Built-in Types
**************

The following sections describe the standard types that are built into
the interpreter.

The principal built-in types are numerics, sequences, mappings,
classes, instances and exceptions.

Some collection classes are mutable.  The methods that add, subtract,
or rearrange their members in place, and don’t return a specific item,
never return the collection instance itself but "None".

Some operations are supported by several object types; in particular,
practically all objects can be compared for equality, tested for truth
value, and converted to a string (with the "repr()" function or the
slightly different "str()" function).  The latter function is
implicitly used when an object is written by the "print()" function.


Truth Value Testing
===================

Any object can be tested for truth value, for use in an "if" or
"while" condition or as operand of the Boolean operations below.

By default, an object is considered true unless its class defines
either a "__bool__()" method that returns "False" or a "__len__()"
method that returns zero, when called with the object. [1]  Here are
most of the built-in objects considered false:

* constants defined to be false: "None" and "False".

* zero of any numeric type: "0", "0.0", "0j", "Decimal(0)",
  "Fraction(0, 1)"

* empty sequences and collections: "''", "()", "[]", "{}", "set()",
  "range(0)"

Operations and built-in functions that have a Boolean result always
return "0" or "False" for false and "1" or "True" for true, unless
otherwise stated. (Important exception: the Boolean operations "or"
and "and" always return one of their operands.)


Boolean Operations — "and", "or", "not"
=======================================

These are the Boolean operations, ordered by ascending priority:

+---------------+-----------------------------------+---------+
| Operation     | Result                            | Notes   |
|===============|===================================|=========|
| "x or y"      | if *x* is false, then *y*, else   | (1)     |
|               | *x*                               |         |
+---------------+-----------------------------------+---------+
| "x and y"     | if *x* is false, then *x*, else   | (2)     |
|               | *y*                               |         |
+---------------+-----------------------------------+---------+
| "not x"       | if *x* is false, then "True",     | (3)     |
|               | else "False"                      |         |
+---------------+-----------------------------------+---------+

Notes:

1. This is a short-circuit operator, so it only evaluates the
   second argument if the first one is false.

2. This is a short-circuit operator, so it only evaluates the
   second argument if the first one is true.

3. "not" has a lower priority than non-Boolean operators, so "not a
   == b" is interpreted as "not (a == b)", and "a == not b" is a
   syntax error.


Comparisons
===========

There are eight comparison operations in Python.  They all have the
same priority (which is higher than that of the Boolean operations).
Comparisons can be chained arbitrarily; for example, "x < y <= z" is
equivalent to "x < y and y <= z", except that *y* is evaluated only
once (but in both cases *z* is not evaluated at all when "x < y" is
found to be false).

This table summarizes the comparison operations:

+--------------+---------------------------+
| Operation    | Meaning                   |
|==============|===========================|
| "<"          | strictly less than        |
+--------------+---------------------------+
| "<="         | less than or equal        |
+--------------+---------------------------+
| ">"          | strictly greater than     |
+--------------+---------------------------+
| ">="         | greater than or equal     |
+--------------+---------------------------+
| "=="         | equal                     |
+--------------+---------------------------+
| "!="         | not equal                 |
+--------------+---------------------------+
| "is"         | object identity           |
+--------------+---------------------------+
| "is not"     | negated object identity   |
+--------------+---------------------------+

Objects of different types, except different numeric types, never
compare equal. The "==" operator is always defined but for some object
types (for example, class objects) is equivalent to "is". The "<",
"<=", ">" and ">=" operators are only defined where they make sense;
for example, they raise a "TypeError" exception when one of the
arguments is a complex number.

Non-identical instances of a class normally compare as non-equal
unless the class defines the "__eq__()" method.

Instances of a class cannot be ordered with respect to other instances
of the same class, or other types of object, unless the class defines
enough of the methods "__lt__()", "__le__()", "__gt__()", and
"__ge__()" (in general, "__lt__()" and "__eq__()" are sufficient, if
you want the conventional meanings of the comparison operators).

The behavior of the "is" and "is not" operators cannot be customized;
also they can be applied to any two objects and never raise an
exception.

Two more operations with the same syntactic priority, "in" and "not
in", are supported by types that are *iterable* or implement the
"__contains__()" method.


Numeric Types — "int", "float", "complex"
=========================================

There are three distinct numeric types: *integers*, *floating point
numbers*, and *complex numbers*.  In addition, Booleans are a subtype
of integers.  Integers have unlimited precision.  Floating point
numbers are usually implemented using "double" in C; information about
the precision and internal representation of floating point numbers
for the machine on which your program is running is available in
"sys.float_info".  Complex numbers have a real and imaginary part,
which are each a floating point number.  To extract these parts from a
complex number *z*, use "z.real" and "z.imag". (The standard library
includes the additional numeric types "fractions.Fraction", for
rationals, and "decimal.Decimal", for floating-point numbers with
user-definable precision.)

Numbers are created by numeric literals or as the result of built-in
functions and operators.  Unadorned integer literals (including hex,
octal and binary numbers) yield integers.  Numeric literals containing
a decimal point or an exponent sign yield floating point numbers.
Appending "'j'" or "'J'" to a numeric literal yields an imaginary
number (a complex number with a zero real part) which you can add to
an integer or float to get a complex number with real and imaginary
parts.

Python fully supports mixed arithmetic: when a binary arithmetic
operator has operands of different numeric types, the operand with the
“narrower” type is widened to that of the other, where integer is
narrower than floating point, which is narrower than complex.
Comparisons between numbers of mixed type use the same rule. [2] The
constructors "int()", "float()", and "complex()" can be used to
produce numbers of a specific type.

All numeric types (except complex) support the following operations
(for priorities of the operations, see Operator precedence):

+-----------------------+-----------------------------------+-----------+----------------------+
| Operation             | Result                            | Notes     | Full documentation   |
|=======================|===================================|===========|======================|
| "x + y"               | sum of *x* and *y*                |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "x - y"               | difference of *x* and *y*         |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "x * y"               | product of *x* and *y*            |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "x / y"               | quotient of *x* and *y*           |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "x // y"              | floored quotient of *x* and *y*   | (1)       |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "x % y"               | remainder of "x / y"              | (2)       |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "-x"                  | *x* negated                       |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "+x"                  | *x* unchanged                     |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "abs(x)"              | absolute value or magnitude of    |           | "abs()"              |
|                       | *x*                               |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "int(x)"              | *x* converted to integer          | (3)(6)    | "int()"              |
+-----------------------+-----------------------------------+-----------+----------------------+
| "float(x)"            | *x* converted to floating point   | (4)(6)    | "float()"            |
+-----------------------+-----------------------------------+-----------+----------------------+
| "complex(re, im)"     | a complex number with real part   | (6)       | "complex()"          |
|                       | *re*, imaginary part *im*. *im*   |           |                      |
|                       | defaults to zero.                 |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "c.conjugate()"       | conjugate of the complex number   |           |                      |
|                       | *c*                               |           |                      |
+-----------------------+-----------------------------------+-----------+----------------------+
| "divmod(x, y)"        | the pair "(x // y, x % y)"        | (2)       | "divmod()"           |
+-----------------------+-----------------------------------+-----------+----------------------+
| "pow(x, y)"           | *x* to the power *y*              | (5)       | "pow()"              |
+-----------------------+-----------------------------------+-----------+----------------------+
| "x ** y"              | *x* to the power *y*              | (5)       |                      |
+-----------------------+-----------------------------------+-----------+----------------------+

Notes:

1. Also referred to as integer division.  The resultant value is a
   whole integer, though the result’s type is not necessarily int. The
   result is always rounded towards minus infinity: "1//2" is "0",
   "(-1)//2" is "-1", "1//(-2)" is "-1", and "(-1)//(-2)" is "0".

2. Not for complex numbers.  Instead convert to floats using
   "abs()" if appropriate.

3. Conversion from floating point to integer may round or truncate
   as in C; see functions "math.floor()" and "math.ceil()" for well-
   defined conversions.

4. float also accepts the strings “nan” and “inf” with an optional
   prefix “+” or “-” for Not a Number (NaN) and positive or negative
   infinity.

5. Python defines "pow(0, 0)" and "0 ** 0" to be "1", as is common
   for programming languages.

6. The numeric literals accepted include the digits "0" to "9" or
   any Unicode equivalent (code points with the "Nd" property).

   See http://www.unicode.org/Public/12.1.0/ucd/extracted/DerivedNume
   ricType.txt for a complete list of code points with the "Nd"
   property.

All "numbers.Real" types ("int" and "float") also include the
following operations:

+----------------------+-----------------------------------------------+
| Operation            | Result                                        |
|======================|===============================================|
| "math.trunc(x)"      | *x* truncated to "Integral"                   |
+----------------------+-----------------------------------------------+
| "round(x[, n])"      | *x* rounded to *n* digits, rounding half to   |
|                      | even. If *n* is omitted, it defaults to 0.    |
+----------------------+-----------------------------------------------+
| "math.floor(x)"      | the greatest "Integral" <= *x*                |
+----------------------+-----------------------------------------------+
| "math.ceil(x)"       | the least "Integral" >= *x*                   |
+----------------------+-----------------------------------------------+

For additional numeric operations see the "math" and "cmath" modules.


Bitwise Operations on Integer Types
-----------------------------------

Bitwise operations only make sense for integers. The result of bitwise
operations is calculated as though carried out in two’s complement
with an infinite number of sign bits.

The priorities of the binary bitwise operations are all lower than the
numeric operations and higher than the comparisons; the unary
operation "~" has the same priority as the other unary numeric
operations ("+" and "-").

This table lists the bitwise operations sorted in ascending priority:

+--------------+----------------------------------+------------+
| Operation    | Result                           | Notes      |
|==============|==================================|============|
| "x | y"      | bitwise *or* of *x* and *y*      | (4)        |
+--------------+----------------------------------+------------+
| "x ^ y"      | bitwise *exclusive or* of *x*    | (4)        |
|              | and *y*                          |            |
+--------------+----------------------------------+------------+
| "x & y"      | bitwise *and* of *x* and *y*     | (4)        |
+--------------+----------------------------------+------------+
| "x << n"     | *x* shifted left by *n* bits     | (1)(2)     |
+--------------+----------------------------------+------------+
| "x >> n"     | *x* shifted right by *n* bits    | (1)(3)     |
+--------------+----------------------------------+------------+
| "~x"         | the bits of *x* inverted         |            |
+--------------+----------------------------------+------------+

Notes:

1. Negative shift counts are illegal and cause a "ValueError" to be
   raised.

2. A left shift by *n* bits is equivalent to multiplication by
   "pow(2, n)" without overflow check.

3. A right shift by *n* bits is equivalent to division by "pow(2,
   n)" without overflow check.

4. Performing these calculations with at least one extra sign
   extension bit in a finite two’s complement representation (a
   working bit-width of "1 + max(x.bit_length(), y.bit_length())" or
   more) is sufficient to get the same result as if there were an
   infinite number of sign bits.


Additional Methods on Integer Types
-----------------------------------

The int type implements the "numbers.Integral" *abstract base class*.
In addition, it provides a few more methods:

int.bit_length()

   Return the number of bits necessary to represent an integer in
   binary, excluding the sign and leading zeros:

      >>> n = -37
      >>> bin(n)
      '-0b100101'
      >>> n.bit_length()
      6

   More precisely, if "x" is nonzero, then "x.bit_length()" is the
   unique positive integer "k" such that "2**(k-1) <= abs(x) < 2**k".
   Equivalently, when "abs(x)" is small enough to have a correctly
   rounded logarithm, then "k = 1 + int(log(abs(x), 2))". If "x" is
   zero, then "x.bit_length()" returns "0".

   Equivalent to:

      def bit_length(self):
          s = bin(self)       # binary representation:  bin(-37) --> '-0b100101'
          s = s.lstrip('-0b') # remove leading zeros and minus sign
          return len(s)       # len('100101') --> 6

   New in version 3.1.

int.to_bytes(length, byteorder, *, signed=False)

   Return an array of bytes representing an integer.

   >>> (1024).to_bytes(2, byteorder='big')
   b'\x04\x00'
   >>> (1024).to_bytes(10, byteorder='big')
   b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00'
   >>> (-1024).to_bytes(10, byteorder='big', signed=True)
   b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00'
   >>> x = 1000
   >>> x.to_bytes((x.bit_length() + 7) // 8, byteorder='little')
   b'\xe8\x03'

   The integer is represented using *length* bytes.  An
   "OverflowError" is raised if the integer is not representable with
   the given number of bytes.

   The *byteorder* argument determines the byte order used to
   represent the integer.  If *byteorder* is ""big"", the most
   significant byte is at the beginning of the byte array.  If
   *byteorder* is ""little"", the most significant byte is at the end
   of the byte array.  To request the native byte order of the host
   system, use "sys.byteorder" as the byte order value.

   The *signed* argument determines whether two’s complement is used
   to represent the integer.  If *signed* is "False" and a negative
   integer is given, an "OverflowError" is raised. The default value
   for *signed* is "False".

   New in version 3.2.

classmethod int.from_bytes(bytes, byteorder, *, signed=False)

   Return the integer represented by the given array of bytes.

   >>> int.from_bytes(b'\x00\x10', byteorder='big')
   16
   >>> int.from_bytes(b'\x00\x10', byteorder='little')
   4096
   >>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=True)
   -1024
   >>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=False)
   64512
   >>> int.from_bytes([255, 0, 0], byteorder='big')
   16711680

   The argument *bytes* must either be a *bytes-like object* or an
   iterable producing bytes.

   The *byteorder* argument determines the byte order used to
   represent the integer.  If *byteorder* is ""big"", the most
   significant byte is at the beginning of the byte array.  If
   *byteorder* is ""little"", the most significant byte is at the end
   of the byte array.  To request the native byte order of the host
   system, use "sys.byteorder" as the byte order value.

   The *signed* argument indicates whether two’s complement is used to
   represent the integer.

   New in version 3.2.

int.as_integer_ratio()

   Return a pair of integers whose ratio is exactly equal to the
   original integer and with a positive denominator. The integer ratio
   of integers (whole numbers) is always the integer as the numerator
   and "1" as the denominator.

   New in version 3.8.


Additional Methods on Float
---------------------------

The float type implements the "numbers.Real" *abstract base class*.
float also has the following additional methods.

float.as_integer_ratio()

   Return a pair of integers whose ratio is exactly equal to the
   original float and with a positive denominator.  Raises
   "OverflowError" on infinities and a "ValueError" on NaNs.

float.is_integer()

   Return "True" if the float instance is finite with integral value,
   and "False" otherwise:

      >>> (-2.0).is_integer()
      True
      >>> (3.2).is_integer()
      False

Two methods support conversion to and from hexadecimal strings.  Since
Python’s floats are stored internally as binary numbers, converting a
float to or from a *decimal* string usually involves a small rounding
error.  In contrast, hexadecimal strings allow exact representation
and specification of floating-point numbers.  This can be useful when
debugging, and in numerical work.

float.hex()

   Return a representation of a floating-point number as a hexadecimal
   string.  For finite floating-point numbers, this representation
   will always include a leading "0x" and a trailing "p" and exponent.

classmethod float.fromhex(s)

   Class method to return the float represented by a hexadecimal
   string *s*.  The string *s* may have leading and trailing
   whitespace.

Note that "float.hex()" is an instance method, while "float.fromhex()"
is a class method.

A hexadecimal string takes the form:

   [sign] ['0x'] integer ['.' fraction] ['p' exponent]

where the optional "sign" may by either "+" or "-", "integer" and
"fraction" are strings of hexadecimal digits, and "exponent" is a
decimal integer with an optional leading sign.  Case is not
significant, and there must be at least one hexadecimal digit in
either the integer or the fraction.  This syntax is similar to the
syntax specified in section 6.4.4.2 of the C99 standard, and also to
the syntax used in Java 1.5 onwards.  In particular, the output of
"float.hex()" is usable as a hexadecimal floating-point literal in C
or Java code, and hexadecimal strings produced by C’s "%a" format
character or Java’s "Double.toHexString" are accepted by
"float.fromhex()".

Note that the exponent is written in decimal rather than hexadecimal,
and that it gives the power of 2 by which to multiply the coefficient.
For example, the hexadecimal string "0x3.a7p10" represents the
floating-point number "(3 + 10./16 + 7./16**2) * 2.0**10", or
"3740.0":

   >>> float.fromhex('0x3.a7p10')
   3740.0

Applying the reverse conversion to "3740.0" gives a different
hexadecimal string representing the same number:

   >>> float.hex(3740.0)
   '0x1.d380000000000p+11'


Hashing of numeric types
------------------------

For numbers "x" and "y", possibly of different types, it’s a
requirement that "hash(x) == hash(y)" whenever "x == y" (see the
"__hash__()" method documentation for more details).  For ease of
implementation and efficiency across a variety of numeric types
(including "int", "float", "decimal.Decimal" and "fractions.Fraction")
Python’s hash for numeric types is based on a single mathematical
function that’s defined for any rational number, and hence applies to
all instances of "int" and "fractions.Fraction", and all finite
instances of "float" and "decimal.Decimal".  Essentially, this
function is given by reduction modulo "P" for a fixed prime "P".  The
value of "P" is made available to Python as the "modulus" attribute of
"sys.hash_info".

**CPython implementation detail:** Currently, the prime used is "P =
2**31 - 1" on machines with 32-bit C longs and "P = 2**61 - 1" on
machines with 64-bit C longs.

Here are the rules in detail:

* If "x = m / n" is a nonnegative rational number and "n" is not
  divisible by "P", define "hash(x)" as "m * invmod(n, P) % P", where
  "invmod(n, P)" gives the inverse of "n" modulo "P".

* If "x = m / n" is a nonnegative rational number and "n" is
  divisible by "P" (but "m" is not) then "n" has no inverse modulo "P"
  and the rule above doesn’t apply; in this case define "hash(x)" to
  be the constant value "sys.hash_info.inf".

* If "x = m / n" is a negative rational number define "hash(x)" as
  "-hash(-x)".  If the resulting hash is "-1", replace it with "-2".

* The particular values "sys.hash_info.inf", "-sys.hash_info.inf"
  and "sys.hash_info.nan" are used as hash values for positive
  infinity, negative infinity, or nans (respectively).  (All hashable
  nans have the same hash value.)

* For a "complex" number "z", the hash values of the real and
  imaginary parts are combined by computing "hash(z.real) +
  sys.hash_info.imag * hash(z.imag)", reduced modulo
  "2**sys.hash_info.width" so that it lies in
  "range(-2**(sys.hash_info.width - 1), 2**(sys.hash_info.width -
  1))".  Again, if the result is "-1", it’s replaced with "-2".

To clarify the above rules, here’s some example Python code,
equivalent to the built-in hash, for computing the hash of a rational
number, "float", or "complex":

   import sys, math

   def hash_fraction(m, n):
       """Compute the hash of a rational number m / n.

       Assumes m and n are integers, with n positive.
       Equivalent to hash(fractions.Fraction(m, n)).

       """
       P = sys.hash_info.modulus
       # Remove common factors of P.  (Unnecessary if m and n already coprime.)
       while m % P == n % P == 0:
           m, n = m // P, n // P

       if n % P == 0:
           hash_value = sys.hash_info.inf
       else:
           # Fermat's Little Theorem: pow(n, P-1, P) is 1, so
           # pow(n, P-2, P) gives the inverse of n modulo P.
           hash_value = (abs(m) % P) * pow(n, P - 2, P) % P
       if m < 0:
           hash_value = -hash_value
       if hash_value == -1:
           hash_value = -2
       return hash_value

   def hash_float(x):
       """Compute the hash of a float x."""

       if math.isnan(x):
           return sys.hash_info.nan
       elif math.isinf(x):
           return sys.hash_info.inf if x > 0 else -sys.hash_info.inf
       else:
           return hash_fraction(*x.as_integer_ratio())

   def hash_complex(z):
       """Compute the hash of a complex number z."""

       hash_value = hash_float(z.real) + sys.hash_info.imag * hash_float(z.imag)
       # do a signed reduction modulo 2**sys.hash_info.width
       M = 2**(sys.hash_info.width - 1)
       hash_value = (hash_value & (M - 1)) - (hash_value & M)
       if hash_value == -1:
           hash_value = -2
       return hash_value


Iterator Types
==============

Python supports a concept of iteration over containers.  This is
implemented using two distinct methods; these are used to allow user-
defined classes to support iteration.  Sequences, described below in
more detail, always support the iteration methods.

One method needs to be defined for container objects to provide
iteration support:

container.__iter__()

   Return an iterator object.  The object is required to support the
   iterator protocol described below.  If a container supports
   different types of iteration, additional methods can be provided to
   specifically request iterators for those iteration types.  (An
   example of an object supporting multiple forms of iteration would
   be a tree structure which supports both breadth-first and depth-
   first traversal.)  This method corresponds to the "tp_iter" slot of
   the type structure for Python objects in the Python/C API.

The iterator objects themselves are required to support the following
two methods, which together form the *iterator protocol*:

iterator.__iter__()

   Return the iterator object itself.  This is required to allow both
   containers and iterators to be used with the "for" and "in"
   statements. This method corresponds to the "tp_iter" slot of the
   type structure for Python objects in the Python/C API.

iterator.__next__()

   Return the next item from the container.  If there are no further
   items, raise the "StopIteration" exception.  This method
   corresponds to the "tp_iternext" slot of the type structure for
   Python objects in the Python/C API.

Python defines several iterator objects to support iteration over
general and specific sequence types, dictionaries, and other more
specialized forms.  The specific types are not important beyond their
implementation of the iterator protocol.

Once an iterator’s "__next__()" method raises "StopIteration", it must
continue to do so on subsequent calls. Implementations that do not
obey this property are deemed broken.


Generator Types
---------------

Python’s *generator*s provide a convenient way to implement the
iterator protocol.  If a container object’s "__iter__()" method is
implemented as a generator, it will automatically return an iterator
object (technically, a generator object) supplying the "__iter__()"
and "__next__()" methods. More information about generators can be
found in the documentation for the yield expression.


Sequence Types — "list", "tuple", "range"
=========================================

There are three basic sequence types: lists, tuples, and range
objects. Additional sequence types tailored for processing of binary
data and text strings are described in dedicated sections.


Common Sequence Operations
--------------------------

The operations in the following table are supported by most sequence
types, both mutable and immutable. The "collections.abc.Sequence" ABC
is provided to make it easier to correctly implement these operations
on custom sequence types.

This table lists the sequence operations sorted in ascending priority.
In the table, *s* and *t* are sequences of the same type, *n*, *i*,
*j* and *k* are integers and *x* is an arbitrary object that meets any
type and value restrictions imposed by *s*.

The "in" and "not in" operations have the same priorities as the
comparison operations. The "+" (concatenation) and "*" (repetition)
operations have the same priority as the corresponding numeric
operations. [3]

+----------------------------+----------------------------------+------------+
| Operation                  | Result                           | Notes      |
|============================|==================================|============|
| "x in s"                   | "True" if an item of *s* is      | (1)        |
|                            | equal to *x*, else "False"       |            |
+----------------------------+----------------------------------+------------+
| "x not in s"               | "False" if an item of *s* is     | (1)        |
|                            | equal to *x*, else "True"        |            |
+----------------------------+----------------------------------+------------+
| "s + t"                    | the concatenation of *s* and *t* | (6)(7)     |
+----------------------------+----------------------------------+------------+
| "s * n" or "n * s"         | equivalent to adding *s* to      | (2)(7)     |
|                            | itself *n* times                 |            |
+----------------------------+----------------------------------+------------+
| "s[i]"                     | *i*th item of *s*, origin 0      | (3)        |
+----------------------------+----------------------------------+------------+
| "s[i:j]"                   | slice of *s* from *i* to *j*     | (3)(4)     |
+----------------------------+----------------------------------+------------+
| "s[i:j:k]"                 | slice of *s* from *i* to *j*     | (3)(5)     |
|                            | with step *k*                    |            |
+----------------------------+----------------------------------+------------+
| "len(s)"                   | length of *s*                    |            |
+----------------------------+----------------------------------+------------+
| "min(s)"                   | smallest item of *s*             |            |
+----------------------------+----------------------------------+------------+
| "max(s)"                   | largest item of *s*              |            |
+----------------------------+----------------------------------+------------+
| "s.index(x[, i[, j]])"     | index of the first occurrence of | (8)        |
|                            | *x* in *s* (at or after index    |            |
|                            | *i* and before index *j*)        |            |
+----------------------------+----------------------------------+------------+
| "s.count(x)"               | total number of occurrences of   |            |
|                            | *x* in *s*                       |            |
+----------------------------+----------------------------------+------------+

Sequences of the same type also support comparisons.  In particular,
tuples and lists are compared lexicographically by comparing
corresponding elements. This means that to compare equal, every
element must compare equal and the two sequences must be of the same
type and have the same length.  (For full details see Comparisons in
the language reference.)

Notes:

1. While the "in" and "not in" operations are used only for simple
   containment testing in the general case, some specialised sequences
   (such as "str", "bytes" and "bytearray") also use them for
   subsequence testing:

      >>> "gg" in "eggs"
      True

2. Values of *n* less than "0" are treated as "0" (which yields an
   empty sequence of the same type as *s*).  Note that items in the
   sequence *s* are not copied; they are referenced multiple times.
   This often haunts new Python programmers; consider:

      >>> lists = [[]] * 3
      >>> lists
      [[], [], []]
      >>> lists[0].append(3)
      >>> lists
      [[3], [3], [3]]

   What has happened is that "[[]]" is a one-element list containing
   an empty list, so all three elements of "[[]] * 3" are references
   to this single empty list.  Modifying any of the elements of
   "lists" modifies this single list. You can create a list of
   different lists this way:

      >>> lists = [[] for i in range(3)]
      >>> lists[0].append(3)
      >>> lists[1].append(5)
      >>> lists[2].append(7)
      >>> lists
      [[3], [5], [7]]

   Further explanation is available in the FAQ entry How do I create a
   multidimensional list?.

3. If *i* or *j* is negative, the index is relative to the end of
   sequence *s*: "len(s) + i" or "len(s) + j" is substituted.  But
   note that "-0" is still "0".

4. The slice of *s* from *i* to *j* is defined as the sequence of
   items with index *k* such that "i <= k < j".  If *i* or *j* is
   greater than "len(s)", use "len(s)".  If *i* is omitted or "None",
   use "0".  If *j* is omitted or "None", use "len(s)".  If *i* is
   greater than or equal to *j*, the slice is empty.

5. The slice of *s* from *i* to *j* with step *k* is defined as the
   sequence of items with index  "x = i + n*k" such that "0 <= n <
   (j-i)/k".  In other words, the indices are "i", "i+k", "i+2*k",
   "i+3*k" and so on, stopping when *j* is reached (but never
   including *j*).  When *k* is positive, *i* and *j* are reduced to
   "len(s)" if they are greater. When *k* is negative, *i* and *j* are
   reduced to "len(s) - 1" if they are greater.  If *i* or *j* are
   omitted or "None", they become “end” values (which end depends on
   the sign of *k*).  Note, *k* cannot be zero. If *k* is "None", it
   is treated like "1".

6. Concatenating immutable sequences always results in a new
   object. This means that building up a sequence by repeated
   concatenation will have a quadratic runtime cost in the total
   sequence length. To get a linear runtime cost, you must switch to
   one of the alternatives below:

   * if concatenating "str" objects, you can build a list and use
     "str.join()" at the end or else write to an "io.StringIO"
     instance and retrieve its value when complete

   * if concatenating "bytes" objects, you can similarly use
     "bytes.join()" or "io.BytesIO", or you can do in-place
     concatenation with a "bytearray" object.  "bytearray" objects are
     mutable and have an efficient overallocation mechanism

   * if concatenating "tuple" objects, extend a "list" instead

   * for other types, investigate the relevant class documentation

7. Some sequence types (such as "range") only support item
   sequences that follow specific patterns, and hence don’t support
   sequence concatenation or repetition.

8. "index" raises "ValueError" when *x* is not found in *s*. Not
   all implementations support passing the additional arguments *i*
   and *j*. These arguments allow efficient searching of subsections
   of the sequence. Passing the extra arguments is roughly equivalent
   to using "s[i:j].index(x)", only without copying any data and with
   the returned index being relative to the start of the sequence
   rather than the start of the slice.


Immutable Sequence Types
------------------------

The only operation that immutable sequence types generally implement
that is not also implemented by mutable sequence types is support for
the "hash()" built-in.

This support allows immutable sequences, such as "tuple" instances, to
be used as "dict" keys and stored in "set" and "frozenset" instances.

Attempting to hash an immutable sequence that contains unhashable
values will result in "TypeError".


Mutable Sequence Types
----------------------

The operations in the following table are defined on mutable sequence
types. The "collections.abc.MutableSequence" ABC is provided to make
it easier to correctly implement these operations on custom sequence
types.

In the table *s* is an instance of a mutable sequence type, *t* is any
iterable object and *x* is an arbitrary object that meets any type and
value restrictions imposed by *s* (for example, "bytearray" only
accepts integers that meet the value restriction "0 <= x <= 255").

+--------------------------------+----------------------------------+-----------------------+
| Operation                      | Result                           | Notes                 |
|================================|==================================|=======================|
| "s[i] = x"                     | item *i* of *s* is replaced by   |                       |
|                                | *x*                              |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s[i:j] = t"                   | slice of *s* from *i* to *j* is  |                       |
|                                | replaced by the contents of the  |                       |
|                                | iterable *t*                     |                       |
+--------------------------------+----------------------------------+-----------------------+
| "del s[i:j]"                   | same as "s[i:j] = []"            |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s[i:j:k] = t"                 | the elements of "s[i:j:k]" are   | (1)                   |
|                                | replaced by those of *t*         |                       |
+--------------------------------+----------------------------------+-----------------------+
| "del s[i:j:k]"                 | removes the elements of          |                       |
|                                | "s[i:j:k]" from the list         |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.append(x)"                  | appends *x* to the end of the    |                       |
|                                | sequence (same as                |                       |
|                                | "s[len(s):len(s)] = [x]")        |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.clear()"                    | removes all items from *s* (same | (5)                   |
|                                | as "del s[:]")                   |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.copy()"                     | creates a shallow copy of *s*    | (5)                   |
|                                | (same as "s[:]")                 |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.extend(t)" or "s += t"      | extends *s* with the contents of |                       |
|                                | *t* (for the most part the same  |                       |
|                                | as "s[len(s):len(s)] = t")       |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s *= n"                       | updates *s* with its contents    | (6)                   |
|                                | repeated *n* times               |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.insert(i, x)"               | inserts *x* into *s* at the      |                       |
|                                | index given by *i* (same as      |                       |
|                                | "s[i:i] = [x]")                  |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.pop([i])"                   | retrieves the item at *i* and    | (2)                   |
|                                | also removes it from *s*         |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.remove(x)"                  | remove the first item from *s*   | (3)                   |
|                                | where "s[i]" is equal to *x*     |                       |
+--------------------------------+----------------------------------+-----------------------+
| "s.reverse()"                  | reverses the items of *s* in     | (4)                   |
|                                | place                            |                       |
+--------------------------------+----------------------------------+-----------------------+

Notes:

1. *t* must have the same length as the slice it is replacing.

2. The optional argument *i* defaults to "-1", so that by default
   the last item is removed and returned.

3. "remove()" raises "ValueError" when *x* is not found in *s*.

4. The "reverse()" method modifies the sequence in place for
   economy of space when reversing a large sequence.  To remind users
   that it operates by side effect, it does not return the reversed
   sequence.

5. "clear()" and "copy()" are included for consistency with the
   interfaces of mutable containers that don’t support slicing
   operations (such as "dict" and "set"). "copy()" is not part of the
   "collections.abc.MutableSequence" ABC, but most concrete mutable
   sequence classes provide it.

   New in version 3.3: "clear()" and "copy()" methods.

6. The value *n* is an integer, or an object implementing
   "__index__()".  Zero and negative values of *n* clear the sequence.
   Items in the sequence are not copied; they are referenced multiple
   times, as explained for "s * n" under Common Sequence Operations.


Lists
-----

Lists are mutable sequences, typically used to store collections of
homogeneous items (where the precise degree of similarity will vary by
application).

class list([iterable])

   Lists may be constructed in several ways:

   * Using a pair of square brackets to denote the empty list: "[]"

   * Using square brackets, separating items with commas: "[a]",
     "[a, b, c]"

   * Using a list comprehension: "[x for x in iterable]"

   * Using the type constructor: "list()" or "list(iterable)"

   The constructor builds a list whose items are the same and in the
   same order as *iterable*’s items.  *iterable* may be either a
   sequence, a container that supports iteration, or an iterator
   object.  If *iterable* is already a list, a copy is made and
   returned, similar to "iterable[:]". For example, "list('abc')"
   returns "['a', 'b', 'c']" and "list( (1, 2, 3) )" returns "[1, 2,
   3]". If no argument is given, the constructor creates a new empty
   list, "[]".

   Many other operations also produce lists, including the "sorted()"
   built-in.

   Lists implement all of the common and mutable sequence operations.
   Lists also provide the following additional method:

   sort(*, key=None, reverse=False)

      This method sorts the list in place, using only "<" comparisons
      between items. Exceptions are not suppressed - if any comparison
      operations fail, the entire sort operation will fail (and the
      list will likely be left in a partially modified state).

      "sort()" accepts two arguments that can only be passed by
      keyword (keyword-only arguments):

      *key* specifies a function of one argument that is used to
      extract a comparison key from each list element (for example,
      "key=str.lower"). The key corresponding to each item in the list
      is calculated once and then used for the entire sorting process.
      The default value of "None" means that list items are sorted
      directly without calculating a separate key value.

      The "functools.cmp_to_key()" utility is available to convert a
      2.x style *cmp* function to a *key* function.

      *reverse* is a boolean value.  If set to "True", then the list
      elements are sorted as if each comparison were reversed.

      This method modifies the sequence in place for economy of space
      when sorting a large sequence.  To remind users that it operates
      by side effect, it does not return the sorted sequence (use
      "sorted()" to explicitly request a new sorted list instance).

      The "sort()" method is guaranteed to be stable.  A sort is
      stable if it guarantees not to change the relative order of
      elements that compare equal — this is helpful for sorting in
      multiple passes (for example, sort by department, then by salary
      grade).

      For sorting examples and a brief sorting tutorial, see Sorting
      HOW TO.

      **CPython implementation detail:** While a list is being sorted,
      the effect of attempting to mutate, or even inspect, the list is
      undefined.  The C implementation of Python makes the list appear
      empty for the duration, and raises "ValueError" if it can detect
      that the list has been mutated during a sort.


Tuples
------

Tuples are immutable sequences, typically used to store collections of
heterogeneous data (such as the 2-tuples produced by the "enumerate()"
built-in). Tuples are also used for cases where an immutable sequence
of homogeneous data is needed (such as allowing storage in a "set" or
"dict" instance).

class tuple([iterable])

   Tuples may be constructed in a number of ways:

   * Using a pair of parentheses to denote the empty tuple: "()"

   * Using a trailing comma for a singleton tuple: "a," or "(a,)"

   * Separating items with commas: "a, b, c" or "(a, b, c)"

   * Using the "tuple()" built-in: "tuple()" or "tuple(iterable)"

   The constructor builds a tuple whose items are the same and in the
   same order as *iterable*’s items.  *iterable* may be either a
   sequence, a container that supports iteration, or an iterator
   object.  If *iterable* is already a tuple, it is returned
   unchanged. For example, "tuple('abc')" returns "('a', 'b', 'c')"
   and "tuple( [1, 2, 3] )" returns "(1, 2, 3)". If no argument is
   given, the constructor creates a new empty tuple, "()".

   Note that it is actually the comma which makes a tuple, not the
   parentheses. The parentheses are optional, except in the empty
   tuple case, or when they are needed to avoid syntactic ambiguity.
   For example, "f(a, b, c)" is a function call with three arguments,
   while "f((a, b, c))" is a function call with a 3-tuple as the sole
   argument.

   Tuples implement all of the common sequence operations.

For heterogeneous collections of data where access by name is clearer
than access by index, "collections.namedtuple()" may be a more
appropriate choice than a simple tuple object.


Ranges
------

The "range" type represents an immutable sequence of numbers and is
commonly used for looping a specific number of times in "for" loops.

class range(stop)
class range(start, stop[, step])

   The arguments to the range constructor must be integers (either
   built-in "int" or any object that implements the "__index__"
   special method).  If the *step* argument is omitted, it defaults to
   "1". If the *start* argument is omitted, it defaults to "0". If
   *step* is zero, "ValueError" is raised.

   For a positive *step*, the contents of a range "r" are determined
   by the formula "r[i] = start + step*i" where "i >= 0" and "r[i] <
   stop".

   For a negative *step*, the contents of the range are still
   determined by the formula "r[i] = start + step*i", but the
   constraints are "i >= 0" and "r[i] > stop".

   A range object will be empty if "r[0]" does not meet the value
   constraint. Ranges do support negative indices, but these are
   interpreted as indexing from the end of the sequence determined by
   the positive indices.

   Ranges containing absolute values larger than "sys.maxsize" are
   permitted but some features (such as "len()") may raise
   "OverflowError".

   Range examples:

      >>> list(range(10))
      [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
      >>> list(range(1, 11))
      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
      >>> list(range(0, 30, 5))
      [0, 5, 10, 15, 20, 25]
      >>> list(range(0, 10, 3))
      [0, 3, 6, 9]
      >>> list(range(0, -10, -1))
      [0, -1, -2, -3, -4, -5, -6, -7, -8, -9]
      >>> list(range(0))
      []
      >>> list(range(1, 0))
      []

   Ranges implement all of the common sequence operations except
   concatenation and repetition (due to the fact that range objects
   can only represent sequences that follow a strict pattern and
   repetition and concatenation will usually violate that pattern).

   start

      The value of the *start* parameter (or "0" if the parameter was
      not supplied)

   stop

      The value of the *stop* parameter

   step

      The value of the *step* parameter (or "1" if the parameter was
      not supplied)

The advantage of the "range" type over a regular "list" or "tuple" is
that a "range" object will always take the same (small) amount of
memory, no matter the size of the range it represents (as it only
stores the "start", "stop" and "step" values, calculating individual
items and subranges as needed).

Range objects implement the "collections.abc.Sequence" ABC, and
provide features such as containment tests, element index lookup,
slicing and support for negative indices (see Sequence Types — list,
tuple, range):

>>> r = range(0, 20, 2)
>>> r
range(0, 20, 2)
>>> 11 in r
False
>>> 10 in r
True
>>> r.index(10)
5
>>> r[5]
10
>>> r[:5]
range(0, 10, 2)
>>> r[-1]
18

Testing range objects for equality with "==" and "!=" compares them as
sequences.  That is, two range objects are considered equal if they
represent the same sequence of values.  (Note that two range objects
that compare equal might have different "start", "stop" and "step"
attributes, for example "range(0) == range(2, 1, 3)" or "range(0, 3,
2) == range(0, 4, 2)".)

Changed in version 3.2: Implement the Sequence ABC. Support slicing
and negative indices. Test "int" objects for membership in constant
time instead of iterating through all items.

Changed in version 3.3: Define ‘==’ and ‘!=’ to compare range objects
based on the sequence of values they define (instead of comparing
based on object identity).

New in version 3.3: The "start", "stop" and "step" attributes.

See also:

  * The linspace recipe shows how to implement a lazy version of
    range suitable for floating point applications.


Text Sequence Type — "str"
==========================

Textual data in Python is handled with "str" objects, or *strings*.
Strings are immutable sequences of Unicode code points.  String
literals are written in a variety of ways:

* Single quotes: "'allows embedded "double" quotes'"

* Double quotes: ""allows embedded 'single' quotes"".

* Triple quoted: "'''Three single quotes'''", """"Three double
  quotes""""

Triple quoted strings may span multiple lines - all associated
whitespace will be included in the string literal.

String literals that are part of a single expression and have only
whitespace between them will be implicitly converted to a single
string literal. That is, "("spam " "eggs") == "spam eggs"".

See String and Bytes literals for more about the various forms of
string literal, including supported escape sequences, and the "r"
(“raw”) prefix that disables most escape sequence processing.

Strings may also be created from other objects using the "str"
constructor.

Since there is no separate “character” type, indexing a string
produces strings of length 1. That is, for a non-empty string *s*,
"s[0] == s[0:1]".

There is also no mutable string type, but "str.join()" or
"io.StringIO" can be used to efficiently construct strings from
multiple fragments.

Changed in version 3.3: For backwards compatibility with the Python 2
series, the "u" prefix is once again permitted on string literals. It
has no effect on the meaning of string literals and cannot be combined
with the "r" prefix.

class str(object='')
class str(object=b'', encoding='utf-8', errors='strict')

   Return a string version of *object*.  If *object* is not provided,
   returns the empty string.  Otherwise, the behavior of "str()"
   depends on whether *encoding* or *errors* is given, as follows.

   If neither *encoding* nor *errors* is given, "str(object)" returns
   "object.__str__()", which is the “informal” or nicely printable
   string representation of *object*.  For string objects, this is the
   string itself.  If *object* does not have a "__str__()" method,
   then "str()" falls back to returning "repr(object)".

   If at least one of *encoding* or *errors* is given, *object* should
   be a *bytes-like object* (e.g. "bytes" or "bytearray").  In this
   case, if *object* is a "bytes" (or "bytearray") object, then
   "str(bytes, encoding, errors)" is equivalent to
   "bytes.decode(encoding, errors)".  Otherwise, the bytes object
   underlying the buffer object is obtained before calling
   "bytes.decode()".  See Binary Sequence Types — bytes, bytearray,
   memoryview and Buffer Protocol for information on buffer objects.

   Passing a "bytes" object to "str()" without the *encoding* or
   *errors* arguments falls under the first case of returning the
   informal string representation (see also the "-b" command-line
   option to Python).  For example:

      >>> str(b'Zoot!')
      "b'Zoot!'"

   For more information on the "str" class and its methods, see Text
   Sequence Type — str and the String Methods section below.  To
   output formatted strings, see the Formatted string literals and
   Format String Syntax sections.  In addition, see the Text
   Processing Services section.


String Methods
--------------

Strings implement all of the common sequence operations, along with
the additional methods described below.

Strings also support two styles of string formatting, one providing a
large degree of flexibility and customization (see "str.format()",
Format String Syntax and Custom String Formatting) and the other based
on C "printf" style formatting that handles a narrower range of types
and is slightly harder to use correctly, but is often faster for the
cases it can handle (printf-style String Formatting).

The Text Processing Services section of the standard library covers a
number of other modules that provide various text related utilities
(including regular expression support in the "re" module).

str.capitalize()

   Return a copy of the string with its first character capitalized
   and the rest lowercased.

   Changed in version 3.8: The first character is now put into
   titlecase rather than uppercase. This means that characters like
   digraphs will only have their first letter capitalized, instead of
   the full character.

str.casefold()

   Return a casefolded copy of the string. Casefolded strings may be
   used for caseless matching.

   Casefolding is similar to lowercasing but more aggressive because
   it is intended to remove all case distinctions in a string. For
   example, the German lowercase letter "'ß'" is equivalent to ""ss"".
   Since it is already lowercase, "lower()" would do nothing to "'ß'";
   "casefold()" converts it to ""ss"".

   The casefolding algorithm is described in section 3.13 of the
   Unicode Standard.

   New in version 3.3.

str.center(width[, fillchar])

   Return centered in a string of length *width*. Padding is done
   using the specified *fillchar* (default is an ASCII space). The
   original string is returned if *width* is less than or equal to
   "len(s)".

str.count(sub[, start[, end]])

   Return the number of non-overlapping occurrences of substring *sub*
   in the range [*start*, *end*].  Optional arguments *start* and
   *end* are interpreted as in slice notation.

str.encode(encoding="utf-8", errors="strict")

   Return an encoded version of the string as a bytes object. Default
   encoding is "'utf-8'". *errors* may be given to set a different
   error handling scheme. The default for *errors* is "'strict'",
   meaning that encoding errors raise a "UnicodeError". Other possible
   values are "'ignore'", "'replace'", "'xmlcharrefreplace'",
   "'backslashreplace'" and any other name registered via
   "codecs.register_error()", see section Error Handlers. For a list
   of possible encodings, see section Standard Encodings.

   Changed in version 3.1: Support for keyword arguments added.

str.endswith(suffix[, start[, end]])

   Return "True" if the string ends with the specified *suffix*,
   otherwise return "False".  *suffix* can also be a tuple of suffixes
   to look for.  With optional *start*, test beginning at that
   position.  With optional *end*, stop comparing at that position.

str.expandtabs(tabsize=8)

   Return a copy of the string where all tab characters are replaced
   by one or more spaces, depending on the current column and the
   given tab size.  Tab positions occur every *tabsize* characters
   (default is 8, giving tab positions at columns 0, 8, 16 and so on).
   To expand the string, the current column is set to zero and the
   string is examined character by character.  If the character is a
   tab ("\t"), one or more space characters are inserted in the result
   until the current column is equal to the next tab position. (The
   tab character itself is not copied.)  If the character is a newline
   ("\n") or return ("\r"), it is copied and the current column is
   reset to zero.  Any other character is copied unchanged and the
   current column is incremented by one regardless of how the
   character is represented when printed.

   >>> '01\t012\t0123\t01234'.expandtabs()
   '01      012     0123    01234'
   >>> '01\t012\t0123\t01234'.expandtabs(4)
   '01  012 0123    01234'

str.find(sub[, start[, end]])

   Return the lowest index in the string where substring *sub* is
   found within the slice "s[start:end]".  Optional arguments *start*
   and *end* are interpreted as in slice notation.  Return "-1" if
   *sub* is not found.

   Note: The "find()" method should be used only if you need to know
     the position of *sub*.  To check if *sub* is a substring or not,
     use the "in" operator:

        >>> 'Py' in 'Python'
        True

str.format(*args, **kwargs)

   Perform a string formatting operation.  The string on which this
   method is called can contain literal text or replacement fields
   delimited by braces "{}".  Each replacement field contains either
   the numeric index of a positional argument, or the name of a
   keyword argument.  Returns a copy of the string where each
   replacement field is replaced with the string value of the
   corresponding argument.

   >>> "The sum of 1 + 2 is {0}".format(1+2)
   'The sum of 1 + 2 is 3'

   See Format String Syntax for a description of the various
   formatting options that can be specified in format strings.

   Note: When formatting a number ("int", "float", "complex",
     "decimal.Decimal" and subclasses) with the "n" type (ex:
     "'{:n}'.format(1234)"), the function temporarily sets the
     "LC_CTYPE" locale to the "LC_NUMERIC" locale to decode
     "decimal_point" and "thousands_sep" fields of "localeconv()" if
     they are non-ASCII or longer than 1 byte, and the "LC_NUMERIC"
     locale is different than the "LC_CTYPE" locale.  This temporary
     change affects other threads.

   Changed in version 3.7: When formatting a number with the "n" type,
   the function sets temporarily the "LC_CTYPE" locale to the
   "LC_NUMERIC" locale in some cases.

str.format_map(mapping)

   Similar to "str.format(**mapping)", except that "mapping" is used
   directly and not copied to a "dict".  This is useful if for example
   "mapping" is a dict subclass:

   >>> class Default(dict):
   ...     def __missing__(self, key):
   ...         return key
   ...
   >>> '{name} was born in {country}'.format_map(Default(name='Guido'))
   'Guido was born in country'

   New in version 3.2.

str.index(sub[, start[, end]])

   Like "find()", but raise "ValueError" when the substring is not
   found.

str.isalnum()

   Return "True" if all characters in the string are alphanumeric and
   there is at least one character, "False" otherwise.  A character
   "c" is alphanumeric if one of the following returns "True":
   "c.isalpha()", "c.isdecimal()", "c.isdigit()", or "c.isnumeric()".

str.isalpha()

   Return "True" if all characters in the string are alphabetic and
   there is at least one character, "False" otherwise.  Alphabetic
   characters are those characters defined in the Unicode character
   database as “Letter”, i.e., those with general category property
   being one of “Lm”, “Lt”, “Lu”, “Ll”, or “Lo”.  Note that this is
   different from the “Alphabetic” property defined in the Unicode
   Standard.

str.isascii()

   Return "True" if the string is empty or all characters in the
   string are ASCII, "False" otherwise. ASCII characters have code
   points in the range U+0000-U+007F.

   New in version 3.7.

str.isdecimal()

   Return "True" if all characters in the string are decimal
   characters and there is at least one character, "False" otherwise.
   Decimal characters are those that can be used to form numbers in
   base 10, e.g. U+0660, ARABIC-INDIC DIGIT ZERO.  Formally a decimal
   character is a character in the Unicode General Category “Nd”.

str.isdigit()

   Return "True" if all characters in the string are digits and there
   is at least one character, "False" otherwise.  Digits include
   decimal characters and digits that need special handling, such as
   the compatibility superscript digits. This covers digits which
   cannot be used to form numbers in base 10, like the Kharosthi
   numbers.  Formally, a digit is a character that has the property
   value Numeric_Type=Digit or Numeric_Type=Decimal.

str.isidentifier()

   Return "True" if the string is a valid identifier according to the
   language definition, section Identifiers and keywords.

   Call "keyword.iskeyword()" to test whether string "s" is a reserved
   identifier, such as "def" and "class".

   Example:

      >>> from keyword import iskeyword

      >>> 'hello'.isidentifier(), iskeyword('hello')
      True, False
      >>> 'def'.isidentifier(), iskeyword('def')
      True, True

str.islower()

   Return "True" if all cased characters [4] in the string are
   lowercase and there is at least one cased character, "False"
   otherwise.

str.isnumeric()

   Return "True" if all characters in the string are numeric
   characters, and there is at least one character, "False" otherwise.
   Numeric characters include digit characters, and all characters
   that have the Unicode numeric value property, e.g. U+2155, VULGAR
   FRACTION ONE FIFTH.  Formally, numeric characters are those with
   the property value Numeric_Type=Digit, Numeric_Type=Decimal or
   Numeric_Type=Numeric.

str.isprintable()

   Return "True" if all characters in the string are printable or the
   string is empty, "False" otherwise.  Nonprintable characters are
   those characters defined in the Unicode character database as
   “Other” or “Separator”, excepting the ASCII space (0x20) which is
   considered printable.  (Note that printable characters in this
   context are those which should not be escaped when "repr()" is
   invoked on a string.  It has no bearing on the handling of strings
   written to "sys.stdout" or "sys.stderr".)

str.isspace()

   Return "True" if there are only whitespace characters in the string
   and there is at least one character, "False" otherwise.

   A character is *whitespace* if in the Unicode character database
   (see "unicodedata"), either its general category is "Zs"
   (“Separator, space”), or its bidirectional class is one of "WS",
   "B", or "S".

str.istitle()

   Return "True" if the string is a titlecased string and there is at
   least one character, for example uppercase characters may only
   follow uncased characters and lowercase characters only cased ones.
   Return "False" otherwise.

str.isupper()

   Return "True" if all cased characters [4] in the string are
   uppercase and there is at least one cased character, "False"
   otherwise.

str.join(iterable)

   Return a string which is the concatenation of the strings in
   *iterable*. A "TypeError" will be raised if there are any non-
   string values in *iterable*, including "bytes" objects.  The
   separator between elements is the string providing this method.

str.ljust(width[, fillchar])

   Return the string left justified in a string of length *width*.
   Padding is done using the specified *fillchar* (default is an ASCII
   space). The original string is returned if *width* is less than or
   equal to "len(s)".

str.lower()

   Return a copy of the string with all the cased characters [4]
   converted to lowercase.

   The lowercasing algorithm used is described in section 3.13 of the
   Unicode Standard.

str.lstrip([chars])

   Return a copy of the string with leading characters removed.  The
   *chars* argument is a string specifying the set of characters to be
   removed.  If omitted or "None", the *chars* argument defaults to
   removing whitespace.  The *chars* argument is not a prefix; rather,
   all combinations of its values are stripped:

      >>> '   spacious   '.lstrip()
      'spacious   '
      >>> 'www.example.com'.lstrip('cmowz.')
      'example.com'

static str.maketrans(x[, y[, z]])

   This static method returns a translation table usable for
   "str.translate()".

   If there is only one argument, it must be a dictionary mapping
   Unicode ordinals (integers) or characters (strings of length 1) to
   Unicode ordinals, strings (of arbitrary lengths) or "None".
   Character keys will then be converted to ordinals.

   If there are two arguments, they must be strings of equal length,
   and in the resulting dictionary, each character in x will be mapped
   to the character at the same position in y.  If there is a third
   argument, it must be a string, whose characters will be mapped to
   "None" in the result.

str.partition(sep)

   Split the string at the first occurrence of *sep*, and return a
   3-tuple containing the part before the separator, the separator
   itself, and the part after the separator.  If the separator is not
   found, return a 3-tuple containing the string itself, followed by
   two empty strings.

str.replace(old, new[, count])

   Return a copy of the string with all occurrences of substring *old*
   replaced by *new*.  If the optional argument *count* is given, only
   the first *count* occurrences are replaced.

str.rfind(sub[, start[, end]])

   Return the highest index in the string where substring *sub* is
   found, such that *sub* is contained within "s[start:end]".
   Optional arguments *start* and *end* are interpreted as in slice
   notation.  Return "-1" on failure.

str.rindex(sub[, start[, end]])

   Like "rfind()" but raises "ValueError" when the substring *sub* is
   not found.

str.rjust(width[, fillchar])

   Return the string right justified in a string of length *width*.
   Padding is done using the specified *fillchar* (default is an ASCII
   space). The original string is returned if *width* is less than or
   equal to "len(s)".

str.rpartition(sep)

   Split the string at the last occurrence of *sep*, and return a
   3-tuple containing the part before the separator, the separator
   itself, and the part after the separator.  If the separator is not
   found, return a 3-tuple containing two empty strings, followed by
   the string itself.

str.rsplit(sep=None, maxsplit=-1)

   Return a list of the words in the string, using *sep* as the
   delimiter string. If *maxsplit* is given, at most *maxsplit* splits
   are done, the *rightmost* ones.  If *sep* is not specified or
   "None", any whitespace string is a separator.  Except for splitting
   from the right, "rsplit()" behaves like "split()" which is
   described in detail below.

str.rstrip([chars])

   Return a copy of the string with trailing characters removed.  The
   *chars* argument is a string specifying the set of characters to be
   removed.  If omitted or "None", the *chars* argument defaults to
   removing whitespace.  The *chars* argument is not a suffix; rather,
   all combinations of its values are stripped:

      >>> '   spacious   '.rstrip()
      '   spacious'
      >>> 'mississippi'.rstrip('ipz')
      'mississ'

str.split(sep=None, maxsplit=-1)

   Return a list of the words in the string, using *sep* as the
   delimiter string.  If *maxsplit* is given, at most *maxsplit*
   splits are done (thus, the list will have at most "maxsplit+1"
   elements).  If *maxsplit* is not specified or "-1", then there is
   no limit on the number of splits (all possible splits are made).

   If *sep* is given, consecutive delimiters are not grouped together
   and are deemed to delimit empty strings (for example,
   "'1,,2'.split(',')" returns "['1', '', '2']").  The *sep* argument
   may consist of multiple characters (for example,
   "'1<>2<>3'.split('<>')" returns "['1', '2', '3']"). Splitting an
   empty string with a specified separator returns "['']".

   For example:

      >>> '1,2,3'.split(',')
      ['1', '2', '3']
      >>> '1,2,3'.split(',', maxsplit=1)
      ['1', '2,3']
      >>> '1,2,,3,'.split(',')
      ['1', '2', '', '3', '']

   If *sep* is not specified or is "None", a different splitting
   algorithm is applied: runs of consecutive whitespace are regarded
   as a single separator, and the result will contain no empty strings
   at the start or end if the string has leading or trailing
   whitespace.  Consequently, splitting an empty string or a string
   consisting of just whitespace with a "None" separator returns "[]".

   For example:

      >>> '1 2 3'.split()
      ['1', '2', '3']
      >>> '1 2 3'.split(maxsplit=1)
      ['1', '2 3']
      >>> '   1   2   3   '.split()
      ['1', '2', '3']

str.splitlines([keepends])

   Return a list of the lines in the string, breaking at line
   boundaries.  Line breaks are not included in the resulting list
   unless *keepends* is given and true.

   This method splits on the following line boundaries.  In
   particular, the boundaries are a superset of *universal newlines*.

   +-------------------------+-------------------------------+
   | Representation          | Description                   |
   |=========================|===============================|
   | "\n"                    | Line Feed                     |
   +-------------------------+-------------------------------+
   | "\r"                    | Carriage Return               |
   +-------------------------+-------------------------------+
   | "\r\n"                  | Carriage Return + Line Feed   |
   +-------------------------+-------------------------------+
   | "\v" or "\x0b"          | Line Tabulation               |
   +-------------------------+-------------------------------+
   | "\f" or "\x0c"          | Form Feed                     |
   +-------------------------+-------------------------------+
   | "\x1c"                  | File Separator                |
   +-------------------------+-------------------------------+
   | "\x1d"                  | Group Separator               |
   +-------------------------+-------------------------------+
   | "\x1e"                  | Record Separator              |
   +-------------------------+-------------------------------+
   | "\x85"                  | Next Line (C1 Control Code)   |
   +-------------------------+-------------------------------+
   | "\u2028"                | Line Separator                |
   +-------------------------+-------------------------------+
   | "\u2029"                | Paragraph Separator           |
   +-------------------------+-------------------------------+

   Changed in version 3.2: "\v" and "\f" added to list of line
   boundaries.

   For example:

      >>> 'ab c\n\nde fg\rkl\r\n'.splitlines()
      ['ab c', '', 'de fg', 'kl']
      >>> 'ab c\n\nde fg\rkl\r\n'.splitlines(keepends=True)
      ['ab c\n', '\n', 'de fg\r', 'kl\r\n']

   Unlike "split()" when a delimiter string *sep* is given, this
   method returns an empty list for the empty string, and a terminal
   line break does not result in an extra line:

      >>> "".splitlines()
      []
      >>> "One line\n".splitlines()
      ['One line']

   For comparison, "split('\n')" gives:

      >>> ''.split('\n')
      ['']
      >>> 'Two lines\n'.split('\n')
      ['Two lines', '']

str.startswith(prefix[, start[, end]])

   Return "True" if string starts with the *prefix*, otherwise return
   "False". *prefix* can also be a tuple of prefixes to look for.
   With optional *start*, test string beginning at that position.
   With optional *end*, stop comparing string at that position.

str.strip([chars])

   Return a copy of the string with the leading and trailing
   characters removed. The *chars* argument is a string specifying the
   set of characters to be removed. If omitted or "None", the *chars*
   argument defaults to removing whitespace. The *chars* argument is
   not a prefix or suffix; rather, all combinations of its values are
   stripped:

      >>> '   spacious   '.strip()
      'spacious'
      >>> 'www.example.com'.strip('cmowz.')
      'example'

   The outermost leading and trailing *chars* argument values are
   stripped from the string. Characters are removed from the leading
   end until reaching a string character that is not contained in the
   set of characters in *chars*. A similar action takes place on the
   trailing end. For example:

      >>> comment_string = '#....... Section 3.2.1 Issue #32 .......'
      >>> comment_string.strip('.#! ')
      'Section 3.2.1 Issue #32'

str.swapcase()

   Return a copy of the string with uppercase characters converted to
   lowercase and vice versa. Note that it is not necessarily true that
   "s.swapcase().swapcase() == s".

str.title()

   Return a titlecased version of the string where words start with an
   uppercase character and the remaining characters are lowercase.

   For example:

      >>> 'Hello world'.title()
      'Hello World'

   The algorithm uses a simple language-independent definition of a
   word as groups of consecutive letters.  The definition works in
   many contexts but it means that apostrophes in contractions and
   possessives form word boundaries, which may not be the desired
   result:

      >>> "they're bill's friends from the UK".title()
      "They'Re Bill'S Friends From The Uk"

   A workaround for apostrophes can be constructed using regular
   expressions:

      >>> import re
      >>> def titlecase(s):
      ...     return re.sub(r"[A-Za-z]+('[A-Za-z]+)?",
      ...                   lambda mo: mo.group(0).capitalize(),
      ...                   s)
      ...
      >>> titlecase("they're bill's friends.")
      "They're Bill's Friends."

str.translate(table)

   Return a copy of the string in which each character has been mapped
   through the given translation table.  The table must be an object
   that implements indexing via "__getitem__()", typically a *mapping*
   or *sequence*.  When indexed by a Unicode ordinal (an integer), the
   table object can do any of the following: return a Unicode ordinal
   or a string, to map the character to one or more other characters;
   return "None", to delete the character from the return string; or
   raise a "LookupError" exception, to map the character to itself.

   You can use "str.maketrans()" to create a translation map from
   character-to-character mappings in different formats.

   See also the "codecs" module for a more flexible approach to custom
   character mappings.

str.upper()

   Return a copy of the string with all the cased characters [4]
   converted to uppercase.  Note that "s.upper().isupper()" might be
   "False" if "s" contains uncased characters or if the Unicode
   category of the resulting character(s) is not “Lu” (Letter,
   uppercase), but e.g. “Lt” (Letter, titlecase).

   The uppercasing algorithm used is described in section 3.13 of the
   Unicode Standard.

str.zfill(width)

   Return a copy of the string left filled with ASCII "'0'" digits to
   make a string of length *width*. A leading sign prefix
   ("'+'"/"'-'") is handled by inserting the padding *after* the sign
   character rather than before. The original string is returned if
   *width* is less than or equal to "len(s)".

   For example:

      >>> "42".zfill(5)
      '00042'
      >>> "-42".zfill(5)
      '-0042'


"printf"-style String Formatting
--------------------------------

Note: The formatting operations described here exhibit a variety of
  quirks that lead to a number of common errors (such as failing to
  display tuples and dictionaries correctly).  Using the newer
  formatted string literals, the "str.format()" interface, or template
  strings may help avoid these errors.  Each of these alternatives
  provides their own trade-offs and benefits of simplicity,
  flexibility, and/or extensibility.

String objects have one unique built-in operation: the "%" operator
(modulo). This is also known as the string *formatting* or
*interpolation* operator. Given "format % values" (where *format* is a
string), "%" conversion specifications in *format* are replaced with
zero or more elements of *values*. The effect is similar to using the
"sprintf()" in the C language.

If *format* requires a single argument, *values* may be a single non-
tuple object. [5]  Otherwise, *values* must be a tuple with exactly
the number of items specified by the format string, or a single
mapping object (for example, a dictionary).

A conversion specifier contains two or more characters and has the
following components, which must occur in this order:

1. The "'%'" character, which marks the start of the specifier.

2. Mapping key (optional), consisting of a parenthesised sequence
   of characters (for example, "(somename)").

3. Conversion flags (optional), which affect the result of some
   conversion types.

4. Minimum field width (optional).  If specified as an "'*'"
   (asterisk), the actual width is read from the next element of the
   tuple in *values*, and the object to convert comes after the
   minimum field width and optional precision.

5. Precision (optional), given as a "'.'" (dot) followed by the
   precision.  If specified as "'*'" (an asterisk), the actual
   precision is read from the next element of the tuple in *values*,
   and the value to convert comes after the precision.

6. Length modifier (optional).

7. Conversion type.

When the right argument is a dictionary (or other mapping type), then
the formats in the string *must* include a parenthesised mapping key
into that dictionary inserted immediately after the "'%'" character.
The mapping key selects the value to be formatted from the mapping.
For example:

>>> print('%(language)s has %(number)03d quote types.' %
...       {'language': "Python", "number": 2})
Python has 002 quote types.

In this case no "*" specifiers may occur in a format (since they
require a sequential parameter list).

The conversion flag characters are:

+-----------+-----------------------------------------------------------------------+
| Flag      | Meaning                                                               |
|===========|=======================================================================|
| "'#'"     | The value conversion will use the “alternate form” (where defined     |
|           | below).                                                               |
+-----------+-----------------------------------------------------------------------+
| "'0'"     | The conversion will be zero padded for numeric values.                |
+-----------+-----------------------------------------------------------------------+
| "'-'"     | The converted value is left adjusted (overrides the "'0'" conversion  |
|           | if both are given).                                                   |
+-----------+-----------------------------------------------------------------------+
| "' '"     | (a space) A blank should be left before a positive number (or empty   |
|           | string) produced by a signed conversion.                              |
+-----------+-----------------------------------------------------------------------+
| "'+'"     | A sign character ("'+'" or "'-'") will precede the conversion         |
|           | (overrides a “space” flag).                                           |
+-----------+-----------------------------------------------------------------------+

A length modifier ("h", "l", or "L") may be present, but is ignored as
it is not necessary for Python – so e.g. "%ld" is identical to "%d".

The conversion types are:

+--------------+-------------------------------------------------------+---------+
| Conversion   | Meaning                                               | Notes   |
|==============|=======================================================|=========|
| "'d'"        | Signed integer decimal.                               |         |
+--------------+-------------------------------------------------------+---------+
| "'i'"        | Signed integer decimal.                               |         |
+--------------+-------------------------------------------------------+---------+
| "'o'"        | Signed octal value.                                   | (1)     |
+--------------+-------------------------------------------------------+---------+
| "'u'"        | Obsolete type – it is identical to "'d'".             | (6)     |
+--------------+-------------------------------------------------------+---------+
| "'x'"        | Signed hexadecimal (lowercase).                       | (2)     |
+--------------+-------------------------------------------------------+---------+
| "'X'"        | Signed hexadecimal (uppercase).                       | (2)     |
+--------------+-------------------------------------------------------+---------+
| "'e'"        | Floating point exponential format (lowercase).        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'E'"        | Floating point exponential format (uppercase).        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'f'"        | Floating point decimal format.                        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'F'"        | Floating point decimal format.                        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'g'"        | Floating point format. Uses lowercase exponential     | (4)     |
|              | format if exponent is less than -4 or not less than   |         |
|              | precision, decimal format otherwise.                  |         |
+--------------+-------------------------------------------------------+---------+
| "'G'"        | Floating point format. Uses uppercase exponential     | (4)     |
|              | format if exponent is less than -4 or not less than   |         |
|              | precision, decimal format otherwise.                  |         |
+--------------+-------------------------------------------------------+---------+
| "'c'"        | Single character (accepts integer or single character |         |
|              | string).                                              |         |
+--------------+-------------------------------------------------------+---------+
| "'r'"        | String (converts any Python object using "repr()").   | (5)     |
+--------------+-------------------------------------------------------+---------+
| "'s'"        | String (converts any Python object using "str()").    | (5)     |
+--------------+-------------------------------------------------------+---------+
| "'a'"        | String (converts any Python object using "ascii()").  | (5)     |
+--------------+-------------------------------------------------------+---------+
| "'%'"        | No argument is converted, results in a "'%'"          |         |
|              | character in the result.                              |         |
+--------------+-------------------------------------------------------+---------+

Notes:

1. The alternate form causes a leading octal specifier ("'0o'") to
   be inserted before the first digit.

2. The alternate form causes a leading "'0x'" or "'0X'" (depending
   on whether the "'x'" or "'X'" format was used) to be inserted
   before the first digit.

3. The alternate form causes the result to always contain a decimal
   point, even if no digits follow it.

   The precision determines the number of digits after the decimal
   point and defaults to 6.

4. The alternate form causes the result to always contain a decimal
   point, and trailing zeroes are not removed as they would otherwise
   be.

   The precision determines the number of significant digits before
   and after the decimal point and defaults to 6.

5. If precision is "N", the output is truncated to "N" characters.

6. See **PEP 237**.

Since Python strings have an explicit length, "%s" conversions do not
assume that "'\0'" is the end of the string.

Changed in version 3.1: "%f" conversions for numbers whose absolute
value is over 1e50 are no longer replaced by "%g" conversions.


Binary Sequence Types — "bytes", "bytearray", "memoryview"
==========================================================

The core built-in types for manipulating binary data are "bytes" and
"bytearray". They are supported by "memoryview" which uses the buffer
protocol to access the memory of other binary objects without needing
to make a copy.

The "array" module supports efficient storage of basic data types like
32-bit integers and IEEE754 double-precision floating values.


Bytes Objects
-------------

Bytes objects are immutable sequences of single bytes. Since many
major binary protocols are based on the ASCII text encoding, bytes
objects offer several methods that are only valid when working with
ASCII compatible data and are closely related to string objects in a
variety of other ways.

class bytes([source[, encoding[, errors]]])

   Firstly, the syntax for bytes literals is largely the same as that
   for string literals, except that a "b" prefix is added:

   * Single quotes: "b'still allows embedded "double" quotes'"

   * Double quotes: "b"still allows embedded 'single' quotes"".

   * Triple quoted: "b'''3 single quotes'''", "b"""3 double
     quotes""""

   Only ASCII characters are permitted in bytes literals (regardless
   of the declared source code encoding). Any binary values over 127
   must be entered into bytes literals using the appropriate escape
   sequence.

   As with string literals, bytes literals may also use a "r" prefix
   to disable processing of escape sequences. See String and Bytes
   literals for more about the various forms of bytes literal,
   including supported escape sequences.

   While bytes literals and representations are based on ASCII text,
   bytes objects actually behave like immutable sequences of integers,
   with each value in the sequence restricted such that "0 <= x < 256"
   (attempts to violate this restriction will trigger "ValueError").
   This is done deliberately to emphasise that while many binary
   formats include ASCII based elements and can be usefully
   manipulated with some text-oriented algorithms, this is not
   generally the case for arbitrary binary data (blindly applying text
   processing algorithms to binary data formats that are not ASCII
   compatible will usually lead to data corruption).

   In addition to the literal forms, bytes objects can be created in a
   number of other ways:

   * A zero-filled bytes object of a specified length: "bytes(10)"

   * From an iterable of integers: "bytes(range(20))"

   * Copying existing binary data via the buffer protocol:
     "bytes(obj)"

   Also see the bytes built-in.

   Since 2 hexadecimal digits correspond precisely to a single byte,
   hexadecimal numbers are a commonly used format for describing
   binary data. Accordingly, the bytes type has an additional class
   method to read data in that format:

   classmethod fromhex(string)

      This "bytes" class method returns a bytes object, decoding the
      given string object.  The string must contain two hexadecimal
      digits per byte, with ASCII whitespace being ignored.

      >>> bytes.fromhex('2Ef0 F1f2  ')
      b'.\xf0\xf1\xf2'

      Changed in version 3.7: "bytes.fromhex()" now skips all ASCII
      whitespace in the string, not just spaces.

   A reverse conversion function exists to transform a bytes object
   into its hexadecimal representation.

   hex()

      Return a string object containing two hexadecimal digits for
      each byte in the instance.

      >>> b'\xf0\xf1\xf2'.hex()
      'f0f1f2'

      If you want to make the hex string easier to read, you can
      specify a single character separator *sep* parameter to include
      in the output. By default between each byte.  A second optional
      *bytes_per_sep* parameter controls the spacing.  Positive values
      calculate the separator position from the right, negative values
      from the left.

      >>> value = b'\xf0\xf1\xf2'
      >>> value.hex('-')
      'f0-f1-f2'
      >>> value.hex('_', 2)
      'f0_f1f2'
      >>> b'UUDDLRLRAB'.hex(' ', -4)
      '55554444 4c524c52 4142'

      New in version 3.5.

      Changed in version 3.8: "bytes.hex()" now supports optional
      *sep* and *bytes_per_sep* parameters to insert separators
      between bytes in the hex output.

Since bytes objects are sequences of integers (akin to a tuple), for a
bytes object *b*, "b[0]" will be an integer, while "b[0:1]" will be a
bytes object of length 1.  (This contrasts with text strings, where
both indexing and slicing will produce a string of length 1)

The representation of bytes objects uses the literal format ("b'...'")
since it is often more useful than e.g. "bytes([46, 46, 46])".  You
can always convert a bytes object into a list of integers using
"list(b)".

Note: For Python 2.x users: In the Python 2.x series, a variety of
  implicit conversions between 8-bit strings (the closest thing 2.x
  offers to a built-in binary data type) and Unicode strings were
  permitted. This was a backwards compatibility workaround to account
  for the fact that Python originally only supported 8-bit text, and
  Unicode text was a later addition. In Python 3.x, those implicit
  conversions are gone - conversions between 8-bit binary data and
  Unicode text must be explicit, and bytes and string objects will
  always compare unequal.


Bytearray Objects
-----------------

"bytearray" objects are a mutable counterpart to "bytes" objects.

class bytearray([source[, encoding[, errors]]])

   There is no dedicated literal syntax for bytearray objects, instead
   they are always created by calling the constructor:

   * Creating an empty instance: "bytearray()"

   * Creating a zero-filled instance with a given length:
     "bytearray(10)"

   * From an iterable of integers: "bytearray(range(20))"

   * Copying existing binary data via the buffer protocol:
     "bytearray(b'Hi!')"

   As bytearray objects are mutable, they support the mutable sequence
   operations in addition to the common bytes and bytearray operations
   described in Bytes and Bytearray Operations.

   Also see the bytearray built-in.

   Since 2 hexadecimal digits correspond precisely to a single byte,
   hexadecimal numbers are a commonly used format for describing
   binary data. Accordingly, the bytearray type has an additional
   class method to read data in that format:

   classmethod fromhex(string)

      This "bytearray" class method returns bytearray object, decoding
      the given string object.  The string must contain two
      hexadecimal digits per byte, with ASCII whitespace being
      ignored.

      >>> bytearray.fromhex('2Ef0 F1f2  ')
      bytearray(b'.\xf0\xf1\xf2')

      Changed in version 3.7: "bytearray.fromhex()" now skips all
      ASCII whitespace in the string, not just spaces.

   A reverse conversion function exists to transform a bytearray
   object into its hexadecimal representation.

   hex()

      Return a string object containing two hexadecimal digits for
      each byte in the instance.

      >>> bytearray(b'\xf0\xf1\xf2').hex()
      'f0f1f2'

      New in version 3.5.

Since bytearray objects are sequences of integers (akin to a list),
for a bytearray object *b*, "b[0]" will be an integer, while "b[0:1]"
will be a bytearray object of length 1.  (This contrasts with text
strings, where both indexing and slicing will produce a string of
length 1)

The representation of bytearray objects uses the bytes literal format
("bytearray(b'...')") since it is often more useful than e.g.
"bytearray([46, 46, 46])".  You can always convert a bytearray object
into a list of integers using "list(b)".


Bytes and Bytearray Operations
------------------------------

Both bytes and bytearray objects support the common sequence
operations. They interoperate not just with operands of the same type,
but with any *bytes-like object*. Due to this flexibility, they can be
freely mixed in operations without causing errors. However, the return
type of the result may depend on the order of operands.

Note: The methods on bytes and bytearray objects don’t accept
  strings as their arguments, just as the methods on strings don’t
  accept bytes as their arguments.  For example, you have to write:

     a = "abc"
     b = a.replace("a", "f")

  and:

     a = b"abc"
     b = a.replace(b"a", b"f")

Some bytes and bytearray operations assume the use of ASCII compatible
binary formats, and hence should be avoided when working with
arbitrary binary data. These restrictions are covered below.

Note: Using these ASCII based operations to manipulate binary data
  that is not stored in an ASCII based format may lead to data
  corruption.

The following methods on bytes and bytearray objects can be used with
arbitrary binary data.

bytes.count(sub[, start[, end]])
bytearray.count(sub[, start[, end]])

   Return the number of non-overlapping occurrences of subsequence
   *sub* in the range [*start*, *end*].  Optional arguments *start*
   and *end* are interpreted as in slice notation.

   The subsequence to search for may be any *bytes-like object* or an
   integer in the range 0 to 255.

   Changed in version 3.3: Also accept an integer in the range 0 to
   255 as the subsequence.

bytes.decode(encoding="utf-8", errors="strict")
bytearray.decode(encoding="utf-8", errors="strict")

   Return a string decoded from the given bytes.  Default encoding is
   "'utf-8'". *errors* may be given to set a different error handling
   scheme.  The default for *errors* is "'strict'", meaning that
   encoding errors raise a "UnicodeError".  Other possible values are
   "'ignore'", "'replace'" and any other name registered via
   "codecs.register_error()", see section Error Handlers. For a list
   of possible encodings, see section Standard Encodings.

   Note: Passing the *encoding* argument to "str" allows decoding
     any *bytes-like object* directly, without needing to make a
     temporary bytes or bytearray object.

   Changed in version 3.1: Added support for keyword arguments.

bytes.endswith(suffix[, start[, end]])
bytearray.endswith(suffix[, start[, end]])

   Return "True" if the binary data ends with the specified *suffix*,
   otherwise return "False".  *suffix* can also be a tuple of suffixes
   to look for.  With optional *start*, test beginning at that
   position.  With optional *end*, stop comparing at that position.

   The suffix(es) to search for may be any *bytes-like object*.

bytes.find(sub[, start[, end]])
bytearray.find(sub[, start[, end]])

   Return the lowest index in the data where the subsequence *sub* is
   found, such that *sub* is contained in the slice "s[start:end]".
   Optional arguments *start* and *end* are interpreted as in slice
   notation.  Return "-1" if *sub* is not found.

   The subsequence to search for may be any *bytes-like object* or an
   integer in the range 0 to 255.

   Note: The "find()" method should be used only if you need to know
     the position of *sub*.  To check if *sub* is a substring or not,
     use the "in" operator:

        >>> b'Py' in b'Python'
        True

   Changed in version 3.3: Also accept an integer in the range 0 to
   255 as the subsequence.

bytes.index(sub[, start[, end]])
bytearray.index(sub[, start[, end]])

   Like "find()", but raise "ValueError" when the subsequence is not
   found.

   The subsequence to search for may be any *bytes-like object* or an
   integer in the range 0 to 255.

   Changed in version 3.3: Also accept an integer in the range 0 to
   255 as the subsequence.

bytes.join(iterable)
bytearray.join(iterable)

   Return a bytes or bytearray object which is the concatenation of
   the binary data sequences in *iterable*.  A "TypeError" will be
   raised if there are any values in *iterable* that are not *bytes-
   like objects*, including "str" objects.  The separator between
   elements is the contents of the bytes or bytearray object providing
   this method.

static bytes.maketrans(from, to)
static bytearray.maketrans(from, to)

   This static method returns a translation table usable for
   "bytes.translate()" that will map each character in *from* into the
   character at the same position in *to*; *from* and *to* must both
   be *bytes-like objects* and have the same length.

   New in version 3.1.

bytes.partition(sep)
bytearray.partition(sep)

   Split the sequence at the first occurrence of *sep*, and return a
   3-tuple containing the part before the separator, the separator
   itself or its bytearray copy, and the part after the separator. If
   the separator is not found, return a 3-tuple containing a copy of
   the original sequence, followed by two empty bytes or bytearray
   objects.

   The separator to search for may be any *bytes-like object*.

bytes.replace(old, new[, count])
bytearray.replace(old, new[, count])

   Return a copy of the sequence with all occurrences of subsequence
   *old* replaced by *new*.  If the optional argument *count* is
   given, only the first *count* occurrences are replaced.

   The subsequence to search for and its replacement may be any
   *bytes-like object*.

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.rfind(sub[, start[, end]])
bytearray.rfind(sub[, start[, end]])

   Return the highest index in the sequence where the subsequence
   *sub* is found, such that *sub* is contained within "s[start:end]".
   Optional arguments *start* and *end* are interpreted as in slice
   notation. Return "-1" on failure.

   The subsequence to search for may be any *bytes-like object* or an
   integer in the range 0 to 255.

   Changed in version 3.3: Also accept an integer in the range 0 to
   255 as the subsequence.

bytes.rindex(sub[, start[, end]])
bytearray.rindex(sub[, start[, end]])

   Like "rfind()" but raises "ValueError" when the subsequence *sub*
   is not found.

   The subsequence to search for may be any *bytes-like object* or an
   integer in the range 0 to 255.

   Changed in version 3.3: Also accept an integer in the range 0 to
   255 as the subsequence.

bytes.rpartition(sep)
bytearray.rpartition(sep)

   Split the sequence at the last occurrence of *sep*, and return a
   3-tuple containing the part before the separator, the separator
   itself or its bytearray copy, and the part after the separator. If
   the separator is not found, return a 3-tuple containing two empty
   bytes or bytearray objects, followed by a copy of the original
   sequence.

   The separator to search for may be any *bytes-like object*.

bytes.startswith(prefix[, start[, end]])
bytearray.startswith(prefix[, start[, end]])

   Return "True" if the binary data starts with the specified
   *prefix*, otherwise return "False".  *prefix* can also be a tuple
   of prefixes to look for.  With optional *start*, test beginning at
   that position.  With optional *end*, stop comparing at that
   position.

   The prefix(es) to search for may be any *bytes-like object*.

bytes.translate(table, /, delete=b'')
bytearray.translate(table, /, delete=b'')

   Return a copy of the bytes or bytearray object where all bytes
   occurring in the optional argument *delete* are removed, and the
   remaining bytes have been mapped through the given translation
   table, which must be a bytes object of length 256.

   You can use the "bytes.maketrans()" method to create a translation
   table.

   Set the *table* argument to "None" for translations that only
   delete characters:

      >>> b'read this short text'.translate(None, b'aeiou')
      b'rd ths shrt txt'

   Changed in version 3.6: *delete* is now supported as a keyword
   argument.

The following methods on bytes and bytearray objects have default
behaviours that assume the use of ASCII compatible binary formats, but
can still be used with arbitrary binary data by passing appropriate
arguments. Note that all of the bytearray methods in this section do
*not* operate in place, and instead produce new objects.

bytes.center(width[, fillbyte])
bytearray.center(width[, fillbyte])

   Return a copy of the object centered in a sequence of length
   *width*. Padding is done using the specified *fillbyte* (default is
   an ASCII space). For "bytes" objects, the original sequence is
   returned if *width* is less than or equal to "len(s)".

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.ljust(width[, fillbyte])
bytearray.ljust(width[, fillbyte])

   Return a copy of the object left justified in a sequence of length
   *width*. Padding is done using the specified *fillbyte* (default is
   an ASCII space). For "bytes" objects, the original sequence is
   returned if *width* is less than or equal to "len(s)".

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.lstrip([chars])
bytearray.lstrip([chars])

   Return a copy of the sequence with specified leading bytes removed.
   The *chars* argument is a binary sequence specifying the set of
   byte values to be removed - the name refers to the fact this method
   is usually used with ASCII characters.  If omitted or "None", the
   *chars* argument defaults to removing ASCII whitespace.  The
   *chars* argument is not a prefix; rather, all combinations of its
   values are stripped:

      >>> b'   spacious   '.lstrip()
      b'spacious   '
      >>> b'www.example.com'.lstrip(b'cmowz.')
      b'example.com'

   The binary sequence of byte values to remove may be any *bytes-like
   object*.

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.rjust(width[, fillbyte])
bytearray.rjust(width[, fillbyte])

   Return a copy of the object right justified in a sequence of length
   *width*. Padding is done using the specified *fillbyte* (default is
   an ASCII space). For "bytes" objects, the original sequence is
   returned if *width* is less than or equal to "len(s)".

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.rsplit(sep=None, maxsplit=-1)
bytearray.rsplit(sep=None, maxsplit=-1)

   Split the binary sequence into subsequences of the same type, using
   *sep* as the delimiter string. If *maxsplit* is given, at most
   *maxsplit* splits are done, the *rightmost* ones.  If *sep* is not
   specified or "None", any subsequence consisting solely of ASCII
   whitespace is a separator. Except for splitting from the right,
   "rsplit()" behaves like "split()" which is described in detail
   below.

bytes.rstrip([chars])
bytearray.rstrip([chars])

   Return a copy of the sequence with specified trailing bytes
   removed.  The *chars* argument is a binary sequence specifying the
   set of byte values to be removed - the name refers to the fact this
   method is usually used with ASCII characters.  If omitted or
   "None", the *chars* argument defaults to removing ASCII whitespace.
   The *chars* argument is not a suffix; rather, all combinations of
   its values are stripped:

      >>> b'   spacious   '.rstrip()
      b'   spacious'
      >>> b'mississippi'.rstrip(b'ipz')
      b'mississ'

   The binary sequence of byte values to remove may be any *bytes-like
   object*.

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.split(sep=None, maxsplit=-1)
bytearray.split(sep=None, maxsplit=-1)

   Split the binary sequence into subsequences of the same type, using
   *sep* as the delimiter string. If *maxsplit* is given and non-
   negative, at most *maxsplit* splits are done (thus, the list will
   have at most "maxsplit+1" elements).  If *maxsplit* is not
   specified or is "-1", then there is no limit on the number of
   splits (all possible splits are made).

   If *sep* is given, consecutive delimiters are not grouped together
   and are deemed to delimit empty subsequences (for example,
   "b'1,,2'.split(b',')" returns "[b'1', b'', b'2']").  The *sep*
   argument may consist of a multibyte sequence (for example,
   "b'1<>2<>3'.split(b'<>')" returns "[b'1', b'2', b'3']"). Splitting
   an empty sequence with a specified separator returns "[b'']" or
   "[bytearray(b'')]" depending on the type of object being split.
   The *sep* argument may be any *bytes-like object*.

   For example:

      >>> b'1,2,3'.split(b',')
      [b'1', b'2', b'3']
      >>> b'1,2,3'.split(b',', maxsplit=1)
      [b'1', b'2,3']
      >>> b'1,2,,3,'.split(b',')
      [b'1', b'2', b'', b'3', b'']

   If *sep* is not specified or is "None", a different splitting
   algorithm is applied: runs of consecutive ASCII whitespace are
   regarded as a single separator, and the result will contain no
   empty strings at the start or end if the sequence has leading or
   trailing whitespace.  Consequently, splitting an empty sequence or
   a sequence consisting solely of ASCII whitespace without a
   specified separator returns "[]".

   For example:

      >>> b'1 2 3'.split()
      [b'1', b'2', b'3']
      >>> b'1 2 3'.split(maxsplit=1)
      [b'1', b'2 3']
      >>> b'   1   2   3   '.split()
      [b'1', b'2', b'3']

bytes.strip([chars])
bytearray.strip([chars])

   Return a copy of the sequence with specified leading and trailing
   bytes removed. The *chars* argument is a binary sequence specifying
   the set of byte values to be removed - the name refers to the fact
   this method is usually used with ASCII characters.  If omitted or
   "None", the *chars* argument defaults to removing ASCII whitespace.
   The *chars* argument is not a prefix or suffix; rather, all
   combinations of its values are stripped:

      >>> b'   spacious   '.strip()
      b'spacious'
      >>> b'www.example.com'.strip(b'cmowz.')
      b'example'

   The binary sequence of byte values to remove may be any *bytes-like
   object*.

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

The following methods on bytes and bytearray objects assume the use of
ASCII compatible binary formats and should not be applied to arbitrary
binary data. Note that all of the bytearray methods in this section do
*not* operate in place, and instead produce new objects.

bytes.capitalize()
bytearray.capitalize()

   Return a copy of the sequence with each byte interpreted as an
   ASCII character, and the first byte capitalized and the rest
   lowercased. Non-ASCII byte values are passed through unchanged.

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.expandtabs(tabsize=8)
bytearray.expandtabs(tabsize=8)

   Return a copy of the sequence where all ASCII tab characters are
   replaced by one or more ASCII spaces, depending on the current
   column and the given tab size.  Tab positions occur every *tabsize*
   bytes (default is 8, giving tab positions at columns 0, 8, 16 and
   so on).  To expand the sequence, the current column is set to zero
   and the sequence is examined byte by byte.  If the byte is an ASCII
   tab character ("b'\t'"), one or more space characters are inserted
   in the result until the current column is equal to the next tab
   position. (The tab character itself is not copied.)  If the current
   byte is an ASCII newline ("b'\n'") or carriage return ("b'\r'"), it
   is copied and the current column is reset to zero.  Any other byte
   value is copied unchanged and the current column is incremented by
   one regardless of how the byte value is represented when printed:

      >>> b'01\t012\t0123\t01234'.expandtabs()
      b'01      012     0123    01234'
      >>> b'01\t012\t0123\t01234'.expandtabs(4)
      b'01  012 0123    01234'

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.isalnum()
bytearray.isalnum()

   Return "True" if all bytes in the sequence are alphabetical ASCII
   characters or ASCII decimal digits and the sequence is not empty,
   "False" otherwise. Alphabetic ASCII characters are those byte
   values in the sequence
   "b'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'". ASCII
   decimal digits are those byte values in the sequence
   "b'0123456789'".

   For example:

      >>> b'ABCabc1'.isalnum()
      True
      >>> b'ABC abc1'.isalnum()
      False

bytes.isalpha()
bytearray.isalpha()

   Return "True" if all bytes in the sequence are alphabetic ASCII
   characters and the sequence is not empty, "False" otherwise.
   Alphabetic ASCII characters are those byte values in the sequence
   "b'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'".

   For example:

      >>> b'ABCabc'.isalpha()
      True
      >>> b'ABCabc1'.isalpha()
      False

bytes.isascii()
bytearray.isascii()

   Return "True" if the sequence is empty or all bytes in the sequence
   are ASCII, "False" otherwise. ASCII bytes are in the range 0-0x7F.

   New in version 3.7.

bytes.isdigit()
bytearray.isdigit()

   Return "True" if all bytes in the sequence are ASCII decimal digits
   and the sequence is not empty, "False" otherwise. ASCII decimal
   digits are those byte values in the sequence "b'0123456789'".

   For example:

      >>> b'1234'.isdigit()
      True
      >>> b'1.23'.isdigit()
      False

bytes.islower()
bytearray.islower()

   Return "True" if there is at least one lowercase ASCII character in
   the sequence and no uppercase ASCII characters, "False" otherwise.

   For example:

      >>> b'hello world'.islower()
      True
      >>> b'Hello world'.islower()
      False

   Lowercase ASCII characters are those byte values in the sequence
   "b'abcdefghijklmnopqrstuvwxyz'". Uppercase ASCII characters are
   those byte values in the sequence "b'ABCDEFGHIJKLMNOPQRSTUVWXYZ'".

bytes.isspace()
bytearray.isspace()

   Return "True" if all bytes in the sequence are ASCII whitespace and
   the sequence is not empty, "False" otherwise.  ASCII whitespace
   characters are those byte values in the sequence "b' \t\n\r\x0b\f'"
   (space, tab, newline, carriage return, vertical tab, form feed).

bytes.istitle()
bytearray.istitle()

   Return "True" if the sequence is ASCII titlecase and the sequence
   is not empty, "False" otherwise. See "bytes.title()" for more
   details on the definition of “titlecase”.

   For example:

      >>> b'Hello World'.istitle()
      True
      >>> b'Hello world'.istitle()
      False

bytes.isupper()
bytearray.isupper()

   Return "True" if there is at least one uppercase alphabetic ASCII
   character in the sequence and no lowercase ASCII characters,
   "False" otherwise.

   For example:

      >>> b'HELLO WORLD'.isupper()
      True
      >>> b'Hello world'.isupper()
      False

   Lowercase ASCII characters are those byte values in the sequence
   "b'abcdefghijklmnopqrstuvwxyz'". Uppercase ASCII characters are
   those byte values in the sequence "b'ABCDEFGHIJKLMNOPQRSTUVWXYZ'".

bytes.lower()
bytearray.lower()

   Return a copy of the sequence with all the uppercase ASCII
   characters converted to their corresponding lowercase counterpart.

   For example:

      >>> b'Hello World'.lower()
      b'hello world'

   Lowercase ASCII characters are those byte values in the sequence
   "b'abcdefghijklmnopqrstuvwxyz'". Uppercase ASCII characters are
   those byte values in the sequence "b'ABCDEFGHIJKLMNOPQRSTUVWXYZ'".

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.splitlines(keepends=False)
bytearray.splitlines(keepends=False)

   Return a list of the lines in the binary sequence, breaking at
   ASCII line boundaries. This method uses the *universal newlines*
   approach to splitting lines. Line breaks are not included in the
   resulting list unless *keepends* is given and true.

   For example:

      >>> b'ab c\n\nde fg\rkl\r\n'.splitlines()
      [b'ab c', b'', b'de fg', b'kl']
      >>> b'ab c\n\nde fg\rkl\r\n'.splitlines(keepends=True)
      [b'ab c\n', b'\n', b'de fg\r', b'kl\r\n']

   Unlike "split()" when a delimiter string *sep* is given, this
   method returns an empty list for the empty string, and a terminal
   line break does not result in an extra line:

      >>> b"".split(b'\n'), b"Two lines\n".split(b'\n')
      ([b''], [b'Two lines', b''])
      >>> b"".splitlines(), b"One line\n".splitlines()
      ([], [b'One line'])

bytes.swapcase()
bytearray.swapcase()

   Return a copy of the sequence with all the lowercase ASCII
   characters converted to their corresponding uppercase counterpart
   and vice-versa.

   For example:

      >>> b'Hello World'.swapcase()
      b'hELLO wORLD'

   Lowercase ASCII characters are those byte values in the sequence
   "b'abcdefghijklmnopqrstuvwxyz'". Uppercase ASCII characters are
   those byte values in the sequence "b'ABCDEFGHIJKLMNOPQRSTUVWXYZ'".

   Unlike "str.swapcase()", it is always the case that
   "bin.swapcase().swapcase() == bin" for the binary versions. Case
   conversions are symmetrical in ASCII, even though that is not
   generally true for arbitrary Unicode code points.

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.title()
bytearray.title()

   Return a titlecased version of the binary sequence where words
   start with an uppercase ASCII character and the remaining
   characters are lowercase. Uncased byte values are left unmodified.

   For example:

      >>> b'Hello world'.title()
      b'Hello World'

   Lowercase ASCII characters are those byte values in the sequence
   "b'abcdefghijklmnopqrstuvwxyz'". Uppercase ASCII characters are
   those byte values in the sequence "b'ABCDEFGHIJKLMNOPQRSTUVWXYZ'".
   All other byte values are uncased.

   The algorithm uses a simple language-independent definition of a
   word as groups of consecutive letters.  The definition works in
   many contexts but it means that apostrophes in contractions and
   possessives form word boundaries, which may not be the desired
   result:

      >>> b"they're bill's friends from the UK".title()
      b"They'Re Bill'S Friends From The Uk"

   A workaround for apostrophes can be constructed using regular
   expressions:

      >>> import re
      >>> def titlecase(s):
      ...     return re.sub(rb"[A-Za-z]+('[A-Za-z]+)?",
      ...                   lambda mo: mo.group(0)[0:1].upper() +
      ...                              mo.group(0)[1:].lower(),
      ...                   s)
      ...
      >>> titlecase(b"they're bill's friends.")
      b"They're Bill's Friends."

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.upper()
bytearray.upper()

   Return a copy of the sequence with all the lowercase ASCII
   characters converted to their corresponding uppercase counterpart.

   For example:

      >>> b'Hello World'.upper()
      b'HELLO WORLD'

   Lowercase ASCII characters are those byte values in the sequence
   "b'abcdefghijklmnopqrstuvwxyz'". Uppercase ASCII characters are
   those byte values in the sequence "b'ABCDEFGHIJKLMNOPQRSTUVWXYZ'".

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.

bytes.zfill(width)
bytearray.zfill(width)

   Return a copy of the sequence left filled with ASCII "b'0'" digits
   to make a sequence of length *width*. A leading sign prefix
   ("b'+'"/ "b'-'") is handled by inserting the padding *after* the
   sign character rather than before. For "bytes" objects, the
   original sequence is returned if *width* is less than or equal to
   "len(seq)".

   For example:

      >>> b"42".zfill(5)
      b'00042'
      >>> b"-42".zfill(5)
      b'-0042'

   Note: The bytearray version of this method does *not* operate in
     place - it always produces a new object, even if no changes were
     made.


"printf"-style Bytes Formatting
-------------------------------

Note: The formatting operations described here exhibit a variety of
  quirks that lead to a number of common errors (such as failing to
  display tuples and dictionaries correctly).  If the value being
  printed may be a tuple or dictionary, wrap it in a tuple.

Bytes objects ("bytes"/"bytearray") have one unique built-in
operation: the "%" operator (modulo). This is also known as the bytes
*formatting* or *interpolation* operator. Given "format % values"
(where *format* is a bytes object), "%" conversion specifications in
*format* are replaced with zero or more elements of *values*. The
effect is similar to using the "sprintf()" in the C language.

If *format* requires a single argument, *values* may be a single non-
tuple object. [5]  Otherwise, *values* must be a tuple with exactly
the number of items specified by the format bytes object, or a single
mapping object (for example, a dictionary).

A conversion specifier contains two or more characters and has the
following components, which must occur in this order:

1. The "'%'" character, which marks the start of the specifier.

2. Mapping key (optional), consisting of a parenthesised sequence
   of characters (for example, "(somename)").

3. Conversion flags (optional), which affect the result of some
   conversion types.

4. Minimum field width (optional).  If specified as an "'*'"
   (asterisk), the actual width is read from the next element of the
   tuple in *values*, and the object to convert comes after the
   minimum field width and optional precision.

5. Precision (optional), given as a "'.'" (dot) followed by the
   precision.  If specified as "'*'" (an asterisk), the actual
   precision is read from the next element of the tuple in *values*,
   and the value to convert comes after the precision.

6. Length modifier (optional).

7. Conversion type.

When the right argument is a dictionary (or other mapping type), then
the formats in the bytes object *must* include a parenthesised mapping
key into that dictionary inserted immediately after the "'%'"
character. The mapping key selects the value to be formatted from the
mapping.  For example:

>>> print(b'%(language)s has %(number)03d quote types.' %
...       {b'language': b"Python", b"number": 2})
b'Python has 002 quote types.'

In this case no "*" specifiers may occur in a format (since they
require a sequential parameter list).

The conversion flag characters are:

+-----------+-----------------------------------------------------------------------+
| Flag      | Meaning                                                               |
|===========|=======================================================================|
| "'#'"     | The value conversion will use the “alternate form” (where defined     |
|           | below).                                                               |
+-----------+-----------------------------------------------------------------------+
| "'0'"     | The conversion will be zero padded for numeric values.                |
+-----------+-----------------------------------------------------------------------+
| "'-'"     | The converted value is left adjusted (overrides the "'0'" conversion  |
|           | if both are given).                                                   |
+-----------+-----------------------------------------------------------------------+
| "' '"     | (a space) A blank should be left before a positive number (or empty   |
|           | string) produced by a signed conversion.                              |
+-----------+-----------------------------------------------------------------------+
| "'+'"     | A sign character ("'+'" or "'-'") will precede the conversion         |
|           | (overrides a “space” flag).                                           |
+-----------+-----------------------------------------------------------------------+

A length modifier ("h", "l", or "L") may be present, but is ignored as
it is not necessary for Python – so e.g. "%ld" is identical to "%d".

The conversion types are:

+--------------+-------------------------------------------------------+---------+
| Conversion   | Meaning                                               | Notes   |
|==============|=======================================================|=========|
| "'d'"        | Signed integer decimal.                               |         |
+--------------+-------------------------------------------------------+---------+
| "'i'"        | Signed integer decimal.                               |         |
+--------------+-------------------------------------------------------+---------+
| "'o'"        | Signed octal value.                                   | (1)     |
+--------------+-------------------------------------------------------+---------+
| "'u'"        | Obsolete type – it is identical to "'d'".             | (8)     |
+--------------+-------------------------------------------------------+---------+
| "'x'"        | Signed hexadecimal (lowercase).                       | (2)     |
+--------------+-------------------------------------------------------+---------+
| "'X'"        | Signed hexadecimal (uppercase).                       | (2)     |
+--------------+-------------------------------------------------------+---------+
| "'e'"        | Floating point exponential format (lowercase).        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'E'"        | Floating point exponential format (uppercase).        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'f'"        | Floating point decimal format.                        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'F'"        | Floating point decimal format.                        | (3)     |
+--------------+-------------------------------------------------------+---------+
| "'g'"        | Floating point format. Uses lowercase exponential     | (4)     |
|              | format if exponent is less than -4 or not less than   |         |
|              | precision, decimal format otherwise.                  |         |
+--------------+-------------------------------------------------------+---------+
| "'G'"        | Floating point format. Uses uppercase exponential     | (4)     |
|              | format if exponent is less than -4 or not less than   |         |
|              | precision, decimal format otherwise.                  |         |
+--------------+-------------------------------------------------------+---------+
| "'c'"        | Single byte (accepts integer or single byte objects). |         |
+--------------+-------------------------------------------------------+---------+
| "'b'"        | Bytes (any object that follows the buffer protocol or | (5)     |
|              | has "__bytes__()").                                   |         |
+--------------+-------------------------------------------------------+---------+
| "'s'"        | "'s'" is an alias for "'b'" and should only be used   | (6)     |
|              | for Python2/3 code bases.                             |         |
+--------------+-------------------------------------------------------+---------+
| "'a'"        | Bytes (converts any Python object using               | (5)     |
|              | "repr(obj).encode('ascii','backslashreplace)").       |         |
+--------------+-------------------------------------------------------+---------+
| "'r'"        | "'r'" is an alias for "'a'" and should only be used   | (7)     |
|              | for Python2/3 code bases.                             |         |
+--------------+-------------------------------------------------------+---------+
| "'%'"        | No argument is converted, results in a "'%'"          |         |
|              | character in the result.                              |         |
+--------------+-------------------------------------------------------+---------+

Notes:

1. The alternate form causes a leading octal specifier ("'0o'") to
   be inserted before the first digit.

2. The alternate form causes a leading "'0x'" or "'0X'" (depending
   on whether the "'x'" or "'X'" format was used) to be inserted
   before the first digit.

3. The alternate form causes the result to always contain a decimal
   point, even if no digits follow it.

   The precision determines the number of digits after the decimal
   point and defaults to 6.

4. The alternate form causes the result to always contain a decimal
   point, and trailing zeroes are not removed as they would otherwise
   be.

   The precision determines the number of significant digits before
   and after the decimal point and defaults to 6.

5. If precision is "N", the output is truncated to "N" characters.

6. "b'%s'" is deprecated, but will not be removed during the 3.x
   series.

7. "b'%r'" is deprecated, but will not be removed during the 3.x
   series.

8. See **PEP 237**.

Note: The bytearray version of this method does *not* operate in
  place - it always produces a new object, even if no changes were
  made.

See also: **PEP 461** - Adding % formatting to bytes and bytearray

New in version 3.5.


Memory Views
------------

"memoryview" objects allow Python code to access the internal data of
an object that supports the buffer protocol without copying.

class memoryview(obj)

   Create a "memoryview" that references *obj*.  *obj* must support
   the buffer protocol.  Built-in objects that support the buffer
   protocol include "bytes" and "bytearray".

   A "memoryview" has the notion of an *element*, which is the atomic
   memory unit handled by the originating object *obj*.  For many
   simple types such as "bytes" and "bytearray", an element is a
   single byte, but other types such as "array.array" may have bigger
   elements.

   "len(view)" is equal to the length of "tolist". If "view.ndim = 0",
   the length is 1. If "view.ndim = 1", the length is equal to the
   number of elements in the view. For higher dimensions, the length
   is equal to the length of the nested list representation of the
   view. The "itemsize" attribute will give you the number of bytes in
   a single element.

   A "memoryview" supports slicing and indexing to expose its data.
   One-dimensional slicing will result in a subview:

      >>> v = memoryview(b'abcefg')
      >>> v[1]
      98
      >>> v[-1]
      103
      >>> v[1:4]
      <memory at 0x7f3ddc9f4350>
      >>> bytes(v[1:4])
      b'bce'

   If "format" is one of the native format specifiers from the
   "struct" module, indexing with an integer or a tuple of integers is
   also supported and returns a single *element* with the correct
   type.  One-dimensional memoryviews can be indexed with an integer
   or a one-integer tuple.  Multi-dimensional memoryviews can be
   indexed with tuples of exactly *ndim* integers where *ndim* is the
   number of dimensions.  Zero-dimensional memoryviews can be indexed
   with the empty tuple.

   Here is an example with a non-byte format:

      >>> import array
      >>> a = array.array('l', [-11111111, 22222222, -33333333, 44444444])
      >>> m = memoryview(a)
      >>> m[0]
      -11111111
      >>> m[-1]
      44444444
      >>> m[::2].tolist()
      [-11111111, -33333333]

   If the underlying object is writable, the memoryview supports one-
   dimensional slice assignment. Resizing is not allowed:

      >>> data = bytearray(b'abcefg')
      >>> v = memoryview(data)
      >>> v.readonly
      False
      >>> v[0] = ord(b'z')
      >>> data
      bytearray(b'zbcefg')
      >>> v[1:4] = b'123'
      >>> data
      bytearray(b'z123fg')
      >>> v[2:3] = b'spam'
      Traceback (most recent call last):
        File "<stdin>", line 1, in <module>
      ValueError: memoryview assignment: lvalue and rvalue have different structures
      >>> v[2:6] = b'spam'
      >>> data
      bytearray(b'z1spam')

   One-dimensional memoryviews of hashable (read-only) types with
   formats ‘B’, ‘b’ or ‘c’ are also hashable. The hash is defined as
   "hash(m) == hash(m.tobytes())":

      >>> v = memoryview(b'abcefg')
      >>> hash(v) == hash(b'abcefg')
      True
      >>> hash(v[2:4]) == hash(b'ce')
      True
      >>> hash(v[::-2]) == hash(b'abcefg'[::-2])
      True

   Changed in version 3.3: One-dimensional memoryviews can now be
   sliced. One-dimensional memoryviews with formats ‘B’, ‘b’ or ‘c’
   are now hashable.

   Changed in version 3.4: memoryview is now registered automatically
   with "collections.abc.Sequence"

   Changed in version 3.5: memoryviews can now be indexed with tuple
   of integers.

   "memoryview" has several methods:

   __eq__(exporter)

      A memoryview and a **PEP 3118** exporter are equal if their
      shapes are equivalent and if all corresponding values are equal
      when the operands’ respective format codes are interpreted using
      "struct" syntax.

      For the subset of "struct" format strings currently supported by
      "tolist()", "v" and "w" are equal if "v.tolist() == w.tolist()":

         >>> import array
         >>> a = array.array('I', [1, 2, 3, 4, 5])
         >>> b = array.array('d', [1.0, 2.0, 3.0, 4.0, 5.0])
         >>> c = array.array('b', [5, 3, 1])
         >>> x = memoryview(a)
         >>> y = memoryview(b)
         >>> x == a == y == b
         True
         >>> x.tolist() == a.tolist() == y.tolist() == b.tolist()
         True
         >>> z = y[::-2]
         >>> z == c
         True
         >>> z.tolist() == c.tolist()
         True

      If either format string is not supported by the "struct" module,
      then the objects will always compare as unequal (even if the
      format strings and buffer contents are identical):

         >>> from ctypes import BigEndianStructure, c_long
         >>> class BEPoint(BigEndianStructure):
         ...     _fields_ = [("x", c_long), ("y", c_long)]
         ...
         >>> point = BEPoint(100, 200)
         >>> a = memoryview(point)
         >>> b = memoryview(point)
         >>> a == point
         False
         >>> a == b
         False

      Note that, as with floating point numbers, "v is w" does *not*
      imply "v == w" for memoryview objects.

      Changed in version 3.3: Previous versions compared the raw
      memory disregarding the item format and the logical array
      structure.

   tobytes(order=None)

      Return the data in the buffer as a bytestring.  This is
      equivalent to calling the "bytes" constructor on the memoryview.

         >>> m = memoryview(b"abc")
         >>> m.tobytes()
         b'abc'
         >>> bytes(m)
         b'abc'

      For non-contiguous arrays the result is equal to the flattened
      list representation with all elements converted to bytes.
      "tobytes()" supports all format strings, including those that
      are not in "struct" module syntax.

      New in version 3.8: *order* can be {‘C’, ‘F’, ‘A’}.  When
      *order* is ‘C’ or ‘F’, the data of the original array is
      converted to C or Fortran order. For contiguous views, ‘A’
      returns an exact copy of the physical memory. In particular, in-
      memory Fortran order is preserved. For non-contiguous views, the
      data is converted to C first. *order=None* is the same as
      *order=’C’*.

   hex()

      Return a string object containing two hexadecimal digits for
      each byte in the buffer.

         >>> m = memoryview(b"abc")
         >>> m.hex()
         '616263'

      New in version 3.5.

   tolist()

      Return the data in the buffer as a list of elements.

         >>> memoryview(b'abc').tolist()
         [97, 98, 99]
         >>> import array
         >>> a = array.array('d', [1.1, 2.2, 3.3])
         >>> m = memoryview(a)
         >>> m.tolist()
         [1.1, 2.2, 3.3]

      Changed in version 3.3: "tolist()" now supports all single
      character native formats in "struct" module syntax as well as
      multi-dimensional representations.

   toreadonly()

      Return a readonly version of the memoryview object.  The
      original memoryview object is unchanged.

         >>> m = memoryview(bytearray(b'abc'))
         >>> mm = m.toreadonly()
         >>> mm.tolist()
         [89, 98, 99]
         >>> mm[0] = 42
         Traceback (most recent call last):
           File "<stdin>", line 1, in <module>
         TypeError: cannot modify read-only memory
         >>> m[0] = 43
         >>> mm.tolist()
         [43, 98, 99]

      New in version 3.8.

   release()

      Release the underlying buffer exposed by the memoryview object.
      Many objects take special actions when a view is held on them
      (for example, a "bytearray" would temporarily forbid resizing);
      therefore, calling release() is handy to remove these
      restrictions (and free any dangling resources) as soon as
      possible.

      After this method has been called, any further operation on the
      view raises a "ValueError" (except "release()" itself which can
      be called multiple times):

         >>> m = memoryview(b'abc')
         >>> m.release()
         >>> m[0]
         Traceback (most recent call last):
           File "<stdin>", line 1, in <module>
         ValueError: operation forbidden on released memoryview object

      The context management protocol can be used for a similar
      effect, using the "with" statement:

         >>> with memoryview(b'abc') as m:
         ...     m[0]
         ...
         97
         >>> m[0]
         Traceback (most recent call last):
           File "<stdin>", line 1, in <module>
         ValueError: operation forbidden on released memoryview object

      New in version 3.2.

   cast(format[, shape])

      Cast a memoryview to a new format or shape. *shape* defaults to
      "[byte_length//new_itemsize]", which means that the result view
      will be one-dimensional. The return value is a new memoryview,
      but the buffer itself is not copied. Supported casts are 1D ->
      C-*contiguous* and C-contiguous -> 1D.

      The destination format is restricted to a single element native
      format in "struct" syntax. One of the formats must be a byte
      format (‘B’, ‘b’ or ‘c’). The byte length of the result must be
      the same as the original length.

      Cast 1D/long to 1D/unsigned bytes:

         >>> import array
         >>> a = array.array('l', [1,2,3])
         >>> x = memoryview(a)
         >>> x.format
         'l'
         >>> x.itemsize
         8
         >>> len(x)
         3
         >>> x.nbytes
         24
         >>> y = x.cast('B')
         >>> y.format
         'B'
         >>> y.itemsize
         1
         >>> len(y)
         24
         >>> y.nbytes
         24

      Cast 1D/unsigned bytes to 1D/char:

         >>> b = bytearray(b'zyz')
         >>> x = memoryview(b)
         >>> x[0] = b'a'
         Traceback (most recent call last):
           File "<stdin>", line 1, in <module>
         ValueError: memoryview: invalid value for format "B"
         >>> y = x.cast('c')
         >>> y[0] = b'a'
         >>> b
         bytearray(b'ayz')

      Cast 1D/bytes to 3D/ints to 1D/signed char:

         >>> import struct
         >>> buf = struct.pack("i"*12, *list(range(12)))
         >>> x = memoryview(buf)
         >>> y = x.cast('i', shape=[2,2,3])
         >>> y.tolist()
         [[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]]]
         >>> y.format
         'i'
         >>> y.itemsize
         4
         >>> len(y)
         2
         >>> y.nbytes
         48
         >>> z = y.cast('b')
         >>> z.format
         'b'
         >>> z.itemsize
         1
         >>> len(z)
         48
         >>> z.nbytes
         48

      Cast 1D/unsigned long to 2D/unsigned long:

         >>> buf = struct.pack("L"*6, *list(range(6)))
         >>> x = memoryview(buf)
         >>> y = x.cast('L', shape=[2,3])
         >>> len(y)
         2
         >>> y.nbytes
         48
         >>> y.tolist()
         [[0, 1, 2], [3, 4, 5]]

      New in version 3.3.

      Changed in version 3.5: The source format is no longer
      restricted when casting to a byte view.

   There are also several readonly attributes available:

   obj

      The underlying object of the memoryview:

         >>> b  = bytearray(b'xyz')
         >>> m = memoryview(b)
         >>> m.obj is b
         True

      New in version 3.3.

   nbytes

      "nbytes == product(shape) * itemsize == len(m.tobytes())". This
      is the amount of space in bytes that the array would use in a
      contiguous representation. It is not necessarily equal to
      "len(m)":

         >>> import array
         >>> a = array.array('i', [1,2,3,4,5])
         >>> m = memoryview(a)
         >>> len(m)
         5
         >>> m.nbytes
         20
         >>> y = m[::2]
         >>> len(y)
         3
         >>> y.nbytes
         12
         >>> len(y.tobytes())
         12

      Multi-dimensional arrays:

         >>> import struct
         >>> buf = struct.pack("d"*12, *[1.5*x for x in range(12)])
         >>> x = memoryview(buf)
         >>> y = x.cast('d', shape=[3,4])
         >>> y.tolist()
         [[0.0, 1.5, 3.0, 4.5], [6.0, 7.5, 9.0, 10.5], [12.0, 13.5, 15.0, 16.5]]
         >>> len(y)
         3
         >>> y.nbytes
         96

      New in version 3.3.

   readonly

      A bool indicating whether the memory is read only.

   format

      A string containing the format (in "struct" module style) for
      each element in the view. A memoryview can be created from
      exporters with arbitrary format strings, but some methods (e.g.
      "tolist()") are restricted to native single element formats.

      Changed in version 3.3: format "'B'" is now handled according to
      the struct module syntax. This means that "memoryview(b'abc')[0]
      == b'abc'[0] == 97".

   itemsize

      The size in bytes of each element of the memoryview:

         >>> import array, struct
         >>> m = memoryview(array.array('H', [32000, 32001, 32002]))
         >>> m.itemsize
         2
         >>> m[0]
         32000
         >>> struct.calcsize('H') == m.itemsize
         True

   ndim

      An integer indicating how many dimensions of a multi-dimensional
      array the memory represents.

   shape

      A tuple of integers the length of "ndim" giving the shape of the
      memory as an N-dimensional array.

      Changed in version 3.3: An empty tuple instead of "None" when
      ndim = 0.

   strides

      A tuple of integers the length of "ndim" giving the size in
      bytes to access each element for each dimension of the array.

      Changed in version 3.3: An empty tuple instead of "None" when
      ndim = 0.

   suboffsets

      Used internally for PIL-style arrays. The value is informational
      only.

   c_contiguous

      A bool indicating whether the memory is C-*contiguous*.

      New in version 3.3.

   f_contiguous

      A bool indicating whether the memory is Fortran *contiguous*.

      New in version 3.3.

   contiguous

      A bool indicating whether the memory is *contiguous*.

      New in version 3.3.


Set Types — "set", "frozenset"
==============================

A *set* object is an unordered collection of distinct *hashable*
objects. Common uses include membership testing, removing duplicates
from a sequence, and computing mathematical operations such as
intersection, union, difference, and symmetric difference. (For other
containers see the built-in "dict", "list", and "tuple" classes, and
the "collections" module.)

Like other collections, sets support "x in set", "len(set)", and "for
x in set".  Being an unordered collection, sets do not record element
position or order of insertion.  Accordingly, sets do not support
indexing, slicing, or other sequence-like behavior.

There are currently two built-in set types, "set" and "frozenset". The
"set" type is mutable — the contents can be changed using methods like
"add()" and "remove()".  Since it is mutable, it has no hash value and
cannot be used as either a dictionary key or as an element of another
set.  The "frozenset" type is immutable and *hashable* — its contents
cannot be altered after it is created; it can therefore be used as a
dictionary key or as an element of another set.

Non-empty sets (not frozensets) can be created by placing a comma-
separated list of elements within braces, for example: "{'jack',
'sjoerd'}", in addition to the "set" constructor.

The constructors for both classes work the same:

class set([iterable])
class frozenset([iterable])

   Return a new set or frozenset object whose elements are taken from
   *iterable*.  The elements of a set must be *hashable*.  To
   represent sets of sets, the inner sets must be "frozenset" objects.
   If *iterable* is not specified, a new empty set is returned.

   Instances of "set" and "frozenset" provide the following
   operations:

   len(s)

      Return the number of elements in set *s* (cardinality of *s*).

   x in s

      Test *x* for membership in *s*.

   x not in s

      Test *x* for non-membership in *s*.

   isdisjoint(other)

      Return "True" if the set has no elements in common with *other*.
      Sets are disjoint if and only if their intersection is the empty
      set.

   issubset(other)
   set <= other

      Test whether every element in the set is in *other*.

   set < other

      Test whether the set is a proper subset of *other*, that is,
      "set <= other and set != other".

   issuperset(other)
   set >= other

      Test whether every element in *other* is in the set.

   set > other

      Test whether the set is a proper superset of *other*, that is,
      "set >= other and set != other".

   union(*others)
   set | other | ...

      Return a new set with elements from the set and all others.

   intersection(*others)
   set & other & ...

      Return a new set with elements common to the set and all others.

   difference(*others)
   set - other - ...

      Return a new set with elements in the set that are not in the
      others.

   symmetric_difference(other)
   set ^ other

      Return a new set with elements in either the set or *other* but
      not both.

   copy()

      Return a shallow copy of the set.

   Note, the non-operator versions of "union()", "intersection()",
   "difference()", and "symmetric_difference()", "issubset()", and
   "issuperset()" methods will accept any iterable as an argument.  In
   contrast, their operator based counterparts require their arguments
   to be sets.  This precludes error-prone constructions like
   "set('abc') & 'cbs'" in favor of the more readable
   "set('abc').intersection('cbs')".

   Both "set" and "frozenset" support set to set comparisons. Two sets
   are equal if and only if every element of each set is contained in
   the other (each is a subset of the other). A set is less than
   another set if and only if the first set is a proper subset of the
   second set (is a subset, but is not equal). A set is greater than
   another set if and only if the first set is a proper superset of
   the second set (is a superset, but is not equal).

   Instances of "set" are compared to instances of "frozenset" based
   on their members.  For example, "set('abc') == frozenset('abc')"
   returns "True" and so does "set('abc') in set([frozenset('abc')])".

   The subset and equality comparisons do not generalize to a total
   ordering function.  For example, any two nonempty disjoint sets are
   not equal and are not subsets of each other, so *all* of the
   following return "False": "a<b", "a==b", or "a>b".

   Since sets only define partial ordering (subset relationships), the
   output of the "list.sort()" method is undefined for lists of sets.

   Set elements, like dictionary keys, must be *hashable*.

   Binary operations that mix "set" instances with "frozenset" return
   the type of the first operand.  For example: "frozenset('ab') |
   set('bc')" returns an instance of "frozenset".

   The following table lists operations available for "set" that do
   not apply to immutable instances of "frozenset":

   update(*others)
   set |= other | ...

      Update the set, adding elements from all others.

   intersection_update(*others)
   set &= other & ...

      Update the set, keeping only elements found in it and all
      others.

   difference_update(*others)
   set -= other | ...

      Update the set, removing elements found in others.

   symmetric_difference_update(other)
   set ^= other

      Update the set, keeping only elements found in either set, but
      not in both.

   add(elem)

      Add element *elem* to the set.

   remove(elem)

      Remove element *elem* from the set.  Raises "KeyError" if *elem*
      is not contained in the set.

   discard(elem)

      Remove element *elem* from the set if it is present.

   pop()

      Remove and return an arbitrary element from the set.  Raises
      "KeyError" if the set is empty.

   clear()

      Remove all elements from the set.

   Note, the non-operator versions of the "update()",
   "intersection_update()", "difference_update()", and
   "symmetric_difference_update()" methods will accept any iterable as
   an argument.

   Note, the *elem* argument to the "__contains__()", "remove()", and
   "discard()" methods may be a set.  To support searching for an
   equivalent frozenset, a temporary one is created from *elem*.


Mapping Types — "dict"
======================

A *mapping* object maps *hashable* values to arbitrary objects.
Mappings are mutable objects.  There is currently only one standard
mapping type, the *dictionary*.  (For other containers see the built-
in "list", "set", and "tuple" classes, and the "collections" module.)

A dictionary’s keys are *almost* arbitrary values.  Values that are
not *hashable*, that is, values containing lists, dictionaries or
other mutable types (that are compared by value rather than by object
identity) may not be used as keys.  Numeric types used for keys obey
the normal rules for numeric comparison: if two numbers compare equal
(such as "1" and "1.0") then they can be used interchangeably to index
the same dictionary entry.  (Note however, that since computers store
floating-point numbers as approximations it is usually unwise to use
them as dictionary keys.)

Dictionaries can be created by placing a comma-separated list of "key:
value" pairs within braces, for example: "{'jack': 4098, 'sjoerd':
4127}" or "{4098: 'jack', 4127: 'sjoerd'}", or by the "dict"
constructor.

class dict(**kwarg)
class dict(mapping, **kwarg)
class dict(iterable, **kwarg)

   Return a new dictionary initialized from an optional positional
   argument and a possibly empty set of keyword arguments.

   If no positional argument is given, an empty dictionary is created.
   If a positional argument is given and it is a mapping object, a
   dictionary is created with the same key-value pairs as the mapping
   object.  Otherwise, the positional argument must be an *iterable*
   object.  Each item in the iterable must itself be an iterable with
   exactly two objects.  The first object of each item becomes a key
   in the new dictionary, and the second object the corresponding
   value.  If a key occurs more than once, the last value for that key
   becomes the corresponding value in the new dictionary.

   If keyword arguments are given, the keyword arguments and their
   values are added to the dictionary created from the positional
   argument.  If a key being added is already present, the value from
   the keyword argument replaces the value from the positional
   argument.

   To illustrate, the following examples all return a dictionary equal
   to "{"one": 1, "two": 2, "three": 3}":

      >>> a = dict(one=1, two=2, three=3)
      >>> b = {'one': 1, 'two': 2, 'three': 3}
      >>> c = dict(zip(['one', 'two', 'three'], [1, 2, 3]))
      >>> d = dict([('two', 2), ('one', 1), ('three', 3)])
      >>> e = dict({'three': 3, 'one': 1, 'two': 2})
      >>> a == b == c == d == e
      True

   Providing keyword arguments as in the first example only works for
   keys that are valid Python identifiers.  Otherwise, any valid keys
   can be used.

   These are the operations that dictionaries support (and therefore,
   custom mapping types should support too):

   list(d)

      Return a list of all the keys used in the dictionary *d*.

   len(d)

      Return the number of items in the dictionary *d*.

   d[key]

      Return the item of *d* with key *key*.  Raises a "KeyError" if
      *key* is not in the map.

      If a subclass of dict defines a method "__missing__()" and *key*
      is not present, the "d[key]" operation calls that method with
      the key *key* as argument.  The "d[key]" operation then returns
      or raises whatever is returned or raised by the
      "__missing__(key)" call. No other operations or methods invoke
      "__missing__()". If "__missing__()" is not defined, "KeyError"
      is raised. "__missing__()" must be a method; it cannot be an
      instance variable:

         >>> class Counter(dict):
         ...     def __missing__(self, key):
         ...         return 0
         >>> c = Counter()
         >>> c['red']
         0
         >>> c['red'] += 1
         >>> c['red']
         1

      The example above shows part of the implementation of
      "collections.Counter".  A different "__missing__" method is used
      by "collections.defaultdict".

   d[key] = value

      Set "d[key]" to *value*.

   del d[key]

      Remove "d[key]" from *d*.  Raises a "KeyError" if *key* is not
      in the map.

   key in d

      Return "True" if *d* has a key *key*, else "False".

   key not in d

      Equivalent to "not key in d".

   iter(d)

      Return an iterator over the keys of the dictionary.  This is a
      shortcut for "iter(d.keys())".

   clear()

      Remove all items from the dictionary.

   copy()

      Return a shallow copy of the dictionary.

   classmethod fromkeys(iterable[, value])

      Create a new dictionary with keys from *iterable* and values set
      to *value*.

      "fromkeys()" is a class method that returns a new dictionary.
      *value* defaults to "None".  All of the values refer to just a
      single instance, so it generally doesn’t make sense for *value*
      to be a mutable object such as an empty list.  To get distinct
      values, use a dict comprehension instead.

   get(key[, default])

      Return the value for *key* if *key* is in the dictionary, else
      *default*. If *default* is not given, it defaults to "None", so
      that this method never raises a "KeyError".

   items()

      Return a new view of the dictionary’s items ("(key, value)"
      pairs). See the documentation of view objects.

   keys()

      Return a new view of the dictionary’s keys.  See the
      documentation of view objects.

   pop(key[, default])

      If *key* is in the dictionary, remove it and return its value,
      else return *default*.  If *default* is not given and *key* is
      not in the dictionary, a "KeyError" is raised.

   popitem()

      Remove and return a "(key, value)" pair from the dictionary.
      Pairs are returned in LIFO (last-in, first-out) order.

      "popitem()" is useful to destructively iterate over a
      dictionary, as often used in set algorithms.  If the dictionary
      is empty, calling "popitem()" raises a "KeyError".

      Changed in version 3.7: LIFO order is now guaranteed. In prior
      versions, "popitem()" would return an arbitrary key/value pair.

   reversed(d)

      Return a reverse iterator over the keys of the dictionary. This
      is a shortcut for "reversed(d.keys())".

   setdefault(key[, default])

      If *key* is in the dictionary, return its value.  If not, insert
      *key* with a value of *default* and return *default*.  *default*
      defaults to "None".

   update([other])

      Update the dictionary with the key/value pairs from *other*,
      overwriting existing keys.  Return "None".

      "update()" accepts either another dictionary object or an
      iterable of key/value pairs (as tuples or other iterables of
      length two).  If keyword arguments are specified, the dictionary
      is then updated with those key/value pairs: "d.update(red=1,
      blue=2)".

   values()

      Return a new view of the dictionary’s values.  See the
      documentation of view objects.

      An equality comparison between one "dict.values()" view and
      another will always return "False". This also applies when
      comparing "dict.values()" to itself:

         >>> d = {'a': 1}
         >>> d.values() == d.values()
         False

   Dictionaries compare equal if and only if they have the same "(key,
   value)" pairs (regardless of ordering). Order comparisons (‘<’,
   ‘<=’, ‘>=’, ‘>’) raise "TypeError".

   Dictionaries preserve insertion order.  Note that updating a key
   does not affect the order.  Keys added after deletion are inserted
   at the end.

      >>> d = {"one": 1, "two": 2, "three": 3, "four": 4}
      >>> d
      {'one': 1, 'two': 2, 'three': 3, 'four': 4}
      >>> list(d)
      ['one', 'two', 'three', 'four']
      >>> list(d.values())
      [1, 2, 3, 4]
      >>> d["one"] = 42
      >>> d
      {'one': 42, 'two': 2, 'three': 3, 'four': 4}
      >>> del d["two"]
      >>> d["two"] = None
      >>> d
      {'one': 42, 'three': 3, 'four': 4, 'two': None}

   Changed in version 3.7: Dictionary order is guaranteed to be
   insertion order.  This behavior was an implementation detail of
   CPython from 3.6.

   Dictionaries and dictionary views are reversible.

      >>> d = {"one": 1, "two": 2, "three": 3, "four": 4}
      >>> d
      {'one': 1, 'two': 2, 'three': 3, 'four': 4}
      >>> list(reversed(d))
      ['four', 'three', 'two', 'one']
      >>> list(reversed(d.values()))
      [4, 3, 2, 1]
      >>> list(reversed(d.items()))
      [('four', 4), ('three', 3), ('two', 2), ('one', 1)]

   Changed in version 3.8: Dictionaries are now reversible.

See also: "types.MappingProxyType" can be used to create a read-only
  view of a "dict".


Dictionary view objects
-----------------------

The objects returned by "dict.keys()", "dict.values()" and
"dict.items()" are *view objects*.  They provide a dynamic view on the
dictionary’s entries, which means that when the dictionary changes,
the view reflects these changes.

Dictionary views can be iterated over to yield their respective data,
and support membership tests:

len(dictview)

   Return the number of entries in the dictionary.

iter(dictview)

   Return an iterator over the keys, values or items (represented as
   tuples of "(key, value)") in the dictionary.

   Keys and values are iterated over in insertion order. This allows
   the creation of "(value, key)" pairs using "zip()": "pairs =
   zip(d.values(), d.keys())".  Another way to create the same list is
   "pairs = [(v, k) for (k, v) in d.items()]".

   Iterating views while adding or deleting entries in the dictionary
   may raise a "RuntimeError" or fail to iterate over all entries.

   Changed in version 3.7: Dictionary order is guaranteed to be
   insertion order.

x in dictview

   Return "True" if *x* is in the underlying dictionary’s keys, values
   or items (in the latter case, *x* should be a "(key, value)"
   tuple).

reversed(dictview)

   Return a reverse iterator over the keys, values or items of the
   dictionary. The view will be iterated in reverse order of the
   insertion.

   Changed in version 3.8: Dictionary views are now reversible.

Keys views are set-like since their entries are unique and hashable.
If all values are hashable, so that "(key, value)" pairs are unique
and hashable, then the items view is also set-like.  (Values views are
not treated as set-like since the entries are generally not unique.)
For set-like views, all of the operations defined for the abstract
base class "collections.abc.Set" are available (for example, "==",
"<", or "^").

An example of dictionary view usage:

   >>> dishes = {'eggs': 2, 'sausage': 1, 'bacon': 1, 'spam': 500}
   >>> keys = dishes.keys()
   >>> values = dishes.values()

   >>> # iteration
   >>> n = 0
   >>> for val in values:
   ...     n += val
   >>> print(n)
   504

   >>> # keys and values are iterated over in the same order (insertion order)
   >>> list(keys)
   ['eggs', 'sausage', 'bacon', 'spam']
   >>> list(values)
   [2, 1, 1, 500]

   >>> # view objects are dynamic and reflect dict changes
   >>> del dishes['eggs']
   >>> del dishes['sausage']
   >>> list(keys)
   ['bacon', 'spam']

   >>> # set operations
   >>> keys & {'eggs', 'bacon', 'salad'}
   {'bacon'}
   >>> keys ^ {'sausage', 'juice'}
   {'juice', 'sausage', 'bacon', 'spam'}


Context Manager Types
=====================

Python’s "with" statement supports the concept of a runtime context
defined by a context manager.  This is implemented using a pair of
methods that allow user-defined classes to define a runtime context
that is entered before the statement body is executed and exited when
the statement ends:

contextmanager.__enter__()

   Enter the runtime context and return either this object or another
   object related to the runtime context. The value returned by this
   method is bound to the identifier in the "as" clause of "with"
   statements using this context manager.

   An example of a context manager that returns itself is a *file
   object*. File objects return themselves from __enter__() to allow
   "open()" to be used as the context expression in a "with"
   statement.

   An example of a context manager that returns a related object is
   the one returned by "decimal.localcontext()". These managers set
   the active decimal context to a copy of the original decimal
   context and then return the copy. This allows changes to be made to
   the current decimal context in the body of the "with" statement
   without affecting code outside the "with" statement.

contextmanager.__exit__(exc_type, exc_val, exc_tb)

   Exit the runtime context and return a Boolean flag indicating if
   any exception that occurred should be suppressed. If an exception
   occurred while executing the body of the "with" statement, the
   arguments contain the exception type, value and traceback
   information. Otherwise, all three arguments are "None".

   Returning a true value from this method will cause the "with"
   statement to suppress the exception and continue execution with the
   statement immediately following the "with" statement. Otherwise the
   exception continues propagating after this method has finished
   executing. Exceptions that occur during execution of this method
   will replace any exception that occurred in the body of the "with"
   statement.

   The exception passed in should never be reraised explicitly -
   instead, this method should return a false value to indicate that
   the method completed successfully and does not want to suppress the
   raised exception. This allows context management code to easily
   detect whether or not an "__exit__()" method has actually failed.

Python defines several context managers to support easy thread
synchronisation, prompt closure of files or other objects, and simpler
manipulation of the active decimal arithmetic context. The specific
types are not treated specially beyond their implementation of the
context management protocol. See the "contextlib" module for some
examples.

Python’s *generator*s and the "contextlib.contextmanager" decorator
provide a convenient way to implement these protocols.  If a generator
function is decorated with the "contextlib.contextmanager" decorator,
it will return a context manager implementing the necessary
"__enter__()" and "__exit__()" methods, rather than the iterator
produced by an undecorated generator function.

Note that there is no specific slot for any of these methods in the
type structure for Python objects in the Python/C API. Extension types
wanting to define these methods must provide them as a normal Python
accessible method. Compared to the overhead of setting up the runtime
context, the overhead of a single class dictionary lookup is
negligible.


Other Built-in Types
====================

The interpreter supports several other kinds of objects. Most of these
support only one or two operations.


Modules
-------

The only special operation on a module is attribute access: "m.name",
where *m* is a module and *name* accesses a name defined in *m*’s
symbol table. Module attributes can be assigned to.  (Note that the
"import" statement is not, strictly speaking, an operation on a module
object; "import foo" does not require a module object named *foo* to
exist, rather it requires an (external) *definition* for a module
named *foo* somewhere.)

A special attribute of every module is "__dict__". This is the
dictionary containing the module’s symbol table. Modifying this
dictionary will actually change the module’s symbol table, but direct
assignment to the "__dict__" attribute is not possible (you can write
"m.__dict__['a'] = 1", which defines "m.a" to be "1", but you can’t
write "m.__dict__ = {}").  Modifying "__dict__" directly is not
recommended.

Modules built into the interpreter are written like this: "<module
'sys' (built-in)>".  If loaded from a file, they are written as
"<module 'os' from '/usr/local/lib/pythonX.Y/os.pyc'>".


Classes and Class Instances
---------------------------

See Objects, values and types and Class definitions for these.


Functions
---------

Function objects are created by function definitions.  The only
operation on a function object is to call it: "func(argument-list)".

There are really two flavors of function objects: built-in functions
and user-defined functions.  Both support the same operation (to call
the function), but the implementation is different, hence the
different object types.

See Function definitions for more information.


Methods
-------

Methods are functions that are called using the attribute notation.
There are two flavors: built-in methods (such as "append()" on lists)
and class instance methods.  Built-in methods are described with the
types that support them.

If you access a method (a function defined in a class namespace)
through an instance, you get a special object: a *bound method* (also
called *instance method*) object. When called, it will add the "self"
argument to the argument list.  Bound methods have two special read-
only attributes: "m.__self__" is the object on which the method
operates, and "m.__func__" is the function implementing the method.
Calling "m(arg-1, arg-2, ..., arg-n)" is completely equivalent to
calling "m.__func__(m.__self__, arg-1, arg-2, ..., arg-n)".

Like function objects, bound method objects support getting arbitrary
attributes.  However, since method attributes are actually stored on
the underlying function object ("meth.__func__"), setting method
attributes on bound methods is disallowed.  Attempting to set an
attribute on a method results in an "AttributeError" being raised.  In
order to set a method attribute, you need to explicitly set it on the
underlying function object:

   >>> class C:
   ...     def method(self):
   ...         pass
   ...
   >>> c = C()
   >>> c.method.whoami = 'my name is method'  # can't set on the method
   Traceback (most recent call last):
     File "<stdin>", line 1, in <module>
   AttributeError: 'method' object has no attribute 'whoami'
   >>> c.method.__func__.whoami = 'my name is method'
   >>> c.method.whoami
   'my name is method'

See The standard type hierarchy for more information.


Code Objects
------------

Code objects are used by the implementation to represent “pseudo-
compiled” executable Python code such as a function body. They differ
from function objects because they don’t contain a reference to their
global execution environment.  Code objects are returned by the built-
in "compile()" function and can be extracted from function objects
through their "__code__" attribute. See also the "code" module.

A code object can be executed or evaluated by passing it (instead of a
source string) to the "exec()" or "eval()"  built-in functions.

See The standard type hierarchy for more information.


Type Objects
------------

Type objects represent the various object types.  An object’s type is
accessed by the built-in function "type()".  There are no special
operations on types.  The standard module "types" defines names for
all standard built-in types.

Types are written like this: "<class 'int'>".


The Null Object
---------------

This object is returned by functions that don’t explicitly return a
value.  It supports no special operations.  There is exactly one null
object, named "None" (a built-in name).  "type(None)()" produces the
same singleton.

It is written as "None".


The Ellipsis Object
-------------------

This object is commonly used by slicing (see Slicings).  It supports
no special operations.  There is exactly one ellipsis object, named
"Ellipsis" (a built-in name).  "type(Ellipsis)()" produces the
"Ellipsis" singleton.

It is written as "Ellipsis" or "...".


The NotImplemented Object
-------------------------

This object is returned from comparisons and binary operations when
they are asked to operate on types they don’t support. See Comparisons
for more information.  There is exactly one "NotImplemented" object.
"type(NotImplemented)()" produces the singleton instance.

It is written as "NotImplemented".


Boolean Values
--------------

Boolean values are the two constant objects "False" and "True".  They
are used to represent truth values (although other values can also be
considered false or true).  In numeric contexts (for example when used
as the argument to an arithmetic operator), they behave like the
integers 0 and 1, respectively. The built-in function "bool()" can be
used to convert any value to a Boolean, if the value can be
interpreted as a truth value (see section Truth Value Testing above).

They are written as "False" and "True", respectively.


Internal Objects
----------------

See The standard type hierarchy for this information.  It describes
stack frame objects, traceback objects, and slice objects.


Special Attributes
==================

The implementation adds a few special read-only attributes to several
object types, where they are relevant.  Some of these are not reported
by the "dir()" built-in function.

object.__dict__

   A dictionary or other mapping object used to store an object’s
   (writable) attributes.

instance.__class__

   The class to which a class instance belongs.

class.__bases__

   The tuple of base classes of a class object.

definition.__name__

   The name of the class, function, method, descriptor, or generator
   instance.

definition.__qualname__

   The *qualified name* of the class, function, method, descriptor, or
   generator instance.

   New in version 3.3.

class.__mro__

   This attribute is a tuple of classes that are considered when
   looking for base classes during method resolution.

class.mro()

   This method can be overridden by a metaclass to customize the
   method resolution order for its instances.  It is called at class
   instantiation, and its result is stored in "__mro__".

class.__subclasses__()

   Each class keeps a list of weak references to its immediate
   subclasses.  This method returns a list of all those references
   still alive. Example:

      >>> int.__subclasses__()
      [<class 'bool'>]

-[ Footnotes ]-

[1] Additional information on these special methods may be found
    in the Python Reference Manual (Basic customization).

[2] As a consequence, the list "[1, 2]" is considered equal to
    "[1.0, 2.0]", and similarly for tuples.

[3] They must have since the parser can’t tell the type of the
    operands.

[4] Cased characters are those with general category property
    being one of “Lu” (Letter, uppercase), “Ll” (Letter, lowercase),
    or “Lt” (Letter, titlecase).

[5] To format only a tuple you should therefore provide a
    singleton tuple whose only element is the tuple to be formatted.
