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= Sorting Mini-HOWTO =
= Sorting Mini-HOW TO =
Line 5: Line 4:
This document is a little tutorial
showing a half dozen ways to sort a list with the built-in
{{{sort()}}} method.

Python lists have a built-in {{{sort()}}} method. There are many
ways to use it to sort a list and there doesn't appear to be a single,
central place in the various manuals describing them, so I'll do so
here.
<<TableOfContents>>

Python lists have a built-in {{{sort()}}} method that modifies the list in-place
and a {{{sorted()}}} built-in function that builds a new sorted list from an iterable.

There are many ways to use them to sort data and there doesn't appear
to be a single, central place in the various manuals describing them,
so I'll do so here.

== Backward compatibility note ==

Many constructs given in the HOWTO assume Python 2.4.
Before that, there was no {{{sorted()}}} builtin and
{{{list.sort()}}} took no keyword arguments.
Line 16: Line 21:
A simple ascending sort is easy; just call the {{{sort()}}} method of a list. A simple ascending sort is very easy: just call the
{{{sorted()}}} function. It returns a new sorted list:

{{{
>>> print sorted([5, 2, 3, 1, 4])
[1, 2, 3, 4, 5]
}}}

You can also use the {{{sort()}}} method of a list.
It modifies the list in-place (and returns None to avoid confusion).
Usually it's less convenient than {{{sorted()}}} - but if you don't
need the original list, it's slightly more efficient.
Line 26: Line 42:
comparisons. The default sort routine is equivalent to:

{{{
>>> a = [5, 2, 3, 1, 4]
>>> a.sort(
cmp)
>>> print a

[1, 2, 3, 4, 5]
}}}

where {{{cmp}}} is the built-in function which compares two objects,
{{{x}}} and {{{y}}}, and returns -1, 0 or 1 depending on whether
x<y, x==y, or x>y. During the course of the sort the
relationships must stay the same for the final list to make sense.

If you want, you can define your own function for the comparison. For 
integers (and numbers in general) we can do:
comparisons. The default sort routine is equivalent to using {{{cmp}}}:

{{{
>>> print sorted([5, 2, 3, 1, 4], cmp)
[1, 2, 3, 4, 5]
}}}

where {{{cmp()}}} is the built-in function that compares two objects,
{{{x}}} and {{{y}}}, and returns a negative number, 0 or a positive
number
depending on whether x<y, x==y, or x>y. During the course of
the sort the
relationships must stay the same for the final list to
make sense.

If you want, you can define your own function for the comparison. For
integers we can do:
Line 46: Line 61:
>>> >>>
}}}

Note thas this does not work for numbers in general, as the comparison
function must return integers.

For numbers in general, but a little more understandably:

{{{
>>> def numeric_compare(x, y):
>>> if x>y:
>>> return 1
>>> elif x==y:
>>> return 0
>>> else: # x<y
>>> return -1
>>>
Line 53: Line 84:
By the way, this function won't work if result of the subtraction
is out of range, as in {{{sys.maxint - (-1)}}}.
By the way, the {{{sort()}}} function won't work if the result of the subtraction is out of range, as in {{{sys.maxint - (-1)}}}.
Line 66: Line 96:
If you want the numbers sorted in reverse you can do
Python 2.4 adds three keyword arguments to {{{sort()}}} that
simplify many common usages: {{{cmp}}}, {{{key}}}, and {{{reverse}}}. The {{{cmp}}} keyword is for providing a sorting function; the previous examples could be written as:
{{{
>>> a.sort(cmp=numeric_compare)
>>> a.sort(cmp=lambda x,y: x-y)
}}}

The {{{reverse}}} parameter is a Boolean value; if it's true, the list is sorted into reverse order.
{{{
>>> a = [5, 2, 3, 1, 4]
>>> a.sort(reverse=True)
>>> a
[5, 4, 3, 2, 1]
}}}

For Python versions before 2.4, you can reverse the sense
of the comparison function:
Line 72: Line 117:
>>>  >>>
Line 74: Line 119:
>>> print a >>> a
Line 81: Line 126:
every comparison, so if you want a reverse-sorted list of basic data
types,
do the forward sort first, then use the {{{reverse()}}} method.
every comparison, so the most efficient solution is to do the forward sort first, then use the {{{reverse()}}} method.
Line 88: Line 132:
>>> print a >>> a
Line 92: Line 136:
Here's a case-insensitive string comparison using a {{{lambda}}} function: == Sorting by keys ==

Python 2.4's {{{key}}} parameter lets you derive a sorting key for each element of the list, and then sort using the key.

For example, here's a case-insensitive string comparison:
{{{
>>> a = "This is a test string from Andrew".split()
>>> a.sort(key=str.lower)
>>> a
['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']
}}}

The value of the {{{key}}} parameter should be a function
that takes a single argument and returns a key to use for sorting purposes.

Often there's a built-in that will match your needs, such as {{{str.lower()}}}. The {{{operator}}} module contains a number of functions useful for this purpose.
For example, you can sort tuples
based on their second element
using {{{operator.itemgetter()}}}:

{{{
>>> import operator
>>> L = [('c', 2), ('d', 1), ('a', 4), ('b', 3)]
>>> map(operator.itemgetter(0), L)
['c', 'd', 'a', 'b']
>>> map(operator.itemgetter(1), L)
[2, 1, 4, 3]
>>> sorted(L, key=operator.itemgetter(1))
[('d', 1), ('c', 2), ('b', 3), ('a', 4)]
}}}

If the invocation of {{{key}}} returns a tuple, second and subsequent items in the tuple will be treated as sub-keys in the same way that Python generally sorts tuples:

{{{
>>> L = [('d', 2), ('a', 4), ('b', 3), ('c', 2)]
>>> sorted(L, key=lambda x:(x[1], x[0]))
[('c', 2), ('d', 2), ('b', 3), ('a', 4)]
}}}

To reverse sort based on the second item in each tuple, but forward sort based on the first item when a tie is met, then forward sort first and then reverse sort based on 2nd item:
{{{
>>> L = [('a', 2), ('d', 4), ('b', 3), ('c', 2)]
>>> L.sort(); L
[('a', 2), ('b', 3), ('c', 2), ('d', 4)]
>>> sorted(L,key=operator.itemgetter(1),reverse=True)
[('d', 4), ('b', 3), ('a', 2), ('c', 2)]
}}}

Versions of Python before 2.4 don't have the convenient
{{{key}}} parameter of {{{sort()}}}, so you have to write a
comparison function that embodies the key-generating logic:
Line 102: Line 196:
every time it must be compared. At times it may be faster to compute
these once and use those values, and the following example shows how.

{{{
>>> words = string.split("This is a test string from Andrew.")
>>> offsets = []
>>> for i in range(len(words)):
>>> offsets.append( (string.lower(words[i]), i) )
>>>
>>> offsets.sort()
>>> new_words = []
>>> for dontcare, i in offsets:
>>> new_words.append(words[i])
>>>
every time it must be compared, roughly O(n lg n) times.
Python 2.4's {{{key}}} parameter is called once for each item in the list, which is O(n) and therefore more efficient.
You can manually perform the same optimization by
computing the keys once
and using those values to control the sort order:

{{{
>>> words = "This is a test string from Andrew.".split()
>>> deco = [ (word.lower(), i, word) for i, word in enumerate(words) ]
>>> deco.sort()
>>> new_words = [ word for _, _, word in deco ]
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}}}

The {{{offsets}}} list is initialized to a tuple of the lower-case
string and its position in the {{{words}}} list. It is then sorted.
Python's sort method sorts tuples by comparing terms; given {{{x}}}
and {{{y}}}, compare {{{x[0]}}} to {{{y[0]}}}, then {{{x[1]}}} to
{{{y[1]}}}, etc. until there is a difference.

The result is that the {{{offsets}}} list is ordered by its first
term, and the second term can be used to figure out where the original
data was stored. (The {{{for}}} loop assigns {{{dontcare}}} and
{{{i}}} to the two fields of each term in the list, but we only need
the index value.)

Another way to implement this is to store the original data as the
second term in the {{{offsets}}} list, as in:

{{{
>>> words = string.split("This is a test string from Andrew.")
>>> offsets = []
>>> for word in words:
>>> offsets.append( (string.lower(word), word) )
>>>
>>> offsets.sort()
>>> new_words = []
>>> for word in offsets:
>>> new_words.append(word[1])
>>>
>>> print new_words
}}}

This isn't always appropriate because the second terms in the list
(the word, in this example) will be compared when the first terms are
the same. If this happens many times, then there will be the unneeded
performance hit of comparing the two objects. This can be a large
cost if most terms are the same and the objects define their own
{{{__cmp__}}} method, but there will still be some overhead to determine if
{{{__cmp__}}} is defined.

Still, for large lists, or for lists where the comparison information
is expensive to calculate, the last two examples are likely to be the
fastest way to sort a list. It will not work on weakly sorted data,
like complex numbers, but if you don't know what that means, you
probably don't need to worry about it.
['a', 'Andrew.', 'from', 'is', 'string', 'test', 'This']
}}}

This idiom is called Decorate-Sort-Undecorate after its three steps:
  * First, the initial list is decorated with new values that control the sort order.
  * Second, the decorated list is sorted.
  * Finally, the decorations are removed, creating a list that contains only the initial values in the new order.

This idiom works because tuples are compared lexicographically; the first items are compared; if they are the same then the second items are compared, and so on.

It is not strictly necessary in all cases to include the index {{{i}}} in the decorated list. Including it gives two benefits:
  * The sort is stable - if two items have the same key, their order will be preserved in the sorted list.
  * The original items do not have to be comparable because the ordering of the decorated tuples will be determined by at most the first two items. So for example the original list could contain {{{complex}}} numbers which cannot be sorted directly.

Another name for this idiom is [[http://en.wikipedia.org/wiki/Schwartzian_transform|Schwartzian transform]], after Randal L. Schwartz, who popularized it among Perl programmers.

For large lists and lists where the comparison information
is expensive to calculate, and Python versions < 2.4, DSU is likely to be the
fastest way to sort the list.
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>>> 
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>>
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
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different attributes at different times. Instead, you'll need to go
back to passing a comparison function to sort, as in:

{{{
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort(lambda x, y: cmp(x.eggs, y.eggs))
different attributes at different times.

Python 2.4 has an {{{operator.attrgetter()}}} function
that makes this easy:
{{{
>>> import operator
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort(key=operator.attrgetter('eggs'))
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In Python 2.4 if you don't want to import the operator module you can:
{{{
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort(key=lambda obj: obj.eggs)
>>> for spam in a:
>>> print spam.eggs, str(spam)
3 12
4 5
6 10
}}}

Again, earlier Python version require you to go
back to passing a comparison function to sort, as in:

{{{
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort(lambda x, y: cmp(x.eggs, y.eggs))
>>> for spam in a:
>>> print spam.eggs, str(spam)
3 12
4 5
6 10
}}}
Line 208: Line 300:
an function by defining the {{{__call__}}} method, as in: a function by defining the {{{__call__}}} method, as in:
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>>>  >>>
Line 220: Line 312:
>>> print spam.spam, spam.eggs, str(spam) >>> print spam.spam(), spam.eggs(), str(spam)
Line 227: Line 319:
>>> print spam.spam, spam.eggs, str(spam) >>> print spam.spam(), spam.eggs(), str(spam)
Line 246: Line 338:

== Topics to be covered ==

 * Rich comparisons
   * With custom comparisons, it is possible to create
   insane combinations, such as {{{((x<y) and (x==y))}}}
   or {{{((x<y) and not (x<=y))}}}.
   * The most important comparisons are __eq__ (but be
   sure to update __hash__ as well), and __lt__ (which
   is used by the sorting algorithms in practice).
 * Sorting stability
   * Python sorts are stable. Guido has indicated that
   this is a promise of the language. Therefore, if
   x == y, sorted ([x, y]) returns [x, y] but
   sorted([y, x]) returns [y, x].
 * The sorted() function
   * It takes any iterable, and returns a sorted version.
   If the items in the iterable are not sensibly compared,
   it will still return a canonical ordering, unless
   someone went out of their way to prevent one.
 * Small info about locale aware sorting, eg:
   {{{
>>> l = [u'\xc4\x85', u'a', u'z']
>>> sorted(l, reverse=False)
['a', 'z', '\xc4\x85']
>>> import locale
>>> locale.setlocale(locale.LC_ALL, "pl_PL.UTF-8")
>>> sorted(l, cmp=locale.strcoll, reverse=False)
['a', '\xc4\x85', 'z']
   }}}


== See Also ==

 * SortingListsOfDictionaries

Sorting Mini-HOW TO

Original version by Andrew Dalke

Python lists have a built-in sort() method that modifies the list in-place and a sorted() built-in function that builds a new sorted list from an iterable.

There are many ways to use them to sort data and there doesn't appear to be a single, central place in the various manuals describing them, so I'll do so here.

Backward compatibility note

Many constructs given in the HOWTO assume Python 2.4. Before that, there was no sorted() builtin and list.sort() took no keyword arguments.

Sorting basic data types

A simple ascending sort is very easy: just call the sorted() function. It returns a new sorted list:

>>> print sorted([5, 2, 3, 1, 4])
[1, 2, 3, 4, 5]

You can also use the sort() method of a list. It modifies the list in-place (and returns None to avoid confusion). Usually it's less convenient than sorted() - but if you don't need the original list, it's slightly more efficient.

>>> a = [5, 2, 3, 1, 4]
>>> a.sort()
>>> print a
[1, 2, 3, 4, 5]

Sort takes an optional function which can be called for doing the comparisons. The default sort routine is equivalent to using cmp:

>>> print sorted([5, 2, 3, 1, 4], cmp)
[1, 2, 3, 4, 5]

where cmp() is the built-in function that compares two objects, x and y, and returns a negative number, 0 or a positive number depending on whether x<y, x==y, or x>y. During the course of the sort the relationships must stay the same for the final list to make sense.

If you want, you can define your own function for the comparison. For integers we can do:

>>> def numeric_compare(x, y):
>>>    return x-y
>>>

Note thas this does not work for numbers in general, as the comparison function must return integers.

For numbers in general, but a little more understandably:

>>> def numeric_compare(x, y):
>>>    if x>y:
>>>       return 1
>>>    elif x==y:
>>>       return 0
>>>    else: # x<y
>>>       return -1
>>>
>>> a = [5, 2, 3, 1, 4]
>>> a.sort(numeric_compare)
>>> print a
[1, 2, 3, 4, 5]

By the way, the sort() function won't work if the result of the subtraction is out of range, as in sys.maxint - (-1).

Or, if you don't want to define a new named function you can create an anonymous one using lambda, as in:

>>> a = [5, 2, 3, 1, 4]
>>> a.sort(lambda x, y: x-y)
>>> print a
[1, 2, 3, 4, 5]

Python 2.4 adds three keyword arguments to sort() that simplify many common usages: cmp, key, and reverse. The cmp keyword is for providing a sorting function; the previous examples could be written as:

>>> a.sort(cmp=numeric_compare)
>>> a.sort(cmp=lambda x,y: x-y)

The reverse parameter is a Boolean value; if it's true, the list is sorted into reverse order.

>>> a = [5, 2, 3, 1, 4]
>>> a.sort(reverse=True)
>>> a
[5, 4, 3, 2, 1]

For Python versions before 2.4, you can reverse the sense of the comparison function:

>>> a = [5, 2, 3, 1, 4]
>>> def reverse_numeric(x, y):
>>>     return y-x
>>>
>>> a.sort(reverse_numeric)
>>> a
[5, 4, 3, 2, 1]

(a more general implementation could return cmp(y,x) or -cmp(x,y)).

However, it's faster if Python doesn't have to call a function for every comparison, so the most efficient solution is to do the forward sort first, then use the reverse() method.

>>> a = [5, 2, 3, 1, 4]
>>> a.sort()
>>> a.reverse()
>>> a
[5, 4, 3, 2, 1]

Sorting by keys

Python 2.4's key parameter lets you derive a sorting key for each element of the list, and then sort using the key.

For example, here's a case-insensitive string comparison:

>>> a = "This is a test string from Andrew".split()
>>> a.sort(key=str.lower)
>>> a
['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']

The value of the key parameter should be a function that takes a single argument and returns a key to use for sorting purposes.

Often there's a built-in that will match your needs, such as str.lower(). The operator module contains a number of functions useful for this purpose. For example, you can sort tuples based on their second element using operator.itemgetter():

>>> import operator
>>> L = [('c', 2), ('d', 1), ('a', 4), ('b', 3)]
>>> map(operator.itemgetter(0), L)
['c', 'd', 'a', 'b']
>>> map(operator.itemgetter(1), L)
[2, 1, 4, 3]
>>> sorted(L, key=operator.itemgetter(1))
[('d', 1), ('c', 2), ('b', 3), ('a', 4)]

If the invocation of key returns a tuple, second and subsequent items in the tuple will be treated as sub-keys in the same way that Python generally sorts tuples:

>>> L = [('d', 2), ('a', 4), ('b', 3), ('c', 2)]
>>> sorted(L, key=lambda x:(x[1], x[0]))
[('c', 2), ('d', 2), ('b', 3), ('a', 4)]

To reverse sort based on the second item in each tuple, but forward sort based on the first item when a tie is met, then forward sort first and then reverse sort based on 2nd item:

>>> L = [('a', 2), ('d', 4), ('b', 3), ('c', 2)]
>>> L.sort(); L
[('a', 2), ('b', 3), ('c', 2), ('d', 4)]
>>> sorted(L,key=operator.itemgetter(1),reverse=True)
[('d', 4), ('b', 3), ('a', 2), ('c', 2)]

Versions of Python before 2.4 don't have the convenient key parameter of sort(), so you have to write a comparison function that embodies the key-generating logic:

>>> a = "This is a test string from Andrew".split()
>>> a.sort(lambda x, y: cmp(x.lower(), y.lower()))
>>> print a
['a', 'Andrew', 'from', 'is', 'string', 'test', 'This']

This goes through the overhead of converting a word to lower case every time it must be compared, roughly O(n lg n) times. Python 2.4's key parameter is called once for each item in the list, which is O(n) and therefore more efficient. You can manually perform the same optimization by computing the keys once and using those values to control the sort order:

>>> words = "This is a test string from Andrew.".split()
>>> deco = [ (word.lower(), i, word) for i, word in enumerate(words) ]
>>> deco.sort()
>>> new_words = [ word for _, _, word in deco ]
>>> print new_words
['a', 'Andrew.', 'from', 'is', 'string', 'test', 'This']

This idiom is called Decorate-Sort-Undecorate after its three steps:

  • First, the initial list is decorated with new values that control the sort order.
  • Second, the decorated list is sorted.
  • Finally, the decorations are removed, creating a list that contains only the initial values in the new order.

This idiom works because tuples are compared lexicographically; the first items are compared; if they are the same then the second items are compared, and so on.

It is not strictly necessary in all cases to include the index i in the decorated list. Including it gives two benefits:

  • The sort is stable - if two items have the same key, their order will be preserved in the sorted list.
  • The original items do not have to be comparable because the ordering of the decorated tuples will be determined by at most the first two items. So for example the original list could contain complex numbers which cannot be sorted directly.

Another name for this idiom is Schwartzian transform, after Randal L. Schwartz, who popularized it among Perl programmers.

For large lists and lists where the comparison information is expensive to calculate, and Python versions < 2.4, DSU is likely to be the fastest way to sort the list.

Comparing classes

The comparison for two basic data types, like ints to ints or string to string, is built into Python and makes sense. There is a default way to compare class instances, but the default manner isn't usually very useful. You can define your own comparison with the __cmp__ method, as in:

>>> class Spam:
>>>     def __init__(self, spam, eggs):
>>>         self.spam = spam
>>>         self.eggs = eggs
>>>     def __cmp__(self, other):
>>>         return cmp(self.spam+self.eggs, other.spam+other.eggs)
>>>     def __str__(self):
>>>         return str(self.spam + self.eggs)
>>>
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort()
>>> for spam in a:
>>>   print str(spam)
5
10
12

Sometimes you may want to sort by a specific attribute of a class. If appropriate you should just define the __cmp__ method to compare those values, but you cannot do this if you want to compare between different attributes at different times.

Python 2.4 has an operator.attrgetter() function that makes this easy:

>>> import operator
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort(key=operator.attrgetter('eggs'))
>>> for spam in a:
>>>   print spam.eggs, str(spam)
3 12
4 5
6 10

In Python 2.4 if you don't want to import the operator module you can:

>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort(key=lambda obj: obj.eggs)
>>> for spam in a:
>>>   print spam.eggs, str(spam)
3 12
4 5
6 10

Again, earlier Python version require you to go back to passing a comparison function to sort, as in:

>>> a = [Spam(1, 4), Spam(9, 3), Spam(4, 6)]
>>> a.sort(lambda x, y: cmp(x.eggs, y.eggs))
>>> for spam in a:
>>>   print spam.eggs, str(spam)
3 12
4 5
6 10

If you want to compare two arbitrary attributes (and aren't overly concerned about performance) you can even define your own comparison function object. This uses the ability of a class instance to emulate a function by defining the __call__ method, as in:

>>> class CmpAttr:
>>>     def __init__(self, attr):
>>>         self.attr = attr
>>>     def __call__(self, x, y):
>>>         return cmp(getattr(x, self.attr), getattr(y, self.attr))
>>>
>>> a = [Spam(1, 4), Spam(9, 3), Spam(4,6)]
>>> a.sort(CmpAttr("spam"))  # sort by the "spam" attribute
>>> for spam in a:
>>>    print spam.spam(), spam.eggs(), str(spam)
1 4 5
4 6 10
9 3 12

>>> a.sort(CmpAttr("eggs"))   # re-sort by the "eggs" attribute
>>> for spam in a:
>>>    print spam.spam(), spam.eggs(), str(spam)
9 3 12
1 4 5
4 6 10

Of course, if you want a faster sort you can extract the attributes into an intermediate list and sort that list.

So, there you have it; about a half-dozen different ways to define how to sort a list:

  1. sort using the default method
  2. sort using a comparison function
  3. reverse sort not using a comparison function
  4. sort on an intermediate list (two forms)
  5. sort using class defined cmp method

  6. sort using a sort function object

Topics to be covered

  • Rich comparisons
    • With custom comparisons, it is possible to create

      insane combinations, such as ((x<y) and (x==y)) or ((x<y) and not (x<=y)).

    • The most important comparisons are eq (but be sure to update hash as well), and lt (which is used by the sorting algorithms in practice).

  • Sorting stability
    • Python sorts are stable. Guido has indicated that this is a promise of the language. Therefore, if x == y, sorted ([x, y]) returns [x, y] but sorted([y, x]) returns [y, x].
  • The sorted() function
    • It takes any iterable, and returns a sorted version. If the items in the iterable are not sensibly compared, it will still return a canonical ordering, unless someone went out of their way to prevent one.
  • Small info about locale aware sorting, eg:
    • >>> l = [u'\xc4\x85', u'a', u'z']
      >>> sorted(l, reverse=False)
      ['a', 'z', '\xc4\x85']
      >>> import locale
      >>> locale.setlocale(locale.LC_ALL, "pl_PL.UTF-8")
      >>> sorted(l, cmp=locale.strcoll, reverse=False)
      ['a', '\xc4\x85', 'z']

See Also

HowTo/Sorting (last edited 2014-10-12 06:26:39 by Paddy3118)

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