shutil
— High-level file operations¶
Source code: Lib/shutil.py
The shutil
module offers a number of high-level operations on files and
collections of files. In particular, functions are provided which support file
copying and removal. For operations on individual files, see also the
os
module.
Warning
Even the higher-level file copying functions (shutil.copy()
,
shutil.copy2()
) cannot copy all file metadata.
On POSIX platforms, this means that file owner and group are lost as well as ACLs. On Mac OS, the resource fork and other metadata are not used. This means that resources will be lost and file type and creator codes will not be correct. On Windows, file owners, ACLs and alternate data streams are not copied.
Directory and files operations¶
- shutil.copyfileobj(fsrc, fdst[, length])¶
Copy the contents of the file-like object fsrc to the file-like object fdst. The integer length, if given, is the buffer size. In particular, a negative length value means to copy the data without looping over the source data in chunks; by default the data is read in chunks to avoid uncontrolled memory consumption. Note that if the current file position of the fsrc object is not 0, only the contents from the current file position to the end of the file will be copied.
- shutil.copyfile(src, dst, *, follow_symlinks=True)¶
Copy the contents (no metadata) of the file named src to a file named dst and return dst in the most efficient way possible. src and dst are path-like objects or path names given as strings.
dst must be the complete target file name; look at
copy()
for a copy that accepts a target directory path. If src and dst specify the same file,SameFileError
is raised.The destination location must be writable; otherwise, an
OSError
exception will be raised. If dst already exists, it will be replaced. Special files such as character or block devices and pipes cannot be copied with this function.If follow_symlinks is false and src is a symbolic link, a new symbolic link will be created instead of copying the file src points to.
Raises an auditing event
shutil.copyfile
with argumentssrc
,dst
.Changed in version 3.3:
IOError
used to be raised instead ofOSError
. Added follow_symlinks argument. Now returns dst.Changed in version 3.4: Raise
SameFileError
instead ofError
. Since the former is a subclass of the latter, this change is backward compatible.Changed in version 3.8: Platform-specific fast-copy syscalls may be used internally in order to copy the file more efficiently. See Platform-dependent efficient copy operations section.
- exception shutil.SameFileError¶
This exception is raised if source and destination in
copyfile()
are the same file.New in version 3.4.
- shutil.copymode(src, dst, *, follow_symlinks=True)¶
Copy the permission bits from src to dst. The file contents, owner, and group are unaffected. src and dst are path-like objects or path names given as strings. If follow_symlinks is false, and both src and dst are symbolic links,
copymode()
will attempt to modify the mode of dst itself (rather than the file it points to). This functionality is not available on every platform; please seecopystat()
for more information. Ifcopymode()
cannot modify symbolic links on the local platform, and it is asked to do so, it will do nothing and return.Raises an auditing event
shutil.copymode
with argumentssrc
,dst
.Changed in version 3.3: Added follow_symlinks argument.
- shutil.copystat(src, dst, *, follow_symlinks=True)¶
Copy the permission bits, last access time, last modification time, and flags from src to dst. On Linux,
copystat()
also copies the “extended attributes” where possible. The file contents, owner, and group are unaffected. src and dst are path-like objects or path names given as strings.If follow_symlinks is false, and src and dst both refer to symbolic links,
copystat()
will operate on the symbolic links themselves rather than the files the symbolic links refer to—reading the information from the src symbolic link, and writing the information to the dst symbolic link.Note
Not all platforms provide the ability to examine and modify symbolic links. Python itself can tell you what functionality is locally available.
If
os.chmod in os.supports_follow_symlinks
isTrue
,copystat()
can modify the permission bits of a symbolic link.If
os.utime in os.supports_follow_symlinks
isTrue
,copystat()
can modify the last access and modification times of a symbolic link.If
os.chflags in os.supports_follow_symlinks
isTrue
,copystat()
can modify the flags of a symbolic link. (os.chflags
is not available on all platforms.)
On platforms where some or all of this functionality is unavailable, when asked to modify a symbolic link,
copystat()
will copy everything it can.copystat()
never returns failure.Please see
os.supports_follow_symlinks
for more information.Raises an auditing event
shutil.copystat
with argumentssrc
,dst
.Changed in version 3.3: Added follow_symlinks argument and support for Linux extended attributes.
- shutil.copy(src, dst, *, follow_symlinks=True)¶
Copies the file src to the file or directory dst. src and dst should be path-like objects or strings. If dst specifies a directory, the file will be copied into dst using the base filename from src. If dst specifies a file that already exists, it will be replaced. Returns the path to the newly created file.
If follow_symlinks is false, and src is a symbolic link, dst will be created as a symbolic link. If follow_symlinks is true and src is a symbolic link, dst will be a copy of the file src refers to.
copy()
copies the file data and the file’s permission mode (seeos.chmod()
). Other metadata, like the file’s creation and modification times, is not preserved. To preserve all file metadata from the original, usecopy2()
instead.Raises an auditing event
shutil.copyfile
with argumentssrc
,dst
.Raises an auditing event
shutil.copymode
with argumentssrc
,dst
.Changed in version 3.3: Added follow_symlinks argument. Now returns path to the newly created file.
Changed in version 3.8: Platform-specific fast-copy syscalls may be used internally in order to copy the file more efficiently. See Platform-dependent efficient copy operations section.
- shutil.copy2(src, dst, *, follow_symlinks=True)¶
Identical to
copy()
except thatcopy2()
also attempts to preserve file metadata.When follow_symlinks is false, and src is a symbolic link,
copy2()
attempts to copy all metadata from the src symbolic link to the newly created dst symbolic link. However, this functionality is not available on all platforms. On platforms where some or all of this functionality is unavailable,copy2()
will preserve all the metadata it can;copy2()
never raises an exception because it cannot preserve file metadata.copy2()
usescopystat()
to copy the file metadata. Please seecopystat()
for more information about platform support for modifying symbolic link metadata.Raises an auditing event
shutil.copyfile
with argumentssrc
,dst
.Raises an auditing event
shutil.copystat
with argumentssrc
,dst
.Changed in version 3.3: Added follow_symlinks argument, try to copy extended file system attributes too (currently Linux only). Now returns path to the newly created file.
Changed in version 3.8: Platform-specific fast-copy syscalls may be used internally in order to copy the file more efficiently. See Platform-dependent efficient copy operations section.
- shutil.ignore_patterns(*patterns)¶
This factory function creates a function that can be used as a callable for
copytree()
's ignore argument, ignoring files and directories that match one of the glob-style patterns provided. See the example below.
- shutil.copytree(src, dst, symlinks=False, ignore=None, copy_function=copy2, ignore_dangling_symlinks=False, dirs_exist_ok=False)¶
Recursively copy an entire directory tree rooted at src to a directory named dst and return the destination directory. All intermediate directories needed to contain dst will also be created by default.
Permissions and times of directories are copied with
copystat()
, individual files are copied usingcopy2()
.If symlinks is true, symbolic links in the source tree are represented as symbolic links in the new tree and the metadata of the original links will be copied as far as the platform allows; if false or omitted, the contents and metadata of the linked files are copied to the new tree.
When symlinks is false, if the file pointed by the symlink doesn’t exist, an exception will be added in the list of errors raised in an
Error
exception at the end of the copy process. You can set the optional ignore_dangling_symlinks flag to true if you want to silence this exception. Notice that this option has no effect on platforms that don’t supportos.symlink()
.If ignore is given, it must be a callable that will receive as its arguments the directory being visited by
copytree()
, and a list of its contents, as returned byos.listdir()
. Sincecopytree()
is called recursively, the ignore callable will be called once for each directory that is copied. The callable must return a sequence of directory and file names relative to the current directory (i.e. a subset of the items in its second argument); these names will then be ignored in the copy process.ignore_patterns()
can be used to create such a callable that ignores names based on glob-style patterns.If exception(s) occur, an
Error
is raised with a list of reasons.If copy_function is given, it must be a callable that will be used to copy each file. It will be called with the source path and the destination path as arguments. By default,
copy2()
is used, but any function that supports the same signature (likecopy()
) can be used.If dirs_exist_ok is false (the default) and dst already exists, a
FileExistsError
is raised. If dirs_exist_ok is true, the copying operation will continue if it encounters existing directories, and files within the dst tree will be overwritten by corresponding files from the src tree.Raises an auditing event
shutil.copytree
with argumentssrc
,dst
.Changed in version 3.3: Copy metadata when symlinks is false. Now returns dst.
Changed in version 3.2: Added the copy_function argument to be able to provide a custom copy function. Added the ignore_dangling_symlinks argument to silence dangling symlinks errors when symlinks is false.
Changed in version 3.8: Platform-specific fast-copy syscalls may be used internally in order to copy the file more efficiently. See Platform-dependent efficient copy operations section.
Changed in version 3.8: Added the dirs_exist_ok parameter.
- shutil.rmtree(path, ignore_errors=False, onerror=None, *, onexc=None, dir_fd=None)¶
Delete an entire directory tree; path must point to a directory (but not a symbolic link to a directory). If ignore_errors is true, errors resulting from failed removals will be ignored; if false or omitted, such errors are handled by calling a handler specified by onexc or onerror or, if both are omitted, exceptions are propagated to the caller.
This function can support paths relative to directory descriptors.
Note
On platforms that support the necessary fd-based functions a symlink attack resistant version of
rmtree()
is used by default. On other platforms, thermtree()
implementation is susceptible to a symlink attack: given proper timing and circumstances, attackers can manipulate symlinks on the filesystem to delete files they wouldn’t be able to access otherwise. Applications can use thermtree.avoids_symlink_attacks
function attribute to determine which case applies.If onexc is provided, it must be a callable that accepts three parameters: function, path, and excinfo.
The first parameter, function, is the function which raised the exception; it depends on the platform and implementation. The second parameter, path, will be the path name passed to function. The third parameter, excinfo, is the exception that was raised. Exceptions raised by onexc will not be caught.
The deprecated onerror is similar to onexc, except that the third parameter it receives is the tuple returned from
sys.exc_info()
.Raises an auditing event
shutil.rmtree
with argumentspath
,dir_fd
.Changed in version 3.3: Added a symlink attack resistant version that is used automatically if platform supports fd-based functions.
Changed in version 3.8: On Windows, will no longer delete the contents of a directory junction before removing the junction.
Changed in version 3.11: The dir_fd parameter.
Changed in version 3.12: Added the onexc parameter, deprecated onerror.
Changed in version 3.13:
rmtree()
now ignoresFileNotFoundError
exceptions for all but the top-level path. Exceptions other thanOSError
and subclasses ofOSError
are now always propagated to the caller.
- shutil.move(src, dst, copy_function=copy2)¶
Recursively move a file or directory (src) to another location and return the destination.
If dst is an existing directory or a symlink to a directory, then src is moved inside that directory. The destination path in that directory must not already exist.
If dst already exists but is not a directory, it may be overwritten depending on
os.rename()
semantics.If the destination is on the current filesystem, then
os.rename()
is used. Otherwise, src is copied to the destination using copy_function and then removed. In case of symlinks, a new symlink pointing to the target of src will be created as the destination and src will be removed.If copy_function is given, it must be a callable that takes two arguments, src and the destination, and will be used to copy src to the destination if
os.rename()
cannot be used. If the source is a directory,copytree()
is called, passing it the copy_function. The default copy_function iscopy2()
. Usingcopy()
as the copy_function allows the move to succeed when it is not possible to also copy the metadata, at the expense of not copying any of the metadata.Raises an auditing event
shutil.move
with argumentssrc
,dst
.Changed in version 3.3: Added explicit symlink handling for foreign filesystems, thus adapting it to the behavior of GNU’s mv. Now returns dst.
Changed in version 3.5: Added the copy_function keyword argument.
Changed in version 3.8: Platform-specific fast-copy syscalls may be used internally in order to copy the file more efficiently. See Platform-dependent efficient copy operations section.
Changed in version 3.9: Accepts a path-like object for both src and dst.
- shutil.disk_usage(path)¶
Return disk usage statistics about the given path as a named tuple with the attributes total, used and free, which are the amount of total, used and free space, in bytes. path may be a file or a directory.
Note
On Unix filesystems, path must point to a path within a mounted filesystem partition. On those platforms, CPython doesn’t attempt to retrieve disk usage information from non-mounted filesystems.
New in version 3.3.
Changed in version 3.8: On Windows, path can now be a file or directory.
Availability: Unix, Windows.
- shutil.chown(path, user=None, group=None)¶
Change owner user and/or group of the given path.
user can be a system user name or a uid; the same applies to group. At least one argument is required.
See also
os.chown()
, the underlying function.Raises an auditing event
shutil.chown
with argumentspath
,user
,group
.Availability: Unix.
New in version 3.3.
- shutil.which(cmd, mode=os.F_OK | os.X_OK, path=None)¶
Return the path to an executable which would be run if the given cmd was called. If no cmd would be called, return
None
.mode is a permission mask passed to
os.access()
, by default determining if the file exists and executable.When no path is specified, the results of
os.environ()
are used, returning either the “PATH” value or a fallback ofos.defpath
.On Windows, the current directory is prepended to the path if mode does not include
os.X_OK
. When the mode does includeos.X_OK
, the Windows APINeedCurrentDirectoryForExePathW
will be consulted to determine if the current directory should be prepended to path. To avoid consulting the current working directory for executables: set the environment variableNoDefaultCurrentDirectoryInExePath
.Also on Windows, the
PATHEXT
variable is used to resolve commands that may not already include an extension. For example, if you callshutil.which("python")
,which()
will searchPATHEXT
to know that it should look forpython.exe
within the path directories. For example, on Windows:>>> shutil.which("python") 'C:\\Python33\\python.EXE'
This is also applied when cmd is a path that contains a directory component:
>> shutil.which("C:\\Python33\\python") 'C:\\Python33\\python.EXE'
New in version 3.3.
Changed in version 3.8: The
bytes
type is now accepted. If cmd type isbytes
, the result type is alsobytes
.Changed in version 3.12: On Windows, the current directory is no longer prepended to the search path if mode includes
os.X_OK
and WinAPINeedCurrentDirectoryForExePathW(cmd)
is false, else the current directory is prepended even if it is already in the search path;PATHEXT
is used now even when cmd includes a directory component or ends with an extension that is inPATHEXT
; and filenames that have no extension can now be found.Changed in version 3.12.1: On Windows, if mode includes
os.X_OK
, executables with an extension inPATHEXT
will be preferred over executables without a matching extension. This brings behavior closer to that of Python 3.11.
- exception shutil.Error¶
This exception collects exceptions that are raised during a multi-file operation. For
copytree()
, the exception argument is a list of 3-tuples (srcname, dstname, exception).
Platform-dependent efficient copy operations¶
Starting from Python 3.8, all functions involving a file copy
(copyfile()
, copy()
, copy2()
,
copytree()
, and move()
) may use
platform-specific “fast-copy” syscalls in order to copy the file more
efficiently (see bpo-33671).
“fast-copy” means that the copying operation occurs within the kernel, avoiding
the use of userspace buffers in Python as in “outfd.write(infd.read())
”.
On macOS fcopyfile is used to copy the file content (not metadata).
On Linux os.sendfile()
is used.
On Windows shutil.copyfile()
uses a bigger default buffer size (1 MiB
instead of 64 KiB) and a memoryview()
-based variant of
shutil.copyfileobj()
is used.
If the fast-copy operation fails and no data was written in the destination
file then shutil will silently fallback on using less efficient
copyfileobj()
function internally.
Changed in version 3.8.
copytree example¶
An example that uses the ignore_patterns()
helper:
from shutil import copytree, ignore_patterns
copytree(source, destination, ignore=ignore_patterns('*.pyc', 'tmp*'))
This will copy everything except .pyc
files and files or directories whose
name starts with tmp
.
Another example that uses the ignore argument to add a logging call:
from shutil import copytree
import logging
def _logpath(path, names):
logging.info('Working in %s', path)
return [] # nothing will be ignored
copytree(source, destination, ignore=_logpath)
rmtree example¶
This example shows how to remove a directory tree on Windows where some of the files have their read-only bit set. It uses the onexc callback to clear the readonly bit and reattempt the remove. Any subsequent failure will propagate.
import os, stat
import shutil
def remove_readonly(func, path, _):
"Clear the readonly bit and reattempt the removal"
os.chmod(path, stat.S_IWRITE)
func(path)
shutil.rmtree(directory, onexc=remove_readonly)
Archiving operations¶
New in version 3.2.
Changed in version 3.5: Added support for the xztar format.
High-level utilities to create and read compressed and archived files are also
provided. They rely on the zipfile
and tarfile
modules.
- shutil.make_archive(base_name, format[, root_dir[, base_dir[, verbose[, dry_run[, owner[, group[, logger]]]]]]])¶
Create an archive file (such as zip or tar) and return its name.
base_name is the name of the file to create, including the path, minus any format-specific extension.
format is the archive format: one of “zip” (if the
zlib
module is available), “tar”, “gztar” (if thezlib
module is available), “bztar” (if thebz2
module is available), or “xztar” (if thelzma
module is available).root_dir is a directory that will be the root directory of the archive, all paths in the archive will be relative to it; for example, we typically chdir into root_dir before creating the archive.
base_dir is the directory where we start archiving from; i.e. base_dir will be the common prefix of all files and directories in the archive. base_dir must be given relative to root_dir. See Archiving example with base_dir for how to use base_dir and root_dir together.
root_dir and base_dir both default to the current directory.
If dry_run is true, no archive is created, but the operations that would be executed are logged to logger.
owner and group are used when creating a tar archive. By default, uses the current owner and group.
logger must be an object compatible with PEP 282, usually an instance of
logging.Logger
.The verbose argument is unused and deprecated.
Raises an auditing event
shutil.make_archive
with argumentsbase_name
,format
,root_dir
,base_dir
.Note
This function is not thread-safe when custom archivers registered with
register_archive_format()
do not support the root_dir argument. In this case it temporarily changes the current working directory of the process to root_dir to perform archiving.Changed in version 3.8: The modern pax (POSIX.1-2001) format is now used instead of the legacy GNU format for archives created with
format="tar"
.Changed in version 3.10.6: This function is now made thread-safe during creation of standard
.zip
and tar archives.
- shutil.get_archive_formats()¶
Return a list of supported formats for archiving. Each element of the returned sequence is a tuple
(name, description)
.By default
shutil
provides these formats:zip: ZIP file (if the
zlib
module is available).tar: Uncompressed tar file. Uses POSIX.1-2001 pax format for new archives.
gztar: gzip’ed tar-file (if the
zlib
module is available).bztar: bzip2’ed tar-file (if the
bz2
module is available).xztar: xz’ed tar-file (if the
lzma
module is available).
You can register new formats or provide your own archiver for any existing formats, by using
register_archive_format()
.
- shutil.register_archive_format(name, function[, extra_args[, description]])¶
Register an archiver for the format name.
function is the callable that will be used to unpack archives. The callable will receive the base_name of the file to create, followed by the base_dir (which defaults to
os.curdir
) to start archiving from. Further arguments are passed as keyword arguments: owner, group, dry_run and logger (as passed inmake_archive()
).If function has the custom attribute
function.supports_root_dir
set toTrue
, the root_dir argument is passed as a keyword argument. Otherwise the current working directory of the process is temporarily changed to root_dir before calling function. In this casemake_archive()
is not thread-safe.If given, extra_args is a sequence of
(name, value)
pairs that will be used as extra keywords arguments when the archiver callable is used.description is used by
get_archive_formats()
which returns the list of archivers. Defaults to an empty string.Changed in version 3.12: Added support for functions supporting the root_dir argument.
- shutil.unregister_archive_format(name)¶
Remove the archive format name from the list of supported formats.
- shutil.unpack_archive(filename[, extract_dir[, format[, filter]]])¶
Unpack an archive. filename is the full path of the archive.
extract_dir is the name of the target directory where the archive is unpacked. If not provided, the current working directory is used.
format is the archive format: one of “zip”, “tar”, “gztar”, “bztar”, or “xztar”. Or any other format registered with
register_unpack_format()
. If not provided,unpack_archive()
will use the archive file name extension and see if an unpacker was registered for that extension. In case none is found, aValueError
is raised.The keyword-only filter argument is passed to the underlying unpacking function. For zip files, filter is not accepted. For tar files, it is recommended to set it to
'data'
, unless using features specific to tar and UNIX-like filesystems. (See Extraction filters for details.) The'data'
filter will become the default for tar files in Python 3.14.Raises an auditing event
shutil.unpack_archive
with argumentsfilename
,extract_dir
,format
.Warning
Never extract archives from untrusted sources without prior inspection. It is possible that files are created outside of the path specified in the extract_dir argument, e.g. members that have absolute filenames starting with “/” or filenames with two dots “..”.
Changed in version 3.7: Accepts a path-like object for filename and extract_dir.
Changed in version 3.12: Added the filter argument.
- shutil.register_unpack_format(name, extensions, function[, extra_args[, description]])¶
Registers an unpack format. name is the name of the format and extensions is a list of extensions corresponding to the format, like
.zip
for Zip files.function is the callable that will be used to unpack archives. The callable will receive:
the path of the archive, as a positional argument;
the directory the archive must be extracted to, as a positional argument;
possibly a filter keyword argument, if it was given to
unpack_archive()
;additional keyword arguments, specified by extra_args as a sequence of
(name, value)
tuples.
description can be provided to describe the format, and will be returned by the
get_unpack_formats()
function.
- shutil.unregister_unpack_format(name)¶
Unregister an unpack format. name is the name of the format.
- shutil.get_unpack_formats()¶
Return a list of all registered formats for unpacking. Each element of the returned sequence is a tuple
(name, extensions, description)
.By default
shutil
provides these formats:zip: ZIP file (unpacking compressed files works only if the corresponding module is available).
tar: uncompressed tar file.
gztar: gzip’ed tar-file (if the
zlib
module is available).bztar: bzip2’ed tar-file (if the
bz2
module is available).xztar: xz’ed tar-file (if the
lzma
module is available).
You can register new formats or provide your own unpacker for any existing formats, by using
register_unpack_format()
.
Archiving example¶
In this example, we create a gzip’ed tar-file archive containing all files
found in the .ssh
directory of the user:
>>> from shutil import make_archive
>>> import os
>>> archive_name = os.path.expanduser(os.path.join('~', 'myarchive'))
>>> root_dir = os.path.expanduser(os.path.join('~', '.ssh'))
>>> make_archive(archive_name, 'gztar', root_dir)
'/Users/tarek/myarchive.tar.gz'
The resulting archive contains:
$ tar -tzvf /Users/tarek/myarchive.tar.gz
drwx------ tarek/staff 0 2010-02-01 16:23:40 ./
-rw-r--r-- tarek/staff 609 2008-06-09 13:26:54 ./authorized_keys
-rwxr-xr-x tarek/staff 65 2008-06-09 13:26:54 ./config
-rwx------ tarek/staff 668 2008-06-09 13:26:54 ./id_dsa
-rwxr-xr-x tarek/staff 609 2008-06-09 13:26:54 ./id_dsa.pub
-rw------- tarek/staff 1675 2008-06-09 13:26:54 ./id_rsa
-rw-r--r-- tarek/staff 397 2008-06-09 13:26:54 ./id_rsa.pub
-rw-r--r-- tarek/staff 37192 2010-02-06 18:23:10 ./known_hosts
Archiving example with base_dir¶
In this example, similar to the one above,
we show how to use make_archive()
, but this time with the usage of
base_dir. We now have the following directory structure:
$ tree tmp
tmp
└── root
└── structure
├── content
└── please_add.txt
└── do_not_add.txt
In the final archive, please_add.txt
should be included, but
do_not_add.txt
should not. Therefore we use the following:
>>> from shutil import make_archive
>>> import os
>>> archive_name = os.path.expanduser(os.path.join('~', 'myarchive'))
>>> make_archive(
... archive_name,
... 'tar',
... root_dir='tmp/root',
... base_dir='structure/content',
... )
'/Users/tarek/my_archive.tar'
Listing the files in the resulting archive gives us:
$ python -m tarfile -l /Users/tarek/myarchive.tar
structure/content/
structure/content/please_add.txt
Querying the size of the output terminal¶
- shutil.get_terminal_size(fallback=(columns, lines))¶
Get the size of the terminal window.
For each of the two dimensions, the environment variable,
COLUMNS
andLINES
respectively, is checked. If the variable is defined and the value is a positive integer, it is used.When
COLUMNS
orLINES
is not defined, which is the common case, the terminal connected tosys.__stdout__
is queried by invokingos.get_terminal_size()
.If the terminal size cannot be successfully queried, either because the system doesn’t support querying, or because we are not connected to a terminal, the value given in
fallback
parameter is used.fallback
defaults to(80, 24)
which is the default size used by many terminal emulators.The value returned is a named tuple of type
os.terminal_size
.See also: The Single UNIX Specification, Version 2, Other Environment Variables.
New in version 3.3.
Changed in version 3.11: The
fallback
values are also used ifos.get_terminal_size()
returns zeroes.