The trip package

Michael Sumner

2019-04-15

Introduction

Basic use of the trip package.

Data input and validation

Tracking data is in essence a grouped series of one-dimensional data1 records.

It is grouped because we may track more than one object, each with its on independent time sequence.

It is one-dimensional because the topology of the data is a linear stream of values. It makes sense that time is constantly increasing, and it is the primary dimension of the process. (Location is often something that we must estimate, but time is usually directly measured and robust).

Commonly we have records in a data frame, and the primary workflow is to provide the trip() function with information about the spatial locations, the temporal data, and the grouping.

The data may contain any other columns, and in general they can be called anything and be in any order, but the simplest way to create a trip is to put the first four columns as X, Y, date-time, grouping.

## Warning in assume_if_longlat(out): input looks like longitude/latitude
## data, assuming +proj=longlat +datum=WGS84
## 
## Object of class trip
##   tripID ("id") No.Records   startTime ("tms")     endTime ("tms")
## 1             1          5 2019-04-15 13:04:34 2019-04-15 13:04:38
## 2             2          5 2019-04-15 13:04:39 2019-04-15 13:04:43
##   tripDuration tripDistance meanSpeed  maxSpeed
## 1       4 secs     756.9747  681277.3  916817.2
## 2       4 secs    1190.0092 1071008.2 1655201.1
## 
## Total trip duration: 8 seconds (0 hours, 8 seconds)
## 
## Derived from Spatial data:
## 
## Object of class SpatialPointsDataFrame
## Coordinates:
##         min       max
## x  1.000000 10.000000
## y -2.520496  1.486936
## Is projected: FALSE 
## proj4string :
## [+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs +towgs84=0,0,0]
## Number of points: 10
## Data attributes:
##       tms                      id   
##  Min.   :2019-04-15 13:04:34   1:5  
##  1st Qu.:2019-04-15 13:04:37   2:5  
##  Median :2019-04-15 13:04:39        
##  Mean   :2019-04-15 13:04:39        
##  3rd Qu.:2019-04-15 13:04:41        
##  Max.   :2019-04-15 13:04:43

(There may be only one group, but we have to be explicit, with a column that identifies at least one group).

When a print or summary is made the data are presented in terms of their grouping, with some handy summary values. When converting to sf or sp form as lines these summary values are recorded with each “multi”-line.

Simple plotting

To plot a trip we use base graphics in the usual ways.

plot(tr)
lines(tr)

The trip object acts as a sp data frame of points, but with the underlying grouping as lines when that is relevant.

plot(tr,pch = ".", col = rainbow(nrow(tr)))
lines(tr, col = c("dodgerblue", "firebrick"))

Gridding for time spent

There is a key functionality to determine the time spent in area on a grid, by leveraging the rasterize() generic function in the raster package. Any raster object may be used, so the specification of pixel area, extent and map projection is up to the user. (The trip line segments must all fall within the raster).

tg <- rasterize(tr)
plot(tg, col = c("transparent", heat.colors(25)))

As with raster::rasterize() the field used may be chosen, by default the time difference between each point in a trip is used, and the final grid contains the sum of these durations.

There is an older version of this in the tripGrid.interp function that uses approximate methods by allowing interpolation to an ‘equal time’ step.

Reading from Argos files

Service Argos has provide various message formats, and the readArgos() function understands some variants of the ‘PRV’ form. Multiple files can be provided, and all messages will be normalized and turned into a trip object with no need for the user to group or clean them in any way.

argosfile <- 
 system.file("extdata/argos/98feb.dat", package = "trip", mustWork = TRUE)
argos <- readArgos(argosfile) 
## 
## Longitudes contain values greater than 180, assuming proj.4 +over
## 
## 
## 
## 
##  Data fully validated: returning object of class  trip
summary(argos)
## 
## Object of class trip
##    tripID ("ptt") No.Records   startTime ("gmt")     endTime ("gmt")
## 1            2163        134 1998-02-01 03:32:32 1998-02-24 07:33:35
## 2            6072        150 1998-02-01 03:30:03 1998-02-28 23:16:54
## 3            6073        149 1998-02-03 20:47:38 1998-02-28 23:11:56
## 4            6074        194 1998-02-01 01:51:52 1998-02-28 09:27:23
## 5            6075        160 1998-02-01 17:25:23 1998-02-28 23:17:54
## 6            6076        157 1998-02-01 03:26:28 1998-02-24 07:34:53
## 7            9301        203 1998-02-01 03:33:42 1998-02-28 06:07:30
## 8            9302         87 1998-02-01 05:09:25 1998-02-26 16:10:40
## 9            9303         12 1998-02-01 01:07:29 1998-02-06 09:12:07
## 10           9373        207 1998-02-01 01:51:09 1998-02-24 07:36:01
## 11           9374        191 1998-02-02 15:34:44 1998-02-28 21:36:10
## 12           9375        109 1998-02-01 01:50:39 1998-02-27 03:48:20
## 13           9376        136 1998-02-01 17:26:47 1998-02-22 16:59:45
## 14           9377        115 1998-02-02 07:17:31 1998-02-22 23:48:03
##     tripDuration tripDistance  meanSpeed     maxSpeed
## 1   23.1674 days    1863.0570   6.432518    37.942286
## 2   27.8242 days    1892.3474   6.121462   145.272310
## 3  25.10021 days    1823.2853   5.996931   178.023461
## 4  27.31633 days    2238.5876  12.305419   577.145686
## 5   27.2448 days    1727.8244 114.413551 17359.733584
## 6  23.17251 days    2274.3382   8.749814   158.320598
## 7  27.10681 days    3103.7016  42.599268  6647.259782
## 8   25.4592 days    1033.1808   3.075486    24.619663
## 9  5.336551 days     159.9482   2.561213     7.672954
## 10 23.23949 days    2367.4532 165.291161 32266.087530
## 11   26.251 days    1861.8685  89.148217 15474.519777
## 12 26.08172 days    2528.5373  14.731275   502.195919
## 13 20.98123 days    1520.4642   5.334161    47.066037
## 14 20.68787 days    1163.4306   4.725903    49.112034
## 
## Total trip duration: 28422949 seconds (7895 hours, 949 seconds)
## 
## Derived from Spatial data:
## 
## Object of class SpatialPointsDataFrame
## Coordinates:
##               min     max
## longitude 318.281 328.453
## latitude  -54.689 -51.449
## Is projected: FALSE 
## proj4string :
## [+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs +towgs84=0,0,0
## +over]
## Number of points: 2004
## Data attributes:
##     prognum         ptt           nlines          nsensor      satname 
##  Min.   :920   Min.   :2163   Min.   : 2.000   Min.   : 1.00   D:1001  
##  1st Qu.:920   1st Qu.:6074   1st Qu.: 3.000   1st Qu.:32.00   J:1003  
##  Median :920   Median :9301   Median : 4.000   Median :32.00           
##  Mean   :920   Mean   :7547   Mean   : 4.428   Mean   :29.93           
##  3rd Qu.:920   3rd Qu.:9374   3rd Qu.: 5.000   3rd Qu.:32.00           
##  Max.   :920   Max.   :9377   Max.   :58.000   Max.   :32.00           
##                                                                        
##  class           date            time         altitude   transfreq        
##  Z:  0   1998-02-04: 106   02:27:48:   3   Min.   :0   Min.   :401648599  
##  B:403   1998-02-10: 106   15:36:45:   3   1st Qu.:0   1st Qu.:401649265  
##  A:376   1998-02-09:  96   19:21:28:   3   Median :0   Median :401649474  
##  0:704   1998-02-03:  95   03:34:41:   2   Mean   :0   Mean   :401649505  
##  1:420   1998-02-20:  93   04:19:04:   2   3rd Qu.:0   3rd Qu.:401649747  
##  2: 83   1998-02-18:  91   05:13:29:   2   Max.   :0   Max.   :401650517  
##  3: 18   (Other)   :1417   (Other) :1989                                  
##       gmt                     
##  Min.   :1998-02-01 01:07:29  
##  1st Qu.:1998-02-07 16:19:52  
##  Median :1998-02-13 04:40:36  
##  Mean   :1998-02-13 20:18:48  
##  3rd Qu.:1998-02-20 07:48:41  
##  Max.   :1998-02-28 23:17:54  
## 

Note that the form of the coordinates is native to the PRV file, and in this case contains longitude values that are greater than 180. Some forms of these files provide wrapped forms, but in general the data are read as-is.

(We need “world2” because we are at 40W, but +360).

plot(argos, pch = ".")
lines(argos)
maps::map("world2", add = TRUE)
axis(1)
sp::degAxis(2)

Destructive filtering

There are some classic data filters based on speed and angle, and we may chain these together for some cheap improvements to track data, or use them separately.

argos$spd <- speedfilter(argos, max.speed = 4)  ## km/h
mean(argos$spd)  ## more than 5% are too fast
## [1] 0.749002
plot(argos)
lines(argos[argos$spd & argos$class > "A", ])

argos$sda <- sda(argos, smax = 12)  ## defaults based on argosfilter, Freitas et al. (2008) 
mean(argos$sda)
## [1] 0.8687625
plot(argos)
lines(argos[argos$sda, ])

Map projections

Data may be stored in longitude latitude or using a map projection, an in-built data set uses the Azimuthal Equidistant family near the anti-meridian in the Bering Strait.

raster::projection(walrus818)
## [1] "+proj=aeqd +ellps=WGS84 +lon_0=-170 +lat_0=70"
data("walrus818")

plot(walrus818, pch = ".")
lines(walrus818)

axis(1)
axis(2)

library(maptools)
## Loading required package: sp
## Checking rgeos availability: TRUE
library(rgdal)
## rgdal: version: 1.4-3, (SVN revision 828)
##  Geospatial Data Abstraction Library extensions to R successfully loaded
##  Loaded GDAL runtime: GDAL 2.4.0, released 2018/12/14
##  Path to GDAL shared files: /usr/share/gdal
##  GDAL binary built with GEOS: TRUE 
##  Loaded PROJ.4 runtime: Rel. 5.2.0, September 15th, 2018, [PJ_VERSION: 520]
##  Path to PROJ.4 shared files: (autodetected)
##  Linking to sp version: 1.3-1
data(wrld_simpl)
world <- sp::spTransform(subset(wrld_simpl, coordinates(wrld_simpl)[,2] > 0), proj4string(walrus818))
p <- par(mar = rep(0.5, 4))
plot(raster::extent(walrus818) + 600000)
plot(walrus818, pch = ".", add = TRUE)
plot(world, add = TRUE, col = "grey")
lines(walrus818)
llgridlines(walrus818); par(p)

Data conversions

There are various conversions from other tracking data types, the trip() function aims to be a helpful function like raster::raster(), simply understanding many formats.

It’s possible to export trips to Google Earth, for interacting with the time slider in continuous time. Use write_track_kml() to produce a ‘KML/KMZ’ file.

When converting to spatial forms we may choose multi-lines, points, or segments.

Conversion to points, in ‘sp’ or ‘spatstat’.

## as points
as(walrus818, "SpatialPointsDataFrame")
## class       : SpatialPointsDataFrame 
## features    : 10558 
## extent      : -117277, 307789, -412557, 84896  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=aeqd +ellps=WGS84 +lon_0=-170 +lat_0=70 
## variables   : 4
## names       : Deployment,              DataDT, Wet, Forage 
## min values  :        353, 2009-09-15 04:00:00,   0,      0 
## max values  :        444, 2010-10-20 19:00:00,   1,      1
as(walrus818, "ppp")
## Marked planar point pattern: 10558 points
## Mark variables: Deployment, DataDT, Wet, Forage 
## window: rectangle = [-117277, 307789] x [-412557, 84896] units

Conversion to lines, in ‘sp’, ‘sf’, or ‘adehabitatLT’.

## as lines
as(walrus818, "SpatialLinesDataFrame")
## class       : SpatialLinesDataFrame 
## features    : 14 
## extent      : -117277, 307789, -412557, 84896  (xmin, xmax, ymin, ymax)
## coord. ref. : +proj=aeqd +ellps=WGS84 +lon_0=-170 +lat_0=70 
## variables   : 4
## names       : tripID,           tripStart,             tripEnd, tripDur 
## min values  :    353, 2009-09-15 04:00:00, 2009-09-30 19:00:00, 1195200 
## max values  :    444, 2010-09-07 17:00:00, 2010-10-20 19:00:00, 5695200
as(walrus818, "sf")
##     tripID           tripStart             tripEnd tripDur
## 353    353 2009-09-15 04:00:00 2009-09-30 19:00:00 1350000
## 354    354 2009-09-16 04:00:00 2009-10-20 00:00:00 2923200
## 355    355 2009-09-16 04:00:00 2009-11-04 19:00:00 4287600
## 356    356 2009-09-16 23:00:00 2009-11-21 21:00:00 5695200
## 357    357 2009-09-16 23:00:00 2009-11-09 22:00:00 4662000
## 358    358 2009-09-16 23:00:00 2009-10-18 19:00:00 2750400
## 359    359 2009-09-16 23:00:00 2009-10-30 19:00:00 3787200
## 361    361 2009-09-17 01:00:00 2009-11-06 04:00:00 4330800
## 362    362 2009-09-17 01:00:00 2009-10-03 17:00:00 1440000
## 366    366 2009-09-19 15:00:00 2009-10-12 20:00:00 2005200
## 367    367 2009-09-17 01:00:00 2009-11-10 16:00:00 4719600
## 368    368 2009-09-19 02:00:00 2009-10-02 22:00:00 1195200
## 443    443 2010-09-07 17:00:00 2010-10-20 19:00:00 3722400
## 444    444 2010-09-07 17:00:00 2010-09-28 05:00:00 1771200
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  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## 366