prp function - RDocumentation (2023)

x

Epartobject. The only argument needed.

type

Plot type. Possible values:

0By default. Draw a slice label on each slice and a node label on each leaf.

1Label all nodes, not just the leaves. Similar totext.rpartofall = TRUE.

2As1but draw the division labels below the node labels. Similar to plots in the CART book.

3Draw separate division labels for the left and right directions.

4As3but label all nodes, not just the leaves. Similar totext.rpartoffancy = TRUE. See tooclip.right.labs.

5Returns the name of the variable split into the inner nodes.

extra

Show additional information about us. Possible values:

"auto"(case insensitive) Automatically select a value based on the model type as follows:additional=106class template with a binary responseadditional=104class template with a response that has more than two levelsadditional=100other models

0By default. No additional information.

1Show the number of observations that fall into the node (by class forclassroomobjects; preceded by the number of events forpoisonyExpmodels). similar totext.rpartofuse.n=TRUE.

2Class Models: Displays the classification rate in the node, expressed as the number of correct classifications and the number of observations in the node. Poisson and exp models: shows the number of events.

3Class models: misclassification rate at the node, expressed as the number of misclassifications and the number of observations at the node.

4Class models: probability by class of observations at node (conditional at node, sum at node is 1).

5Class templates: how4but it doesn't show the adjusted class.

6Class models: second class probability only. Useful for binary responses.

7Class templates: how6but it doesn't show the adjusted class.

8Class models: the probability of the adjusted class.

9Class models: the probability relative toallobservations: the sum of these probabilities across all worksheets is 1. This contrasts with the previous options, which give the probability relative to observations fallingno no-- the sum of probabilities at the node is 1.

10Class templates: I like9but it only shows the probability of the second class. Useful for binary responses.

11Class templates: I like10but it doesn't show the adjusted class.

+100To add100to any of the above to also display the percentage of observations in the node. For exampleadditional=101displays the number and percentage of observations in the node. It is actually a percentage weighted using thepesosstep topart.

Note: On the contrarytext.rpart, by defaultprpit uses its own routine to generate node labels (not the function attached to the object). see thenode.funargument.

low

Applies only ifadditional > 0. by defaultFALSE, which means to put the extra textemBox. WearTRUEput the textlowBox. See toobajo.cex.

fallen leaves

by defaultFALSE. ETRUE, place the leaf nodes at the bottom of the graph.

nn

Show node numbers. by defaultFALSE. (In the current implementation, some overplot may occur withnn=TRUE.)

em

Returns the node indices, that is, the row numbers of the nodes in the object.Marco. by defaultFALSE.

but

One of0Do not writeSimyNoon the tree1(default) writeSimyNoin the first division2to writeSimyNoin all divisions. It seems to work better withfall.leaves=TRUE, split.border.col=1. (Hebutthe argument is ignored iftype=3o4. To usenn.coland the othernnparameters to change the color, etc. from theSimyNotext. To useyes.textyno textto change the actual text displayed).

rama

Controls the shape of branches. Specify a value between0(V-shaped branches) and1(branches with square shoulders). The default isif(fallen.hoaves) 1 else .2.

uniform

ETRUE(default), the vertical spacing of the nodes is uniform. YesFALSE, the nodes are spaced proportionally to the fit (more precisely, to the difference between the deviation of a node and the sum of the deviations of its two children). Very small vertical spaces are automatically artificially expanded to make room for labels, seemining industry. To use:uniform=FALSEswindlercex=NULL(the default) can sometimes cause text to be too small.

left

by defaultTRUE, which means that the left side of a split is the path taken if the split condition is true. Withleft=FALSEthe division labels are changed so that the right side is true.

turn x

by defaultFALSE. ETRUE, flips the tree horizontally.

to turn

by defaultFALSE. ETRUE, turn the tree vertically so that the root is at the bottom.

digits

The number of significant digits in the displayed numbers. by default2. E0, to usegetOption("digits"). If negative, use default.Formatfunction (with the absolute value ofdigits). Whendigitsis positive, the following details apply:0,001a9999are printed without exponent (and the number of digits is just a suggestion, seeFormatfor details). Numbers outside this range are printed with an "engineering" exponent (a multiple of 3).

bulls

Length of variable names in sliced ​​text (and, for class responses, the class in the node label). by default-8, which means truncate to eight characters. Possible values:

0use full names.

greater than 0to callabbreviatewith the dicebulls.

less than 0truncate variable names to the shortest length where they are still unique, but never truncate them to shorter thanabdomen.

face

Length of factor level names in splits. by default3, meaningabbreviateto three characters. Possible values ​​are likebullsabove, except that for backwards compatibility withtext.rpartthe special value1means to represent the factor levels with alphabetic characters (afor the first level,bfor the second, etc.).

redondo

Eroundint=TRUE(default) and all values ​​of a predictor in the training data are integers, divisions for that predictor are rounded to integers. For example, showbrothers < 3rather thansiblings < 2.5. Eroundint=TRUEand the data used to build the model is no longer available, a warning will be issued. Dressinground=FALSEis recommended if non-integer values ​​are actually possible for a predictor, even if all values ​​in the training data for that predictor are integers.

boss

by defaultNULL, which means calculate the text size automatically. Because font sizes are discrete, thebossyou ask may not be exactly thebossyou can.

retouch

Adjust o (possibly calculated automatically)boss. Usingretouchit's usually easier than specifyingboss. the default valueretouches1, which means that there is no fit. use sayadjust = 1,2to make the text 20% larger. Because font sizes are discrete, a small change in the setting might not change the font size or change it more than you want.

clip.facs

by defaultFALSE.ETRUE, print divisions on factors likefemalerather thangender = female; variable name and equal values ​​are removed.

Another example: printingsurvivedodiedinstead ofsurvived = survivedosurvived = died.

clip.right.labs

Applies only iftype=3o4. The default isTRUEwhat does it mean to "cut off" the right split labels i.e. do not printvariables=. See tooclip.left.labs.

compress

ETRUE(default), free up more space by moving the nodes horizontally where space is available. This usually allows for larger text. (This is the same asparcel.rpartthe argument of the same name, except that here the default value isTRUE.)

and compress

ETRUE(the default, unlessuniform=FALSE), free up more space by moving labels vertically where space is available. This actually only fires if the initial is calculated automaticallybossIt is less than0,7. To useandcompress=FALSEif you think the resulting screen is too messy. In the current implementation, the scrolling algorithm works a little better (allowing for larger text) withtype=1,2, o3.

Margin

Extra white space around the tree, as a fraction of the graph's width. by default0, which means there is no additional space. To add, say, 10% space around the tree, useMargin = 0.1. (This is himmarginargument fromparcel.rpart. Name changed to avoid partial matches withMarch, which can be passed as an argument ....)

space

Horizontal space to the edge of the box on either side of the node label text, in character widths. by default1. Use this (andand space) for larger boxes. As this affects the size of the (possibly invisible) boxes, it also affects the chart layout and therefore also the automatic calculation ofboss.

gap

Minimum horizontal space between (possibly invisible) boxes, in character widths. by defaultNULL, which means automatically choosing a suitable value (usually1, but if the graph is too full it will be set to0, allowing the boxes to touch each other to allow greaterboss). See toospace.

clipping

by defaultFALSE. To placeTRUEto clip the tree interactively with the mouse. see thepacking label(or just try).

cutout.fun

Function called after each mouse click whentrim=TRUE. by defaultNULL, which means it has no function. otherwise setcutout.funfor your own function with the prototypefunction (tree), wheretreeit is the cut tree. see thepacking labelFor example.

The following controls the node labels.

trail

by defaultFALSE. To useTRUEprint the calculation automaticallyboss,xlim, yousuperior. Use integer values ​​greater than 1 for more detailed tracing.

caja.col

Color of the boxes around the text. by default0, which means to use the background color. If this argument is used, thebox.palletthe argument is ignored.

box.pallet

Palette for coloring the node boxes according to the adjusted value. This is a vector ofcores,For examplebox.palette=c("verde", "verde2", "verde4")Small fitted values ​​are displayed in color at the beginning of the vector; large values ​​with colors at the end. Quantiles are used to divide the fitted values.

the special valuebox.pallet=0(default toprp) uses the background color (usually white).

the special valuebox.pallet="carro"(default torpart.plot, case insensitive) automatically selects a predefined palette based on the model type.

Otherwise, specify apreset palettephysical education.box.palette="Grises"for the default gray palette (a range of grays). The predefined palettes are (seeshow.prp.palettesFunction):grises grises Vegetables Blues chestnuts oranges red purple Gy gn That's it thousand millions O two PU(alternate names for the palettes above)this avg GnRd buoretc (two-color divergent palettes: any combination of two of the above palettes)RdYlGn GnYlRd BlGnYl YlGnBl(three color palettes)

Prefix the palette name with"-"to reverse the order of the colorsse.p.box.pallet="-auto"obox.palette="-Grises".

Hebox.palletthe argument is ignored if thecaja.colthe palette argument is specified.

amigo.thresh

Applies whenbox.palletis a divergent palette of two colors (likethis avg). Specifies the response threshold for splitting the two subpalettes (such asThat's itygn).

For example, to display fitted values ​​less than 90 in blue tones and values ​​greater than 90 in green tones, usepal.thresh=90swindlercaja.paleta="BuGn".

by defaultamigo.threshis calculated automatically. (For a two-class response, the default limit is0,5; for a continuous response, the default is the adjusted median value).

Node boxes for fitted values ​​less than the threshold are displayed using colors from the first subpalette; node boxes for fitted values ​​greater than the threshold are displayed using colors from the second subpalette.

This argument is ignored ifbox.palletit is not a divergent palette of two colors and is ignored for models with multiclass responses (more than two classes).

friend.no.fun

Specifies how thebox.palletargument is handled when thenode.funthe argument is specified.

The default isFALSEWhat does ignore mean?node.funand use the adjusted value to select the color of the nodebox.palletlike always.

ETRUE, use the label returned by the node function (instead of the wrapped value) to select the color. The first number of each label returned by the node function is used, ignoring any leading non-numeric text in the label. An error message will appear. issued if a label does not include a number.

This argument is ignored ifnode.fununspecified and ignored for models with multiclass responses (more than two classes).

frontera.col

Border color of the box around the text. by defaultcolumn, the color of the text in the box. Wear0by no borders. (Observation:partweaks likecolumncan be passed as ... arguments. If that does not happen,by("col")if one.)

redondo

Controls the roundness of the corners of node boxes. by defaultNULL, which means calculate automatically. Otherwise, specify0for sharp edges and values ​​greater than0for rounded edges. Bigger is rounder. Values ​​that are too large for the box size are reduced silently.

round sheet

Controls the roundness of the corners of leaf node boxes. by defaultNULLwhat does use meanredondo. Otherwise, specify a value greater than or equal to0.

shadow.col

Shadow color under the boxes. by default0, without shadow. To try"gris"o"dark grey". (Note: Shadow overlays look better on supported devicesalfachannels If you get the message "Warning: semi-transparency is not supported", please let me know; means a fix is ​​needed in the code that determines whether the device supports alpha channels).

prefix

by default"". Append this string to the node labels. This could be the name of the bundled response, for example.

suffix

by default"". Add this string to the node labels. Text after a new double line"\n\n"(if any) will be plottedlowBox. (Actually, double newlines can be used in any of the prefix or postfix arguments for this purpose.)

xsep

A string that separates the individual counts and probabilities into the node labels whenadditional>0. default NULL means automatic selection: usually" "(two spaces) but" / "for fees. Wearxsep="/"for compatibility withtext.rpart. See toofacsep, which separates factor levels into split labels.

low.percentage

Check for blank spaces before the percentage (when 100 is used with theextraargument). One of0put a space before the percentage1put a new line before the percentage2(default) Automatically chooses a space or newline before the percentage.

The following controls the text below the boxes.(applies only iflow = TRUEor is there a new double line\n\nemprefixosuffix).

low font

Text font below the image. by defaultsource(which can be passed as an argument...).

bajo.col

Text color below the box. by default1.

bajo.cex

Size of the text below the box relative to the text in the box. by default.8, smaller than the text in the box.

The following controls split the labels.

split.cex

Split text size relative toboss(which is automatically calculated by default). by default1.

split.source

Font for split labels. by default2, audacious. (Note: usesourceto change theItlabel text).

divided family

Font family for split labels. by default"", use something likedivision.family="serif". (Nota: usefamilyto change theItlabel text).

split.col

The color of the division label text. by default1. (Nota: usecolumnto change theItlabel text).

split.box.col

Color of split boxes. by default0, which means to use the background color.

split.border.col

Color of split box borders. by default0, invisible.

dividir.lty

Linetype for split box borders. The default is1, but the border will be invisible unless you change the defaultsplit.border.col. (Nota: uselimitedto change theItbox edges.)

divide.lwd

Line width of split box border in relation toboss(which is automatically calculated by default). The border is invisible by default, see codesplit.border.col.

divide.round

Controls the roundness of the corners of split boxes. by default0, which means sharp corners. Otherwise, specify a value greater than or equal to0. Split boxes are invisible by default, seesplit.box.colysplit.border.col).

split.shadow.col

Shadow color under split boxes. by default0, without shadow.

split.prefix

by default"". Append this string to split tags.

right.division.prefix

by defaultsplit.prefix. Append this string to the correct division labels. Applies only whentype=3o4.

split.suffix

by default"". Add this string to the split tags.

direito.split.suffix

by defaultsplit.suffix. Add this string to the correct split tags. Applies only whentype=3o4.

facsep

by default",". A string that separates factor levels into split labels. See tooxsep, which separates individual counts whenextraif one

equivalent

by default" = ". A string that separates the factor name from the levels in the split labels. The idea is that you can add or remove spaces around the=, or use words if that suits you.

es

by default" < ". String representing ``less than'' in division labels.

age

by default" >= ". String representing ``greater than or equal'' in division labels.

The following control the branches.

branch. with the

Branch color. by default1, but set to"gris"ebranch.typeis different from zero.

rama.lty

branch type by default1.

rama.lwd

Width of the line of branches in relation to theboss(which is automatically calculated by default). (Observation:rama.lwddoes not control the width of the ``wide branches'' drawn whenbranch.typeis different from zero.)

branch.type

by default0. If non-zero, draw ``wide branches'', with branch widths proportional to the parameter selected bybranch.typeAs follows:

0The default value. The branches are drawn in the conventional way.1Detour2square (offset)3diversion / nobs4sqrt(deviation/nobs) (the standard deviation whenmethod="anova")5weight (structure $peso). This is the number of observations in the node, unlesspartofweightargument was used.6complexity7abs (predicted value)8predicted value - min(predicted value)9constant (to verify the visual perception of the relative width of the branches).

otherwise setbranch.typeto its own function. The function must take a single argument.x(hepartobject) and return a numeric vector of non-negative widths corresponding to the lines inMarco. verget.branch.widthsin the source code.

Note: with a non-zerobranch.type, in the current implementation, theramathe argument will be silently changed to1(eram > 0,5) o0(eram < 0,5)

branch.tweak

by default1. Applies only ifbranch.typeis different from zero. Use this argument to scale branch widths, for example,branch.tweak=.5reduce the width of the branches by half. (By default,prpnormalizes the widths so that the widest branch is one-fifth the width of the patch).

min.branch.width

by default0,002. Applies only ifbranch.typeis different from zero. The minimum width of a branch, as a fraction of the page width. The width of branches that would be thinner thanmin.branch.widthis stuck Enlargemin.branch.widthif the thinnest branches are too thin on your display device.

branch.fill

Color used to fill in the wide branches. Applies only ifbranch.typeis different from zero. by defaultbranch. with the.

The following control node numbers (withnn=TRUE).

nn.cex

by defaultNULL, which means calculating thebossnode numbers automatically. This and the following arguments apply only whennn=TRUE.

nn.fuente

Origin of node numbers. by default3, italic.

nn.familia

Font family for node numbers. by default"".

nn.col

Node number text color. by default1.

nn.box.col

Color of boxes around node numbers. by default0, which means to use the background color.

nn.border.col

Box border color around node numbers. by defaultnn.col.

nn.lty

Node number box border linetype. by default1.

nn.lwd

Width of the node box border line in relation toboss(which is automatically calculated by default). by defaultNULLwhat does use meanlwd(which can be passed as an argument...).

nn. redondo

Controls the rounding of the corners of node number boxes. by default.3, i.e. small corners. Otherwise, specify a value greater than or equal to0.

yes.text, no.text

Text displayed whenyes=TRUE. by defaultsim.text="si"yno.text="no".

Following are the user definable functions.

node.fun

The function that generates the text in the node labels. The default isNULL, which means using a built-in pattern function toprp. (This is required for full support ofextraas described in the section onextraabove.) Otherwise, setnode.funfor your own function with the prototypefunction(x, labs, digits, varlen)see thepacking labelfor details. See also thefriend.no.funargument.

split.fun

The function that generates the text on the slices. The default isNULL, which means using a built-in pattern function toprp. otherwise setsplit.funfor your own function with the prototypefunction(x, labs, digits, varlen, faclen)

FUNNY

The function that displays text on the screen. by defaulttext.

The following are esoteric parameters, mainly for the graphical layout engine.

No space

Applies only whencompress=TRUE. by defaultnspace=rama. The size of the space between a slice and a sheet, relative to the space between the sheets.

mining industry

Applies only whenuniform=FALSE. by default.3. The minimum height between levels is fixed atmining industrytimes the average distance between levels. Necessary because sometimes a split gives little or no improvement in the deviation, and a distance between levels strictly proportional to the improvement would leave no room for the label.

do for

by defaultTRUE, which means adjusting theMarchparameter for the tree to fill the region of the figure. This also definesxpd=NA. These graphics parameters are restored to their original state beforeprpexits. If you explicitly defineMarchoxpd,prpwill use your configuration regardless of the configuration ofdo for.

add.labs

by defaultTRUE, which means to display the labels. YesFALSE, provides a basic screen similar toparcel.rpart.

clip.left.labs

Asclip.right.labsbut for the labels on the left. The default isFALSE. keep in mind thatclip.left.labsyclip.right.labsthey can be vectors, indexed on the divided number.

fam.principal

Font family for main text. by default"". The (inconsistent) name was chosen to minimize partial matching withdirectoryfamilywhich can be passed as... arguments.

change and

Vertical position of labels, in character heights relative to their default position. by default0. Negative values ​​move the text down; positive upwards (the box around the text will follow it).

and space

Vertical space to the edge of the box above and below the node label text, at character height. by defaultspace. See comments forspace.

shadow.offset

Box shadow offset, in character widths. by default.4(but the shadow will be invisible unless the default valueshadow.colChanged).

divide.adj

Horizontal position of split text. In units of string width, as is the convention foradj.default argumentsNULLwhat does use meanadj.(which by default is0,5but it can be passed as an argument...). Use values ​​less than/greater than.5to shift the text left/right (the box around the text will follow).

divide.yshift

Vertical position of split labels, at character heights relative to their default positions. by default0. Negative values ​​move the text down; positive upwards (the box around the text will follow it). This adjusts the positions of the division labels relative to the node labels. (Wearchange andif you want to changeboththe division and node labels.)

divide.space

Horizontal space between split label text and box, character width. by defaultspace. Affects the size of the box drawn around the text. Split boxes are invisible by default (seesplit.box.colysplit.border.col), but nevertheless affect the layout of the graph used in the automatic calculation ofboss.

divide.yspace

Vertical space between the split label text and the box, at character height. by defaultand space.

split.shadow.offset

Split box shadow offset, in character widths. by defaultshadow.offset. (but the shadow will be invisible unless the default valueshadow.colChanged).

nn.adj

Horizontal position of node label text. by default.5.

nn.yshift

Vertical position of node numbers, in character heights, relative to their default positions. by default0.

nn. space

Horizontal space to the edge of the box on either side of the node number text, in character widths. by default.8.

nn.yspace

Vertical space to the edge of the box above and below the node number text, at character height. by default.5.

bajo.ygap

Applies if text is drawn below the box (that is, iflow = TRUEor is there a new double line inprefixosuffix). Vertical space (character height) between the bottom edge of the box and the top of the text below the box.

yesno.yshift

Vertical position of "yes" and "no" character heights relative to their default position. by default0. Applies only whenyes=TRUE.

ygap

Minimum vertical space between boxes, at character height. by defaultlacuna/2.

xcompacto

ETRUE(default) and there is a lot of white space, automatically changexlimto compress the entire tree horizontally. This is usually only enabled for small trees. (Hexcompactoyycompactarguments compress the tree as a whole, while argumentscompressyand compressArguments move parts of the tree into available space.)

ycompact

ETRUE(default) and there is a lot of vertical space, automatically changesuperiorto compress the entire tree vertically.

xcompact.ratio

by default.8. Applies only whenxcompact=TRUE. The maximum possible without overlap is1, further compacting by.8usually gives better spacing (gives more space).

min.inter.height

by default4. Applies only whenycompacto=TRUE. The minimum height (in character height units) between the lowest label on a layer and the highest label on the layer below.

max.auto.chex

Keep the maximum calculated automaticallybossat this default value1, which means never expandboss, hire only when necessary.

min.auto.cex

by default.15. Never scale below this when automatically calculatingboss, even if there are overlapping labels. (Graph layout algorithm is unstable withbossis below0,15-- which means that the size of the automatic type may be smaller than necessary).

ycompress.cex

by default.7. Applies only whenandcompress=TRUE. Apply theand compressalgorithm if initial is calculated automaticallybossit's smaller than that. The idea is that we don't want to change if we get an acceptable cex without changing. To doInformationalways try to change.

accept.chex

Accept the change only if it causes at least this big improvement inboss(because we don't want to change if it only gives a small improvement in cex). by default1.1that is, they require at least a 10% improvement. Wear0always take turns andInformationnever accept (or useandcompress=FALSE).

shift.amounts

by defaultc(1.5, 2, 3). Forand compress, choose the bestbossproduced by changing the nodes by these values, in multiples of the box heights (after initial scaling).

Fallen.yspace

Extra space for fallen leaves. by default.1, which means leaving 10% of the vertical space for fallen leaves. (The nameFallen.yspaceuses capital letters to avoid partial matches withfallen leaves.)

boxes.include.gap

by defaultFALSE. Includegapyygapwhen drawing the boxes, for debugging purposes. (To draw the boxes, seecaja.col,frontera.col,split.box.col, yousplit.border.col.) This argument only affects the way charts are drawn, not the chart layout algorithm in any way. with the idealbossat least some frames displayed this way will just touch each other (but none will overlap).

legend. x

Applies only to models with a multilevel class response (not binary or anova models, for which no legend is drawn). Legend horizontal position. Usually a value between0y1, although values ​​beyond these limits are often useful. The default isNULLwhich means automatically placing the subtitle (assuming there is enough space). WearTHATby no legend. Weartrace=TRUEto see the auto-calculated legend position.

legend.y

Aslegend. xbut by the vertical position of the legend.

legend.cex

Aslegend. xbut by the relative size of the caption text. The default is1.

…

ExtraparArguments Only the ``important ones''parArguments are allowed. Note that arguments likecolumnapplies only toItlabels. To affect division labels or branch lines, usesplit.colybranch. with theinstead of.

examples

run this code

# NOT RUN {data (ptitanic)tree <- rpart(survived ~ ., data = ptitanic, cp =.02) # cp = .02 because I want a small tree for the demoviejo.par <- par(mfrow =C(2,2)) # put 4 figures on a pageprp(tree, parent ="pattern prp\n(type = 0, extra = 0)")prp(tree, parent ="type = 4, extra = 6\nbox.palette = \"auto\"",type =4, additional =6,# label all nodes, show the second-class problembox.pallet ="auto",# color nodes automatically based on model typefaclen =0)# faclen = 0 to print the full names of the factorscols <- ifelse(tree$frame$yval ==1,"dark red","verde4") # green if you surviveprp(tree, parent ="various arguments",additional =106,# displays probability of survival and percentage of obs.n =TRUE,# display node numbersfallen.leaves =TRUE,# place the worksheets at the bottom of the pageshadow.col ="gris",# shadows under the leavesrama.lty =3,# draw branches using dotted linesrama =.5,# change the angle of the minor linesfaclen =0,# faclen = 0 to print the full names of the factorstrail =1,# print the automatically calculated cex, xlim, ylimdivide.cex =1.2,# make the split text larger than the node textdivide.prefix ="It is",# put "es" before split or textsplit.suffix ="?",# to place "?" after splitting the textcolumn = columns, border. column = columns,# green if you survivedivide.box.col ="light gray",# light gray split boxes (default is white)split.border.col ="dark grey",# dark gray border on split boxesdivide.round =.5)# round the corners of the split box a bit# compare with the trace functions in the rpart packageplot(tree, uniform =TRUE, compress =TRUE, rama =.2)text(tree, use.n =TRUE, cex =.8, xpd =THAT)# cex is a guess, depends on window sizetitle("compare with the plotting functions\in the rpart package", cex.sub =.8)by(old.by)# }

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