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Here, we introduce R, a statistical programming language. Doing statistics within a programming language brings many advantages, including allowing one to organize all analyses into program files that can be rerun to replicate analyses. In addition to using R, we will be using RStudio, an integrated development environment (IDE), which assists us in working with R and outputs of our code as we develop it. Our objective today is to get everyone up to speed with working knowledge of R and programming to be able to do exercises as a part of the rest of the course.
Both R and RStudio are freely available online.
Download the appropriate “base” version of R for your operating system from CRAN: https://cran.r-project.org/
Install the software with default settings.
Download the appropriate RStudio version for your operating system: https://www.rstudio.com/products/rstudio/download/#download
Follow along in your R console with the code in each of the code chunks as we explore the different aspects of R! Clicking on the github logo on the top right corner of the webpage will take you to the repository for this website, where you can download the R markdown file for this page to load into RStudio to follow along.
Many familiar operators work in R, allowing you to work with numbers like you would in a calculator. Operators such as inequalities also work, returning “TRUE” if the proposed logical expression is true and “FALSE” otherwise.
2+4 #addition
[1] 6
2-4 #subtraction
[1] -2
2*4 #multiplication
[1] 8
2/4 #division
[1] 0.5
2^4 #exponentiation
[1] 16
log(2) #the default log base is the natural log
[1] 0.6931472
2 < 4
[1] TRUE
2 > 4
[1] FALSE
2 >= 4 #greater than or equal to
[1] FALSE
2 == 2 #is equal to (notice that there are two equal signs, as a single equal sign denotes assignment)
[1] TRUE
2 != 4 #is not equal to
[1] TRUE
2 != 4 | 2 + 2 == 4 #OR
[1] TRUE
2 != 4 & 2 + 2 == 4 #AND
[1] TRUE
"Red" == "Red"
[1] TRUE
In addition to being able to work with actual numbers, R works in objects, which can represent anything from numbers to strings to vectors to matrices. Everything in R is an object. The best practice for assigning variable names to objects is the “<-” operator. After objects are created, they are stored in in the “Environment” tab in your RStudio console and can be called upon to perform different operations.
R has many data structures, including:
R has 6 atomic vector types, or classes. Atomic means that a vector only contains elements of one class (i.e. the elements inside the vector do not come from mutliple classes).
a <- 2
b <- 3
a + b
[1] 5
class(a) #the "class" function tells you what class of object a is
[1] "numeric"
d <- c(1,2,3,4,5) #the "c" function concatenates the arguments contained within it into a vector
d
[1] 1 2 3 4 5
d <- c(d, 1) #The "c" function also allows you to append items to an existing vector
d
[1] 1 2 3 4 5 1
class(d)
[1] "numeric"
d[3] #brackets allow you index vectors or matrices. Here, we call the third value from our d vector.
[1] 3
#Matrices are just like vectors, but with two dimensions
my_matrix <- matrix(seq(1:9), ncol = 3)
my_matrix
[,1] [,2] [,3]
[1,] 1 4 7
[2,] 2 5 8
[3,] 3 6 9
#vectors and matrices can only contain objects of one class. If you include objects of multiple types into the same vector, R will perform coersion to force all the objects contained in the vector into a shared class
x <- c(1.7, "a")
x
[1] "1.7" "a"
class("a")
[1] "character"
class(1.7)
[1] "numeric"
class(x)
[1] "character"
y <- c(TRUE, 2)
y
[1] 1 2
z <- c("a", TRUE)
z
[1] "a" "TRUE"
#If you would like to store objects of multiple classes into one object, a list can accomodate such a task.
x_y_z_list <- list(x,y,z)
x_y_z_list
[[1]]
[1] "1.7" "a"
[[2]]
[1] 1 2
[[3]]
[1] "a" "TRUE"
#to index an element in a list, use double brackets [[]]. You can further index elements within an element of a list.
x_y_z_list[[1]]
[1] "1.7" "a"
x_y_z_list[[1]][2]
[1] "a"
#elements in a list can be assigned names
x_y_z_list <- list(a=x, b=y, c=z)
x_y_z_list
$a
[1] "1.7" "a"
$b
[1] 1 2
$c
[1] "a" "TRUE"
#Dataframes are a very commonly used type of object in R. You can think of a dataframe as a rectangular combination of lists.
#The below code stores the stated values in a dataframe which contains employee ids, names, salaries, and start dates for 5 employees
emp.data <- data.frame(
emp_id = c (1:5),
emp_name = c("Rick","Dan","Michelle","Ryan","Gary"),
salary = c(623.3,515.2,611.0,729.0,843.25),
start_date = as.Date(c("2012-01-01", "2013-09-23", "2014-11-15", "2014-05-11",
"2015-03-27")),
stringsAsFactors = FALSE
)
emp.data
emp_id emp_name salary start_date
1 1 Rick 623.30 2012-01-01
2 2 Dan 515.20 2013-09-23
3 3 Michelle 611.00 2014-11-15
4 4 Ryan 729.00 2014-05-11
5 5 Gary 843.25 2015-03-27
emp.data$emp_id #the $ operator calls on a certain column of a dataframe
[1] 1 2 3 4 5
class(emp.data$emp_id) #As noted earlier, a dataframe can be thought of as a rectangular list, combining different data classes together, each in a different column.
[1] "integer"
class(emp.data$salary)
[1] "numeric"
emp.data$emp_name[emp.data$salary > 620] #You can combine logical operators, brackets, and the $ sign to subset your dataframe in any way you choose! Here, we print out all the employee names for employees who have a salary greater than 620.
[1] "Rick" "Ryan" "Gary"
ls() #ls lists all the variable names that have been assigned to objects in your workspace
[1] "a" "b" "d" "emp.data" "my_matrix"
[6] "x" "x_y_z_list" "y" "z"
In addition to the basic functions provided in R, oftentimes we will be working with packages that contain functions written by other people to perform common tasks or specific analyses. Packages can also contain datasets. We can load these packages into our R environment after installing them in R.
usePackage <- function(p)
{
if (!is.element(p, installed.packages()[,1]))
install.packages(p, dep = TRUE)
require(p, character.only = TRUE)
}
usePackage("gapminder")#This code installs the gapminder packages, which contains vital statistics data from multiple countries. install.packages() is the function that will install a package for you if you know it's name.
Loading required package: gapminder
library("gapminder") #After installing the package, we need to tell R to load it into our current environment with this function.
head(gapminder) #The package gapminder contains a dataset called gapminder. We can use the "head" function to print out the first 6 rows of this dataset.
# A tibble: 6 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779.
2 Afghanistan Asia 1957 30.3 9240934 821.
3 Afghanistan Asia 1962 32.0 10267083 853.
4 Afghanistan Asia 1967 34.0 11537966 836.
5 Afghanistan Asia 1972 36.1 13079460 740.
6 Afghanistan Asia 1977 38.4 14880372 786.
?gapminder #the ? operator lauches a help page to describe a particular function, including the arguments it takes. Whenever using a new function, it is good practice to first explore it through ?.
Oftentimes, we may want to perform the same operation or function many many times. Rather than having to explicitly write out each individual operation, we can make use of loops. For example, let’s say that we want to raise the number 2 to the power of each integer from 0 to 20. We could either write out 2^0, 2^1, 2^2 …, or make use of a for loop to condense our code while getting the same result.
2^0
[1] 1
2^1
[1] 2
2^2
[1] 4
2^3
[1] 8
# ...
#This is a for loop. in the parentheses after the for function, we specify over what range of values we want to loop over, and assign a dummy variable name to take on each of those values in sequence. Within the curly braces, we state what operation we want to perform over all the values taken on by the dummy variable.
for(i in 0:20){
print(2^i)
}
[1] 1
[1] 2
[1] 4
[1] 8
[1] 16
[1] 32
[1] 64
[1] 128
[1] 256
[1] 512
[1] 1024
[1] 2048
[1] 4096
[1] 8192
[1] 16384
[1] 32768
[1] 65536
[1] 131072
[1] 262144
[1] 524288
[1] 1048576
Another way to avoid writing out or copy-pasting the same exact thing over and over again when working with data is to write a function to contain a certain combination of operations you find yourself running mutliple times. For example, you may find yourself needing to calculate the Hardy-Weinberg Equillibrium genotype frequencies of a population given the allele frequencies. We can wrap up all the code that you would need to calculate this in a function that we can call upon again and again.
calc_HWE_geno <- function(p = 0.5){
q <- 1-p
pp <- p^2
pq <- 2*p*q
qq <- q^2
return(c(pp, pq, qq))
}
log. <- function(number){
return(log(number))
}
calc_HWE_geno(p = 0.1)
[1] 0.01 0.18 0.81
#note that in our UDF we assigned a default value to p (p = 0.5). This means that if we do not specify a value for our argument of p, it will default to using that value.
calc_HWE_geno()
[1] 0.25 0.50 0.25
In addition to mathematical operations, R can help with data visualization. Base R has a few useful plotting functions, but popular packages such as ggplot2 give more customization and control to the user.
hist(gapminder$lifeExp)
boxplot(lifeExp ~ continent, data = gapminder) #box plot for the life expectancies of all years per continent
R has many functions that use a random number generator to generate an output. For example, the r____ functions (e.g. rbinom, runif) pull numbers from a probability distribution of your choice. In order to create reproducible analyses, it is often advantageous to be able to reliably obtain the same “random” number after running the same function over again. In order to do so, we can set a seed for the random number generator.
runif(1,0,1) #runif pulls a number from the uniform distribution with a set of given parameters
[1] 0.1944457
runif(1,0,1) #we can see that running runif twice gives you differnt results
[1] 0.205278
set.seed(1234) #setting a seed allows us to obtain reproducible results from functions that use the random number generator
runif(1,0,1)
[1] 0.1137034
set.seed(1234)
runif(1,0,1)
[1] 0.1137034
Finally, let us address probably one of the most important points when working with statistics in science: how to get the data you have collected into your R environment. For this part of the lesson, we will be working with the bandersnatch.csv file (created by Katie Long) located here: https://raw.githubusercontent.com/anthonyhung/MSTPsummerstatistics/master/data/bandersnatch.csv. If you would like to have your own copy of this dataset, you can open up a terminal window and run the commands.
cd ~/Desktop
mkdir data
cd data
wget https://raw.githubusercontent.com/anthonyhung/MSTPsummerstatistics/master/data/bandersnatch.csv
Now that we have a copy of the data in a data directory on our desktop, we can load it into R using a relative or absolute directory path and the read.csv function.
data <- read.csv("~/Desktop/data/bandersnatch.csv")
#let's take a look at the dataset we've just loaded
head(data)
Color Fur Baseline.Frumiosity Post.Frumiosity
1 Red Nude 4.477127 11.46590
2 Red Nude 4.113727 11.09354
3 Red Nude 4.806221 11.81268
4 Red Nude 5.357348 12.36704
5 Red Nude 5.951754 12.96135
6 Red Nude 3.593995 10.62375
summary(data)
Color Fur Baseline.Frumiosity Post.Frumiosity
Blue:200000 Furry:200000 Min. :-1.108 Min. : 1.887
Red :200000 Nude :200000 1st Qu.: 4.001 1st Qu.: 4.044
Median : 6.980 Median : 8.976
Mean : 6.001 Mean : 9.001
3rd Qu.: 8.961 3rd Qu.:13.956
Max. : 9.174 Max. :16.192
#what is the difference between these two function calls?
head(read.csv("~/Desktop/data/bandersnatch.csv", header = T))
Color Fur Baseline.Frumiosity Post.Frumiosity
1 Red Nude 4.477127 11.46590
2 Red Nude 4.113727 11.09354
3 Red Nude 4.806221 11.81268
4 Red Nude 5.357348 12.36704
5 Red Nude 5.951754 12.96135
6 Red Nude 3.593995 10.62375
head(read.csv("~/Desktop/data/bandersnatch.csv", header = F))
V1 V2 V3 V4
1 Color Fur Baseline Frumiosity Post-Frumiosity
2 Red Nude 4.477127244 11.46590322
3 Red Nude 4.113726932 11.09353649
4 Red Nude 4.806220524 11.81268077
5 Red Nude 5.357347878 12.36703951
6 Red Nude 5.951754455 12.96134984
#let's look at the structure of the data
class(data)
[1] "data.frame"
class(data$Color)
[1] "factor"
class(data$Baseline.Frumiosity)
[1] "numeric"
#let's make some plots with the data
hist(data$Baseline.Frumiosity)
hist(data$Post.Frumiosity)
plot(data$Baseline.Frumiosity, data$Post.Frumiosity)
#we can also write data files and export them using R
data$Size <- rnorm(nrow(data))
write.csv(data, "~/Desktop/data/new_bandersnatch.csv")
Write a function called calc_KE that takes as arguments the mass (in kg) and velocity (in m/s) of an object and returns the kinetic energy (in Joules) of an object. Use it to find the KE of a 0.5 kg rock moving at 1.2 m/s.
Working with the gapminder dataset, find the country with the highest life expectancy in 1962.
The dplyr package is a powerful tool for working with dataframes (what is a dataframe?) in R. The framework of dplyr relies on the use of “pipes” or the “%>%” operator, to apply multiple useful functions to a dataframe sequentially. Today we will cover these functions:
mutate() adds new variables that are functions of existing variables select() picks variables based on their names. filter() picks cases based on their values. summarise() reduces multiple values down to a single summary. arrange() changes the ordering of the rows.
However, there are many more useful functions in the package that may come in handy depending on your specific problem!
library(dplyr)
Attaching package: 'dplyr'
The following objects are masked from 'package:stats':
filter, lag
The following objects are masked from 'package:base':
intersect, setdiff, setequal, union
gapminder
# A tibble: 1,704 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779.
2 Afghanistan Asia 1957 30.3 9240934 821.
3 Afghanistan Asia 1962 32.0 10267083 853.
4 Afghanistan Asia 1967 34.0 11537966 836.
5 Afghanistan Asia 1972 36.1 13079460 740.
6 Afghanistan Asia 1977 38.4 14880372 786.
7 Afghanistan Asia 1982 39.9 12881816 978.
8 Afghanistan Asia 1987 40.8 13867957 852.
9 Afghanistan Asia 1992 41.7 16317921 649.
10 Afghanistan Asia 1997 41.8 22227415 635.
# … with 1,694 more rows
#mutate
mutate(gapminder, GDP = gdpPercap * pop)
# A tibble: 1,704 x 7
country continent year lifeExp pop gdpPercap GDP
<fct> <fct> <int> <dbl> <int> <dbl> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779. 6567086330.
2 Afghanistan Asia 1957 30.3 9240934 821. 7585448670.
3 Afghanistan Asia 1962 32.0 10267083 853. 8758855797.
4 Afghanistan Asia 1967 34.0 11537966 836. 9648014150.
5 Afghanistan Asia 1972 36.1 13079460 740. 9678553274.
6 Afghanistan Asia 1977 38.4 14880372 786. 11697659231.
7 Afghanistan Asia 1982 39.9 12881816 978. 12598563401.
8 Afghanistan Asia 1987 40.8 13867957 852. 11820990309.
9 Afghanistan Asia 1992 41.7 16317921 649. 10595901589.
10 Afghanistan Asia 1997 41.8 22227415 635. 14121995875.
# … with 1,694 more rows
gapminder %>% mutate(GDP = gdpPercap * pop) #pipes
# A tibble: 1,704 x 7
country continent year lifeExp pop gdpPercap GDP
<fct> <fct> <int> <dbl> <int> <dbl> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779. 6567086330.
2 Afghanistan Asia 1957 30.3 9240934 821. 7585448670.
3 Afghanistan Asia 1962 32.0 10267083 853. 8758855797.
4 Afghanistan Asia 1967 34.0 11537966 836. 9648014150.
5 Afghanistan Asia 1972 36.1 13079460 740. 9678553274.
6 Afghanistan Asia 1977 38.4 14880372 786. 11697659231.
7 Afghanistan Asia 1982 39.9 12881816 978. 12598563401.
8 Afghanistan Asia 1987 40.8 13867957 852. 11820990309.
9 Afghanistan Asia 1992 41.7 16317921 649. 10595901589.
10 Afghanistan Asia 1997 41.8 22227415 635. 14121995875.
# … with 1,694 more rows
gapminder_with_GDP <- gapminder %>% mutate(GDP = gdpPercap * pop) #assign output to variable
gapminder_with_GDP
# A tibble: 1,704 x 7
country continent year lifeExp pop gdpPercap GDP
<fct> <fct> <int> <dbl> <int> <dbl> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779. 6567086330.
2 Afghanistan Asia 1957 30.3 9240934 821. 7585448670.
3 Afghanistan Asia 1962 32.0 10267083 853. 8758855797.
4 Afghanistan Asia 1967 34.0 11537966 836. 9648014150.
5 Afghanistan Asia 1972 36.1 13079460 740. 9678553274.
6 Afghanistan Asia 1977 38.4 14880372 786. 11697659231.
7 Afghanistan Asia 1982 39.9 12881816 978. 12598563401.
8 Afghanistan Asia 1987 40.8 13867957 852. 11820990309.
9 Afghanistan Asia 1992 41.7 16317921 649. 10595901589.
10 Afghanistan Asia 1997 41.8 22227415 635. 14121995875.
# … with 1,694 more rows
#select
gapminder %>% select(c(country, continent, year))
# A tibble: 1,704 x 3
country continent year
<fct> <fct> <int>
1 Afghanistan Asia 1952
2 Afghanistan Asia 1957
3 Afghanistan Asia 1962
4 Afghanistan Asia 1967
5 Afghanistan Asia 1972
6 Afghanistan Asia 1977
7 Afghanistan Asia 1982
8 Afghanistan Asia 1987
9 Afghanistan Asia 1992
10 Afghanistan Asia 1997
# … with 1,694 more rows
data %>% select(contains("frumiosity"))
Baseline.Frumiosity Post.Frumiosity
1 4.4771272 11.465903
2 4.1137269 11.093536
3 4.8062205 11.812681
4 5.3573479 12.367040
5 5.9517545 12.961350
6 3.5939949 10.623747
7 5.3490368 12.364961
8 4.1917213 11.167766
9 5.8279043 12.832270
10 4.8944966 11.871473
11 4.3439489 11.372715
12 5.2619523 12.248492
13 4.8403817 11.851436
14 5.3594114 12.372434
15 6.4822183 13.507131
16 6.0509554 13.080639
17 5.8266867 12.813596
18 5.3689744 12.352238
19 5.3259553 12.314148
20 4.9361894 11.946488
21 4.2347204 11.235789
22 3.0468689 10.073550
23 4.1929852 11.214008
24 5.3446392 12.367471
25 6.6478214 13.676934
26 4.9569126 11.984350
27 3.6995661 10.666928
28 5.8767910 12.915261
29 5.6491350 12.662528
30 5.9874522 12.986545
31 5.1614084 12.164069
32 4.9768114 11.969604
33 2.8993810 9.907457
34 5.5025639 12.500121
35 2.8930196 9.909410
36 5.1166162 12.118122
37 5.5580922 12.567972
38 4.7209083 11.724678
39 5.2179284 12.231664
40 4.0936239 11.053131
41 5.5801864 12.562098
42 3.6377103 10.649007
43 5.5552585 12.540225
44 4.0990299 11.110147
45 6.0817972 13.060625
46 4.0171294 11.024481
47 3.8669036 10.902406
48 5.1407890 12.147328
49 3.5756030 10.597268
50 3.9106530 10.900501
51 4.2882750 11.263726
52 4.8553496 11.865918
53 6.2684787 13.240602
54 5.6182651 12.582063
55 5.1241967 12.116564
56 4.7065468 11.713021
57 6.9582747 13.954522
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1315 6.7033109 13.693778
1316 4.2161538 11.202124
1317 4.4638243 11.480102
1318 5.7802090 12.772246
1319 4.5526427 11.577015
1320 8.4828036 15.476492
1321 5.4703207 12.435441
1322 4.5525664 11.551023
1323 4.8864509 11.917011
1324 3.8213100 10.815083
1325 4.0559933 11.028023
1326 3.8262948 10.860703
1327 6.0208073 12.989673
1328 5.4534031 12.421269
1329 4.6580286 11.627826
1330 4.5227537 11.540369
1331 3.5847414 10.574311
1332 6.1634372 13.186584
1333 4.2830358 11.297668
1334 4.5656184 11.578912
1335 4.3399928 11.337434
1336 4.3619996 11.377189
1337 6.1526569 13.134182
1338 3.6093213 10.594371
1339 3.0646710 10.061941
1340 3.5267924 10.538113
1341 4.8037254 11.841934
1342 4.7718012 11.757953
1343 3.6930572 10.721102
1344 5.0347048 12.061455
1345 4.5738941 11.547229
1346 4.9751139 11.990046
1347 6.1710960 13.185250
1348 6.2886629 13.267561
1349 5.3794360 12.372107
1350 2.4785420 9.447930
1351 4.3950237 11.413149
1352 5.5262834 12.541461
1353 5.2789534 12.309449
1354 5.8673141 12.873931
1355 6.1985531 13.213389
1356 5.9608475 13.016322
1357 4.6636119 11.675701
1358 4.8784524 11.894533
1359 5.0310033 12.017857
1360 3.0436506 10.053893
1361 4.2917705 11.321200
1362 3.2389325 10.239900
1363 4.4064959 11.415208
1364 2.8480630 9.834932
1365 5.8544062 12.859813
1366 5.1948630 12.227752
1367 4.6792318 11.668403
1368 3.9572977 10.991715
1369 6.3641550 13.408130
1370 3.8445438 10.831557
1371 5.3564448 12.393760
1372 4.6328327 11.635476
1373 5.9703823 12.998068
1374 6.2513409 13.252458
1375 4.6171174 11.633321
1376 5.7406340 12.764048
1377 4.9074727 11.967669
1378 3.1627444 10.145630
1379 4.8076296 11.802474
1380 5.7711003 12.768362
1381 6.3118438 13.319362
1382 5.6141392 12.630385
1383 4.2058419 11.187833
1384 5.3810800 12.398048
1385 6.0430341 12.998211
1386 5.9660683 12.986921
1387 3.7814735 10.792563
1388 4.2656630 11.257770
1389 4.1945327 11.169362
1390 5.4469006 12.468471
1391 3.3570670 10.368379
1392 5.2367715 12.257736
1393 6.4074099 13.389610
1394 2.5748385 9.585500
1395 5.0448923 12.032672
1396 4.0951023 11.083121
1397 5.6258672 12.635681
1398 6.8668133 13.875659
1399 5.0599109 12.069404
1400 4.5186493 11.529401
1401 4.3631126 11.360274
1402 5.6345614 12.636639
1403 5.3121539 12.322151
1404 5.7630038 12.804679
1405 4.9813965 11.995230
1406 5.3168124 12.325168
1407 4.0013026 11.015382
1408 3.0038962 10.006697
1409 6.6212716 13.635679
1410 5.4089819 12.411633
1411 6.2217435 13.204730
1412 5.9688089 12.944055
1413 4.0221375 11.002526
1414 6.5536865 13.542570
1415 4.3718052 11.361433
1416 6.6120564 13.634171
1417 4.3559062 11.353213
1418 5.1962501 12.186887
1419 6.2916598 13.324396
1420 6.7124737 13.693412
1421 4.7908737 11.783486
1422 4.3742120 11.399314
1423 4.5392311 11.519580
1424 5.1024985 12.085097
1425 4.9514668 11.978473
1426 5.4052049 12.399925
1427 5.1928433 12.194379
1428 5.4616032 12.473627
1429 5.9658042 12.992963
1430 4.6736994 11.660846
1431 4.1024591 11.075345
1432 4.0135992 11.025820
1433 4.4121188 11.400463
1434 3.8414545 10.835803
1435 5.3623469 12.367845
1436 5.5757129 12.582707
1437 2.2893916 9.323212
1438 4.1300338 11.106117
1439 4.9914732 12.009247
1440 5.3775771 12.377868
1441 4.8025373 11.778505
1442 5.3644365 12.304742
1443 5.1057096 12.113669
1444 5.2677034 12.295235
1445 6.0713469 13.080196
1446 6.6054251 13.612913
1447 5.1590962 12.163695
1448 6.4292743 13.414456
1449 3.8477937 10.862521
1450 3.2561305 10.242628
1451 3.9305060 10.926510
1452 3.2076283 10.202644
1453 3.9100255 10.936882
1454 4.9747187 11.986465
1455 3.9699719 11.007938
1456 5.8914809 12.841475
1457 4.4930364 11.495224
1458 3.4227718 10.417449
1459 3.8305869 10.841517
1460 4.7133866 11.719516
1461 4.1496580 11.159604
1462 6.9522427 13.969148
1463 5.0443776 12.019485
1464 6.1294659 13.100508
1465 4.8850891 11.892114
1466 3.2743025 10.215897
1467 5.9379406 12.967698
1468 3.5120112 10.506149
1469 6.1046673 13.102869
1470 4.8883227 11.874552
1471 6.0933088 13.071435
1472 5.2127700 12.181753
1473 5.7575033 12.764629
1474 7.0434060 14.008096
1475 4.0642751 11.101084
1476 4.1936665 11.196927
1477 3.7686692 10.775972
1478 4.5819803 11.554653
1479 3.6611317 10.683569
1480 3.6508551 10.665521
1481 3.8665716 10.869228
1482 3.9379473 10.959704
1483 4.7162258 11.689852
1484 4.5673318 11.558960
1485 7.1261219 14.159350
1486 6.0698261 13.061888
1487 4.3910506 11.402728
1488 3.8296730 10.849569
1489 4.8731858 11.854784
1490 5.5732067 12.565353
1491 4.7266937 11.734331
1492 5.2512563 12.262177
1493 6.3496278 13.332403
1494 5.7823820 12.786376
1495 3.1419537 10.140972
1496 6.4778253 13.503278
1497 6.0888188 13.098157
1498 3.7790637 10.820283
1499 5.9062512 12.930622
1500 4.6025813 11.573707
1501 3.3049569 10.318245
1502 5.6440272 12.671666
1503 6.0953941 13.089746
1504 4.3771155 11.363371
1505 4.5911029 11.583248
1506 4.2255172 11.243351
1507 4.2859300 11.285888
1508 5.8570628 12.849920
1509 3.9142328 10.910710
1510 6.0208912 13.041767
1511 5.0824551 12.104858
1512 6.5492104 13.515272
1513 4.9635123 11.981747
1514 4.5139401 11.484455
1515 6.2962452 13.303586
1516 2.7049608 9.697864
1517 4.5346658 11.548803
1518 7.6752765 14.643446
1519 5.7233698 12.746030
1520 5.0865640 12.063929
1521 4.7688121 11.771855
1522 4.4931645 11.485237
1523 5.7021814 12.728275
1524 5.9579017 12.939736
1525 6.4816702 13.476010
1526 5.9818383 12.981617
1527 5.4142851 12.408463
1528 5.3521470 12.378178
1529 6.1433018 13.181563
1530 4.6221768 11.638767
1531 5.0470892 12.025179
1532 2.9059175 9.879641
1533 4.8489581 11.876003
1534 4.2725453 11.298847
1535 4.4934971 11.467022
1536 4.6260021 11.629054
1537 5.8478138 12.834659
1538 5.8749499 12.854260
1539 6.2934100 13.288648
1540 4.8877865 11.891449
1541 5.6548183 12.658106
1542 4.6582731 11.662689
1543 3.4355412 10.454520
1544 4.1544571 11.155373
1545 3.5900716 10.589165
1546 5.2932313 12.304376
1547 3.9921361 10.985190
1548 5.0132981 12.026608
1549 3.4123180 10.389906
1550 4.0891718 11.068248
1551 4.7010610 11.702962
1552 3.3073944 10.323469
1553 4.8585991 11.872007
1554 4.8893671 11.858980
1555 5.4015287 12.388017
1556 4.6424324 11.632867
1557 6.1647501 13.174408
1558 4.7206679 11.715928
1559 4.2781152 11.212014
1560 5.7095112 12.703080
1561 5.1110008 12.147018
1562 6.3117367 13.350732
1563 5.2679697 12.276332
1564 5.0664358 12.052762
1565 5.2375381 12.215516
1566 4.1953288 11.225342
1567 5.6558991 12.687976
1568 3.2945133 10.306134
1569 4.0512654 11.057302
1570 5.4134447 12.415256
1571 7.0106098 13.981072
1572 5.8018569 12.789576
1573 4.3345890 11.327978
1574 5.1492953 12.150815
1575 4.3236121 11.308993
1576 6.2979031 13.329767
1577 5.1555697 12.130798
1578 4.9470761 11.947834
1579 3.6220361 10.631395
1580 5.0130270 11.994101
1581 4.3841550 11.353016
1582 4.9153167 11.916876
1583 3.9300729 10.943888
1584 3.7460477 10.743756
1585 3.8670810 10.871935
1586 5.7292071 12.725002
1587 3.5140969 10.491368
1588 3.4026076 10.397714
1589 6.0261426 13.036084
1590 3.8076617 10.806386
1591 5.8413691 12.842212
1592 3.4608581 10.465993
1593 5.6762902 12.686499
1594 4.7238445 11.695788
1595 6.0002529 13.035295
1596 3.7607555 10.755155
1597 2.6828999 9.678329
1598 3.3330878 10.324906
1599 4.5723038 11.586023
1600 5.7757490 12.799876
1601 6.3664430 13.360606
1602 5.5807947 12.556308
1603 4.8872576 11.897104
1604 5.2002477 12.191732
1605 6.4304686 13.473714
1606 5.8220775 12.831384
1607 4.9898673 11.983396
1608 3.0352585 10.028142
1609 7.5296723 14.505840
1610 4.2568291 11.234770
1611 6.5329697 13.532699
1612 6.7261632 13.743452
1613 4.3077709 11.304091
1614 5.2304532 12.222694
1615 5.5176934 12.515693
1616 5.8442251 12.867739
1617 5.5069018 12.494000
1618 5.6998924 12.702651
1619 3.4997097 10.501702
1620 6.9916309 13.990298
1621 4.1589875 11.172413
1622 7.1749096 14.147334
1623 3.8030799 10.812148
1624 5.9619857 13.011483
1625 4.8272201 11.789045
1626 3.8299381 10.846559
1627 5.9641963 12.956698
1628 4.8136017 11.827555
1629 4.7156123 11.734838
1630 5.8839646 12.907364
1631 4.3823201 11.335229
1632 4.7698349 11.783570
1633 6.3236231 13.289515
1634 3.8888613 10.897152
1635 5.0260360 12.006911
1636 5.7645463 12.795607
1637 3.9158376 10.940413
1638 4.0019801 10.997140
1639 4.6494821 11.641920
1640 3.8752244 10.890203
1641 4.4876642 11.488016
1642 6.1208445 13.140109
1643 4.7493306 11.741570
1644 5.6308194 12.629189
1645 5.9724761 12.981951
1646 5.2964087 12.291914
1647 5.0652806 12.079817
1648 5.0558487 12.077230
1649 3.2670370 10.269822
1650 4.1621421 11.177891
1651 5.7915542 12.841755
1652 4.8477822 11.836473
1653 6.0106671 12.971429
1654 3.4843888 10.474625
1655 6.1881583 13.184285
1656 6.6641226 13.671704
1657 3.6404281 10.626170
1658 4.6563617 11.669060
1659 5.6051774 12.603900
1660 4.6423020 11.671829
1661 5.1410872 12.121630
1662 4.0274315 11.028097
1663 5.0155911 12.014758
1664 4.4799448 11.482694
1665 4.2452135 11.260209
1666 5.9491928 12.944139
1667 3.2370547 10.232589
1668 5.3327441 12.326907
1669 3.8684314 10.845263
1670 4.8452939 11.825145
1671 6.4253690 13.439670
1672 5.6722380 12.669553
1673 4.3628405 11.385507
1674 6.4849287 13.493034
1675 5.7865456 12.757323
1676 4.7317953 11.747453
1677 6.2359116 13.218259
1678 4.1506228 11.118003
1679 4.9968614 11.962757
1680 5.3720697 12.373490
1681 5.7420967 12.737140
1682 6.4430563 13.461629
1683 2.1204076 9.132847
1684 4.3891878 11.370721
1685 6.2367362 13.229406
1686 6.4368532 13.448060
1687 4.5792796 11.559306
1688 4.5790226 11.537590
1689 3.8121771 10.841583
1690 4.0667627 11.069844
1691 2.8497255 9.855181
1692 4.1603069 11.156293
1693 4.9766362 11.962777
1694 5.2142456 12.211756
1695 3.3053837 10.287995
1696 5.8785488 12.843863
1697 3.8790131 10.904292
1698 5.0418943 12.029401
1699 4.5990973 11.587726
1700 4.5939245 11.603661
1701 5.4134564 12.434343
1702 5.4651290 12.485127
1703 2.8073081 9.845925
1704 5.1935254 12.232833
1705 5.0966848 12.088813
1706 4.2273418 11.205861
1707 4.8882217 11.856521
1708 5.1397408 12.118949
1709 5.2227862 12.219242
1710 3.9441370 10.937543
1711 3.9238997 10.896266
1712 5.1369632 12.173058
1713 5.5285932 12.514678
1714 5.4386596 12.439036
1715 5.4696124 12.443041
1716 3.8416331 10.822454
1717 4.2874323 11.296200
1718 3.4313421 10.471547
1719 6.1686605 13.180644
1720 4.3445290 11.361716
1721 4.6385113 11.594298
1722 4.9878059 11.981859
1723 4.7352859 11.768332
1724 4.6229000 11.584040
1725 2.8679925 9.872182
1726 5.1702920 12.164863
1727 3.9209785 10.915244
1728 4.3441862 11.367311
1729 4.7402319 11.753584
1730 7.6014549 14.598521
1731 4.5986909 11.607291
1732 3.9405291 10.963065
1733 4.4700007 11.459059
1734 4.4733066 11.451359
1735 5.0377085 12.058884
1736 6.0630012 13.075473
1737 4.4361557 11.438188
1738 5.8037469 12.837303
1739 4.0059621 11.024423
1740 1.5938948 8.586643
1741 5.7252737 12.734371
1742 4.8356716 11.858766
1743 3.9895985 10.959597
1744 6.3047313 13.280044
1745 5.0333937 12.038905
1746 3.9154104 10.917694
1747 4.5108372 11.544216
1748 3.6981583 10.705461
1749 5.1788854 12.150824
1750 5.2127723 12.221750
1751 5.1177587 12.097044
1752 3.9514990 10.951904
1753 4.3785302 11.342931
1754 5.9776886 12.968648
1755 6.4208025 13.430020
1756 5.0453587 12.013391
1757 5.4389591 12.467359
1758 4.2770108 11.293239
1759 4.8349785 11.843849
1760 7.9795719 15.008919
1761 4.1868940 11.160960
1762 4.2093950 11.189251
1763 3.9255501 10.924835
1764 3.8563975 10.870540
1765 4.8419807 11.831626
1766 6.1885108 13.190190
1767 4.6818463 11.735517
1768 5.2972007 12.265010
1769 4.8975992 11.913691
1770 4.0041532 10.986559
1771 5.1188695 12.095246
1772 4.3753304 11.376494
1773 4.8671385 11.838424
1774 4.4267780 11.474962
1775 4.7250355 11.712884
1776 4.6608691 11.640213
1777 4.9455871 11.914753
1778 6.0030172 12.986040
1779 5.8790820 12.867842
1780 5.5451668 12.577460
1781 4.8984096 11.918853
1782 4.7084408 11.691929
1783 5.1020381 12.083690
1784 4.6421709 11.604555
1785 4.7028578 11.693118
1786 5.2222559 12.210117
1787 4.2383431 11.247715
1788 3.5236378 10.495212
1789 5.1039998 12.059425
1790 4.0824249 11.077204
1791 3.7634431 10.784256
1792 4.7150312 11.694781
1793 3.8998551 10.880223
1794 3.8538904 10.847186
1795 5.0921169 12.080196
1796 5.6517716 12.673976
1797 6.0500572 13.035646
1798 3.8888646 10.902165
1799 4.8858334 11.894112
1800 5.2055475 12.191270
1801 5.3574817 12.352880
1802 4.0687497 11.064480
1803 7.2620879 14.208864
1804 5.6064453 12.554897
1805 4.2632412 11.308663
1806 4.4303192 11.428349
1807 1.9158872 8.892507
1808 4.4278012 11.415125
1809 2.9794498 9.979653
1810 5.0161087 12.012525
1811 5.0935336 12.095007
1812 5.1537858 12.183381
1813 5.6280599 12.652021
1814 6.5201710 13.527421
1815 5.8030597 12.778313
1816 6.0833438 13.105305
1817 4.8702680 11.829742
1818 5.3690178 12.355510
1819 4.3885831 11.386019
1820 5.1759172 12.170576
1821 5.3381497 12.342829
1822 3.9812897 10.980235
1823 6.3238810 13.357361
1824 6.1564125 13.161815
1825 4.9963722 12.036912
1826 3.7804496 10.776360
1827 4.7809035 11.761586
1828 5.8126482 12.803403
1829 4.7115506 11.710435
1830 4.4531326 11.455601
1831 3.0841568 10.079544
1832 3.2334763 10.207491
1833 4.0307532 11.021819
1834 3.4189160 10.428247
1835 3.7701196 10.795614
1836 5.1163805 12.156435
1837 4.5314665 11.551347
1838 4.0099255 11.018055
1839 4.6685373 11.692105
1840 4.3741263 11.341770
1841 4.0354538 11.050692
1842 4.6196785 11.626303
1843 5.1090236 12.113739
1844 6.3326792 13.303367
1845 5.2682549 12.261424
1846 3.8318336 10.836721
1847 4.4059285 11.391259
1848 3.9493194 10.981114
1849 3.9383301 10.905943
1850 4.8218184 11.823596
1851 6.7502272 13.715036
1852 3.9581783 10.924569
1853 3.0131796 10.014125
1854 4.4577194 11.462669
1855 5.1037111 12.085778
1856 4.9347872 11.935017
1857 5.0581246 12.058290
1858 4.5035247 11.497233
1859 5.8583818 12.863342
1860 4.6082337 11.595514
1861 4.5671895 11.554091
1862 5.8194910 12.788597
1863 4.4178118 11.420663
1864 5.4303064 12.431753
1865 3.5588529 10.576613
1866 5.7464179 12.733740
1867 4.2614276 11.246234
1868 4.8963386 11.894200
1869 4.3022358 11.323087
1870 6.3538356 13.369836
1871 4.2906350 11.268199
1872 5.0463776 12.054563
1873 4.5249094 11.541986
1874 3.4300268 10.440109
1875 5.0747404 12.084461
1876 5.5597524 12.579178
1877 5.2662603 12.282207
1878 5.3560785 12.360420
1879 5.8909760 12.898508
1880 4.9180942 11.890338
1881 4.0792664 11.059796
1882 4.0699657 11.037674
1883 3.7915835 10.772459
1884 6.4840694 13.471221
1885 5.5942920 12.596116
1886 3.4788263 10.475834
1887 7.5316264 14.533796
1888 6.4834104 13.493505
1889 5.1022646 12.091801
1890 4.9311729 11.904815
1891 3.7946541 10.785556
1892 3.9735882 10.956550
1893 2.7041300 9.699077
1894 5.2995029 12.293407
1895 5.6705367 12.677703
1896 5.5339330 12.524196
1897 4.2824718 11.240690
1898 5.4687237 12.446891
1899 4.2736888 11.285803
1900 5.9477454 12.981291
1901 6.4163691 13.432303
1902 6.0704811 13.061602
1903 4.1959777 11.198566
1904 2.4395360 9.435304
1905 5.1263161 12.103738
1906 4.7709403 11.768627
1907 5.3270190 12.347897
1908 4.4398278 11.446090
1909 4.7834736 11.824681
1910 5.6830112 12.682453
1911 3.1987706 10.154576
1912 4.2843373 11.279870
1913 5.5900845 12.600266
1914 6.5981525 13.620470
1915 4.3046142 11.314554
1916 4.9942982 11.999492
1917 5.5315919 12.543559
1918 5.0476453 12.080010
1919 3.9576953 10.973119
1920 3.0295067 10.075846
1921 5.4879830 12.483801
1922 3.9553113 10.952864
1923 3.9154197 10.907407
1924 3.8019144 10.814550
1925 6.3644922 13.368373
1926 5.3063285 12.323674
1927 5.9154435 12.934539
1928 4.8163051 11.814424
1929 4.4920634 11.504587
1930 4.0872087 11.110214
1931 5.4647011 12.458393
1932 4.1414758 11.139066
1933 4.4914139 11.484269
1934 5.4126658 12.424867
1935 5.6898840 12.655104
1936 4.2929565 11.298526
1937 5.4131593 12.437459
1938 5.1777041 12.150523
1939 6.7991076 13.773005
1940 6.7431967 13.717637
1941 5.1517954 12.160280
1942 4.8128359 11.790999
1943 3.3726868 10.419044
1944 5.5569895 12.584620
1945 5.3725363 12.396855
1946 4.8662609 11.828506
1947 2.7798046 9.767728
1948 3.8548986 10.848566
1949 6.0825008 13.090065
1950 5.0450731 12.067969
1951 4.9452649 11.958332
1952 4.6774467 11.672484
1953 5.1869684 12.180982
1954 4.7979932 11.791445
1955 3.9702464 10.938119
1956 4.7549756 11.750186
1957 5.2190754 12.223192
1958 2.5502120 9.550788
1959 3.8549477 10.844831
1960 6.4562687 13.458726
1961 4.7127737 11.725756
1962 5.5381130 12.512254
1963 6.4760649 13.473535
1964 2.9955330 9.989141
1965 4.6162672 11.595730
1966 5.2352318 12.233079
1967 5.0913358 12.073053
1968 5.2063920 12.204633
1969 5.9553978 12.956698
1970 5.2503064 12.274566
1971 4.9887097 12.011966
1972 6.2713388 13.275119
1973 4.3981701 11.406352
1974 5.1110339 12.084193
1975 4.8953299 11.875778
1976 5.3526927 12.366457
1977 3.9313822 10.957941
1978 4.0837065 11.083577
1979 4.6935421 11.676109
1980 5.7827822 12.763905
1981 5.1204764 12.106215
1982 5.4596641 12.486198
1983 4.0905577 11.075004
1984 4.9877238 12.035173
1985 5.3718889 12.361599
1986 6.0950294 13.108424
1987 3.0291202 10.028796
1988 3.1515291 10.123199
1989 4.7917559 11.803240
1990 6.9143796 13.965216
1991 5.7681149 12.767070
1992 5.1155970 12.092568
1993 4.9164313 11.953935
1994 6.4920967 13.505469
1995 4.4592837 11.473816
1996 4.5383243 11.554228
1997 4.6762655 11.663538
1998 5.3589531 12.378289
1999 5.9317190 12.928015
2000 5.9814691 12.997313
2001 5.4300781 12.405243
2002 5.4850712 12.482067
2003 3.0686772 10.049753
2004 4.2023875 11.210534
2005 5.3755681 12.349590
2006 5.1102114 12.100468
2007 3.4266984 10.428015
2008 4.8611304 11.870173
2009 4.9664775 11.965199
2010 4.3262809 11.319552
2011 7.4073494 14.423188
2012 5.2047059 12.220274
2013 5.9243153 12.908616
2014 2.9856461 9.989990
2015 4.5917005 11.591377
2016 5.3855886 12.416271
2017 5.1875450 12.157298
2018 5.5709207 12.570721
2019 4.4642790 11.427417
2020 4.7957837 11.788527
2021 3.5240721 10.516032
2022 5.6750737 12.685135
2023 5.6055674 12.608610
2024 4.9984228 11.996376
2025 5.5364835 12.510635
2026 4.5312970 11.530764
2027 4.0989690 11.061634
2028 6.9950686 14.003621
2029 5.2510970 12.243392
2030 6.3764898 13.410691
2031 2.8017447 9.798524
2032 4.7004421 11.750352
2033 4.1283905 11.147132
2034 4.4685571 11.461930
2035 5.7624907 12.785960
2036 5.7390626 12.718653
2037 3.9489906 10.947252
2038 5.5183121 12.499767
2039 5.9609165 12.955983
2040 3.9606091 10.977502
2041 6.3641050 13.360028
2042 6.2311554 13.241763
2043 6.2638160 13.304612
2044 4.8528140 11.870594
2045 3.2231385 10.193732
2046 4.5717535 11.556423
2047 4.1679007 11.188056
2048 5.9757230 12.980824
2049 4.3692055 11.353538
2050 5.6772468 12.672225
2051 3.5409693 10.546941
2052 5.7903968 12.793572
2053 7.5749713 14.571956
2054 5.7922372 12.793136
2055 3.8629439 10.895522
2056 4.9267690 11.899977
2057 5.8415437 12.842643
2058 4.9493111 11.942690
2059 4.3303382 11.324905
2060 6.4350196 13.404337
2061 3.5605334 10.601629
2062 5.2693284 12.281700
2063 3.4553177 10.419537
2064 4.1312806 11.135102
2065 6.2809369 13.290313
2066 5.8444884 12.833783
2067 4.0672359 11.082397
2068 6.5891387 13.611831
2069 6.4079214 13.418564
2070 5.6319508 12.650791
2071 6.6857876 13.679863
2072 5.6608683 12.635228
2073 5.0584764 12.080709
2074 4.3903032 11.383644
2075 3.7754961 10.818477
2076 5.7108538 12.699844
2077 5.3963366 12.385054
2078 5.2404070 12.240548
2079 4.5781700 11.594258
2080 3.0664648 10.057028
2081 5.3826139 12.406161
2082 5.1244479 12.135400
2083 3.9011529 10.909646
2084 5.0225164 12.046588
2085 4.9419532 11.955195
2086 5.0957506 12.075871
2087 5.2203548 12.217266
2088 5.1659632 12.170447
2089 4.3890257 11.368825
2090 5.5795736 12.580034
2091 6.7858876 13.788618
2092 5.6465024 12.657944
2093 4.9987093 12.010627
2094 6.5265170 13.556835
2095 3.4957405 10.502951
2096 3.5891799 10.597351
2097 4.3146396 11.315189
2098 4.7072933 11.710253
2099 8.5598718 15.552881
2100 3.0831526 10.072396
2101 3.7025059 10.688985
2102 3.7781181 10.759155
2103 6.0231068 13.046173
2104 4.6657164 11.617357
2105 5.2811825 12.280325
2106 3.8540385 10.857908
2107 5.9876640 12.990595
2108 5.4113281 12.408587
2109 4.6142305 11.647824
2110 2.6261928 9.625523
2111 6.1467444 13.163650
2112 5.5990769 12.628906
2113 6.6552826 13.631573
2114 5.1341938 12.131568
2115 2.8317430 9.829144
2116 4.7897990 11.802380
2117 4.4060305 11.388249
2118 2.7871800 9.785374
2119 6.9118695 13.904594
2120 5.6841507 12.730160
2121 5.2398227 12.234636
2122 6.7483208 13.736155
2123 4.8312553 11.862508
2124 5.5682539 12.554827
2125 8.6141888 15.600399
2126 4.2183280 11.213808
2127 5.7161354 12.722122
2128 5.3493816 12.364056
2129 5.4388964 12.435485
2130 4.0722447 11.083776
2131 4.7882048 11.810366
2132 6.0623029 13.066737
2133 5.2397763 12.250675
2134 4.0665470 11.062074
2135 4.1499545 11.124640
2136 5.3926565 12.376068
2137 6.1099796 13.066514
2138 7.0260602 13.999245
2139 5.1859339 12.199474
2140 5.8616967 12.842018
2141 4.2468690 11.276273
2142 3.8778506 10.882835
2143 5.7146971 12.687950
2144 4.6563134 11.682464
2145 4.8772461 11.869925
2146 5.9653440 12.945750
2147 5.2892295 12.280013
2148 3.7483765 10.715085
2149 7.0823668 14.064233
2150 6.3197827 13.316518
2151 4.6021076 11.607345
2152 6.1302885 13.106500
2153 3.5125882 10.520222
2154 4.6677185 11.693745
2155 5.6048506 12.570796
2156 4.7411623 11.730812
2157 5.2952296 12.316059
2158 4.0282377 11.027003
2159 5.5625561 12.583210
2160 5.1991343 12.207681
2161 4.9559437 11.972491
2162 5.0645847 12.077944
2163 3.3350248 10.353355
2164 4.8289163 11.857623
2165 4.3813208 11.374291
2166 6.7079087 13.720856
2167 6.0017243 13.015661
2168 3.8965339 10.904328
2169 5.3166776 12.305781
2170 5.8499784 12.861171
2171 5.6974290 12.685374
2172 5.1370748 12.161512
2173 4.6552721 11.686881
2174 4.9371635 11.937961
2175 6.1683758 13.170432
2176 5.2567094 12.261370
2177 4.1865199 11.173035
2178 5.6480681 12.681542
2179 5.9055204 12.925521
2180 6.3465232 13.292045
2181 6.8539226 13.874350
2182 5.4615839 12.490141
2183 3.6490375 10.654791
2184 4.8954771 11.873360
2185 3.0180187 9.999557
2186 3.7383686 10.704040
2187 5.0818563 12.066030
2188 6.4354003 13.449687
2189 4.2178385 11.227234
2190 5.5454159 12.513130
2191 5.6689754 12.670282
2192 5.1378815 12.153269
2193 3.8847629 10.879695
2194 6.9427481 13.951969
2195 5.5118891 12.537182
2196 6.3599530 13.360308
2197 3.8287704 10.852495
2198 6.2395726 13.240919
2199 4.2279033 11.252670
2200 4.8843572 11.874735
2201 6.5440036 13.525537
2202 6.0734904 13.062708
2203 6.1261286 13.118951
2204 6.1641192 13.135330
2205 4.3857917 11.383534
2206 5.4600973 12.440799
2207 5.0843004 12.065653
2208 4.4821957 11.477100
2209 5.0346355 12.033380
2210 5.0171615 12.015634
2211 2.4104489 9.417056
2212 6.2799819 13.256173
2213 6.1172530 13.084277
2214 3.6270269 10.608653
2215 6.1040324 13.112745
2216 5.2467140 12.282580
2217 4.6665305 11.629473
2218 5.1452309 12.142714
2219 4.9663830 11.992610
2220 4.9538236 11.948732
2221 3.6125735 10.610833
2222 5.7347573 12.740006
2223 7.0253918 14.033199
2224 4.5221996 11.537850
2225 4.1358034 11.103985
2226 5.4689482 12.469011
2227 5.6742149 12.653032
2228 3.4343006 10.439761
2229 5.2639467 12.234750
2230 3.8730039 10.857220
2231 6.1205685 13.121134
2232 4.3719687 11.364203
2233 5.2161203 12.215903
2234 5.0224133 12.000272
2235 5.8691608 12.877044
2236 4.3680044 11.356940
2237 5.2810805 12.278316
2238 4.4732827 11.480477
2239 5.8137076 12.791197
2240 4.1346779 11.115815
2241 3.7962238 10.756380
2242 5.4230365 12.442722
2243 5.7105569 12.712221
2244 4.3166293 11.295409
2245 5.2733479 12.310752
2246 6.4173813 13.390523
2247 7.0286675 14.055909
2248 5.8576101 12.893862
2249 6.4440248 13.465467
2250 4.5762710 11.588258
2251 4.5978566 11.599827
2252 6.5747473 13.581007
2253 5.9618004 12.955752
2254 4.2579916 11.272559
2255 5.0541593 12.096987
2256 3.7232378 10.736309
2257 2.6799612 9.677604
2258 5.4850567 12.541481
2259 3.5316682 10.511660
2260 3.9284094 10.933963
2261 3.7765947 10.790548
2262 4.5081143 11.524881
2263 3.1255034 10.115479
2264 4.8192816 11.833316
2265 7.0591844 14.051620
2266 5.9718179 12.958336
2267 5.0205192 12.012636
2268 5.4956213 12.478430
2269 4.0270747 11.028356
2270 4.5774614 11.585966
2271 4.5369849 11.575494
2272 4.8509293 11.846040
2273 1.8399323 8.841568
2274 4.9414381 11.935132
2275 5.0162884 12.020508
2276 6.1378101 13.171409
2277 5.9719574 13.000737
2278 4.8342354 11.832155
2279 4.3513343 11.358488
2280 5.8452792 12.877946
2281 5.8537354 12.840741
2282 2.9593658 9.944882
2283 4.9916630 11.974493
2284 7.2099455 14.200747
2285 6.1009697 13.140437
2286 4.0003981 11.030805
2287 4.0233685 11.020871
2288 5.6315502 12.635269
2289 5.9185068 12.894873
2290 3.8419081 10.806591
2291 5.3385055 12.332488
2292 3.7040025 10.751942
2293 5.3219058 12.336013
2294 6.2071221 13.191632
2295 3.5549311 10.588343
2296 5.5365807 12.509549
2297 4.4453408 11.444900
2298 5.0263737 11.994361
2299 4.2644497 11.233103
2300 4.6804251 11.627743
2301 4.7643592 11.729053
2302 3.9671810 10.926177
2303 4.9721672 11.977918
2304 4.0827657 11.099258
2305 4.3151249 11.291686
2306 3.4686963 10.459295
2307 4.7962968 11.778760
2308 4.9937890 11.987407
2309 7.1303425 14.137755
2310 5.2527459 12.269948
2311 4.2693594 11.264881
2312 6.0132364 13.012592
2313 5.5326532 12.535923
2314 6.3124972 13.342163
2315 3.9473293 10.991278
2316 3.9274829 10.945911
2317 4.8560101 11.844766
2318 6.2539273 13.276207
2319 3.3273926 10.315792
2320 5.8033973 12.812249
2321 4.1354556 11.156663
2322 4.5433483 11.513028
2323 4.8791812 11.857298
2324 4.1656154 11.156415
2325 5.5653739 12.552522
2326 5.0236265 12.013622
2327 4.7005258 11.679195
2328 4.8968805 11.899446
2329 3.7097814 10.708216
2330 5.9806693 12.984461
2331 5.2897061 12.243833
2332 3.5546372 10.612225
2333 3.9684667 10.957246
2334 5.4682720 12.463675
2335 6.0687681 13.056931
2336 4.9201709 11.948194
2337 5.5177779 12.532567
2338 4.4116403 11.380113
2339 5.3159928 12.292980
2340 5.4829286 12.514476
2341 4.7313562 11.727372
2342 5.3177691 12.323286
2343 3.6790011 10.670564
2344 5.2984836 12.269129
2345 4.8961071 11.871199
2346 4.6562817 11.681328
2347 4.6462466 11.644846
2348 6.0513429 13.041105
2349 3.6679717 10.660041
2350 5.9055684 12.915397
2351 3.5451749 10.557022
2352 5.4419262 12.451070
2353 5.5019540 12.492756
2354 6.3491020 13.350880
2355 5.5894165 12.571143
2356 4.3148211 11.340478
2357 2.6504977 9.646689
2358 5.8117183 12.782691
2359 4.3598306 11.363569
2360 5.1863901 12.199896
2361 5.5067371 12.478306
2362 4.9089740 11.900025
2363 3.0711684 10.031392
2364 5.0173567 12.006002
2365 3.8990551 10.873259
2366 4.4181972 11.416497
2367 4.9735741 12.005338
2368 5.0147741 12.014622
2369 5.1480426 12.120535
2370 4.6081222 11.581965
2371 5.4283419 12.390527
2372 5.1098795 12.124556
2373 4.9717842 11.968324
2374 2.9831051 9.990335
2375 7.1788416 14.182438
2376 4.0542470 11.037315
2377 5.8063216 12.829925
2378 6.4865408 13.511240
2379 5.2774990 12.251823
2380 5.5259510 12.558632
2381 3.8195447 10.793202
2382 3.0428654 10.005015
2383 4.2245952 11.217349
2384 4.7655984 11.769886
2385 4.7175942 11.742017
2386 4.9345923 11.942579
2387 5.6365501 12.617083
2388 4.2275191 11.228052
2389 4.7206197 11.745814
2390 6.4750564 13.499711
2391 5.9069226 12.926571
2392 5.2186192 12.239712
2393 4.3707266 11.342176
2394 5.7074145 12.702200
2395 5.1917506 12.173231
2396 5.5482954 12.532750
2397 5.4511531 12.438816
2398 3.1047040 10.134485
2399 5.7661740 12.747464
2400 6.5225393 13.534500
2401 4.8011671 11.790274
2402 4.9612223 11.965993
2403 3.2161673 10.193735
2404 5.6071727 12.601945
2405 4.9937885 11.998156
2406 3.9701046 10.955851
2407 4.3918948 11.377226
2408 4.8733895 11.901624
2409 4.7664024 11.747853
2410 5.8153017 12.839743
2411 6.4591418 13.482880
2412 4.0913785 11.050173
2413 3.5994055 10.599890
2414 6.2328626 13.263280
2415 4.9709307 11.985001
2416 2.3731196 9.427958
2417 5.4653970 12.464890
2418 4.8064407 11.805098
2419 5.1232923 12.145513
2420 3.2107355 10.195664
2421 5.7641866 12.722270
2422 5.2632969 12.278854
2423 4.2780454 11.283444
2424 6.6523346 13.649318
2425 4.4401916 11.453994
2426 5.1665908 12.175579
2427 4.8522430 11.842593
2428 5.1923111 12.172512
2429 4.4612915 11.459454
2430 4.8573312 11.847370
2431 4.2611758 11.263730
2432 2.2491063 9.240049
2433 3.5042954 10.523837
2434 4.1563699 11.167404
2435 4.6761297 11.678586
2436 4.7144129 11.705286
2437 3.4710482 10.448322
2438 5.3158034 12.317987
2439 5.1009829 12.103080
2440 4.3520675 11.375770
2441 5.7988074 12.780600
2442 6.9546865 13.955787
2443 5.4158589 12.445643
2444 5.5689109 12.567690
2445 5.1035111 12.093908
2446 3.5749465 10.578542
2447 5.6172177 12.654875
2448 5.0752537 12.037447
2449 4.1412590 11.143515
2450 4.5429207 11.525634
2451 6.0022889 12.995450
2452 3.9463825 10.932743
2453 4.1761031 11.208922
2454 3.7516401 10.756487
2455 4.7004178 11.691408
2456 5.3475667 12.339694
2457 3.6899841 10.689596
2458 5.0474486 12.036198
2459 4.5136937 11.526110
2460 5.4864162 12.435838
2461 5.9236100 12.929959
2462 6.0754610 13.072274
2463 4.1627552 11.180008
2464 4.2900451 11.291267
2465 4.3168085 11.286822
2466 6.6787252 13.695397
2467 3.8784256 10.879728
2468 4.4854694 11.479557
2469 3.0952097 10.127919
2470 6.3651742 13.366029
2471 6.3687189 13.375143
2472 5.4893497 12.498586
2473 4.5604117 11.570126
2474 2.9620183 9.945990
2475 5.6553172 12.677401
2476 4.3465111 11.330173
2477 5.9739991 12.974869
2478 3.4340842 10.482886
2479 4.6338618 11.631277
2480 3.9019392 10.897587
2481 5.2656588 12.262693
2482 4.8176810 11.812513
2483 4.9673599 11.980076
2484 5.4020380 12.387569
2485 4.3395397 11.329600
2486 4.5901051 11.611257
2487 4.5352344 11.544468
2488 6.5200029 13.523636
2489 4.8180300 11.828924
2490 4.1021910 11.081515
2491 3.7063326 10.715561
2492 4.4995785 11.490116
2493 4.6825265 11.698101
2494 4.0544718 11.057370
2495 6.4630736 13.464963
2496 5.3495766 12.366407
2497 5.4713707 12.513751
2498 3.6137351 10.601534
2499 6.4029180 13.418778
2500 3.8867821 10.912586
2501 4.1530168 11.161301
2502 6.9883802 13.971479
2503 4.9625199 11.973060
2504 6.0054031 12.988552
2505 4.0871854 11.080720
2506 5.8277014 12.828147
2507 4.1565078 11.161994
2508 4.4082955 11.391444
2509 7.6091479 14.578127
2510 6.5678459 13.578552
2511 5.7859580 12.802013
2512 2.7336669 9.757676
2513 4.6201414 11.635080
2514 4.2102913 11.205621
2515 5.5195388 12.491850
2516 3.1181220 10.093538
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19246 5.5486757 12.544055
19247 4.9597896 11.946872
19248 4.2071222 11.202181
19249 6.1967893 13.202384
19250 6.2495798 13.256253
19251 6.0090604 13.012968
19252 4.9680708 11.973049
19253 6.9070359 13.924935
19254 5.4533840 12.465497
19255 6.3827622 13.350099
19256 5.9247961 12.926104
19257 4.7764758 11.813333
19258 5.6221291 12.614111
19259 5.4963346 12.493296
19260 5.1540545 12.149857
19261 5.0976365 12.082322
19262 5.2922918 12.291859
19263 4.2035653 11.208799
19264 6.5663558 13.558469
19265 4.6494999 11.679177
19266 6.0144359 13.026678
19267 3.1642463 10.140833
19268 5.7692873 12.775996
19269 5.3262081 12.327144
19270 4.4854404 11.480607
19271 4.5685375 11.555896
19272 4.4200761 11.432871
19273 5.0432167 12.040307
19274 3.9700326 10.933088
19275 4.8651152 11.897708
19276 5.2573801 12.240549
19277 6.6197821 13.658764
19278 4.6033045 11.583112
19279 6.2780004 13.299887
19280 2.6666119 9.726528
19281 4.3743995 11.382207
19282 5.6811881 12.671661
19283 5.3092883 12.270650
19284 5.7292895 12.745363
19285 4.4127352 11.409784
19286 5.4699164 12.472210
19287 5.5188977 12.517939
19288 5.1986753 12.184453
19289 5.8698033 12.899138
19290 7.1475167 14.137348
19291 3.5393483 10.549311
19292 4.0265484 11.029738
19293 5.5637497 12.564506
19294 5.5218325 12.528050
19295 5.5754577 12.572779
19296 6.1885763 13.182519
19297 6.0981042 13.107130
19298 5.0983139 12.073632
19299 4.9457812 11.934027
19300 3.9723165 10.985326
19301 6.6146020 13.571438
19302 4.0716484 11.057782
19303 6.5822721 13.568709
19304 5.3108986 12.310514
19305 4.6457893 11.661075
19306 2.5047417 9.522244
19307 6.4894930 13.496445
19308 6.4759976 13.503993
19309 4.1615606 11.158432
19310 6.4146463 13.434650
19311 4.8652684 11.842987
19312 5.1063146 12.132949
19313 3.8339995 10.827615
19314 4.7762355 11.799827
19315 4.3804344 11.408653
19316 5.1978211 12.189930
19317 4.4405550 11.440816
19318 5.1770775 12.173841
19319 5.0707399 12.036683
19320 5.9542332 12.950654
19321 3.9509962 10.987253
19322 5.8039913 12.812358
19323 4.4654559 11.451541
19324 5.5865595 12.616262
19325 3.8998070 10.902631
19326 3.9325290 10.925867
19327 4.2507528 11.235429
19328 5.4144974 12.401696
19329 2.2520049 9.266779
19330 4.6908014 11.672490
19331 6.8842848 13.896000
19332 4.0256753 11.012833
19333 7.3876093 14.379561
19334 3.6735507 10.655880
19335 4.5627254 11.544687
19336 5.0874353 12.068404
19337 5.3316471 12.326479
19338 4.7541384 11.762433
19339 6.4051799 13.397427
19340 6.1049600 13.100907
19341 5.1978614 12.192047
19342 4.8585222 11.861467
19343 3.9491646 10.969784
19344 3.5719885 10.556685
19345 4.2673209 11.259816
19346 5.8433696 12.855770
19347 4.2097836 11.232706
19348 3.8065141 10.815030
19349 5.3454625 12.332384
19350 3.8988665 10.894715
19351 4.2925475 11.281067
19352 2.6204926 9.644652
19353 3.3633853 10.358663
19354 4.4278352 11.422183
19355 5.7654038 12.760969
19356 6.0587772 13.057106
19357 3.7509087 10.732017
19358 6.4879499 13.453845
19359 5.3325014 12.333801
19360 4.3525739 11.342460
19361 6.1790580 13.203502
19362 5.3683356 12.369969
19363 5.4871264 12.470629
19364 6.0218359 13.035390
19365 6.2593382 13.312444
19366 5.4575032 12.479156
19367 3.8021199 10.772444
19368 4.9848950 12.009043
19369 4.8150647 11.801061
19370 5.2242236 12.210376
19371 5.7306431 12.702347
19372 5.5721193 12.558916
19373 3.7416660 10.790168
19374 5.5480933 12.571652
19375 6.0805041 13.101040
19376 3.9577314 10.947355
19377 4.8341199 11.868054
19378 5.3381424 12.333410
19379 3.5421682 10.544376
19380 3.3959499 10.384768
19381 4.7702568 11.736632
19382 4.4465946 11.409319
19383 4.6511066 11.637067
19384 6.1174665 13.147951
19385 6.0583686 13.068907
19386 3.4663428 10.471726
19387 5.4671204 12.443073
19388 5.5436518 12.551097
19389 6.2110879 13.204616
19390 5.4568477 12.468916
19391 6.1015659 13.097129
19392 5.2751058 12.268964
19393 5.1555055 12.161007
19394 6.5911018 13.611337
19395 6.5256796 13.512310
19396 6.6830249 13.705591
19397 4.3748051 11.374588
19398 5.8093363 12.779590
19399 5.4858489 12.478672
19400 4.8302715 11.812882
19401 3.0333553 10.062560
19402 4.9437444 11.949280
19403 3.6903204 10.698652
19404 6.9981002 13.963470
19405 4.7552696 11.781110
19406 4.8598623 11.883864
19407 4.9896177 12.036659
19408 4.7210597 11.713847
19409 4.2960814 11.315731
19410 4.7349495 11.717207
19411 4.6909261 11.688136
19412 5.1864376 12.181580
19413 5.5135249 12.516673
19414 5.9089140 12.889568
19415 4.6712693 11.654681
19416 5.9773935 12.994542
19417 5.1096537 12.076766
19418 5.2655356 12.266488
19419 4.1281615 11.141394
19420 6.3852237 13.354682
19421 6.6048258 13.602502
19422 4.2400858 11.243950
19423 6.6286877 13.604778
19424 3.7983078 10.807172
19425 4.5300364 11.585234
19426 4.0733172 11.054914
19427 6.1720460 13.147964
19428 5.0920245 12.120161
19429 4.9630949 11.986224
19430 3.5336593 10.510921
19431 4.0236723 11.036208
19432 6.0015218 13.001908
19433 5.1732397 12.165584
19434 5.7004105 12.709215
19435 5.0724697 12.060742
19436 5.6796873 12.657565
19437 5.9808918 12.982677
19438 3.9856316 11.019209
19439 5.1337592 12.123786
19440 5.0326686 12.044255
19441 4.5595982 11.556170
19442 6.0115955 12.992749
19443 4.5745645 11.599094
19444 5.7769662 12.773728
19445 5.8735816 12.849589
19446 3.4824687 10.458435
19447 6.0951198 13.089289
19448 4.6185782 11.614466
19449 4.2845164 11.297449
19450 5.7458371 12.752688
19451 5.4960459 12.491172
19452 4.7495366 11.752136
19453 6.0567899 13.049027
19454 5.1060268 12.144403
19455 2.9712139 9.996580
19456 5.2526264 12.249784
19457 5.7590314 12.740165
19458 5.0783634 12.070165
19459 4.4931057 11.475533
19460 4.2176493 11.192581
19461 4.0258171 11.022185
19462 3.7791306 10.767287
19463 5.9262356 12.918630
19464 5.6355760 12.649032
19465 4.1121692 11.111525
19466 3.1550092 10.169107
19467 6.3186674 13.341174
19468 5.1671258 12.133210
19469 4.1334261 11.146763
19470 5.0476869 12.056798
19471 5.3488985 12.314334
19472 4.5419761 11.566344
19473 5.0687006 12.102937
19474 5.0192976 12.035792
19475 4.5335979 11.533495
19476 4.9204982 11.878884
19477 5.8580065 12.854460
19478 4.0352671 11.029868
19479 5.2785752 12.301756
19480 4.5659876 11.546247
19481 4.9189212 11.926826
19482 4.8043020 11.833817
19483 4.8346901 11.804589
19484 4.8850090 11.914572
19485 7.5521563 14.571599
19486 4.0314817 11.049278
19487 4.2820069 11.264530
19488 5.0694346 12.041642
19489 4.8724609 11.883770
19490 3.7793167 10.784861
19491 5.4412810 12.443161
19492 4.7069283 11.722965
19493 4.6345528 11.651518
19494 4.2563539 11.246165
19495 7.2527741 14.268127
19496 5.0561511 12.036213
19497 5.6739573 12.660686
19498 6.0452192 13.050999
19499 4.6727626 11.688279
19500 6.3876301 13.406410
19501 5.3024445 12.286933
19502 6.8900350 13.899676
19503 4.2740614 11.271899
19504 5.7775923 12.764240
19505 5.0510142 12.083964
19506 6.1763221 13.142111
19507 3.7736287 10.759164
19508 4.1676310 11.184905
19509 5.8269109 12.820234
19510 4.3631253 11.353663
19511 5.6860361 12.692508
19512 4.3315176 11.329302
19513 3.8046492 10.779969
19514 5.5073749 12.483174
19515 4.0962588 11.113958
19516 6.1569019 13.179806
19517 4.9536181 11.969595
19518 4.5032225 11.528384
19519 3.5198026 10.515672
19520 6.3549987 13.357249
19521 5.9374225 12.910370
19522 5.9952031 12.974154
19523 7.1203154 14.124581
19524 7.6764992 14.639125
19525 3.4412664 10.446032
19526 3.9347236 10.945654
19527 5.6380213 12.618354
19528 4.0327960 11.006257
19529 5.2113515 12.218943
19530 6.2184470 13.194538
19531 4.2715535 11.214620
19532 4.1832286 11.190045
19533 4.6273717 11.669165
19534 4.5584875 11.569287
19535 7.0657038 14.076599
19536 3.1253656 10.109070
19537 4.3994924 11.405040
19538 6.6621673 13.644688
19539 4.0033211 10.994458
19540 5.8219393 12.842078
19541 3.0357989 10.007814
19542 4.1779656 11.121395
19543 2.7781046 9.792209
19544 4.3599513 11.352138
19545 5.8822816 12.853608
19546 6.5378373 13.545109
19547 4.8067579 11.792777
19548 5.1226883 12.140381
19549 5.2804716 12.272958
19550 4.3818204 11.389899
19551 4.7188612 11.711614
19552 6.3956395 13.389135
19553 5.9505520 12.951832
19554 5.0938871 12.100772
19555 5.2937951 12.317056
19556 4.7974044 11.825992
19557 3.5673701 10.568454
19558 5.7242746 12.706626
19559 2.9513479 9.965147
19560 4.9398851 11.918488
19561 4.0394784 10.983576
19562 4.5713859 11.594392
19563 5.8804368 12.904797
19564 5.6974667 12.685103
19565 5.0435512 12.047711
19566 5.8486605 12.841108
19567 3.6409301 10.622807
19568 3.9732826 11.012356
19569 3.9665485 10.964386
19570 5.9712120 12.981042
19571 5.3685631 12.379376
19572 6.3901269 13.379686
19573 4.3182294 11.314892
19574 5.7197576 12.721564
19575 4.5477121 11.549242
19576 6.8027531 13.810863
19577 5.7170059 12.736486
19578 5.9135202 12.917786
19579 4.2760063 11.243873
19580 4.8445066 11.835705
19581 3.0288636 10.025282
19582 4.8329192 11.863260
19583 6.1938214 13.187286
19584 4.7577798 11.774989
19585 5.1377431 12.131321
19586 5.1634992 12.191842
19587 4.0867447 11.064994
19588 4.9110215 11.915131
19589 4.5765476 11.592016
19590 4.7616133 11.747393
19591 5.2539942 12.246118
19592 6.1150306 13.119253
19593 6.1544268 13.157914
19594 4.4686894 11.480682
19595 4.4362964 11.420576
19596 4.7957741 11.785772
19597 6.1202025 13.118342
19598 3.5390825 10.548018
19599 4.9387840 11.971218
19600 4.9665371 11.956694
19601 4.0203933 11.012093
19602 5.9048730 12.875119
19603 3.9770418 10.953928
19604 6.2899370 13.292618
19605 5.6441395 12.623028
19606 6.7940032 13.803112
19607 6.1407096 13.136644
19608 5.8609712 12.855078
19609 5.8020281 12.816075
19610 4.0202454 10.996513
19611 3.6777961 10.682180
19612 5.6334642 12.637714
19613 4.9731655 11.989209
19614 4.6478306 11.691155
19615 4.5543507 11.546304
19616 3.9451738 10.961623
19617 3.6376195 10.635762
19618 3.8201057 10.784302
19619 5.0155835 12.005310
19620 5.5444945 12.537442
19621 6.2273179 13.237742
19622 5.4045368 12.388870
19623 4.7107610 11.734357
19624 3.8859163 10.849096
19625 5.5407241 12.541633
19626 3.8112233 10.782739
19627 5.3268998 12.327053
19628 4.4293299 11.430437
19629 5.1233490 12.123073
19630 3.6887271 10.677688
19631 6.3519161 13.379853
19632 5.0450436 12.045283
19633 5.6724145 12.675135
19634 3.5202280 10.497544
19635 2.9367530 9.930800
19636 4.9509070 11.959262
19637 5.7046209 12.706913
19638 4.8179178 11.811411
19639 4.8689039 11.850483
19640 5.3284328 12.343610
19641 4.9612165 11.960556
19642 1.6377454 8.664486
19643 3.3834069 10.403228
19644 5.2936476 12.261634
19645 3.9137190 10.938131
19646 3.7241521 10.753184
19647 5.0861346 12.039485
19648 5.2589326 12.254364
19649 5.7723026 12.744078
19650 6.5887554 13.592429
19651 4.0933847 11.099848
19652 4.9460231 11.929409
19653 5.2331418 12.226194
19654 5.3126793 12.296312
19655 6.4786094 13.475408
19656 5.1608494 12.161648
19657 4.7145537 11.739809
19658 4.1603703 11.154853
19659 4.8489327 11.849330
19660 4.3669280 11.359152
19661 5.8423088 12.839841
19662 6.4903797 13.517942
19663 5.0012097 12.003623
19664 4.4648230 11.457993
19665 4.0387431 11.061574
19666 3.1296455 10.125739
19667 4.2157326 11.237926
19668 5.4884695 12.473740
19669 4.8022669 11.792624
19670 5.1387609 12.152545
19671 4.5552966 11.574188
19672 4.5859985 11.617587
19673 6.3275762 13.297862
19674 5.3479258 12.316800
19675 5.5306384 12.527411
19676 4.9616191 11.958420
19677 4.4317459 11.442459
19678 4.1695895 11.175191
19679 5.7230151 12.717203
19680 3.5346741 10.547980
19681 4.4905396 11.515804
19682 4.3256355 11.312813
19683 4.1208473 11.117380
19684 3.8566405 10.846996
19685 6.5435145 13.530824
19686 6.3571581 13.339475
19687 4.6340104 11.657680
19688 5.0379419 12.018111
19689 4.1589335 11.155708
19690 5.0235571 12.034141
19691 4.8665072 11.876682
19692 5.2567955 12.292715
19693 5.9431459 12.913592
19694 6.1424495 13.166479
19695 6.1363533 13.117540
19696 4.6818408 11.714897
19697 4.4308086 11.435603
19698 3.6313935 10.625798
19699 2.4260889 9.415773
19700 4.8129783 11.794560
19701 3.3973282 10.394444
19702 5.3851282 12.391562
19703 5.4569021 12.478287
19704 4.8554883 11.872986
19705 4.0996024 11.098436
19706 4.2620986 11.247996
19707 6.4676949 13.466154
19708 4.7830050 11.788735
19709 6.7616353 13.788650
19710 5.7058482 12.720652
19711 4.3221675 11.341505
19712 5.4733620 12.473684
19713 6.2571122 13.233790
19714 4.7548470 11.776950
19715 5.1317047 12.152289
19716 5.0687677 12.069160
19717 6.1047013 13.123678
19718 5.4859835 12.515816
19719 4.8456533 11.842132
19720 5.1251846 12.108941
19721 5.2024654 12.208520
19722 4.4967759 11.493625
19723 3.9095489 10.911576
19724 5.7342148 12.725069
19725 5.1559932 12.219177
19726 5.2014551 12.176387
19727 6.1768143 13.165576
19728 4.8962571 11.893413
19729 6.3759020 13.352662
19730 5.7558608 12.767894
19731 6.5637044 13.584500
19732 4.2985995 11.327309
19733 4.6967978 11.658580
19734 6.7651982 13.733642
19735 6.6330354 13.631893
19736 5.1248929 12.125898
19737 4.7513832 11.734898
19738 7.1591927 14.157244
19739 5.5592010 12.541650
19740 4.8580896 11.871248
19741 4.3895210 11.394876
19742 5.5522710 12.519978
19743 5.2622040 12.273685
19744 6.8306338 13.828165
19745 6.5079396 13.478100
19746 5.5158661 12.469620
19747 3.0069591 9.983829
19748 3.4231568 10.390416
19749 5.0017206 11.996842
19750 4.5226686 11.491614
19751 5.3464710 12.372421
19752 4.8895213 11.880722
19753 4.6955188 11.698101
19754 4.2022243 11.198147
19755 6.5457040 13.543754
19756 4.7597569 11.744081
19757 5.4061761 12.415009
19758 6.4461215 13.464913
19759 5.6167093 12.623763
19760 4.3190787 11.291853
19761 5.8345395 12.880112
19762 4.4877596 11.512949
19763 4.2139321 11.194928
19764 3.4129156 10.403228
19765 2.9807104 10.016600
19766 4.8568319 11.903759
19767 4.3228117 11.283839
19768 4.8725374 11.853675
19769 4.1282609 11.106102
19770 4.8907840 11.895621
19771 3.9078220 10.861455
19772 4.6831528 11.682754
19773 2.9972834 9.999316
19774 5.9795599 13.005721
19775 4.2036022 11.195442
19776 4.4445562 11.430340
19777 4.9402296 11.968921
19778 6.1782104 13.160690
19779 3.4721249 10.462440
19780 5.2937096 12.299791
19781 4.0331215 11.021898
19782 4.2127182 11.215643
19783 5.6146605 12.620644
19784 5.6755978 12.651523
19785 5.9338744 12.954115
19786 6.0940951 13.125984
19787 4.2346350 11.234853
19788 4.8915596 11.871469
19789 4.0520033 11.048790
19790 7.6548019 14.662262
19791 5.6422271 12.654082
19792 5.7434851 12.772022
19793 6.5625422 13.528967
19794 3.8172826 10.852097
19795 3.5827536 10.575273
19796 4.5099671 11.522938
19797 6.1064943 13.076738
19798 3.2322486 10.271301
19799 6.9168154 13.916966
19800 7.0971978 14.137910
19801 4.7297540 11.676902
19802 5.1470297 12.143690
19803 4.2730578 11.264872
19804 6.6910470 13.689636
19805 5.8028984 12.792465
19806 4.7824558 11.794759
19807 4.3889286 11.386513
19808 4.5554120 11.551899
19809 5.4710596 12.471829
19810 4.2942425 11.287813
19811 2.8313897 9.828805
19812 4.1691288 11.197912
19813 5.1973170 12.189741
19814 4.2045157 11.203769
19815 5.8627150 12.866940
19816 7.0860300 14.105338
19817 4.4562083 11.471342
19818 6.9161558 13.940951
19819 6.5684526 13.549698
19820 6.7944275 13.800745
19821 4.2197250 11.248130
19822 5.0322056 12.043232
19823 5.5555239 12.557587
19824 6.7452412 13.740061
19825 6.0291075 13.046763
19826 5.9691563 12.972240
19827 3.4419111 10.462805
19828 4.9654051 11.954164
19829 4.4311392 11.446833
19830 3.5523579 10.564592
19831 4.7566674 11.765802
19832 5.5703575 12.568135
19833 5.6130619 12.641184
19834 7.3413380 14.366123
19835 5.1210532 12.141841
19836 5.1896580 12.190254
19837 3.8108372 10.830829
19838 3.5956156 10.611718
19839 3.8592886 10.854641
19840 4.5986446 11.597849
19841 4.5793377 11.602176
19842 5.9157384 12.922761
19843 4.0722262 11.050859
19844 3.6969808 10.698663
19845 4.2849350 11.283078
19846 4.9559161 11.925317
19847 4.5609534 11.566059
19848 4.9996713 11.984631
19849 4.1601881 11.152568
19850 5.7939533 12.829499
19851 4.5416169 11.551496
19852 3.7650458 10.761773
19853 4.6825683 11.729337
19854 6.9100994 13.944991
19855 4.8204179 11.796891
19856 4.1260543 11.104699
19857 5.1731819 12.153276
19858 4.8415828 11.854772
19859 4.5805855 11.575532
19860 4.7990091 11.785140
19861 4.0756818 11.074655
19862 5.3584137 12.351943
19863 3.7607137 10.771840
19864 4.1881248 11.186097
19865 6.6554923 13.646361
19866 3.4808877 10.479241
19867 5.6427963 12.622230
19868 3.9428400 10.960764
19869 6.1287435 13.118698
19870 4.2025761 11.221737
19871 7.0013790 13.991924
19872 3.4935265 10.489419
19873 4.6436442 11.648922
19874 3.4447768 10.443612
19875 5.2275678 12.218802
19876 6.0298124 13.027345
19877 5.7036297 12.725222
19878 4.1076851 11.107310
19879 6.0428167 13.036343
19880 5.9449667 12.911171
19881 4.9084471 11.897038
19882 6.0487154 13.047249
19883 5.8261630 12.819466
19884 4.5934489 11.607596
19885 4.1183457 11.103273
19886 5.7630207 12.770872
19887 3.6393690 10.620302
19888 5.2778101 12.277771
19889 5.5634102 12.554737
19890 4.4110305 11.427344
19891 5.0809064 12.101061
19892 4.9166858 11.881947
19893 6.6434280 13.654835
19894 4.5236906 11.527509
19895 4.9087201 11.919393
19896 5.5827679 12.587642
19897 5.1816135 12.184025
19898 4.7749435 11.762453
19899 5.2019305 12.246439
19900 4.7066695 11.703759
19901 6.0675938 13.067763
19902 3.2941701 10.268363
19903 5.6079953 12.621799
19904 5.4523917 12.448396
19905 7.2340890 14.206188
19906 4.9852998 11.985766
19907 5.8971980 12.902149
19908 5.8467356 12.868581
19909 5.2417276 12.261287
19910 7.4615977 14.463618
19911 6.0248691 13.019825
19912 6.2832686 13.262192
19913 3.9070584 10.872963
19914 4.9213501 11.930714
19915 4.2903255 11.307333
19916 3.6110279 10.598889
19917 4.8446512 11.838488
19918 4.6861930 11.693456
19919 6.3371964 13.363901
19920 5.0511526 12.039363
19921 7.7309181 14.706399
19922 3.6449355 10.699108
19923 4.0805752 11.071711
19924 4.2014099 11.209400
19925 5.5840269 12.585112
19926 4.6063308 11.620987
19927 3.7298483 10.710701
19928 5.2632382 12.262774
19929 5.9264885 12.918957
19930 4.6837517 11.700276
19931 7.0788775 14.049603
19932 4.5515283 11.558537
19933 4.3865016 11.377319
19934 5.2644597 12.298181
19935 6.2709847 13.280964
19936 5.6190005 12.629722
19937 5.6265227 12.647612
19938 4.1210167 11.129804
19939 4.5623769 11.520852
19940 2.2840913 9.283242
19941 2.8075765 9.789700
19942 5.2513992 12.258895
19943 5.0952916 12.092439
19944 4.9247581 11.924457
19945 6.1792271 13.162412
19946 4.1545902 11.139629
19947 6.5439431 13.545272
19948 4.6131742 11.627916
19949 4.3915615 11.440479
19950 4.2255699 11.192450
19951 5.3441542 12.376213
19952 4.6222932 11.573033
19953 4.8321503 11.822477
19954 4.6888195 11.688420
19955 5.7159305 12.735336
19956 4.4767263 11.461775
19957 6.1758646 13.178231
19958 5.2415967 12.267978
19959 5.8600118 12.886374
19960 5.7994396 12.802755
19961 6.1582997 13.125711
19962 5.9030599 12.947558
19963 6.9155184 13.914034
19964 5.2265200 12.223800
19965 3.9844431 10.968250
19966 5.4549499 12.499111
19967 4.8264930 11.832063
19968 4.0131971 10.989189
19969 5.0378792 12.009570
19970 4.5285721 11.488192
19971 4.4621560 11.448305
19972 4.5339622 11.534719
19973 5.9162648 12.941924
19974 5.7269793 12.710589
19975 7.8427447 14.875998
19976 4.2049878 11.214752
19977 5.4958749 12.526521
19978 4.9289281 11.930630
19979 3.9006486 10.905017
19980 4.5871528 11.595838
19981 3.5899802 10.582297
19982 4.3517805 11.333396
19983 6.2326257 13.203016
19984 5.8657664 12.870885
19985 4.3855837 11.393798
19986 4.3914765 11.376943
19987 5.6377807 12.663095
19988 3.9597498 10.963944
19989 5.1706854 12.193320
19990 5.9315570 12.980972
19991 3.2894083 10.302147
19992 5.3092232 12.292942
19993 4.9496631 11.980572
19994 5.8683223 12.853052
19995 4.1922726 11.177761
19996 5.1863586 12.185753
19997 6.6823868 13.689199
19998 6.7371309 13.755051
19999 4.1728615 11.152395
20000 5.2571326 12.229219
20001 5.0292104 12.029196
20002 4.6583491 11.640388
20003 2.9576409 9.984419
20004 5.4912546 12.491956
20005 5.5690082 12.552845
20006 4.5501971 11.521836
20007 4.3795991 11.392626
20008 4.0304467 11.026252
20009 4.8252444 11.821681
20010 6.2006287 13.190877
20011 4.3841162 11.373816
20012 3.7248557 10.727620
20013 6.6267428 13.610516
20014 6.0395997 13.035020
20015 6.7106467 13.669272
20016 4.1670796 11.164308
20017 3.7947896 10.776025
20018 3.5564528 10.539732
20019 4.9475713 11.940718
20020 3.6251275 10.613067
20021 5.3009744 12.293248
20022 6.7925405 13.815879
20023 5.9486331 12.938596
20024 4.7260941 11.712696
20025 5.1503710 12.202135
20026 5.5339685 12.515052
20027 5.8893351 12.865597
20028 3.4378432 10.470642
20029 3.7450927 10.736910
20030 6.2316079 13.232012
20031 7.1105669 14.143322
20032 3.9092433 10.906733
20033 5.6010983 12.601253
20034 4.5236414 11.518153
20035 5.0647483 12.088985
20036 7.3050683 14.329802
20037 3.0861970 10.074506
20038 2.7394632 9.767342
20039 2.3631498 9.378186
20040 4.5597610 11.552811
20041 4.8279293 11.853065
20042 3.8198906 10.812688
20043 5.4574236 12.424896
20044 5.0632985 12.069897
20045 4.5817040 11.592874
20046 3.2953924 10.300419
20047 4.5691113 11.534341
20048 3.4838436 10.449817
20049 6.6934963 13.683322
20050 3.2150626 10.243212
20051 4.3335793 11.307637
20052 6.6086905 13.600956
20053 4.5354315 11.506421
20054 4.3212906 11.294603
20055 3.6627582 10.655693
20056 6.4853321 13.529758
20057 5.7228017 12.702145
20058 5.0461151 12.029677
20059 4.1343110 11.166328
20060 5.3716898 12.384707
20061 5.1596897 12.166637
20062 5.1087011 12.122483
20063 6.7080568 13.713204
20064 5.9271675 12.902134
20065 4.4930527 11.475414
20066 5.7220364 12.687974
20067 2.9325491 9.946625
20068 4.8854855 11.879904
20069 6.1268516 13.139077
20070 4.4774388 11.474487
20071 3.6194795 10.621019
20072 5.0777676 12.089423
20073 4.4070968 11.401975
20074 5.5388254 12.537561
20075 2.8728483 9.892267
20076 5.4146643 12.433308
20077 4.5503534 11.559118
20078 2.6052193 9.659914
20079 6.9530433 13.964136
20080 5.3222864 12.319487
20081 6.7877405 13.827243
20082 5.8309339 12.867574
20083 4.2509545 11.199616
20084 4.9432242 11.928923
20085 5.1789922 12.152613
20086 4.8249949 11.819037
20087 5.3708467 12.361738
20088 5.7197614 12.722859
20089 3.0444890 10.026071
20090 5.5379691 12.545873
20091 4.6288486 11.622930
20092 3.5024507 10.538957
20093 4.3558116 11.360408
20094 5.4666156 12.441402
20095 4.1218132 11.134521
20096 4.3078206 11.305137
20097 4.8475504 11.848367
20098 5.4673413 12.469551
20099 5.3480100 12.346714
20100 5.4387145 12.450820
20101 4.8221131 11.816379
20102 3.1206553 10.092229
20103 6.3986493 13.413731
20104 4.0151534 11.022202
20105 4.5086642 11.505063
20106 5.3223533 12.357291
20107 4.9905420 11.983833
20108 5.4527942 12.430093
20109 6.3026242 13.313443
20110 4.3867160 11.373042
20111 4.4084233 11.415443
20112 6.2452063 13.267447
20113 5.3478068 12.311529
20114 4.4465096 11.433358
20115 4.6564575 11.689084
20116 6.1515146 13.154480
20117 5.2858172 12.322582
20118 5.9594019 12.925840
20119 5.7027870 12.693035
20120 4.9253811 11.917136
20121 4.5048457 11.539285
20122 5.3563122 12.377098
20123 4.7069490 11.740038
20124 4.3271872 11.330647
20125 4.3193862 11.328705
20126 4.9132922 11.938241
20127 3.7529869 10.756097
20128 4.3660220 11.397367
20129 5.0126939 12.004650
20130 4.9612977 11.942725
20131 4.8554165 11.839276
20132 4.2966728 11.289950
20133 3.9068829 10.935336
20134 5.7955882 12.807345
20135 4.5346069 11.556411
20136 5.0233112 12.023397
20137 4.4418272 11.408597
20138 3.8427142 10.843266
20139 6.3539406 13.356626
20140 4.4595229 11.486533
20141 6.8963331 13.876723
20142 5.3338173 12.363479
20143 3.0210119 10.000929
20144 4.7688631 11.765611
20145 5.1749152 12.167732
20146 6.0884871 13.071751
20147 5.4516778 12.442947
20148 3.6252868 10.608169
20149 4.0919583 11.118485
20150 4.3514777 11.334532
20151 3.0675447 10.070082
20152 5.0168438 12.006301
20153 4.4345708 11.402595
20154 5.7426731 12.777020
20155 4.7725953 11.801451
20156 3.9443178 10.921458
20157 6.3808782 13.362872
20158 4.0120061 11.044926
20159 3.2553091 10.237127
20160 5.8260296 12.838874
20161 5.7569933 12.761165
20162 6.2589584 13.252659
20163 4.9583554 11.978844
20164 5.8613007 12.886799
20165 5.1151255 12.151770
20166 5.7843730 12.750262
20167 6.4117342 13.418544
20168 3.3044893 10.342538
20169 4.4010506 11.365670
20170 7.1887838 14.167561
20171 3.9951685 11.034510
20172 5.1439845 12.146909
20173 5.8436503 12.806043
20174 3.9399904 10.931217
20175 2.9821896 10.008327
20176 5.4594718 12.444253
20177 6.4022010 13.365972
20178 5.3504791 12.364141
20179 5.0593133 12.086065
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20181 4.6196461 11.633827
20182 6.4098757 13.382680
20183 6.2611114 13.246026
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20185 3.7118072 10.682311
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20187 5.2777165 12.251436
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20189 4.7190352 11.714190
20190 5.1161926 12.133756
20191 4.4665101 11.447689
20192 4.5696440 11.553908
20193 3.2270748 10.215450
20194 5.4819510 12.485950
20195 6.3851081 13.385085
20196 5.7430783 12.755664
20197 5.1613780 12.176505
20198 4.8082554 11.787846
20199 5.4351225 12.438415
20200 4.9267066 11.915930
20201 4.8980508 11.894022
20202 3.5629443 10.543425
20203 6.0075336 12.974526
20204 5.3113933 12.281750
20205 5.4117897 12.415586
20206 5.6626136 12.664623
20207 4.8974871 11.896195
20208 4.2916608 11.290108
20209 4.1533652 11.191925
20210 4.4785067 11.478709
20211 5.9140166 12.899598
20212 3.9311169 10.927990
20213 4.2972659 11.283625
20214 5.5322858 12.509098
20215 5.0615036 12.061022
20216 4.5082932 11.507526
20217 5.2309056 12.233825
20218 3.5417227 10.533637
20219 3.4973734 10.556877
20220 6.9667215 13.963668
20221 5.2100397 12.211319
20222 7.0093592 14.027882
20223 3.4429845 10.423781
20224 4.4189909 11.402380
20225 4.7779507 11.752774
20226 4.4271678 11.435870
20227 5.9394293 12.930417
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20229 5.5578150 12.545001
20230 4.1603112 11.171705
20231 5.0569155 12.060876
20232 5.7280813 12.720176
20233 4.7744623 11.755687
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20236 3.6635571 10.657815
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20240 5.2623730 12.249793
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20243 3.9021014 10.917401
20244 4.2940782 11.295092
20245 4.2340657 11.202961
20246 3.3227483 10.275931
20247 6.3334994 13.324012
20248 4.5754582 11.579520
20249 5.3454973 12.311755
20250 5.1222411 12.118660
20251 3.8717879 10.842462
20252 4.2213039 11.183987
20253 6.8350082 13.838420
20254 4.9128293 11.899894
20255 4.4277600 11.425184
20256 5.1357183 12.126518
20257 5.2064666 12.197343
20258 6.2591725 13.242859
20259 6.5051092 13.514500
20260 6.1148202 13.069161
20261 6.1632211 13.125633
20262 5.1028957 12.072427
20263 5.0044380 12.014744
20264 6.2815190 13.270183
20265 6.2880623 13.293978
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20267 6.6157099 13.643390
20268 5.3138098 12.319323
20269 5.4373553 12.427447
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20272 6.3266636 13.303556
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20274 3.2344827 10.238070
20275 5.2649418 12.272808
20276 5.1175314 12.113904
20277 6.6125541 13.603764
20278 6.1156789 13.093555
20279 6.1740656 13.211461
20280 5.2229295 12.240910
20281 5.2661124 12.244561
20282 4.6019772 11.590721
20283 5.1965449 12.182381
20284 6.8853572 13.895606
20285 3.8271055 10.855928
20286 4.2968765 11.294688
20287 4.7688272 11.786794
20288 5.9789272 12.959017
20289 6.0384534 13.017738
20290 5.3584155 12.369313
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20292 6.0104766 13.006961
20293 5.3640975 12.383607
20294 5.9552432 12.953507
20295 4.7147406 11.719987
20296 5.7638229 12.801641
20297 5.4139738 12.437452
20298 6.0702768 13.085337
20299 4.7475988 11.760773
20300 3.9637373 10.975447
20301 5.9480775 12.947853
20302 5.0939803 12.083306
20303 5.5713665 12.572145
20304 6.4649649 13.464827
20305 6.0081843 13.034027
20306 5.4278545 12.404964
20307 6.8662079 13.868977
20308 6.0858306 13.079368
20309 5.0168615 11.987844
20310 3.7808903 10.794080
20311 5.8591137 12.884620
20312 5.0885730 12.097148
20313 5.4552235 12.471225
20314 4.7104246 11.684513
20315 4.6238297 11.606151
20316 6.1215428 13.100893
20317 6.1044069 13.101531
20318 5.2312114 12.249988
20319 4.7636249 11.757147
20320 5.1546831 12.162689
20321 3.9836790 10.944553
20322 6.2823429 13.296221
20323 5.8115783 12.809003
20324 5.7285300 12.708345
20325 4.9242088 11.902488
20326 5.2313774 12.250867
20327 5.0190828 12.018420
20328 5.1619631 12.151030
20329 5.4316933 12.437055
20330 7.0255872 14.012290
20331 4.0005811 11.001540
20332 7.1257781 14.123422
20333 3.1534535 10.137490
20334 3.9582500 10.950820
20335 5.9287524 12.913960
20336 5.7099483 12.702239
20337 5.8387009 12.857461
20338 3.8947263 10.886276
20339 5.6949716 12.719145
20340 3.5585904 10.549526
20341 5.6131851 12.607643
20342 4.9893890 11.978932
20343 6.1550909 13.194031
20344 5.7364076 12.710906
20345 4.5590210 11.569119
20346 3.9420164 10.941754
20347 6.0260220 13.011492
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20349 4.6907422 11.675665
20350 4.1436589 11.162058
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20364 5.5803007 12.575155
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20375 6.5528016 13.582659
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20377 4.5279773 11.524441
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20379 5.2822736 12.291381
20380 5.5650496 12.542311
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20388 4.6491957 11.655428
20389 5.8383814 12.853938
20390 6.3104198 13.292564
20391 6.4760752 13.460064
20392 3.3878042 10.397881
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20394 6.0353961 13.045686
20395 5.1550632 12.145094
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20397 5.2492587 12.271830
20398 4.9542092 11.922346
20399 5.2132520 12.225339
20400 4.6863727 11.679014
20401 6.5548307 13.587773
20402 5.5096501 12.470833
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20404 5.1753531 12.180511
20405 3.0666198 10.062444
20406 4.6675240 11.660675
20407 4.3264260 11.345391
20408 4.6660139 11.699331
20409 4.5108681 11.549066
20410 4.7321506 11.747399
20411 5.2439606 12.257472
20412 3.0587760 10.092529
20413 5.8956795 12.882300
20414 4.6119787 11.566587
20415 4.7848103 11.751153
20416 4.5014041 11.503841
20417 5.7781933 12.808069
20418 5.6171700 12.625079
20419 4.9123369 11.920412
20420 4.3973412 11.383883
20421 4.8231016 11.823642
20422 4.9616605 11.982143
20423 4.3903392 11.376259
20424 6.5802027 13.616170
20425 4.5455217 11.554370
20426 5.8998565 12.880702
20427 4.2368434 11.252669
20428 3.8999109 10.957434
20429 6.2035995 13.221533
20430 6.0737242 13.105344
20431 5.6783535 12.707450
20432 4.6595179 11.676561
20433 5.1593126 12.178110
20434 8.1591878 15.155991
20435 4.3147672 11.278311
20436 3.8321136 10.821469
20437 3.5241688 10.509278
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49714 3.8492613 10.829694
49715 3.9543728 10.927449
49716 4.9244282 11.938769
49717 3.0712832 10.039238
49718 3.5630931 10.551782
49719 5.1683476 12.185353
49720 4.5367433 11.536750
49721 6.0436910 13.023407
49722 4.6918402 11.679512
49723 5.0371185 12.011858
49724 4.6588013 11.662599
49725 5.3970633 12.384889
49726 5.0555083 12.041940
49727 4.9871126 11.962203
49728 4.4402057 11.411255
49729 3.3533823 10.339159
49730 7.0397883 14.037899
49731 6.6749797 13.683011
49732 5.5813902 12.639679
49733 5.4774951 12.479096
49734 4.9559722 11.954498
49735 4.7278962 11.734865
49736 5.1231396 12.120819
49737 4.6782975 11.675761
49738 5.3872388 12.374389
49739 3.2679081 10.260043
49740 5.3922669 12.402769
49741 5.2121701 12.191645
49742 5.6352895 12.653681
49743 4.4570249 11.467429
49744 5.8409412 12.842717
49745 5.5429447 12.562451
49746 7.2559243 14.217561
49747 6.2468388 13.245501
49748 3.2756136 10.300126
49749 5.5613580 12.568915
49750 5.6798598 12.710224
49751 5.2689032 12.315136
49752 4.0761097 11.072708
49753 3.9643755 10.970240
49754 6.0566460 13.052837
49755 5.9046480 12.902947
49756 5.4344960 12.472067
49757 5.2945588 12.285105
49758 4.1856476 11.155244
49759 5.1554974 12.158192
49760 4.8111532 11.823338
49761 5.7611483 12.770435
49762 5.4895609 12.479300
49763 5.4485299 12.476311
49764 4.2260087 11.237306
49765 3.3736854 10.406087
49766 4.6044169 11.603608
49767 5.5628377 12.595271
49768 4.8723248 11.869541
49769 6.5871546 13.581386
49770 4.4790214 11.471193
49771 6.0134572 13.007897
49772 2.2781647 9.271790
49773 3.3348001 10.322709
49774 4.7723963 11.758470
49775 4.2410529 11.258691
49776 5.8582433 12.861474
49777 5.4779205 12.498623
49778 4.9172431 11.899347
49779 4.0607691 11.073777
49780 7.0446467 14.056587
49781 3.4930852 10.472807
49782 6.3878195 13.344603
49783 5.1537681 12.137653
49784 4.9421490 11.931924
49785 3.8854537 10.872229
49786 3.3404323 10.339494
49787 4.6320539 11.624785
49788 3.7290635 10.734071
49789 4.6569652 11.650663
49790 6.6212994 13.649241
49791 5.2984288 12.308198
49792 5.1146922 12.090347
49793 4.8896676 11.886278
49794 1.4778518 8.463369
49795 3.3074144 10.321789
49796 5.9347110 12.943400
49797 4.1311448 11.115402
49798 7.0930788 14.102471
49799 4.6268664 11.614317
49800 5.1137675 12.089939
49801 5.1409436 12.121945
49802 5.0420964 12.054220
49803 5.0616840 12.099600
49804 4.7124347 11.734268
49805 4.3197282 11.328294
49806 4.6137052 11.639808
49807 5.6821491 12.656677
49808 3.6595732 10.636704
49809 4.3076290 11.305736
49810 4.5589599 11.532330
49811 3.6140073 10.596936
49812 6.2781995 13.273197
49813 5.3697200 12.364337
49814 2.6211555 9.597607
49815 5.4741396 12.495245
49816 7.5564585 14.570734
49817 4.5307815 11.536225
49818 3.4963170 10.485107
49819 4.6442815 11.698630
49820 5.3453802 12.374098
49821 5.3747600 12.366182
49822 4.3373736 11.337780
49823 5.0128208 12.016658
49824 4.4134534 11.389285
49825 3.3283115 10.331364
49826 5.5928785 12.566267
49827 5.8042244 12.815990
49828 6.3503779 13.380439
49829 4.8055830 11.800200
49830 4.5420388 11.525920
49831 5.4454623 12.447573
49832 5.3316312 12.355348
49833 4.7999227 11.795359
49834 4.3505073 11.354805
49835 5.3388191 12.312996
49836 6.2281523 13.207519
49837 4.3208349 11.347191
49838 4.6918060 11.685843
49839 3.4818738 10.441850
49840 4.0683526 11.073598
49841 5.0396273 12.002316
49842 6.3031070 13.259614
49843 4.9953049 11.991685
49844 4.0346007 11.043265
49845 4.1948764 11.194084
49846 5.1854461 12.213538
49847 4.5542196 11.546458
49848 4.9250748 11.929363
49849 5.4269545 12.413434
49850 2.8252993 9.826692
49851 4.4624392 11.473066
49852 4.0700866 11.095379
49853 4.3219761 11.308218
49854 5.6720531 12.673534
49855 4.9427203 11.897365
49856 6.3370340 13.341028
49857 4.3237179 11.328408
49858 3.9082110 10.880234
49859 3.9287799 10.896859
49860 2.7995356 9.824884
49861 6.3072609 13.300934
49862 5.6510209 12.628390
49863 6.8567799 13.850967
49864 5.2411329 12.259676
49865 3.0177582 10.022269
49866 4.9966092 12.011365
49867 6.5724613 13.588422
49868 4.6869928 11.667045
49869 5.8897071 12.876920
49870 4.7734349 11.790928
49871 4.6215991 11.596938
49872 5.7017442 12.730831
49873 6.5532314 13.549283
49874 4.4763202 11.460907
49875 5.0752401 12.086594
49876 6.5231507 13.504266
49877 5.2970032 12.299793
49878 3.8301548 10.804524
49879 5.3510367 12.320715
49880 4.9456474 11.955856
49881 4.1438697 11.143592
49882 2.4790241 9.460460
49883 6.5540092 13.555473
49884 4.5145614 11.538674
49885 5.1457851 12.140569
49886 4.3377443 11.341216
49887 4.8229939 11.828509
49888 4.9687163 11.962390
49889 4.8696448 11.883432
49890 3.6202329 10.610611
49891 5.6585562 12.620848
49892 4.6114307 11.618102
49893 5.3177403 12.316156
49894 4.9801112 11.968422
49895 6.2084029 13.214588
49896 6.7606190 13.755753
49897 6.0332879 13.019602
49898 5.3295821 12.315618
49899 4.7528456 11.766172
49900 5.7354481 12.734939
49901 4.6710168 11.629075
49902 4.6226494 11.609090
49903 4.8175691 11.802159
49904 3.3294123 10.357990
49905 4.6900793 11.690523
49906 4.1592172 11.178862
49907 3.6989636 10.695896
49908 4.0872994 11.095988
49909 4.9517039 11.944876
49910 6.5640071 13.579278
49911 6.5319055 13.565917
49912 4.2322216 11.240097
49913 5.7226695 12.715402
49914 4.8508139 11.889169
49915 4.2119395 11.200977
49916 4.6515229 11.665675
49917 5.9722198 12.956496
49918 4.2138002 11.207071
49919 5.3780128 12.421741
49920 4.9315478 11.931661
49921 3.4923513 10.502957
49922 5.7803743 12.756125
49923 5.8102814 12.813455
49924 4.3094052 11.313495
49925 3.5777596 10.555378
49926 5.2004130 12.158135
49927 4.9071246 11.921075
49928 5.1550853 12.151790
49929 3.6923471 10.691537
49930 3.8906817 10.893472
49931 5.7329725 12.729567
49932 4.6919196 11.678721
49933 3.8940986 10.901243
49934 4.4877822 11.503276
49935 4.8991403 11.874237
49936 6.6125021 13.639299
49937 4.0702897 11.067792
49938 5.1176531 12.134357
49939 4.6826106 11.702933
49940 3.7818995 10.820371
49941 5.1057987 12.129059
49942 6.1723181 13.138826
49943 5.0450890 12.056052
49944 4.2343013 11.211476
49945 4.0643236 11.026084
49946 5.0979815 12.083835
49947 4.6961073 11.721876
49948 4.8233432 11.834022
49949 4.7311256 11.735956
49950 5.5997835 12.619257
49951 5.4109859 12.444004
49952 4.2392871 11.248695
49953 5.3543522 12.341062
49954 5.2132545 12.234110
49955 4.5647469 11.571469
49956 5.4291637 12.407906
49957 4.8222954 11.819629
49958 3.0298857 10.034635
49959 4.0330945 11.010630
49960 4.1077618 11.084846
49961 3.3734157 10.357995
49962 5.2399638 12.226945
49963 3.7532262 10.754089
49964 4.9687314 11.979896
49965 3.3763092 10.392607
49966 7.0126017 14.026809
49967 6.7693731 13.750321
49968 7.3510855 14.362429
49969 5.1512276 12.184358
49970 6.0279977 13.035699
49971 5.6262404 12.628537
49972 4.8565335 11.856906
49973 4.1797334 11.197062
49974 6.2638813 13.253046
49975 5.7520627 12.792846
49976 5.5580868 12.558214
49977 5.5495581 12.516510
49978 4.8865988 11.887195
49979 5.1977627 12.228928
49980 5.2743232 12.273349
49981 3.8593253 10.846229
49982 4.9071578 11.917789
49983 4.0125811 11.001972
49984 4.2101112 11.213208
49985 3.8931497 10.901924
49986 5.6517955 12.646542
49987 4.8763822 11.871390
49988 5.6025894 12.637095
49989 5.5484984 12.560395
49990 4.4280584 11.435145
49991 3.5734835 10.559061
49992 5.2291884 12.238416
49993 3.5582900 10.561948
49994 6.8233063 13.847850
49995 5.3211074 12.304769
49996 5.4838932 12.516872
49997 5.1706103 12.179115
49998 4.5158001 11.495652
49999 5.8499312 12.871817
[ reached 'max' / getOption("max.print") -- omitted 350001 rows ]
gapminder %>% select(starts_with("c"))
# A tibble: 1,704 x 2
country continent
<fct> <fct>
1 Afghanistan Asia
2 Afghanistan Asia
3 Afghanistan Asia
4 Afghanistan Asia
5 Afghanistan Asia
6 Afghanistan Asia
7 Afghanistan Asia
8 Afghanistan Asia
9 Afghanistan Asia
10 Afghanistan Asia
# … with 1,694 more rows
gapminder %>% select(ends_with("p"))
# A tibble: 1,704 x 3
lifeExp pop gdpPercap
<dbl> <int> <dbl>
1 28.8 8425333 779.
2 30.3 9240934 821.
3 32.0 10267083 853.
4 34.0 11537966 836.
5 36.1 13079460 740.
6 38.4 14880372 786.
7 39.9 12881816 978.
8 40.8 13867957 852.
9 41.7 16317921 649.
10 41.8 22227415 635.
# … with 1,694 more rows
#filter
gapminder %>% filter(country == "United States")
# A tibble: 12 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 United States Americas 1952 68.4 157553000 13990.
2 United States Americas 1957 69.5 171984000 14847.
3 United States Americas 1962 70.2 186538000 16173.
4 United States Americas 1967 70.8 198712000 19530.
5 United States Americas 1972 71.3 209896000 21806.
6 United States Americas 1977 73.4 220239000 24073.
7 United States Americas 1982 74.6 232187835 25010.
8 United States Americas 1987 75.0 242803533 29884.
9 United States Americas 1992 76.1 256894189 32004.
10 United States Americas 1997 76.8 272911760 35767.
11 United States Americas 2002 77.3 287675526 39097.
12 United States Americas 2007 78.2 301139947 42952.
gapminder %>% filter(year > 1999)
# A tibble: 284 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 2002 42.1 25268405 727.
2 Afghanistan Asia 2007 43.8 31889923 975.
3 Albania Europe 2002 75.7 3508512 4604.
4 Albania Europe 2007 76.4 3600523 5937.
5 Algeria Africa 2002 71.0 31287142 5288.
6 Algeria Africa 2007 72.3 33333216 6223.
7 Angola Africa 2002 41.0 10866106 2773.
8 Angola Africa 2007 42.7 12420476 4797.
9 Argentina Americas 2002 74.3 38331121 8798.
10 Argentina Americas 2007 75.3 40301927 12779.
# … with 274 more rows
gapminder %>% filter()
# A tibble: 1,704 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779.
2 Afghanistan Asia 1957 30.3 9240934 821.
3 Afghanistan Asia 1962 32.0 10267083 853.
4 Afghanistan Asia 1967 34.0 11537966 836.
5 Afghanistan Asia 1972 36.1 13079460 740.
6 Afghanistan Asia 1977 38.4 14880372 786.
7 Afghanistan Asia 1982 39.9 12881816 978.
8 Afghanistan Asia 1987 40.8 13867957 852.
9 Afghanistan Asia 1992 41.7 16317921 649.
10 Afghanistan Asia 1997 41.8 22227415 635.
# … with 1,694 more rows
#summarise
gapminder %>% summarise(mean(gdpPercap))
# A tibble: 1 x 1
`mean(gdpPercap)`
<dbl>
1 7215.
#arrange
gapminder %>% arrange(year)
# A tibble: 1,704 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 1952 28.8 8425333 779.
2 Albania Europe 1952 55.2 1282697 1601.
3 Algeria Africa 1952 43.1 9279525 2449.
4 Angola Africa 1952 30.0 4232095 3521.
5 Argentina Americas 1952 62.5 17876956 5911.
6 Australia Oceania 1952 69.1 8691212 10040.
7 Austria Europe 1952 66.8 6927772 6137.
8 Bahrain Asia 1952 50.9 120447 9867.
9 Bangladesh Asia 1952 37.5 46886859 684.
10 Belgium Europe 1952 68 8730405 8343.
# … with 1,694 more rows
gapminder %>% arrange(desc(year))
# A tibble: 1,704 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 2007 43.8 31889923 975.
2 Albania Europe 2007 76.4 3600523 5937.
3 Algeria Africa 2007 72.3 33333216 6223.
4 Angola Africa 2007 42.7 12420476 4797.
5 Argentina Americas 2007 75.3 40301927 12779.
6 Australia Oceania 2007 81.2 20434176 34435.
7 Austria Europe 2007 79.8 8199783 36126.
8 Bahrain Asia 2007 75.6 708573 29796.
9 Bangladesh Asia 2007 64.1 150448339 1391.
10 Belgium Europe 2007 79.4 10392226 33693.
# … with 1,694 more rows
gapminder %>% arrange(country, desc(year))
# A tibble: 1,704 x 6
country continent year lifeExp pop gdpPercap
<fct> <fct> <int> <dbl> <int> <dbl>
1 Afghanistan Asia 2007 43.8 31889923 975.
2 Afghanistan Asia 2002 42.1 25268405 727.
3 Afghanistan Asia 1997 41.8 22227415 635.
4 Afghanistan Asia 1992 41.7 16317921 649.
5 Afghanistan Asia 1987 40.8 13867957 852.
6 Afghanistan Asia 1982 39.9 12881816 978.
7 Afghanistan Asia 1977 38.4 14880372 786.
8 Afghanistan Asia 1972 36.1 13079460 740.
9 Afghanistan Asia 1967 34.0 11537966 836.
10 Afghanistan Asia 1962 32.0 10267083 853.
# … with 1,694 more rows
#putting it all together. what if we wanted to know the highest absolute GDP of Zimbabwe between 1982 and 2007? (printing out only 1 value)
gapminder %>%
mutate(GDP = gdpPercap * pop) %>%
filter(country == "Zimbabwe", between(year, 1982, 2007)) %>% #between!
arrange(desc(GDP)) %>%
select(GDP) %>%
top_n(1)
Selecting by GDP
# A tibble: 1 x 1
GDP
<dbl>
1 9037850590.
# what if we wanted the average GDP of Zimbabwe between 1982 and 2007?
gapminder %>%
mutate(GDP = gdpPercap * pop) %>%
filter(country == "Zimbabwe", between(year, 1982, 2007)) %>% #between!
summarise(mean(GDP))
# A tibble: 1 x 1
`mean(GDP)`
<dbl>
1 7131763852.
#Bonus: group_by
gapminder %>%
group_by(country) %>%
summarise(mean(gdpPercap))
# A tibble: 142 x 2
country `mean(gdpPercap)`
<fct> <dbl>
1 Afghanistan 803.
2 Albania 3255.
3 Algeria 4426.
4 Angola 3607.
5 Argentina 8956.
6 Australia 19981.
7 Austria 20412.
8 Bahrain 18078.
9 Bangladesh 818.
10 Belgium 19901.
# … with 132 more rows
gapminder %>%
group_by(continent) %>%
filter(year == "2007") %>%
summarise(n())
# A tibble: 5 x 2
continent `n()`
<fct> <int>
1 Africa 52
2 Americas 25
3 Asia 33
4 Europe 30
5 Oceania 2
Exercise: Using dplyr functions, find the Country in Asia that had the largest population in 1982 and tell me it’s total GDP that year.
Exercise: The labs data contains information about labs taken for patients over a period of time. Using dplyr, compute the ratio of PaO2/FiO2 for each patient at each time point and output a table of the minimum recorded PaO2/FiO2 ratio for each patient in the data. (not very useful but necessary hint: what is the difference between “PAO2” and “PO2 (ARTERIAL)”?)
labs <- read.csv("data/labs.csv")
sessionInfo()
R version 3.6.3 (2020-02-29)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Catalina 10.15.4
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] dplyr_0.8.5 gapminder_0.3.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.4.6 knitr_1.26 whisker_0.4 magrittr_1.5
[5] workflowr_1.5.0 tidyselect_1.0.0 R6_2.4.1 rlang_0.4.5
[9] fansi_0.4.1 stringr_1.4.0 tools_3.6.3 xfun_0.12
[13] utf8_1.1.4 cli_2.0.2 git2r_0.26.1 htmltools_0.4.0
[17] ellipsis_0.3.0 assertthat_0.2.1 yaml_2.2.1 digest_0.6.25
[21] rprojroot_1.3-2 tibble_3.0.1 lifecycle_0.2.0 crayon_1.3.4
[25] purrr_0.3.4 later_1.0.0 vctrs_0.2.4 promises_1.1.0
[29] fs_1.3.1 glue_1.4.0 evaluate_0.14 rmarkdown_1.18
[33] stringi_1.4.5 compiler_3.6.3 pillar_1.4.3 backports_1.1.6
[37] httpuv_1.5.2 pkgconfig_2.0.3