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Histogram plot
Histograms are a type of bar plot for numeric data that group the data into
bins. After you create a Histogram
object, you can modify aspects of
the histogram by changing its property values. This is particularly useful for quickly
modifying the properties of the bins or changing the display.
histogram(X)
histogram(X,nbins)
histogram(X,edges)
histogram('BinEdges',edges,'BinCounts',counts)
histogram(C)
histogram(C,Categories)
histogram('Categories',Categories,'BinCounts',counts)
histogram(___,Name,Value)
histogram(ax,___)
h = histogram(___)
histogram(
creates a histogram
plot of X
)X
. The histogram
function uses
an automatic binning algorithm that returns bins with a uniform width,
chosen to cover the range of elements in X
and reveal the
underlying shape of the distribution. histogram
displays the bins as rectangles such that the height of each rectangle
indicates the number of elements in the bin.
histogram(
, where
C
)C
is a categorical array, plots a histogram with a
bar for each category in C
.
histogram(
plots only the subset of categories specified by
C
,Categories
)Categories
.
histogram('Categories',
manually specifies categories and associated bin counts.
Categories
,'BinCounts',counts
)histogram
plots the specified bin counts and does
not do any data binning.
histogram(___,
specifies additional options with one or more Name,Value
)Name,Value
pair arguments using any of the previous syntaxes. For example, you can
specify 'BinWidth'
and a scalar to adjust the width of
the bins, or 'Normalization'
with a valid option
('count'
, 'probability'
,
'countdensity'
, 'pdf'
,
'cumcount'
, or 'cdf'
) to use a
different type of normalization. For a list of properties, see Histogram Properties.
histogram(
plots into the axes specified by ax
,___)ax
instead of into the
current axes (gca
). The option ax
can
precede any of the input argument combinations in the previous
syntaxes.
returns a h
= histogram(___)Histogram
object. Use this to inspect and
adjust the properties of the histogram. For a list of properties, see
Histogram Properties.
X
— Data to distribute among binsData to distribute among bins, specified as a vector, matrix, or
multidimensional array. If X
is not a vector, then
histogram
treats it as a single column vector,
X(:)
, and plots a single histogram.
histogram
ignores all NaN
and
NaT
values. Similarly,
histogram
ignores Inf
and
Inf
values, unless the bin edges explicitly
specify Inf
or Inf
as a bin edge.
Although NaN
, NaT
,
Inf
, and Inf
values are
typically not plotted, they are still included in normalization
calculations that include the total number of data elements, such as
'probability'
.
If X
contains integers of type
int64
or uint64
that are
larger than flintmax
, then it is recommended that
you explicitly specify the histogram bin edges.
histogram
automatically bins the input data
using double precision, which lacks integer precision for numbers
greater than flintmax
.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 logical
 datetime
 duration
C
— Categorical dataCategorical data, specified as a categorical array.
histogram
does not plot undefined categorical
values. However, undefined categorical values are still included in
normalization calculations that include the total number of data
elements, such as 'probability'
.
Data Types: categorical
nbins
— Number of binsNumber of bins, specified as a positive integer. If you do not specify
nbins
, then histogram
automatically calculates how many bins to use based on the values in
X
.
Example: histogram(X,15)
creates a histogram with 15
bins.
edges
— Bin edgesBin edges, specified as a vector. edges(1)
is the
left edge of the first bin, and edges(end)
is the
right edge of the last bin.
The value X(i)
is in the k
th bin
if edges(k)
≤ X(i)
<
edges(k+1)
. The last bin also includes the right
bin edge, so that it contains X(i)
if
edges(end1)
≤ X(i)
≤
edges(end)
.
For datetime and duration data, edges
must be a
datetime or duration vector in monotonically increasing order.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 logical
 datetime
 duration
Categories
— Categories included in histogramThis option only applies to categorical histograms.
Categories included in histogram, specified as a cell array of character vectors or categorical vector.
If you specify an input categorical array C
,
then by default, histogram
plots a bar for each
category in C
. In that case, use Categories
to
specify a unique subset of the categories instead.
If you specify bin counts, then Categories
specifies
the associated category names for the histogram.
Example: h = histogram(C,{'Large','Small'})
plots
only the categorical data in the categories 'Large'
and 'Small'
.
Example: histogram('Categories',{'Yes','No','Maybe'},'BinCounts',[22
18 3])
plots a histogram that has three categories with
the associated bin counts.
Example: h.Categories
queries
the categories that are in histogram object h
.
Data Types: cell
 categorical
counts
— Bin countsBin counts, specified as a vector. Use this input to pass bin counts
to histogram
when the bin counts calculation is
performed separately and you do not want histogram
to do any data binning.
The length of counts
must be equal to the number of
bins.
For numeric histograms, the number of bins is
length(edges)1
.
For categorical histograms, the number of bins is equal to the number of categories.
Example: histogram('BinEdges',2:2,'BinCounts',[5 8 15
9])
Example: histogram('Categories',{'Yes','No','Maybe'},'BinCounts',[22
18 3])
ax
— Target axesAxes
object  PolarAxes
objectTarget axes, specified as an Axes
object or a
PolarAxes
object. If you do not specify the axes
and if the current axes are Cartesian axes, then the
histogram
function uses the current axes
(gca
). To plot into polar axes, specify the
PolarAxes
object as the first input argument or
use the polarhistogram
function.
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as Name1,Value1,...,NameN,ValueN
.
histogram(X,'BinWidth',5)
The histogram properties listed here are only a subset. For a complete list, see Histogram Properties.
'BarWidth'
— Relative width of categorical bars0.9
(default)  scalar in range [0,1]
This option only applies to histograms of categorical data.
Relative width of categorical bars, specified as a scalar value
in the range [0,1]
. Use this property to control
the separation of categorical bars within the histogram. The default
value is 0.9
, which means that the bar width is
90% of the space from the previous bar to the next bar, with 5% of
that space on each side.
If you set this property to 1
, then adjacent
bars touch.
Example: 0.5
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
'BinLimits'
— Bin limitsBin limits, specified as a twoelement vector, [bmin,bmax]
.
This option plots a histogram using the values in the input array, X
,
that fall between bmin
and bmax
inclusive.
That is, X(X>=bmin & X<=bmax)
.
This option does not apply to histograms of categorical data.
Example: histogram(X,'BinLimits',[1,10])
plots
a histogram using only the values in X
that are
between 1
and 10
inclusive.
'BinLimitsMode'
— Selection mode for bin limits'auto'
(default)  'manual'
Selection mode for bin limits, specified as 'auto'
or 'manual'
.
The default value is 'auto'
, so that the bin limits
automatically adjust to the data.
If you explicitly specify either BinLimits
or BinEdges
,
then BinLimitsMode
is automatically set to 'manual'
.
In that case, specify BinLimitsMode
as 'auto'
to
rescale the bin limits to the data.
This option does not apply to histograms of categorical data.
'BinMethod'
— Binning algorithm'auto'
(default)  'scott'
 'fd'
 'integers'
 'sturges'
 'sqrt'
 ...Binning algorithm, specified as one of the values in this table.
Value 
Description 


The default 

Scott’s rule is optimal if the data is close
to being normally distributed. This rule is
appropriate for most other distributions, as well.
It uses a bin width of


The FreedmanDiaconis rule is less sensitive
to outliers in the data, and might be more
suitable for data with heavytailed distributions.
It uses a bin width of


The integer rule is useful with integer data, as it creates a bin for each integer. It uses a bin width of 1 and places bin edges halfway between integers. To avoid accidentally creating too many bins, you can use this rule to create a limit of 65536 bins (2^{16}). If the data range is greater than 65536, then the integer rule uses wider bins instead. Note


Sturges’ rule is popular due to its
simplicity. It chooses the number of bins to be


The Square Root rule is widely used in other
software packages. It chooses the number of bins
to be

For datetime data, the bin method can be one of these units of time:
'second'  'month' 
'minute'  'quarter' 
'hour'  'year' 
'day'  'decade' 
'week'  'century' 
For duration data, the bin method can be one of these units of time:
'second'  'day' 
'minute'  'year' 
'hour' 
If you specify BinMethod
with datetime or duration data, then
histogram
can use a maximum of 65,536 bins (or
2^{16}). If the specified bin duration requires more bins,
then histogram
uses a larger bin width corresponding to the maximum
number of bins.
This option does not apply to histograms of categorical data.
If you set the BinLimits
, NumBins
, BinEdges
,
or BinWidth
property, then the BinMethod
property
is set to 'manual'
.
Example: histogram(X,'BinMethod','integers')
creates
a histogram with the bins centered on integers.
'BinWidth'
— Width of binsWidth of bins, specified as a scalar. When you specify BinWidth
,
then histogram
can use a maximum of 65,536 bins
(or 2^{16}).
If instead the specified bin width requires more bins, then histogram
uses
a larger bin width corresponding to the maximum number of bins.
For datetime and duration data, the value of 'BinWidth'
can
be a scalar duration or calendar duration.
This option does not apply to histograms of categorical data.
Example: histogram(X,'BinWidth',5)
uses bins
with a width of 5.
'DisplayOrder'
— Category display order'data'
(default)  'ascend'
 'descend'
Category display order, specified as 'ascend'
, 'descend'
,
or 'data'
. With 'ascend'
or 'descend'
,
the histogram displays with increasing or decreasing bar heights.
The default 'data'
value uses the category order
in the input data, C
.
This option only works with categorical data.
'DisplayStyle'
— Histogram display style'bar'
(default)  'stairs'
Histogram display style, specified as either 'bar'
or 'stairs'
.
Specify 'stairs'
to display a stairstep plot, which
displays the outline of the histogram without filling the interior.
The default value of 'bar'
displays a histogram
bar plot.
Example: histogram(X,'DisplayStyle','stairs')
plots
the outline of the histogram.
'EdgeAlpha'
— Transparency of histogram bar edges1
(default)  scalar value between 0
and
1
inclusiveTransparency of histogram bar edges, specified as a scalar value
between 0
and 1
inclusive. A
value of 1
means fully opaque and
0
means completely transparent
(invisible).
Example: histogram(X,'EdgeAlpha',0.5)
creates a
histogram plot with semitransparent bar edges.
'EdgeColor'
— Histogram edge color[0 0 0]
or black (default)  'none'
 'auto'
 RGB triplet or color nameHistogram edge color, specified as one of these values:
'none'
— Edges are not
drawn.
'auto'
— Color of each edge is
chosen automatically.
RGB triplet or a color name — Edges use the specified color.
An RGB triplet is a threeelement row vector whose elements
specify the intensities of the red, green, and blue components of the color. The intensities
must be in the range [0,1]
; for example, [0.4 0.6 0.7]
.
Alternatively, you can specify some common colors by name. This table lists the long and short
color name options and the equivalent RGB triplet values.
Option  Description  Equivalent RGB Triplet 

'red' or 'r'  Red  [1 0 0] 
'green' or 'g'  Green  [0 1 0] 
'blue' or 'b'  Blue  [0 0 1] 
'yellow' or 'y'  Yellow  [1 1 0] 
'magenta' or 'm'  Magenta  [1 0 1] 
'cyan' or 'c'  Cyan  [0 1 1] 
'white' or 'w'  White  [1 1 1] 
'black' or 'k'  Black  [0 0 0] 
Example: histogram(X,'EdgeColor','r')
creates a
histogram plot with red bar edges.
'FaceAlpha'
— Transparency of histogram bars0.6
(default)  scalar value between 0
and
1
inclusiveTransparency of histogram bars, specified as a scalar value
between 0
and 1
inclusive.
histogram
uses the same transparency for all
the bars of the histogram. A value of 1
means
fully opaque and 0
means completely transparent
(invisible).
Example: histogram(X,'FaceAlpha',1)
creates a
histogram plot with fully opaque bars.
'FaceColor'
— Histogram bar color'auto'
(default)  'none'
 RGB triplet or color nameHistogram bar color, specified as one of these values:
'none'
— Bars are not
filled.
'auto'
— Histogram bar color is
chosen automatically (default).
RGB triplet or a color name — Bars are filled with the specified color.
An RGB triplet is a threeelement row vector whose elements
specify the intensities of the red, green, and blue components of the color. The intensities
must be in the range [0,1]
; for example, [0.4 0.6 0.7]
.
Alternatively, you can specify some common colors by name. This table lists the long and short
color name options and the equivalent RGB triplet values.
Option  Description  Equivalent RGB Triplet 

'red' or 'r'  Red  [1 0 0] 
'green' or 'g'  Green  [0 1 0] 
'blue' or 'b'  Blue  [0 0 1] 
'yellow' or 'y'  Yellow  [1 1 0] 
'magenta' or 'm'  Magenta  [1 0 1] 
'cyan' or 'c'  Cyan  [0 1 1] 
'white' or 'w'  White  [1 1 1] 
'black' or 'k'  Black  [0 0 0] 
If you specify DisplayStyle
as
'stairs'
, then histogram
does not use the FaceColor
property.
Example: histogram(X,'FaceColor','g')
creates a
histogram plot with green bars.
'LineStyle'
— Line style''
(default)  ''
 ':'
 '.'
 'none'
Line style, specified as one of the options listed in this table.
Line Style  Description  Resulting Line 

''  Solid line 

''  Dashed line 

':'  Dotted line 

'.'  Dashdotted line 

'none'  No line  No line 
'LineWidth'
— Width of bar outlines0.5
(default)  positive valueWidth of bar outlines, specified as a positive value in point units. One point equals 1/72 inch.
Example: 1.5
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
'Normalization'
— Type of normalization'count'
(default)  'probability'
 'countdensity'
 'pdf'
 'cumcount'
 'cdf'
Type of normalization, specified as one of the values in this
table. For each bin i
:
$${v}_{i}$$ is the bin value.
$${c}_{i}$$ is the number of elements in the bin.
$${w}_{i}$$ is the width of the bin.
$$N$$ is
the number of elements in the input data. This value can be greater
than the binned data if the data contains NaN
, NaT
,
or <undefined>
values, or if some of the
data lies outside the bin limits.
Value  Bin Values  Notes 

'count' (default) 
$${v}_{i}={c}_{i}$$ 

'countdensity' 
$${v}_{i}=\frac{{c}_{i}}{{w}_{i}}$$ 
Note

'cumcount' 
$${v}_{i}={\displaystyle \sum _{j=1}^{i}{c}_{j}}$$ 

'probability' 
$${v}_{i}=\frac{{c}_{i}}{N}$$ 

'pdf' 
$${v}_{i}=\frac{{c}_{i}}{N\text{\hspace{0.17em}}\text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{w}_{i}}$$ 
Note

'cdf' 
$${v}_{i}={\displaystyle \sum _{j=1}^{i}\text{\hspace{0.17em}}\frac{{c}_{j}}{N}}$$ 

Example: histogram(X,'Normalization','pdf')
plots
an estimate of the probability density function for X
.
'NumDisplayBins'
— Number of categories to displayNumber of categories to display, specified as a scalar. You
can change the ordering of categories displayed in the histogram using
the 'DisplayOrder'
option.
This option only works with categorical data.
'Orientation'
— Orientation of bars'vertical'
(default)  'horizontal'
Orientation of bars, specified as 'vertical'
or 'horizontal'
.
Example: histogram(X,'Orientation','horizontal')
creates
a histogram plot with horizontal bars.
'ShowOthers'
— Toggle summary display of data belonging to undisplayed categories'off'
(default)  'on'
Toggle summary display of data belonging to undisplayed categories,
specified as 'off'
or 'on'
.
Set this option to 'on'
to display an additional
bar in the histogram with the name 'Others'
. This
extra bar counts all elements that do not belong to categories displayed
in the histogram.
You can change the number of categories displayed in the histogram,
as well as their order, using the 'NumDisplayBins'
and 'DisplayOrder'
options.
This option only works with categorical data.
h
— HistogramHistogram, returned as an object. For more information, see histogram
.
Histogram Properties  Histogram appearance and behavior 
Generate 10,000 random numbers and create a histogram. The histogram
function automatically chooses an appropriate number of bins to cover the range of values in x
and show the shape of the underlying distribution.
x = randn(10000,1); h = histogram(x)
h = Histogram with properties: Data: [10000x1 double] Values: [1x37 double] NumBins: 37 BinEdges: [1x38 double] BinWidth: 0.2000 BinLimits: [3.8000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties
When you specify an output argument to the histogram
function, it returns a histogram object. You can use this object to inspect the properties of the histogram, such as the number of bins or the width of the bins.
Find the number of histogram bins.
nbins = h.NumBins
nbins = 37
Plot a histogram of 1,000 random numbers sorted into 25 equally spaced bins.
x = randn(1000,1); nbins = 25; h = histogram(x,nbins)
h = Histogram with properties: Data: [1000x1 double] Values: [1x25 double] NumBins: 25 BinEdges: [1x26 double] BinWidth: 0.2800 BinLimits: [3.4000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties
Find the bin counts.
counts = h.Values
counts = 1×25
1 3 0 6 14 19 31 54 74 80 92 122 104 115 88 80 38 32 21 9 5 5 5 0 2
Generate 1,000 random numbers and create a histogram.
X = randn(1000,1); h = histogram(X)
h = Histogram with properties: Data: [1000x1 double] Values: [1x23 double] NumBins: 23 BinEdges: [1x24 double] BinWidth: 0.3000 BinLimits: [3.3000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties
Use the morebins
function to coarsely adjust the number of bins.
Nbins = morebins(h); Nbins = morebins(h)
Nbins = 29
Adjust the bins at a fine grain level by explicitly setting the number of bins.
h.NumBins = 31;
Generate 1,000 random numbers and create a histogram. Specify the bin edges as a vector with wide bins on the edges of the histogram to capture the outliers that do not satisfy . The first vector element is the left edge of the first bin, and the last vector element is the right edge of the last bin.
x = randn(1000,1); edges = [10 2:0.25:2 10]; h = histogram(x,edges);
Specify the Normalization
property as 'countdensity'
to flatten out the bins containing the outliers. Now, the area of each bin (rather than the height) represents the frequency of observations in that interval.
h.Normalization = 'countdensity';
Create a categorical vector that represents votes. The categories in the vector are 'yes'
, 'no'
, or 'undecided'
.
A = [0 0 1 1 1 0 0 0 0 NaN NaN 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1]; C = categorical(A,[1 0 NaN],{'yes','no','undecided'})
C = 1x27 categorical array
Columns 1 through 9
no no yes yes yes no no no no
Columns 10 through 16
undecided undecided yes no no no yes
Columns 17 through 25
no yes no yes no no no yes yes
Columns 26 through 27
yes yes
Plot a categorical histogram of the votes, using a relative bar width of 0.5
.
h = histogram(C,'BarWidth',0.5)
h = Histogram with properties: Data: [1x27 categorical] Values: [11 14 2] NumDisplayBins: 3 Categories: {'yes' 'no' 'undecided'} DisplayOrder: 'data' Normalization: 'count' DisplayStyle: 'bar' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties
Generate 1,000 random numbers and create a histogram using the 'probability'
normalization.
x = randn(1000,1); h = histogram(x,'Normalization','probability')
h = Histogram with properties: Data: [1000x1 double] Values: [1x23 double] NumBins: 23 BinEdges: [1x24 double] BinWidth: 0.3000 BinLimits: [3.3000 3.6000] Normalization: 'probability' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties
Compute the sum of the bar heights. With this normalization, the height of each bar is equal to the probability of selecting an observation within that bin interval, and the height of all of the bars sums to 1.
S = sum(h.Values)
S = 1
Generate two vectors of random numbers and plot a histogram for each vector in the same figure.
x = randn(2000,1);
y = 1 + randn(5000,1);
h1 = histogram(x);
hold on
h2 = histogram(y);
Since the sample size and bin width of the histograms are different, it is difficult to compare them. Normalize the histograms so that all of the bar heights add to 1, and use a uniform bin width.
h1.Normalization = 'probability'; h1.BinWidth = 0.25; h2.Normalization = 'probability'; h2.BinWidth = 0.25;
Generate 1,000 random numbers and create a histogram. Return the histogram object to adjust the properties of the histogram without recreating the entire plot.
x = randn(1000,1); h = histogram(x)
h = Histogram with properties: Data: [1000x1 double] Values: [1x23 double] NumBins: 23 BinEdges: [1x24 double] BinWidth: 0.3000 BinLimits: [3.3000 3.6000] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties
Specify exactly how many bins to use.
h.NumBins = 15;
Specify the edges of the bins with a vector. The first value in the vector is the left edge of the first bin. The last value is the right edge of the last bin.
h.BinEdges = [3:3];
Change the color of the histogram bars.
h.FaceColor = [0 0.5 0.5];
h.EdgeColor = 'r';
Generate 5,000 normally distributed random numbers with a mean of 5 and a standard deviation of 2. Plot a histogram with Normalization
set to 'pdf'
to produce an estimation of the probability density function.
x = 2*randn(5000,1) + 5; histogram(x,'Normalization','pdf')
In this example, the underlying distribution for the normally distributed data is known. You can, however, use the 'pdf'
histogram plot to determine the underlying probability distribution of the data by comparing it against a known probability density function.
The probability density function for a normal distribution with mean , standard deviation , and variance is
Overlay a plot of the probability density function for a normal distribution with a mean of 5 and a standard deviation of 2.
hold on y = 5:0.1:15; mu = 5; sigma = 2; f = exp((ymu).^2./(2*sigma^2))./(sigma*sqrt(2*pi)); plot(y,f,'LineWidth',1.5)
Use the savefig
function to save a histogram figure.
y = histogram(randn(10));
savefig('histogram.fig');
clear all close all
Use openfig
to load the histogram figure back into MATLAB. openfig
also returns a handle to the figure, h
.
h = openfig('histogram.fig');
Use the findobj
function to locate the correct object handle from the figure handle. This allows you to continue manipulating the original histogram object used to generate the figure.
y = findobj(h, 'type', 'histogram')
y = Histogram with properties: Data: [10x10 double] Values: [2 17 28 32 16 3 2] NumBins: 7 BinEdges: [3 2 1 0 1 2 3 4] BinWidth: 1 BinLimits: [3 4] Normalization: 'count' FaceColor: 'auto' EdgeColor: [0 0 0] Show all properties
Histogram plots created using histogram
have a context menu
in plot edit mode that enables interactive manipulations in the figure window.
For example, you can use the context menu to interactively change the number of
bins, align multiple histograms, or change the display order.
This function supports tall arrays with the limitations:
Some input options are not supported. The allowed options are:
'BinWidth'
'BinLimits'
'Normalization'
'DisplayStyle'
'BinMethod'
— The 'auto'
and 'scott'
bin
methods are the same. The 'fd'
bin method is not
supported.
'EdgeAlpha'
'EdgeColor'
'FaceAlpha'
'FaceColor'
'LineStyle'
'LineWidth'
'Orientation'
Additionally, there is a cap on the maximum number of bars. The default maximum is 100.
The morebins
and fewerbins
methods
are not supported.
Editing properties of the histogram object that require recomputing the bins is not supported.
For more information, see Tall Arrays.
Usage notes and limitations:
This function accepts GPU arrays, but does not run on a GPU.
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Usage notes and limitations:
This function operates on distributed arrays, but executes in the client MATLAB^{®}.
For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Histogram Properties  discretize
 fewerbins
 histcounts
 histcounts2
 histogram2
 morebins
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