings for the output), or as a dict of
+    formula:value pairs.
+
+    In order not to produce spurious results, :func:`~mpmath.identify` should
+    be used with high precision; preferably 50 digits or more.
+
+    **Examples**
+
+    Simple identifications can be performed safely at standard
+    precision. Here the default recognition of rational, algebraic,
+    and exp/log of algebraic numbers is demonstrated::
+
+        >>> mp.dps = 15
+        >>> identify(0.22222222222222222)
+        '(2/9)'
+        >>> identify(1.9662210973805663)
+        'sqrt(((24+sqrt(48))/8))'
+        >>> identify(4.1132503787829275)
+        'exp((sqrt(8)/2))'
+        >>> identify(0.881373587019543)
+        'log(((2+sqrt(8))/2))'
+
+    By default, :func:`~mpmath.identify` does not recognize `\pi`. At standard
+    precision it finds a not too useful approximation. At slightly
+    increased precision, this approximation is no longer accurate
+    enough and :func:`~mpmath.identify` more correctly returns ``None``::
+
+        >>> identify(pi)
+        '(2**(176/117)*3**(20/117)*5**(35/39))/(7**(92/117))'
+        >>> mp.dps = 30
+        >>> identify(pi)
+        >>>
+
+    Numbers such as `\pi`, and simple combinations of user-defined
+    constants, can be identified if they are provided explicitly::
+
+        >>> identify(3*pi-2*e, ['pi', 'e'])
+        '(3*pi + (-2)*e)'
+
+    Here is an example using a dict of constants. Note that the
+    constants need not be "atomic"; :func:`~mpmath.identify` can just
+    as well express the given number in terms of expressions
+    given by formulas::
+
+        >>> identify(pi+e, {'a':pi+2, 'b':2*e})
+        '((-2) + 1*a + (1/2)*b)'
+
+    Next, we attempt some identifications with a set of base constants.
+    It is necessary to increase the precision a bit.
+
+        >>> mp.dps = 50
+        >>> base = ['sqrt(2)','pi','log(2)']
+        >>> identify(0.25, base)
+        '(1/4)'
+        >>> identify(3*pi + 2*sqrt(2) + 5*log(2)/7, base)
+        '(2*sqrt(2) + 3*pi + (5/7)*log(2))'
+        >>> identify(exp(pi+2), base)
+        'exp((2 + 1*pi))'
+        >>> identify(1/(3+sqrt(2)), base)
+        '((3/7) + (-1/7)*sqrt(2))'
+        >>> identify(sqrt(2)/(3*pi+4), base)
+        'sqrt(2)/(4 + 3*pi)'
+        >>> identify(5**(mpf(1)/3)*pi*log(2)**2, base)
+        '5**(1/3)*pi*log(2)**2'
+
+    An example of an erroneous solution being found when too low
+    precision is used::
+
+        >>> mp.dps = 15
+        >>> identify(1/(3*pi-4*e+sqrt(8)), ['pi', 'e', 'sqrt(2)'])
+        '((11/25) + (-158/75)*pi + (76/75)*e + (44/15)*sqrt(2))'
+        >>> mp.dps = 50
+        >>> identify(1/(3*pi-4*e+sqrt(8)), ['pi', 'e', 'sqrt(2)'])
+        '1/(3*pi + (-4)*e + 2*sqrt(2))'
+
+    **Finding approximate solutions**
+
+    The tolerance ``tol`` defaults to 3/4 of the working precision.
+    Lowering the tolerance is useful for finding approximate matches.
+    We can for example try to generate approximations for pi::
+
+        >>> mp.dps = 15
+        >>> identify(pi, tol=1e-2)
+        '(22/7)'
+        >>> identify(pi, tol=1e-3)
+        '(355/113)'
+        >>> identify(pi, tol=1e-10)
+        '(5**(339/269))/(2**(64/269)*3**(13/269)*7**(92/269))'
+
+    With ``full=True``, and by supplying a few base constants,
+    ``identify`` can generate almost endless lists of approximations
+    for any number (the output below has been truncated to show only
+    the first few)::
+
+        >>> for p in identify(pi, ['e', 'catalan'], tol=1e-5, full=True):
+        ...     print(p)
+        ...  # doctest: +ELLIPSIS
+        e/log((6 + (-4/3)*e))
+        (3**3*5*e*catalan**2)/(2*7**2)
+        sqrt(((-13) + 1*e + 22*catalan))
+        log(((-6) + 24*e + 4*catalan)/e)
+        exp(catalan*((-1/5) + (8/15)*e))
+        catalan*(6 + (-6)*e + 15*catalan)
+        sqrt((5 + 26*e + (-3)*catalan))/e
+        e*sqrt(((-27) + 2*e + 25*catalan))
+        log(((-1) + (-11)*e + 59*catalan))
+        ((3/20) + (21/20)*e + (3/20)*catalan)
+        ...
+
+    The numerical values are roughly as close to `\pi` as permitted by the
+    specified tolerance:
+
+        >>> e/log(6-4*e/3)
+        3.14157719846001
+        >>> 135*e*catalan**2/98
+        3.14166950419369
+        >>> sqrt(e-13+22*catalan)
+        3.14158000062992
+        >>> log(24*e-6+4*catalan)-1
+        3.14158791577159
+
+    **Symbolic processing**
+
+    The output formula can be evaluated as a Python expression.
+    Note however that if fractions (like '2/3') are present in
+    the formula, Python's :func:`~mpmath.eval()` may erroneously perform
+    integer division. Note also that the output is not necessarily
+    in the algebraically simplest form::
+
+        >>> identify(sqrt(2))
+        '(sqrt(8)/2)'
+
+    As a solution to both problems, consider using SymPy's
+    :func:`~mpmath.sympify` to convert the formula into a symbolic expression.
+    SymPy can be used to pretty-print or further simplify the formula
+    symbolically::
+
+        >>> from sympy import sympify # doctest: +SKIP
+        >>> sympify(identify(sqrt(2))) # doctest: +SKIP
+        2**(1/2)
+
+    Sometimes :func:`~mpmath.identify` can simplify an expression further than
+    a symbolic algorithm::
+
+        >>> from sympy import simplify # doctest: +SKIP
+        >>> x = sympify('-1/(-3/2+(1/2)*5**(1/2))*(3/2-1/2*5**(1/2))**(1/2)') # doctest: +SKIP
+        >>> x # doctest: +SKIP
+        (3/2 - 5**(1/2)/2)**(-1/2)
+        >>> x = simplify(x) # doctest: +SKIP
+        >>> x # doctest: +SKIP
+        2/(6 - 2*5**(1/2))**(1/2)
+        >>> mp.dps = 30 # doctest: +SKIP
+        >>> x = sympify(identify(x.evalf(30))) # doctest: +SKIP
+        >>> x # doctest: +SKIP
+        1/2 + 5**(1/2)/2
+
+    (In fact, this functionality is available directly in SymPy as the
+    function :func:`~mpmath.nsimplify`, which is essentially a wrapper for
+    :func:`~mpmath.identify`.)
+
+    **Miscellaneous issues and limitations**
+
+    The input `x` must be a real number. All base constants must be
+    positive real numbers and must not be rationals or rational linear
+    combinations of each other.
+
+    The worst-case computation time grows quickly with the number of
+    base constants. Already with 3 or 4 base constants,
+    :func:`~mpmath.identify` may require several seconds to finish. To search
+    for relations among a large number of constants, you should
+    consider using :func:`~mpmath.pslq` directly.
+
+    The extended transformations are applied to x, not the constants
+    separately. As a result, ``identify`` will for example be able to
+    recognize ``exp(2*pi+3)`` with ``pi`` given as a base constant, but
+    not ``2*exp(pi)+3``. It will be able to recognize the latter if
+    ``exp(pi)`` is given explicitly as a base constant.
+
+    """
+
+    solutions = []
+
+    def addsolution(s):
+        if verbose: print("Found: ", s)
+        solutions.append(s)
+
+    x = ctx.mpf(x)
+
+    # Further along, x will be assumed positive
+    if x == 0:
+        if full: return ['0']
+        else:    return '0'
+    if x < 0:
+        sol = ctx.identify(-x, constants, tol, maxcoeff, full, verbose)
+        if sol is None:
+            return sol
+        if full:
+            return ["-(%s)"%s for s in sol]
+        else:
+            return "-(%s)" % sol
+
+    if tol:
+        tol = ctx.mpf(tol)
+    else:
+        tol = ctx.eps**0.7
+    M = maxcoeff
+
+    if constants:
+        if isinstance(constants, dict):
+            constants = [(ctx.mpf(v), name) for (name, v) in sorted(constants.items())]
+        else:
+            namespace = dict((name, getattr(ctx,name)) for name in dir(ctx))
+            constants = [(eval(p, namespace), p) for p in constants]
+    else:
+        constants = []
+
+    # We always want to find at least rational terms
+    if 1 not in [value for (name, value) in constants]:
+        constants = [(ctx.mpf(1), '1')] + constants
+
+    # PSLQ with simple algebraic and functional transformations
+    for ft, ftn, red in transforms:
+        for c, cn in constants:
+            if red and cn == '1':
+                continue
+            t = ft(ctx,x,c)
+            # Prevent exponential transforms from wreaking havoc
+            if abs(t) > M**2 or abs(t) < tol:
+                continue
+            # Linear combination of base constants
+            r = ctx.pslq([t] + [a[0] for a in constants], tol, M)
+            s = None
+            if r is not None and max(abs(uw) for uw in r) <= M and r[0]:
+                s = pslqstring(r, constants)
+            # Quadratic algebraic numbers
+            else:
+                q = ctx.pslq([ctx.one, t, t**2], tol, M)
+                if q is not None and len(q) == 3 and q[2]:
+                    aa, bb, cc = q
+                    if max(abs(aa),abs(bb),abs(cc)) <= M:
+                        s = quadraticstring(ctx,t,aa,bb,cc)
+            if s:
+                if cn == '1' and ('/$c' in ftn):
+                    s = ftn.replace('$y', s).replace('/$c', '')
+                else:
+                    s = ftn.replace('$y', s).replace('$c', cn)
+                addsolution(s)
+                if not full: return solutions[0]
+
+            if verbose:
+                print(".")
+
+    # Check for a direct multiplicative formula
+    if x != 1:
+        # Allow fractional powers of fractions
+        ilogs = [2,3,5,7]
+        # Watch out for existing fractional powers of fractions
+        logs = []
+        for a, s in constants:
+            if not sum(bool(ctx.findpoly(ctx.ln(a)/ctx.ln(i),1)) for i in ilogs):
+                logs.append((ctx.ln(a), s))
+        logs = [(ctx.ln(i),str(i)) for i in ilogs] + logs
+        r = ctx.pslq([ctx.ln(x)] + [a[0] for a in logs], tol, M)
+        if r is not None and max(abs(uw) for uw in r) <= M and r[0]:
+            addsolution(prodstring(r, logs))
+            if not full: return solutions[0]
+
+    if full:
+        return sorted(solutions, key=len)
+    else:
+        return None
+
+IdentificationMethods.pslq = pslq
+IdentificationMethods.findpoly = findpoly
+IdentificationMethods.identify = identify
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/rational.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/rational.py
new file mode 100644
index 0000000000000000000000000000000000000000..58745205319ac3548ad5feb49371d2d154b2d3c8
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/rational.py
@@ -0,0 +1,240 @@
+import operator
+import sys
+from .libmp import int_types, mpf_hash, bitcount, from_man_exp, HASH_MODULUS
+
+new = object.__new__
+
+def create_reduced(p, q, _cache={}):
+    key = p, q
+    if key in _cache:
+        return _cache[key]
+    x, y = p, q
+    while y:
+        x, y = y, x % y
+    if x != 1:
+        p //= x
+        q //= x
+    v = new(mpq)
+    v._mpq_ = p, q
+    # Speedup integers, half-integers and other small fractions
+    if q <= 4 and abs(key[0]) < 100:
+        _cache[key] = v
+    return v
+
+class mpq(object):
+    """
+    Exact rational type, currently only intended for internal use.
+    """
+
+    __slots__ = ["_mpq_"]
+
+    def __new__(cls, p, q=1):
+        if type(p) is tuple:
+            p, q = p
+        elif hasattr(p, '_mpq_'):
+            p, q = p._mpq_
+        return create_reduced(p, q)
+
+    def __repr__(s):
+        return "mpq(%s,%s)" % s._mpq_
+
+    def __str__(s):
+        return "(%s/%s)" % s._mpq_
+
+    def __int__(s):
+        a, b = s._mpq_
+        return a // b
+
+    def __nonzero__(s):
+        return bool(s._mpq_[0])
+
+    __bool__ = __nonzero__
+
+    def __hash__(s):
+        a, b = s._mpq_
+        if sys.version_info >= (3, 2):
+            inverse = pow(b, HASH_MODULUS-2, HASH_MODULUS)
+            if not inverse:
+                h = sys.hash_info.inf
+            else:
+                h = (abs(a) * inverse) % HASH_MODULUS
+            if a < 0: h = -h
+            if h == -1: h = -2
+            return h
+        else:
+            if b == 1:
+                return hash(a)
+            # Power of two: mpf compatible hash
+            if not (b & (b-1)):
+                return mpf_hash(from_man_exp(a, 1-bitcount(b)))
+            return hash((a,b))
+
+    def __eq__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            return s._mpq_ == t._mpq_
+        if ttype in int_types:
+            a, b = s._mpq_
+            if b != 1:
+                return False
+            return a == t
+        return NotImplemented
+
+    def __ne__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            return s._mpq_ != t._mpq_
+        if ttype in int_types:
+            a, b = s._mpq_
+            if b != 1:
+                return True
+            return a != t
+        return NotImplemented
+
+    def _cmp(s, t, op):
+        ttype = type(t)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return op(a, t*b)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return op(a*d, b*c)
+        return NotImplementedError
+
+    def __lt__(s, t): return s._cmp(t, operator.lt)
+    def __le__(s, t): return s._cmp(t, operator.le)
+    def __gt__(s, t): return s._cmp(t, operator.gt)
+    def __ge__(s, t): return s._cmp(t, operator.ge)
+
+    def __abs__(s):
+        a, b = s._mpq_
+        if a >= 0:
+            return s
+        v = new(mpq)
+        v._mpq_ = -a, b
+        return v
+
+    def __neg__(s):
+        a, b = s._mpq_
+        v = new(mpq)
+        v._mpq_ = -a, b
+        return v
+
+    def __pos__(s):
+        return s
+
+    def __add__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*d+b*c, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            v = new(mpq)
+            v._mpq_ = a+b*t, b
+            return v
+        return NotImplemented
+
+    __radd__ = __add__
+
+    def __sub__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*d-b*c, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            v = new(mpq)
+            v._mpq_ = a-b*t, b
+            return v
+        return NotImplemented
+
+    def __rsub__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(b*c-a*d, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            v = new(mpq)
+            v._mpq_ = b*t-a, b
+            return v
+        return NotImplemented
+
+    def __mul__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*c, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return create_reduced(a*t, b)
+        return NotImplemented
+
+    __rmul__ = __mul__
+
+    def __div__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*d, b*c)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return create_reduced(a, b*t)
+        return NotImplemented
+
+    def __rdiv__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(b*c, a*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return create_reduced(b*t, a)
+        return NotImplemented
+
+    def __pow__(s, t):
+        ttype = type(t)
+        if ttype in int_types:
+            a, b = s._mpq_
+            if t:
+                if t < 0:
+                    a, b, t = b, a, -t
+                v = new(mpq)
+                v._mpq_ = a**t, b**t
+                return v
+            raise ZeroDivisionError
+        return NotImplemented
+
+
+mpq_1 = mpq((1,1))
+mpq_0 = mpq((0,1))
+mpq_1_2 = mpq((1,2))
+mpq_3_2 = mpq((3,2))
+mpq_1_4 = mpq((1,4))
+mpq_1_16 = mpq((1,16))
+mpq_3_16 = mpq((3,16))
+mpq_5_2 = mpq((5,2))
+mpq_3_4 = mpq((3,4))
+mpq_7_4 = mpq((7,4))
+mpq_5_4 = mpq((5,4))
+
+
+# Register with "numbers" ABC
+#     We do not subclass, hence we do not use the @abstractmethod checks. While
+#     this is less invasive it may turn out that we do not actually support
+#     parts of the expected interfaces.  See
+#     http://docs.python.org/2/library/numbers.html for list of abstract
+#     methods.
+try:
+    import numbers
+    numbers.Rational.register(mpq)
+except ImportError:
+    pass
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/usertools.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/usertools.py
new file mode 100644
index 0000000000000000000000000000000000000000..8028a4c46f1c635a6857f1f2de48ac6675d3c6d3
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/usertools.py
@@ -0,0 +1,93 @@
+
+def monitor(f, input='print', output='print'):
+    """
+    Returns a wrapped copy of *f* that monitors evaluation by calling
+    *input* with every input (*args*, *kwargs*) passed to *f* and
+    *output* with every value returned from *f*. The default action
+    (specify using the special string value ``'print'``) is to print
+    inputs and outputs to stdout, along with the total evaluation
+    count::
+
+        >>> from mpmath import *
+        >>> mp.dps = 5; mp.pretty = False
+        >>> diff(monitor(exp), 1)   # diff will eval f(x-h) and f(x+h)
+        in  0 (mpf('0.99999999906867742538452148'),) {}
+        out 0 mpf('2.7182818259274480055282064')
+        in  1 (mpf('1.0000000009313225746154785'),) {}
+        out 1 mpf('2.7182818309906424675501024')
+        mpf('2.7182808')
+
+    To disable either the input or the output handler, you may
+    pass *None* as argument.
+
+    Custom input and output handlers may be used e.g. to store
+    results for later analysis::
+
+        >>> mp.dps = 15
+        >>> input = []
+        >>> output = []
+        >>> findroot(monitor(sin, input.append, output.append), 3.0)
+        mpf('3.1415926535897932')
+        >>> len(input)  # Count number of evaluations
+        9
+        >>> print(input[3]); print(output[3])
+        ((mpf('3.1415076583334066'),), {})
+        8.49952562843408e-5
+        >>> print(input[4]); print(output[4])
+        ((mpf('3.1415928201669122'),), {})
+        -1.66577118985331e-7
+
+    """
+    if not input:
+        input = lambda v: None
+    elif input == 'print':
+        incount = [0]
+        def input(value):
+            args, kwargs = value
+            print("in  %s %r %r" % (incount[0], args, kwargs))
+            incount[0] += 1
+    if not output:
+        output = lambda v: None
+    elif output == 'print':
+        outcount = [0]
+        def output(value):
+            print("out %s %r" % (outcount[0], value))
+            outcount[0] += 1
+    def f_monitored(*args, **kwargs):
+        input((args, kwargs))
+        v = f(*args, **kwargs)
+        output(v)
+        return v
+    return f_monitored
+
+def timing(f, *args, **kwargs):
+    """
+    Returns time elapsed for evaluating ``f()``. Optionally arguments
+    may be passed to time the execution of ``f(*args, **kwargs)``.
+
+    If the first call is very quick, ``f`` is called
+    repeatedly and the best time is returned.
+    """
+    once = kwargs.get('once')
+    if 'once' in kwargs:
+        del kwargs['once']
+    if args or kwargs:
+        if len(args) == 1 and not kwargs:
+            arg = args[0]
+            g = lambda: f(arg)
+        else:
+            g = lambda: f(*args, **kwargs)
+    else:
+        g = f
+    from timeit import default_timer as clock
+    t1=clock(); v=g(); t2=clock(); t=t2-t1
+    if t > 0.05 or once:
+        return t
+    for i in range(3):
+        t1=clock();
+        # Evaluate multiple times because the timer function
+        # has a significant overhead
+        g();g();g();g();g();g();g();g();g();g()
+        t2=clock()
+        t=min(t,(t2-t1)/10)
+    return t
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/visualization.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/visualization.py
new file mode 100644
index 0000000000000000000000000000000000000000..17e12e97bead4f2977b59361a4de7672f0e9b75f
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/mpmath/visualization.py
@@ -0,0 +1,313 @@
+"""
+Plotting (requires matplotlib)
+"""
+
+from colorsys import hsv_to_rgb, hls_to_rgb
+from .libmp import NoConvergence
+from .libmp.backend import xrange
+
+class VisualizationMethods(object):
+    plot_ignore = (ValueError, ArithmeticError, ZeroDivisionError, NoConvergence)
+
+def plot(ctx, f, xlim=[-5,5], ylim=None, points=200, file=None, dpi=None,
+    singularities=[], axes=None):
+    r"""
+    Shows a simple 2D plot of a function `f(x)` or list of functions
+    `[f_0(x), f_1(x), \ldots, f_n(x)]` over a given interval
+    specified by *xlim*. Some examples::
+
+        plot(lambda x: exp(x)*li(x), [1, 4])
+        plot([cos, sin], [-4, 4])
+        plot([fresnels, fresnelc], [-4, 4])
+        plot([sqrt, cbrt], [-4, 4])
+        plot(lambda t: zeta(0.5+t*j), [-20, 20])
+        plot([floor, ceil, abs, sign], [-5, 5])
+
+    Points where the function raises a numerical exception or
+    returns an infinite value are removed from the graph.
+    Singularities can also be excluded explicitly
+    as follows (useful for removing erroneous vertical lines)::
+
+        plot(cot, ylim=[-5, 5])   # bad
+        plot(cot, ylim=[-5, 5], singularities=[-pi, 0, pi])  # good
+
+    For parts where the function assumes complex values, the
+    real part is plotted with dashes and the imaginary part
+    is plotted with dots.
+
+    .. note :: This function requires matplotlib (pylab).
+    """
+    if file:
+        axes = None
+    fig = None
+    if not axes:
+        import pylab
+        fig = pylab.figure()
+        axes = fig.add_subplot(111)
+    if not isinstance(f, (tuple, list)):
+        f = [f]
+    a, b = xlim
+    colors = ['b', 'r', 'g', 'm', 'k']
+    for n, func in enumerate(f):
+        x = ctx.arange(a, b, (b-a)/float(points))
+        segments = []
+        segment = []
+        in_complex = False
+        for i in xrange(len(x)):
+            try:
+                if i != 0:
+                    for sing in singularities:
+                        if x[i-1] <= sing and x[i] >= sing:
+                            raise ValueError
+                v = func(x[i])
+                if ctx.isnan(v) or abs(v) > 1e300:
+                    raise ValueError
+                if hasattr(v, "imag") and v.imag:
+                    re = float(v.real)
+                    im = float(v.imag)
+                    if not in_complex:
+                        in_complex = True
+                        segments.append(segment)
+                        segment = []
+                    segment.append((float(x[i]), re, im))
+                else:
+                    if in_complex:
+                        in_complex = False
+                        segments.append(segment)
+                        segment = []
+                    if hasattr(v, "real"):
+                        v = v.real
+                    segment.append((float(x[i]), v))
+            except ctx.plot_ignore:
+                if segment:
+                    segments.append(segment)
+                segment = []
+        if segment:
+            segments.append(segment)
+        for segment in segments:
+            x = [s[0] for s in segment]
+            y = [s[1] for s in segment]
+            if not x:
+                continue
+            c = colors[n % len(colors)]
+            if len(segment[0]) == 3:
+                z = [s[2] for s in segment]
+                axes.plot(x, y, '--'+c, linewidth=3)
+                axes.plot(x, z, ':'+c, linewidth=3)
+            else:
+                axes.plot(x, y, c, linewidth=3)
+    axes.set_xlim([float(_) for _ in xlim])
+    if ylim:
+        axes.set_ylim([float(_) for _ in ylim])
+    axes.set_xlabel('x')
+    axes.set_ylabel('f(x)')
+    axes.grid(True)
+    if fig:
+        if file:
+            pylab.savefig(file, dpi=dpi)
+        else:
+            pylab.show()
+
+def default_color_function(ctx, z):
+    if ctx.isinf(z):
+        return (1.0, 1.0, 1.0)
+    if ctx.isnan(z):
+        return (0.5, 0.5, 0.5)
+    pi = 3.1415926535898
+    a = (float(ctx.arg(z)) + ctx.pi) / (2*ctx.pi)
+    a = (a + 0.5) % 1.0
+    b = 1.0 - float(1/(1.0+abs(z)**0.3))
+    return hls_to_rgb(a, b, 0.8)
+
+blue_orange_colors = [
+  (-1.0,  (0.0, 0.0, 0.0)),
+  (-0.95, (0.1, 0.2, 0.5)),   # dark blue
+  (-0.5,  (0.0, 0.5, 1.0)),   # blueish
+  (-0.05, (0.4, 0.8, 0.8)),   # cyanish
+  ( 0.0,  (1.0, 1.0, 1.0)),
+  ( 0.05, (1.0, 0.9, 0.3)),   # yellowish
+  ( 0.5,  (0.9, 0.5, 0.0)),   # orangeish
+  ( 0.95, (0.7, 0.1, 0.0)),   # redish
+  ( 1.0,  (0.0, 0.0, 0.0)),
+  ( 2.0,  (0.0, 0.0, 0.0)),
+]
+
+def phase_color_function(ctx, z):
+    if ctx.isinf(z):
+        return (1.0, 1.0, 1.0)
+    if ctx.isnan(z):
+        return (0.5, 0.5, 0.5)
+    pi = 3.1415926535898
+    w = float(ctx.arg(z)) / pi
+    w = max(min(w, 1.0), -1.0)
+    for i in range(1,len(blue_orange_colors)):
+        if blue_orange_colors[i][0] > w:
+            a, (ra, ga, ba) = blue_orange_colors[i-1]
+            b, (rb, gb, bb) = blue_orange_colors[i]
+            s = (w-a) / (b-a)
+            return ra+(rb-ra)*s, ga+(gb-ga)*s, ba+(bb-ba)*s
+
+def cplot(ctx, f, re=[-5,5], im=[-5,5], points=2000, color=None,
+    verbose=False, file=None, dpi=None, axes=None):
+    """
+    Plots the given complex-valued function *f* over a rectangular part
+    of the complex plane specified by the pairs of intervals *re* and *im*.
+    For example::
+
+        cplot(lambda z: z, [-2, 2], [-10, 10])
+        cplot(exp)
+        cplot(zeta, [0, 1], [0, 50])
+
+    By default, the complex argument (phase) is shown as color (hue) and
+    the magnitude is show as brightness. You can also supply a
+    custom color function (*color*). This function should take a
+    complex number as input and return an RGB 3-tuple containing
+    floats in the range 0.0-1.0.
+
+    Alternatively, you can select a builtin color function by passing
+    a string as *color*:
+
+      * "default" - default color scheme
+      * "phase" - a color scheme that only renders the phase of the function,
+         with white for positive reals, black for negative reals, gold in the
+         upper half plane, and blue in the lower half plane.
+
+    To obtain a sharp image, the number of points may need to be
+    increased to 100,000 or thereabout. Since evaluating the
+    function that many times is likely to be slow, the 'verbose'
+    option is useful to display progress.
+
+    .. note :: This function requires matplotlib (pylab).
+    """
+    if color is None or color == "default":
+        color = ctx.default_color_function
+    if color == "phase":
+        color = ctx.phase_color_function
+    import pylab
+    if file:
+        axes = None
+    fig = None
+    if not axes:
+        fig = pylab.figure()
+        axes = fig.add_subplot(111)
+    rea, reb = re
+    ima, imb = im
+    dre = reb - rea
+    dim = imb - ima
+    M = int(ctx.sqrt(points*dre/dim)+1)
+    N = int(ctx.sqrt(points*dim/dre)+1)
+    x = pylab.linspace(rea, reb, M)
+    y = pylab.linspace(ima, imb, N)
+    # Note: we have to be careful to get the right rotation.
+    # Test with these plots:
+    #   cplot(lambda z: z if z.real < 0 else 0)
+    #   cplot(lambda z: z if z.imag < 0 else 0)
+    w = pylab.zeros((N, M, 3))
+    for n in xrange(N):
+        for m in xrange(M):
+            z = ctx.mpc(x[m], y[n])
+            try:
+                v = color(f(z))
+            except ctx.plot_ignore:
+                v = (0.5, 0.5, 0.5)
+            w[n,m] = v
+        if verbose:
+            print(str(n) + ' of ' + str(N))
+    rea, reb, ima, imb = [float(_) for _ in [rea, reb, ima, imb]]
+    axes.imshow(w, extent=(rea, reb, ima, imb), origin='lower')
+    axes.set_xlabel('Re(z)')
+    axes.set_ylabel('Im(z)')
+    if fig:
+        if file:
+            pylab.savefig(file, dpi=dpi)
+        else:
+            pylab.show()
+
+def splot(ctx, f, u=[-5,5], v=[-5,5], points=100, keep_aspect=True, \
+          wireframe=False, file=None, dpi=None, axes=None):
+    """
+    Plots the surface defined by `f`.
+
+    If `f` returns a single component, then this plots the surface
+    defined by `z = f(x,y)` over the rectangular domain with
+    `x = u` and `y = v`.
+
+    If `f` returns three components, then this plots the parametric
+    surface `x, y, z = f(u,v)` over the pairs of intervals `u` and `v`.
+
+    For example, to plot a simple function::
+
+        >>> from mpmath import *
+        >>> f = lambda x, y: sin(x+y)*cos(y)
+        >>> splot(f, [-pi,pi], [-pi,pi])    # doctest: +SKIP
+
+    Plotting a donut::
+
+        >>> r, R = 1, 2.5
+        >>> f = lambda u, v: [r*cos(u), (R+r*sin(u))*cos(v), (R+r*sin(u))*sin(v)]
+        >>> splot(f, [0, 2*pi], [0, 2*pi])    # doctest: +SKIP
+
+    .. note :: This function requires matplotlib (pylab) 0.98.5.3 or higher.
+    """
+    import pylab
+    import mpl_toolkits.mplot3d as mplot3d
+    if file:
+        axes = None
+    fig = None
+    if not axes:
+        fig = pylab.figure()
+        axes = mplot3d.axes3d.Axes3D(fig)
+    ua, ub = u
+    va, vb = v
+    du = ub - ua
+    dv = vb - va
+    if not isinstance(points, (list, tuple)):
+        points = [points, points]
+    M, N = points
+    u = pylab.linspace(ua, ub, M)
+    v = pylab.linspace(va, vb, N)
+    x, y, z = [pylab.zeros((M, N)) for i in xrange(3)]
+    xab, yab, zab = [[0, 0] for i in xrange(3)]
+    for n in xrange(N):
+        for m in xrange(M):
+            fdata = f(ctx.convert(u[m]), ctx.convert(v[n]))
+            try:
+                x[m,n], y[m,n], z[m,n] = fdata
+            except TypeError:
+                x[m,n], y[m,n], z[m,n] = u[m], v[n], fdata
+            for c, cab in [(x[m,n], xab), (y[m,n], yab), (z[m,n], zab)]:
+                if c < cab[0]:
+                    cab[0] = c
+                if c > cab[1]:
+                    cab[1] = c
+    if wireframe:
+        axes.plot_wireframe(x, y, z, rstride=4, cstride=4)
+    else:
+        axes.plot_surface(x, y, z, rstride=4, cstride=4)
+    axes.set_xlabel('x')
+    axes.set_ylabel('y')
+    axes.set_zlabel('z')
+    if keep_aspect:
+        dx, dy, dz = [cab[1] - cab[0] for cab in [xab, yab, zab]]
+        maxd = max(dx, dy, dz)
+        if dx < maxd:
+            delta = maxd - dx
+            axes.set_xlim3d(xab[0] - delta / 2.0, xab[1] + delta / 2.0)
+        if dy < maxd:
+            delta = maxd - dy
+            axes.set_ylim3d(yab[0] - delta / 2.0, yab[1] + delta / 2.0)
+        if dz < maxd:
+            delta = maxd - dz
+            axes.set_zlim3d(zab[0] - delta / 2.0, zab[1] + delta / 2.0)
+    if fig:
+        if file:
+            pylab.savefig(file, dpi=dpi)
+        else:
+            pylab.show()
+
+
+VisualizationMethods.plot = plot
+VisualizationMethods.default_color_function = default_color_function
+VisualizationMethods.phase_color_function = phase_color_function
+VisualizationMethods.cplot = cplot
+VisualizationMethods.splot = splot
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/locations/__init__.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/locations/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..32382be7fe5f6781047e9774679aa8bcf5bbce8a
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/locations/__init__.py
@@ -0,0 +1,456 @@
+import functools
+import logging
+import os
+import pathlib
+import sys
+import sysconfig
+from typing import Any, Dict, Generator, Optional, Tuple
+
+from pip._internal.models.scheme import SCHEME_KEYS, Scheme
+from pip._internal.utils.compat import WINDOWS
+from pip._internal.utils.deprecation import deprecated
+from pip._internal.utils.virtualenv import running_under_virtualenv
+
+from . import _sysconfig
+from .base import (
+    USER_CACHE_DIR,
+    get_major_minor_version,
+    get_src_prefix,
+    is_osx_framework,
+    site_packages,
+    user_site,
+)
+
+__all__ = [
+    "USER_CACHE_DIR",
+    "get_bin_prefix",
+    "get_bin_user",
+    "get_major_minor_version",
+    "get_platlib",
+    "get_purelib",
+    "get_scheme",
+    "get_src_prefix",
+    "site_packages",
+    "user_site",
+]
+
+
+logger = logging.getLogger(__name__)
+
+
+_PLATLIBDIR: str = getattr(sys, "platlibdir", "lib")
+
+_USE_SYSCONFIG_DEFAULT = sys.version_info >= (3, 10)
+
+
+def _should_use_sysconfig() -> bool:
+    """This function determines the value of _USE_SYSCONFIG.
+
+    By default, pip uses sysconfig on Python 3.10+.
+    But Python distributors can override this decision by setting:
+        sysconfig._PIP_USE_SYSCONFIG = True / False
+    Rationale in https://github.com/pypa/pip/issues/10647
+
+    This is a function for testability, but should be constant during any one
+    run.
+    """
+    return bool(getattr(sysconfig, "_PIP_USE_SYSCONFIG", _USE_SYSCONFIG_DEFAULT))
+
+
+_USE_SYSCONFIG = _should_use_sysconfig()
+
+if not _USE_SYSCONFIG:
+    # Import distutils lazily to avoid deprecation warnings,
+    # but import it soon enough that it is in memory and available during
+    # a pip reinstall.
+    from . import _distutils
+
+# Be noisy about incompatibilities if this platforms "should" be using
+# sysconfig, but is explicitly opting out and using distutils instead.
+if _USE_SYSCONFIG_DEFAULT and not _USE_SYSCONFIG:
+    _MISMATCH_LEVEL = logging.WARNING
+else:
+    _MISMATCH_LEVEL = logging.DEBUG
+
+
+def _looks_like_bpo_44860() -> bool:
+    """The resolution to bpo-44860 will change this incorrect platlib.
+
+    See <https://bugs.python.org/issue44860>.
+    """
+    from distutils.command.install import INSTALL_SCHEMES
+
+    try:
+        unix_user_platlib = INSTALL_SCHEMES["unix_user"]["platlib"]
+    except KeyError:
+        return False
+    return unix_user_platlib == "$usersite"
+
+
+def _looks_like_red_hat_patched_platlib_purelib(scheme: Dict[str, str]) -> bool:
+    platlib = scheme["platlib"]
+    if "/$platlibdir/" in platlib:
+        platlib = platlib.replace("/$platlibdir/", f"/{_PLATLIBDIR}/")
+    if "/lib64/" not in platlib:
+        return False
+    unpatched = platlib.replace("/lib64/", "/lib/")
+    return unpatched.replace("$platbase/", "$base/") == scheme["purelib"]
+
+
+@functools.lru_cache(maxsize=None)
+def _looks_like_red_hat_lib() -> bool:
+    """Red Hat patches platlib in unix_prefix and unix_home, but not purelib.
+
+    This is the only way I can see to tell a Red Hat-patched Python.
+    """
+    from distutils.command.install import INSTALL_SCHEMES
+
+    return all(
+        k in INSTALL_SCHEMES
+        and _looks_like_red_hat_patched_platlib_purelib(INSTALL_SCHEMES[k])
+        for k in ("unix_prefix", "unix_home")
+    )
+
+
+@functools.lru_cache(maxsize=None)
+def _looks_like_debian_scheme() -> bool:
+    """Debian adds two additional schemes."""
+    from distutils.command.install import INSTALL_SCHEMES
+
+    return "deb_system" in INSTALL_SCHEMES and "unix_local" in INSTALL_SCHEMES
+
+
+@functools.lru_cache(maxsize=None)
+def _looks_like_red_hat_scheme() -> bool:
+    """Red Hat patches ``sys.prefix`` and ``sys.exec_prefix``.
+
+    Red Hat's ``00251-change-user-install-location.patch`` changes the install
+    command's ``prefix`` and ``exec_prefix`` to append ``"/local"``. This is
+    (fortunately?) done quite unconditionally, so we create a default command
+    object without any configuration to detect this.
+    """
+    from distutils.command.install import install
+    from distutils.dist import Distribution
+
+    cmd: Any = install(Distribution())
+    cmd.finalize_options()
+    return (
+        cmd.exec_prefix == f"{os.path.normpath(sys.exec_prefix)}/local"
+        and cmd.prefix == f"{os.path.normpath(sys.prefix)}/local"
+    )
+
+
+@functools.lru_cache(maxsize=None)
+def _looks_like_slackware_scheme() -> bool:
+    """Slackware patches sysconfig but fails to patch distutils and site.
+
+    Slackware changes sysconfig's user scheme to use ``"lib64"`` for the lib
+    path, but does not do the same to the site module.
+    """
+    if user_site is None:  # User-site not available.
+        return False
+    try:
+        paths = sysconfig.get_paths(scheme="posix_user", expand=False)
+    except KeyError:  # User-site not available.
+        return False
+    return "/lib64/" in paths["purelib"] and "/lib64/" not in user_site
+
+
+@functools.lru_cache(maxsize=None)
+def _looks_like_msys2_mingw_scheme() -> bool:
+    """MSYS2 patches distutils and sysconfig to use a UNIX-like scheme.
+
+    However, MSYS2 incorrectly patches sysconfig ``nt`` scheme. The fix is
+    likely going to be included in their 3.10 release, so we ignore the warning.
+    See msys2/MINGW-packages#9319.
+
+    MSYS2 MINGW's patch uses lowercase ``"lib"`` instead of the usual uppercase,
+    and is missing the final ``"site-packages"``.
+    """
+    paths = sysconfig.get_paths("nt", expand=False)
+    return all(
+        "Lib" not in p and "lib" in p and not p.endswith("site-packages")
+        for p in (paths[key] for key in ("platlib", "purelib"))
+    )
+
+
+def _fix_abiflags(parts: Tuple[str]) -> Generator[str, None, None]:
+    ldversion = sysconfig.get_config_var("LDVERSION")
+    abiflags = getattr(sys, "abiflags", None)
+
+    # LDVERSION does not end with sys.abiflags. Just return the path unchanged.
+    if not ldversion or not abiflags or not ldversion.endswith(abiflags):
+        yield from parts
+        return
+
+    # Strip sys.abiflags from LDVERSION-based path components.
+    for part in parts:
+        if part.endswith(ldversion):
+            part = part[: (0 - len(abiflags))]
+        yield part
+
+
+@functools.lru_cache(maxsize=None)
+def _warn_mismatched(old: pathlib.Path, new: pathlib.Path, *, key: str) -> None:
+    issue_url = "https://github.com/pypa/pip/issues/10151"
+    message = (
+        "Value for %s does not match. Please report this to <%s>"
+        "\ndistutils: %s"
+        "\nsysconfig: %s"
+    )
+    logger.log(_MISMATCH_LEVEL, message, key, issue_url, old, new)
+
+
+def _warn_if_mismatch(old: pathlib.Path, new: pathlib.Path, *, key: str) -> bool:
+    if old == new:
+        return False
+    _warn_mismatched(old, new, key=key)
+    return True
+
+
+@functools.lru_cache(maxsize=None)
+def _log_context(
+    *,
+    user: bool = False,
+    home: Optional[str] = None,
+    root: Optional[str] = None,
+    prefix: Optional[str] = None,
+) -> None:
+    parts = [
+        "Additional context:",
+        "user = %r",
+        "home = %r",
+        "root = %r",
+        "prefix = %r",
+    ]
+
+    logger.log(_MISMATCH_LEVEL, "\n".join(parts), user, home, root, prefix)
+
+
+def get_scheme(
+    dist_name: str,
+    user: bool = False,
+    home: Optional[str] = None,
+    root: Optional[str] = None,
+    isolated: bool = False,
+    prefix: Optional[str] = None,
+) -> Scheme:
+    new = _sysconfig.get_scheme(
+        dist_name,
+        user=user,
+        home=home,
+        root=root,
+        isolated=isolated,
+        prefix=prefix,
+    )
+    if _USE_SYSCONFIG:
+        return new
+
+    old = _distutils.get_scheme(
+        dist_name,
+        user=user,
+        home=home,
+        root=root,
+        isolated=isolated,
+        prefix=prefix,
+    )
+
+    warning_contexts = []
+    for k in SCHEME_KEYS:
+        old_v = pathlib.Path(getattr(old, k))
+        new_v = pathlib.Path(getattr(new, k))
+
+        if old_v == new_v:
+            continue
+
+        # distutils incorrectly put PyPy packages under ``site-packages/python``
+        # in the ``posix_home`` scheme, but PyPy devs said they expect the
+        # directory name to be ``pypy`` instead. So we treat this as a bug fix
+        # and not warn about it. See bpo-43307 and python/cpython#24628.
+        skip_pypy_special_case = (
+            sys.implementation.name == "pypy"
+            and home is not None
+            and k in ("platlib", "purelib")
+            and old_v.parent == new_v.parent
+            and old_v.name.startswith("python")
+            and new_v.name.startswith("pypy")
+        )
+        if skip_pypy_special_case:
+            continue
+
+        # sysconfig's ``osx_framework_user`` does not include ``pythonX.Y`` in
+        # the ``include`` value, but distutils's ``headers`` does. We'll let
+        # CPython decide whether this is a bug or feature. See bpo-43948.
+        skip_osx_framework_user_special_case = (
+            user
+            and is_osx_framework()
+            and k == "headers"
+            and old_v.parent.parent == new_v.parent
+            and old_v.parent.name.startswith("python")
+        )
+        if skip_osx_framework_user_special_case:
+            continue
+
+        # On Red Hat and derived Linux distributions, distutils is patched to
+        # use "lib64" instead of "lib" for platlib.
+        if k == "platlib" and _looks_like_red_hat_lib():
+            continue
+
+        # On Python 3.9+, sysconfig's posix_user scheme sets platlib against
+        # sys.platlibdir, but distutils's unix_user incorrectly coninutes
+        # using the same $usersite for both platlib and purelib. This creates a
+        # mismatch when sys.platlibdir is not "lib".
+        skip_bpo_44860 = (
+            user
+            and k == "platlib"
+            and not WINDOWS
+            and sys.version_info >= (3, 9)
+            and _PLATLIBDIR != "lib"
+            and _looks_like_bpo_44860()
+        )
+        if skip_bpo_44860:
+            continue
+
+        # Slackware incorrectly patches posix_user to use lib64 instead of lib,
+        # but not usersite to match the location.
+        skip_slackware_user_scheme = (
+            user
+            and k in ("platlib", "purelib")
+            and not WINDOWS
+            and _looks_like_slackware_scheme()
+        )
+        if skip_slackware_user_scheme:
+            continue
+
+        # Both Debian and Red Hat patch Python to place the system site under
+        # /usr/local instead of /usr. Debian also places lib in dist-packages
+        # instead of site-packages, but the /usr/local check should cover it.
+        skip_linux_system_special_case = (
+            not (user or home or prefix or running_under_virtualenv())
+            and old_v.parts[1:3] == ("usr", "local")
+            and len(new_v.parts) > 1
+            and new_v.parts[1] == "usr"
+            and (len(new_v.parts) < 3 or new_v.parts[2] != "local")
+            and (_looks_like_red_hat_scheme() or _looks_like_debian_scheme())
+        )
+        if skip_linux_system_special_case:
+            continue
+
+        # MSYS2 MINGW's sysconfig patch does not include the "site-packages"
+        # part of the path. This is incorrect and will be fixed in MSYS.
+        skip_msys2_mingw_bug = (
+            WINDOWS and k in ("platlib", "purelib") and _looks_like_msys2_mingw_scheme()
+        )
+        if skip_msys2_mingw_bug:
+            continue
+
+        # CPython's POSIX install script invokes pip (via ensurepip) against the
+        # interpreter located in the source tree, not the install site. This
+        # triggers special logic in sysconfig that's not present in distutils.
+        # https://github.com/python/cpython/blob/8c21941ddaf/Lib/sysconfig.py#L178-L194
+        skip_cpython_build = (
+            sysconfig.is_python_build(check_home=True)
+            and not WINDOWS
+            and k in ("headers", "include", "platinclude")
+        )
+        if skip_cpython_build:
+            continue
+
+        warning_contexts.append((old_v, new_v, f"scheme.{k}"))
+
+    if not warning_contexts:
+        return old
+
+    # Check if this path mismatch is caused by distutils config files. Those
+    # files will no longer work once we switch to sysconfig, so this raises a
+    # deprecation message for them.
+    default_old = _distutils.distutils_scheme(
+        dist_name,
+        user,
+        home,
+        root,
+        isolated,
+        prefix,
+        ignore_config_files=True,
+    )
+    if any(default_old[k] != getattr(old, k) for k in SCHEME_KEYS):
+        deprecated(
+            reason=(
+                "Configuring installation scheme with distutils config files "
+                "is deprecated and will no longer work in the near future. If you "
+                "are using a Homebrew or Linuxbrew Python, please see discussion "
+                "at https://github.com/Homebrew/homebrew-core/issues/76621"
+            ),
+            replacement=None,
+            gone_in=None,
+        )
+        return old
+
+    # Post warnings about this mismatch so user can report them back.
+    for old_v, new_v, key in warning_contexts:
+        _warn_mismatched(old_v, new_v, key=key)
+    _log_context(user=user, home=home, root=root, prefix=prefix)
+
+    return old
+
+
+def get_bin_prefix() -> str:
+    new = _sysconfig.get_bin_prefix()
+    if _USE_SYSCONFIG:
+        return new
+
+    old = _distutils.get_bin_prefix()
+    if _warn_if_mismatch(pathlib.Path(old), pathlib.Path(new), key="bin_prefix"):
+        _log_context()
+    return old
+
+
+def get_bin_user() -> str:
+    return _sysconfig.get_scheme("", user=True).scripts
+
+
+def _looks_like_deb_system_dist_packages(value: str) -> bool:
+    """Check if the value is Debian's APT-controlled dist-packages.
+
+    Debian's ``distutils.sysconfig.get_python_lib()`` implementation returns the
+    default package path controlled by APT, but does not patch ``sysconfig`` to
+    do the same. This is similar to the bug worked around in ``get_scheme()``,
+    but here the default is ``deb_system`` instead of ``unix_local``. Ultimately
+    we can't do anything about this Debian bug, and this detection allows us to
+    skip the warning when needed.
+    """
+    if not _looks_like_debian_scheme():
+        return False
+    if value == "/usr/lib/python3/dist-packages":
+        return True
+    return False
+
+
+def get_purelib() -> str:
+    """Return the default pure-Python lib location."""
+    new = _sysconfig.get_purelib()
+    if _USE_SYSCONFIG:
+        return new
+
+    old = _distutils.get_purelib()
+    if _looks_like_deb_system_dist_packages(old):
+        return old
+    if _warn_if_mismatch(pathlib.Path(old), pathlib.Path(new), key="purelib"):
+        _log_context()
+    return old
+
+
+def get_platlib() -> str:
+    """Return the default platform-shared lib location."""
+    new = _sysconfig.get_platlib()
+    if _USE_SYSCONFIG:
+        return new
+
+    from . import _distutils
+
+    old = _distutils.get_platlib()
+    if _looks_like_deb_system_dist_packages(old):
+        return old
+    if _warn_if_mismatch(pathlib.Path(old), pathlib.Path(new), key="platlib"):
+        _log_context()
+    return old
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diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/locations/_sysconfig.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/locations/_sysconfig.py
new file mode 100644
index 0000000000000000000000000000000000000000..ca860ea562c2c0c30982ba6cff654355e9f21c8a
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/locations/_sysconfig.py
@@ -0,0 +1,214 @@
+import logging
+import os
+import sys
+import sysconfig
+import typing
+
+from pip._internal.exceptions import InvalidSchemeCombination, UserInstallationInvalid
+from pip._internal.models.scheme import SCHEME_KEYS, Scheme
+from pip._internal.utils.virtualenv import running_under_virtualenv
+
+from .base import change_root, get_major_minor_version, is_osx_framework
+
+logger = logging.getLogger(__name__)
+
+
+# Notes on _infer_* functions.
+# Unfortunately ``get_default_scheme()`` didn't exist before 3.10, so there's no
+# way to ask things like "what is the '_prefix' scheme on this platform". These
+# functions try to answer that with some heuristics while accounting for ad-hoc
+# platforms not covered by CPython's default sysconfig implementation. If the
+# ad-hoc implementation does not fully implement sysconfig, we'll fall back to
+# a POSIX scheme.
+
+_AVAILABLE_SCHEMES = set(sysconfig.get_scheme_names())
+
+_PREFERRED_SCHEME_API = getattr(sysconfig, "get_preferred_scheme", None)
+
+
+def _should_use_osx_framework_prefix() -> bool:
+    """Check for Apple's ``osx_framework_library`` scheme.
+
+    Python distributed by Apple's Command Line Tools has this special scheme
+    that's used when:
+
+    * This is a framework build.
+    * We are installing into the system prefix.
+
+    This does not account for ``pip install --prefix`` (also means we're not
+    installing to the system prefix), which should use ``posix_prefix``, but
+    logic here means ``_infer_prefix()`` outputs ``osx_framework_library``. But
+    since ``prefix`` is not available for ``sysconfig.get_default_scheme()``,
+    which is the stdlib replacement for ``_infer_prefix()``, presumably Apple
+    wouldn't be able to magically switch between ``osx_framework_library`` and
+    ``posix_prefix``. ``_infer_prefix()`` returning ``osx_framework_library``
+    means its behavior is consistent whether we use the stdlib implementation
+    or our own, and we deal with this special case in ``get_scheme()`` instead.
+    """
+    return (
+        "osx_framework_library" in _AVAILABLE_SCHEMES
+        and not running_under_virtualenv()
+        and is_osx_framework()
+    )
+
+
+def _infer_prefix() -> str:
+    """Try to find a prefix scheme for the current platform.
+
+    This tries:
+
+    * A special ``osx_framework_library`` for Python distributed by Apple's
+      Command Line Tools, when not running in a virtual environment.
+    * Implementation + OS, used by PyPy on Windows (``pypy_nt``).
+    * Implementation without OS, used by PyPy on POSIX (``pypy``).
+    * OS + "prefix", used by CPython on POSIX (``posix_prefix``).
+    * Just the OS name, used by CPython on Windows (``nt``).
+
+    If none of the above works, fall back to ``posix_prefix``.
+    """
+    if _PREFERRED_SCHEME_API:
+        return _PREFERRED_SCHEME_API("prefix")
+    if _should_use_osx_framework_prefix():
+        return "osx_framework_library"
+    implementation_suffixed = f"{sys.implementation.name}_{os.name}"
+    if implementation_suffixed in _AVAILABLE_SCHEMES:
+        return implementation_suffixed
+    if sys.implementation.name in _AVAILABLE_SCHEMES:
+        return sys.implementation.name
+    suffixed = f"{os.name}_prefix"
+    if suffixed in _AVAILABLE_SCHEMES:
+        return suffixed
+    if os.name in _AVAILABLE_SCHEMES:  # On Windows, prefx is just called "nt".
+        return os.name
+    return "posix_prefix"
+
+
+def _infer_user() -> str:
+    """Try to find a user scheme for the current platform."""
+    if _PREFERRED_SCHEME_API:
+        return _PREFERRED_SCHEME_API("user")
+    if is_osx_framework() and not running_under_virtualenv():
+        suffixed = "osx_framework_user"
+    else:
+        suffixed = f"{os.name}_user"
+    if suffixed in _AVAILABLE_SCHEMES:
+        return suffixed
+    if "posix_user" not in _AVAILABLE_SCHEMES:  # User scheme unavailable.
+        raise UserInstallationInvalid()
+    return "posix_user"
+
+
+def _infer_home() -> str:
+    """Try to find a home for the current platform."""
+    if _PREFERRED_SCHEME_API:
+        return _PREFERRED_SCHEME_API("home")
+    suffixed = f"{os.name}_home"
+    if suffixed in _AVAILABLE_SCHEMES:
+        return suffixed
+    return "posix_home"
+
+
+# Update these keys if the user sets a custom home.
+_HOME_KEYS = [
+    "installed_base",
+    "base",
+    "installed_platbase",
+    "platbase",
+    "prefix",
+    "exec_prefix",
+]
+if sysconfig.get_config_var("userbase") is not None:
+    _HOME_KEYS.append("userbase")
+
+
+def get_scheme(
+    dist_name: str,
+    user: bool = False,
+    home: typing.Optional[str] = None,
+    root: typing.Optional[str] = None,
+    isolated: bool = False,
+    prefix: typing.Optional[str] = None,
+) -> Scheme:
+    """
+    Get the "scheme" corresponding to the input parameters.
+
+    :param dist_name: the name of the package to retrieve the scheme for, used
+        in the headers scheme path
+    :param user: indicates to use the "user" scheme
+    :param home: indicates to use the "home" scheme
+    :param root: root under which other directories are re-based
+    :param isolated: ignored, but kept for distutils compatibility (where
+        this controls whether the user-site pydistutils.cfg is honored)
+    :param prefix: indicates to use the "prefix" scheme and provides the
+        base directory for the same
+    """
+    if user and prefix:
+        raise InvalidSchemeCombination("--user", "--prefix")
+    if home and prefix:
+        raise InvalidSchemeCombination("--home", "--prefix")
+
+    if home is not None:
+        scheme_name = _infer_home()
+    elif user:
+        scheme_name = _infer_user()
+    else:
+        scheme_name = _infer_prefix()
+
+    # Special case: When installing into a custom prefix, use posix_prefix
+    # instead of osx_framework_library. See _should_use_osx_framework_prefix()
+    # docstring for details.
+    if prefix is not None and scheme_name == "osx_framework_library":
+        scheme_name = "posix_prefix"
+
+    if home is not None:
+        variables = {k: home for k in _HOME_KEYS}
+    elif prefix is not None:
+        variables = {k: prefix for k in _HOME_KEYS}
+    else:
+        variables = {}
+
+    paths = sysconfig.get_paths(scheme=scheme_name, vars=variables)
+
+    # Logic here is very arbitrary, we're doing it for compatibility, don't ask.
+    # 1. Pip historically uses a special header path in virtual environments.
+    # 2. If the distribution name is not known, distutils uses 'UNKNOWN'. We
+    #    only do the same when not running in a virtual environment because
+    #    pip's historical header path logic (see point 1) did not do this.
+    if running_under_virtualenv():
+        if user:
+            base = variables.get("userbase", sys.prefix)
+        else:
+            base = variables.get("base", sys.prefix)
+        python_xy = f"python{get_major_minor_version()}"
+        paths["include"] = os.path.join(base, "include", "site", python_xy)
+    elif not dist_name:
+        dist_name = "UNKNOWN"
+
+    scheme = Scheme(
+        platlib=paths["platlib"],
+        purelib=paths["purelib"],
+        headers=os.path.join(paths["include"], dist_name),
+        scripts=paths["scripts"],
+        data=paths["data"],
+    )
+    if root is not None:
+        converted_keys = {}
+        for key in SCHEME_KEYS:
+            converted_keys[key] = change_root(root, getattr(scheme, key))
+        scheme = Scheme(**converted_keys)
+    return scheme
+
+
+def get_bin_prefix() -> str:
+    # Forcing to use /usr/local/bin for standard macOS framework installs.
+    if sys.platform[:6] == "darwin" and sys.prefix[:16] == "/System/Library/":
+        return "/usr/local/bin"
+    return sysconfig.get_paths()["scripts"]
+
+
+def get_purelib() -> str:
+    return sysconfig.get_paths()["purelib"]
+
+
+def get_platlib() -> str:
+    return sysconfig.get_paths()["platlib"]
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/metadata/importlib/__pycache__/_compat.cpython-311.pyc b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/metadata/importlib/__pycache__/_compat.cpython-311.pyc
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diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/network/__init__.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/network/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..b51bde91b2e5b4e557ed9b70fc113843cc3d49ae
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/network/__init__.py
@@ -0,0 +1,2 @@
+"""Contains purely network-related utilities.
+"""
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/network/session.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/network/session.py
new file mode 100644
index 0000000000000000000000000000000000000000..1765b4f6bd74cb10ca7af93f819c6a6f063f3a84
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/network/session.py
@@ -0,0 +1,522 @@
+"""PipSession and supporting code, containing all pip-specific
+network request configuration and behavior.
+"""
+
+import email.utils
+import functools
+import io
+import ipaddress
+import json
+import logging
+import mimetypes
+import os
+import platform
+import shutil
+import subprocess
+import sys
+import urllib.parse
+import warnings
+from typing import (
+    TYPE_CHECKING,
+    Any,
+    Dict,
+    Generator,
+    List,
+    Mapping,
+    Optional,
+    Sequence,
+    Tuple,
+    Union,
+)
+
+from pip._vendor import requests, urllib3
+from pip._vendor.cachecontrol import CacheControlAdapter as _BaseCacheControlAdapter
+from pip._vendor.requests.adapters import DEFAULT_POOLBLOCK, BaseAdapter
+from pip._vendor.requests.adapters import HTTPAdapter as _BaseHTTPAdapter
+from pip._vendor.requests.models import PreparedRequest, Response
+from pip._vendor.requests.structures import CaseInsensitiveDict
+from pip._vendor.urllib3.connectionpool import ConnectionPool
+from pip._vendor.urllib3.exceptions import InsecureRequestWarning
+
+from pip import __version__
+from pip._internal.metadata import get_default_environment
+from pip._internal.models.link import Link
+from pip._internal.network.auth import MultiDomainBasicAuth
+from pip._internal.network.cache import SafeFileCache
+
+# Import ssl from compat so the initial import occurs in only one place.
+from pip._internal.utils.compat import has_tls
+from pip._internal.utils.glibc import libc_ver
+from pip._internal.utils.misc import build_url_from_netloc, parse_netloc
+from pip._internal.utils.urls import url_to_path
+
+if TYPE_CHECKING:
+    from ssl import SSLContext
+
+    from pip._vendor.urllib3.poolmanager import PoolManager
+
+
+logger = logging.getLogger(__name__)
+
+SecureOrigin = Tuple[str, str, Optional[Union[int, str]]]
+
+
+# Ignore warning raised when using --trusted-host.
+warnings.filterwarnings("ignore", category=InsecureRequestWarning)
+
+
+SECURE_ORIGINS: List[SecureOrigin] = [
+    # protocol, hostname, port
+    # Taken from Chrome's list of secure origins (See: http://bit.ly/1qrySKC)
+    ("https", "*", "*"),
+    ("*", "localhost", "*"),
+    ("*", "127.0.0.0/8", "*"),
+    ("*", "::1/128", "*"),
+    ("file", "*", None),
+    # ssh is always secure.
+    ("ssh", "*", "*"),
+]
+
+
+# These are environment variables present when running under various
+# CI systems.  For each variable, some CI systems that use the variable
+# are indicated.  The collection was chosen so that for each of a number
+# of popular systems, at least one of the environment variables is used.
+# This list is used to provide some indication of and lower bound for
+# CI traffic to PyPI.  Thus, it is okay if the list is not comprehensive.
+# For more background, see: https://github.com/pypa/pip/issues/5499
+CI_ENVIRONMENT_VARIABLES = (
+    # Azure Pipelines
+    "BUILD_BUILDID",
+    # Jenkins
+    "BUILD_ID",
+    # AppVeyor, CircleCI, Codeship, Gitlab CI, Shippable, Travis CI
+    "CI",
+    # Explicit environment variable.
+    "PIP_IS_CI",
+)
+
+
+def looks_like_ci() -> bool:
+    """
+    Return whether it looks like pip is running under CI.
+    """
+    # We don't use the method of checking for a tty (e.g. using isatty())
+    # because some CI systems mimic a tty (e.g. Travis CI).  Thus that
+    # method doesn't provide definitive information in either direction.
+    return any(name in os.environ for name in CI_ENVIRONMENT_VARIABLES)
+
+
+@functools.lru_cache(maxsize=1)
+def user_agent() -> str:
+    """
+    Return a string representing the user agent.
+    """
+    data: Dict[str, Any] = {
+        "installer": {"name": "pip", "version": __version__},
+        "python": platform.python_version(),
+        "implementation": {
+            "name": platform.python_implementation(),
+        },
+    }
+
+    if data["implementation"]["name"] == "CPython":
+        data["implementation"]["version"] = platform.python_version()
+    elif data["implementation"]["name"] == "PyPy":
+        pypy_version_info = sys.pypy_version_info  # type: ignore
+        if pypy_version_info.releaselevel == "final":
+            pypy_version_info = pypy_version_info[:3]
+        data["implementation"]["version"] = ".".join(
+            [str(x) for x in pypy_version_info]
+        )
+    elif data["implementation"]["name"] == "Jython":
+        # Complete Guess
+        data["implementation"]["version"] = platform.python_version()
+    elif data["implementation"]["name"] == "IronPython":
+        # Complete Guess
+        data["implementation"]["version"] = platform.python_version()
+
+    if sys.platform.startswith("linux"):
+        from pip._vendor import distro
+
+        linux_distribution = distro.name(), distro.version(), distro.codename()
+        distro_infos: Dict[str, Any] = dict(
+            filter(
+                lambda x: x[1],
+                zip(["name", "version", "id"], linux_distribution),
+            )
+        )
+        libc = dict(
+            filter(
+                lambda x: x[1],
+                zip(["lib", "version"], libc_ver()),
+            )
+        )
+        if libc:
+            distro_infos["libc"] = libc
+        if distro_infos:
+            data["distro"] = distro_infos
+
+    if sys.platform.startswith("darwin") and platform.mac_ver()[0]:
+        data["distro"] = {"name": "macOS", "version": platform.mac_ver()[0]}
+
+    if platform.system():
+        data.setdefault("system", {})["name"] = platform.system()
+
+    if platform.release():
+        data.setdefault("system", {})["release"] = platform.release()
+
+    if platform.machine():
+        data["cpu"] = platform.machine()
+
+    if has_tls():
+        import _ssl as ssl
+
+        data["openssl_version"] = ssl.OPENSSL_VERSION
+
+    setuptools_dist = get_default_environment().get_distribution("setuptools")
+    if setuptools_dist is not None:
+        data["setuptools_version"] = str(setuptools_dist.version)
+
+    if shutil.which("rustc") is not None:
+        # If for any reason `rustc --version` fails, silently ignore it
+        try:
+            rustc_output = subprocess.check_output(
+                ["rustc", "--version"], stderr=subprocess.STDOUT, timeout=0.5
+            )
+        except Exception:
+            pass
+        else:
+            if rustc_output.startswith(b"rustc "):
+                # The format of `rustc --version` is:
+                # `b'rustc 1.52.1 (9bc8c42bb 2021-05-09)\n'`
+                # We extract just the middle (1.52.1) part
+                data["rustc_version"] = rustc_output.split(b" ")[1].decode()
+
+    # Use None rather than False so as not to give the impression that
+    # pip knows it is not being run under CI.  Rather, it is a null or
+    # inconclusive result.  Also, we include some value rather than no
+    # value to make it easier to know that the check has been run.
+    data["ci"] = True if looks_like_ci() else None
+
+    user_data = os.environ.get("PIP_USER_AGENT_USER_DATA")
+    if user_data is not None:
+        data["user_data"] = user_data
+
+    return "{data[installer][name]}/{data[installer][version]} {json}".format(
+        data=data,
+        json=json.dumps(data, separators=(",", ":"), sort_keys=True),
+    )
+
+
+class LocalFSAdapter(BaseAdapter):
+    def send(
+        self,
+        request: PreparedRequest,
+        stream: bool = False,
+        timeout: Optional[Union[float, Tuple[float, float]]] = None,
+        verify: Union[bool, str] = True,
+        cert: Optional[Union[str, Tuple[str, str]]] = None,
+        proxies: Optional[Mapping[str, str]] = None,
+    ) -> Response:
+        pathname = url_to_path(request.url)
+
+        resp = Response()
+        resp.status_code = 200
+        resp.url = request.url
+
+        try:
+            stats = os.stat(pathname)
+        except OSError as exc:
+            # format the exception raised as a io.BytesIO object,
+            # to return a better error message:
+            resp.status_code = 404
+            resp.reason = type(exc).__name__
+            resp.raw = io.BytesIO(f"{resp.reason}: {exc}".encode())
+        else:
+            modified = email.utils.formatdate(stats.st_mtime, usegmt=True)
+            content_type = mimetypes.guess_type(pathname)[0] or "text/plain"
+            resp.headers = CaseInsensitiveDict(
+                {
+                    "Content-Type": content_type,
+                    "Content-Length": stats.st_size,
+                    "Last-Modified": modified,
+                }
+            )
+
+            resp.raw = open(pathname, "rb")
+            resp.close = resp.raw.close
+
+        return resp
+
+    def close(self) -> None:
+        pass
+
+
+class _SSLContextAdapterMixin:
+    """Mixin to add the ``ssl_context`` constructor argument to HTTP adapters.
+
+    The additional argument is forwarded directly to the pool manager. This allows us
+    to dynamically decide what SSL store to use at runtime, which is used to implement
+    the optional ``truststore`` backend.
+    """
+
+    def __init__(
+        self,
+        *,
+        ssl_context: Optional["SSLContext"] = None,
+        **kwargs: Any,
+    ) -> None:
+        self._ssl_context = ssl_context
+        super().__init__(**kwargs)
+
+    def init_poolmanager(
+        self,
+        connections: int,
+        maxsize: int,
+        block: bool = DEFAULT_POOLBLOCK,
+        **pool_kwargs: Any,
+    ) -> "PoolManager":
+        if self._ssl_context is not None:
+            pool_kwargs.setdefault("ssl_context", self._ssl_context)
+        return super().init_poolmanager(  # type: ignore[misc]
+            connections=connections,
+            maxsize=maxsize,
+            block=block,
+            **pool_kwargs,
+        )
+
+
+class HTTPAdapter(_SSLContextAdapterMixin, _BaseHTTPAdapter):
+    pass
+
+
+class CacheControlAdapter(_SSLContextAdapterMixin, _BaseCacheControlAdapter):
+    pass
+
+
+class InsecureHTTPAdapter(HTTPAdapter):
+    def cert_verify(
+        self,
+        conn: ConnectionPool,
+        url: str,
+        verify: Union[bool, str],
+        cert: Optional[Union[str, Tuple[str, str]]],
+    ) -> None:
+        super().cert_verify(conn=conn, url=url, verify=False, cert=cert)
+
+
+class InsecureCacheControlAdapter(CacheControlAdapter):
+    def cert_verify(
+        self,
+        conn: ConnectionPool,
+        url: str,
+        verify: Union[bool, str],
+        cert: Optional[Union[str, Tuple[str, str]]],
+    ) -> None:
+        super().cert_verify(conn=conn, url=url, verify=False, cert=cert)
+
+
+class PipSession(requests.Session):
+    timeout: Optional[int] = None
+
+    def __init__(
+        self,
+        *args: Any,
+        retries: int = 0,
+        cache: Optional[str] = None,
+        trusted_hosts: Sequence[str] = (),
+        index_urls: Optional[List[str]] = None,
+        ssl_context: Optional["SSLContext"] = None,
+        **kwargs: Any,
+    ) -> None:
+        """
+        :param trusted_hosts: Domains not to emit warnings for when not using
+            HTTPS.
+        """
+        super().__init__(*args, **kwargs)
+
+        # Namespace the attribute with "pip_" just in case to prevent
+        # possible conflicts with the base class.
+        self.pip_trusted_origins: List[Tuple[str, Optional[int]]] = []
+
+        # Attach our User Agent to the request
+        self.headers["User-Agent"] = user_agent()
+
+        # Attach our Authentication handler to the session
+        self.auth = MultiDomainBasicAuth(index_urls=index_urls)
+
+        # Create our urllib3.Retry instance which will allow us to customize
+        # how we handle retries.
+        retries = urllib3.Retry(
+            # Set the total number of retries that a particular request can
+            # have.
+            total=retries,
+            # A 503 error from PyPI typically means that the Fastly -> Origin
+            # connection got interrupted in some way. A 503 error in general
+            # is typically considered a transient error so we'll go ahead and
+            # retry it.
+            # A 500 may indicate transient error in Amazon S3
+            # A 502 may be a transient error from a CDN like CloudFlare or CloudFront
+            # A 520 or 527 - may indicate transient error in CloudFlare
+            status_forcelist=[500, 502, 503, 520, 527],
+            # Add a small amount of back off between failed requests in
+            # order to prevent hammering the service.
+            backoff_factor=0.25,
+        )  # type: ignore
+
+        # Our Insecure HTTPAdapter disables HTTPS validation. It does not
+        # support caching so we'll use it for all http:// URLs.
+        # If caching is disabled, we will also use it for
+        # https:// hosts that we've marked as ignoring
+        # TLS errors for (trusted-hosts).
+        insecure_adapter = InsecureHTTPAdapter(max_retries=retries)
+
+        # We want to _only_ cache responses on securely fetched origins or when
+        # the host is specified as trusted. We do this because
+        # we can't validate the response of an insecurely/untrusted fetched
+        # origin, and we don't want someone to be able to poison the cache and
+        # require manual eviction from the cache to fix it.
+        if cache:
+            secure_adapter = CacheControlAdapter(
+                cache=SafeFileCache(cache),
+                max_retries=retries,
+                ssl_context=ssl_context,
+            )
+            self._trusted_host_adapter = InsecureCacheControlAdapter(
+                cache=SafeFileCache(cache),
+                max_retries=retries,
+            )
+        else:
+            secure_adapter = HTTPAdapter(max_retries=retries, ssl_context=ssl_context)
+            self._trusted_host_adapter = insecure_adapter
+
+        self.mount("https://", secure_adapter)
+        self.mount("http://", insecure_adapter)
+
+        # Enable file:// urls
+        self.mount("file://", LocalFSAdapter())
+
+        for host in trusted_hosts:
+            self.add_trusted_host(host, suppress_logging=True)
+
+    def update_index_urls(self, new_index_urls: List[str]) -> None:
+        """
+        :param new_index_urls: New index urls to update the authentication
+            handler with.
+        """
+        self.auth.index_urls = new_index_urls
+
+    def add_trusted_host(
+        self, host: str, source: Optional[str] = None, suppress_logging: bool = False
+    ) -> None:
+        """
+        :param host: It is okay to provide a host that has previously been
+            added.
+        :param source: An optional source string, for logging where the host
+            string came from.
+        """
+        if not suppress_logging:
+            msg = f"adding trusted host: {host!r}"
+            if source is not None:
+                msg += f" (from {source})"
+            logger.info(msg)
+
+        parsed_host, parsed_port = parse_netloc(host)
+        if parsed_host is None:
+            raise ValueError(f"Trusted host URL must include a host part: {host!r}")
+        if (parsed_host, parsed_port) not in self.pip_trusted_origins:
+            self.pip_trusted_origins.append((parsed_host, parsed_port))
+
+        self.mount(
+            build_url_from_netloc(host, scheme="http") + "/", self._trusted_host_adapter
+        )
+        self.mount(build_url_from_netloc(host) + "/", self._trusted_host_adapter)
+        if not parsed_port:
+            self.mount(
+                build_url_from_netloc(host, scheme="http") + ":",
+                self._trusted_host_adapter,
+            )
+            # Mount wildcard ports for the same host.
+            self.mount(build_url_from_netloc(host) + ":", self._trusted_host_adapter)
+
+    def iter_secure_origins(self) -> Generator[SecureOrigin, None, None]:
+        yield from SECURE_ORIGINS
+        for host, port in self.pip_trusted_origins:
+            yield ("*", host, "*" if port is None else port)
+
+    def is_secure_origin(self, location: Link) -> bool:
+        # Determine if this url used a secure transport mechanism
+        parsed = urllib.parse.urlparse(str(location))
+        origin_protocol, origin_host, origin_port = (
+            parsed.scheme,
+            parsed.hostname,
+            parsed.port,
+        )
+
+        # The protocol to use to see if the protocol matches.
+        # Don't count the repository type as part of the protocol: in
+        # cases such as "git+ssh", only use "ssh". (I.e., Only verify against
+        # the last scheme.)
+        origin_protocol = origin_protocol.rsplit("+", 1)[-1]
+
+        # Determine if our origin is a secure origin by looking through our
+        # hardcoded list of secure origins, as well as any additional ones
+        # configured on this PackageFinder instance.
+        for secure_origin in self.iter_secure_origins():
+            secure_protocol, secure_host, secure_port = secure_origin
+            if origin_protocol != secure_protocol and secure_protocol != "*":
+                continue
+
+            try:
+                addr = ipaddress.ip_address(origin_host or "")
+                network = ipaddress.ip_network(secure_host)
+            except ValueError:
+                # We don't have both a valid address or a valid network, so
+                # we'll check this origin against hostnames.
+                if (
+                    origin_host
+                    and origin_host.lower() != secure_host.lower()
+                    and secure_host != "*"
+                ):
+                    continue
+            else:
+                # We have a valid address and network, so see if the address
+                # is contained within the network.
+                if addr not in network:
+                    continue
+
+            # Check to see if the port matches.
+            if (
+                origin_port != secure_port
+                and secure_port != "*"
+                and secure_port is not None
+            ):
+                continue
+
+            # If we've gotten here, then this origin matches the current
+            # secure origin and we should return True
+            return True
+
+        # If we've gotten to this point, then the origin isn't secure and we
+        # will not accept it as a valid location to search. We will however
+        # log a warning that we are ignoring it.
+        logger.warning(
+            "The repository located at %s is not a trusted or secure host and "
+            "is being ignored. If this repository is available via HTTPS we "
+            "recommend you use HTTPS instead, otherwise you may silence "
+            "this warning and allow it anyway with '--trusted-host %s'.",
+            origin_host,
+            origin_host,
+        )
+
+        return False
+
+    def request(self, method: str, url: str, *args: Any, **kwargs: Any) -> Response:
+        # Allow setting a default timeout on a session
+        kwargs.setdefault("timeout", self.timeout)
+        # Allow setting a default proxies on a session
+        kwargs.setdefault("proxies", self.proxies)
+
+        # Dispatch the actual request
+        return super().request(method, url, *args, **kwargs)
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diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/base.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/base.py
new file mode 100644
index 0000000000000000000000000000000000000000..0f31dc9b3073ecf2a9ae234b752e33c8caf5798a
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/base.py
@@ -0,0 +1,139 @@
+from dataclasses import dataclass
+from typing import FrozenSet, Iterable, Optional, Tuple
+
+from pip._vendor.packaging.specifiers import SpecifierSet
+from pip._vendor.packaging.utils import NormalizedName
+from pip._vendor.packaging.version import Version
+
+from pip._internal.models.link import Link, links_equivalent
+from pip._internal.req.req_install import InstallRequirement
+from pip._internal.utils.hashes import Hashes
+
+CandidateLookup = Tuple[Optional["Candidate"], Optional[InstallRequirement]]
+
+
+def format_name(project: NormalizedName, extras: FrozenSet[NormalizedName]) -> str:
+    if not extras:
+        return project
+    extras_expr = ",".join(sorted(extras))
+    return f"{project}[{extras_expr}]"
+
+
+@dataclass(frozen=True)
+class Constraint:
+    specifier: SpecifierSet
+    hashes: Hashes
+    links: FrozenSet[Link]
+
+    @classmethod
+    def empty(cls) -> "Constraint":
+        return Constraint(SpecifierSet(), Hashes(), frozenset())
+
+    @classmethod
+    def from_ireq(cls, ireq: InstallRequirement) -> "Constraint":
+        links = frozenset([ireq.link]) if ireq.link else frozenset()
+        return Constraint(ireq.specifier, ireq.hashes(trust_internet=False), links)
+
+    def __bool__(self) -> bool:
+        return bool(self.specifier) or bool(self.hashes) or bool(self.links)
+
+    def __and__(self, other: InstallRequirement) -> "Constraint":
+        if not isinstance(other, InstallRequirement):
+            return NotImplemented
+        specifier = self.specifier & other.specifier
+        hashes = self.hashes & other.hashes(trust_internet=False)
+        links = self.links
+        if other.link:
+            links = links.union([other.link])
+        return Constraint(specifier, hashes, links)
+
+    def is_satisfied_by(self, candidate: "Candidate") -> bool:
+        # Reject if there are any mismatched URL constraints on this package.
+        if self.links and not all(_match_link(link, candidate) for link in self.links):
+            return False
+        # We can safely always allow prereleases here since PackageFinder
+        # already implements the prerelease logic, and would have filtered out
+        # prerelease candidates if the user does not expect them.
+        return self.specifier.contains(candidate.version, prereleases=True)
+
+
+class Requirement:
+    @property
+    def project_name(self) -> NormalizedName:
+        """The "project name" of a requirement.
+
+        This is different from ``name`` if this requirement contains extras,
+        in which case ``name`` would contain the ``[...]`` part, while this
+        refers to the name of the project.
+        """
+        raise NotImplementedError("Subclass should override")
+
+    @property
+    def name(self) -> str:
+        """The name identifying this requirement in the resolver.
+
+        This is different from ``project_name`` if this requirement contains
+        extras, where ``project_name`` would not contain the ``[...]`` part.
+        """
+        raise NotImplementedError("Subclass should override")
+
+    def is_satisfied_by(self, candidate: "Candidate") -> bool:
+        return False
+
+    def get_candidate_lookup(self) -> CandidateLookup:
+        raise NotImplementedError("Subclass should override")
+
+    def format_for_error(self) -> str:
+        raise NotImplementedError("Subclass should override")
+
+
+def _match_link(link: Link, candidate: "Candidate") -> bool:
+    if candidate.source_link:
+        return links_equivalent(link, candidate.source_link)
+    return False
+
+
+class Candidate:
+    @property
+    def project_name(self) -> NormalizedName:
+        """The "project name" of the candidate.
+
+        This is different from ``name`` if this candidate contains extras,
+        in which case ``name`` would contain the ``[...]`` part, while this
+        refers to the name of the project.
+        """
+        raise NotImplementedError("Override in subclass")
+
+    @property
+    def name(self) -> str:
+        """The name identifying this candidate in the resolver.
+
+        This is different from ``project_name`` if this candidate contains
+        extras, where ``project_name`` would not contain the ``[...]`` part.
+        """
+        raise NotImplementedError("Override in subclass")
+
+    @property
+    def version(self) -> Version:
+        raise NotImplementedError("Override in subclass")
+
+    @property
+    def is_installed(self) -> bool:
+        raise NotImplementedError("Override in subclass")
+
+    @property
+    def is_editable(self) -> bool:
+        raise NotImplementedError("Override in subclass")
+
+    @property
+    def source_link(self) -> Optional[Link]:
+        raise NotImplementedError("Override in subclass")
+
+    def iter_dependencies(self, with_requires: bool) -> Iterable[Optional[Requirement]]:
+        raise NotImplementedError("Override in subclass")
+
+    def get_install_requirement(self) -> Optional[InstallRequirement]:
+        raise NotImplementedError("Override in subclass")
+
+    def format_for_error(self) -> str:
+        raise NotImplementedError("Subclass should override")
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/factory.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/factory.py
new file mode 100644
index 0000000000000000000000000000000000000000..dc6e2e12e1f9c633e272e674e50c6f48aaded4a4
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/factory.py
@@ -0,0 +1,823 @@
+import contextlib
+import functools
+import logging
+from typing import (
+    TYPE_CHECKING,
+    Callable,
+    Dict,
+    FrozenSet,
+    Iterable,
+    Iterator,
+    List,
+    Mapping,
+    NamedTuple,
+    Optional,
+    Protocol,
+    Sequence,
+    Set,
+    Tuple,
+    TypeVar,
+    cast,
+)
+
+from pip._vendor.packaging.requirements import InvalidRequirement
+from pip._vendor.packaging.specifiers import SpecifierSet
+from pip._vendor.packaging.utils import NormalizedName, canonicalize_name
+from pip._vendor.packaging.version import InvalidVersion, Version
+from pip._vendor.resolvelib import ResolutionImpossible
+
+from pip._internal.cache import CacheEntry, WheelCache
+from pip._internal.exceptions import (
+    DistributionNotFound,
+    InstallationError,
+    InvalidInstalledPackage,
+    MetadataInconsistent,
+    MetadataInvalid,
+    UnsupportedPythonVersion,
+    UnsupportedWheel,
+)
+from pip._internal.index.package_finder import PackageFinder
+from pip._internal.metadata import BaseDistribution, get_default_environment
+from pip._internal.models.link import Link
+from pip._internal.models.wheel import Wheel
+from pip._internal.operations.prepare import RequirementPreparer
+from pip._internal.req.constructors import (
+    install_req_drop_extras,
+    install_req_from_link_and_ireq,
+)
+from pip._internal.req.req_install import (
+    InstallRequirement,
+    check_invalid_constraint_type,
+)
+from pip._internal.resolution.base import InstallRequirementProvider
+from pip._internal.utils.compatibility_tags import get_supported
+from pip._internal.utils.hashes import Hashes
+from pip._internal.utils.packaging import get_requirement
+from pip._internal.utils.virtualenv import running_under_virtualenv
+
+from .base import Candidate, Constraint, Requirement
+from .candidates import (
+    AlreadyInstalledCandidate,
+    BaseCandidate,
+    EditableCandidate,
+    ExtrasCandidate,
+    LinkCandidate,
+    RequiresPythonCandidate,
+    as_base_candidate,
+)
+from .found_candidates import FoundCandidates, IndexCandidateInfo
+from .requirements import (
+    ExplicitRequirement,
+    RequiresPythonRequirement,
+    SpecifierRequirement,
+    SpecifierWithoutExtrasRequirement,
+    UnsatisfiableRequirement,
+)
+
+if TYPE_CHECKING:
+
+    class ConflictCause(Protocol):
+        requirement: RequiresPythonRequirement
+        parent: Candidate
+
+
+logger = logging.getLogger(__name__)
+
+C = TypeVar("C")
+Cache = Dict[Link, C]
+
+
+class CollectedRootRequirements(NamedTuple):
+    requirements: List[Requirement]
+    constraints: Dict[str, Constraint]
+    user_requested: Dict[str, int]
+
+
+class Factory:
+    def __init__(
+        self,
+        finder: PackageFinder,
+        preparer: RequirementPreparer,
+        make_install_req: InstallRequirementProvider,
+        wheel_cache: Optional[WheelCache],
+        use_user_site: bool,
+        force_reinstall: bool,
+        ignore_installed: bool,
+        ignore_requires_python: bool,
+        py_version_info: Optional[Tuple[int, ...]] = None,
+    ) -> None:
+        self._finder = finder
+        self.preparer = preparer
+        self._wheel_cache = wheel_cache
+        self._python_candidate = RequiresPythonCandidate(py_version_info)
+        self._make_install_req_from_spec = make_install_req
+        self._use_user_site = use_user_site
+        self._force_reinstall = force_reinstall
+        self._ignore_requires_python = ignore_requires_python
+
+        self._build_failures: Cache[InstallationError] = {}
+        self._link_candidate_cache: Cache[LinkCandidate] = {}
+        self._editable_candidate_cache: Cache[EditableCandidate] = {}
+        self._installed_candidate_cache: Dict[str, AlreadyInstalledCandidate] = {}
+        self._extras_candidate_cache: Dict[
+            Tuple[int, FrozenSet[NormalizedName]], ExtrasCandidate
+        ] = {}
+        self._supported_tags_cache = get_supported()
+
+        if not ignore_installed:
+            env = get_default_environment()
+            self._installed_dists = {
+                dist.canonical_name: dist
+                for dist in env.iter_installed_distributions(local_only=False)
+            }
+        else:
+            self._installed_dists = {}
+
+    @property
+    def force_reinstall(self) -> bool:
+        return self._force_reinstall
+
+    def _fail_if_link_is_unsupported_wheel(self, link: Link) -> None:
+        if not link.is_wheel:
+            return
+        wheel = Wheel(link.filename)
+        if wheel.supported(self._finder.target_python.get_unsorted_tags()):
+            return
+        msg = f"{link.filename} is not a supported wheel on this platform."
+        raise UnsupportedWheel(msg)
+
+    def _make_extras_candidate(
+        self,
+        base: BaseCandidate,
+        extras: FrozenSet[str],
+        *,
+        comes_from: Optional[InstallRequirement] = None,
+    ) -> ExtrasCandidate:
+        cache_key = (id(base), frozenset(canonicalize_name(e) for e in extras))
+        try:
+            candidate = self._extras_candidate_cache[cache_key]
+        except KeyError:
+            candidate = ExtrasCandidate(base, extras, comes_from=comes_from)
+            self._extras_candidate_cache[cache_key] = candidate
+        return candidate
+
+    def _make_candidate_from_dist(
+        self,
+        dist: BaseDistribution,
+        extras: FrozenSet[str],
+        template: InstallRequirement,
+    ) -> Candidate:
+        try:
+            base = self._installed_candidate_cache[dist.canonical_name]
+        except KeyError:
+            base = AlreadyInstalledCandidate(dist, template, factory=self)
+            self._installed_candidate_cache[dist.canonical_name] = base
+        if not extras:
+            return base
+        return self._make_extras_candidate(base, extras, comes_from=template)
+
+    def _make_candidate_from_link(
+        self,
+        link: Link,
+        extras: FrozenSet[str],
+        template: InstallRequirement,
+        name: Optional[NormalizedName],
+        version: Optional[Version],
+    ) -> Optional[Candidate]:
+        base: Optional[BaseCandidate] = self._make_base_candidate_from_link(
+            link, template, name, version
+        )
+        if not extras or base is None:
+            return base
+        return self._make_extras_candidate(base, extras, comes_from=template)
+
+    def _make_base_candidate_from_link(
+        self,
+        link: Link,
+        template: InstallRequirement,
+        name: Optional[NormalizedName],
+        version: Optional[Version],
+    ) -> Optional[BaseCandidate]:
+        # TODO: Check already installed candidate, and use it if the link and
+        # editable flag match.
+
+        if link in self._build_failures:
+            # We already tried this candidate before, and it does not build.
+            # Don't bother trying again.
+            return None
+
+        if template.editable:
+            if link not in self._editable_candidate_cache:
+                try:
+                    self._editable_candidate_cache[link] = EditableCandidate(
+                        link,
+                        template,
+                        factory=self,
+                        name=name,
+                        version=version,
+                    )
+                except (MetadataInconsistent, MetadataInvalid) as e:
+                    logger.info(
+                        "Discarding [blue underline]%s[/]: [yellow]%s[reset]",
+                        link,
+                        e,
+                        extra={"markup": True},
+                    )
+                    self._build_failures[link] = e
+                    return None
+
+            return self._editable_candidate_cache[link]
+        else:
+            if link not in self._link_candidate_cache:
+                try:
+                    self._link_candidate_cache[link] = LinkCandidate(
+                        link,
+                        template,
+                        factory=self,
+                        name=name,
+                        version=version,
+                    )
+                except MetadataInconsistent as e:
+                    logger.info(
+                        "Discarding [blue underline]%s[/]: [yellow]%s[reset]",
+                        link,
+                        e,
+                        extra={"markup": True},
+                    )
+                    self._build_failures[link] = e
+                    return None
+            return self._link_candidate_cache[link]
+
+    def _iter_found_candidates(
+        self,
+        ireqs: Sequence[InstallRequirement],
+        specifier: SpecifierSet,
+        hashes: Hashes,
+        prefers_installed: bool,
+        incompatible_ids: Set[int],
+    ) -> Iterable[Candidate]:
+        if not ireqs:
+            return ()
+
+        # The InstallRequirement implementation requires us to give it a
+        # "template". Here we just choose the first requirement to represent
+        # all of them.
+        # Hopefully the Project model can correct this mismatch in the future.
+        template = ireqs[0]
+        assert template.req, "Candidates found on index must be PEP 508"
+        name = canonicalize_name(template.req.name)
+
+        extras: FrozenSet[str] = frozenset()
+        for ireq in ireqs:
+            assert ireq.req, "Candidates found on index must be PEP 508"
+            specifier &= ireq.req.specifier
+            hashes &= ireq.hashes(trust_internet=False)
+            extras |= frozenset(ireq.extras)
+
+        def _get_installed_candidate() -> Optional[Candidate]:
+            """Get the candidate for the currently-installed version."""
+            # If --force-reinstall is set, we want the version from the index
+            # instead, so we "pretend" there is nothing installed.
+            if self._force_reinstall:
+                return None
+            try:
+                installed_dist = self._installed_dists[name]
+            except KeyError:
+                return None
+
+            try:
+                # Don't use the installed distribution if its version
+                # does not fit the current dependency graph.
+                if not specifier.contains(installed_dist.version, prereleases=True):
+                    return None
+            except InvalidVersion as e:
+                raise InvalidInstalledPackage(dist=installed_dist, invalid_exc=e)
+
+            candidate = self._make_candidate_from_dist(
+                dist=installed_dist,
+                extras=extras,
+                template=template,
+            )
+            # The candidate is a known incompatibility. Don't use it.
+            if id(candidate) in incompatible_ids:
+                return None
+            return candidate
+
+        def iter_index_candidate_infos() -> Iterator[IndexCandidateInfo]:
+            result = self._finder.find_best_candidate(
+                project_name=name,
+                specifier=specifier,
+                hashes=hashes,
+            )
+            icans = list(result.iter_applicable())
+
+            # PEP 592: Yanked releases are ignored unless the specifier
+            # explicitly pins a version (via '==' or '===') that can be
+            # solely satisfied by a yanked release.
+            all_yanked = all(ican.link.is_yanked for ican in icans)
+
+            def is_pinned(specifier: SpecifierSet) -> bool:
+                for sp in specifier:
+                    if sp.operator == "===":
+                        return True
+                    if sp.operator != "==":
+                        continue
+                    if sp.version.endswith(".*"):
+                        continue
+                    return True
+                return False
+
+            pinned = is_pinned(specifier)
+
+            # PackageFinder returns earlier versions first, so we reverse.
+            for ican in reversed(icans):
+                if not (all_yanked and pinned) and ican.link.is_yanked:
+                    continue
+                func = functools.partial(
+                    self._make_candidate_from_link,
+                    link=ican.link,
+                    extras=extras,
+                    template=template,
+                    name=name,
+                    version=ican.version,
+                )
+                yield ican.version, func
+
+        return FoundCandidates(
+            iter_index_candidate_infos,
+            _get_installed_candidate(),
+            prefers_installed,
+            incompatible_ids,
+        )
+
+    def _iter_explicit_candidates_from_base(
+        self,
+        base_requirements: Iterable[Requirement],
+        extras: FrozenSet[str],
+    ) -> Iterator[Candidate]:
+        """Produce explicit candidates from the base given an extra-ed package.
+
+        :param base_requirements: Requirements known to the resolver. The
+            requirements are guaranteed to not have extras.
+        :param extras: The extras to inject into the explicit requirements'
+            candidates.
+        """
+        for req in base_requirements:
+            lookup_cand, _ = req.get_candidate_lookup()
+            if lookup_cand is None:  # Not explicit.
+                continue
+            # We've stripped extras from the identifier, and should always
+            # get a BaseCandidate here, unless there's a bug elsewhere.
+            base_cand = as_base_candidate(lookup_cand)
+            assert base_cand is not None, "no extras here"
+            yield self._make_extras_candidate(base_cand, extras)
+
+    def _iter_candidates_from_constraints(
+        self,
+        identifier: str,
+        constraint: Constraint,
+        template: InstallRequirement,
+    ) -> Iterator[Candidate]:
+        """Produce explicit candidates from constraints.
+
+        This creates "fake" InstallRequirement objects that are basically clones
+        of what "should" be the template, but with original_link set to link.
+        """
+        for link in constraint.links:
+            self._fail_if_link_is_unsupported_wheel(link)
+            candidate = self._make_base_candidate_from_link(
+                link,
+                template=install_req_from_link_and_ireq(link, template),
+                name=canonicalize_name(identifier),
+                version=None,
+            )
+            if candidate:
+                yield candidate
+
+    def find_candidates(
+        self,
+        identifier: str,
+        requirements: Mapping[str, Iterable[Requirement]],
+        incompatibilities: Mapping[str, Iterator[Candidate]],
+        constraint: Constraint,
+        prefers_installed: bool,
+        is_satisfied_by: Callable[[Requirement, Candidate], bool],
+    ) -> Iterable[Candidate]:
+        # Collect basic lookup information from the requirements.
+        explicit_candidates: Set[Candidate] = set()
+        ireqs: List[InstallRequirement] = []
+        for req in requirements[identifier]:
+            cand, ireq = req.get_candidate_lookup()
+            if cand is not None:
+                explicit_candidates.add(cand)
+            if ireq is not None:
+                ireqs.append(ireq)
+
+        # If the current identifier contains extras, add requires and explicit
+        # candidates from entries from extra-less identifier.
+        with contextlib.suppress(InvalidRequirement):
+            parsed_requirement = get_requirement(identifier)
+            if parsed_requirement.name != identifier:
+                explicit_candidates.update(
+                    self._iter_explicit_candidates_from_base(
+                        requirements.get(parsed_requirement.name, ()),
+                        frozenset(parsed_requirement.extras),
+                    ),
+                )
+                for req in requirements.get(parsed_requirement.name, []):
+                    _, ireq = req.get_candidate_lookup()
+                    if ireq is not None:
+                        ireqs.append(ireq)
+
+        # Add explicit candidates from constraints. We only do this if there are
+        # known ireqs, which represent requirements not already explicit. If
+        # there are no ireqs, we're constraining already-explicit requirements,
+        # which is handled later when we return the explicit candidates.
+        if ireqs:
+            try:
+                explicit_candidates.update(
+                    self._iter_candidates_from_constraints(
+                        identifier,
+                        constraint,
+                        template=ireqs[0],
+                    ),
+                )
+            except UnsupportedWheel:
+                # If we're constrained to install a wheel incompatible with the
+                # target architecture, no candidates will ever be valid.
+                return ()
+
+        # Since we cache all the candidates, incompatibility identification
+        # can be made quicker by comparing only the id() values.
+        incompat_ids = {id(c) for c in incompatibilities.get(identifier, ())}
+
+        # If none of the requirements want an explicit candidate, we can ask
+        # the finder for candidates.
+        if not explicit_candidates:
+            return self._iter_found_candidates(
+                ireqs,
+                constraint.specifier,
+                constraint.hashes,
+                prefers_installed,
+                incompat_ids,
+            )
+
+        return (
+            c
+            for c in explicit_candidates
+            if id(c) not in incompat_ids
+            and constraint.is_satisfied_by(c)
+            and all(is_satisfied_by(req, c) for req in requirements[identifier])
+        )
+
+    def _make_requirements_from_install_req(
+        self, ireq: InstallRequirement, requested_extras: Iterable[str]
+    ) -> Iterator[Requirement]:
+        """
+        Returns requirement objects associated with the given InstallRequirement. In
+        most cases this will be a single object but the following special cases exist:
+            - the InstallRequirement has markers that do not apply -> result is empty
+            - the InstallRequirement has both a constraint (or link) and extras
+                -> result is split in two requirement objects: one with the constraint
+                (or link) and one with the extra. This allows centralized constraint
+                handling for the base, resulting in fewer candidate rejections.
+        """
+        if not ireq.match_markers(requested_extras):
+            logger.info(
+                "Ignoring %s: markers '%s' don't match your environment",
+                ireq.name,
+                ireq.markers,
+            )
+        elif not ireq.link:
+            if ireq.extras and ireq.req is not None and ireq.req.specifier:
+                yield SpecifierWithoutExtrasRequirement(ireq)
+            yield SpecifierRequirement(ireq)
+        else:
+            self._fail_if_link_is_unsupported_wheel(ireq.link)
+            # Always make the link candidate for the base requirement to make it
+            # available to `find_candidates` for explicit candidate lookup for any
+            # set of extras.
+            # The extras are required separately via a second requirement.
+            cand = self._make_base_candidate_from_link(
+                ireq.link,
+                template=install_req_drop_extras(ireq) if ireq.extras else ireq,
+                name=canonicalize_name(ireq.name) if ireq.name else None,
+                version=None,
+            )
+            if cand is None:
+                # There's no way we can satisfy a URL requirement if the underlying
+                # candidate fails to build. An unnamed URL must be user-supplied, so
+                # we fail eagerly. If the URL is named, an unsatisfiable requirement
+                # can make the resolver do the right thing, either backtrack (and
+                # maybe find some other requirement that's buildable) or raise a
+                # ResolutionImpossible eventually.
+                if not ireq.name:
+                    raise self._build_failures[ireq.link]
+                yield UnsatisfiableRequirement(canonicalize_name(ireq.name))
+            else:
+                # require the base from the link
+                yield self.make_requirement_from_candidate(cand)
+                if ireq.extras:
+                    # require the extras on top of the base candidate
+                    yield self.make_requirement_from_candidate(
+                        self._make_extras_candidate(cand, frozenset(ireq.extras))
+                    )
+
+    def collect_root_requirements(
+        self, root_ireqs: List[InstallRequirement]
+    ) -> CollectedRootRequirements:
+        collected = CollectedRootRequirements([], {}, {})
+        for i, ireq in enumerate(root_ireqs):
+            if ireq.constraint:
+                # Ensure we only accept valid constraints
+                problem = check_invalid_constraint_type(ireq)
+                if problem:
+                    raise InstallationError(problem)
+                if not ireq.match_markers():
+                    continue
+                assert ireq.name, "Constraint must be named"
+                name = canonicalize_name(ireq.name)
+                if name in collected.constraints:
+                    collected.constraints[name] &= ireq
+                else:
+                    collected.constraints[name] = Constraint.from_ireq(ireq)
+            else:
+                reqs = list(
+                    self._make_requirements_from_install_req(
+                        ireq,
+                        requested_extras=(),
+                    )
+                )
+                if not reqs:
+                    continue
+                template = reqs[0]
+                if ireq.user_supplied and template.name not in collected.user_requested:
+                    collected.user_requested[template.name] = i
+                collected.requirements.extend(reqs)
+        # Put requirements with extras at the end of the root requires. This does not
+        # affect resolvelib's picking preference but it does affect its initial criteria
+        # population: by putting extras at the end we enable the candidate finder to
+        # present resolvelib with a smaller set of candidates to resolvelib, already
+        # taking into account any non-transient constraints on the associated base. This
+        # means resolvelib will have fewer candidates to visit and reject.
+        # Python's list sort is stable, meaning relative order is kept for objects with
+        # the same key.
+        collected.requirements.sort(key=lambda r: r.name != r.project_name)
+        return collected
+
+    def make_requirement_from_candidate(
+        self, candidate: Candidate
+    ) -> ExplicitRequirement:
+        return ExplicitRequirement(candidate)
+
+    def make_requirements_from_spec(
+        self,
+        specifier: str,
+        comes_from: Optional[InstallRequirement],
+        requested_extras: Iterable[str] = (),
+    ) -> Iterator[Requirement]:
+        """
+        Returns requirement objects associated with the given specifier. In most cases
+        this will be a single object but the following special cases exist:
+            - the specifier has markers that do not apply -> result is empty
+            - the specifier has both a constraint and extras -> result is split
+                in two requirement objects: one with the constraint and one with the
+                extra. This allows centralized constraint handling for the base,
+                resulting in fewer candidate rejections.
+        """
+        ireq = self._make_install_req_from_spec(specifier, comes_from)
+        return self._make_requirements_from_install_req(ireq, requested_extras)
+
+    def make_requires_python_requirement(
+        self,
+        specifier: SpecifierSet,
+    ) -> Optional[Requirement]:
+        if self._ignore_requires_python:
+            return None
+        # Don't bother creating a dependency for an empty Requires-Python.
+        if not str(specifier):
+            return None
+        return RequiresPythonRequirement(specifier, self._python_candidate)
+
+    def get_wheel_cache_entry(
+        self, link: Link, name: Optional[str]
+    ) -> Optional[CacheEntry]:
+        """Look up the link in the wheel cache.
+
+        If ``preparer.require_hashes`` is True, don't use the wheel cache,
+        because cached wheels, always built locally, have different hashes
+        than the files downloaded from the index server and thus throw false
+        hash mismatches. Furthermore, cached wheels at present have
+        nondeterministic contents due to file modification times.
+        """
+        if self._wheel_cache is None:
+            return None
+        return self._wheel_cache.get_cache_entry(
+            link=link,
+            package_name=name,
+            supported_tags=self._supported_tags_cache,
+        )
+
+    def get_dist_to_uninstall(self, candidate: Candidate) -> Optional[BaseDistribution]:
+        # TODO: Are there more cases this needs to return True? Editable?
+        dist = self._installed_dists.get(candidate.project_name)
+        if dist is None:  # Not installed, no uninstallation required.
+            return None
+
+        # We're installing into global site. The current installation must
+        # be uninstalled, no matter it's in global or user site, because the
+        # user site installation has precedence over global.
+        if not self._use_user_site:
+            return dist
+
+        # We're installing into user site. Remove the user site installation.
+        if dist.in_usersite:
+            return dist
+
+        # We're installing into user site, but the installed incompatible
+        # package is in global site. We can't uninstall that, and would let
+        # the new user installation to "shadow" it. But shadowing won't work
+        # in virtual environments, so we error out.
+        if running_under_virtualenv() and dist.in_site_packages:
+            message = (
+                f"Will not install to the user site because it will lack "
+                f"sys.path precedence to {dist.raw_name} in {dist.location}"
+            )
+            raise InstallationError(message)
+        return None
+
+    def _report_requires_python_error(
+        self, causes: Sequence["ConflictCause"]
+    ) -> UnsupportedPythonVersion:
+        assert causes, "Requires-Python error reported with no cause"
+
+        version = self._python_candidate.version
+
+        if len(causes) == 1:
+            specifier = str(causes[0].requirement.specifier)
+            message = (
+                f"Package {causes[0].parent.name!r} requires a different "
+                f"Python: {version} not in {specifier!r}"
+            )
+            return UnsupportedPythonVersion(message)
+
+        message = f"Packages require a different Python. {version} not in:"
+        for cause in causes:
+            package = cause.parent.format_for_error()
+            specifier = str(cause.requirement.specifier)
+            message += f"\n{specifier!r} (required by {package})"
+        return UnsupportedPythonVersion(message)
+
+    def _report_single_requirement_conflict(
+        self, req: Requirement, parent: Optional[Candidate]
+    ) -> DistributionNotFound:
+        if parent is None:
+            req_disp = str(req)
+        else:
+            req_disp = f"{req} (from {parent.name})"
+
+        cands = self._finder.find_all_candidates(req.project_name)
+        skipped_by_requires_python = self._finder.requires_python_skipped_reasons()
+
+        versions_set: Set[Version] = set()
+        yanked_versions_set: Set[Version] = set()
+        for c in cands:
+            is_yanked = c.link.is_yanked if c.link else False
+            if is_yanked:
+                yanked_versions_set.add(c.version)
+            else:
+                versions_set.add(c.version)
+
+        versions = [str(v) for v in sorted(versions_set)]
+        yanked_versions = [str(v) for v in sorted(yanked_versions_set)]
+
+        if yanked_versions:
+            # Saying "version X is yanked" isn't entirely accurate.
+            # https://github.com/pypa/pip/issues/11745#issuecomment-1402805842
+            logger.critical(
+                "Ignored the following yanked versions: %s",
+                ", ".join(yanked_versions) or "none",
+            )
+        if skipped_by_requires_python:
+            logger.critical(
+                "Ignored the following versions that require a different python "
+                "version: %s",
+                "; ".join(skipped_by_requires_python) or "none",
+            )
+        logger.critical(
+            "Could not find a version that satisfies the requirement %s "
+            "(from versions: %s)",
+            req_disp,
+            ", ".join(versions) or "none",
+        )
+        if str(req) == "requirements.txt":
+            logger.info(
+                "HINT: You are attempting to install a package literally "
+                'named "requirements.txt" (which cannot exist). Consider '
+                "using the '-r' flag to install the packages listed in "
+                "requirements.txt"
+            )
+
+        return DistributionNotFound(f"No matching distribution found for {req}")
+
+    def get_installation_error(
+        self,
+        e: "ResolutionImpossible[Requirement, Candidate]",
+        constraints: Dict[str, Constraint],
+    ) -> InstallationError:
+        assert e.causes, "Installation error reported with no cause"
+
+        # If one of the things we can't solve is "we need Python X.Y",
+        # that is what we report.
+        requires_python_causes = [
+            cause
+            for cause in e.causes
+            if isinstance(cause.requirement, RequiresPythonRequirement)
+            and not cause.requirement.is_satisfied_by(self._python_candidate)
+        ]
+        if requires_python_causes:
+            # The comprehension above makes sure all Requirement instances are
+            # RequiresPythonRequirement, so let's cast for convenience.
+            return self._report_requires_python_error(
+                cast("Sequence[ConflictCause]", requires_python_causes),
+            )
+
+        # Otherwise, we have a set of causes which can't all be satisfied
+        # at once.
+
+        # The simplest case is when we have *one* cause that can't be
+        # satisfied. We just report that case.
+        if len(e.causes) == 1:
+            req, parent = e.causes[0]
+            if req.name not in constraints:
+                return self._report_single_requirement_conflict(req, parent)
+
+        # OK, we now have a list of requirements that can't all be
+        # satisfied at once.
+
+        # A couple of formatting helpers
+        def text_join(parts: List[str]) -> str:
+            if len(parts) == 1:
+                return parts[0]
+
+            return ", ".join(parts[:-1]) + " and " + parts[-1]
+
+        def describe_trigger(parent: Candidate) -> str:
+            ireq = parent.get_install_requirement()
+            if not ireq or not ireq.comes_from:
+                return f"{parent.name}=={parent.version}"
+            if isinstance(ireq.comes_from, InstallRequirement):
+                return str(ireq.comes_from.name)
+            return str(ireq.comes_from)
+
+        triggers = set()
+        for req, parent in e.causes:
+            if parent is None:
+                # This is a root requirement, so we can report it directly
+                trigger = req.format_for_error()
+            else:
+                trigger = describe_trigger(parent)
+            triggers.add(trigger)
+
+        if triggers:
+            info = text_join(sorted(triggers))
+        else:
+            info = "the requested packages"
+
+        msg = (
+            f"Cannot install {info} because these package versions "
+            "have conflicting dependencies."
+        )
+        logger.critical(msg)
+        msg = "\nThe conflict is caused by:"
+
+        relevant_constraints = set()
+        for req, parent in e.causes:
+            if req.name in constraints:
+                relevant_constraints.add(req.name)
+            msg = msg + "\n    "
+            if parent:
+                msg = msg + f"{parent.name} {parent.version} depends on "
+            else:
+                msg = msg + "The user requested "
+            msg = msg + req.format_for_error()
+        for key in relevant_constraints:
+            spec = constraints[key].specifier
+            msg += f"\n    The user requested (constraint) {key}{spec}"
+
+        msg = (
+            msg
+            + "\n\n"
+            + "To fix this you could try to:\n"
+            + "1. loosen the range of package versions you've specified\n"
+            + "2. remove package versions to allow pip to attempt to solve "
+            + "the dependency conflict\n"
+        )
+
+        logger.info(msg)
+
+        return DistributionNotFound(
+            "ResolutionImpossible: for help visit "
+            "https://pip.pypa.io/en/latest/topics/dependency-resolution/"
+            "#dealing-with-dependency-conflicts"
+        )
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/found_candidates.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/found_candidates.py
new file mode 100644
index 0000000000000000000000000000000000000000..a1d57e0f4b275cd5783c950381ddfff0184da138
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/resolution/resolvelib/found_candidates.py
@@ -0,0 +1,174 @@
+"""Utilities to lazily create and visit candidates found.
+
+Creating and visiting a candidate is a *very* costly operation. It involves
+fetching, extracting, potentially building modules from source, and verifying
+distribution metadata. It is therefore crucial for performance to keep
+everything here lazy all the way down, so we only touch candidates that we
+absolutely need, and not "download the world" when we only need one version of
+something.
+"""
+
+import functools
+import logging
+from collections.abc import Sequence
+from typing import TYPE_CHECKING, Any, Callable, Iterator, Optional, Set, Tuple
+
+from pip._vendor.packaging.version import _BaseVersion
+
+from pip._internal.exceptions import MetadataInvalid
+
+from .base import Candidate
+
+logger = logging.getLogger(__name__)
+
+IndexCandidateInfo = Tuple[_BaseVersion, Callable[[], Optional[Candidate]]]
+
+if TYPE_CHECKING:
+    SequenceCandidate = Sequence[Candidate]
+else:
+    # For compatibility: Python before 3.9 does not support using [] on the
+    # Sequence class.
+    #
+    # >>> from collections.abc import Sequence
+    # >>> Sequence[str]
+    # Traceback (most recent call last):
+    #   File "<stdin>", line 1, in <module>
+    # TypeError: 'ABCMeta' object is not subscriptable
+    #
+    # TODO: Remove this block after dropping Python 3.8 support.
+    SequenceCandidate = Sequence
+
+
+def _iter_built(infos: Iterator[IndexCandidateInfo]) -> Iterator[Candidate]:
+    """Iterator for ``FoundCandidates``.
+
+    This iterator is used when the package is not already installed. Candidates
+    from index come later in their normal ordering.
+    """
+    versions_found: Set[_BaseVersion] = set()
+    for version, func in infos:
+        if version in versions_found:
+            continue
+        try:
+            candidate = func()
+        except MetadataInvalid as e:
+            logger.warning(
+                "Ignoring version %s of %s since it has invalid metadata:\n"
+                "%s\n"
+                "Please use pip<24.1 if you need to use this version.",
+                version,
+                e.ireq.name,
+                e,
+            )
+            # Mark version as found to avoid trying other candidates with the same
+            # version, since they most likely have invalid metadata as well.
+            versions_found.add(version)
+        else:
+            if candidate is None:
+                continue
+            yield candidate
+            versions_found.add(version)
+
+
+def _iter_built_with_prepended(
+    installed: Candidate, infos: Iterator[IndexCandidateInfo]
+) -> Iterator[Candidate]:
+    """Iterator for ``FoundCandidates``.
+
+    This iterator is used when the resolver prefers the already-installed
+    candidate and NOT to upgrade. The installed candidate is therefore
+    always yielded first, and candidates from index come later in their
+    normal ordering, except skipped when the version is already installed.
+    """
+    yield installed
+    versions_found: Set[_BaseVersion] = {installed.version}
+    for version, func in infos:
+        if version in versions_found:
+            continue
+        candidate = func()
+        if candidate is None:
+            continue
+        yield candidate
+        versions_found.add(version)
+
+
+def _iter_built_with_inserted(
+    installed: Candidate, infos: Iterator[IndexCandidateInfo]
+) -> Iterator[Candidate]:
+    """Iterator for ``FoundCandidates``.
+
+    This iterator is used when the resolver prefers to upgrade an
+    already-installed package. Candidates from index are returned in their
+    normal ordering, except replaced when the version is already installed.
+
+    The implementation iterates through and yields other candidates, inserting
+    the installed candidate exactly once before we start yielding older or
+    equivalent candidates, or after all other candidates if they are all newer.
+    """
+    versions_found: Set[_BaseVersion] = set()
+    for version, func in infos:
+        if version in versions_found:
+            continue
+        # If the installed candidate is better, yield it first.
+        if installed.version >= version:
+            yield installed
+            versions_found.add(installed.version)
+        candidate = func()
+        if candidate is None:
+            continue
+        yield candidate
+        versions_found.add(version)
+
+    # If the installed candidate is older than all other candidates.
+    if installed.version not in versions_found:
+        yield installed
+
+
+class FoundCandidates(SequenceCandidate):
+    """A lazy sequence to provide candidates to the resolver.
+
+    The intended usage is to return this from `find_matches()` so the resolver
+    can iterate through the sequence multiple times, but only access the index
+    page when remote packages are actually needed. This improve performances
+    when suitable candidates are already installed on disk.
+    """
+
+    def __init__(
+        self,
+        get_infos: Callable[[], Iterator[IndexCandidateInfo]],
+        installed: Optional[Candidate],
+        prefers_installed: bool,
+        incompatible_ids: Set[int],
+    ):
+        self._get_infos = get_infos
+        self._installed = installed
+        self._prefers_installed = prefers_installed
+        self._incompatible_ids = incompatible_ids
+
+    def __getitem__(self, index: Any) -> Any:
+        # Implemented to satisfy the ABC check. This is not needed by the
+        # resolver, and should not be used by the provider either (for
+        # performance reasons).
+        raise NotImplementedError("don't do this")
+
+    def __iter__(self) -> Iterator[Candidate]:
+        infos = self._get_infos()
+        if not self._installed:
+            iterator = _iter_built(infos)
+        elif self._prefers_installed:
+            iterator = _iter_built_with_prepended(self._installed, infos)
+        else:
+            iterator = _iter_built_with_inserted(self._installed, infos)
+        return (c for c in iterator if id(c) not in self._incompatible_ids)
+
+    def __len__(self) -> int:
+        # Implemented to satisfy the ABC check. This is not needed by the
+        # resolver, and should not be used by the provider either (for
+        # performance reasons).
+        raise NotImplementedError("don't do this")
+
+    @functools.lru_cache(maxsize=1)
+    def __bool__(self) -> bool:
+        if self._prefers_installed and self._installed:
+            return True
+        return any(self)
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diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/_log.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/_log.py
new file mode 100644
index 0000000000000000000000000000000000000000..92c4c6a193873ce09629f6cfaa2dabc4f14ecb03
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/_log.py
@@ -0,0 +1,38 @@
+"""Customize logging
+
+Defines custom logger class for the `logger.verbose(...)` method.
+
+init_logging() must be called before any other modules that call logging.getLogger.
+"""
+
+import logging
+from typing import Any, cast
+
+# custom log level for `--verbose` output
+# between DEBUG and INFO
+VERBOSE = 15
+
+
+class VerboseLogger(logging.Logger):
+    """Custom Logger, defining a verbose log-level
+
+    VERBOSE is between INFO and DEBUG.
+    """
+
+    def verbose(self, msg: str, *args: Any, **kwargs: Any) -> None:
+        return self.log(VERBOSE, msg, *args, **kwargs)
+
+
+def getLogger(name: str) -> VerboseLogger:
+    """logging.getLogger, but ensures our VerboseLogger class is returned"""
+    return cast(VerboseLogger, logging.getLogger(name))
+
+
+def init_logging() -> None:
+    """Register our VerboseLogger and VERBOSE log level.
+
+    Should be called before any calls to getLogger(),
+    i.e. in pip._internal.__init__
+    """
+    logging.setLoggerClass(VerboseLogger)
+    logging.addLevelName(VERBOSE, "VERBOSE")
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/filetypes.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/filetypes.py
new file mode 100644
index 0000000000000000000000000000000000000000..5948570178f3e6e79d1ff574241d09d4d8ed78de
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/filetypes.py
@@ -0,0 +1,27 @@
+"""Filetype information.
+"""
+
+from typing import Tuple
+
+from pip._internal.utils.misc import splitext
+
+WHEEL_EXTENSION = ".whl"
+BZ2_EXTENSIONS: Tuple[str, ...] = (".tar.bz2", ".tbz")
+XZ_EXTENSIONS: Tuple[str, ...] = (
+    ".tar.xz",
+    ".txz",
+    ".tlz",
+    ".tar.lz",
+    ".tar.lzma",
+)
+ZIP_EXTENSIONS: Tuple[str, ...] = (".zip", WHEEL_EXTENSION)
+TAR_EXTENSIONS: Tuple[str, ...] = (".tar.gz", ".tgz", ".tar")
+ARCHIVE_EXTENSIONS = ZIP_EXTENSIONS + BZ2_EXTENSIONS + TAR_EXTENSIONS + XZ_EXTENSIONS
+
+
+def is_archive_file(name: str) -> bool:
+    """Return True if `name` is a considered as an archive file."""
+    ext = splitext(name)[1].lower()
+    if ext in ARCHIVE_EXTENSIONS:
+        return True
+    return False
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/misc.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/misc.py
new file mode 100644
index 0000000000000000000000000000000000000000..c0a3e4d3b9d221570b11ce0e2b64a3bbbf18cf7f
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/misc.py
@@ -0,0 +1,772 @@
+import errno
+import getpass
+import hashlib
+import logging
+import os
+import posixpath
+import shutil
+import stat
+import sys
+import sysconfig
+import urllib.parse
+from dataclasses import dataclass
+from functools import partial
+from io import StringIO
+from itertools import filterfalse, tee, zip_longest
+from pathlib import Path
+from types import FunctionType, TracebackType
+from typing import (
+    Any,
+    BinaryIO,
+    Callable,
+    Dict,
+    Generator,
+    Iterable,
+    Iterator,
+    List,
+    Optional,
+    TextIO,
+    Tuple,
+    Type,
+    TypeVar,
+    Union,
+    cast,
+)
+
+from pip._vendor.packaging.requirements import Requirement
+from pip._vendor.pyproject_hooks import BuildBackendHookCaller
+
+from pip import __version__
+from pip._internal.exceptions import CommandError, ExternallyManagedEnvironment
+from pip._internal.locations import get_major_minor_version
+from pip._internal.utils.compat import WINDOWS
+from pip._internal.utils.retry import retry
+from pip._internal.utils.virtualenv import running_under_virtualenv
+
+__all__ = [
+    "rmtree",
+    "display_path",
+    "backup_dir",
+    "ask",
+    "splitext",
+    "format_size",
+    "is_installable_dir",
+    "normalize_path",
+    "renames",
+    "get_prog",
+    "ensure_dir",
+    "remove_auth_from_url",
+    "check_externally_managed",
+    "ConfiguredBuildBackendHookCaller",
+]
+
+logger = logging.getLogger(__name__)
+
+T = TypeVar("T")
+ExcInfo = Tuple[Type[BaseException], BaseException, TracebackType]
+VersionInfo = Tuple[int, int, int]
+NetlocTuple = Tuple[str, Tuple[Optional[str], Optional[str]]]
+OnExc = Callable[[FunctionType, Path, BaseException], Any]
+OnErr = Callable[[FunctionType, Path, ExcInfo], Any]
+
+FILE_CHUNK_SIZE = 1024 * 1024
+
+
+def get_pip_version() -> str:
+    pip_pkg_dir = os.path.join(os.path.dirname(__file__), "..", "..")
+    pip_pkg_dir = os.path.abspath(pip_pkg_dir)
+
+    return f"pip {__version__} from {pip_pkg_dir} (python {get_major_minor_version()})"
+
+
+def normalize_version_info(py_version_info: Tuple[int, ...]) -> Tuple[int, int, int]:
+    """
+    Convert a tuple of ints representing a Python version to one of length
+    three.
+
+    :param py_version_info: a tuple of ints representing a Python version,
+        or None to specify no version. The tuple can have any length.
+
+    :return: a tuple of length three if `py_version_info` is non-None.
+        Otherwise, return `py_version_info` unchanged (i.e. None).
+    """
+    if len(py_version_info) < 3:
+        py_version_info += (3 - len(py_version_info)) * (0,)
+    elif len(py_version_info) > 3:
+        py_version_info = py_version_info[:3]
+
+    return cast("VersionInfo", py_version_info)
+
+
+def ensure_dir(path: str) -> None:
+    """os.path.makedirs without EEXIST."""
+    try:
+        os.makedirs(path)
+    except OSError as e:
+        # Windows can raise spurious ENOTEMPTY errors. See #6426.
+        if e.errno != errno.EEXIST and e.errno != errno.ENOTEMPTY:
+            raise
+
+
+def get_prog() -> str:
+    try:
+        prog = os.path.basename(sys.argv[0])
+        if prog in ("__main__.py", "-c"):
+            return f"{sys.executable} -m pip"
+        else:
+            return prog
+    except (AttributeError, TypeError, IndexError):
+        pass
+    return "pip"
+
+
+# Retry every half second for up to 3 seconds
+@retry(stop_after_delay=3, wait=0.5)
+def rmtree(
+    dir: str, ignore_errors: bool = False, onexc: Optional[OnExc] = None
+) -> None:
+    if ignore_errors:
+        onexc = _onerror_ignore
+    if onexc is None:
+        onexc = _onerror_reraise
+    handler: OnErr = partial(rmtree_errorhandler, onexc=onexc)
+    if sys.version_info >= (3, 12):
+        # See https://docs.python.org/3.12/whatsnew/3.12.html#shutil.
+        shutil.rmtree(dir, onexc=handler)  # type: ignore
+    else:
+        shutil.rmtree(dir, onerror=handler)  # type: ignore
+
+
+def _onerror_ignore(*_args: Any) -> None:
+    pass
+
+
+def _onerror_reraise(*_args: Any) -> None:
+    raise  # noqa: PLE0704 - Bare exception used to reraise existing exception
+
+
+def rmtree_errorhandler(
+    func: FunctionType,
+    path: Path,
+    exc_info: Union[ExcInfo, BaseException],
+    *,
+    onexc: OnExc = _onerror_reraise,
+) -> None:
+    """
+    `rmtree` error handler to 'force' a file remove (i.e. like `rm -f`).
+
+    * If a file is readonly then it's write flag is set and operation is
+      retried.
+
+    * `onerror` is the original callback from `rmtree(... onerror=onerror)`
+      that is chained at the end if the "rm -f" still fails.
+    """
+    try:
+        st_mode = os.stat(path).st_mode
+    except OSError:
+        # it's equivalent to os.path.exists
+        return
+
+    if not st_mode & stat.S_IWRITE:
+        # convert to read/write
+        try:
+            os.chmod(path, st_mode | stat.S_IWRITE)
+        except OSError:
+            pass
+        else:
+            # use the original function to repeat the operation
+            try:
+                func(path)
+                return
+            except OSError:
+                pass
+
+    if not isinstance(exc_info, BaseException):
+        _, exc_info, _ = exc_info
+    onexc(func, path, exc_info)
+
+
+def display_path(path: str) -> str:
+    """Gives the display value for a given path, making it relative to cwd
+    if possible."""
+    path = os.path.normcase(os.path.abspath(path))
+    if path.startswith(os.getcwd() + os.path.sep):
+        path = "." + path[len(os.getcwd()) :]
+    return path
+
+
+def backup_dir(dir: str, ext: str = ".bak") -> str:
+    """Figure out the name of a directory to back up the given dir to
+    (adding .bak, .bak2, etc)"""
+    n = 1
+    extension = ext
+    while os.path.exists(dir + extension):
+        n += 1
+        extension = ext + str(n)
+    return dir + extension
+
+
+def ask_path_exists(message: str, options: Iterable[str]) -> str:
+    for action in os.environ.get("PIP_EXISTS_ACTION", "").split():
+        if action in options:
+            return action
+    return ask(message, options)
+
+
+def _check_no_input(message: str) -> None:
+    """Raise an error if no input is allowed."""
+    if os.environ.get("PIP_NO_INPUT"):
+        raise Exception(
+            f"No input was expected ($PIP_NO_INPUT set); question: {message}"
+        )
+
+
+def ask(message: str, options: Iterable[str]) -> str:
+    """Ask the message interactively, with the given possible responses"""
+    while 1:
+        _check_no_input(message)
+        response = input(message)
+        response = response.strip().lower()
+        if response not in options:
+            print(
+                "Your response ({!r}) was not one of the expected responses: "
+                "{}".format(response, ", ".join(options))
+            )
+        else:
+            return response
+
+
+def ask_input(message: str) -> str:
+    """Ask for input interactively."""
+    _check_no_input(message)
+    return input(message)
+
+
+def ask_password(message: str) -> str:
+    """Ask for a password interactively."""
+    _check_no_input(message)
+    return getpass.getpass(message)
+
+
+def strtobool(val: str) -> int:
+    """Convert a string representation of truth to true (1) or false (0).
+
+    True values are 'y', 'yes', 't', 'true', 'on', and '1'; false values
+    are 'n', 'no', 'f', 'false', 'off', and '0'.  Raises ValueError if
+    'val' is anything else.
+    """
+    val = val.lower()
+    if val in ("y", "yes", "t", "true", "on", "1"):
+        return 1
+    elif val in ("n", "no", "f", "false", "off", "0"):
+        return 0
+    else:
+        raise ValueError(f"invalid truth value {val!r}")
+
+
+def format_size(bytes: float) -> str:
+    if bytes > 1000 * 1000:
+        return f"{bytes / 1000.0 / 1000:.1f} MB"
+    elif bytes > 10 * 1000:
+        return f"{int(bytes / 1000)} kB"
+    elif bytes > 1000:
+        return f"{bytes / 1000.0:.1f} kB"
+    else:
+        return f"{int(bytes)} bytes"
+
+
+def tabulate(rows: Iterable[Iterable[Any]]) -> Tuple[List[str], List[int]]:
+    """Return a list of formatted rows and a list of column sizes.
+
+    For example::
+
+    >>> tabulate([['foobar', 2000], [0xdeadbeef]])
+    (['foobar     2000', '3735928559'], [10, 4])
+    """
+    rows = [tuple(map(str, row)) for row in rows]
+    sizes = [max(map(len, col)) for col in zip_longest(*rows, fillvalue="")]
+    table = [" ".join(map(str.ljust, row, sizes)).rstrip() for row in rows]
+    return table, sizes
+
+
+def is_installable_dir(path: str) -> bool:
+    """Is path is a directory containing pyproject.toml or setup.py?
+
+    If pyproject.toml exists, this is a PEP 517 project. Otherwise we look for
+    a legacy setuptools layout by identifying setup.py. We don't check for the
+    setup.cfg because using it without setup.py is only available for PEP 517
+    projects, which are already covered by the pyproject.toml check.
+    """
+    if not os.path.isdir(path):
+        return False
+    if os.path.isfile(os.path.join(path, "pyproject.toml")):
+        return True
+    if os.path.isfile(os.path.join(path, "setup.py")):
+        return True
+    return False
+
+
+def read_chunks(
+    file: BinaryIO, size: int = FILE_CHUNK_SIZE
+) -> Generator[bytes, None, None]:
+    """Yield pieces of data from a file-like object until EOF."""
+    while True:
+        chunk = file.read(size)
+        if not chunk:
+            break
+        yield chunk
+
+
+def normalize_path(path: str, resolve_symlinks: bool = True) -> str:
+    """
+    Convert a path to its canonical, case-normalized, absolute version.
+
+    """
+    path = os.path.expanduser(path)
+    if resolve_symlinks:
+        path = os.path.realpath(path)
+    else:
+        path = os.path.abspath(path)
+    return os.path.normcase(path)
+
+
+def splitext(path: str) -> Tuple[str, str]:
+    """Like os.path.splitext, but take off .tar too"""
+    base, ext = posixpath.splitext(path)
+    if base.lower().endswith(".tar"):
+        ext = base[-4:] + ext
+        base = base[:-4]
+    return base, ext
+
+
+def renames(old: str, new: str) -> None:
+    """Like os.renames(), but handles renaming across devices."""
+    # Implementation borrowed from os.renames().
+    head, tail = os.path.split(new)
+    if head and tail and not os.path.exists(head):
+        os.makedirs(head)
+
+    shutil.move(old, new)
+
+    head, tail = os.path.split(old)
+    if head and tail:
+        try:
+            os.removedirs(head)
+        except OSError:
+            pass
+
+
+def is_local(path: str) -> bool:
+    """
+    Return True if path is within sys.prefix, if we're running in a virtualenv.
+
+    If we're not in a virtualenv, all paths are considered "local."
+
+    Caution: this function assumes the head of path has been normalized
+    with normalize_path.
+    """
+    if not running_under_virtualenv():
+        return True
+    return path.startswith(normalize_path(sys.prefix))
+
+
+def write_output(msg: Any, *args: Any) -> None:
+    logger.info(msg, *args)
+
+
+class StreamWrapper(StringIO):
+    orig_stream: TextIO
+
+    @classmethod
+    def from_stream(cls, orig_stream: TextIO) -> "StreamWrapper":
+        ret = cls()
+        ret.orig_stream = orig_stream
+        return ret
+
+    # compileall.compile_dir() needs stdout.encoding to print to stdout
+    # type ignore is because TextIOBase.encoding is writeable
+    @property
+    def encoding(self) -> str:  # type: ignore
+        return self.orig_stream.encoding
+
+
+# Simulates an enum
+def enum(*sequential: Any, **named: Any) -> Type[Any]:
+    enums = dict(zip(sequential, range(len(sequential))), **named)
+    reverse = {value: key for key, value in enums.items()}
+    enums["reverse_mapping"] = reverse
+    return type("Enum", (), enums)
+
+
+def build_netloc(host: str, port: Optional[int]) -> str:
+    """
+    Build a netloc from a host-port pair
+    """
+    if port is None:
+        return host
+    if ":" in host:
+        # Only wrap host with square brackets when it is IPv6
+        host = f"[{host}]"
+    return f"{host}:{port}"
+
+
+def build_url_from_netloc(netloc: str, scheme: str = "https") -> str:
+    """
+    Build a full URL from a netloc.
+    """
+    if netloc.count(":") >= 2 and "@" not in netloc and "[" not in netloc:
+        # It must be a bare IPv6 address, so wrap it with brackets.
+        netloc = f"[{netloc}]"
+    return f"{scheme}://{netloc}"
+
+
+def parse_netloc(netloc: str) -> Tuple[Optional[str], Optional[int]]:
+    """
+    Return the host-port pair from a netloc.
+    """
+    url = build_url_from_netloc(netloc)
+    parsed = urllib.parse.urlparse(url)
+    return parsed.hostname, parsed.port
+
+
+def split_auth_from_netloc(netloc: str) -> NetlocTuple:
+    """
+    Parse out and remove the auth information from a netloc.
+
+    Returns: (netloc, (username, password)).
+    """
+    if "@" not in netloc:
+        return netloc, (None, None)
+
+    # Split from the right because that's how urllib.parse.urlsplit()
+    # behaves if more than one @ is present (which can be checked using
+    # the password attribute of urlsplit()'s return value).
+    auth, netloc = netloc.rsplit("@", 1)
+    pw: Optional[str] = None
+    if ":" in auth:
+        # Split from the left because that's how urllib.parse.urlsplit()
+        # behaves if more than one : is present (which again can be checked
+        # using the password attribute of the return value)
+        user, pw = auth.split(":", 1)
+    else:
+        user, pw = auth, None
+
+    user = urllib.parse.unquote(user)
+    if pw is not None:
+        pw = urllib.parse.unquote(pw)
+
+    return netloc, (user, pw)
+
+
+def redact_netloc(netloc: str) -> str:
+    """
+    Replace the sensitive data in a netloc with "****", if it exists.
+
+    For example:
+        - "user:pass@example.com" returns "user:****@example.com"
+        - "accesstoken@example.com" returns "****@example.com"
+    """
+    netloc, (user, password) = split_auth_from_netloc(netloc)
+    if user is None:
+        return netloc
+    if password is None:
+        user = "****"
+        password = ""
+    else:
+        user = urllib.parse.quote(user)
+        password = ":****"
+    return f"{user}{password}@{netloc}"
+
+
+def _transform_url(
+    url: str, transform_netloc: Callable[[str], Tuple[Any, ...]]
+) -> Tuple[str, NetlocTuple]:
+    """Transform and replace netloc in a url.
+
+    transform_netloc is a function taking the netloc and returning a
+    tuple. The first element of this tuple is the new netloc. The
+    entire tuple is returned.
+
+    Returns a tuple containing the transformed url as item 0 and the
+    original tuple returned by transform_netloc as item 1.
+    """
+    purl = urllib.parse.urlsplit(url)
+    netloc_tuple = transform_netloc(purl.netloc)
+    # stripped url
+    url_pieces = (purl.scheme, netloc_tuple[0], purl.path, purl.query, purl.fragment)
+    surl = urllib.parse.urlunsplit(url_pieces)
+    return surl, cast("NetlocTuple", netloc_tuple)
+
+
+def _get_netloc(netloc: str) -> NetlocTuple:
+    return split_auth_from_netloc(netloc)
+
+
+def _redact_netloc(netloc: str) -> Tuple[str]:
+    return (redact_netloc(netloc),)
+
+
+def split_auth_netloc_from_url(
+    url: str,
+) -> Tuple[str, str, Tuple[Optional[str], Optional[str]]]:
+    """
+    Parse a url into separate netloc, auth, and url with no auth.
+
+    Returns: (url_without_auth, netloc, (username, password))
+    """
+    url_without_auth, (netloc, auth) = _transform_url(url, _get_netloc)
+    return url_without_auth, netloc, auth
+
+
+def remove_auth_from_url(url: str) -> str:
+    """Return a copy of url with 'username:password@' removed."""
+    # username/pass params are passed to subversion through flags
+    # and are not recognized in the url.
+    return _transform_url(url, _get_netloc)[0]
+
+
+def redact_auth_from_url(url: str) -> str:
+    """Replace the password in a given url with ****."""
+    return _transform_url(url, _redact_netloc)[0]
+
+
+def redact_auth_from_requirement(req: Requirement) -> str:
+    """Replace the password in a given requirement url with ****."""
+    if not req.url:
+        return str(req)
+    return str(req).replace(req.url, redact_auth_from_url(req.url))
+
+
+@dataclass(frozen=True)
+class HiddenText:
+    secret: str
+    redacted: str
+
+    def __repr__(self) -> str:
+        return f"<HiddenText {str(self)!r}>"
+
+    def __str__(self) -> str:
+        return self.redacted
+
+    # This is useful for testing.
+    def __eq__(self, other: Any) -> bool:
+        if type(self) is not type(other):
+            return False
+
+        # The string being used for redaction doesn't also have to match,
+        # just the raw, original string.
+        return self.secret == other.secret
+
+
+def hide_value(value: str) -> HiddenText:
+    return HiddenText(value, redacted="****")
+
+
+def hide_url(url: str) -> HiddenText:
+    redacted = redact_auth_from_url(url)
+    return HiddenText(url, redacted=redacted)
+
+
+def protect_pip_from_modification_on_windows(modifying_pip: bool) -> None:
+    """Protection of pip.exe from modification on Windows
+
+    On Windows, any operation modifying pip should be run as:
+        python -m pip ...
+    """
+    pip_names = [
+        "pip",
+        f"pip{sys.version_info.major}",
+        f"pip{sys.version_info.major}.{sys.version_info.minor}",
+    ]
+
+    # See https://github.com/pypa/pip/issues/1299 for more discussion
+    should_show_use_python_msg = (
+        modifying_pip and WINDOWS and os.path.basename(sys.argv[0]) in pip_names
+    )
+
+    if should_show_use_python_msg:
+        new_command = [sys.executable, "-m", "pip"] + sys.argv[1:]
+        raise CommandError(
+            "To modify pip, please run the following command:\n{}".format(
+                " ".join(new_command)
+            )
+        )
+
+
+def check_externally_managed() -> None:
+    """Check whether the current environment is externally managed.
+
+    If the ``EXTERNALLY-MANAGED`` config file is found, the current environment
+    is considered externally managed, and an ExternallyManagedEnvironment is
+    raised.
+    """
+    if running_under_virtualenv():
+        return
+    marker = os.path.join(sysconfig.get_path("stdlib"), "EXTERNALLY-MANAGED")
+    if not os.path.isfile(marker):
+        return
+    raise ExternallyManagedEnvironment.from_config(marker)
+
+
+def is_console_interactive() -> bool:
+    """Is this console interactive?"""
+    return sys.stdin is not None and sys.stdin.isatty()
+
+
+def hash_file(path: str, blocksize: int = 1 << 20) -> Tuple[Any, int]:
+    """Return (hash, length) for path using hashlib.sha256()"""
+
+    h = hashlib.sha256()
+    length = 0
+    with open(path, "rb") as f:
+        for block in read_chunks(f, size=blocksize):
+            length += len(block)
+            h.update(block)
+    return h, length
+
+
+def pairwise(iterable: Iterable[Any]) -> Iterator[Tuple[Any, Any]]:
+    """
+    Return paired elements.
+
+    For example:
+        s -> (s0, s1), (s2, s3), (s4, s5), ...
+    """
+    iterable = iter(iterable)
+    return zip_longest(iterable, iterable)
+
+
+def partition(
+    pred: Callable[[T], bool], iterable: Iterable[T]
+) -> Tuple[Iterable[T], Iterable[T]]:
+    """
+    Use a predicate to partition entries into false entries and true entries,
+    like
+
+        partition(is_odd, range(10)) --> 0 2 4 6 8   and  1 3 5 7 9
+    """
+    t1, t2 = tee(iterable)
+    return filterfalse(pred, t1), filter(pred, t2)
+
+
+class ConfiguredBuildBackendHookCaller(BuildBackendHookCaller):
+    def __init__(
+        self,
+        config_holder: Any,
+        source_dir: str,
+        build_backend: str,
+        backend_path: Optional[str] = None,
+        runner: Optional[Callable[..., None]] = None,
+        python_executable: Optional[str] = None,
+    ):
+        super().__init__(
+            source_dir, build_backend, backend_path, runner, python_executable
+        )
+        self.config_holder = config_holder
+
+    def build_wheel(
+        self,
+        wheel_directory: str,
+        config_settings: Optional[Dict[str, Union[str, List[str]]]] = None,
+        metadata_directory: Optional[str] = None,
+    ) -> str:
+        cs = self.config_holder.config_settings
+        return super().build_wheel(
+            wheel_directory, config_settings=cs, metadata_directory=metadata_directory
+        )
+
+    def build_sdist(
+        self,
+        sdist_directory: str,
+        config_settings: Optional[Dict[str, Union[str, List[str]]]] = None,
+    ) -> str:
+        cs = self.config_holder.config_settings
+        return super().build_sdist(sdist_directory, config_settings=cs)
+
+    def build_editable(
+        self,
+        wheel_directory: str,
+        config_settings: Optional[Dict[str, Union[str, List[str]]]] = None,
+        metadata_directory: Optional[str] = None,
+    ) -> str:
+        cs = self.config_holder.config_settings
+        return super().build_editable(
+            wheel_directory, config_settings=cs, metadata_directory=metadata_directory
+        )
+
+    def get_requires_for_build_wheel(
+        self, config_settings: Optional[Dict[str, Union[str, List[str]]]] = None
+    ) -> List[str]:
+        cs = self.config_holder.config_settings
+        return super().get_requires_for_build_wheel(config_settings=cs)
+
+    def get_requires_for_build_sdist(
+        self, config_settings: Optional[Dict[str, Union[str, List[str]]]] = None
+    ) -> List[str]:
+        cs = self.config_holder.config_settings
+        return super().get_requires_for_build_sdist(config_settings=cs)
+
+    def get_requires_for_build_editable(
+        self, config_settings: Optional[Dict[str, Union[str, List[str]]]] = None
+    ) -> List[str]:
+        cs = self.config_holder.config_settings
+        return super().get_requires_for_build_editable(config_settings=cs)
+
+    def prepare_metadata_for_build_wheel(
+        self,
+        metadata_directory: str,
+        config_settings: Optional[Dict[str, Union[str, List[str]]]] = None,
+        _allow_fallback: bool = True,
+    ) -> str:
+        cs = self.config_holder.config_settings
+        return super().prepare_metadata_for_build_wheel(
+            metadata_directory=metadata_directory,
+            config_settings=cs,
+            _allow_fallback=_allow_fallback,
+        )
+
+    def prepare_metadata_for_build_editable(
+        self,
+        metadata_directory: str,
+        config_settings: Optional[Dict[str, Union[str, List[str]]]] = None,
+        _allow_fallback: bool = True,
+    ) -> str:
+        cs = self.config_holder.config_settings
+        return super().prepare_metadata_for_build_editable(
+            metadata_directory=metadata_directory,
+            config_settings=cs,
+            _allow_fallback=_allow_fallback,
+        )
+
+
+def warn_if_run_as_root() -> None:
+    """Output a warning for sudo users on Unix.
+
+    In a virtual environment, sudo pip still writes to virtualenv.
+    On Windows, users may run pip as Administrator without issues.
+    This warning only applies to Unix root users outside of virtualenv.
+    """
+    if running_under_virtualenv():
+        return
+    if not hasattr(os, "getuid"):
+        return
+    # On Windows, there are no "system managed" Python packages. Installing as
+    # Administrator via pip is the correct way of updating system environments.
+    #
+    # We choose sys.platform over utils.compat.WINDOWS here to enable Mypy platform
+    # checks: https://mypy.readthedocs.io/en/stable/common_issues.html
+    if sys.platform == "win32" or sys.platform == "cygwin":
+        return
+
+    if os.getuid() != 0:
+        return
+
+    logger.warning(
+        "Running pip as the 'root' user can result in broken permissions and "
+        "conflicting behaviour with the system package manager, possibly "
+        "rendering your system unusable."
+        "It is recommended to use a virtual environment instead: "
+        "https://pip.pypa.io/warnings/venv. "
+        "Use the --root-user-action option if you know what you are doing and "
+        "want to suppress this warning."
+    )
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/wheel.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/wheel.py
new file mode 100644
index 0000000000000000000000000000000000000000..f85aee8a3f925ad831431de5251c4e9daa6877ea
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_internal/utils/wheel.py
@@ -0,0 +1,134 @@
+"""Support functions for working with wheel files.
+"""
+
+import logging
+from email.message import Message
+from email.parser import Parser
+from typing import Tuple
+from zipfile import BadZipFile, ZipFile
+
+from pip._vendor.packaging.utils import canonicalize_name
+
+from pip._internal.exceptions import UnsupportedWheel
+
+VERSION_COMPATIBLE = (1, 0)
+
+
+logger = logging.getLogger(__name__)
+
+
+def parse_wheel(wheel_zip: ZipFile, name: str) -> Tuple[str, Message]:
+    """Extract information from the provided wheel, ensuring it meets basic
+    standards.
+
+    Returns the name of the .dist-info directory and the parsed WHEEL metadata.
+    """
+    try:
+        info_dir = wheel_dist_info_dir(wheel_zip, name)
+        metadata = wheel_metadata(wheel_zip, info_dir)
+        version = wheel_version(metadata)
+    except UnsupportedWheel as e:
+        raise UnsupportedWheel(f"{name} has an invalid wheel, {e}")
+
+    check_compatibility(version, name)
+
+    return info_dir, metadata
+
+
+def wheel_dist_info_dir(source: ZipFile, name: str) -> str:
+    """Returns the name of the contained .dist-info directory.
+
+    Raises AssertionError or UnsupportedWheel if not found, >1 found, or
+    it doesn't match the provided name.
+    """
+    # Zip file path separators must be /
+    subdirs = {p.split("/", 1)[0] for p in source.namelist()}
+
+    info_dirs = [s for s in subdirs if s.endswith(".dist-info")]
+
+    if not info_dirs:
+        raise UnsupportedWheel(".dist-info directory not found")
+
+    if len(info_dirs) > 1:
+        raise UnsupportedWheel(
+            "multiple .dist-info directories found: {}".format(", ".join(info_dirs))
+        )
+
+    info_dir = info_dirs[0]
+
+    info_dir_name = canonicalize_name(info_dir)
+    canonical_name = canonicalize_name(name)
+    if not info_dir_name.startswith(canonical_name):
+        raise UnsupportedWheel(
+            f".dist-info directory {info_dir!r} does not start with {canonical_name!r}"
+        )
+
+    return info_dir
+
+
+def read_wheel_metadata_file(source: ZipFile, path: str) -> bytes:
+    try:
+        return source.read(path)
+        # BadZipFile for general corruption, KeyError for missing entry,
+        # and RuntimeError for password-protected files
+    except (BadZipFile, KeyError, RuntimeError) as e:
+        raise UnsupportedWheel(f"could not read {path!r} file: {e!r}")
+
+
+def wheel_metadata(source: ZipFile, dist_info_dir: str) -> Message:
+    """Return the WHEEL metadata of an extracted wheel, if possible.
+    Otherwise, raise UnsupportedWheel.
+    """
+    path = f"{dist_info_dir}/WHEEL"
+    # Zip file path separators must be /
+    wheel_contents = read_wheel_metadata_file(source, path)
+
+    try:
+        wheel_text = wheel_contents.decode()
+    except UnicodeDecodeError as e:
+        raise UnsupportedWheel(f"error decoding {path!r}: {e!r}")
+
+    # FeedParser (used by Parser) does not raise any exceptions. The returned
+    # message may have .defects populated, but for backwards-compatibility we
+    # currently ignore them.
+    return Parser().parsestr(wheel_text)
+
+
+def wheel_version(wheel_data: Message) -> Tuple[int, ...]:
+    """Given WHEEL metadata, return the parsed Wheel-Version.
+    Otherwise, raise UnsupportedWheel.
+    """
+    version_text = wheel_data["Wheel-Version"]
+    if version_text is None:
+        raise UnsupportedWheel("WHEEL is missing Wheel-Version")
+
+    version = version_text.strip()
+
+    try:
+        return tuple(map(int, version.split(".")))
+    except ValueError:
+        raise UnsupportedWheel(f"invalid Wheel-Version: {version!r}")
+
+
+def check_compatibility(version: Tuple[int, ...], name: str) -> None:
+    """Raises errors or warns if called with an incompatible Wheel-Version.
+
+    pip should refuse to install a Wheel-Version that's a major series
+    ahead of what it's compatible with (e.g 2.0 > 1.1); and warn when
+    installing a version only minor version ahead (e.g 1.2 > 1.1).
+
+    version: a 2-tuple representing a Wheel-Version (Major, Minor)
+    name: name of wheel or package to raise exception about
+
+    :raises UnsupportedWheel: when an incompatible Wheel-Version is given
+    """
+    if version[0] > VERSION_COMPATIBLE[0]:
+        raise UnsupportedWheel(
+            "{}'s Wheel-Version ({}) is not compatible with this version "
+            "of pip".format(name, ".".join(map(str, version)))
+        )
+    elif version > VERSION_COMPATIBLE:
+        logger.warning(
+            "Installing from a newer Wheel-Version (%s)",
+            ".".join(map(str, version)),
+        )
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/_musllinux.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/_musllinux.py
new file mode 100644
index 0000000000000000000000000000000000000000..d2bf30b56319ba862c5c9a1a39a87c6d1cb68718
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/_musllinux.py
@@ -0,0 +1,85 @@
+"""PEP 656 support.
+
+This module implements logic to detect if the currently running Python is
+linked against musl, and what musl version is used.
+"""
+
+from __future__ import annotations
+
+import functools
+import re
+import subprocess
+import sys
+from typing import Iterator, NamedTuple, Sequence
+
+from ._elffile import ELFFile
+
+
+class _MuslVersion(NamedTuple):
+    major: int
+    minor: int
+
+
+def _parse_musl_version(output: str) -> _MuslVersion | None:
+    lines = [n for n in (n.strip() for n in output.splitlines()) if n]
+    if len(lines) < 2 or lines[0][:4] != "musl":
+        return None
+    m = re.match(r"Version (\d+)\.(\d+)", lines[1])
+    if not m:
+        return None
+    return _MuslVersion(major=int(m.group(1)), minor=int(m.group(2)))
+
+
+@functools.lru_cache
+def _get_musl_version(executable: str) -> _MuslVersion | None:
+    """Detect currently-running musl runtime version.
+
+    This is done by checking the specified executable's dynamic linking
+    information, and invoking the loader to parse its output for a version
+    string. If the loader is musl, the output would be something like::
+
+        musl libc (x86_64)
+        Version 1.2.2
+        Dynamic Program Loader
+    """
+    try:
+        with open(executable, "rb") as f:
+            ld = ELFFile(f).interpreter
+    except (OSError, TypeError, ValueError):
+        return None
+    if ld is None or "musl" not in ld:
+        return None
+    proc = subprocess.run([ld], stderr=subprocess.PIPE, text=True)
+    return _parse_musl_version(proc.stderr)
+
+
+def platform_tags(archs: Sequence[str]) -> Iterator[str]:
+    """Generate musllinux tags compatible to the current platform.
+
+    :param archs: Sequence of compatible architectures.
+        The first one shall be the closest to the actual architecture and be the part of
+        platform tag after the ``linux_`` prefix, e.g. ``x86_64``.
+        The ``linux_`` prefix is assumed as a prerequisite for the current platform to
+        be musllinux-compatible.
+
+    :returns: An iterator of compatible musllinux tags.
+    """
+    sys_musl = _get_musl_version(sys.executable)
+    if sys_musl is None:  # Python not dynamically linked against musl.
+        return
+    for arch in archs:
+        for minor in range(sys_musl.minor, -1, -1):
+            yield f"musllinux_{sys_musl.major}_{minor}_{arch}"
+
+
+if __name__ == "__main__":  # pragma: no cover
+    import sysconfig
+
+    plat = sysconfig.get_platform()
+    assert plat.startswith("linux-"), "not linux"
+
+    print("plat:", plat)
+    print("musl:", _get_musl_version(sys.executable))
+    print("tags:", end=" ")
+    for t in platform_tags(re.sub(r"[.-]", "_", plat.split("-", 1)[-1])):
+        print(t, end="\n      ")
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/_parser.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/_parser.py
new file mode 100644
index 0000000000000000000000000000000000000000..c1238c06eab95f8c90c393383a703aa3b8c366a5
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/_parser.py
@@ -0,0 +1,354 @@
+"""Handwritten parser of dependency specifiers.
+
+The docstring for each __parse_* function contains EBNF-inspired grammar representing
+the implementation.
+"""
+
+from __future__ import annotations
+
+import ast
+from typing import NamedTuple, Sequence, Tuple, Union
+
+from ._tokenizer import DEFAULT_RULES, Tokenizer
+
+
+class Node:
+    def __init__(self, value: str) -> None:
+        self.value = value
+
+    def __str__(self) -> str:
+        return self.value
+
+    def __repr__(self) -> str:
+        return f"<{self.__class__.__name__}('{self}')>"
+
+    def serialize(self) -> str:
+        raise NotImplementedError
+
+
+class Variable(Node):
+    def serialize(self) -> str:
+        return str(self)
+
+
+class Value(Node):
+    def serialize(self) -> str:
+        return f'"{self}"'
+
+
+class Op(Node):
+    def serialize(self) -> str:
+        return str(self)
+
+
+MarkerVar = Union[Variable, Value]
+MarkerItem = Tuple[MarkerVar, Op, MarkerVar]
+MarkerAtom = Union[MarkerItem, Sequence["MarkerAtom"]]
+MarkerList = Sequence[Union["MarkerList", MarkerAtom, str]]
+
+
+class ParsedRequirement(NamedTuple):
+    name: str
+    url: str
+    extras: list[str]
+    specifier: str
+    marker: MarkerList | None
+
+
+# --------------------------------------------------------------------------------------
+# Recursive descent parser for dependency specifier
+# --------------------------------------------------------------------------------------
+def parse_requirement(source: str) -> ParsedRequirement:
+    return _parse_requirement(Tokenizer(source, rules=DEFAULT_RULES))
+
+
+def _parse_requirement(tokenizer: Tokenizer) -> ParsedRequirement:
+    """
+    requirement = WS? IDENTIFIER WS? extras WS? requirement_details
+    """
+    tokenizer.consume("WS")
+
+    name_token = tokenizer.expect(
+        "IDENTIFIER", expected="package name at the start of dependency specifier"
+    )
+    name = name_token.text
+    tokenizer.consume("WS")
+
+    extras = _parse_extras(tokenizer)
+    tokenizer.consume("WS")
+
+    url, specifier, marker = _parse_requirement_details(tokenizer)
+    tokenizer.expect("END", expected="end of dependency specifier")
+
+    return ParsedRequirement(name, url, extras, specifier, marker)
+
+
+def _parse_requirement_details(
+    tokenizer: Tokenizer,
+) -> tuple[str, str, MarkerList | None]:
+    """
+    requirement_details = AT URL (WS requirement_marker?)?
+                        | specifier WS? (requirement_marker)?
+    """
+
+    specifier = ""
+    url = ""
+    marker = None
+
+    if tokenizer.check("AT"):
+        tokenizer.read()
+        tokenizer.consume("WS")
+
+        url_start = tokenizer.position
+        url = tokenizer.expect("URL", expected="URL after @").text
+        if tokenizer.check("END", peek=True):
+            return (url, specifier, marker)
+
+        tokenizer.expect("WS", expected="whitespace after URL")
+
+        # The input might end after whitespace.
+        if tokenizer.check("END", peek=True):
+            return (url, specifier, marker)
+
+        marker = _parse_requirement_marker(
+            tokenizer, span_start=url_start, after="URL and whitespace"
+        )
+    else:
+        specifier_start = tokenizer.position
+        specifier = _parse_specifier(tokenizer)
+        tokenizer.consume("WS")
+
+        if tokenizer.check("END", peek=True):
+            return (url, specifier, marker)
+
+        marker = _parse_requirement_marker(
+            tokenizer,
+            span_start=specifier_start,
+            after=(
+                "version specifier"
+                if specifier
+                else "name and no valid version specifier"
+            ),
+        )
+
+    return (url, specifier, marker)
+
+
+def _parse_requirement_marker(
+    tokenizer: Tokenizer, *, span_start: int, after: str
+) -> MarkerList:
+    """
+    requirement_marker = SEMICOLON marker WS?
+    """
+
+    if not tokenizer.check("SEMICOLON"):
+        tokenizer.raise_syntax_error(
+            f"Expected end or semicolon (after {after})",
+            span_start=span_start,
+        )
+    tokenizer.read()
+
+    marker = _parse_marker(tokenizer)
+    tokenizer.consume("WS")
+
+    return marker
+
+
+def _parse_extras(tokenizer: Tokenizer) -> list[str]:
+    """
+    extras = (LEFT_BRACKET wsp* extras_list? wsp* RIGHT_BRACKET)?
+    """
+    if not tokenizer.check("LEFT_BRACKET", peek=True):
+        return []
+
+    with tokenizer.enclosing_tokens(
+        "LEFT_BRACKET",
+        "RIGHT_BRACKET",
+        around="extras",
+    ):
+        tokenizer.consume("WS")
+        extras = _parse_extras_list(tokenizer)
+        tokenizer.consume("WS")
+
+    return extras
+
+
+def _parse_extras_list(tokenizer: Tokenizer) -> list[str]:
+    """
+    extras_list = identifier (wsp* ',' wsp* identifier)*
+    """
+    extras: list[str] = []
+
+    if not tokenizer.check("IDENTIFIER"):
+        return extras
+
+    extras.append(tokenizer.read().text)
+
+    while True:
+        tokenizer.consume("WS")
+        if tokenizer.check("IDENTIFIER", peek=True):
+            tokenizer.raise_syntax_error("Expected comma between extra names")
+        elif not tokenizer.check("COMMA"):
+            break
+
+        tokenizer.read()
+        tokenizer.consume("WS")
+
+        extra_token = tokenizer.expect("IDENTIFIER", expected="extra name after comma")
+        extras.append(extra_token.text)
+
+    return extras
+
+
+def _parse_specifier(tokenizer: Tokenizer) -> str:
+    """
+    specifier = LEFT_PARENTHESIS WS? version_many WS? RIGHT_PARENTHESIS
+              | WS? version_many WS?
+    """
+    with tokenizer.enclosing_tokens(
+        "LEFT_PARENTHESIS",
+        "RIGHT_PARENTHESIS",
+        around="version specifier",
+    ):
+        tokenizer.consume("WS")
+        parsed_specifiers = _parse_version_many(tokenizer)
+        tokenizer.consume("WS")
+
+    return parsed_specifiers
+
+
+def _parse_version_many(tokenizer: Tokenizer) -> str:
+    """
+    version_many = (SPECIFIER (WS? COMMA WS? SPECIFIER)*)?
+    """
+    parsed_specifiers = ""
+    while tokenizer.check("SPECIFIER"):
+        span_start = tokenizer.position
+        parsed_specifiers += tokenizer.read().text
+        if tokenizer.check("VERSION_PREFIX_TRAIL", peek=True):
+            tokenizer.raise_syntax_error(
+                ".* suffix can only be used with `==` or `!=` operators",
+                span_start=span_start,
+                span_end=tokenizer.position + 1,
+            )
+        if tokenizer.check("VERSION_LOCAL_LABEL_TRAIL", peek=True):
+            tokenizer.raise_syntax_error(
+                "Local version label can only be used with `==` or `!=` operators",
+                span_start=span_start,
+                span_end=tokenizer.position,
+            )
+        tokenizer.consume("WS")
+        if not tokenizer.check("COMMA"):
+            break
+        parsed_specifiers += tokenizer.read().text
+        tokenizer.consume("WS")
+
+    return parsed_specifiers
+
+
+# --------------------------------------------------------------------------------------
+# Recursive descent parser for marker expression
+# --------------------------------------------------------------------------------------
+def parse_marker(source: str) -> MarkerList:
+    return _parse_full_marker(Tokenizer(source, rules=DEFAULT_RULES))
+
+
+def _parse_full_marker(tokenizer: Tokenizer) -> MarkerList:
+    retval = _parse_marker(tokenizer)
+    tokenizer.expect("END", expected="end of marker expression")
+    return retval
+
+
+def _parse_marker(tokenizer: Tokenizer) -> MarkerList:
+    """
+    marker = marker_atom (BOOLOP marker_atom)+
+    """
+    expression = [_parse_marker_atom(tokenizer)]
+    while tokenizer.check("BOOLOP"):
+        token = tokenizer.read()
+        expr_right = _parse_marker_atom(tokenizer)
+        expression.extend((token.text, expr_right))
+    return expression
+
+
+def _parse_marker_atom(tokenizer: Tokenizer) -> MarkerAtom:
+    """
+    marker_atom = WS? LEFT_PARENTHESIS WS? marker WS? RIGHT_PARENTHESIS WS?
+                | WS? marker_item WS?
+    """
+
+    tokenizer.consume("WS")
+    if tokenizer.check("LEFT_PARENTHESIS", peek=True):
+        with tokenizer.enclosing_tokens(
+            "LEFT_PARENTHESIS",
+            "RIGHT_PARENTHESIS",
+            around="marker expression",
+        ):
+            tokenizer.consume("WS")
+            marker: MarkerAtom = _parse_marker(tokenizer)
+            tokenizer.consume("WS")
+    else:
+        marker = _parse_marker_item(tokenizer)
+    tokenizer.consume("WS")
+    return marker
+
+
+def _parse_marker_item(tokenizer: Tokenizer) -> MarkerItem:
+    """
+    marker_item = WS? marker_var WS? marker_op WS? marker_var WS?
+    """
+    tokenizer.consume("WS")
+    marker_var_left = _parse_marker_var(tokenizer)
+    tokenizer.consume("WS")
+    marker_op = _parse_marker_op(tokenizer)
+    tokenizer.consume("WS")
+    marker_var_right = _parse_marker_var(tokenizer)
+    tokenizer.consume("WS")
+    return (marker_var_left, marker_op, marker_var_right)
+
+
+def _parse_marker_var(tokenizer: Tokenizer) -> MarkerVar:
+    """
+    marker_var = VARIABLE | QUOTED_STRING
+    """
+    if tokenizer.check("VARIABLE"):
+        return process_env_var(tokenizer.read().text.replace(".", "_"))
+    elif tokenizer.check("QUOTED_STRING"):
+        return process_python_str(tokenizer.read().text)
+    else:
+        tokenizer.raise_syntax_error(
+            message="Expected a marker variable or quoted string"
+        )
+
+
+def process_env_var(env_var: str) -> Variable:
+    if env_var in ("platform_python_implementation", "python_implementation"):
+        return Variable("platform_python_implementation")
+    else:
+        return Variable(env_var)
+
+
+def process_python_str(python_str: str) -> Value:
+    value = ast.literal_eval(python_str)
+    return Value(str(value))
+
+
+def _parse_marker_op(tokenizer: Tokenizer) -> Op:
+    """
+    marker_op = IN | NOT IN | OP
+    """
+    if tokenizer.check("IN"):
+        tokenizer.read()
+        return Op("in")
+    elif tokenizer.check("NOT"):
+        tokenizer.read()
+        tokenizer.expect("WS", expected="whitespace after 'not'")
+        tokenizer.expect("IN", expected="'in' after 'not'")
+        return Op("not in")
+    elif tokenizer.check("OP"):
+        return Op(tokenizer.read().text)
+    else:
+        return tokenizer.raise_syntax_error(
+            "Expected marker operator, one of "
+            "<=, <, !=, ==, >=, >, ~=, ===, in, not in"
+        )
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/markers.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/markers.py
new file mode 100644
index 0000000000000000000000000000000000000000..7ac7bb69a5325a6d9866885f2266539e8413a3c9
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/markers.py
@@ -0,0 +1,325 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+
+from __future__ import annotations
+
+import operator
+import os
+import platform
+import sys
+from typing import Any, Callable, TypedDict, cast
+
+from ._parser import MarkerAtom, MarkerList, Op, Value, Variable
+from ._parser import parse_marker as _parse_marker
+from ._tokenizer import ParserSyntaxError
+from .specifiers import InvalidSpecifier, Specifier
+from .utils import canonicalize_name
+
+__all__ = [
+    "InvalidMarker",
+    "UndefinedComparison",
+    "UndefinedEnvironmentName",
+    "Marker",
+    "default_environment",
+]
+
+Operator = Callable[[str, str], bool]
+
+
+class InvalidMarker(ValueError):
+    """
+    An invalid marker was found, users should refer to PEP 508.
+    """
+
+
+class UndefinedComparison(ValueError):
+    """
+    An invalid operation was attempted on a value that doesn't support it.
+    """
+
+
+class UndefinedEnvironmentName(ValueError):
+    """
+    A name was attempted to be used that does not exist inside of the
+    environment.
+    """
+
+
+class Environment(TypedDict):
+    implementation_name: str
+    """The implementation's identifier, e.g. ``'cpython'``."""
+
+    implementation_version: str
+    """
+    The implementation's version, e.g. ``'3.13.0a2'`` for CPython 3.13.0a2, or
+    ``'7.3.13'`` for PyPy3.10 v7.3.13.
+    """
+
+    os_name: str
+    """
+    The value of :py:data:`os.name`. The name of the operating system dependent module
+    imported, e.g. ``'posix'``.
+    """
+
+    platform_machine: str
+    """
+    Returns the machine type, e.g. ``'i386'``.
+
+    An empty string if the value cannot be determined.
+    """
+
+    platform_release: str
+    """
+    The system's release, e.g. ``'2.2.0'`` or ``'NT'``.
+
+    An empty string if the value cannot be determined.
+    """
+
+    platform_system: str
+    """
+    The system/OS name, e.g. ``'Linux'``, ``'Windows'`` or ``'Java'``.
+
+    An empty string if the value cannot be determined.
+    """
+
+    platform_version: str
+    """
+    The system's release version, e.g. ``'#3 on degas'``.
+
+    An empty string if the value cannot be determined.
+    """
+
+    python_full_version: str
+    """
+    The Python version as string ``'major.minor.patchlevel'``.
+
+    Note that unlike the Python :py:data:`sys.version`, this value will always include
+    the patchlevel (it defaults to 0).
+    """
+
+    platform_python_implementation: str
+    """
+    A string identifying the Python implementation, e.g. ``'CPython'``.
+    """
+
+    python_version: str
+    """The Python version as string ``'major.minor'``."""
+
+    sys_platform: str
+    """
+    This string contains a platform identifier that can be used to append
+    platform-specific components to :py:data:`sys.path`, for instance.
+
+    For Unix systems, except on Linux and AIX, this is the lowercased OS name as
+    returned by ``uname -s`` with the first part of the version as returned by
+    ``uname -r`` appended, e.g. ``'sunos5'`` or ``'freebsd8'``, at the time when Python
+    was built.
+    """
+
+
+def _normalize_extra_values(results: Any) -> Any:
+    """
+    Normalize extra values.
+    """
+    if isinstance(results[0], tuple):
+        lhs, op, rhs = results[0]
+        if isinstance(lhs, Variable) and lhs.value == "extra":
+            normalized_extra = canonicalize_name(rhs.value)
+            rhs = Value(normalized_extra)
+        elif isinstance(rhs, Variable) and rhs.value == "extra":
+            normalized_extra = canonicalize_name(lhs.value)
+            lhs = Value(normalized_extra)
+        results[0] = lhs, op, rhs
+    return results
+
+
+def _format_marker(
+    marker: list[str] | MarkerAtom | str, first: bool | None = True
+) -> str:
+    assert isinstance(marker, (list, tuple, str))
+
+    # Sometimes we have a structure like [[...]] which is a single item list
+    # where the single item is itself it's own list. In that case we want skip
+    # the rest of this function so that we don't get extraneous () on the
+    # outside.
+    if (
+        isinstance(marker, list)
+        and len(marker) == 1
+        and isinstance(marker[0], (list, tuple))
+    ):
+        return _format_marker(marker[0])
+
+    if isinstance(marker, list):
+        inner = (_format_marker(m, first=False) for m in marker)
+        if first:
+            return " ".join(inner)
+        else:
+            return "(" + " ".join(inner) + ")"
+    elif isinstance(marker, tuple):
+        return " ".join([m.serialize() for m in marker])
+    else:
+        return marker
+
+
+_operators: dict[str, Operator] = {
+    "in": lambda lhs, rhs: lhs in rhs,
+    "not in": lambda lhs, rhs: lhs not in rhs,
+    "<": operator.lt,
+    "<=": operator.le,
+    "==": operator.eq,
+    "!=": operator.ne,
+    ">=": operator.ge,
+    ">": operator.gt,
+}
+
+
+def _eval_op(lhs: str, op: Op, rhs: str) -> bool:
+    try:
+        spec = Specifier("".join([op.serialize(), rhs]))
+    except InvalidSpecifier:
+        pass
+    else:
+        return spec.contains(lhs, prereleases=True)
+
+    oper: Operator | None = _operators.get(op.serialize())
+    if oper is None:
+        raise UndefinedComparison(f"Undefined {op!r} on {lhs!r} and {rhs!r}.")
+
+    return oper(lhs, rhs)
+
+
+def _normalize(*values: str, key: str) -> tuple[str, ...]:
+    # PEP 685 – Comparison of extra names for optional distribution dependencies
+    # https://peps.python.org/pep-0685/
+    # > When comparing extra names, tools MUST normalize the names being
+    # > compared using the semantics outlined in PEP 503 for names
+    if key == "extra":
+        return tuple(canonicalize_name(v) for v in values)
+
+    # other environment markers don't have such standards
+    return values
+
+
+def _evaluate_markers(markers: MarkerList, environment: dict[str, str]) -> bool:
+    groups: list[list[bool]] = [[]]
+
+    for marker in markers:
+        assert isinstance(marker, (list, tuple, str))
+
+        if isinstance(marker, list):
+            groups[-1].append(_evaluate_markers(marker, environment))
+        elif isinstance(marker, tuple):
+            lhs, op, rhs = marker
+
+            if isinstance(lhs, Variable):
+                environment_key = lhs.value
+                lhs_value = environment[environment_key]
+                rhs_value = rhs.value
+            else:
+                lhs_value = lhs.value
+                environment_key = rhs.value
+                rhs_value = environment[environment_key]
+
+            lhs_value, rhs_value = _normalize(lhs_value, rhs_value, key=environment_key)
+            groups[-1].append(_eval_op(lhs_value, op, rhs_value))
+        else:
+            assert marker in ["and", "or"]
+            if marker == "or":
+                groups.append([])
+
+    return any(all(item) for item in groups)
+
+
+def format_full_version(info: sys._version_info) -> str:
+    version = "{0.major}.{0.minor}.{0.micro}".format(info)
+    kind = info.releaselevel
+    if kind != "final":
+        version += kind[0] + str(info.serial)
+    return version
+
+
+def default_environment() -> Environment:
+    iver = format_full_version(sys.implementation.version)
+    implementation_name = sys.implementation.name
+    return {
+        "implementation_name": implementation_name,
+        "implementation_version": iver,
+        "os_name": os.name,
+        "platform_machine": platform.machine(),
+        "platform_release": platform.release(),
+        "platform_system": platform.system(),
+        "platform_version": platform.version(),
+        "python_full_version": platform.python_version(),
+        "platform_python_implementation": platform.python_implementation(),
+        "python_version": ".".join(platform.python_version_tuple()[:2]),
+        "sys_platform": sys.platform,
+    }
+
+
+class Marker:
+    def __init__(self, marker: str) -> None:
+        # Note: We create a Marker object without calling this constructor in
+        #       packaging.requirements.Requirement. If any additional logic is
+        #       added here, make sure to mirror/adapt Requirement.
+        try:
+            self._markers = _normalize_extra_values(_parse_marker(marker))
+            # The attribute `_markers` can be described in terms of a recursive type:
+            # MarkerList = List[Union[Tuple[Node, ...], str, MarkerList]]
+            #
+            # For example, the following expression:
+            # python_version > "3.6" or (python_version == "3.6" and os_name == "unix")
+            #
+            # is parsed into:
+            # [
+            #     (<Variable('python_version')>, <Op('>')>, <Value('3.6')>),
+            #     'and',
+            #     [
+            #         (<Variable('python_version')>, <Op('==')>, <Value('3.6')>),
+            #         'or',
+            #         (<Variable('os_name')>, <Op('==')>, <Value('unix')>)
+            #     ]
+            # ]
+        except ParserSyntaxError as e:
+            raise InvalidMarker(str(e)) from e
+
+    def __str__(self) -> str:
+        return _format_marker(self._markers)
+
+    def __repr__(self) -> str:
+        return f"<Marker('{self}')>"
+
+    def __hash__(self) -> int:
+        return hash((self.__class__.__name__, str(self)))
+
+    def __eq__(self, other: Any) -> bool:
+        if not isinstance(other, Marker):
+            return NotImplemented
+
+        return str(self) == str(other)
+
+    def evaluate(self, environment: dict[str, str] | None = None) -> bool:
+        """Evaluate a marker.
+
+        Return the boolean from evaluating the given marker against the
+        environment. environment is an optional argument to override all or
+        part of the determined environment.
+
+        The environment is determined from the current Python process.
+        """
+        current_environment = cast("dict[str, str]", default_environment())
+        current_environment["extra"] = ""
+        # Work around platform.python_version() returning something that is not PEP 440
+        # compliant for non-tagged Python builds. We preserve default_environment()'s
+        # behavior of returning platform.python_version() verbatim, and leave it to the
+        # caller to provide a syntactically valid version if they want to override it.
+        if current_environment["python_full_version"].endswith("+"):
+            current_environment["python_full_version"] += "local"
+        if environment is not None:
+            current_environment.update(environment)
+            # The API used to allow setting extra to None. We need to handle this
+            # case for backwards compatibility.
+            if current_environment["extra"] is None:
+                current_environment["extra"] = ""
+
+        return _evaluate_markers(self._markers, current_environment)
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/metadata.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/metadata.py
new file mode 100644
index 0000000000000000000000000000000000000000..eb8dc844d285dadecdce8be98cffd8bc39310595
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/metadata.py
@@ -0,0 +1,804 @@
+from __future__ import annotations
+
+import email.feedparser
+import email.header
+import email.message
+import email.parser
+import email.policy
+import typing
+from typing import (
+    Any,
+    Callable,
+    Generic,
+    Literal,
+    TypedDict,
+    cast,
+)
+
+from . import requirements, specifiers, utils
+from . import version as version_module
+
+T = typing.TypeVar("T")
+
+
+try:
+    ExceptionGroup
+except NameError:  # pragma: no cover
+
+    class ExceptionGroup(Exception):
+        """A minimal implementation of :external:exc:`ExceptionGroup` from Python 3.11.
+
+        If :external:exc:`ExceptionGroup` is already defined by Python itself,
+        that version is used instead.
+        """
+
+        message: str
+        exceptions: list[Exception]
+
+        def __init__(self, message: str, exceptions: list[Exception]) -> None:
+            self.message = message
+            self.exceptions = exceptions
+
+        def __repr__(self) -> str:
+            return f"{self.__class__.__name__}({self.message!r}, {self.exceptions!r})"
+
+else:  # pragma: no cover
+    ExceptionGroup = ExceptionGroup
+
+
+class InvalidMetadata(ValueError):
+    """A metadata field contains invalid data."""
+
+    field: str
+    """The name of the field that contains invalid data."""
+
+    def __init__(self, field: str, message: str) -> None:
+        self.field = field
+        super().__init__(message)
+
+
+# The RawMetadata class attempts to make as few assumptions about the underlying
+# serialization formats as possible. The idea is that as long as a serialization
+# formats offer some very basic primitives in *some* way then we can support
+# serializing to and from that format.
+class RawMetadata(TypedDict, total=False):
+    """A dictionary of raw core metadata.
+
+    Each field in core metadata maps to a key of this dictionary (when data is
+    provided). The key is lower-case and underscores are used instead of dashes
+    compared to the equivalent core metadata field. Any core metadata field that
+    can be specified multiple times or can hold multiple values in a single
+    field have a key with a plural name. See :class:`Metadata` whose attributes
+    match the keys of this dictionary.
+
+    Core metadata fields that can be specified multiple times are stored as a
+    list or dict depending on which is appropriate for the field. Any fields
+    which hold multiple values in a single field are stored as a list.
+
+    """
+
+    # Metadata 1.0 - PEP 241
+    metadata_version: str
+    name: str
+    version: str
+    platforms: list[str]
+    summary: str
+    description: str
+    keywords: list[str]
+    home_page: str
+    author: str
+    author_email: str
+    license: str
+
+    # Metadata 1.1 - PEP 314
+    supported_platforms: list[str]
+    download_url: str
+    classifiers: list[str]
+    requires: list[str]
+    provides: list[str]
+    obsoletes: list[str]
+
+    # Metadata 1.2 - PEP 345
+    maintainer: str
+    maintainer_email: str
+    requires_dist: list[str]
+    provides_dist: list[str]
+    obsoletes_dist: list[str]
+    requires_python: str
+    requires_external: list[str]
+    project_urls: dict[str, str]
+
+    # Metadata 2.0
+    # PEP 426 attempted to completely revamp the metadata format
+    # but got stuck without ever being able to build consensus on
+    # it and ultimately ended up withdrawn.
+    #
+    # However, a number of tools had started emitting METADATA with
+    # `2.0` Metadata-Version, so for historical reasons, this version
+    # was skipped.
+
+    # Metadata 2.1 - PEP 566
+    description_content_type: str
+    provides_extra: list[str]
+
+    # Metadata 2.2 - PEP 643
+    dynamic: list[str]
+
+    # Metadata 2.3 - PEP 685
+    # No new fields were added in PEP 685, just some edge case were
+    # tightened up to provide better interoptability.
+
+
+_STRING_FIELDS = {
+    "author",
+    "author_email",
+    "description",
+    "description_content_type",
+    "download_url",
+    "home_page",
+    "license",
+    "maintainer",
+    "maintainer_email",
+    "metadata_version",
+    "name",
+    "requires_python",
+    "summary",
+    "version",
+}
+
+_LIST_FIELDS = {
+    "classifiers",
+    "dynamic",
+    "obsoletes",
+    "obsoletes_dist",
+    "platforms",
+    "provides",
+    "provides_dist",
+    "provides_extra",
+    "requires",
+    "requires_dist",
+    "requires_external",
+    "supported_platforms",
+}
+
+_DICT_FIELDS = {
+    "project_urls",
+}
+
+
+def _parse_keywords(data: str) -> list[str]:
+    """Split a string of comma-separate keyboards into a list of keywords."""
+    return [k.strip() for k in data.split(",")]
+
+
+def _parse_project_urls(data: list[str]) -> dict[str, str]:
+    """Parse a list of label/URL string pairings separated by a comma."""
+    urls = {}
+    for pair in data:
+        # Our logic is slightly tricky here as we want to try and do
+        # *something* reasonable with malformed data.
+        #
+        # The main thing that we have to worry about, is data that does
+        # not have a ',' at all to split the label from the Value. There
+        # isn't a singular right answer here, and we will fail validation
+        # later on (if the caller is validating) so it doesn't *really*
+        # matter, but since the missing value has to be an empty str
+        # and our return value is dict[str, str], if we let the key
+        # be the missing value, then they'd have multiple '' values that
+        # overwrite each other in a accumulating dict.
+        #
+        # The other potentional issue is that it's possible to have the
+        # same label multiple times in the metadata, with no solid "right"
+        # answer with what to do in that case. As such, we'll do the only
+        # thing we can, which is treat the field as unparseable and add it
+        # to our list of unparsed fields.
+        parts = [p.strip() for p in pair.split(",", 1)]
+        parts.extend([""] * (max(0, 2 - len(parts))))  # Ensure 2 items
+
+        # TODO: The spec doesn't say anything about if the keys should be
+        #       considered case sensitive or not... logically they should
+        #       be case-preserving and case-insensitive, but doing that
+        #       would open up more cases where we might have duplicate
+        #       entries.
+        label, url = parts
+        if label in urls:
+            # The label already exists in our set of urls, so this field
+            # is unparseable, and we can just add the whole thing to our
+            # unparseable data and stop processing it.
+            raise KeyError("duplicate labels in project urls")
+        urls[label] = url
+
+    return urls
+
+
+def _get_payload(msg: email.message.Message, source: bytes | str) -> str:
+    """Get the body of the message."""
+    # If our source is a str, then our caller has managed encodings for us,
+    # and we don't need to deal with it.
+    if isinstance(source, str):
+        payload: str = msg.get_payload()
+        return payload
+    # If our source is a bytes, then we're managing the encoding and we need
+    # to deal with it.
+    else:
+        bpayload: bytes = msg.get_payload(decode=True)
+        try:
+            return bpayload.decode("utf8", "strict")
+        except UnicodeDecodeError:
+            raise ValueError("payload in an invalid encoding")
+
+
+# The various parse_FORMAT functions here are intended to be as lenient as
+# possible in their parsing, while still returning a correctly typed
+# RawMetadata.
+#
+# To aid in this, we also generally want to do as little touching of the
+# data as possible, except where there are possibly some historic holdovers
+# that make valid data awkward to work with.
+#
+# While this is a lower level, intermediate format than our ``Metadata``
+# class, some light touch ups can make a massive difference in usability.
+
+# Map METADATA fields to RawMetadata.
+_EMAIL_TO_RAW_MAPPING = {
+    "author": "author",
+    "author-email": "author_email",
+    "classifier": "classifiers",
+    "description": "description",
+    "description-content-type": "description_content_type",
+    "download-url": "download_url",
+    "dynamic": "dynamic",
+    "home-page": "home_page",
+    "keywords": "keywords",
+    "license": "license",
+    "maintainer": "maintainer",
+    "maintainer-email": "maintainer_email",
+    "metadata-version": "metadata_version",
+    "name": "name",
+    "obsoletes": "obsoletes",
+    "obsoletes-dist": "obsoletes_dist",
+    "platform": "platforms",
+    "project-url": "project_urls",
+    "provides": "provides",
+    "provides-dist": "provides_dist",
+    "provides-extra": "provides_extra",
+    "requires": "requires",
+    "requires-dist": "requires_dist",
+    "requires-external": "requires_external",
+    "requires-python": "requires_python",
+    "summary": "summary",
+    "supported-platform": "supported_platforms",
+    "version": "version",
+}
+_RAW_TO_EMAIL_MAPPING = {raw: email for email, raw in _EMAIL_TO_RAW_MAPPING.items()}
+
+
+def parse_email(data: bytes | str) -> tuple[RawMetadata, dict[str, list[str]]]:
+    """Parse a distribution's metadata stored as email headers (e.g. from ``METADATA``).
+
+    This function returns a two-item tuple of dicts. The first dict is of
+    recognized fields from the core metadata specification. Fields that can be
+    parsed and translated into Python's built-in types are converted
+    appropriately. All other fields are left as-is. Fields that are allowed to
+    appear multiple times are stored as lists.
+
+    The second dict contains all other fields from the metadata. This includes
+    any unrecognized fields. It also includes any fields which are expected to
+    be parsed into a built-in type but were not formatted appropriately. Finally,
+    any fields that are expected to appear only once but are repeated are
+    included in this dict.
+
+    """
+    raw: dict[str, str | list[str] | dict[str, str]] = {}
+    unparsed: dict[str, list[str]] = {}
+
+    if isinstance(data, str):
+        parsed = email.parser.Parser(policy=email.policy.compat32).parsestr(data)
+    else:
+        parsed = email.parser.BytesParser(policy=email.policy.compat32).parsebytes(data)
+
+    # We have to wrap parsed.keys() in a set, because in the case of multiple
+    # values for a key (a list), the key will appear multiple times in the
+    # list of keys, but we're avoiding that by using get_all().
+    for name in frozenset(parsed.keys()):
+        # Header names in RFC are case insensitive, so we'll normalize to all
+        # lower case to make comparisons easier.
+        name = name.lower()
+
+        # We use get_all() here, even for fields that aren't multiple use,
+        # because otherwise someone could have e.g. two Name fields, and we
+        # would just silently ignore it rather than doing something about it.
+        headers = parsed.get_all(name) or []
+
+        # The way the email module works when parsing bytes is that it
+        # unconditionally decodes the bytes as ascii using the surrogateescape
+        # handler. When you pull that data back out (such as with get_all() ),
+        # it looks to see if the str has any surrogate escapes, and if it does
+        # it wraps it in a Header object instead of returning the string.
+        #
+        # As such, we'll look for those Header objects, and fix up the encoding.
+        value = []
+        # Flag if we have run into any issues processing the headers, thus
+        # signalling that the data belongs in 'unparsed'.
+        valid_encoding = True
+        for h in headers:
+            # It's unclear if this can return more types than just a Header or
+            # a str, so we'll just assert here to make sure.
+            assert isinstance(h, (email.header.Header, str))
+
+            # If it's a header object, we need to do our little dance to get
+            # the real data out of it. In cases where there is invalid data
+            # we're going to end up with mojibake, but there's no obvious, good
+            # way around that without reimplementing parts of the Header object
+            # ourselves.
+            #
+            # That should be fine since, if mojibacked happens, this key is
+            # going into the unparsed dict anyways.
+            if isinstance(h, email.header.Header):
+                # The Header object stores it's data as chunks, and each chunk
+                # can be independently encoded, so we'll need to check each
+                # of them.
+                chunks: list[tuple[bytes, str | None]] = []
+                for bin, encoding in email.header.decode_header(h):
+                    try:
+                        bin.decode("utf8", "strict")
+                    except UnicodeDecodeError:
+                        # Enable mojibake.
+                        encoding = "latin1"
+                        valid_encoding = False
+                    else:
+                        encoding = "utf8"
+                    chunks.append((bin, encoding))
+
+                # Turn our chunks back into a Header object, then let that
+                # Header object do the right thing to turn them into a
+                # string for us.
+                value.append(str(email.header.make_header(chunks)))
+            # This is already a string, so just add it.
+            else:
+                value.append(h)
+
+        # We've processed all of our values to get them into a list of str,
+        # but we may have mojibake data, in which case this is an unparsed
+        # field.
+        if not valid_encoding:
+            unparsed[name] = value
+            continue
+
+        raw_name = _EMAIL_TO_RAW_MAPPING.get(name)
+        if raw_name is None:
+            # This is a bit of a weird situation, we've encountered a key that
+            # we don't know what it means, so we don't know whether it's meant
+            # to be a list or not.
+            #
+            # Since we can't really tell one way or another, we'll just leave it
+            # as a list, even though it may be a single item list, because that's
+            # what makes the most sense for email headers.
+            unparsed[name] = value
+            continue
+
+        # If this is one of our string fields, then we'll check to see if our
+        # value is a list of a single item. If it is then we'll assume that
+        # it was emitted as a single string, and unwrap the str from inside
+        # the list.
+        #
+        # If it's any other kind of data, then we haven't the faintest clue
+        # what we should parse it as, and we have to just add it to our list
+        # of unparsed stuff.
+        if raw_name in _STRING_FIELDS and len(value) == 1:
+            raw[raw_name] = value[0]
+        # If this is one of our list of string fields, then we can just assign
+        # the value, since email *only* has strings, and our get_all() call
+        # above ensures that this is a list.
+        elif raw_name in _LIST_FIELDS:
+            raw[raw_name] = value
+        # Special Case: Keywords
+        # The keywords field is implemented in the metadata spec as a str,
+        # but it conceptually is a list of strings, and is serialized using
+        # ", ".join(keywords), so we'll do some light data massaging to turn
+        # this into what it logically is.
+        elif raw_name == "keywords" and len(value) == 1:
+            raw[raw_name] = _parse_keywords(value[0])
+        # Special Case: Project-URL
+        # The project urls is implemented in the metadata spec as a list of
+        # specially-formatted strings that represent a key and a value, which
+        # is fundamentally a mapping, however the email format doesn't support
+        # mappings in a sane way, so it was crammed into a list of strings
+        # instead.
+        #
+        # We will do a little light data massaging to turn this into a map as
+        # it logically should be.
+        elif raw_name == "project_urls":
+            try:
+                raw[raw_name] = _parse_project_urls(value)
+            except KeyError:
+                unparsed[name] = value
+        # Nothing that we've done has managed to parse this, so it'll just
+        # throw it in our unparseable data and move on.
+        else:
+            unparsed[name] = value
+
+    # We need to support getting the Description from the message payload in
+    # addition to getting it from the the headers. This does mean, though, there
+    # is the possibility of it being set both ways, in which case we put both
+    # in 'unparsed' since we don't know which is right.
+    try:
+        payload = _get_payload(parsed, data)
+    except ValueError:
+        unparsed.setdefault("description", []).append(
+            parsed.get_payload(decode=isinstance(data, bytes))
+        )
+    else:
+        if payload:
+            # Check to see if we've already got a description, if so then both
+            # it, and this body move to unparseable.
+            if "description" in raw:
+                description_header = cast(str, raw.pop("description"))
+                unparsed.setdefault("description", []).extend(
+                    [description_header, payload]
+                )
+            elif "description" in unparsed:
+                unparsed["description"].append(payload)
+            else:
+                raw["description"] = payload
+
+    # We need to cast our `raw` to a metadata, because a TypedDict only support
+    # literal key names, but we're computing our key names on purpose, but the
+    # way this function is implemented, our `TypedDict` can only have valid key
+    # names.
+    return cast(RawMetadata, raw), unparsed
+
+
+_NOT_FOUND = object()
+
+
+# Keep the two values in sync.
+_VALID_METADATA_VERSIONS = ["1.0", "1.1", "1.2", "2.1", "2.2", "2.3"]
+_MetadataVersion = Literal["1.0", "1.1", "1.2", "2.1", "2.2", "2.3"]
+
+_REQUIRED_ATTRS = frozenset(["metadata_version", "name", "version"])
+
+
+class _Validator(Generic[T]):
+    """Validate a metadata field.
+
+    All _process_*() methods correspond to a core metadata field. The method is
+    called with the field's raw value. If the raw value is valid it is returned
+    in its "enriched" form (e.g. ``version.Version`` for the ``Version`` field).
+    If the raw value is invalid, :exc:`InvalidMetadata` is raised (with a cause
+    as appropriate).
+    """
+
+    name: str
+    raw_name: str
+    added: _MetadataVersion
+
+    def __init__(
+        self,
+        *,
+        added: _MetadataVersion = "1.0",
+    ) -> None:
+        self.added = added
+
+    def __set_name__(self, _owner: Metadata, name: str) -> None:
+        self.name = name
+        self.raw_name = _RAW_TO_EMAIL_MAPPING[name]
+
+    def __get__(self, instance: Metadata, _owner: type[Metadata]) -> T:
+        # With Python 3.8, the caching can be replaced with functools.cached_property().
+        # No need to check the cache as attribute lookup will resolve into the
+        # instance's __dict__ before __get__ is called.
+        cache = instance.__dict__
+        value = instance._raw.get(self.name)
+
+        # To make the _process_* methods easier, we'll check if the value is None
+        # and if this field is NOT a required attribute, and if both of those
+        # things are true, we'll skip the the converter. This will mean that the
+        # converters never have to deal with the None union.
+        if self.name in _REQUIRED_ATTRS or value is not None:
+            try:
+                converter: Callable[[Any], T] = getattr(self, f"_process_{self.name}")
+            except AttributeError:
+                pass
+            else:
+                value = converter(value)
+
+        cache[self.name] = value
+        try:
+            del instance._raw[self.name]  # type: ignore[misc]
+        except KeyError:
+            pass
+
+        return cast(T, value)
+
+    def _invalid_metadata(
+        self, msg: str, cause: Exception | None = None
+    ) -> InvalidMetadata:
+        exc = InvalidMetadata(
+            self.raw_name, msg.format_map({"field": repr(self.raw_name)})
+        )
+        exc.__cause__ = cause
+        return exc
+
+    def _process_metadata_version(self, value: str) -> _MetadataVersion:
+        # Implicitly makes Metadata-Version required.
+        if value not in _VALID_METADATA_VERSIONS:
+            raise self._invalid_metadata(f"{value!r} is not a valid metadata version")
+        return cast(_MetadataVersion, value)
+
+    def _process_name(self, value: str) -> str:
+        if not value:
+            raise self._invalid_metadata("{field} is a required field")
+        # Validate the name as a side-effect.
+        try:
+            utils.canonicalize_name(value, validate=True)
+        except utils.InvalidName as exc:
+            raise self._invalid_metadata(
+                f"{value!r} is invalid for {{field}}", cause=exc
+            )
+        else:
+            return value
+
+    def _process_version(self, value: str) -> version_module.Version:
+        if not value:
+            raise self._invalid_metadata("{field} is a required field")
+        try:
+            return version_module.parse(value)
+        except version_module.InvalidVersion as exc:
+            raise self._invalid_metadata(
+                f"{value!r} is invalid for {{field}}", cause=exc
+            )
+
+    def _process_summary(self, value: str) -> str:
+        """Check the field contains no newlines."""
+        if "\n" in value:
+            raise self._invalid_metadata("{field} must be a single line")
+        return value
+
+    def _process_description_content_type(self, value: str) -> str:
+        content_types = {"text/plain", "text/x-rst", "text/markdown"}
+        message = email.message.EmailMessage()
+        message["content-type"] = value
+
+        content_type, parameters = (
+            # Defaults to `text/plain` if parsing failed.
+            message.get_content_type().lower(),
+            message["content-type"].params,
+        )
+        # Check if content-type is valid or defaulted to `text/plain` and thus was
+        # not parseable.
+        if content_type not in content_types or content_type not in value.lower():
+            raise self._invalid_metadata(
+                f"{{field}} must be one of {list(content_types)}, not {value!r}"
+            )
+
+        charset = parameters.get("charset", "UTF-8")
+        if charset != "UTF-8":
+            raise self._invalid_metadata(
+                f"{{field}} can only specify the UTF-8 charset, not {list(charset)}"
+            )
+
+        markdown_variants = {"GFM", "CommonMark"}
+        variant = parameters.get("variant", "GFM")  # Use an acceptable default.
+        if content_type == "text/markdown" and variant not in markdown_variants:
+            raise self._invalid_metadata(
+                f"valid Markdown variants for {{field}} are {list(markdown_variants)}, "
+                f"not {variant!r}",
+            )
+        return value
+
+    def _process_dynamic(self, value: list[str]) -> list[str]:
+        for dynamic_field in map(str.lower, value):
+            if dynamic_field in {"name", "version", "metadata-version"}:
+                raise self._invalid_metadata(
+                    f"{value!r} is not allowed as a dynamic field"
+                )
+            elif dynamic_field not in _EMAIL_TO_RAW_MAPPING:
+                raise self._invalid_metadata(f"{value!r} is not a valid dynamic field")
+        return list(map(str.lower, value))
+
+    def _process_provides_extra(
+        self,
+        value: list[str],
+    ) -> list[utils.NormalizedName]:
+        normalized_names = []
+        try:
+            for name in value:
+                normalized_names.append(utils.canonicalize_name(name, validate=True))
+        except utils.InvalidName as exc:
+            raise self._invalid_metadata(
+                f"{name!r} is invalid for {{field}}", cause=exc
+            )
+        else:
+            return normalized_names
+
+    def _process_requires_python(self, value: str) -> specifiers.SpecifierSet:
+        try:
+            return specifiers.SpecifierSet(value)
+        except specifiers.InvalidSpecifier as exc:
+            raise self._invalid_metadata(
+                f"{value!r} is invalid for {{field}}", cause=exc
+            )
+
+    def _process_requires_dist(
+        self,
+        value: list[str],
+    ) -> list[requirements.Requirement]:
+        reqs = []
+        try:
+            for req in value:
+                reqs.append(requirements.Requirement(req))
+        except requirements.InvalidRequirement as exc:
+            raise self._invalid_metadata(f"{req!r} is invalid for {{field}}", cause=exc)
+        else:
+            return reqs
+
+
+class Metadata:
+    """Representation of distribution metadata.
+
+    Compared to :class:`RawMetadata`, this class provides objects representing
+    metadata fields instead of only using built-in types. Any invalid metadata
+    will cause :exc:`InvalidMetadata` to be raised (with a
+    :py:attr:`~BaseException.__cause__` attribute as appropriate).
+    """
+
+    _raw: RawMetadata
+
+    @classmethod
+    def from_raw(cls, data: RawMetadata, *, validate: bool = True) -> Metadata:
+        """Create an instance from :class:`RawMetadata`.
+
+        If *validate* is true, all metadata will be validated. All exceptions
+        related to validation will be gathered and raised as an :class:`ExceptionGroup`.
+        """
+        ins = cls()
+        ins._raw = data.copy()  # Mutations occur due to caching enriched values.
+
+        if validate:
+            exceptions: list[Exception] = []
+            try:
+                metadata_version = ins.metadata_version
+                metadata_age = _VALID_METADATA_VERSIONS.index(metadata_version)
+            except InvalidMetadata as metadata_version_exc:
+                exceptions.append(metadata_version_exc)
+                metadata_version = None
+
+            # Make sure to check for the fields that are present, the required
+            # fields (so their absence can be reported).
+            fields_to_check = frozenset(ins._raw) | _REQUIRED_ATTRS
+            # Remove fields that have already been checked.
+            fields_to_check -= {"metadata_version"}
+
+            for key in fields_to_check:
+                try:
+                    if metadata_version:
+                        # Can't use getattr() as that triggers descriptor protocol which
+                        # will fail due to no value for the instance argument.
+                        try:
+                            field_metadata_version = cls.__dict__[key].added
+                        except KeyError:
+                            exc = InvalidMetadata(key, f"unrecognized field: {key!r}")
+                            exceptions.append(exc)
+                            continue
+                        field_age = _VALID_METADATA_VERSIONS.index(
+                            field_metadata_version
+                        )
+                        if field_age > metadata_age:
+                            field = _RAW_TO_EMAIL_MAPPING[key]
+                            exc = InvalidMetadata(
+                                field,
+                                "{field} introduced in metadata version "
+                                "{field_metadata_version}, not {metadata_version}",
+                            )
+                            exceptions.append(exc)
+                            continue
+                    getattr(ins, key)
+                except InvalidMetadata as exc:
+                    exceptions.append(exc)
+
+            if exceptions:
+                raise ExceptionGroup("invalid metadata", exceptions)
+
+        return ins
+
+    @classmethod
+    def from_email(cls, data: bytes | str, *, validate: bool = True) -> Metadata:
+        """Parse metadata from email headers.
+
+        If *validate* is true, the metadata will be validated. All exceptions
+        related to validation will be gathered and raised as an :class:`ExceptionGroup`.
+        """
+        raw, unparsed = parse_email(data)
+
+        if validate:
+            exceptions: list[Exception] = []
+            for unparsed_key in unparsed:
+                if unparsed_key in _EMAIL_TO_RAW_MAPPING:
+                    message = f"{unparsed_key!r} has invalid data"
+                else:
+                    message = f"unrecognized field: {unparsed_key!r}"
+                exceptions.append(InvalidMetadata(unparsed_key, message))
+
+            if exceptions:
+                raise ExceptionGroup("unparsed", exceptions)
+
+        try:
+            return cls.from_raw(raw, validate=validate)
+        except ExceptionGroup as exc_group:
+            raise ExceptionGroup(
+                "invalid or unparsed metadata", exc_group.exceptions
+            ) from None
+
+    metadata_version: _Validator[_MetadataVersion] = _Validator()
+    """:external:ref:`core-metadata-metadata-version`
+    (required; validated to be a valid metadata version)"""
+    name: _Validator[str] = _Validator()
+    """:external:ref:`core-metadata-name`
+    (required; validated using :func:`~packaging.utils.canonicalize_name` and its
+    *validate* parameter)"""
+    version: _Validator[version_module.Version] = _Validator()
+    """:external:ref:`core-metadata-version` (required)"""
+    dynamic: _Validator[list[str] | None] = _Validator(
+        added="2.2",
+    )
+    """:external:ref:`core-metadata-dynamic`
+    (validated against core metadata field names and lowercased)"""
+    platforms: _Validator[list[str] | None] = _Validator()
+    """:external:ref:`core-metadata-platform`"""
+    supported_platforms: _Validator[list[str] | None] = _Validator(added="1.1")
+    """:external:ref:`core-metadata-supported-platform`"""
+    summary: _Validator[str | None] = _Validator()
+    """:external:ref:`core-metadata-summary` (validated to contain no newlines)"""
+    description: _Validator[str | None] = _Validator()  # TODO 2.1: can be in body
+    """:external:ref:`core-metadata-description`"""
+    description_content_type: _Validator[str | None] = _Validator(added="2.1")
+    """:external:ref:`core-metadata-description-content-type` (validated)"""
+    keywords: _Validator[list[str] | None] = _Validator()
+    """:external:ref:`core-metadata-keywords`"""
+    home_page: _Validator[str | None] = _Validator()
+    """:external:ref:`core-metadata-home-page`"""
+    download_url: _Validator[str | None] = _Validator(added="1.1")
+    """:external:ref:`core-metadata-download-url`"""
+    author: _Validator[str | None] = _Validator()
+    """:external:ref:`core-metadata-author`"""
+    author_email: _Validator[str | None] = _Validator()
+    """:external:ref:`core-metadata-author-email`"""
+    maintainer: _Validator[str | None] = _Validator(added="1.2")
+    """:external:ref:`core-metadata-maintainer`"""
+    maintainer_email: _Validator[str | None] = _Validator(added="1.2")
+    """:external:ref:`core-metadata-maintainer-email`"""
+    license: _Validator[str | None] = _Validator()
+    """:external:ref:`core-metadata-license`"""
+    classifiers: _Validator[list[str] | None] = _Validator(added="1.1")
+    """:external:ref:`core-metadata-classifier`"""
+    requires_dist: _Validator[list[requirements.Requirement] | None] = _Validator(
+        added="1.2"
+    )
+    """:external:ref:`core-metadata-requires-dist`"""
+    requires_python: _Validator[specifiers.SpecifierSet | None] = _Validator(
+        added="1.2"
+    )
+    """:external:ref:`core-metadata-requires-python`"""
+    # Because `Requires-External` allows for non-PEP 440 version specifiers, we
+    # don't do any processing on the values.
+    requires_external: _Validator[list[str] | None] = _Validator(added="1.2")
+    """:external:ref:`core-metadata-requires-external`"""
+    project_urls: _Validator[dict[str, str] | None] = _Validator(added="1.2")
+    """:external:ref:`core-metadata-project-url`"""
+    # PEP 685 lets us raise an error if an extra doesn't pass `Name` validation
+    # regardless of metadata version.
+    provides_extra: _Validator[list[utils.NormalizedName] | None] = _Validator(
+        added="2.1",
+    )
+    """:external:ref:`core-metadata-provides-extra`"""
+    provides_dist: _Validator[list[str] | None] = _Validator(added="1.2")
+    """:external:ref:`core-metadata-provides-dist`"""
+    obsoletes_dist: _Validator[list[str] | None] = _Validator(added="1.2")
+    """:external:ref:`core-metadata-obsoletes-dist`"""
+    requires: _Validator[list[str] | None] = _Validator(added="1.1")
+    """``Requires`` (deprecated)"""
+    provides: _Validator[list[str] | None] = _Validator(added="1.1")
+    """``Provides`` (deprecated)"""
+    obsoletes: _Validator[list[str] | None] = _Validator(added="1.1")
+    """``Obsoletes`` (deprecated)"""
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/py.typed b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/py.typed
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/requirements.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/requirements.py
new file mode 100644
index 0000000000000000000000000000000000000000..4e068c9567def3564f238a76fe7ab46b569f33e5
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/requirements.py
@@ -0,0 +1,91 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+from __future__ import annotations
+
+from typing import Any, Iterator
+
+from ._parser import parse_requirement as _parse_requirement
+from ._tokenizer import ParserSyntaxError
+from .markers import Marker, _normalize_extra_values
+from .specifiers import SpecifierSet
+from .utils import canonicalize_name
+
+
+class InvalidRequirement(ValueError):
+    """
+    An invalid requirement was found, users should refer to PEP 508.
+    """
+
+
+class Requirement:
+    """Parse a requirement.
+
+    Parse a given requirement string into its parts, such as name, specifier,
+    URL, and extras. Raises InvalidRequirement on a badly-formed requirement
+    string.
+    """
+
+    # TODO: Can we test whether something is contained within a requirement?
+    #       If so how do we do that? Do we need to test against the _name_ of
+    #       the thing as well as the version? What about the markers?
+    # TODO: Can we normalize the name and extra name?
+
+    def __init__(self, requirement_string: str) -> None:
+        try:
+            parsed = _parse_requirement(requirement_string)
+        except ParserSyntaxError as e:
+            raise InvalidRequirement(str(e)) from e
+
+        self.name: str = parsed.name
+        self.url: str | None = parsed.url or None
+        self.extras: set[str] = set(parsed.extras or [])
+        self.specifier: SpecifierSet = SpecifierSet(parsed.specifier)
+        self.marker: Marker | None = None
+        if parsed.marker is not None:
+            self.marker = Marker.__new__(Marker)
+            self.marker._markers = _normalize_extra_values(parsed.marker)
+
+    def _iter_parts(self, name: str) -> Iterator[str]:
+        yield name
+
+        if self.extras:
+            formatted_extras = ",".join(sorted(self.extras))
+            yield f"[{formatted_extras}]"
+
+        if self.specifier:
+            yield str(self.specifier)
+
+        if self.url:
+            yield f"@ {self.url}"
+            if self.marker:
+                yield " "
+
+        if self.marker:
+            yield f"; {self.marker}"
+
+    def __str__(self) -> str:
+        return "".join(self._iter_parts(self.name))
+
+    def __repr__(self) -> str:
+        return f"<Requirement('{self}')>"
+
+    def __hash__(self) -> int:
+        return hash(
+            (
+                self.__class__.__name__,
+                *self._iter_parts(canonicalize_name(self.name)),
+            )
+        )
+
+    def __eq__(self, other: Any) -> bool:
+        if not isinstance(other, Requirement):
+            return NotImplemented
+
+        return (
+            canonicalize_name(self.name) == canonicalize_name(other.name)
+            and self.extras == other.extras
+            and self.specifier == other.specifier
+            and self.url == other.url
+            and self.marker == other.marker
+        )
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/tags.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/tags.py
new file mode 100644
index 0000000000000000000000000000000000000000..703f0ed53c0f4624460c49a9619f15b5b8deab9a
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/tags.py
@@ -0,0 +1,627 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+
+from __future__ import annotations
+
+import logging
+import platform
+import re
+import struct
+import subprocess
+import sys
+import sysconfig
+from importlib.machinery import EXTENSION_SUFFIXES
+from typing import (
+    Iterable,
+    Iterator,
+    Sequence,
+    Tuple,
+    cast,
+)
+
+from . import _manylinux, _musllinux
+
+logger = logging.getLogger(__name__)
+
+PythonVersion = Sequence[int]
+AppleVersion = Tuple[int, int]
+
+INTERPRETER_SHORT_NAMES: dict[str, str] = {
+    "python": "py",  # Generic.
+    "cpython": "cp",
+    "pypy": "pp",
+    "ironpython": "ip",
+    "jython": "jy",
+}
+
+
+_32_BIT_INTERPRETER = struct.calcsize("P") == 4
+
+
+class Tag:
+    """
+    A representation of the tag triple for a wheel.
+
+    Instances are considered immutable and thus are hashable. Equality checking
+    is also supported.
+    """
+
+    __slots__ = ["_interpreter", "_abi", "_platform", "_hash"]
+
+    def __init__(self, interpreter: str, abi: str, platform: str) -> None:
+        self._interpreter = interpreter.lower()
+        self._abi = abi.lower()
+        self._platform = platform.lower()
+        # The __hash__ of every single element in a Set[Tag] will be evaluated each time
+        # that a set calls its `.disjoint()` method, which may be called hundreds of
+        # times when scanning a page of links for packages with tags matching that
+        # Set[Tag]. Pre-computing the value here produces significant speedups for
+        # downstream consumers.
+        self._hash = hash((self._interpreter, self._abi, self._platform))
+
+    @property
+    def interpreter(self) -> str:
+        return self._interpreter
+
+    @property
+    def abi(self) -> str:
+        return self._abi
+
+    @property
+    def platform(self) -> str:
+        return self._platform
+
+    def __eq__(self, other: object) -> bool:
+        if not isinstance(other, Tag):
+            return NotImplemented
+
+        return (
+            (self._hash == other._hash)  # Short-circuit ASAP for perf reasons.
+            and (self._platform == other._platform)
+            and (self._abi == other._abi)
+            and (self._interpreter == other._interpreter)
+        )
+
+    def __hash__(self) -> int:
+        return self._hash
+
+    def __str__(self) -> str:
+        return f"{self._interpreter}-{self._abi}-{self._platform}"
+
+    def __repr__(self) -> str:
+        return f"<{self} @ {id(self)}>"
+
+
+def parse_tag(tag: str) -> frozenset[Tag]:
+    """
+    Parses the provided tag (e.g. `py3-none-any`) into a frozenset of Tag instances.
+
+    Returning a set is required due to the possibility that the tag is a
+    compressed tag set.
+    """
+    tags = set()
+    interpreters, abis, platforms = tag.split("-")
+    for interpreter in interpreters.split("."):
+        for abi in abis.split("."):
+            for platform_ in platforms.split("."):
+                tags.add(Tag(interpreter, abi, platform_))
+    return frozenset(tags)
+
+
+def _get_config_var(name: str, warn: bool = False) -> int | str | None:
+    value: int | str | None = sysconfig.get_config_var(name)
+    if value is None and warn:
+        logger.debug(
+            "Config variable '%s' is unset, Python ABI tag may be incorrect", name
+        )
+    return value
+
+
+def _normalize_string(string: str) -> str:
+    return string.replace(".", "_").replace("-", "_").replace(" ", "_")
+
+
+def _is_threaded_cpython(abis: list[str]) -> bool:
+    """
+    Determine if the ABI corresponds to a threaded (`--disable-gil`) build.
+
+    The threaded builds are indicated by a "t" in the abiflags.
+    """
+    if len(abis) == 0:
+        return False
+    # expect e.g., cp313
+    m = re.match(r"cp\d+(.*)", abis[0])
+    if not m:
+        return False
+    abiflags = m.group(1)
+    return "t" in abiflags
+
+
+def _abi3_applies(python_version: PythonVersion, threading: bool) -> bool:
+    """
+    Determine if the Python version supports abi3.
+
+    PEP 384 was first implemented in Python 3.2. The threaded (`--disable-gil`)
+    builds do not support abi3.
+    """
+    return len(python_version) > 1 and tuple(python_version) >= (3, 2) and not threading
+
+
+def _cpython_abis(py_version: PythonVersion, warn: bool = False) -> list[str]:
+    py_version = tuple(py_version)  # To allow for version comparison.
+    abis = []
+    version = _version_nodot(py_version[:2])
+    threading = debug = pymalloc = ucs4 = ""
+    with_debug = _get_config_var("Py_DEBUG", warn)
+    has_refcount = hasattr(sys, "gettotalrefcount")
+    # Windows doesn't set Py_DEBUG, so checking for support of debug-compiled
+    # extension modules is the best option.
+    # https://github.com/pypa/pip/issues/3383#issuecomment-173267692
+    has_ext = "_d.pyd" in EXTENSION_SUFFIXES
+    if with_debug or (with_debug is None and (has_refcount or has_ext)):
+        debug = "d"
+    if py_version >= (3, 13) and _get_config_var("Py_GIL_DISABLED", warn):
+        threading = "t"
+    if py_version < (3, 8):
+        with_pymalloc = _get_config_var("WITH_PYMALLOC", warn)
+        if with_pymalloc or with_pymalloc is None:
+            pymalloc = "m"
+        if py_version < (3, 3):
+            unicode_size = _get_config_var("Py_UNICODE_SIZE", warn)
+            if unicode_size == 4 or (
+                unicode_size is None and sys.maxunicode == 0x10FFFF
+            ):
+                ucs4 = "u"
+    elif debug:
+        # Debug builds can also load "normal" extension modules.
+        # We can also assume no UCS-4 or pymalloc requirement.
+        abis.append(f"cp{version}{threading}")
+    abis.insert(0, f"cp{version}{threading}{debug}{pymalloc}{ucs4}")
+    return abis
+
+
+def cpython_tags(
+    python_version: PythonVersion | None = None,
+    abis: Iterable[str] | None = None,
+    platforms: Iterable[str] | None = None,
+    *,
+    warn: bool = False,
+) -> Iterator[Tag]:
+    """
+    Yields the tags for a CPython interpreter.
+
+    The tags consist of:
+    - cp<python_version>-<abi>-<platform>
+    - cp<python_version>-abi3-<platform>
+    - cp<python_version>-none-<platform>
+    - cp<less than python_version>-abi3-<platform>  # Older Python versions down to 3.2.
+
+    If python_version only specifies a major version then user-provided ABIs and
+    the 'none' ABItag will be used.
+
+    If 'abi3' or 'none' are specified in 'abis' then they will be yielded at
+    their normal position and not at the beginning.
+    """
+    if not python_version:
+        python_version = sys.version_info[:2]
+
+    interpreter = f"cp{_version_nodot(python_version[:2])}"
+
+    if abis is None:
+        if len(python_version) > 1:
+            abis = _cpython_abis(python_version, warn)
+        else:
+            abis = []
+    abis = list(abis)
+    # 'abi3' and 'none' are explicitly handled later.
+    for explicit_abi in ("abi3", "none"):
+        try:
+            abis.remove(explicit_abi)
+        except ValueError:
+            pass
+
+    platforms = list(platforms or platform_tags())
+    for abi in abis:
+        for platform_ in platforms:
+            yield Tag(interpreter, abi, platform_)
+
+    threading = _is_threaded_cpython(abis)
+    use_abi3 = _abi3_applies(python_version, threading)
+    if use_abi3:
+        yield from (Tag(interpreter, "abi3", platform_) for platform_ in platforms)
+    yield from (Tag(interpreter, "none", platform_) for platform_ in platforms)
+
+    if use_abi3:
+        for minor_version in range(python_version[1] - 1, 1, -1):
+            for platform_ in platforms:
+                interpreter = "cp{version}".format(
+                    version=_version_nodot((python_version[0], minor_version))
+                )
+                yield Tag(interpreter, "abi3", platform_)
+
+
+def _generic_abi() -> list[str]:
+    """
+    Return the ABI tag based on EXT_SUFFIX.
+    """
+    # The following are examples of `EXT_SUFFIX`.
+    # We want to keep the parts which are related to the ABI and remove the
+    # parts which are related to the platform:
+    # - linux:   '.cpython-310-x86_64-linux-gnu.so' => cp310
+    # - mac:     '.cpython-310-darwin.so'           => cp310
+    # - win:     '.cp310-win_amd64.pyd'             => cp310
+    # - win:     '.pyd'                             => cp37 (uses _cpython_abis())
+    # - pypy:    '.pypy38-pp73-x86_64-linux-gnu.so' => pypy38_pp73
+    # - graalpy: '.graalpy-38-native-x86_64-darwin.dylib'
+    #                                               => graalpy_38_native
+
+    ext_suffix = _get_config_var("EXT_SUFFIX", warn=True)
+    if not isinstance(ext_suffix, str) or ext_suffix[0] != ".":
+        raise SystemError("invalid sysconfig.get_config_var('EXT_SUFFIX')")
+    parts = ext_suffix.split(".")
+    if len(parts) < 3:
+        # CPython3.7 and earlier uses ".pyd" on Windows.
+        return _cpython_abis(sys.version_info[:2])
+    soabi = parts[1]
+    if soabi.startswith("cpython"):
+        # non-windows
+        abi = "cp" + soabi.split("-")[1]
+    elif soabi.startswith("cp"):
+        # windows
+        abi = soabi.split("-")[0]
+    elif soabi.startswith("pypy"):
+        abi = "-".join(soabi.split("-")[:2])
+    elif soabi.startswith("graalpy"):
+        abi = "-".join(soabi.split("-")[:3])
+    elif soabi:
+        # pyston, ironpython, others?
+        abi = soabi
+    else:
+        return []
+    return [_normalize_string(abi)]
+
+
+def generic_tags(
+    interpreter: str | None = None,
+    abis: Iterable[str] | None = None,
+    platforms: Iterable[str] | None = None,
+    *,
+    warn: bool = False,
+) -> Iterator[Tag]:
+    """
+    Yields the tags for a generic interpreter.
+
+    The tags consist of:
+    - <interpreter>-<abi>-<platform>
+
+    The "none" ABI will be added if it was not explicitly provided.
+    """
+    if not interpreter:
+        interp_name = interpreter_name()
+        interp_version = interpreter_version(warn=warn)
+        interpreter = "".join([interp_name, interp_version])
+    if abis is None:
+        abis = _generic_abi()
+    else:
+        abis = list(abis)
+    platforms = list(platforms or platform_tags())
+    if "none" not in abis:
+        abis.append("none")
+    for abi in abis:
+        for platform_ in platforms:
+            yield Tag(interpreter, abi, platform_)
+
+
+def _py_interpreter_range(py_version: PythonVersion) -> Iterator[str]:
+    """
+    Yields Python versions in descending order.
+
+    After the latest version, the major-only version will be yielded, and then
+    all previous versions of that major version.
+    """
+    if len(py_version) > 1:
+        yield f"py{_version_nodot(py_version[:2])}"
+    yield f"py{py_version[0]}"
+    if len(py_version) > 1:
+        for minor in range(py_version[1] - 1, -1, -1):
+            yield f"py{_version_nodot((py_version[0], minor))}"
+
+
+def compatible_tags(
+    python_version: PythonVersion | None = None,
+    interpreter: str | None = None,
+    platforms: Iterable[str] | None = None,
+) -> Iterator[Tag]:
+    """
+    Yields the sequence of tags that are compatible with a specific version of Python.
+
+    The tags consist of:
+    - py*-none-<platform>
+    - <interpreter>-none-any  # ... if `interpreter` is provided.
+    - py*-none-any
+    """
+    if not python_version:
+        python_version = sys.version_info[:2]
+    platforms = list(platforms or platform_tags())
+    for version in _py_interpreter_range(python_version):
+        for platform_ in platforms:
+            yield Tag(version, "none", platform_)
+    if interpreter:
+        yield Tag(interpreter, "none", "any")
+    for version in _py_interpreter_range(python_version):
+        yield Tag(version, "none", "any")
+
+
+def _mac_arch(arch: str, is_32bit: bool = _32_BIT_INTERPRETER) -> str:
+    if not is_32bit:
+        return arch
+
+    if arch.startswith("ppc"):
+        return "ppc"
+
+    return "i386"
+
+
+def _mac_binary_formats(version: AppleVersion, cpu_arch: str) -> list[str]:
+    formats = [cpu_arch]
+    if cpu_arch == "x86_64":
+        if version < (10, 4):
+            return []
+        formats.extend(["intel", "fat64", "fat32"])
+
+    elif cpu_arch == "i386":
+        if version < (10, 4):
+            return []
+        formats.extend(["intel", "fat32", "fat"])
+
+    elif cpu_arch == "ppc64":
+        # TODO: Need to care about 32-bit PPC for ppc64 through 10.2?
+        if version > (10, 5) or version < (10, 4):
+            return []
+        formats.append("fat64")
+
+    elif cpu_arch == "ppc":
+        if version > (10, 6):
+            return []
+        formats.extend(["fat32", "fat"])
+
+    if cpu_arch in {"arm64", "x86_64"}:
+        formats.append("universal2")
+
+    if cpu_arch in {"x86_64", "i386", "ppc64", "ppc", "intel"}:
+        formats.append("universal")
+
+    return formats
+
+
+def mac_platforms(
+    version: AppleVersion | None = None, arch: str | None = None
+) -> Iterator[str]:
+    """
+    Yields the platform tags for a macOS system.
+
+    The `version` parameter is a two-item tuple specifying the macOS version to
+    generate platform tags for. The `arch` parameter is the CPU architecture to
+    generate platform tags for. Both parameters default to the appropriate value
+    for the current system.
+    """
+    version_str, _, cpu_arch = platform.mac_ver()
+    if version is None:
+        version = cast("AppleVersion", tuple(map(int, version_str.split(".")[:2])))
+        if version == (10, 16):
+            # When built against an older macOS SDK, Python will report macOS 10.16
+            # instead of the real version.
+            version_str = subprocess.run(
+                [
+                    sys.executable,
+                    "-sS",
+                    "-c",
+                    "import platform; print(platform.mac_ver()[0])",
+                ],
+                check=True,
+                env={"SYSTEM_VERSION_COMPAT": "0"},
+                stdout=subprocess.PIPE,
+                text=True,
+            ).stdout
+            version = cast("AppleVersion", tuple(map(int, version_str.split(".")[:2])))
+    else:
+        version = version
+    if arch is None:
+        arch = _mac_arch(cpu_arch)
+    else:
+        arch = arch
+
+    if (10, 0) <= version and version < (11, 0):
+        # Prior to Mac OS 11, each yearly release of Mac OS bumped the
+        # "minor" version number.  The major version was always 10.
+        for minor_version in range(version[1], -1, -1):
+            compat_version = 10, minor_version
+            binary_formats = _mac_binary_formats(compat_version, arch)
+            for binary_format in binary_formats:
+                yield "macosx_{major}_{minor}_{binary_format}".format(
+                    major=10, minor=minor_version, binary_format=binary_format
+                )
+
+    if version >= (11, 0):
+        # Starting with Mac OS 11, each yearly release bumps the major version
+        # number.   The minor versions are now the midyear updates.
+        for major_version in range(version[0], 10, -1):
+            compat_version = major_version, 0
+            binary_formats = _mac_binary_formats(compat_version, arch)
+            for binary_format in binary_formats:
+                yield "macosx_{major}_{minor}_{binary_format}".format(
+                    major=major_version, minor=0, binary_format=binary_format
+                )
+
+    if version >= (11, 0):
+        # Mac OS 11 on x86_64 is compatible with binaries from previous releases.
+        # Arm64 support was introduced in 11.0, so no Arm binaries from previous
+        # releases exist.
+        #
+        # However, the "universal2" binary format can have a
+        # macOS version earlier than 11.0 when the x86_64 part of the binary supports
+        # that version of macOS.
+        if arch == "x86_64":
+            for minor_version in range(16, 3, -1):
+                compat_version = 10, minor_version
+                binary_formats = _mac_binary_formats(compat_version, arch)
+                for binary_format in binary_formats:
+                    yield "macosx_{major}_{minor}_{binary_format}".format(
+                        major=compat_version[0],
+                        minor=compat_version[1],
+                        binary_format=binary_format,
+                    )
+        else:
+            for minor_version in range(16, 3, -1):
+                compat_version = 10, minor_version
+                binary_format = "universal2"
+                yield "macosx_{major}_{minor}_{binary_format}".format(
+                    major=compat_version[0],
+                    minor=compat_version[1],
+                    binary_format=binary_format,
+                )
+
+
+def ios_platforms(
+    version: AppleVersion | None = None, multiarch: str | None = None
+) -> Iterator[str]:
+    """
+    Yields the platform tags for an iOS system.
+
+    :param version: A two-item tuple specifying the iOS version to generate
+        platform tags for. Defaults to the current iOS version.
+    :param multiarch: The CPU architecture+ABI to generate platform tags for -
+        (the value used by `sys.implementation._multiarch` e.g.,
+        `arm64_iphoneos` or `x84_64_iphonesimulator`). Defaults to the current
+        multiarch value.
+    """
+    if version is None:
+        # if iOS is the current platform, ios_ver *must* be defined. However,
+        # it won't exist for CPython versions before 3.13, which causes a mypy
+        # error.
+        _, release, _, _ = platform.ios_ver()  # type: ignore[attr-defined]
+        version = cast("AppleVersion", tuple(map(int, release.split(".")[:2])))
+
+    if multiarch is None:
+        multiarch = sys.implementation._multiarch
+    multiarch = multiarch.replace("-", "_")
+
+    ios_platform_template = "ios_{major}_{minor}_{multiarch}"
+
+    # Consider any iOS major.minor version from the version requested, down to
+    # 12.0. 12.0 is the first iOS version that is known to have enough features
+    # to support CPython. Consider every possible minor release up to X.9. There
+    # highest the minor has ever gone is 8 (14.8 and 15.8) but having some extra
+    # candidates that won't ever match doesn't really hurt, and it saves us from
+    # having to keep an explicit list of known iOS versions in the code. Return
+    # the results descending order of version number.
+
+    # If the requested major version is less than 12, there won't be any matches.
+    if version[0] < 12:
+        return
+
+    # Consider the actual X.Y version that was requested.
+    yield ios_platform_template.format(
+        major=version[0], minor=version[1], multiarch=multiarch
+    )
+
+    # Consider every minor version from X.0 to the minor version prior to the
+    # version requested by the platform.
+    for minor in range(version[1] - 1, -1, -1):
+        yield ios_platform_template.format(
+            major=version[0], minor=minor, multiarch=multiarch
+        )
+
+    for major in range(version[0] - 1, 11, -1):
+        for minor in range(9, -1, -1):
+            yield ios_platform_template.format(
+                major=major, minor=minor, multiarch=multiarch
+            )
+
+
+def _linux_platforms(is_32bit: bool = _32_BIT_INTERPRETER) -> Iterator[str]:
+    linux = _normalize_string(sysconfig.get_platform())
+    if not linux.startswith("linux_"):
+        # we should never be here, just yield the sysconfig one and return
+        yield linux
+        return
+    if is_32bit:
+        if linux == "linux_x86_64":
+            linux = "linux_i686"
+        elif linux == "linux_aarch64":
+            linux = "linux_armv8l"
+    _, arch = linux.split("_", 1)
+    archs = {"armv8l": ["armv8l", "armv7l"]}.get(arch, [arch])
+    yield from _manylinux.platform_tags(archs)
+    yield from _musllinux.platform_tags(archs)
+    for arch in archs:
+        yield f"linux_{arch}"
+
+
+def _generic_platforms() -> Iterator[str]:
+    yield _normalize_string(sysconfig.get_platform())
+
+
+def platform_tags() -> Iterator[str]:
+    """
+    Provides the platform tags for this installation.
+    """
+    if platform.system() == "Darwin":
+        return mac_platforms()
+    elif platform.system() == "iOS":
+        return ios_platforms()
+    elif platform.system() == "Linux":
+        return _linux_platforms()
+    else:
+        return _generic_platforms()
+
+
+def interpreter_name() -> str:
+    """
+    Returns the name of the running interpreter.
+
+    Some implementations have a reserved, two-letter abbreviation which will
+    be returned when appropriate.
+    """
+    name = sys.implementation.name
+    return INTERPRETER_SHORT_NAMES.get(name) or name
+
+
+def interpreter_version(*, warn: bool = False) -> str:
+    """
+    Returns the version of the running interpreter.
+    """
+    version = _get_config_var("py_version_nodot", warn=warn)
+    if version:
+        version = str(version)
+    else:
+        version = _version_nodot(sys.version_info[:2])
+    return version
+
+
+def _version_nodot(version: PythonVersion) -> str:
+    return "".join(map(str, version))
+
+
+def sys_tags(*, warn: bool = False) -> Iterator[Tag]:
+    """
+    Returns the sequence of tag triples for the running interpreter.
+
+    The order of the sequence corresponds to priority order for the
+    interpreter, from most to least important.
+    """
+
+    interp_name = interpreter_name()
+    if interp_name == "cp":
+        yield from cpython_tags(warn=warn)
+    else:
+        yield from generic_tags()
+
+    if interp_name == "pp":
+        interp = "pp3"
+    elif interp_name == "cp":
+        interp = "cp" + interpreter_version(warn=warn)
+    else:
+        interp = None
+    yield from compatible_tags(interpreter=interp)
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/version.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/version.py
new file mode 100644
index 0000000000000000000000000000000000000000..8b0a040848d1253de6557fe0d9e93481c1252006
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/packaging/version.py
@@ -0,0 +1,563 @@
+# This file is dual licensed under the terms of the Apache License, Version
+# 2.0, and the BSD License. See the LICENSE file in the root of this repository
+# for complete details.
+"""
+.. testsetup::
+
+    from pip._vendor.packaging.version import parse, Version
+"""
+
+from __future__ import annotations
+
+import itertools
+import re
+from typing import Any, Callable, NamedTuple, SupportsInt, Tuple, Union
+
+from ._structures import Infinity, InfinityType, NegativeInfinity, NegativeInfinityType
+
+__all__ = ["VERSION_PATTERN", "parse", "Version", "InvalidVersion"]
+
+LocalType = Tuple[Union[int, str], ...]
+
+CmpPrePostDevType = Union[InfinityType, NegativeInfinityType, Tuple[str, int]]
+CmpLocalType = Union[
+    NegativeInfinityType,
+    Tuple[Union[Tuple[int, str], Tuple[NegativeInfinityType, Union[int, str]]], ...],
+]
+CmpKey = Tuple[
+    int,
+    Tuple[int, ...],
+    CmpPrePostDevType,
+    CmpPrePostDevType,
+    CmpPrePostDevType,
+    CmpLocalType,
+]
+VersionComparisonMethod = Callable[[CmpKey, CmpKey], bool]
+
+
+class _Version(NamedTuple):
+    epoch: int
+    release: tuple[int, ...]
+    dev: tuple[str, int] | None
+    pre: tuple[str, int] | None
+    post: tuple[str, int] | None
+    local: LocalType | None
+
+
+def parse(version: str) -> Version:
+    """Parse the given version string.
+
+    >>> parse('1.0.dev1')
+    <Version('1.0.dev1')>
+
+    :param version: The version string to parse.
+    :raises InvalidVersion: When the version string is not a valid version.
+    """
+    return Version(version)
+
+
+class InvalidVersion(ValueError):
+    """Raised when a version string is not a valid version.
+
+    >>> Version("invalid")
+    Traceback (most recent call last):
+        ...
+    packaging.version.InvalidVersion: Invalid version: 'invalid'
+    """
+
+
+class _BaseVersion:
+    _key: tuple[Any, ...]
+
+    def __hash__(self) -> int:
+        return hash(self._key)
+
+    # Please keep the duplicated `isinstance` check
+    # in the six comparisons hereunder
+    # unless you find a way to avoid adding overhead function calls.
+    def __lt__(self, other: _BaseVersion) -> bool:
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key < other._key
+
+    def __le__(self, other: _BaseVersion) -> bool:
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key <= other._key
+
+    def __eq__(self, other: object) -> bool:
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key == other._key
+
+    def __ge__(self, other: _BaseVersion) -> bool:
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key >= other._key
+
+    def __gt__(self, other: _BaseVersion) -> bool:
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key > other._key
+
+    def __ne__(self, other: object) -> bool:
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return self._key != other._key
+
+
+# Deliberately not anchored to the start and end of the string, to make it
+# easier for 3rd party code to reuse
+_VERSION_PATTERN = r"""
+    v?
+    (?:
+        (?:(?P<epoch>[0-9]+)!)?                           # epoch
+        (?P<release>[0-9]+(?:\.[0-9]+)*)                  # release segment
+        (?P<pre>                                          # pre-release
+            [-_\.]?
+            (?P<pre_l>alpha|a|beta|b|preview|pre|c|rc)
+            [-_\.]?
+            (?P<pre_n>[0-9]+)?
+        )?
+        (?P<post>                                         # post release
+            (?:-(?P<post_n1>[0-9]+))
+            |
+            (?:
+                [-_\.]?
+                (?P<post_l>post|rev|r)
+                [-_\.]?
+                (?P<post_n2>[0-9]+)?
+            )
+        )?
+        (?P<dev>                                          # dev release
+            [-_\.]?
+            (?P<dev_l>dev)
+            [-_\.]?
+            (?P<dev_n>[0-9]+)?
+        )?
+    )
+    (?:\+(?P<local>[a-z0-9]+(?:[-_\.][a-z0-9]+)*))?       # local version
+"""
+
+VERSION_PATTERN = _VERSION_PATTERN
+"""
+A string containing the regular expression used to match a valid version.
+
+The pattern is not anchored at either end, and is intended for embedding in larger
+expressions (for example, matching a version number as part of a file name). The
+regular expression should be compiled with the ``re.VERBOSE`` and ``re.IGNORECASE``
+flags set.
+
+:meta hide-value:
+"""
+
+
+class Version(_BaseVersion):
+    """This class abstracts handling of a project's versions.
+
+    A :class:`Version` instance is comparison aware and can be compared and
+    sorted using the standard Python interfaces.
+
+    >>> v1 = Version("1.0a5")
+    >>> v2 = Version("1.0")
+    >>> v1
+    <Version('1.0a5')>
+    >>> v2
+    <Version('1.0')>
+    >>> v1 < v2
+    True
+    >>> v1 == v2
+    False
+    >>> v1 > v2
+    False
+    >>> v1 >= v2
+    False
+    >>> v1 <= v2
+    True
+    """
+
+    _regex = re.compile(r"^\s*" + VERSION_PATTERN + r"\s*$", re.VERBOSE | re.IGNORECASE)
+    _key: CmpKey
+
+    def __init__(self, version: str) -> None:
+        """Initialize a Version object.
+
+        :param version:
+            The string representation of a version which will be parsed and normalized
+            before use.
+        :raises InvalidVersion:
+            If the ``version`` does not conform to PEP 440 in any way then this
+            exception will be raised.
+        """
+
+        # Validate the version and parse it into pieces
+        match = self._regex.search(version)
+        if not match:
+            raise InvalidVersion(f"Invalid version: '{version}'")
+
+        # Store the parsed out pieces of the version
+        self._version = _Version(
+            epoch=int(match.group("epoch")) if match.group("epoch") else 0,
+            release=tuple(int(i) for i in match.group("release").split(".")),
+            pre=_parse_letter_version(match.group("pre_l"), match.group("pre_n")),
+            post=_parse_letter_version(
+                match.group("post_l"), match.group("post_n1") or match.group("post_n2")
+            ),
+            dev=_parse_letter_version(match.group("dev_l"), match.group("dev_n")),
+            local=_parse_local_version(match.group("local")),
+        )
+
+        # Generate a key which will be used for sorting
+        self._key = _cmpkey(
+            self._version.epoch,
+            self._version.release,
+            self._version.pre,
+            self._version.post,
+            self._version.dev,
+            self._version.local,
+        )
+
+    def __repr__(self) -> str:
+        """A representation of the Version that shows all internal state.
+
+        >>> Version('1.0.0')
+        <Version('1.0.0')>
+        """
+        return f"<Version('{self}')>"
+
+    def __str__(self) -> str:
+        """A string representation of the version that can be rounded-tripped.
+
+        >>> str(Version("1.0a5"))
+        '1.0a5'
+        """
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append(f"{self.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        # Pre-release
+        if self.pre is not None:
+            parts.append("".join(str(x) for x in self.pre))
+
+        # Post-release
+        if self.post is not None:
+            parts.append(f".post{self.post}")
+
+        # Development release
+        if self.dev is not None:
+            parts.append(f".dev{self.dev}")
+
+        # Local version segment
+        if self.local is not None:
+            parts.append(f"+{self.local}")
+
+        return "".join(parts)
+
+    @property
+    def epoch(self) -> int:
+        """The epoch of the version.
+
+        >>> Version("2.0.0").epoch
+        0
+        >>> Version("1!2.0.0").epoch
+        1
+        """
+        return self._version.epoch
+
+    @property
+    def release(self) -> tuple[int, ...]:
+        """The components of the "release" segment of the version.
+
+        >>> Version("1.2.3").release
+        (1, 2, 3)
+        >>> Version("2.0.0").release
+        (2, 0, 0)
+        >>> Version("1!2.0.0.post0").release
+        (2, 0, 0)
+
+        Includes trailing zeroes but not the epoch or any pre-release / development /
+        post-release suffixes.
+        """
+        return self._version.release
+
+    @property
+    def pre(self) -> tuple[str, int] | None:
+        """The pre-release segment of the version.
+
+        >>> print(Version("1.2.3").pre)
+        None
+        >>> Version("1.2.3a1").pre
+        ('a', 1)
+        >>> Version("1.2.3b1").pre
+        ('b', 1)
+        >>> Version("1.2.3rc1").pre
+        ('rc', 1)
+        """
+        return self._version.pre
+
+    @property
+    def post(self) -> int | None:
+        """The post-release number of the version.
+
+        >>> print(Version("1.2.3").post)
+        None
+        >>> Version("1.2.3.post1").post
+        1
+        """
+        return self._version.post[1] if self._version.post else None
+
+    @property
+    def dev(self) -> int | None:
+        """The development number of the version.
+
+        >>> print(Version("1.2.3").dev)
+        None
+        >>> Version("1.2.3.dev1").dev
+        1
+        """
+        return self._version.dev[1] if self._version.dev else None
+
+    @property
+    def local(self) -> str | None:
+        """The local version segment of the version.
+
+        >>> print(Version("1.2.3").local)
+        None
+        >>> Version("1.2.3+abc").local
+        'abc'
+        """
+        if self._version.local:
+            return ".".join(str(x) for x in self._version.local)
+        else:
+            return None
+
+    @property
+    def public(self) -> str:
+        """The public portion of the version.
+
+        >>> Version("1.2.3").public
+        '1.2.3'
+        >>> Version("1.2.3+abc").public
+        '1.2.3'
+        >>> Version("1.2.3+abc.dev1").public
+        '1.2.3'
+        """
+        return str(self).split("+", 1)[0]
+
+    @property
+    def base_version(self) -> str:
+        """The "base version" of the version.
+
+        >>> Version("1.2.3").base_version
+        '1.2.3'
+        >>> Version("1.2.3+abc").base_version
+        '1.2.3'
+        >>> Version("1!1.2.3+abc.dev1").base_version
+        '1!1.2.3'
+
+        The "base version" is the public version of the project without any pre or post
+        release markers.
+        """
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append(f"{self.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        return "".join(parts)
+
+    @property
+    def is_prerelease(self) -> bool:
+        """Whether this version is a pre-release.
+
+        >>> Version("1.2.3").is_prerelease
+        False
+        >>> Version("1.2.3a1").is_prerelease
+        True
+        >>> Version("1.2.3b1").is_prerelease
+        True
+        >>> Version("1.2.3rc1").is_prerelease
+        True
+        >>> Version("1.2.3dev1").is_prerelease
+        True
+        """
+        return self.dev is not None or self.pre is not None
+
+    @property
+    def is_postrelease(self) -> bool:
+        """Whether this version is a post-release.
+
+        >>> Version("1.2.3").is_postrelease
+        False
+        >>> Version("1.2.3.post1").is_postrelease
+        True
+        """
+        return self.post is not None
+
+    @property
+    def is_devrelease(self) -> bool:
+        """Whether this version is a development release.
+
+        >>> Version("1.2.3").is_devrelease
+        False
+        >>> Version("1.2.3.dev1").is_devrelease
+        True
+        """
+        return self.dev is not None
+
+    @property
+    def major(self) -> int:
+        """The first item of :attr:`release` or ``0`` if unavailable.
+
+        >>> Version("1.2.3").major
+        1
+        """
+        return self.release[0] if len(self.release) >= 1 else 0
+
+    @property
+    def minor(self) -> int:
+        """The second item of :attr:`release` or ``0`` if unavailable.
+
+        >>> Version("1.2.3").minor
+        2
+        >>> Version("1").minor
+        0
+        """
+        return self.release[1] if len(self.release) >= 2 else 0
+
+    @property
+    def micro(self) -> int:
+        """The third item of :attr:`release` or ``0`` if unavailable.
+
+        >>> Version("1.2.3").micro
+        3
+        >>> Version("1").micro
+        0
+        """
+        return self.release[2] if len(self.release) >= 3 else 0
+
+
+def _parse_letter_version(
+    letter: str | None, number: str | bytes | SupportsInt | None
+) -> tuple[str, int] | None:
+    if letter:
+        # We consider there to be an implicit 0 in a pre-release if there is
+        # not a numeral associated with it.
+        if number is None:
+            number = 0
+
+        # We normalize any letters to their lower case form
+        letter = letter.lower()
+
+        # We consider some words to be alternate spellings of other words and
+        # in those cases we want to normalize the spellings to our preferred
+        # spelling.
+        if letter == "alpha":
+            letter = "a"
+        elif letter == "beta":
+            letter = "b"
+        elif letter in ["c", "pre", "preview"]:
+            letter = "rc"
+        elif letter in ["rev", "r"]:
+            letter = "post"
+
+        return letter, int(number)
+    if not letter and number:
+        # We assume if we are given a number, but we are not given a letter
+        # then this is using the implicit post release syntax (e.g. 1.0-1)
+        letter = "post"
+
+        return letter, int(number)
+
+    return None
+
+
+_local_version_separators = re.compile(r"[\._-]")
+
+
+def _parse_local_version(local: str | None) -> LocalType | None:
+    """
+    Takes a string like abc.1.twelve and turns it into ("abc", 1, "twelve").
+    """
+    if local is not None:
+        return tuple(
+            part.lower() if not part.isdigit() else int(part)
+            for part in _local_version_separators.split(local)
+        )
+    return None
+
+
+def _cmpkey(
+    epoch: int,
+    release: tuple[int, ...],
+    pre: tuple[str, int] | None,
+    post: tuple[str, int] | None,
+    dev: tuple[str, int] | None,
+    local: LocalType | None,
+) -> CmpKey:
+    # When we compare a release version, we want to compare it with all of the
+    # trailing zeros removed. So we'll use a reverse the list, drop all the now
+    # leading zeros until we come to something non zero, then take the rest
+    # re-reverse it back into the correct order and make it a tuple and use
+    # that for our sorting key.
+    _release = tuple(
+        reversed(list(itertools.dropwhile(lambda x: x == 0, reversed(release))))
+    )
+
+    # We need to "trick" the sorting algorithm to put 1.0.dev0 before 1.0a0.
+    # We'll do this by abusing the pre segment, but we _only_ want to do this
+    # if there is not a pre or a post segment. If we have one of those then
+    # the normal sorting rules will handle this case correctly.
+    if pre is None and post is None and dev is not None:
+        _pre: CmpPrePostDevType = NegativeInfinity
+    # Versions without a pre-release (except as noted above) should sort after
+    # those with one.
+    elif pre is None:
+        _pre = Infinity
+    else:
+        _pre = pre
+
+    # Versions without a post segment should sort before those with one.
+    if post is None:
+        _post: CmpPrePostDevType = NegativeInfinity
+
+    else:
+        _post = post
+
+    # Versions without a development segment should sort after those with one.
+    if dev is None:
+        _dev: CmpPrePostDevType = Infinity
+
+    else:
+        _dev = dev
+
+    if local is None:
+        # Versions without a local segment should sort before those with one.
+        _local: CmpLocalType = NegativeInfinity
+    else:
+        # Versions with a local segment need that segment parsed to implement
+        # the sorting rules in PEP440.
+        # - Alpha numeric segments sort before numeric segments
+        # - Alpha numeric segments sort lexicographically
+        # - Numeric segments sort numerically
+        # - Shorter versions sort before longer versions when the prefixes
+        #   match exactly
+        _local = tuple(
+            (i, "") if isinstance(i, int) else (NegativeInfinity, i) for i in local
+        )
+
+    return epoch, _release, _pre, _post, _dev, _local
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/typing_extensions.py b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/typing_extensions.py
new file mode 100644
index 0000000000000000000000000000000000000000..e429384e76aa9a27c3168ffc998d187ebb84ab93
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/pip/_vendor/typing_extensions.py
@@ -0,0 +1,3641 @@
+import abc
+import collections
+import collections.abc
+import contextlib
+import functools
+import inspect
+import operator
+import sys
+import types as _types
+import typing
+import warnings
+
+__all__ = [
+    # Super-special typing primitives.
+    'Any',
+    'ClassVar',
+    'Concatenate',
+    'Final',
+    'LiteralString',
+    'ParamSpec',
+    'ParamSpecArgs',
+    'ParamSpecKwargs',
+    'Self',
+    'Type',
+    'TypeVar',
+    'TypeVarTuple',
+    'Unpack',
+
+    # ABCs (from collections.abc).
+    'Awaitable',
+    'AsyncIterator',
+    'AsyncIterable',
+    'Coroutine',
+    'AsyncGenerator',
+    'AsyncContextManager',
+    'Buffer',
+    'ChainMap',
+
+    # Concrete collection types.
+    'ContextManager',
+    'Counter',
+    'Deque',
+    'DefaultDict',
+    'NamedTuple',
+    'OrderedDict',
+    'TypedDict',
+
+    # Structural checks, a.k.a. protocols.
+    'SupportsAbs',
+    'SupportsBytes',
+    'SupportsComplex',
+    'SupportsFloat',
+    'SupportsIndex',
+    'SupportsInt',
+    'SupportsRound',
+
+    # One-off things.
+    'Annotated',
+    'assert_never',
+    'assert_type',
+    'clear_overloads',
+    'dataclass_transform',
+    'deprecated',
+    'Doc',
+    'get_overloads',
+    'final',
+    'get_args',
+    'get_origin',
+    'get_original_bases',
+    'get_protocol_members',
+    'get_type_hints',
+    'IntVar',
+    'is_protocol',
+    'is_typeddict',
+    'Literal',
+    'NewType',
+    'overload',
+    'override',
+    'Protocol',
+    'reveal_type',
+    'runtime',
+    'runtime_checkable',
+    'Text',
+    'TypeAlias',
+    'TypeAliasType',
+    'TypeGuard',
+    'TypeIs',
+    'TYPE_CHECKING',
+    'Never',
+    'NoReturn',
+    'ReadOnly',
+    'Required',
+    'NotRequired',
+
+    # Pure aliases, have always been in typing
+    'AbstractSet',
+    'AnyStr',
+    'BinaryIO',
+    'Callable',
+    'Collection',
+    'Container',
+    'Dict',
+    'ForwardRef',
+    'FrozenSet',
+    'Generator',
+    'Generic',
+    'Hashable',
+    'IO',
+    'ItemsView',
+    'Iterable',
+    'Iterator',
+    'KeysView',
+    'List',
+    'Mapping',
+    'MappingView',
+    'Match',
+    'MutableMapping',
+    'MutableSequence',
+    'MutableSet',
+    'NoDefault',
+    'Optional',
+    'Pattern',
+    'Reversible',
+    'Sequence',
+    'Set',
+    'Sized',
+    'TextIO',
+    'Tuple',
+    'Union',
+    'ValuesView',
+    'cast',
+    'no_type_check',
+    'no_type_check_decorator',
+]
+
+# for backward compatibility
+PEP_560 = True
+GenericMeta = type
+_PEP_696_IMPLEMENTED = sys.version_info >= (3, 13, 0, "beta")
+
+# The functions below are modified copies of typing internal helpers.
+# They are needed by _ProtocolMeta and they provide support for PEP 646.
+
+
+class _Sentinel:
+    def __repr__(self):
+        return "<sentinel>"
+
+
+_marker = _Sentinel()
+
+
+if sys.version_info >= (3, 10):
+    def _should_collect_from_parameters(t):
+        return isinstance(
+            t, (typing._GenericAlias, _types.GenericAlias, _types.UnionType)
+        )
+elif sys.version_info >= (3, 9):
+    def _should_collect_from_parameters(t):
+        return isinstance(t, (typing._GenericAlias, _types.GenericAlias))
+else:
+    def _should_collect_from_parameters(t):
+        return isinstance(t, typing._GenericAlias) and not t._special
+
+
+NoReturn = typing.NoReturn
+
+# Some unconstrained type variables.  These are used by the container types.
+# (These are not for export.)
+T = typing.TypeVar('T')  # Any type.
+KT = typing.TypeVar('KT')  # Key type.
+VT = typing.TypeVar('VT')  # Value type.
+T_co = typing.TypeVar('T_co', covariant=True)  # Any type covariant containers.
+T_contra = typing.TypeVar('T_contra', contravariant=True)  # Ditto contravariant.
+
+
+if sys.version_info >= (3, 11):
+    from typing import Any
+else:
+
+    class _AnyMeta(type):
+        def __instancecheck__(self, obj):
+            if self is Any:
+                raise TypeError("typing_extensions.Any cannot be used with isinstance()")
+            return super().__instancecheck__(obj)
+
+        def __repr__(self):
+            if self is Any:
+                return "typing_extensions.Any"
+            return super().__repr__()
+
+    class Any(metaclass=_AnyMeta):
+        """Special type indicating an unconstrained type.
+        - Any is compatible with every type.
+        - Any assumed to have all methods.
+        - All values assumed to be instances of Any.
+        Note that all the above statements are true from the point of view of
+        static type checkers. At runtime, Any should not be used with instance
+        checks.
+        """
+        def __new__(cls, *args, **kwargs):
+            if cls is Any:
+                raise TypeError("Any cannot be instantiated")
+            return super().__new__(cls, *args, **kwargs)
+
+
+ClassVar = typing.ClassVar
+
+
+class _ExtensionsSpecialForm(typing._SpecialForm, _root=True):
+    def __repr__(self):
+        return 'typing_extensions.' + self._name
+
+
+Final = typing.Final
+
+if sys.version_info >= (3, 11):
+    final = typing.final
+else:
+    # @final exists in 3.8+, but we backport it for all versions
+    # before 3.11 to keep support for the __final__ attribute.
+    # See https://bugs.python.org/issue46342
+    def final(f):
+        """This decorator can be used to indicate to type checkers that
+        the decorated method cannot be overridden, and decorated class
+        cannot be subclassed. For example:
+
+            class Base:
+                @final
+                def done(self) -> None:
+                    ...
+            class Sub(Base):
+                def done(self) -> None:  # Error reported by type checker
+                    ...
+            @final
+            class Leaf:
+                ...
+            class Other(Leaf):  # Error reported by type checker
+                ...
+
+        There is no runtime checking of these properties. The decorator
+        sets the ``__final__`` attribute to ``True`` on the decorated object
+        to allow runtime introspection.
+        """
+        try:
+            f.__final__ = True
+        except (AttributeError, TypeError):
+            # Skip the attribute silently if it is not writable.
+            # AttributeError happens if the object has __slots__ or a
+            # read-only property, TypeError if it's a builtin class.
+            pass
+        return f
+
+
+def IntVar(name):
+    return typing.TypeVar(name)
+
+
+# A Literal bug was fixed in 3.11.0, 3.10.1 and 3.9.8
+if sys.version_info >= (3, 10, 1):
+    Literal = typing.Literal
+else:
+    def _flatten_literal_params(parameters):
+        """An internal helper for Literal creation: flatten Literals among parameters"""
+        params = []
+        for p in parameters:
+            if isinstance(p, _LiteralGenericAlias):
+                params.extend(p.__args__)
+            else:
+                params.append(p)
+        return tuple(params)
+
+    def _value_and_type_iter(params):
+        for p in params:
+            yield p, type(p)
+
+    class _LiteralGenericAlias(typing._GenericAlias, _root=True):
+        def __eq__(self, other):
+            if not isinstance(other, _LiteralGenericAlias):
+                return NotImplemented
+            these_args_deduped = set(_value_and_type_iter(self.__args__))
+            other_args_deduped = set(_value_and_type_iter(other.__args__))
+            return these_args_deduped == other_args_deduped
+
+        def __hash__(self):
+            return hash(frozenset(_value_and_type_iter(self.__args__)))
+
+    class _LiteralForm(_ExtensionsSpecialForm, _root=True):
+        def __init__(self, doc: str):
+            self._name = 'Literal'
+            self._doc = self.__doc__ = doc
+
+        def __getitem__(self, parameters):
+            if not isinstance(parameters, tuple):
+                parameters = (parameters,)
+
+            parameters = _flatten_literal_params(parameters)
+
+            val_type_pairs = list(_value_and_type_iter(parameters))
+            try:
+                deduped_pairs = set(val_type_pairs)
+            except TypeError:
+                # unhashable parameters
+                pass
+            else:
+                # similar logic to typing._deduplicate on Python 3.9+
+                if len(deduped_pairs) < len(val_type_pairs):
+                    new_parameters = []
+                    for pair in val_type_pairs:
+                        if pair in deduped_pairs:
+                            new_parameters.append(pair[0])
+                            deduped_pairs.remove(pair)
+                    assert not deduped_pairs, deduped_pairs
+                    parameters = tuple(new_parameters)
+
+            return _LiteralGenericAlias(self, parameters)
+
+    Literal = _LiteralForm(doc="""\
+                           A type that can be used to indicate to type checkers
+                           that the corresponding value has a value literally equivalent
+                           to the provided parameter. For example:
+
+                               var: Literal[4] = 4
+
+                           The type checker understands that 'var' is literally equal to
+                           the value 4 and no other value.
+
+                           Literal[...] cannot be subclassed. There is no runtime
+                           checking verifying that the parameter is actually a value
+                           instead of a type.""")
+
+
+_overload_dummy = typing._overload_dummy
+
+
+if hasattr(typing, "get_overloads"):  # 3.11+
+    overload = typing.overload
+    get_overloads = typing.get_overloads
+    clear_overloads = typing.clear_overloads
+else:
+    # {module: {qualname: {firstlineno: func}}}
+    _overload_registry = collections.defaultdict(
+        functools.partial(collections.defaultdict, dict)
+    )
+
+    def overload(func):
+        """Decorator for overloaded functions/methods.
+
+        In a stub file, place two or more stub definitions for the same
+        function in a row, each decorated with @overload.  For example:
+
+        @overload
+        def utf8(value: None) -> None: ...
+        @overload
+        def utf8(value: bytes) -> bytes: ...
+        @overload
+        def utf8(value: str) -> bytes: ...
+
+        In a non-stub file (i.e. a regular .py file), do the same but
+        follow it with an implementation.  The implementation should *not*
+        be decorated with @overload.  For example:
+
+        @overload
+        def utf8(value: None) -> None: ...
+        @overload
+        def utf8(value: bytes) -> bytes: ...
+        @overload
+        def utf8(value: str) -> bytes: ...
+        def utf8(value):
+            # implementation goes here
+
+        The overloads for a function can be retrieved at runtime using the
+        get_overloads() function.
+        """
+        # classmethod and staticmethod
+        f = getattr(func, "__func__", func)
+        try:
+            _overload_registry[f.__module__][f.__qualname__][
+                f.__code__.co_firstlineno
+            ] = func
+        except AttributeError:
+            # Not a normal function; ignore.
+            pass
+        return _overload_dummy
+
+    def get_overloads(func):
+        """Return all defined overloads for *func* as a sequence."""
+        # classmethod and staticmethod
+        f = getattr(func, "__func__", func)
+        if f.__module__ not in _overload_registry:
+            return []
+        mod_dict = _overload_registry[f.__module__]
+        if f.__qualname__ not in mod_dict:
+            return []
+        return list(mod_dict[f.__qualname__].values())
+
+    def clear_overloads():
+        """Clear all overloads in the registry."""
+        _overload_registry.clear()
+
+
+# This is not a real generic class.  Don't use outside annotations.
+Type = typing.Type
+
+# Various ABCs mimicking those in collections.abc.
+# A few are simply re-exported for completeness.
+Awaitable = typing.Awaitable
+Coroutine = typing.Coroutine
+AsyncIterable = typing.AsyncIterable
+AsyncIterator = typing.AsyncIterator
+Deque = typing.Deque
+DefaultDict = typing.DefaultDict
+OrderedDict = typing.OrderedDict
+Counter = typing.Counter
+ChainMap = typing.ChainMap
+Text = typing.Text
+TYPE_CHECKING = typing.TYPE_CHECKING
+
+
+if sys.version_info >= (3, 13, 0, "beta"):
+    from typing import AsyncContextManager, AsyncGenerator, ContextManager, Generator
+else:
+    def _is_dunder(attr):
+        return attr.startswith('__') and attr.endswith('__')
+
+    # Python <3.9 doesn't have typing._SpecialGenericAlias
+    _special_generic_alias_base = getattr(
+        typing, "_SpecialGenericAlias", typing._GenericAlias
+    )
+
+    class _SpecialGenericAlias(_special_generic_alias_base, _root=True):
+        def __init__(self, origin, nparams, *, inst=True, name=None, defaults=()):
+            if _special_generic_alias_base is typing._GenericAlias:
+                # Python <3.9
+                self.__origin__ = origin
+                self._nparams = nparams
+                super().__init__(origin, nparams, special=True, inst=inst, name=name)
+            else:
+                # Python >= 3.9
+                super().__init__(origin, nparams, inst=inst, name=name)
+            self._defaults = defaults
+
+        def __setattr__(self, attr, val):
+            allowed_attrs = {'_name', '_inst', '_nparams', '_defaults'}
+            if _special_generic_alias_base is typing._GenericAlias:
+                # Python <3.9
+                allowed_attrs.add("__origin__")
+            if _is_dunder(attr) or attr in allowed_attrs:
+                object.__setattr__(self, attr, val)
+            else:
+                setattr(self.__origin__, attr, val)
+
+        @typing._tp_cache
+        def __getitem__(self, params):
+            if not isinstance(params, tuple):
+                params = (params,)
+            msg = "Parameters to generic types must be types."
+            params = tuple(typing._type_check(p, msg) for p in params)
+            if (
+                self._defaults
+                and len(params) < self._nparams
+                and len(params) + len(self._defaults) >= self._nparams
+            ):
+                params = (*params, *self._defaults[len(params) - self._nparams:])
+            actual_len = len(params)
+
+            if actual_len != self._nparams:
+                if self._defaults:
+                    expected = f"at least {self._nparams - len(self._defaults)}"
+                else:
+                    expected = str(self._nparams)
+                if not self._nparams:
+                    raise TypeError(f"{self} is not a generic class")
+                raise TypeError(
+                    f"Too {'many' if actual_len > self._nparams else 'few'}"
+                    f" arguments for {self};"
+                    f" actual {actual_len}, expected {expected}"
+                )
+            return self.copy_with(params)
+
+    _NoneType = type(None)
+    Generator = _SpecialGenericAlias(
+        collections.abc.Generator, 3, defaults=(_NoneType, _NoneType)
+    )
+    AsyncGenerator = _SpecialGenericAlias(
+        collections.abc.AsyncGenerator, 2, defaults=(_NoneType,)
+    )
+    ContextManager = _SpecialGenericAlias(
+        contextlib.AbstractContextManager,
+        2,
+        name="ContextManager",
+        defaults=(typing.Optional[bool],)
+    )
+    AsyncContextManager = _SpecialGenericAlias(
+        contextlib.AbstractAsyncContextManager,
+        2,
+        name="AsyncContextManager",
+        defaults=(typing.Optional[bool],)
+    )
+
+
+_PROTO_ALLOWLIST = {
+    'collections.abc': [
+        'Callable', 'Awaitable', 'Iterable', 'Iterator', 'AsyncIterable',
+        'Hashable', 'Sized', 'Container', 'Collection', 'Reversible', 'Buffer',
+    ],
+    'contextlib': ['AbstractContextManager', 'AbstractAsyncContextManager'],
+    'typing_extensions': ['Buffer'],
+}
+
+
+_EXCLUDED_ATTRS = frozenset(typing.EXCLUDED_ATTRIBUTES) | {
+    "__match_args__", "__protocol_attrs__", "__non_callable_proto_members__",
+    "__final__",
+}
+
+
+def _get_protocol_attrs(cls):
+    attrs = set()
+    for base in cls.__mro__[:-1]:  # without object
+        if base.__name__ in {'Protocol', 'Generic'}:
+            continue
+        annotations = getattr(base, '__annotations__', {})
+        for attr in (*base.__dict__, *annotations):
+            if (not attr.startswith('_abc_') and attr not in _EXCLUDED_ATTRS):
+                attrs.add(attr)
+    return attrs
+
+
+def _caller(depth=2):
+    try:
+        return sys._getframe(depth).f_globals.get('__name__', '__main__')
+    except (AttributeError, ValueError):  # For platforms without _getframe()
+        return None
+
+
+# `__match_args__` attribute was removed from protocol members in 3.13,
+# we want to backport this change to older Python versions.
+if sys.version_info >= (3, 13):
+    Protocol = typing.Protocol
+else:
+    def _allow_reckless_class_checks(depth=3):
+        """Allow instance and class checks for special stdlib modules.
+        The abc and functools modules indiscriminately call isinstance() and
+        issubclass() on the whole MRO of a user class, which may contain protocols.
+        """
+        return _caller(depth) in {'abc', 'functools', None}
+
+    def _no_init(self, *args, **kwargs):
+        if type(self)._is_protocol:
+            raise TypeError('Protocols cannot be instantiated')
+
+    def _type_check_issubclass_arg_1(arg):
+        """Raise TypeError if `arg` is not an instance of `type`
+        in `issubclass(arg, <protocol>)`.
+
+        In most cases, this is verified by type.__subclasscheck__.
+        Checking it again unnecessarily would slow down issubclass() checks,
+        so, we don't perform this check unless we absolutely have to.
+
+        For various error paths, however,
+        we want to ensure that *this* error message is shown to the user
+        where relevant, rather than a typing.py-specific error message.
+        """
+        if not isinstance(arg, type):
+            # Same error message as for issubclass(1, int).
+            raise TypeError('issubclass() arg 1 must be a class')
+
+    # Inheriting from typing._ProtocolMeta isn't actually desirable,
+    # but is necessary to allow typing.Protocol and typing_extensions.Protocol
+    # to mix without getting TypeErrors about "metaclass conflict"
+    class _ProtocolMeta(type(typing.Protocol)):
+        # This metaclass is somewhat unfortunate,
+        # but is necessary for several reasons...
+        #
+        # NOTE: DO NOT call super() in any methods in this class
+        # That would call the methods on typing._ProtocolMeta on Python 3.8-3.11
+        # and those are slow
+        def __new__(mcls, name, bases, namespace, **kwargs):
+            if name == "Protocol" and len(bases) < 2:
+                pass
+            elif {Protocol, typing.Protocol} & set(bases):
+                for base in bases:
+                    if not (
+                        base in {object, typing.Generic, Protocol, typing.Protocol}
+                        or base.__name__ in _PROTO_ALLOWLIST.get(base.__module__, [])
+                        or is_protocol(base)
+                    ):
+                        raise TypeError(
+                            f"Protocols can only inherit from other protocols, "
+                            f"got {base!r}"
+                        )
+            return abc.ABCMeta.__new__(mcls, name, bases, namespace, **kwargs)
+
+        def __init__(cls, *args, **kwargs):
+            abc.ABCMeta.__init__(cls, *args, **kwargs)
+            if getattr(cls, "_is_protocol", False):
+                cls.__protocol_attrs__ = _get_protocol_attrs(cls)
+
+        def __subclasscheck__(cls, other):
+            if cls is Protocol:
+                return type.__subclasscheck__(cls, other)
+            if (
+                getattr(cls, '_is_protocol', False)
+                and not _allow_reckless_class_checks()
+            ):
+                if not getattr(cls, '_is_runtime_protocol', False):
+                    _type_check_issubclass_arg_1(other)
+                    raise TypeError(
+                        "Instance and class checks can only be used with "
+                        "@runtime_checkable protocols"
+                    )
+                if (
+                    # this attribute is set by @runtime_checkable:
+                    cls.__non_callable_proto_members__
+                    and cls.__dict__.get("__subclasshook__") is _proto_hook
+                ):
+                    _type_check_issubclass_arg_1(other)
+                    non_method_attrs = sorted(cls.__non_callable_proto_members__)
+                    raise TypeError(
+                        "Protocols with non-method members don't support issubclass()."
+                        f" Non-method members: {str(non_method_attrs)[1:-1]}."
+                    )
+            return abc.ABCMeta.__subclasscheck__(cls, other)
+
+        def __instancecheck__(cls, instance):
+            # We need this method for situations where attributes are
+            # assigned in __init__.
+            if cls is Protocol:
+                return type.__instancecheck__(cls, instance)
+            if not getattr(cls, "_is_protocol", False):
+                # i.e., it's a concrete subclass of a protocol
+                return abc.ABCMeta.__instancecheck__(cls, instance)
+
+            if (
+                not getattr(cls, '_is_runtime_protocol', False) and
+                not _allow_reckless_class_checks()
+            ):
+                raise TypeError("Instance and class checks can only be used with"
+                                " @runtime_checkable protocols")
+
+            if abc.ABCMeta.__instancecheck__(cls, instance):
+                return True
+
+            for attr in cls.__protocol_attrs__:
+                try:
+                    val = inspect.getattr_static(instance, attr)
+                except AttributeError:
+                    break
+                # this attribute is set by @runtime_checkable:
+                if val is None and attr not in cls.__non_callable_proto_members__:
+                    break
+            else:
+                return True
+
+            return False
+
+        def __eq__(cls, other):
+            # Hack so that typing.Generic.__class_getitem__
+            # treats typing_extensions.Protocol
+            # as equivalent to typing.Protocol
+            if abc.ABCMeta.__eq__(cls, other) is True:
+                return True
+            return cls is Protocol and other is typing.Protocol
+
+        # This has to be defined, or the abc-module cache
+        # complains about classes with this metaclass being unhashable,
+        # if we define only __eq__!
+        def __hash__(cls) -> int:
+            return type.__hash__(cls)
+
+    @classmethod
+    def _proto_hook(cls, other):
+        if not cls.__dict__.get('_is_protocol', False):
+            return NotImplemented
+
+        for attr in cls.__protocol_attrs__:
+            for base in other.__mro__:
+                # Check if the members appears in the class dictionary...
+                if attr in base.__dict__:
+                    if base.__dict__[attr] is None:
+                        return NotImplemented
+                    break
+
+                # ...or in annotations, if it is a sub-protocol.
+                annotations = getattr(base, '__annotations__', {})
+                if (
+                    isinstance(annotations, collections.abc.Mapping)
+                    and attr in annotations
+                    and is_protocol(other)
+                ):
+                    break
+            else:
+                return NotImplemented
+        return True
+
+    class Protocol(typing.Generic, metaclass=_ProtocolMeta):
+        __doc__ = typing.Protocol.__doc__
+        __slots__ = ()
+        _is_protocol = True
+        _is_runtime_protocol = False
+
+        def __init_subclass__(cls, *args, **kwargs):
+            super().__init_subclass__(*args, **kwargs)
+
+            # Determine if this is a protocol or a concrete subclass.
+            if not cls.__dict__.get('_is_protocol', False):
+                cls._is_protocol = any(b is Protocol for b in cls.__bases__)
+
+            # Set (or override) the protocol subclass hook.
+            if '__subclasshook__' not in cls.__dict__:
+                cls.__subclasshook__ = _proto_hook
+
+            # Prohibit instantiation for protocol classes
+            if cls._is_protocol and cls.__init__ is Protocol.__init__:
+                cls.__init__ = _no_init
+
+
+if sys.version_info >= (3, 13):
+    runtime_checkable = typing.runtime_checkable
+else:
+    def runtime_checkable(cls):
+        """Mark a protocol class as a runtime protocol.
+
+        Such protocol can be used with isinstance() and issubclass().
+        Raise TypeError if applied to a non-protocol class.
+        This allows a simple-minded structural check very similar to
+        one trick ponies in collections.abc such as Iterable.
+
+        For example::
+
+            @runtime_checkable
+            class Closable(Protocol):
+                def close(self): ...
+
+            assert isinstance(open('/some/file'), Closable)
+
+        Warning: this will check only the presence of the required methods,
+        not their type signatures!
+        """
+        if not issubclass(cls, typing.Generic) or not getattr(cls, '_is_protocol', False):
+            raise TypeError(f'@runtime_checkable can be only applied to protocol classes,'
+                            f' got {cls!r}')
+        cls._is_runtime_protocol = True
+
+        # typing.Protocol classes on <=3.11 break if we execute this block,
+        # because typing.Protocol classes on <=3.11 don't have a
+        # `__protocol_attrs__` attribute, and this block relies on the
+        # `__protocol_attrs__` attribute. Meanwhile, typing.Protocol classes on 3.12.2+
+        # break if we *don't* execute this block, because *they* assume that all
+        # protocol classes have a `__non_callable_proto_members__` attribute
+        # (which this block sets)
+        if isinstance(cls, _ProtocolMeta) or sys.version_info >= (3, 12, 2):
+            # PEP 544 prohibits using issubclass()
+            # with protocols that have non-method members.
+            # See gh-113320 for why we compute this attribute here,
+            # rather than in `_ProtocolMeta.__init__`
+            cls.__non_callable_proto_members__ = set()
+            for attr in cls.__protocol_attrs__:
+                try:
+                    is_callable = callable(getattr(cls, attr, None))
+                except Exception as e:
+                    raise TypeError(
+                        f"Failed to determine whether protocol member {attr!r} "
+                        "is a method member"
+                    ) from e
+                else:
+                    if not is_callable:
+                        cls.__non_callable_proto_members__.add(attr)
+
+        return cls
+
+
+# The "runtime" alias exists for backwards compatibility.
+runtime = runtime_checkable
+
+
+# Our version of runtime-checkable protocols is faster on Python 3.8-3.11
+if sys.version_info >= (3, 12):
+    SupportsInt = typing.SupportsInt
+    SupportsFloat = typing.SupportsFloat
+    SupportsComplex = typing.SupportsComplex
+    SupportsBytes = typing.SupportsBytes
+    SupportsIndex = typing.SupportsIndex
+    SupportsAbs = typing.SupportsAbs
+    SupportsRound = typing.SupportsRound
+else:
+    @runtime_checkable
+    class SupportsInt(Protocol):
+        """An ABC with one abstract method __int__."""
+        __slots__ = ()
+
+        @abc.abstractmethod
+        def __int__(self) -> int:
+            pass
+
+    @runtime_checkable
+    class SupportsFloat(Protocol):
+        """An ABC with one abstract method __float__."""
+        __slots__ = ()
+
+        @abc.abstractmethod
+        def __float__(self) -> float:
+            pass
+
+    @runtime_checkable
+    class SupportsComplex(Protocol):
+        """An ABC with one abstract method __complex__."""
+        __slots__ = ()
+
+        @abc.abstractmethod
+        def __complex__(self) -> complex:
+            pass
+
+    @runtime_checkable
+    class SupportsBytes(Protocol):
+        """An ABC with one abstract method __bytes__."""
+        __slots__ = ()
+
+        @abc.abstractmethod
+        def __bytes__(self) -> bytes:
+            pass
+
+    @runtime_checkable
+    class SupportsIndex(Protocol):
+        __slots__ = ()
+
+        @abc.abstractmethod
+        def __index__(self) -> int:
+            pass
+
+    @runtime_checkable
+    class SupportsAbs(Protocol[T_co]):
+        """
+        An ABC with one abstract method __abs__ that is covariant in its return type.
+        """
+        __slots__ = ()
+
+        @abc.abstractmethod
+        def __abs__(self) -> T_co:
+            pass
+
+    @runtime_checkable
+    class SupportsRound(Protocol[T_co]):
+        """
+        An ABC with one abstract method __round__ that is covariant in its return type.
+        """
+        __slots__ = ()
+
+        @abc.abstractmethod
+        def __round__(self, ndigits: int = 0) -> T_co:
+            pass
+
+
+def _ensure_subclassable(mro_entries):
+    def inner(func):
+        if sys.implementation.name == "pypy" and sys.version_info < (3, 9):
+            cls_dict = {
+                "__call__": staticmethod(func),
+                "__mro_entries__": staticmethod(mro_entries)
+            }
+            t = type(func.__name__, (), cls_dict)
+            return functools.update_wrapper(t(), func)
+        else:
+            func.__mro_entries__ = mro_entries
+            return func
+    return inner
+
+
+# Update this to something like >=3.13.0b1 if and when
+# PEP 728 is implemented in CPython
+_PEP_728_IMPLEMENTED = False
+
+if _PEP_728_IMPLEMENTED:
+    # The standard library TypedDict in Python 3.8 does not store runtime information
+    # about which (if any) keys are optional.  See https://bugs.python.org/issue38834
+    # The standard library TypedDict in Python 3.9.0/1 does not honour the "total"
+    # keyword with old-style TypedDict().  See https://bugs.python.org/issue42059
+    # The standard library TypedDict below Python 3.11 does not store runtime
+    # information about optional and required keys when using Required or NotRequired.
+    # Generic TypedDicts are also impossible using typing.TypedDict on Python <3.11.
+    # Aaaand on 3.12 we add __orig_bases__ to TypedDict
+    # to enable better runtime introspection.
+    # On 3.13 we deprecate some odd ways of creating TypedDicts.
+    # Also on 3.13, PEP 705 adds the ReadOnly[] qualifier.
+    # PEP 728 (still pending) makes more changes.
+    TypedDict = typing.TypedDict
+    _TypedDictMeta = typing._TypedDictMeta
+    is_typeddict = typing.is_typeddict
+else:
+    # 3.10.0 and later
+    _TAKES_MODULE = "module" in inspect.signature(typing._type_check).parameters
+
+    def _get_typeddict_qualifiers(annotation_type):
+        while True:
+            annotation_origin = get_origin(annotation_type)
+            if annotation_origin is Annotated:
+                annotation_args = get_args(annotation_type)
+                if annotation_args:
+                    annotation_type = annotation_args[0]
+                else:
+                    break
+            elif annotation_origin is Required:
+                yield Required
+                annotation_type, = get_args(annotation_type)
+            elif annotation_origin is NotRequired:
+                yield NotRequired
+                annotation_type, = get_args(annotation_type)
+            elif annotation_origin is ReadOnly:
+                yield ReadOnly
+                annotation_type, = get_args(annotation_type)
+            else:
+                break
+
+    class _TypedDictMeta(type):
+        def __new__(cls, name, bases, ns, *, total=True, closed=False):
+            """Create new typed dict class object.
+
+            This method is called when TypedDict is subclassed,
+            or when TypedDict is instantiated. This way
+            TypedDict supports all three syntax forms described in its docstring.
+            Subclasses and instances of TypedDict return actual dictionaries.
+            """
+            for base in bases:
+                if type(base) is not _TypedDictMeta and base is not typing.Generic:
+                    raise TypeError('cannot inherit from both a TypedDict type '
+                                    'and a non-TypedDict base class')
+
+            if any(issubclass(b, typing.Generic) for b in bases):
+                generic_base = (typing.Generic,)
+            else:
+                generic_base = ()
+
+            # typing.py generally doesn't let you inherit from plain Generic, unless
+            # the name of the class happens to be "Protocol"
+            tp_dict = type.__new__(_TypedDictMeta, "Protocol", (*generic_base, dict), ns)
+            tp_dict.__name__ = name
+            if tp_dict.__qualname__ == "Protocol":
+                tp_dict.__qualname__ = name
+
+            if not hasattr(tp_dict, '__orig_bases__'):
+                tp_dict.__orig_bases__ = bases
+
+            annotations = {}
+            if "__annotations__" in ns:
+                own_annotations = ns["__annotations__"]
+            elif "__annotate__" in ns:
+                # TODO: Use inspect.VALUE here, and make the annotations lazily evaluated
+                own_annotations = ns["__annotate__"](1)
+            else:
+                own_annotations = {}
+            msg = "TypedDict('Name', {f0: t0, f1: t1, ...}); each t must be a type"
+            if _TAKES_MODULE:
+                own_annotations = {
+                    n: typing._type_check(tp, msg, module=tp_dict.__module__)
+                    for n, tp in own_annotations.items()
+                }
+            else:
+                own_annotations = {
+                    n: typing._type_check(tp, msg)
+                    for n, tp in own_annotations.items()
+                }
+            required_keys = set()
+            optional_keys = set()
+            readonly_keys = set()
+            mutable_keys = set()
+            extra_items_type = None
+
+            for base in bases:
+                base_dict = base.__dict__
+
+                annotations.update(base_dict.get('__annotations__', {}))
+                required_keys.update(base_dict.get('__required_keys__', ()))
+                optional_keys.update(base_dict.get('__optional_keys__', ()))
+                readonly_keys.update(base_dict.get('__readonly_keys__', ()))
+                mutable_keys.update(base_dict.get('__mutable_keys__', ()))
+                base_extra_items_type = base_dict.get('__extra_items__', None)
+                if base_extra_items_type is not None:
+                    extra_items_type = base_extra_items_type
+
+            if closed and extra_items_type is None:
+                extra_items_type = Never
+            if closed and "__extra_items__" in own_annotations:
+                annotation_type = own_annotations.pop("__extra_items__")
+                qualifiers = set(_get_typeddict_qualifiers(annotation_type))
+                if Required in qualifiers:
+                    raise TypeError(
+                        "Special key __extra_items__ does not support "
+                        "Required"
+                    )
+                if NotRequired in qualifiers:
+                    raise TypeError(
+                        "Special key __extra_items__ does not support "
+                        "NotRequired"
+                    )
+                extra_items_type = annotation_type
+
+            annotations.update(own_annotations)
+            for annotation_key, annotation_type in own_annotations.items():
+                qualifiers = set(_get_typeddict_qualifiers(annotation_type))
+
+                if Required in qualifiers:
+                    required_keys.add(annotation_key)
+                elif NotRequired in qualifiers:
+                    optional_keys.add(annotation_key)
+                elif total:
+                    required_keys.add(annotation_key)
+                else:
+                    optional_keys.add(annotation_key)
+                if ReadOnly in qualifiers:
+                    mutable_keys.discard(annotation_key)
+                    readonly_keys.add(annotation_key)
+                else:
+                    mutable_keys.add(annotation_key)
+                    readonly_keys.discard(annotation_key)
+
+            tp_dict.__annotations__ = annotations
+            tp_dict.__required_keys__ = frozenset(required_keys)
+            tp_dict.__optional_keys__ = frozenset(optional_keys)
+            tp_dict.__readonly_keys__ = frozenset(readonly_keys)
+            tp_dict.__mutable_keys__ = frozenset(mutable_keys)
+            if not hasattr(tp_dict, '__total__'):
+                tp_dict.__total__ = total
+            tp_dict.__closed__ = closed
+            tp_dict.__extra_items__ = extra_items_type
+            return tp_dict
+
+        __call__ = dict  # static method
+
+        def __subclasscheck__(cls, other):
+            # Typed dicts are only for static structural subtyping.
+            raise TypeError('TypedDict does not support instance and class checks')
+
+        __instancecheck__ = __subclasscheck__
+
+    _TypedDict = type.__new__(_TypedDictMeta, 'TypedDict', (), {})
+
+    @_ensure_subclassable(lambda bases: (_TypedDict,))
+    def TypedDict(typename, fields=_marker, /, *, total=True, closed=False, **kwargs):
+        """A simple typed namespace. At runtime it is equivalent to a plain dict.
+
+        TypedDict creates a dictionary type such that a type checker will expect all
+        instances to have a certain set of keys, where each key is
+        associated with a value of a consistent type. This expectation
+        is not checked at runtime.
+
+        Usage::
+
+            class Point2D(TypedDict):
+                x: int
+                y: int
+                label: str
+
+            a: Point2D = {'x': 1, 'y': 2, 'label': 'good'}  # OK
+            b: Point2D = {'z': 3, 'label': 'bad'}           # Fails type check
+
+            assert Point2D(x=1, y=2, label='first') == dict(x=1, y=2, label='first')
+
+        The type info can be accessed via the Point2D.__annotations__ dict, and
+        the Point2D.__required_keys__ and Point2D.__optional_keys__ frozensets.
+        TypedDict supports an additional equivalent form::
+
+            Point2D = TypedDict('Point2D', {'x': int, 'y': int, 'label': str})
+
+        By default, all keys must be present in a TypedDict. It is possible
+        to override this by specifying totality::
+
+            class Point2D(TypedDict, total=False):
+                x: int
+                y: int
+
+        This means that a Point2D TypedDict can have any of the keys omitted. A type
+        checker is only expected to support a literal False or True as the value of
+        the total argument. True is the default, and makes all items defined in the
+        class body be required.
+
+        The Required and NotRequired special forms can also be used to mark
+        individual keys as being required or not required::
+
+            class Point2D(TypedDict):
+                x: int  # the "x" key must always be present (Required is the default)
+                y: NotRequired[int]  # the "y" key can be omitted
+
+        See PEP 655 for more details on Required and NotRequired.
+        """
+        if fields is _marker or fields is None:
+            if fields is _marker:
+                deprecated_thing = "Failing to pass a value for the 'fields' parameter"
+            else:
+                deprecated_thing = "Passing `None` as the 'fields' parameter"
+
+            example = f"`{typename} = TypedDict({typename!r}, {{}})`"
+            deprecation_msg = (
+                f"{deprecated_thing} is deprecated and will be disallowed in "
+                "Python 3.15. To create a TypedDict class with 0 fields "
+                "using the functional syntax, pass an empty dictionary, e.g. "
+            ) + example + "."
+            warnings.warn(deprecation_msg, DeprecationWarning, stacklevel=2)
+            if closed is not False and closed is not True:
+                kwargs["closed"] = closed
+                closed = False
+            fields = kwargs
+        elif kwargs:
+            raise TypeError("TypedDict takes either a dict or keyword arguments,"
+                            " but not both")
+        if kwargs:
+            if sys.version_info >= (3, 13):
+                raise TypeError("TypedDict takes no keyword arguments")
+            warnings.warn(
+                "The kwargs-based syntax for TypedDict definitions is deprecated "
+                "in Python 3.11, will be removed in Python 3.13, and may not be "
+                "understood by third-party type checkers.",
+                DeprecationWarning,
+                stacklevel=2,
+            )
+
+        ns = {'__annotations__': dict(fields)}
+        module = _caller()
+        if module is not None:
+            # Setting correct module is necessary to make typed dict classes pickleable.
+            ns['__module__'] = module
+
+        td = _TypedDictMeta(typename, (), ns, total=total, closed=closed)
+        td.__orig_bases__ = (TypedDict,)
+        return td
+
+    if hasattr(typing, "_TypedDictMeta"):
+        _TYPEDDICT_TYPES = (typing._TypedDictMeta, _TypedDictMeta)
+    else:
+        _TYPEDDICT_TYPES = (_TypedDictMeta,)
+
+    def is_typeddict(tp):
+        """Check if an annotation is a TypedDict class
+
+        For example::
+            class Film(TypedDict):
+                title: str
+                year: int
+
+            is_typeddict(Film)  # => True
+            is_typeddict(Union[list, str])  # => False
+        """
+        # On 3.8, this would otherwise return True
+        if hasattr(typing, "TypedDict") and tp is typing.TypedDict:
+            return False
+        return isinstance(tp, _TYPEDDICT_TYPES)
+
+
+if hasattr(typing, "assert_type"):
+    assert_type = typing.assert_type
+
+else:
+    def assert_type(val, typ, /):
+        """Assert (to the type checker) that the value is of the given type.
+
+        When the type checker encounters a call to assert_type(), it
+        emits an error if the value is not of the specified type::
+
+            def greet(name: str) -> None:
+                assert_type(name, str)  # ok
+                assert_type(name, int)  # type checker error
+
+        At runtime this returns the first argument unchanged and otherwise
+        does nothing.
+        """
+        return val
+
+
+if hasattr(typing, "ReadOnly"):  # 3.13+
+    get_type_hints = typing.get_type_hints
+else:  # <=3.13
+    # replaces _strip_annotations()
+    def _strip_extras(t):
+        """Strips Annotated, Required and NotRequired from a given type."""
+        if isinstance(t, _AnnotatedAlias):
+            return _strip_extras(t.__origin__)
+        if hasattr(t, "__origin__") and t.__origin__ in (Required, NotRequired, ReadOnly):
+            return _strip_extras(t.__args__[0])
+        if isinstance(t, typing._GenericAlias):
+            stripped_args = tuple(_strip_extras(a) for a in t.__args__)
+            if stripped_args == t.__args__:
+                return t
+            return t.copy_with(stripped_args)
+        if hasattr(_types, "GenericAlias") and isinstance(t, _types.GenericAlias):
+            stripped_args = tuple(_strip_extras(a) for a in t.__args__)
+            if stripped_args == t.__args__:
+                return t
+            return _types.GenericAlias(t.__origin__, stripped_args)
+        if hasattr(_types, "UnionType") and isinstance(t, _types.UnionType):
+            stripped_args = tuple(_strip_extras(a) for a in t.__args__)
+            if stripped_args == t.__args__:
+                return t
+            return functools.reduce(operator.or_, stripped_args)
+
+        return t
+
+    def get_type_hints(obj, globalns=None, localns=None, include_extras=False):
+        """Return type hints for an object.
+
+        This is often the same as obj.__annotations__, but it handles
+        forward references encoded as string literals, adds Optional[t] if a
+        default value equal to None is set and recursively replaces all
+        'Annotated[T, ...]', 'Required[T]' or 'NotRequired[T]' with 'T'
+        (unless 'include_extras=True').
+
+        The argument may be a module, class, method, or function. The annotations
+        are returned as a dictionary. For classes, annotations include also
+        inherited members.
+
+        TypeError is raised if the argument is not of a type that can contain
+        annotations, and an empty dictionary is returned if no annotations are
+        present.
+
+        BEWARE -- the behavior of globalns and localns is counterintuitive
+        (unless you are familiar with how eval() and exec() work).  The
+        search order is locals first, then globals.
+
+        - If no dict arguments are passed, an attempt is made to use the
+          globals from obj (or the respective module's globals for classes),
+          and these are also used as the locals.  If the object does not appear
+          to have globals, an empty dictionary is used.
+
+        - If one dict argument is passed, it is used for both globals and
+          locals.
+
+        - If two dict arguments are passed, they specify globals and
+          locals, respectively.
+        """
+        if hasattr(typing, "Annotated"):  # 3.9+
+            hint = typing.get_type_hints(
+                obj, globalns=globalns, localns=localns, include_extras=True
+            )
+        else:  # 3.8
+            hint = typing.get_type_hints(obj, globalns=globalns, localns=localns)
+        if include_extras:
+            return hint
+        return {k: _strip_extras(t) for k, t in hint.items()}
+
+
+# Python 3.9+ has PEP 593 (Annotated)
+if hasattr(typing, 'Annotated'):
+    Annotated = typing.Annotated
+    # Not exported and not a public API, but needed for get_origin() and get_args()
+    # to work.
+    _AnnotatedAlias = typing._AnnotatedAlias
+# 3.8
+else:
+    class _AnnotatedAlias(typing._GenericAlias, _root=True):
+        """Runtime representation of an annotated type.
+
+        At its core 'Annotated[t, dec1, dec2, ...]' is an alias for the type 't'
+        with extra annotations. The alias behaves like a normal typing alias,
+        instantiating is the same as instantiating the underlying type, binding
+        it to types is also the same.
+        """
+        def __init__(self, origin, metadata):
+            if isinstance(origin, _AnnotatedAlias):
+                metadata = origin.__metadata__ + metadata
+                origin = origin.__origin__
+            super().__init__(origin, origin)
+            self.__metadata__ = metadata
+
+        def copy_with(self, params):
+            assert len(params) == 1
+            new_type = params[0]
+            return _AnnotatedAlias(new_type, self.__metadata__)
+
+        def __repr__(self):
+            return (f"typing_extensions.Annotated[{typing._type_repr(self.__origin__)}, "
+                    f"{', '.join(repr(a) for a in self.__metadata__)}]")
+
+        def __reduce__(self):
+            return operator.getitem, (
+                Annotated, (self.__origin__, *self.__metadata__)
+            )
+
+        def __eq__(self, other):
+            if not isinstance(other, _AnnotatedAlias):
+                return NotImplemented
+            if self.__origin__ != other.__origin__:
+                return False
+            return self.__metadata__ == other.__metadata__
+
+        def __hash__(self):
+            return hash((self.__origin__, self.__metadata__))
+
+    class Annotated:
+        """Add context specific metadata to a type.
+
+        Example: Annotated[int, runtime_check.Unsigned] indicates to the
+        hypothetical runtime_check module that this type is an unsigned int.
+        Every other consumer of this type can ignore this metadata and treat
+        this type as int.
+
+        The first argument to Annotated must be a valid type (and will be in
+        the __origin__ field), the remaining arguments are kept as a tuple in
+        the __extra__ field.
+
+        Details:
+
+        - It's an error to call `Annotated` with less than two arguments.
+        - Nested Annotated are flattened::
+
+            Annotated[Annotated[T, Ann1, Ann2], Ann3] == Annotated[T, Ann1, Ann2, Ann3]
+
+        - Instantiating an annotated type is equivalent to instantiating the
+        underlying type::
+
+            Annotated[C, Ann1](5) == C(5)
+
+        - Annotated can be used as a generic type alias::
+
+            Optimized = Annotated[T, runtime.Optimize()]
+            Optimized[int] == Annotated[int, runtime.Optimize()]
+
+            OptimizedList = Annotated[List[T], runtime.Optimize()]
+            OptimizedList[int] == Annotated[List[int], runtime.Optimize()]
+        """
+
+        __slots__ = ()
+
+        def __new__(cls, *args, **kwargs):
+            raise TypeError("Type Annotated cannot be instantiated.")
+
+        @typing._tp_cache
+        def __class_getitem__(cls, params):
+            if not isinstance(params, tuple) or len(params) < 2:
+                raise TypeError("Annotated[...] should be used "
+                                "with at least two arguments (a type and an "
+                                "annotation).")
+            allowed_special_forms = (ClassVar, Final)
+            if get_origin(params[0]) in allowed_special_forms:
+                origin = params[0]
+            else:
+                msg = "Annotated[t, ...]: t must be a type."
+                origin = typing._type_check(params[0], msg)
+            metadata = tuple(params[1:])
+            return _AnnotatedAlias(origin, metadata)
+
+        def __init_subclass__(cls, *args, **kwargs):
+            raise TypeError(
+                f"Cannot subclass {cls.__module__}.Annotated"
+            )
+
+# Python 3.8 has get_origin() and get_args() but those implementations aren't
+# Annotated-aware, so we can't use those. Python 3.9's versions don't support
+# ParamSpecArgs and ParamSpecKwargs, so only Python 3.10's versions will do.
+if sys.version_info[:2] >= (3, 10):
+    get_origin = typing.get_origin
+    get_args = typing.get_args
+# 3.8-3.9
+else:
+    try:
+        # 3.9+
+        from typing import _BaseGenericAlias
+    except ImportError:
+        _BaseGenericAlias = typing._GenericAlias
+    try:
+        # 3.9+
+        from typing import GenericAlias as _typing_GenericAlias
+    except ImportError:
+        _typing_GenericAlias = typing._GenericAlias
+
+    def get_origin(tp):
+        """Get the unsubscripted version of a type.
+
+        This supports generic types, Callable, Tuple, Union, Literal, Final, ClassVar
+        and Annotated. Return None for unsupported types. Examples::
+
+            get_origin(Literal[42]) is Literal
+            get_origin(int) is None
+            get_origin(ClassVar[int]) is ClassVar
+            get_origin(Generic) is Generic
+            get_origin(Generic[T]) is Generic
+            get_origin(Union[T, int]) is Union
+            get_origin(List[Tuple[T, T]][int]) == list
+            get_origin(P.args) is P
+        """
+        if isinstance(tp, _AnnotatedAlias):
+            return Annotated
+        if isinstance(tp, (typing._GenericAlias, _typing_GenericAlias, _BaseGenericAlias,
+                           ParamSpecArgs, ParamSpecKwargs)):
+            return tp.__origin__
+        if tp is typing.Generic:
+            return typing.Generic
+        return None
+
+    def get_args(tp):
+        """Get type arguments with all substitutions performed.
+
+        For unions, basic simplifications used by Union constructor are performed.
+        Examples::
+            get_args(Dict[str, int]) == (str, int)
+            get_args(int) == ()
+            get_args(Union[int, Union[T, int], str][int]) == (int, str)
+            get_args(Union[int, Tuple[T, int]][str]) == (int, Tuple[str, int])
+            get_args(Callable[[], T][int]) == ([], int)
+        """
+        if isinstance(tp, _AnnotatedAlias):
+            return (tp.__origin__, *tp.__metadata__)
+        if isinstance(tp, (typing._GenericAlias, _typing_GenericAlias)):
+            if getattr(tp, "_special", False):
+                return ()
+            res = tp.__args__
+            if get_origin(tp) is collections.abc.Callable and res[0] is not Ellipsis:
+                res = (list(res[:-1]), res[-1])
+            return res
+        return ()
+
+
+# 3.10+
+if hasattr(typing, 'TypeAlias'):
+    TypeAlias = typing.TypeAlias
+# 3.9
+elif sys.version_info[:2] >= (3, 9):
+    @_ExtensionsSpecialForm
+    def TypeAlias(self, parameters):
+        """Special marker indicating that an assignment should
+        be recognized as a proper type alias definition by type
+        checkers.
+
+        For example::
+
+            Predicate: TypeAlias = Callable[..., bool]
+
+        It's invalid when used anywhere except as in the example above.
+        """
+        raise TypeError(f"{self} is not subscriptable")
+# 3.8
+else:
+    TypeAlias = _ExtensionsSpecialForm(
+        'TypeAlias',
+        doc="""Special marker indicating that an assignment should
+        be recognized as a proper type alias definition by type
+        checkers.
+
+        For example::
+
+            Predicate: TypeAlias = Callable[..., bool]
+
+        It's invalid when used anywhere except as in the example
+        above."""
+    )
+
+
+if hasattr(typing, "NoDefault"):
+    NoDefault = typing.NoDefault
+else:
+    class NoDefaultTypeMeta(type):
+        def __setattr__(cls, attr, value):
+            # TypeError is consistent with the behavior of NoneType
+            raise TypeError(
+                f"cannot set {attr!r} attribute of immutable type {cls.__name__!r}"
+            )
+
+    class NoDefaultType(metaclass=NoDefaultTypeMeta):
+        """The type of the NoDefault singleton."""
+
+        __slots__ = ()
+
+        def __new__(cls):
+            return globals().get("NoDefault") or object.__new__(cls)
+
+        def __repr__(self):
+            return "typing_extensions.NoDefault"
+
+        def __reduce__(self):
+            return "NoDefault"
+
+    NoDefault = NoDefaultType()
+    del NoDefaultType, NoDefaultTypeMeta
+
+
+def _set_default(type_param, default):
+    type_param.has_default = lambda: default is not NoDefault
+    type_param.__default__ = default
+
+
+def _set_module(typevarlike):
+    # for pickling:
+    def_mod = _caller(depth=3)
+    if def_mod != 'typing_extensions':
+        typevarlike.__module__ = def_mod
+
+
+class _DefaultMixin:
+    """Mixin for TypeVarLike defaults."""
+
+    __slots__ = ()
+    __init__ = _set_default
+
+
+# Classes using this metaclass must provide a _backported_typevarlike ClassVar
+class _TypeVarLikeMeta(type):
+    def __instancecheck__(cls, __instance: Any) -> bool:
+        return isinstance(__instance, cls._backported_typevarlike)
+
+
+if _PEP_696_IMPLEMENTED:
+    from typing import TypeVar
+else:
+    # Add default and infer_variance parameters from PEP 696 and 695
+    class TypeVar(metaclass=_TypeVarLikeMeta):
+        """Type variable."""
+
+        _backported_typevarlike = typing.TypeVar
+
+        def __new__(cls, name, *constraints, bound=None,
+                    covariant=False, contravariant=False,
+                    default=NoDefault, infer_variance=False):
+            if hasattr(typing, "TypeAliasType"):
+                # PEP 695 implemented (3.12+), can pass infer_variance to typing.TypeVar
+                typevar = typing.TypeVar(name, *constraints, bound=bound,
+                                         covariant=covariant, contravariant=contravariant,
+                                         infer_variance=infer_variance)
+            else:
+                typevar = typing.TypeVar(name, *constraints, bound=bound,
+                                         covariant=covariant, contravariant=contravariant)
+                if infer_variance and (covariant or contravariant):
+                    raise ValueError("Variance cannot be specified with infer_variance.")
+                typevar.__infer_variance__ = infer_variance
+
+            _set_default(typevar, default)
+            _set_module(typevar)
+
+            def _tvar_prepare_subst(alias, args):
+                if (
+                    typevar.has_default()
+                    and alias.__parameters__.index(typevar) == len(args)
+                ):
+                    args += (typevar.__default__,)
+                return args
+
+            typevar.__typing_prepare_subst__ = _tvar_prepare_subst
+            return typevar
+
+        def __init_subclass__(cls) -> None:
+            raise TypeError(f"type '{__name__}.TypeVar' is not an acceptable base type")
+
+
+# Python 3.10+ has PEP 612
+if hasattr(typing, 'ParamSpecArgs'):
+    ParamSpecArgs = typing.ParamSpecArgs
+    ParamSpecKwargs = typing.ParamSpecKwargs
+# 3.8-3.9
+else:
+    class _Immutable:
+        """Mixin to indicate that object should not be copied."""
+        __slots__ = ()
+
+        def __copy__(self):
+            return self
+
+        def __deepcopy__(self, memo):
+            return self
+
+    class ParamSpecArgs(_Immutable):
+        """The args for a ParamSpec object.
+
+        Given a ParamSpec object P, P.args is an instance of ParamSpecArgs.
+
+        ParamSpecArgs objects have a reference back to their ParamSpec:
+
+        P.args.__origin__ is P
+
+        This type is meant for runtime introspection and has no special meaning to
+        static type checkers.
+        """
+        def __init__(self, origin):
+            self.__origin__ = origin
+
+        def __repr__(self):
+            return f"{self.__origin__.__name__}.args"
+
+        def __eq__(self, other):
+            if not isinstance(other, ParamSpecArgs):
+                return NotImplemented
+            return self.__origin__ == other.__origin__
+
+    class ParamSpecKwargs(_Immutable):
+        """The kwargs for a ParamSpec object.
+
+        Given a ParamSpec object P, P.kwargs is an instance of ParamSpecKwargs.
+
+        ParamSpecKwargs objects have a reference back to their ParamSpec:
+
+        P.kwargs.__origin__ is P
+
+        This type is meant for runtime introspection and has no special meaning to
+        static type checkers.
+        """
+        def __init__(self, origin):
+            self.__origin__ = origin
+
+        def __repr__(self):
+            return f"{self.__origin__.__name__}.kwargs"
+
+        def __eq__(self, other):
+            if not isinstance(other, ParamSpecKwargs):
+                return NotImplemented
+            return self.__origin__ == other.__origin__
+
+
+if _PEP_696_IMPLEMENTED:
+    from typing import ParamSpec
+
+# 3.10+
+elif hasattr(typing, 'ParamSpec'):
+
+    # Add default parameter - PEP 696
+    class ParamSpec(metaclass=_TypeVarLikeMeta):
+        """Parameter specification."""
+
+        _backported_typevarlike = typing.ParamSpec
+
+        def __new__(cls, name, *, bound=None,
+                    covariant=False, contravariant=False,
+                    infer_variance=False, default=NoDefault):
+            if hasattr(typing, "TypeAliasType"):
+                # PEP 695 implemented, can pass infer_variance to typing.TypeVar
+                paramspec = typing.ParamSpec(name, bound=bound,
+                                             covariant=covariant,
+                                             contravariant=contravariant,
+                                             infer_variance=infer_variance)
+            else:
+                paramspec = typing.ParamSpec(name, bound=bound,
+                                             covariant=covariant,
+                                             contravariant=contravariant)
+                paramspec.__infer_variance__ = infer_variance
+
+            _set_default(paramspec, default)
+            _set_module(paramspec)
+
+            def _paramspec_prepare_subst(alias, args):
+                params = alias.__parameters__
+                i = params.index(paramspec)
+                if i == len(args) and paramspec.has_default():
+                    args = [*args, paramspec.__default__]
+                if i >= len(args):
+                    raise TypeError(f"Too few arguments for {alias}")
+                # Special case where Z[[int, str, bool]] == Z[int, str, bool] in PEP 612.
+                if len(params) == 1 and not typing._is_param_expr(args[0]):
+                    assert i == 0
+                    args = (args,)
+                # Convert lists to tuples to help other libraries cache the results.
+                elif isinstance(args[i], list):
+                    args = (*args[:i], tuple(args[i]), *args[i + 1:])
+                return args
+
+            paramspec.__typing_prepare_subst__ = _paramspec_prepare_subst
+            return paramspec
+
+        def __init_subclass__(cls) -> None:
+            raise TypeError(f"type '{__name__}.ParamSpec' is not an acceptable base type")
+
+# 3.8-3.9
+else:
+
+    # Inherits from list as a workaround for Callable checks in Python < 3.9.2.
+    class ParamSpec(list, _DefaultMixin):
+        """Parameter specification variable.
+
+        Usage::
+
+           P = ParamSpec('P')
+
+        Parameter specification variables exist primarily for the benefit of static
+        type checkers.  They are used to forward the parameter types of one
+        callable to another callable, a pattern commonly found in higher order
+        functions and decorators.  They are only valid when used in ``Concatenate``,
+        or s the first argument to ``Callable``. In Python 3.10 and higher,
+        they are also supported in user-defined Generics at runtime.
+        See class Generic for more information on generic types.  An
+        example for annotating a decorator::
+
+           T = TypeVar('T')
+           P = ParamSpec('P')
+
+           def add_logging(f: Callable[P, T]) -> Callable[P, T]:
+               '''A type-safe decorator to add logging to a function.'''
+               def inner(*args: P.args, **kwargs: P.kwargs) -> T:
+                   logging.info(f'{f.__name__} was called')
+                   return f(*args, **kwargs)
+               return inner
+
+           @add_logging
+           def add_two(x: float, y: float) -> float:
+               '''Add two numbers together.'''
+               return x + y
+
+        Parameter specification variables defined with covariant=True or
+        contravariant=True can be used to declare covariant or contravariant
+        generic types.  These keyword arguments are valid, but their actual semantics
+        are yet to be decided.  See PEP 612 for details.
+
+        Parameter specification variables can be introspected. e.g.:
+
+           P.__name__ == 'T'
+           P.__bound__ == None
+           P.__covariant__ == False
+           P.__contravariant__ == False
+
+        Note that only parameter specification variables defined in global scope can
+        be pickled.
+        """
+
+        # Trick Generic __parameters__.
+        __class__ = typing.TypeVar
+
+        @property
+        def args(self):
+            return ParamSpecArgs(self)
+
+        @property
+        def kwargs(self):
+            return ParamSpecKwargs(self)
+
+        def __init__(self, name, *, bound=None, covariant=False, contravariant=False,
+                     infer_variance=False, default=NoDefault):
+            list.__init__(self, [self])
+            self.__name__ = name
+            self.__covariant__ = bool(covariant)
+            self.__contravariant__ = bool(contravariant)
+            self.__infer_variance__ = bool(infer_variance)
+            if bound:
+                self.__bound__ = typing._type_check(bound, 'Bound must be a type.')
+            else:
+                self.__bound__ = None
+            _DefaultMixin.__init__(self, default)
+
+            # for pickling:
+            def_mod = _caller()
+            if def_mod != 'typing_extensions':
+                self.__module__ = def_mod
+
+        def __repr__(self):
+            if self.__infer_variance__:
+                prefix = ''
+            elif self.__covariant__:
+                prefix = '+'
+            elif self.__contravariant__:
+                prefix = '-'
+            else:
+                prefix = '~'
+            return prefix + self.__name__
+
+        def __hash__(self):
+            return object.__hash__(self)
+
+        def __eq__(self, other):
+            return self is other
+
+        def __reduce__(self):
+            return self.__name__
+
+        # Hack to get typing._type_check to pass.
+        def __call__(self, *args, **kwargs):
+            pass
+
+
+# 3.8-3.9
+if not hasattr(typing, 'Concatenate'):
+    # Inherits from list as a workaround for Callable checks in Python < 3.9.2.
+    class _ConcatenateGenericAlias(list):
+
+        # Trick Generic into looking into this for __parameters__.
+        __class__ = typing._GenericAlias
+
+        # Flag in 3.8.
+        _special = False
+
+        def __init__(self, origin, args):
+            super().__init__(args)
+            self.__origin__ = origin
+            self.__args__ = args
+
+        def __repr__(self):
+            _type_repr = typing._type_repr
+            return (f'{_type_repr(self.__origin__)}'
+                    f'[{", ".join(_type_repr(arg) for arg in self.__args__)}]')
+
+        def __hash__(self):
+            return hash((self.__origin__, self.__args__))
+
+        # Hack to get typing._type_check to pass in Generic.
+        def __call__(self, *args, **kwargs):
+            pass
+
+        @property
+        def __parameters__(self):
+            return tuple(
+                tp for tp in self.__args__ if isinstance(tp, (typing.TypeVar, ParamSpec))
+            )
+
+
+# 3.8-3.9
+@typing._tp_cache
+def _concatenate_getitem(self, parameters):
+    if parameters == ():
+        raise TypeError("Cannot take a Concatenate of no types.")
+    if not isinstance(parameters, tuple):
+        parameters = (parameters,)
+    if not isinstance(parameters[-1], ParamSpec):
+        raise TypeError("The last parameter to Concatenate should be a "
+                        "ParamSpec variable.")
+    msg = "Concatenate[arg, ...]: each arg must be a type."
+    parameters = tuple(typing._type_check(p, msg) for p in parameters)
+    return _ConcatenateGenericAlias(self, parameters)
+
+
+# 3.10+
+if hasattr(typing, 'Concatenate'):
+    Concatenate = typing.Concatenate
+    _ConcatenateGenericAlias = typing._ConcatenateGenericAlias
+# 3.9
+elif sys.version_info[:2] >= (3, 9):
+    @_ExtensionsSpecialForm
+    def Concatenate(self, parameters):
+        """Used in conjunction with ``ParamSpec`` and ``Callable`` to represent a
+        higher order function which adds, removes or transforms parameters of a
+        callable.
+
+        For example::
+
+           Callable[Concatenate[int, P], int]
+
+        See PEP 612 for detailed information.
+        """
+        return _concatenate_getitem(self, parameters)
+# 3.8
+else:
+    class _ConcatenateForm(_ExtensionsSpecialForm, _root=True):
+        def __getitem__(self, parameters):
+            return _concatenate_getitem(self, parameters)
+
+    Concatenate = _ConcatenateForm(
+        'Concatenate',
+        doc="""Used in conjunction with ``ParamSpec`` and ``Callable`` to represent a
+        higher order function which adds, removes or transforms parameters of a
+        callable.
+
+        For example::
+
+           Callable[Concatenate[int, P], int]
+
+        See PEP 612 for detailed information.
+        """)
+
+# 3.10+
+if hasattr(typing, 'TypeGuard'):
+    TypeGuard = typing.TypeGuard
+# 3.9
+elif sys.version_info[:2] >= (3, 9):
+    @_ExtensionsSpecialForm
+    def TypeGuard(self, parameters):
+        """Special typing form used to annotate the return type of a user-defined
+        type guard function.  ``TypeGuard`` only accepts a single type argument.
+        At runtime, functions marked this way should return a boolean.
+
+        ``TypeGuard`` aims to benefit *type narrowing* -- a technique used by static
+        type checkers to determine a more precise type of an expression within a
+        program's code flow.  Usually type narrowing is done by analyzing
+        conditional code flow and applying the narrowing to a block of code.  The
+        conditional expression here is sometimes referred to as a "type guard".
+
+        Sometimes it would be convenient to use a user-defined boolean function
+        as a type guard.  Such a function should use ``TypeGuard[...]`` as its
+        return type to alert static type checkers to this intention.
+
+        Using  ``-> TypeGuard`` tells the static type checker that for a given
+        function:
+
+        1. The return value is a boolean.
+        2. If the return value is ``True``, the type of its argument
+        is the type inside ``TypeGuard``.
+
+        For example::
+
+            def is_str(val: Union[str, float]):
+                # "isinstance" type guard
+                if isinstance(val, str):
+                    # Type of ``val`` is narrowed to ``str``
+                    ...
+                else:
+                    # Else, type of ``val`` is narrowed to ``float``.
+                    ...
+
+        Strict type narrowing is not enforced -- ``TypeB`` need not be a narrower
+        form of ``TypeA`` (it can even be a wider form) and this may lead to
+        type-unsafe results.  The main reason is to allow for things like
+        narrowing ``List[object]`` to ``List[str]`` even though the latter is not
+        a subtype of the former, since ``List`` is invariant.  The responsibility of
+        writing type-safe type guards is left to the user.
+
+        ``TypeGuard`` also works with type variables.  For more information, see
+        PEP 647 (User-Defined Type Guards).
+        """
+        item = typing._type_check(parameters, f'{self} accepts only a single type.')
+        return typing._GenericAlias(self, (item,))
+# 3.8
+else:
+    class _TypeGuardForm(_ExtensionsSpecialForm, _root=True):
+        def __getitem__(self, parameters):
+            item = typing._type_check(parameters,
+                                      f'{self._name} accepts only a single type')
+            return typing._GenericAlias(self, (item,))
+
+    TypeGuard = _TypeGuardForm(
+        'TypeGuard',
+        doc="""Special typing form used to annotate the return type of a user-defined
+        type guard function.  ``TypeGuard`` only accepts a single type argument.
+        At runtime, functions marked this way should return a boolean.
+
+        ``TypeGuard`` aims to benefit *type narrowing* -- a technique used by static
+        type checkers to determine a more precise type of an expression within a
+        program's code flow.  Usually type narrowing is done by analyzing
+        conditional code flow and applying the narrowing to a block of code.  The
+        conditional expression here is sometimes referred to as a "type guard".
+
+        Sometimes it would be convenient to use a user-defined boolean function
+        as a type guard.  Such a function should use ``TypeGuard[...]`` as its
+        return type to alert static type checkers to this intention.
+
+        Using  ``-> TypeGuard`` tells the static type checker that for a given
+        function:
+
+        1. The return value is a boolean.
+        2. If the return value is ``True``, the type of its argument
+        is the type inside ``TypeGuard``.
+
+        For example::
+
+            def is_str(val: Union[str, float]):
+                # "isinstance" type guard
+                if isinstance(val, str):
+                    # Type of ``val`` is narrowed to ``str``
+                    ...
+                else:
+                    # Else, type of ``val`` is narrowed to ``float``.
+                    ...
+
+        Strict type narrowing is not enforced -- ``TypeB`` need not be a narrower
+        form of ``TypeA`` (it can even be a wider form) and this may lead to
+        type-unsafe results.  The main reason is to allow for things like
+        narrowing ``List[object]`` to ``List[str]`` even though the latter is not
+        a subtype of the former, since ``List`` is invariant.  The responsibility of
+        writing type-safe type guards is left to the user.
+
+        ``TypeGuard`` also works with type variables.  For more information, see
+        PEP 647 (User-Defined Type Guards).
+        """)
+
+# 3.13+
+if hasattr(typing, 'TypeIs'):
+    TypeIs = typing.TypeIs
+# 3.9
+elif sys.version_info[:2] >= (3, 9):
+    @_ExtensionsSpecialForm
+    def TypeIs(self, parameters):
+        """Special typing form used to annotate the return type of a user-defined
+        type narrower function.  ``TypeIs`` only accepts a single type argument.
+        At runtime, functions marked this way should return a boolean.
+
+        ``TypeIs`` aims to benefit *type narrowing* -- a technique used by static
+        type checkers to determine a more precise type of an expression within a
+        program's code flow.  Usually type narrowing is done by analyzing
+        conditional code flow and applying the narrowing to a block of code.  The
+        conditional expression here is sometimes referred to as a "type guard".
+
+        Sometimes it would be convenient to use a user-defined boolean function
+        as a type guard.  Such a function should use ``TypeIs[...]`` as its
+        return type to alert static type checkers to this intention.
+
+        Using  ``-> TypeIs`` tells the static type checker that for a given
+        function:
+
+        1. The return value is a boolean.
+        2. If the return value is ``True``, the type of its argument
+        is the intersection of the type inside ``TypeGuard`` and the argument's
+        previously known type.
+
+        For example::
+
+            def is_awaitable(val: object) -> TypeIs[Awaitable[Any]]:
+                return hasattr(val, '__await__')
+
+            def f(val: Union[int, Awaitable[int]]) -> int:
+                if is_awaitable(val):
+                    assert_type(val, Awaitable[int])
+                else:
+                    assert_type(val, int)
+
+        ``TypeIs`` also works with type variables.  For more information, see
+        PEP 742 (Narrowing types with TypeIs).
+        """
+        item = typing._type_check(parameters, f'{self} accepts only a single type.')
+        return typing._GenericAlias(self, (item,))
+# 3.8
+else:
+    class _TypeIsForm(_ExtensionsSpecialForm, _root=True):
+        def __getitem__(self, parameters):
+            item = typing._type_check(parameters,
+                                      f'{self._name} accepts only a single type')
+            return typing._GenericAlias(self, (item,))
+
+    TypeIs = _TypeIsForm(
+        'TypeIs',
+        doc="""Special typing form used to annotate the return type of a user-defined
+        type narrower function.  ``TypeIs`` only accepts a single type argument.
+        At runtime, functions marked this way should return a boolean.
+
+        ``TypeIs`` aims to benefit *type narrowing* -- a technique used by static
+        type checkers to determine a more precise type of an expression within a
+        program's code flow.  Usually type narrowing is done by analyzing
+        conditional code flow and applying the narrowing to a block of code.  The
+        conditional expression here is sometimes referred to as a "type guard".
+
+        Sometimes it would be convenient to use a user-defined boolean function
+        as a type guard.  Such a function should use ``TypeIs[...]`` as its
+        return type to alert static type checkers to this intention.
+
+        Using  ``-> TypeIs`` tells the static type checker that for a given
+        function:
+
+        1. The return value is a boolean.
+        2. If the return value is ``True``, the type of its argument
+        is the intersection of the type inside ``TypeGuard`` and the argument's
+        previously known type.
+
+        For example::
+
+            def is_awaitable(val: object) -> TypeIs[Awaitable[Any]]:
+                return hasattr(val, '__await__')
+
+            def f(val: Union[int, Awaitable[int]]) -> int:
+                if is_awaitable(val):
+                    assert_type(val, Awaitable[int])
+                else:
+                    assert_type(val, int)
+
+        ``TypeIs`` also works with type variables.  For more information, see
+        PEP 742 (Narrowing types with TypeIs).
+        """)
+
+
+# Vendored from cpython typing._SpecialFrom
+class _SpecialForm(typing._Final, _root=True):
+    __slots__ = ('_name', '__doc__', '_getitem')
+
+    def __init__(self, getitem):
+        self._getitem = getitem
+        self._name = getitem.__name__
+        self.__doc__ = getitem.__doc__
+
+    def __getattr__(self, item):
+        if item in {'__name__', '__qualname__'}:
+            return self._name
+
+        raise AttributeError(item)
+
+    def __mro_entries__(self, bases):
+        raise TypeError(f"Cannot subclass {self!r}")
+
+    def __repr__(self):
+        return f'typing_extensions.{self._name}'
+
+    def __reduce__(self):
+        return self._name
+
+    def __call__(self, *args, **kwds):
+        raise TypeError(f"Cannot instantiate {self!r}")
+
+    def __or__(self, other):
+        return typing.Union[self, other]
+
+    def __ror__(self, other):
+        return typing.Union[other, self]
+
+    def __instancecheck__(self, obj):
+        raise TypeError(f"{self} cannot be used with isinstance()")
+
+    def __subclasscheck__(self, cls):
+        raise TypeError(f"{self} cannot be used with issubclass()")
+
+    @typing._tp_cache
+    def __getitem__(self, parameters):
+        return self._getitem(self, parameters)
+
+
+if hasattr(typing, "LiteralString"):  # 3.11+
+    LiteralString = typing.LiteralString
+else:
+    @_SpecialForm
+    def LiteralString(self, params):
+        """Represents an arbitrary literal string.
+
+        Example::
+
+          from pip._vendor.typing_extensions import LiteralString
+
+          def query(sql: LiteralString) -> ...:
+              ...
+
+          query("SELECT * FROM table")  # ok
+          query(f"SELECT * FROM {input()}")  # not ok
+
+        See PEP 675 for details.
+
+        """
+        raise TypeError(f"{self} is not subscriptable")
+
+
+if hasattr(typing, "Self"):  # 3.11+
+    Self = typing.Self
+else:
+    @_SpecialForm
+    def Self(self, params):
+        """Used to spell the type of "self" in classes.
+
+        Example::
+
+          from typing import Self
+
+          class ReturnsSelf:
+              def parse(self, data: bytes) -> Self:
+                  ...
+                  return self
+
+        """
+
+        raise TypeError(f"{self} is not subscriptable")
+
+
+if hasattr(typing, "Never"):  # 3.11+
+    Never = typing.Never
+else:
+    @_SpecialForm
+    def Never(self, params):
+        """The bottom type, a type that has no members.
+
+        This can be used to define a function that should never be
+        called, or a function that never returns::
+
+            from pip._vendor.typing_extensions import Never
+
+            def never_call_me(arg: Never) -> None:
+                pass
+
+            def int_or_str(arg: int | str) -> None:
+                never_call_me(arg)  # type checker error
+                match arg:
+                    case int():
+                        print("It's an int")
+                    case str():
+                        print("It's a str")
+                    case _:
+                        never_call_me(arg)  # ok, arg is of type Never
+
+        """
+
+        raise TypeError(f"{self} is not subscriptable")
+
+
+if hasattr(typing, 'Required'):  # 3.11+
+    Required = typing.Required
+    NotRequired = typing.NotRequired
+elif sys.version_info[:2] >= (3, 9):  # 3.9-3.10
+    @_ExtensionsSpecialForm
+    def Required(self, parameters):
+        """A special typing construct to mark a key of a total=False TypedDict
+        as required. For example:
+
+            class Movie(TypedDict, total=False):
+                title: Required[str]
+                year: int
+
+            m = Movie(
+                title='The Matrix',  # typechecker error if key is omitted
+                year=1999,
+            )
+
+        There is no runtime checking that a required key is actually provided
+        when instantiating a related TypedDict.
+        """
+        item = typing._type_check(parameters, f'{self._name} accepts only a single type.')
+        return typing._GenericAlias(self, (item,))
+
+    @_ExtensionsSpecialForm
+    def NotRequired(self, parameters):
+        """A special typing construct to mark a key of a TypedDict as
+        potentially missing. For example:
+
+            class Movie(TypedDict):
+                title: str
+                year: NotRequired[int]
+
+            m = Movie(
+                title='The Matrix',  # typechecker error if key is omitted
+                year=1999,
+            )
+        """
+        item = typing._type_check(parameters, f'{self._name} accepts only a single type.')
+        return typing._GenericAlias(self, (item,))
+
+else:  # 3.8
+    class _RequiredForm(_ExtensionsSpecialForm, _root=True):
+        def __getitem__(self, parameters):
+            item = typing._type_check(parameters,
+                                      f'{self._name} accepts only a single type.')
+            return typing._GenericAlias(self, (item,))
+
+    Required = _RequiredForm(
+        'Required',
+        doc="""A special typing construct to mark a key of a total=False TypedDict
+        as required. For example:
+
+            class Movie(TypedDict, total=False):
+                title: Required[str]
+                year: int
+
+            m = Movie(
+                title='The Matrix',  # typechecker error if key is omitted
+                year=1999,
+            )
+
+        There is no runtime checking that a required key is actually provided
+        when instantiating a related TypedDict.
+        """)
+    NotRequired = _RequiredForm(
+        'NotRequired',
+        doc="""A special typing construct to mark a key of a TypedDict as
+        potentially missing. For example:
+
+            class Movie(TypedDict):
+                title: str
+                year: NotRequired[int]
+
+            m = Movie(
+                title='The Matrix',  # typechecker error if key is omitted
+                year=1999,
+            )
+        """)
+
+
+if hasattr(typing, 'ReadOnly'):
+    ReadOnly = typing.ReadOnly
+elif sys.version_info[:2] >= (3, 9):  # 3.9-3.12
+    @_ExtensionsSpecialForm
+    def ReadOnly(self, parameters):
+        """A special typing construct to mark an item of a TypedDict as read-only.
+
+        For example:
+
+            class Movie(TypedDict):
+                title: ReadOnly[str]
+                year: int
+
+            def mutate_movie(m: Movie) -> None:
+                m["year"] = 1992  # allowed
+                m["title"] = "The Matrix"  # typechecker error
+
+        There is no runtime checking for this property.
+        """
+        item = typing._type_check(parameters, f'{self._name} accepts only a single type.')
+        return typing._GenericAlias(self, (item,))
+
+else:  # 3.8
+    class _ReadOnlyForm(_ExtensionsSpecialForm, _root=True):
+        def __getitem__(self, parameters):
+            item = typing._type_check(parameters,
+                                      f'{self._name} accepts only a single type.')
+            return typing._GenericAlias(self, (item,))
+
+    ReadOnly = _ReadOnlyForm(
+        'ReadOnly',
+        doc="""A special typing construct to mark a key of a TypedDict as read-only.
+
+        For example:
+
+            class Movie(TypedDict):
+                title: ReadOnly[str]
+                year: int
+
+            def mutate_movie(m: Movie) -> None:
+                m["year"] = 1992  # allowed
+                m["title"] = "The Matrix"  # typechecker error
+
+        There is no runtime checking for this propery.
+        """)
+
+
+_UNPACK_DOC = """\
+Type unpack operator.
+
+The type unpack operator takes the child types from some container type,
+such as `tuple[int, str]` or a `TypeVarTuple`, and 'pulls them out'. For
+example:
+
+  # For some generic class `Foo`:
+  Foo[Unpack[tuple[int, str]]]  # Equivalent to Foo[int, str]
+
+  Ts = TypeVarTuple('Ts')
+  # Specifies that `Bar` is generic in an arbitrary number of types.
+  # (Think of `Ts` as a tuple of an arbitrary number of individual
+  #  `TypeVar`s, which the `Unpack` is 'pulling out' directly into the
+  #  `Generic[]`.)
+  class Bar(Generic[Unpack[Ts]]): ...
+  Bar[int]  # Valid
+  Bar[int, str]  # Also valid
+
+From Python 3.11, this can also be done using the `*` operator:
+
+    Foo[*tuple[int, str]]
+    class Bar(Generic[*Ts]): ...
+
+The operator can also be used along with a `TypedDict` to annotate
+`**kwargs` in a function signature. For instance:
+
+  class Movie(TypedDict):
+    name: str
+    year: int
+
+  # This function expects two keyword arguments - *name* of type `str` and
+  # *year* of type `int`.
+  def foo(**kwargs: Unpack[Movie]): ...
+
+Note that there is only some runtime checking of this operator. Not
+everything the runtime allows may be accepted by static type checkers.
+
+For more information, see PEP 646 and PEP 692.
+"""
+
+
+if sys.version_info >= (3, 12):  # PEP 692 changed the repr of Unpack[]
+    Unpack = typing.Unpack
+
+    def _is_unpack(obj):
+        return get_origin(obj) is Unpack
+
+elif sys.version_info[:2] >= (3, 9):  # 3.9+
+    class _UnpackSpecialForm(_ExtensionsSpecialForm, _root=True):
+        def __init__(self, getitem):
+            super().__init__(getitem)
+            self.__doc__ = _UNPACK_DOC
+
+    class _UnpackAlias(typing._GenericAlias, _root=True):
+        __class__ = typing.TypeVar
+
+        @property
+        def __typing_unpacked_tuple_args__(self):
+            assert self.__origin__ is Unpack
+            assert len(self.__args__) == 1
+            arg, = self.__args__
+            if isinstance(arg, (typing._GenericAlias, _types.GenericAlias)):
+                if arg.__origin__ is not tuple:
+                    raise TypeError("Unpack[...] must be used with a tuple type")
+                return arg.__args__
+            return None
+
+    @_UnpackSpecialForm
+    def Unpack(self, parameters):
+        item = typing._type_check(parameters, f'{self._name} accepts only a single type.')
+        return _UnpackAlias(self, (item,))
+
+    def _is_unpack(obj):
+        return isinstance(obj, _UnpackAlias)
+
+else:  # 3.8
+    class _UnpackAlias(typing._GenericAlias, _root=True):
+        __class__ = typing.TypeVar
+
+    class _UnpackForm(_ExtensionsSpecialForm, _root=True):
+        def __getitem__(self, parameters):
+            item = typing._type_check(parameters,
+                                      f'{self._name} accepts only a single type.')
+            return _UnpackAlias(self, (item,))
+
+    Unpack = _UnpackForm('Unpack', doc=_UNPACK_DOC)
+
+    def _is_unpack(obj):
+        return isinstance(obj, _UnpackAlias)
+
+
+if _PEP_696_IMPLEMENTED:
+    from typing import TypeVarTuple
+
+elif hasattr(typing, "TypeVarTuple"):  # 3.11+
+
+    def _unpack_args(*args):
+        newargs = []
+        for arg in args:
+            subargs = getattr(arg, '__typing_unpacked_tuple_args__', None)
+            if subargs is not None and not (subargs and subargs[-1] is ...):
+                newargs.extend(subargs)
+            else:
+                newargs.append(arg)
+        return newargs
+
+    # Add default parameter - PEP 696
+    class TypeVarTuple(metaclass=_TypeVarLikeMeta):
+        """Type variable tuple."""
+
+        _backported_typevarlike = typing.TypeVarTuple
+
+        def __new__(cls, name, *, default=NoDefault):
+            tvt = typing.TypeVarTuple(name)
+            _set_default(tvt, default)
+            _set_module(tvt)
+
+            def _typevartuple_prepare_subst(alias, args):
+                params = alias.__parameters__
+                typevartuple_index = params.index(tvt)
+                for param in params[typevartuple_index + 1:]:
+                    if isinstance(param, TypeVarTuple):
+                        raise TypeError(
+                            f"More than one TypeVarTuple parameter in {alias}"
+                        )
+
+                alen = len(args)
+                plen = len(params)
+                left = typevartuple_index
+                right = plen - typevartuple_index - 1
+                var_tuple_index = None
+                fillarg = None
+                for k, arg in enumerate(args):
+                    if not isinstance(arg, type):
+                        subargs = getattr(arg, '__typing_unpacked_tuple_args__', None)
+                        if subargs and len(subargs) == 2 and subargs[-1] is ...:
+                            if var_tuple_index is not None:
+                                raise TypeError(
+                                    "More than one unpacked "
+                                    "arbitrary-length tuple argument"
+                                )
+                            var_tuple_index = k
+                            fillarg = subargs[0]
+                if var_tuple_index is not None:
+                    left = min(left, var_tuple_index)
+                    right = min(right, alen - var_tuple_index - 1)
+                elif left + right > alen:
+                    raise TypeError(f"Too few arguments for {alias};"
+                                    f" actual {alen}, expected at least {plen - 1}")
+                if left == alen - right and tvt.has_default():
+                    replacement = _unpack_args(tvt.__default__)
+                else:
+                    replacement = args[left: alen - right]
+
+                return (
+                    *args[:left],
+                    *([fillarg] * (typevartuple_index - left)),
+                    replacement,
+                    *([fillarg] * (plen - right - left - typevartuple_index - 1)),
+                    *args[alen - right:],
+                )
+
+            tvt.__typing_prepare_subst__ = _typevartuple_prepare_subst
+            return tvt
+
+        def __init_subclass__(self, *args, **kwds):
+            raise TypeError("Cannot subclass special typing classes")
+
+else:  # <=3.10
+    class TypeVarTuple(_DefaultMixin):
+        """Type variable tuple.
+
+        Usage::
+
+            Ts = TypeVarTuple('Ts')
+
+        In the same way that a normal type variable is a stand-in for a single
+        type such as ``int``, a type variable *tuple* is a stand-in for a *tuple*
+        type such as ``Tuple[int, str]``.
+
+        Type variable tuples can be used in ``Generic`` declarations.
+        Consider the following example::
+
+            class Array(Generic[*Ts]): ...
+
+        The ``Ts`` type variable tuple here behaves like ``tuple[T1, T2]``,
+        where ``T1`` and ``T2`` are type variables. To use these type variables
+        as type parameters of ``Array``, we must *unpack* the type variable tuple using
+        the star operator: ``*Ts``. The signature of ``Array`` then behaves
+        as if we had simply written ``class Array(Generic[T1, T2]): ...``.
+        In contrast to ``Generic[T1, T2]``, however, ``Generic[*Shape]`` allows
+        us to parameterise the class with an *arbitrary* number of type parameters.
+
+        Type variable tuples can be used anywhere a normal ``TypeVar`` can.
+        This includes class definitions, as shown above, as well as function
+        signatures and variable annotations::
+
+            class Array(Generic[*Ts]):
+
+                def __init__(self, shape: Tuple[*Ts]):
+                    self._shape: Tuple[*Ts] = shape
+
+                def get_shape(self) -> Tuple[*Ts]:
+                    return self._shape
+
+            shape = (Height(480), Width(640))
+            x: Array[Height, Width] = Array(shape)
+            y = abs(x)  # Inferred type is Array[Height, Width]
+            z = x + x   #        ...    is Array[Height, Width]
+            x.get_shape()  #     ...    is tuple[Height, Width]
+
+        """
+
+        # Trick Generic __parameters__.
+        __class__ = typing.TypeVar
+
+        def __iter__(self):
+            yield self.__unpacked__
+
+        def __init__(self, name, *, default=NoDefault):
+            self.__name__ = name
+            _DefaultMixin.__init__(self, default)
+
+            # for pickling:
+            def_mod = _caller()
+            if def_mod != 'typing_extensions':
+                self.__module__ = def_mod
+
+            self.__unpacked__ = Unpack[self]
+
+        def __repr__(self):
+            return self.__name__
+
+        def __hash__(self):
+            return object.__hash__(self)
+
+        def __eq__(self, other):
+            return self is other
+
+        def __reduce__(self):
+            return self.__name__
+
+        def __init_subclass__(self, *args, **kwds):
+            if '_root' not in kwds:
+                raise TypeError("Cannot subclass special typing classes")
+
+
+if hasattr(typing, "reveal_type"):  # 3.11+
+    reveal_type = typing.reveal_type
+else:  # <=3.10
+    def reveal_type(obj: T, /) -> T:
+        """Reveal the inferred type of a variable.
+
+        When a static type checker encounters a call to ``reveal_type()``,
+        it will emit the inferred type of the argument::
+
+            x: int = 1
+            reveal_type(x)
+
+        Running a static type checker (e.g., ``mypy``) on this example
+        will produce output similar to 'Revealed type is "builtins.int"'.
+
+        At runtime, the function prints the runtime type of the
+        argument and returns it unchanged.
+
+        """
+        print(f"Runtime type is {type(obj).__name__!r}", file=sys.stderr)
+        return obj
+
+
+if hasattr(typing, "_ASSERT_NEVER_REPR_MAX_LENGTH"):  # 3.11+
+    _ASSERT_NEVER_REPR_MAX_LENGTH = typing._ASSERT_NEVER_REPR_MAX_LENGTH
+else:  # <=3.10
+    _ASSERT_NEVER_REPR_MAX_LENGTH = 100
+
+
+if hasattr(typing, "assert_never"):  # 3.11+
+    assert_never = typing.assert_never
+else:  # <=3.10
+    def assert_never(arg: Never, /) -> Never:
+        """Assert to the type checker that a line of code is unreachable.
+
+        Example::
+
+            def int_or_str(arg: int | str) -> None:
+                match arg:
+                    case int():
+                        print("It's an int")
+                    case str():
+                        print("It's a str")
+                    case _:
+                        assert_never(arg)
+
+        If a type checker finds that a call to assert_never() is
+        reachable, it will emit an error.
+
+        At runtime, this throws an exception when called.
+
+        """
+        value = repr(arg)
+        if len(value) > _ASSERT_NEVER_REPR_MAX_LENGTH:
+            value = value[:_ASSERT_NEVER_REPR_MAX_LENGTH] + '...'
+        raise AssertionError(f"Expected code to be unreachable, but got: {value}")
+
+
+if sys.version_info >= (3, 12):  # 3.12+
+    # dataclass_transform exists in 3.11 but lacks the frozen_default parameter
+    dataclass_transform = typing.dataclass_transform
+else:  # <=3.11
+    def dataclass_transform(
+        *,
+        eq_default: bool = True,
+        order_default: bool = False,
+        kw_only_default: bool = False,
+        frozen_default: bool = False,
+        field_specifiers: typing.Tuple[
+            typing.Union[typing.Type[typing.Any], typing.Callable[..., typing.Any]],
+            ...
+        ] = (),
+        **kwargs: typing.Any,
+    ) -> typing.Callable[[T], T]:
+        """Decorator that marks a function, class, or metaclass as providing
+        dataclass-like behavior.
+
+        Example:
+
+            from pip._vendor.typing_extensions import dataclass_transform
+
+            _T = TypeVar("_T")
+
+            # Used on a decorator function
+            @dataclass_transform()
+            def create_model(cls: type[_T]) -> type[_T]:
+                ...
+                return cls
+
+            @create_model
+            class CustomerModel:
+                id: int
+                name: str
+
+            # Used on a base class
+            @dataclass_transform()
+            class ModelBase: ...
+
+            class CustomerModel(ModelBase):
+                id: int
+                name: str
+
+            # Used on a metaclass
+            @dataclass_transform()
+            class ModelMeta(type): ...
+
+            class ModelBase(metaclass=ModelMeta): ...
+
+            class CustomerModel(ModelBase):
+                id: int
+                name: str
+
+        Each of the ``CustomerModel`` classes defined in this example will now
+        behave similarly to a dataclass created with the ``@dataclasses.dataclass``
+        decorator. For example, the type checker will synthesize an ``__init__``
+        method.
+
+        The arguments to this decorator can be used to customize this behavior:
+        - ``eq_default`` indicates whether the ``eq`` parameter is assumed to be
+          True or False if it is omitted by the caller.
+        - ``order_default`` indicates whether the ``order`` parameter is
+          assumed to be True or False if it is omitted by the caller.
+        - ``kw_only_default`` indicates whether the ``kw_only`` parameter is
+          assumed to be True or False if it is omitted by the caller.
+        - ``frozen_default`` indicates whether the ``frozen`` parameter is
+          assumed to be True or False if it is omitted by the caller.
+        - ``field_specifiers`` specifies a static list of supported classes
+          or functions that describe fields, similar to ``dataclasses.field()``.
+
+        At runtime, this decorator records its arguments in the
+        ``__dataclass_transform__`` attribute on the decorated object.
+
+        See PEP 681 for details.
+
+        """
+        def decorator(cls_or_fn):
+            cls_or_fn.__dataclass_transform__ = {
+                "eq_default": eq_default,
+                "order_default": order_default,
+                "kw_only_default": kw_only_default,
+                "frozen_default": frozen_default,
+                "field_specifiers": field_specifiers,
+                "kwargs": kwargs,
+            }
+            return cls_or_fn
+        return decorator
+
+
+if hasattr(typing, "override"):  # 3.12+
+    override = typing.override
+else:  # <=3.11
+    _F = typing.TypeVar("_F", bound=typing.Callable[..., typing.Any])
+
+    def override(arg: _F, /) -> _F:
+        """Indicate that a method is intended to override a method in a base class.
+
+        Usage:
+
+            class Base:
+                def method(self) -> None:
+                    pass
+
+            class Child(Base):
+                @override
+                def method(self) -> None:
+                    super().method()
+
+        When this decorator is applied to a method, the type checker will
+        validate that it overrides a method with the same name on a base class.
+        This helps prevent bugs that may occur when a base class is changed
+        without an equivalent change to a child class.
+
+        There is no runtime checking of these properties. The decorator
+        sets the ``__override__`` attribute to ``True`` on the decorated object
+        to allow runtime introspection.
+
+        See PEP 698 for details.
+
+        """
+        try:
+            arg.__override__ = True
+        except (AttributeError, TypeError):
+            # Skip the attribute silently if it is not writable.
+            # AttributeError happens if the object has __slots__ or a
+            # read-only property, TypeError if it's a builtin class.
+            pass
+        return arg
+
+
+if hasattr(warnings, "deprecated"):
+    deprecated = warnings.deprecated
+else:
+    _T = typing.TypeVar("_T")
+
+    class deprecated:
+        """Indicate that a class, function or overload is deprecated.
+
+        When this decorator is applied to an object, the type checker
+        will generate a diagnostic on usage of the deprecated object.
+
+        Usage:
+
+            @deprecated("Use B instead")
+            class A:
+                pass
+
+            @deprecated("Use g instead")
+            def f():
+                pass
+
+            @overload
+            @deprecated("int support is deprecated")
+            def g(x: int) -> int: ...
+            @overload
+            def g(x: str) -> int: ...
+
+        The warning specified by *category* will be emitted at runtime
+        on use of deprecated objects. For functions, that happens on calls;
+        for classes, on instantiation and on creation of subclasses.
+        If the *category* is ``None``, no warning is emitted at runtime.
+        The *stacklevel* determines where the
+        warning is emitted. If it is ``1`` (the default), the warning
+        is emitted at the direct caller of the deprecated object; if it
+        is higher, it is emitted further up the stack.
+        Static type checker behavior is not affected by the *category*
+        and *stacklevel* arguments.
+
+        The deprecation message passed to the decorator is saved in the
+        ``__deprecated__`` attribute on the decorated object.
+        If applied to an overload, the decorator
+        must be after the ``@overload`` decorator for the attribute to
+        exist on the overload as returned by ``get_overloads()``.
+
+        See PEP 702 for details.
+
+        """
+        def __init__(
+            self,
+            message: str,
+            /,
+            *,
+            category: typing.Optional[typing.Type[Warning]] = DeprecationWarning,
+            stacklevel: int = 1,
+        ) -> None:
+            if not isinstance(message, str):
+                raise TypeError(
+                    "Expected an object of type str for 'message', not "
+                    f"{type(message).__name__!r}"
+                )
+            self.message = message
+            self.category = category
+            self.stacklevel = stacklevel
+
+        def __call__(self, arg: _T, /) -> _T:
+            # Make sure the inner functions created below don't
+            # retain a reference to self.
+            msg = self.message
+            category = self.category
+            stacklevel = self.stacklevel
+            if category is None:
+                arg.__deprecated__ = msg
+                return arg
+            elif isinstance(arg, type):
+                import functools
+                from types import MethodType
+
+                original_new = arg.__new__
+
+                @functools.wraps(original_new)
+                def __new__(cls, *args, **kwargs):
+                    if cls is arg:
+                        warnings.warn(msg, category=category, stacklevel=stacklevel + 1)
+                    if original_new is not object.__new__:
+                        return original_new(cls, *args, **kwargs)
+                    # Mirrors a similar check in object.__new__.
+                    elif cls.__init__ is object.__init__ and (args or kwargs):
+                        raise TypeError(f"{cls.__name__}() takes no arguments")
+                    else:
+                        return original_new(cls)
+
+                arg.__new__ = staticmethod(__new__)
+
+                original_init_subclass = arg.__init_subclass__
+                # We need slightly different behavior if __init_subclass__
+                # is a bound method (likely if it was implemented in Python)
+                if isinstance(original_init_subclass, MethodType):
+                    original_init_subclass = original_init_subclass.__func__
+
+                    @functools.wraps(original_init_subclass)
+                    def __init_subclass__(*args, **kwargs):
+                        warnings.warn(msg, category=category, stacklevel=stacklevel + 1)
+                        return original_init_subclass(*args, **kwargs)
+
+                    arg.__init_subclass__ = classmethod(__init_subclass__)
+                # Or otherwise, which likely means it's a builtin such as
+                # object's implementation of __init_subclass__.
+                else:
+                    @functools.wraps(original_init_subclass)
+                    def __init_subclass__(*args, **kwargs):
+                        warnings.warn(msg, category=category, stacklevel=stacklevel + 1)
+                        return original_init_subclass(*args, **kwargs)
+
+                    arg.__init_subclass__ = __init_subclass__
+
+                arg.__deprecated__ = __new__.__deprecated__ = msg
+                __init_subclass__.__deprecated__ = msg
+                return arg
+            elif callable(arg):
+                import functools
+
+                @functools.wraps(arg)
+                def wrapper(*args, **kwargs):
+                    warnings.warn(msg, category=category, stacklevel=stacklevel + 1)
+                    return arg(*args, **kwargs)
+
+                arg.__deprecated__ = wrapper.__deprecated__ = msg
+                return wrapper
+            else:
+                raise TypeError(
+                    "@deprecated decorator with non-None category must be applied to "
+                    f"a class or callable, not {arg!r}"
+                )
+
+
+# We have to do some monkey patching to deal with the dual nature of
+# Unpack/TypeVarTuple:
+# - We want Unpack to be a kind of TypeVar so it gets accepted in
+#   Generic[Unpack[Ts]]
+# - We want it to *not* be treated as a TypeVar for the purposes of
+#   counting generic parameters, so that when we subscript a generic,
+#   the runtime doesn't try to substitute the Unpack with the subscripted type.
+if not hasattr(typing, "TypeVarTuple"):
+    def _check_generic(cls, parameters, elen=_marker):
+        """Check correct count for parameters of a generic cls (internal helper).
+
+        This gives a nice error message in case of count mismatch.
+        """
+        if not elen:
+            raise TypeError(f"{cls} is not a generic class")
+        if elen is _marker:
+            if not hasattr(cls, "__parameters__") or not cls.__parameters__:
+                raise TypeError(f"{cls} is not a generic class")
+            elen = len(cls.__parameters__)
+        alen = len(parameters)
+        if alen != elen:
+            expect_val = elen
+            if hasattr(cls, "__parameters__"):
+                parameters = [p for p in cls.__parameters__ if not _is_unpack(p)]
+                num_tv_tuples = sum(isinstance(p, TypeVarTuple) for p in parameters)
+                if (num_tv_tuples > 0) and (alen >= elen - num_tv_tuples):
+                    return
+
+                # deal with TypeVarLike defaults
+                # required TypeVarLikes cannot appear after a defaulted one.
+                if alen < elen:
+                    # since we validate TypeVarLike default in _collect_type_vars
+                    # or _collect_parameters we can safely check parameters[alen]
+                    if (
+                        getattr(parameters[alen], '__default__', NoDefault)
+                        is not NoDefault
+                    ):
+                        return
+
+                    num_default_tv = sum(getattr(p, '__default__', NoDefault)
+                                         is not NoDefault for p in parameters)
+
+                    elen -= num_default_tv
+
+                    expect_val = f"at least {elen}"
+
+            things = "arguments" if sys.version_info >= (3, 10) else "parameters"
+            raise TypeError(f"Too {'many' if alen > elen else 'few'} {things}"
+                            f" for {cls}; actual {alen}, expected {expect_val}")
+else:
+    # Python 3.11+
+
+    def _check_generic(cls, parameters, elen):
+        """Check correct count for parameters of a generic cls (internal helper).
+
+        This gives a nice error message in case of count mismatch.
+        """
+        if not elen:
+            raise TypeError(f"{cls} is not a generic class")
+        alen = len(parameters)
+        if alen != elen:
+            expect_val = elen
+            if hasattr(cls, "__parameters__"):
+                parameters = [p for p in cls.__parameters__ if not _is_unpack(p)]
+
+                # deal with TypeVarLike defaults
+                # required TypeVarLikes cannot appear after a defaulted one.
+                if alen < elen:
+                    # since we validate TypeVarLike default in _collect_type_vars
+                    # or _collect_parameters we can safely check parameters[alen]
+                    if (
+                        getattr(parameters[alen], '__default__', NoDefault)
+                        is not NoDefault
+                    ):
+                        return
+
+                    num_default_tv = sum(getattr(p, '__default__', NoDefault)
+                                         is not NoDefault for p in parameters)
+
+                    elen -= num_default_tv
+
+                    expect_val = f"at least {elen}"
+
+            raise TypeError(f"Too {'many' if alen > elen else 'few'} arguments"
+                            f" for {cls}; actual {alen}, expected {expect_val}")
+
+if not _PEP_696_IMPLEMENTED:
+    typing._check_generic = _check_generic
+
+
+def _has_generic_or_protocol_as_origin() -> bool:
+    try:
+        frame = sys._getframe(2)
+    # - Catch AttributeError: not all Python implementations have sys._getframe()
+    # - Catch ValueError: maybe we're called from an unexpected module
+    #   and the call stack isn't deep enough
+    except (AttributeError, ValueError):
+        return False  # err on the side of leniency
+    else:
+        # If we somehow get invoked from outside typing.py,
+        # also err on the side of leniency
+        if frame.f_globals.get("__name__") != "typing":
+            return False
+        origin = frame.f_locals.get("origin")
+        # Cannot use "in" because origin may be an object with a buggy __eq__ that
+        # throws an error.
+        return origin is typing.Generic or origin is Protocol or origin is typing.Protocol
+
+
+_TYPEVARTUPLE_TYPES = {TypeVarTuple, getattr(typing, "TypeVarTuple", None)}
+
+
+def _is_unpacked_typevartuple(x) -> bool:
+    if get_origin(x) is not Unpack:
+        return False
+    args = get_args(x)
+    return (
+        bool(args)
+        and len(args) == 1
+        and type(args[0]) in _TYPEVARTUPLE_TYPES
+    )
+
+
+# Python 3.11+ _collect_type_vars was renamed to _collect_parameters
+if hasattr(typing, '_collect_type_vars'):
+    def _collect_type_vars(types, typevar_types=None):
+        """Collect all type variable contained in types in order of
+        first appearance (lexicographic order). For example::
+
+            _collect_type_vars((T, List[S, T])) == (T, S)
+        """
+        if typevar_types is None:
+            typevar_types = typing.TypeVar
+        tvars = []
+
+        # A required TypeVarLike cannot appear after a TypeVarLike with a default
+        # if it was a direct call to `Generic[]` or `Protocol[]`
+        enforce_default_ordering = _has_generic_or_protocol_as_origin()
+        default_encountered = False
+
+        # Also, a TypeVarLike with a default cannot appear after a TypeVarTuple
+        type_var_tuple_encountered = False
+
+        for t in types:
+            if _is_unpacked_typevartuple(t):
+                type_var_tuple_encountered = True
+            elif isinstance(t, typevar_types) and t not in tvars:
+                if enforce_default_ordering:
+                    has_default = getattr(t, '__default__', NoDefault) is not NoDefault
+                    if has_default:
+                        if type_var_tuple_encountered:
+                            raise TypeError('Type parameter with a default'
+                                            ' follows TypeVarTuple')
+                        default_encountered = True
+                    elif default_encountered:
+                        raise TypeError(f'Type parameter {t!r} without a default'
+                                        ' follows type parameter with a default')
+
+                tvars.append(t)
+            if _should_collect_from_parameters(t):
+                tvars.extend([t for t in t.__parameters__ if t not in tvars])
+        return tuple(tvars)
+
+    typing._collect_type_vars = _collect_type_vars
+else:
+    def _collect_parameters(args):
+        """Collect all type variables and parameter specifications in args
+        in order of first appearance (lexicographic order).
+
+        For example::
+
+            assert _collect_parameters((T, Callable[P, T])) == (T, P)
+        """
+        parameters = []
+
+        # A required TypeVarLike cannot appear after a TypeVarLike with default
+        # if it was a direct call to `Generic[]` or `Protocol[]`
+        enforce_default_ordering = _has_generic_or_protocol_as_origin()
+        default_encountered = False
+
+        # Also, a TypeVarLike with a default cannot appear after a TypeVarTuple
+        type_var_tuple_encountered = False
+
+        for t in args:
+            if isinstance(t, type):
+                # We don't want __parameters__ descriptor of a bare Python class.
+                pass
+            elif isinstance(t, tuple):
+                # `t` might be a tuple, when `ParamSpec` is substituted with
+                # `[T, int]`, or `[int, *Ts]`, etc.
+                for x in t:
+                    for collected in _collect_parameters([x]):
+                        if collected not in parameters:
+                            parameters.append(collected)
+            elif hasattr(t, '__typing_subst__'):
+                if t not in parameters:
+                    if enforce_default_ordering:
+                        has_default = (
+                            getattr(t, '__default__', NoDefault) is not NoDefault
+                        )
+
+                        if type_var_tuple_encountered and has_default:
+                            raise TypeError('Type parameter with a default'
+                                            ' follows TypeVarTuple')
+
+                        if has_default:
+                            default_encountered = True
+                        elif default_encountered:
+                            raise TypeError(f'Type parameter {t!r} without a default'
+                                            ' follows type parameter with a default')
+
+                    parameters.append(t)
+            else:
+                if _is_unpacked_typevartuple(t):
+                    type_var_tuple_encountered = True
+                for x in getattr(t, '__parameters__', ()):
+                    if x not in parameters:
+                        parameters.append(x)
+
+        return tuple(parameters)
+
+    if not _PEP_696_IMPLEMENTED:
+        typing._collect_parameters = _collect_parameters
+
+# Backport typing.NamedTuple as it exists in Python 3.13.
+# In 3.11, the ability to define generic `NamedTuple`s was supported.
+# This was explicitly disallowed in 3.9-3.10, and only half-worked in <=3.8.
+# On 3.12, we added __orig_bases__ to call-based NamedTuples
+# On 3.13, we deprecated kwargs-based NamedTuples
+if sys.version_info >= (3, 13):
+    NamedTuple = typing.NamedTuple
+else:
+    def _make_nmtuple(name, types, module, defaults=()):
+        fields = [n for n, t in types]
+        annotations = {n: typing._type_check(t, f"field {n} annotation must be a type")
+                       for n, t in types}
+        nm_tpl = collections.namedtuple(name, fields,
+                                        defaults=defaults, module=module)
+        nm_tpl.__annotations__ = nm_tpl.__new__.__annotations__ = annotations
+        # The `_field_types` attribute was removed in 3.9;
+        # in earlier versions, it is the same as the `__annotations__` attribute
+        if sys.version_info < (3, 9):
+            nm_tpl._field_types = annotations
+        return nm_tpl
+
+    _prohibited_namedtuple_fields = typing._prohibited
+    _special_namedtuple_fields = frozenset({'__module__', '__name__', '__annotations__'})
+
+    class _NamedTupleMeta(type):
+        def __new__(cls, typename, bases, ns):
+            assert _NamedTuple in bases
+            for base in bases:
+                if base is not _NamedTuple and base is not typing.Generic:
+                    raise TypeError(
+                        'can only inherit from a NamedTuple type and Generic')
+            bases = tuple(tuple if base is _NamedTuple else base for base in bases)
+            if "__annotations__" in ns:
+                types = ns["__annotations__"]
+            elif "__annotate__" in ns:
+                # TODO: Use inspect.VALUE here, and make the annotations lazily evaluated
+                types = ns["__annotate__"](1)
+            else:
+                types = {}
+            default_names = []
+            for field_name in types:
+                if field_name in ns:
+                    default_names.append(field_name)
+                elif default_names:
+                    raise TypeError(f"Non-default namedtuple field {field_name} "
+                                    f"cannot follow default field"
+                                    f"{'s' if len(default_names) > 1 else ''} "
+                                    f"{', '.join(default_names)}")
+            nm_tpl = _make_nmtuple(
+                typename, types.items(),
+                defaults=[ns[n] for n in default_names],
+                module=ns['__module__']
+            )
+            nm_tpl.__bases__ = bases
+            if typing.Generic in bases:
+                if hasattr(typing, '_generic_class_getitem'):  # 3.12+
+                    nm_tpl.__class_getitem__ = classmethod(typing._generic_class_getitem)
+                else:
+                    class_getitem = typing.Generic.__class_getitem__.__func__
+                    nm_tpl.__class_getitem__ = classmethod(class_getitem)
+            # update from user namespace without overriding special namedtuple attributes
+            for key, val in ns.items():
+                if key in _prohibited_namedtuple_fields:
+                    raise AttributeError("Cannot overwrite NamedTuple attribute " + key)
+                elif key not in _special_namedtuple_fields:
+                    if key not in nm_tpl._fields:
+                        setattr(nm_tpl, key, ns[key])
+                    try:
+                        set_name = type(val).__set_name__
+                    except AttributeError:
+                        pass
+                    else:
+                        try:
+                            set_name(val, nm_tpl, key)
+                        except BaseException as e:
+                            msg = (
+                                f"Error calling __set_name__ on {type(val).__name__!r} "
+                                f"instance {key!r} in {typename!r}"
+                            )
+                            # BaseException.add_note() existed on py311,
+                            # but the __set_name__ machinery didn't start
+                            # using add_note() until py312.
+                            # Making sure exceptions are raised in the same way
+                            # as in "normal" classes seems most important here.
+                            if sys.version_info >= (3, 12):
+                                e.add_note(msg)
+                                raise
+                            else:
+                                raise RuntimeError(msg) from e
+
+            if typing.Generic in bases:
+                nm_tpl.__init_subclass__()
+            return nm_tpl
+
+    _NamedTuple = type.__new__(_NamedTupleMeta, 'NamedTuple', (), {})
+
+    def _namedtuple_mro_entries(bases):
+        assert NamedTuple in bases
+        return (_NamedTuple,)
+
+    @_ensure_subclassable(_namedtuple_mro_entries)
+    def NamedTuple(typename, fields=_marker, /, **kwargs):
+        """Typed version of namedtuple.
+
+        Usage::
+
+            class Employee(NamedTuple):
+                name: str
+                id: int
+
+        This is equivalent to::
+
+            Employee = collections.namedtuple('Employee', ['name', 'id'])
+
+        The resulting class has an extra __annotations__ attribute, giving a
+        dict that maps field names to types.  (The field names are also in
+        the _fields attribute, which is part of the namedtuple API.)
+        An alternative equivalent functional syntax is also accepted::
+
+            Employee = NamedTuple('Employee', [('name', str), ('id', int)])
+        """
+        if fields is _marker:
+            if kwargs:
+                deprecated_thing = "Creating NamedTuple classes using keyword arguments"
+                deprecation_msg = (
+                    "{name} is deprecated and will be disallowed in Python {remove}. "
+                    "Use the class-based or functional syntax instead."
+                )
+            else:
+                deprecated_thing = "Failing to pass a value for the 'fields' parameter"
+                example = f"`{typename} = NamedTuple({typename!r}, [])`"
+                deprecation_msg = (
+                    "{name} is deprecated and will be disallowed in Python {remove}. "
+                    "To create a NamedTuple class with 0 fields "
+                    "using the functional syntax, "
+                    "pass an empty list, e.g. "
+                ) + example + "."
+        elif fields is None:
+            if kwargs:
+                raise TypeError(
+                    "Cannot pass `None` as the 'fields' parameter "
+                    "and also specify fields using keyword arguments"
+                )
+            else:
+                deprecated_thing = "Passing `None` as the 'fields' parameter"
+                example = f"`{typename} = NamedTuple({typename!r}, [])`"
+                deprecation_msg = (
+                    "{name} is deprecated and will be disallowed in Python {remove}. "
+                    "To create a NamedTuple class with 0 fields "
+                    "using the functional syntax, "
+                    "pass an empty list, e.g. "
+                ) + example + "."
+        elif kwargs:
+            raise TypeError("Either list of fields or keywords"
+                            " can be provided to NamedTuple, not both")
+        if fields is _marker or fields is None:
+            warnings.warn(
+                deprecation_msg.format(name=deprecated_thing, remove="3.15"),
+                DeprecationWarning,
+                stacklevel=2,
+            )
+            fields = kwargs.items()
+        nt = _make_nmtuple(typename, fields, module=_caller())
+        nt.__orig_bases__ = (NamedTuple,)
+        return nt
+
+
+if hasattr(collections.abc, "Buffer"):
+    Buffer = collections.abc.Buffer
+else:
+    class Buffer(abc.ABC):  # noqa: B024
+        """Base class for classes that implement the buffer protocol.
+
+        The buffer protocol allows Python objects to expose a low-level
+        memory buffer interface. Before Python 3.12, it is not possible
+        to implement the buffer protocol in pure Python code, or even
+        to check whether a class implements the buffer protocol. In
+        Python 3.12 and higher, the ``__buffer__`` method allows access
+        to the buffer protocol from Python code, and the
+        ``collections.abc.Buffer`` ABC allows checking whether a class
+        implements the buffer protocol.
+
+        To indicate support for the buffer protocol in earlier versions,
+        inherit from this ABC, either in a stub file or at runtime,
+        or use ABC registration. This ABC provides no methods, because
+        there is no Python-accessible methods shared by pre-3.12 buffer
+        classes. It is useful primarily for static checks.
+
+        """
+
+    # As a courtesy, register the most common stdlib buffer classes.
+    Buffer.register(memoryview)
+    Buffer.register(bytearray)
+    Buffer.register(bytes)
+
+
+# Backport of types.get_original_bases, available on 3.12+ in CPython
+if hasattr(_types, "get_original_bases"):
+    get_original_bases = _types.get_original_bases
+else:
+    def get_original_bases(cls, /):
+        """Return the class's "original" bases prior to modification by `__mro_entries__`.
+
+        Examples::
+
+            from typing import TypeVar, Generic
+            from pip._vendor.typing_extensions import NamedTuple, TypedDict
+
+            T = TypeVar("T")
+            class Foo(Generic[T]): ...
+            class Bar(Foo[int], float): ...
+            class Baz(list[str]): ...
+            Eggs = NamedTuple("Eggs", [("a", int), ("b", str)])
+            Spam = TypedDict("Spam", {"a": int, "b": str})
+
+            assert get_original_bases(Bar) == (Foo[int], float)
+            assert get_original_bases(Baz) == (list[str],)
+            assert get_original_bases(Eggs) == (NamedTuple,)
+            assert get_original_bases(Spam) == (TypedDict,)
+            assert get_original_bases(int) == (object,)
+        """
+        try:
+            return cls.__dict__.get("__orig_bases__", cls.__bases__)
+        except AttributeError:
+            raise TypeError(
+                f'Expected an instance of type, not {type(cls).__name__!r}'
+            ) from None
+
+
+# NewType is a class on Python 3.10+, making it pickleable
+# The error message for subclassing instances of NewType was improved on 3.11+
+if sys.version_info >= (3, 11):
+    NewType = typing.NewType
+else:
+    class NewType:
+        """NewType creates simple unique types with almost zero
+        runtime overhead. NewType(name, tp) is considered a subtype of tp
+        by static type checkers. At runtime, NewType(name, tp) returns
+        a dummy callable that simply returns its argument. Usage::
+            UserId = NewType('UserId', int)
+            def name_by_id(user_id: UserId) -> str:
+                ...
+            UserId('user')          # Fails type check
+            name_by_id(42)          # Fails type check
+            name_by_id(UserId(42))  # OK
+            num = UserId(5) + 1     # type: int
+        """
+
+        def __call__(self, obj, /):
+            return obj
+
+        def __init__(self, name, tp):
+            self.__qualname__ = name
+            if '.' in name:
+                name = name.rpartition('.')[-1]
+            self.__name__ = name
+            self.__supertype__ = tp
+            def_mod = _caller()
+            if def_mod != 'typing_extensions':
+                self.__module__ = def_mod
+
+        def __mro_entries__(self, bases):
+            # We defined __mro_entries__ to get a better error message
+            # if a user attempts to subclass a NewType instance. bpo-46170
+            supercls_name = self.__name__
+
+            class Dummy:
+                def __init_subclass__(cls):
+                    subcls_name = cls.__name__
+                    raise TypeError(
+                        f"Cannot subclass an instance of NewType. "
+                        f"Perhaps you were looking for: "
+                        f"`{subcls_name} = NewType({subcls_name!r}, {supercls_name})`"
+                    )
+
+            return (Dummy,)
+
+        def __repr__(self):
+            return f'{self.__module__}.{self.__qualname__}'
+
+        def __reduce__(self):
+            return self.__qualname__
+
+        if sys.version_info >= (3, 10):
+            # PEP 604 methods
+            # It doesn't make sense to have these methods on Python <3.10
+
+            def __or__(self, other):
+                return typing.Union[self, other]
+
+            def __ror__(self, other):
+                return typing.Union[other, self]
+
+
+if hasattr(typing, "TypeAliasType"):
+    TypeAliasType = typing.TypeAliasType
+else:
+    def _is_unionable(obj):
+        """Corresponds to is_unionable() in unionobject.c in CPython."""
+        return obj is None or isinstance(obj, (
+            type,
+            _types.GenericAlias,
+            _types.UnionType,
+            TypeAliasType,
+        ))
+
+    class TypeAliasType:
+        """Create named, parameterized type aliases.
+
+        This provides a backport of the new `type` statement in Python 3.12:
+
+            type ListOrSet[T] = list[T] | set[T]
+
+        is equivalent to:
+
+            T = TypeVar("T")
+            ListOrSet = TypeAliasType("ListOrSet", list[T] | set[T], type_params=(T,))
+
+        The name ListOrSet can then be used as an alias for the type it refers to.
+
+        The type_params argument should contain all the type parameters used
+        in the value of the type alias. If the alias is not generic, this
+        argument is omitted.
+
+        Static type checkers should only support type aliases declared using
+        TypeAliasType that follow these rules:
+
+        - The first argument (the name) must be a string literal.
+        - The TypeAliasType instance must be immediately assigned to a variable
+          of the same name. (For example, 'X = TypeAliasType("Y", int)' is invalid,
+          as is 'X, Y = TypeAliasType("X", int), TypeAliasType("Y", int)').
+
+        """
+
+        def __init__(self, name: str, value, *, type_params=()):
+            if not isinstance(name, str):
+                raise TypeError("TypeAliasType name must be a string")
+            self.__value__ = value
+            self.__type_params__ = type_params
+
+            parameters = []
+            for type_param in type_params:
+                if isinstance(type_param, TypeVarTuple):
+                    parameters.extend(type_param)
+                else:
+                    parameters.append(type_param)
+            self.__parameters__ = tuple(parameters)
+            def_mod = _caller()
+            if def_mod != 'typing_extensions':
+                self.__module__ = def_mod
+            # Setting this attribute closes the TypeAliasType from further modification
+            self.__name__ = name
+
+        def __setattr__(self, name: str, value: object, /) -> None:
+            if hasattr(self, "__name__"):
+                self._raise_attribute_error(name)
+            super().__setattr__(name, value)
+
+        def __delattr__(self, name: str, /) -> Never:
+            self._raise_attribute_error(name)
+
+        def _raise_attribute_error(self, name: str) -> Never:
+            # Match the Python 3.12 error messages exactly
+            if name == "__name__":
+                raise AttributeError("readonly attribute")
+            elif name in {"__value__", "__type_params__", "__parameters__", "__module__"}:
+                raise AttributeError(
+                    f"attribute '{name}' of 'typing.TypeAliasType' objects "
+                    "is not writable"
+                )
+            else:
+                raise AttributeError(
+                    f"'typing.TypeAliasType' object has no attribute '{name}'"
+                )
+
+        def __repr__(self) -> str:
+            return self.__name__
+
+        def __getitem__(self, parameters):
+            if not isinstance(parameters, tuple):
+                parameters = (parameters,)
+            parameters = [
+                typing._type_check(
+                    item, f'Subscripting {self.__name__} requires a type.'
+                )
+                for item in parameters
+            ]
+            return typing._GenericAlias(self, tuple(parameters))
+
+        def __reduce__(self):
+            return self.__name__
+
+        def __init_subclass__(cls, *args, **kwargs):
+            raise TypeError(
+                "type 'typing_extensions.TypeAliasType' is not an acceptable base type"
+            )
+
+        # The presence of this method convinces typing._type_check
+        # that TypeAliasTypes are types.
+        def __call__(self):
+            raise TypeError("Type alias is not callable")
+
+        if sys.version_info >= (3, 10):
+            def __or__(self, right):
+                # For forward compatibility with 3.12, reject Unions
+                # that are not accepted by the built-in Union.
+                if not _is_unionable(right):
+                    return NotImplemented
+                return typing.Union[self, right]
+
+            def __ror__(self, left):
+                if not _is_unionable(left):
+                    return NotImplemented
+                return typing.Union[left, self]
+
+
+if hasattr(typing, "is_protocol"):
+    is_protocol = typing.is_protocol
+    get_protocol_members = typing.get_protocol_members
+else:
+    def is_protocol(tp: type, /) -> bool:
+        """Return True if the given type is a Protocol.
+
+        Example::
+
+            >>> from typing_extensions import Protocol, is_protocol
+            >>> class P(Protocol):
+            ...     def a(self) -> str: ...
+            ...     b: int
+            >>> is_protocol(P)
+            True
+            >>> is_protocol(int)
+            False
+        """
+        return (
+            isinstance(tp, type)
+            and getattr(tp, '_is_protocol', False)
+            and tp is not Protocol
+            and tp is not typing.Protocol
+        )
+
+    def get_protocol_members(tp: type, /) -> typing.FrozenSet[str]:
+        """Return the set of members defined in a Protocol.
+
+        Example::
+
+            >>> from typing_extensions import Protocol, get_protocol_members
+            >>> class P(Protocol):
+            ...     def a(self) -> str: ...
+            ...     b: int
+            >>> get_protocol_members(P)
+            frozenset({'a', 'b'})
+
+        Raise a TypeError for arguments that are not Protocols.
+        """
+        if not is_protocol(tp):
+            raise TypeError(f'{tp!r} is not a Protocol')
+        if hasattr(tp, '__protocol_attrs__'):
+            return frozenset(tp.__protocol_attrs__)
+        return frozenset(_get_protocol_attrs(tp))
+
+
+if hasattr(typing, "Doc"):
+    Doc = typing.Doc
+else:
+    class Doc:
+        """Define the documentation of a type annotation using ``Annotated``, to be
+         used in class attributes, function and method parameters, return values,
+         and variables.
+
+        The value should be a positional-only string literal to allow static tools
+        like editors and documentation generators to use it.
+
+        This complements docstrings.
+
+        The string value passed is available in the attribute ``documentation``.
+
+        Example::
+
+            >>> from typing_extensions import Annotated, Doc
+            >>> def hi(to: Annotated[str, Doc("Who to say hi to")]) -> None: ...
+        """
+        def __init__(self, documentation: str, /) -> None:
+            self.documentation = documentation
+
+        def __repr__(self) -> str:
+            return f"Doc({self.documentation!r})"
+
+        def __hash__(self) -> int:
+            return hash(self.documentation)
+
+        def __eq__(self, other: object) -> bool:
+            if not isinstance(other, Doc):
+                return NotImplemented
+            return self.documentation == other.documentation
+
+
+_CapsuleType = getattr(_types, "CapsuleType", None)
+
+if _CapsuleType is None:
+    try:
+        import _socket
+    except ImportError:
+        pass
+    else:
+        _CAPI = getattr(_socket, "CAPI", None)
+        if _CAPI is not None:
+            _CapsuleType = type(_CAPI)
+
+if _CapsuleType is not None:
+    CapsuleType = _CapsuleType
+    __all__.append("CapsuleType")
+
+
+# Aliases for items that have always been in typing.
+# Explicitly assign these (rather than using `from typing import *` at the top),
+# so that we get a CI error if one of these is deleted from typing.py
+# in a future version of Python
+AbstractSet = typing.AbstractSet
+AnyStr = typing.AnyStr
+BinaryIO = typing.BinaryIO
+Callable = typing.Callable
+Collection = typing.Collection
+Container = typing.Container
+Dict = typing.Dict
+ForwardRef = typing.ForwardRef
+FrozenSet = typing.FrozenSet
+Generic = typing.Generic
+Hashable = typing.Hashable
+IO = typing.IO
+ItemsView = typing.ItemsView
+Iterable = typing.Iterable
+Iterator = typing.Iterator
+KeysView = typing.KeysView
+List = typing.List
+Mapping = typing.Mapping
+MappingView = typing.MappingView
+Match = typing.Match
+MutableMapping = typing.MutableMapping
+MutableSequence = typing.MutableSequence
+MutableSet = typing.MutableSet
+Optional = typing.Optional
+Pattern = typing.Pattern
+Reversible = typing.Reversible
+Sequence = typing.Sequence
+Set = typing.Set
+Sized = typing.Sized
+TextIO = typing.TextIO
+Tuple = typing.Tuple
+Union = typing.Union
+ValuesView = typing.ValuesView
+cast = typing.cast
+no_type_check = typing.no_type_check
+no_type_check_decorator = typing.no_type_check_decorator
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/LICENSE b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/LICENSE
new file mode 100644
index 0000000000000000000000000000000000000000..f26bcf4d2de6eb136e31006ca3ab447d5e488adf
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/LICENSE
@@ -0,0 +1,279 @@
+A. HISTORY OF THE SOFTWARE
+==========================
+
+Python was created in the early 1990s by Guido van Rossum at Stichting
+Mathematisch Centrum (CWI, see https://www.cwi.nl) in the Netherlands
+as a successor of a language called ABC.  Guido remains Python's
+principal author, although it includes many contributions from others.
+
+In 1995, Guido continued his work on Python at the Corporation for
+National Research Initiatives (CNRI, see https://www.cnri.reston.va.us)
+in Reston, Virginia where he released several versions of the
+software.
+
+In May 2000, Guido and the Python core development team moved to
+BeOpen.com to form the BeOpen PythonLabs team.  In October of the same
+year, the PythonLabs team moved to Digital Creations, which became
+Zope Corporation.  In 2001, the Python Software Foundation (PSF, see
+https://www.python.org/psf/) was formed, a non-profit organization
+created specifically to own Python-related Intellectual Property.
+Zope Corporation was a sponsoring member of the PSF.
+
+All Python releases are Open Source (see https://opensource.org for
+the Open Source Definition).  Historically, most, but not all, Python
+releases have also been GPL-compatible; the table below summarizes
+the various releases.
+
+    Release         Derived     Year        Owner       GPL-
+                    from                                compatible? (1)
+
+    0.9.0 thru 1.2              1991-1995   CWI         yes
+    1.3 thru 1.5.2  1.2         1995-1999   CNRI        yes
+    1.6             1.5.2       2000        CNRI        no
+    2.0             1.6         2000        BeOpen.com  no
+    1.6.1           1.6         2001        CNRI        yes (2)
+    2.1             2.0+1.6.1   2001        PSF         no
+    2.0.1           2.0+1.6.1   2001        PSF         yes
+    2.1.1           2.1+2.0.1   2001        PSF         yes
+    2.1.2           2.1.1       2002        PSF         yes
+    2.1.3           2.1.2       2002        PSF         yes
+    2.2 and above   2.1.1       2001-now    PSF         yes
+
+Footnotes:
+
+(1) GPL-compatible doesn't mean that we're distributing Python under
+    the GPL.  All Python licenses, unlike the GPL, let you distribute
+    a modified version without making your changes open source.  The
+    GPL-compatible licenses make it possible to combine Python with
+    other software that is released under the GPL; the others don't.
+
+(2) According to Richard Stallman, 1.6.1 is not GPL-compatible,
+    because its license has a choice of law clause.  According to
+    CNRI, however, Stallman's lawyer has told CNRI's lawyer that 1.6.1
+    is "not incompatible" with the GPL.
+
+Thanks to the many outside volunteers who have worked under Guido's
+direction to make these releases possible.
+
+
+B. TERMS AND CONDITIONS FOR ACCESSING OR OTHERWISE USING PYTHON
+===============================================================
+
+Python software and documentation are licensed under the
+Python Software Foundation License Version 2.
+
+Starting with Python 3.8.6, examples, recipes, and other code in
+the documentation are dual licensed under the PSF License Version 2
+and the Zero-Clause BSD license.
+
+Some software incorporated into Python is under different licenses.
+The licenses are listed with code falling under that license.
+
+
+PYTHON SOFTWARE FOUNDATION LICENSE VERSION 2
+--------------------------------------------
+
+1. This LICENSE AGREEMENT is between the Python Software Foundation
+("PSF"), and the Individual or Organization ("Licensee") accessing and
+otherwise using this software ("Python") in source or binary form and
+its associated documentation.
+
+2. Subject to the terms and conditions of this License Agreement, PSF hereby
+grants Licensee a nonexclusive, royalty-free, world-wide license to reproduce,
+analyze, test, perform and/or display publicly, prepare derivative works,
+distribute, and otherwise use Python alone or in any derivative version,
+provided, however, that PSF's License Agreement and PSF's notice of copyright,
+i.e., "Copyright (c) 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
+2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023 Python Software Foundation;
+All Rights Reserved" are retained in Python alone or in any derivative version
+prepared by Licensee.
+
+3. In the event Licensee prepares a derivative work that is based on
+or incorporates Python or any part thereof, and wants to make
+the derivative work available to others as provided herein, then
+Licensee hereby agrees to include in any such work a brief summary of
+the changes made to Python.
+
+4. PSF is making Python available to Licensee on an "AS IS"
+basis.  PSF MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
+IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, PSF MAKES NO AND
+DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
+FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON WILL NOT
+INFRINGE ANY THIRD PARTY RIGHTS.
+
+5. PSF SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
+FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
+A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON,
+OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
+
+6. This License Agreement will automatically terminate upon a material
+breach of its terms and conditions.
+
+7. Nothing in this License Agreement shall be deemed to create any
+relationship of agency, partnership, or joint venture between PSF and
+Licensee.  This License Agreement does not grant permission to use PSF
+trademarks or trade name in a trademark sense to endorse or promote
+products or services of Licensee, or any third party.
+
+8. By copying, installing or otherwise using Python, Licensee
+agrees to be bound by the terms and conditions of this License
+Agreement.
+
+
+BEOPEN.COM LICENSE AGREEMENT FOR PYTHON 2.0
+-------------------------------------------
+
+BEOPEN PYTHON OPEN SOURCE LICENSE AGREEMENT VERSION 1
+
+1. This LICENSE AGREEMENT is between BeOpen.com ("BeOpen"), having an
+office at 160 Saratoga Avenue, Santa Clara, CA 95051, and the
+Individual or Organization ("Licensee") accessing and otherwise using
+this software in source or binary form and its associated
+documentation ("the Software").
+
+2. Subject to the terms and conditions of this BeOpen Python License
+Agreement, BeOpen hereby grants Licensee a non-exclusive,
+royalty-free, world-wide license to reproduce, analyze, test, perform
+and/or display publicly, prepare derivative works, distribute, and
+otherwise use the Software alone or in any derivative version,
+provided, however, that the BeOpen Python License is retained in the
+Software, alone or in any derivative version prepared by Licensee.
+
+3. BeOpen is making the Software available to Licensee on an "AS IS"
+basis.  BEOPEN MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
+IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, BEOPEN MAKES NO AND
+DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
+FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF THE SOFTWARE WILL NOT
+INFRINGE ANY THIRD PARTY RIGHTS.
+
+4. BEOPEN SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF THE
+SOFTWARE FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS
+AS A RESULT OF USING, MODIFYING OR DISTRIBUTING THE SOFTWARE, OR ANY
+DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
+
+5. This License Agreement will automatically terminate upon a material
+breach of its terms and conditions.
+
+6. This License Agreement shall be governed by and interpreted in all
+respects by the law of the State of California, excluding conflict of
+law provisions.  Nothing in this License Agreement shall be deemed to
+create any relationship of agency, partnership, or joint venture
+between BeOpen and Licensee.  This License Agreement does not grant
+permission to use BeOpen trademarks or trade names in a trademark
+sense to endorse or promote products or services of Licensee, or any
+third party.  As an exception, the "BeOpen Python" logos available at
+http://www.pythonlabs.com/logos.html may be used according to the
+permissions granted on that web page.
+
+7. By copying, installing or otherwise using the software, Licensee
+agrees to be bound by the terms and conditions of this License
+Agreement.
+
+
+CNRI LICENSE AGREEMENT FOR PYTHON 1.6.1
+---------------------------------------
+
+1. This LICENSE AGREEMENT is between the Corporation for National
+Research Initiatives, having an office at 1895 Preston White Drive,
+Reston, VA 20191 ("CNRI"), and the Individual or Organization
+("Licensee") accessing and otherwise using Python 1.6.1 software in
+source or binary form and its associated documentation.
+
+2. Subject to the terms and conditions of this License Agreement, CNRI
+hereby grants Licensee a nonexclusive, royalty-free, world-wide
+license to reproduce, analyze, test, perform and/or display publicly,
+prepare derivative works, distribute, and otherwise use Python 1.6.1
+alone or in any derivative version, provided, however, that CNRI's
+License Agreement and CNRI's notice of copyright, i.e., "Copyright (c)
+1995-2001 Corporation for National Research Initiatives; All Rights
+Reserved" are retained in Python 1.6.1 alone or in any derivative
+version prepared by Licensee.  Alternately, in lieu of CNRI's License
+Agreement, Licensee may substitute the following text (omitting the
+quotes): "Python 1.6.1 is made available subject to the terms and
+conditions in CNRI's License Agreement.  This Agreement together with
+Python 1.6.1 may be located on the internet using the following
+unique, persistent identifier (known as a handle): 1895.22/1013.  This
+Agreement may also be obtained from a proxy server on the internet
+using the following URL: http://hdl.handle.net/1895.22/1013".
+
+3. In the event Licensee prepares a derivative work that is based on
+or incorporates Python 1.6.1 or any part thereof, and wants to make
+the derivative work available to others as provided herein, then
+Licensee hereby agrees to include in any such work a brief summary of
+the changes made to Python 1.6.1.
+
+4. CNRI is making Python 1.6.1 available to Licensee on an "AS IS"
+basis.  CNRI MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR
+IMPLIED.  BY WAY OF EXAMPLE, BUT NOT LIMITATION, CNRI MAKES NO AND
+DISCLAIMS ANY REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS
+FOR ANY PARTICULAR PURPOSE OR THAT THE USE OF PYTHON 1.6.1 WILL NOT
+INFRINGE ANY THIRD PARTY RIGHTS.
+
+5. CNRI SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PYTHON
+1.6.1 FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS
+A RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PYTHON 1.6.1,
+OR ANY DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
+
+6. This License Agreement will automatically terminate upon a material
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+The Netherlands.  All rights reserved.
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+Permission to use, copy, modify, and distribute this software and its
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diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/METADATA b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/METADATA
new file mode 100644
index 0000000000000000000000000000000000000000..863e977c2f7b65007b97a0bf4daba39aa19dbbf4
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/METADATA
@@ -0,0 +1,66 @@
+Metadata-Version: 2.1
+Name: typing_extensions
+Version: 4.9.0
+Summary: Backported and Experimental Type Hints for Python 3.8+
+Keywords: annotations,backport,checker,checking,function,hinting,hints,type,typechecking,typehinting,typehints,typing
+Author-email: "Guido van Rossum, Jukka Lehtosalo, Łukasz Langa, Michael Lee" <levkivskyi@gmail.com>
+Requires-Python: >=3.8
+Description-Content-Type: text/markdown
+Classifier: Development Status :: 5 - Production/Stable
+Classifier: Environment :: Console
+Classifier: Intended Audience :: Developers
+Classifier: License :: OSI Approved :: Python Software Foundation License
+Classifier: Operating System :: OS Independent
+Classifier: Programming Language :: Python :: 3
+Classifier: Programming Language :: Python :: 3 :: Only
+Classifier: Programming Language :: Python :: 3.8
+Classifier: Programming Language :: Python :: 3.9
+Classifier: Programming Language :: Python :: 3.10
+Classifier: Programming Language :: Python :: 3.11
+Classifier: Programming Language :: Python :: 3.12
+Classifier: Topic :: Software Development
+Project-URL: Bug Tracker, https://github.com/python/typing_extensions/issues
+Project-URL: Changes, https://github.com/python/typing_extensions/blob/main/CHANGELOG.md
+Project-URL: Documentation, https://typing-extensions.readthedocs.io/
+Project-URL: Home, https://github.com/python/typing_extensions
+Project-URL: Q & A, https://github.com/python/typing/discussions
+Project-URL: Repository, https://github.com/python/typing_extensions
+
+# Typing Extensions
+
+[![Chat at https://gitter.im/python/typing](https://badges.gitter.im/python/typing.svg)](https://gitter.im/python/typing)
+
+[Documentation](https://typing-extensions.readthedocs.io/en/latest/#) –
+[PyPI](https://pypi.org/project/typing-extensions/)
+
+## Overview
+
+The `typing_extensions` module serves two related purposes:
+
+- Enable use of new type system features on older Python versions. For example,
+  `typing.TypeGuard` is new in Python 3.10, but `typing_extensions` allows
+  users on previous Python versions to use it too.
+- Enable experimentation with new type system PEPs before they are accepted and
+  added to the `typing` module.
+
+`typing_extensions` is treated specially by static type checkers such as
+mypy and pyright. Objects defined in `typing_extensions` are treated the same
+way as equivalent forms in `typing`.
+
+`typing_extensions` uses
+[Semantic Versioning](https://semver.org/). The
+major version will be incremented only for backwards-incompatible changes.
+Therefore, it's safe to depend
+on `typing_extensions` like this: `typing_extensions >=x.y, <(x+1)`,
+where `x.y` is the first version that includes all features you need.
+
+## Included items
+
+See [the documentation](https://typing-extensions.readthedocs.io/en/latest/#) for a
+complete listing of module contents.
+
+## Contributing
+
+See [CONTRIBUTING.md](https://github.com/python/typing_extensions/blob/main/CONTRIBUTING.md)
+for how to contribute to `typing_extensions`.
+
diff --git a/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/WHEEL b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/WHEEL
new file mode 100644
index 0000000000000000000000000000000000000000..3b5e64b5e6c4a210201d1676a891fd57b15cda99
--- /dev/null
+++ b/tuning-competition-baseline/.venv/lib/python3.11/site-packages/typing_extensions-4.9.0.dist-info/WHEEL
@@ -0,0 +1,4 @@
+Wheel-Version: 1.0
+Generator: flit 3.9.0
+Root-Is-Purelib: true
+Tag: py3-none-any