Population Histogram Demo
Getting Started
Hi everyone!
Here’s a step-by-step demo of how we might use statistical analysis to help us understand the NLSS 2011 dataset.
Libraries
We’re going to start by loading up the libraries we want to use.
Libraries are the most common way of adding new features to R. The most
important library we’ll use is tidyverse, which gives us a
wonderful set of tools for data manipulation and graphing that are much
nicer than the ones built into base R. We’ll also use
haven, which is a library by the same authors that helps us
work with different file types.
library(tidyverse)
library(haven)Loading Data
Next, we’ll import the data files we need. The NLSS data is published
as .dta files, which are created by another statistics
program called Stata. R doesn’t know how to read Stata files by it, but
haven provides a read_dta function that can do it.
s01 <- read_dta("nlss2011/data/xh01_s01.dta") |> as_factor()This command imports the NLSS file xh01_s01.dta and
saves it to the variable s01.
A few technical notes:
- The variable name we picked (
s01) is completely arbitrary. We can choose pretty much anything we want, but here we’re calling its01because this file represents responses to Section 1 of the NLSS survey. The<-symbol tells R to save the output from the right side to the variable nameds01. - The filename is also arbitrary. The published NLSS files are all
named something like
xhXX_sYY.dta. XX refers to the file number and YY refers to the section of the survey. The file number is irrelevant, but we’ll use the section number to help us locate the data that interests us. - The
read_dtafunction imports .dta files and returns a data frame. Data frames are the most common way of storing data in R. A data frame is a table, where each column represents a variable (e.g., age, sex, type of roof, etc.) and each row represents an observation (e.g, either one of the 5988 households that took the survey or one of the individuals in those households). - After we run the
read_dtafunction, we’re also going to run the result through theas_factorfunction. This is just another part of how we convert Stata files to be useful in R.- In Stata, categorical variables are stored as numbers. So, for the
variable sex (
v01_02in our files01), values are stored as either 1 (male) or 2 (female). Not very progressive, but it’s how the data was recorded. - In R, we store categorical variables as “factors”, which are more
flexible and more intuitive We don’t have to worry about the specifics
here, but but the
as_factorfunction will convert all of Stata’s numerical encodings to R’s factor system.
- In Stata, categorical variables are stored as numbers. So, for the
variable sex (
Pipes
One other thing worth noting: the |> symbol is called
a pipe. It takes the output of the thing on the left and feeds it into
the function on the right as the first parameter. This is a very common
pattern in R, as it allows us to connect many functions together in a
sequence.
Logially, the code above using the pipe is exactly the same as either of these options:
s01 <- read_dta("nlss2011/data/xh01_s01.dta")
s01 <- as_factor(s01)-or-
s01 <- as_factor( read_dta("nlss2011/data/xh01_s01.dta") )All produce the exact same result, but we’ll use the pipe most of the time because it usually produces code that is easier to read and understand.
Looking at our data
Now that we’ve got everything loaded, we can start looking at the
data. Every variable in our data frame has a name that combines the
section number and the question number. So, for example, the variable
for “age” is called v01_03 because it is Queston 3 in
Section 1 of the survey.
Variables in data frames
To access a variable in a data frame, we first have to tell R the
name of the data frame and then the name of the variable, joined
together with a $ symbol. Why $? I have no
idea. It’s completely arbitrary, but it’s the way that R knows how to
fetch a variable that is contained inside a data frame. So, if we
type:
s01$v01_03## [1] 49 29 10 4 25 19 50 44 25 17 10 17 31 7 42 45 22 15 11 53 52 25 42 14
## [25] 46 37 13 47 45 18 18 56 50 31 32 9 3 24 21 1 21 16 55 72 55 14 9 62
## [49] 47 3 28 34 7 49 42 17 35 35 7 3 61 57 51 20 50 49 23 76 55 16 13 70
## [73] 46 40 14 12 10 56 20 2 26 27 8 3 3 35 13 11 10 7 29 8 6 53 65 63
## [97] 14 13 32 29 9 5 63 52 19 15 52 40 15 13 24 2 12 39 18 8 5 35 34 15
## [121] 10 63 33 25 3 0 31 28 17 58 54 45 24 21 0 27 30 11 7 4 64 28 49 45
## [145] 71 75 65 59 38 7 5 3 65 24 20 19 1 29 25 10 7 48 38 19 17 14 11 32
## [169] 27 7 5 35 43 20 12 18 56 37 31 14 12 10 7 70 40 40 16 13 58 50 22 7
## [193] 1 45 33 14 12 54 50 30 28 9 1 54 82 42 35 15 14 9 7 5 72 39 38 12
## [217] 8 3 53 17 29 28 4 45 8 57 54 22 20 18 6 21 18 55 50 31 12 9 9 44
## [241] 51 24 23 0 46 35 17 16 9 6 4 89 67 57 35 25 26 50 33 6 2 45 40 26
## [265] 18 20 1 55 20 13 35 27 11 8 3 39 15 13 41 37 15 18 31 6 5 46 35 20
## [289] 16 12 10 28 24 6 3 34 27 7 3 86 75 47 24 11 9 35 30 12 7 46 47 17
## [313] 15 12 9 8 18 48 44 20 17 32 25 7 1 23 6 1 10 9 25 21 2 1 27 30
## [337] 7 5 37 16 14 40 21 14 12 11 9 42 41 19 12 56 50 26 21 36 34 16 14 7
## [361] 60 45 28 20 2 0 19 15 11 9 50 37 17 12 11 10 3 54 49 30 29 21 67 56
## [385] 32 27 5 2 20 19 17 55 74 63 55 38 35 18 38 35 13 11 8 84 29 23 7 5
## [409] 3 3 31 33 2 55 73 60 32 24 1 71 25 1 15 68 62 40 36 14 10 5 27 24
## [433] 22 0 15 30 24 6 4 59 21 25 56 49 25 50 44 23 35 24 1 27 70 34 33 41
## [457] 40 36 15 13 27 40 5 42 15 2 20 19 48 51 31 25 7 1 23 22 51 66 56 31
## [481] 30 3 0 29 14 17 26 55 27 64 53 58 53 30 22 1 45 38 11 9 79 25 7 41
## [505] 36 3 0 66 60 35 35 7 3 36 36 11 10 8 38 32 9 6 3 1 42 68 55 60
## [529] 54 35 26 2 22 9 60 60 23 5 39 26 14 12 71 74 72 67 51 33 14 11 9 21
## [553] 19 16 24 4 55 43 36 10 11 10 54 46 19 28 2 33 33 12 8 45 42 17 15 66
## [577] 56 42 16 15 33 27 9 3 31 26 5 60 50 44 18 54 66 19 42 38 22 17 14 12
## [601] 10 7 4 74 70 36 13 8 44 29 16 35 24 0 56 46 24 22 47 43 16 56 55 24
## [625] 57 52 31 27 8 5 2 25 22 95 62 55 67 58 56 46 35 16 15 33 24 0 32 28
## [649] 59 55 32 29 29 3 58 48 20 10 4 47 42 21 17 16 16 60 55 16 18 15 12 35
## [673] 27 60 25 22 3 16 46 38 20 19 80 45 42 24 16 55 26 24 0 36 25 6 4 47
## [697] 45 17 14 11 9 6 28 9 7 35 32 15 12 10 5 53 45 40 16 14 8 7 4 26
## [721] 28 9 14 57 65 55 30 23 3 22 20 65 60 35 29 11 6 30 26 23 39 29 12 10
## [745] 7 39 18 16 13 13 28 22 2 40 28 18 16 13 3 43 40 22 20 17 10 7 46 40
## [769] 18 16 14 12 21 35 30 11 9 1 37 35 19 17 16 14 12 50 45 11 7 4 27 24
## [793] 4 3 52 45 25 20 1 22 19 47 21 20 8 59 20 3 1 16 39 36 19 15 15 11
## [817] 61 30 9 7 4 38 32 9 7 5 2 72 27 24 18 27 26 8 6 60 45 17 51 37
## [841] 36 15 10 8 6 72 44 42 18 17 15 12 75 4 1 22 50 47 16 14 12 23 3 2
## [865] 55 61 55 34 27 12 10 7 22 62 51 16 15 48 45 27 21 18 16 11 49 41 16 50
## [889] 46 42 15 9 51 45 23 18 16 38 28 10 9 7 32 30 12 10 6 65 59 51 21 13
## [913] 50 14 12 22 17 32 15 12 48 48 20 19 16 39 30 13 11 9 6 49 50 19 14 36
## [937] 33 4 1 50 46 19 17 15 87 38 37 9 6 51 41 21 13 27 8 7 3 57 49 27
## [961] 20 19 15 50 45 16 14 12 8 59 26 14 35 9 44 37 14 14 11 31 30 32 27 1
## [985] 48 35 18 15 12 35 14 11 49 45 17 78 70 53 51 27 33 25 0 30 29 6 3 70
## [1009] 65 37 34 10 2 13 38 48 56 38 8 62 56 27 25 22 7 63 63 40 35 9 7 33
## [1033] 22 48 44 43 45 12 33 18 38 18 14 12 80 49 7 40 50 17 15 8 37 8 66 34
## [1057] 27 6 2 39 38 13 35 16 13 32 32 13 56 50 52 51 22 29 74 24 10 24 8 6
## [1081] 5 56 56 35 25 42 41 18 17 47 38 11 8 48 48 83 50 20 70 25 25 9 7 5
## [1105] 35 32 15 9 7 56 45 17 88 78 51 40 21 16 10 68 67 39 35 10 8 44 35 16
## [1129] 12 27 7 2 0 34 40 10 7 14 40 38 18 15 12 70 60 9 53 35 19 17 15 13
## [1153] 11 2 40 21 19 18 57 21 2 0 12 11 55 45 21 19 16 22 2 34 28 10 2 43
## [1177] 42 20 2 15 4 30 8 20 51 48 24 21 68 27 72 18 12 79 44 42 19 17 14 12
## [1201] 32 38 9 11 8 67 62 55 40 26 39 15 11 11 65 27 24 6 58 19 21 29 7 2
## [1225] 37 18 37 35 10 9 3 1 72 50 28 6 1 37 33 11 3 66 46 16 13 37 32 19
## [1249] 13 0 34 7 3 67 60 53 17 15 10 45 43 18 16 66 51 15 5 30 21 70 28 9
## [1273] 90 38 32 19 17 15 42 40 23 20 18 16 9 88 60 55 34 23 0 20 70 50 42 13
## [1297] 13 66 55 15 7 60 55 46 31 22 7 3 27 21 0 10 37 65 22 22 29 39 33 14
## [1321] 17 45 21 17 17 27 28 18 17 41 8 3 69 43 16 12 8 55 48 14 12 66 79 40
## [1345] 62 53 22 2 55 24 23 4 62 59 52 27 25 22 37 31 12 10 8 6 2 36 30 8
## [1369] 5 44 41 14 12 50 58 20 18 2 0 17 15 15 45 42 30 25 5 2 0 22 20 3
## [1393] 1 40 35 18 17 14 12 32 28 8 6 4 2 62 58 40 36 15 14 10 65 55 27 18
## [1417] 1 23 16 16 38 36 18 17 15 60 45 29 27 0 30 10 8 42 38 12 7 5 65 36
## [1441] 16 12 3 55 51 25 3 20 2 70 65 28 10 7 3 0 46 43 25 50 17 15 13 10
## [1465] 10 52 45 15 9 7 4 0 52 47 19 16 72 70 40 16 15 14 13 39 15 11 8 6
## [1489] 28 18 32 28 21 2 0 51 14 11 8 42 36 15 13 8 17 14 11 34 32 15 10 7
## [1513] 65 22 16 30 25 8 7 4 46 44 20 18 15 14 10 30 22 2 60 15 43 40 18 16
## [1537] 14 12 10 8 26 23 5 2 0 85 70 63 60 35 25 13 9 7 28 8 6 3 43 31
## [1561] 10 7 69 62 42 22 20 18 15 12 38 17 16 14 9 25 23 42 36 12 10 8 5 45
## [1585] 42 19 16 15 24 20 5 1 45 43 22 14 50 25 3 1 20 18 19 45 93 65 25 18
## [1609] 1 55 26 23 59 54 13 51 39 15 13 11 9 6 80 32 15 12 11 24 18 38 35 7
## [1633] 5 2 31 28 34 31 12 10 8 39 33 16 12 65 30 9 6 4 45 43 14 15 12 32
## [1657] 30 9 6 2 72 50 45 19 16 60 57 25 22 2 23 27 32 21 15 60 50 26 19 32
## [1681] 21 5 1 40 18 15 55 52 45 40 45 42 18 65 50 16 68 38 14 11 30 28 7 1
## [1705] 0 27 18 48 40 27 22 35 32 11 9 39 38 10 3 34 17 15 41 35 18 16 10 45
## [1729] 43 26 21 18 15 13 52 47 22 24 21 50 44 21 19 32 9 8 6 5 65 62 58 60
## [1753] 48 45 16 45 43 17 15 13 11 36 33 9 6 3 30 26 10 8 3 1 35 32 14 11
## [1777] 7 35 32 13 10 9 8 42 39 20 18 16 61 55 53 24 2 18 12 55 48 30 26 0
## [1801] 20 19 54 47 26 18 47 45 45 42 16 11 32 24 10 8 5 2 56 25 22 12 10 8
## [1825] 6 2 0 78 35 12 10 8 2 65 63 39 30 11 9 6 3 70 55 55 48 32 26 8
## [1849] 6 2 23 19 36 33 4 50 48 18 16 14 12 45 35 18 16 13 11 8 6 3 40 35
## [1873] 12 10 7 73 65 32 27 16 10 25 40 38 15 13 10 4 45 30 12 7 50 45 30 25
## [1897] 0 19 38 35 15 10 35 15 37 32 10 8 6 60 55 32 30 10 8 4 45 42 18 15
## [1921] 12 30 16 7 4 0 35 34 15 13 10 6 61 55 50 24 4 0 22 2 0 23 50 45
## [1945] 25 20 22 18 1 18 14 12 83 78 60 52 45 23 22 6 4 2 0 20 17 7 56 40
## [1969] 16 13 11 8 40 30 14 10 8 9 7 34 33 17 14 7 50 28 26 6 4 23 18 30
## [1993] 21 5 3 60 41 41 24 20 4 2 22 2 16 12 60 13 58 56 25 23 1 30 25 2
## [2017] 49 46 28 25 6 4 3 24 21 1 21 18 74 65 65 29 25 6 2 25 22 6 5 2
## [2041] 52 45 20 18 16 14 12 56 52 20 18 14 35 30 16 13 11 22 18 0 40 35 13 10
## [2065] 35 30 14 13 12 7 50 44 52 48 18 10 60 55 40 10 7 6 6 72 61 30 13 7
## [2089] 50 45 30 26 7 5 2 70 55 45 27 22 7 6 4 28 20 18 16 38 33 15 13 11
## [2113] 0 25 22 0 40 38 20 3 0 16 45 40 18 17 12 9 7 6 4 1 57 53 25 17
## [2137] 0 21 16 26 8 5 3 14 65 49 42 25 4 2 1 18 15 6 34 24 7 2 36 40
## [2161] 14 12 11 8 29 23 6 4 30 28 12 10 8 5 3 0 55 25 23 5 0 20 15 44
## [2185] 41 20 15 32 31 12 8 65 55 25 16 8 34 30 10 8 3 66 60 29 29 23 72 68
## [2209] 30 31 11 10 7 52 55 16 12 48 41 12 40 38 17 12 10 32 30 12 6 47 18 13
## [2233] 13 32 14 12 36 18 16 12 45 44 24 49 49 10 64 31 54 51 25 22 35 23 17 13
## [2257] 0 54 26 25 0 20 30 25 11 2 1 27 19 62 44 81 37 33 12 10 8 6 59 35
## [2281] 15 12 10 36 10 29 35 32 16 15 14 10 33 30 13 11 10 6 15 24 22 3 1 48
## [2305] 48 24 19 17 10 8 39 26 8 7 50 49 13 30 36 14 13 11 45 38 35 17 15 12
## [2329] 54 49 20 15 17 50 34 25 46 43 39 34 82 28 35 20 15 15 15 15 15 50 48 25
## [2353] 79 18 46 38 19 14 8 52 52 23 21 58 46 24 24 3 20 21 60 59 26 6 26 0
## [2377] 30 10 6 17 48 38 21 15 10 36 39 13 1 46 46 47 44 17 15 71 65 67 48 57
## [2401] 29 18 53 51 27 29 6 4 20 18 31 27 11 8 6 51 44 20 18 35 31 12 4 2
## [2425] 50 43 21 13 3 22 21 19 60 33 2 49 48 42 25 21 0 19 22 21 20 47 22 19
## [2449] 40 21 19 33 13 8 3 40 32 11 7 39 14 6 49 26 5 76 59 58 34 23 4 14
## [2473] 12 10 49 45 22 20 17 24 3 43 45 81 9 36 29 9 45 37 18 17 14 11 7 77
## [2497] 42 62 52 25 21 0 64 61 49 48 16 48 36 17 1 50 45 24 20 3 1 22 50 26
## [2521] 21 42 38 17 14 10 39 42 16 15 12 10 30 13 10 23 7 2 31 26 5 1 58 58
## [2545] 21 35 27 10 7 4 2 60 29 8 5 80 66 55 40 14 74 33 25 3 2 12 54 53
## [2569] 13 11 9 78 59 47 46 18 12 33 9 6 3 35 14 12 7 54 52 29 22 18 48 45
## [2593] 21 20 88 38 28 16 12 10 36 36 48 41 12 5 2 26 10 8 34 35 16 15 14 70
## [2617] 70 56 38 17 28 19 16 35 35 12 6 68 30 12 42 41 16 15 13 45 42 22 19 16
## [2641] 73 66 39 35 15 13 12 42 35 16 15 46 45 21 52 52 27 20 35 12 36 36 15 13
## [2665] 42 38 21 17 1 43 21 51 50 17 14 32 30 14 12 10 76 60 6 36 36 18 60 13
## [2689] 44 40 16 12 10 9 65 46 44 24 1 19 35 79 44 25 23 68 52 43 20 15 30 25
## [2713] 0 22 20 52 23 20 0 21 31 27 3 29 67 61 52 70 68 48 22 22 0 20 34 26
## [2737] 14 28 24 4 2 25 17 52 41 21 19 40 35 16 12 21 20 1 50 46 27 22 48 31
## [2761] 12 43 42 38 17 15 50 42 20 22 52 31 30 6 2 27 58 57 32 32 5 1 45 45
## [2785] 22 20 24 55 40 32 14 12 5 77 69 84 73 45 67 64 35 32 9 1 50 45 21 15
## [2809] 10 8 44 42 22 20 44 39 19 15 3 40 16 10 65 51 35 24 67 62 60 35 12 49
## [2833] 49 20 29 31 8 51 49 23 21 45 30 16 15 4 56 55 32 30 29 24 23 78 38 36
## [2857] 12 6 75 56 24 17 32 23 0 74 76 60 59 35 30 2 81 13 61 40 62 55 32 30
## [2881] 0 30 30 28 48 46 18 16 9 34 23 53 46 22 15 36 44 14 9 6 61 55 26 21
## [2905] 41 37 9 6 76 74 39 37 16 11 0 27 23 23 2 40 30 9 4 42 39 17 55 42
## [2929] 20 17 12 11 18 57 22 30 5 60 33 40 40 12 40 38 19 16 15 62 38 34 18 13
## [2953] 70 67 18 50 48 28 28 7 1 19 52 53 28 25 5 26 17 35 32 16 13 42 39 21
## [2977] 21 18 49 23 40 34 16 9 52 52 30 19 15 61 57 28 25 2 32 23 6 35 40 13
## [3001] 50 48 42 42 17 14 6 57 28 25 2 30 29 29 6 3 20 42 34 12 11 9 36 32
## [3025] 13 30 30 8 3 66 64 36 35 14 10 47 42 16 50 47 40 13 5 40 36 73 43 78
## [3049] 77 31 30 9 0 43 34 11 3 39 36 7 75 74 32 31 3 62 52 38 30 7 0 34
## [3073] 32 5 32 24 70 50 55 28 26 52 40 21 20 19 16 36 41 18 13 71 69 30 27 24
## [3097] 40 40 20 18 15 45 44 18 53 47 55 50 22 40 37 11 43 37 11 6 49 27 24 32
## [3121] 29 9 6 24 20 3 21 17 15 64 61 29 4 68 41 33 14 8 33 30 31 60 55 7
## [3145] 52 46 18 10 65 60 33 31 32 29 21 63 58 37 35 5 32 31 0 62 35 32 8 21
## [3169] 65 42 40 22 18 7 86 39 37 15 7 41 41 20 16 12 7 65 62 68 60 46 40 16
## [3193] 13 30 29 1 23 36 30 14 12 24 19 18 41 41 19 18 16 13 7 65 65 30 25 23
## [3217] 4 0 72 62 32 32 0 44 40 19 17 35 28 1 30 28 8 2 1 48 45 24 35 33
## [3241] 7 4 26 40 22 18 44 37 19 3 33 28 2 15 28 64 33 31 4 39 34 22 15 7
## [3265] 2 46 45 26 22 60 53 30 20 27 31 30 22 5 32 27 9 2 56 56 29 9 32 14
## [3289] 10 39 37 36 15 13 42 29 8 49 36 15 9 73 68 45 38 12 45 39 15 12 62 54
## [3313] 15 30 11 10 23 60 30 37 33 55 70 20 16 71 64 43 36 14 2 32 29 40 18 17
## [3337] 43 37 18 16 41 36 18 12 39 33 13 3 36 34 27 4 30 27 3 62 20 48 45 18
## [3361] 15 41 40 15 11 45 42 15 12 40 36 13 61 56 35 33 18 16 14 35 35 15 20 15
## [3385] 68 39 28 12 61 53 18 30 61 55 23 21 17 63 55 30 13 11 19 31 59 50 22 21
## [3409] 19 41 39 21 18 68 28 58 57 28 25 55 55 31 31 5 29 68 64 16 41 36 7 4
## [3433] 64 58 50 28 27 4 82 73 72 31 27 0 78 45 43 27 25 25 41 40 11 10 6 78
## [3457] 41 36 16 15 45 24 21 34 24 27 27 5 1 32 30 13 12 48 47 28 21 1 26 86
## [3481] 53 51 26 22 22 75 40 34 9 4 70 34 16 14 41 31 6 66 52 47 29 26 24 1
## [3505] 36 40 17 15 13 54 52 28 26 24 44 40 15 6 71 25 22 42 40 24 21 2 46 45
## [3529] 23 20 25 8 52 26 40 34 16 33 27 10 4 17 34 32 1 23 21 54 50 87 84 50
## [3553] 49 22 20 53 58 34 34 5 2 28 32 35 19 14 6 29 21 17 4 1 26 54 52 34
## [3577] 31 0 48 19 14 44 20 33 11 57 45 24 22 20 57 35 29 55 72 62 41 31 30 25
## [3601] 28 44 38 16 28 39 27 8 0 52 48 14 9 5 25 30 25 6 0 79 79 65 60 42
## [3625] 40 15 36 33 12 7 33 30 10 6 22 26 49 49 24 23 3 47 30 15 14 7 5 42
## [3649] 42 17 16 13 37 36 11 8 3 44 36 17 14 68 33 29 24 21 39 41 18 15 46 47
## [3673] 26 27 7 20 17 56 56 23 35 32 12 8 4 34 12 8 82 38 44 39 20 14 50 34
## [3697] 34 10 5 75 38 73 74 30 30 8 6 33 32 13 10 32 31 9 8 25 32 43 17 12
## [3721] 45 44 24 18 22 18 17 42 42 21 16 64 46 46 23 17 35 14 12 45 38 35 13 11
## [3745] 9 8 45 42 16 13 18 31 24 6 4 0 64 40 18 16 14 16 58 48 28 28 21 19
## [3769] 71 54 28 23 1 68 47 45 22 16 50 49 19 58 52 27 24 35 29 67 64 40 35 11
## [3793] 1 37 30 8 31 27 63 61 37 56 29 29 7 26 17 82 85 50 18 76 67 43 39 11
## [3817] 6 41 35 9 39 35 4 17 22 39 33 1 78 49 52 37 18 17 14 50 48 16 11 14
## [3841] 14 24 25 59 60 24 22 20 83 75 71 65 39 39 16 11 35 33 3 70 70 25 23 28
## [3865] 25 69 62 28 9 74 50 37 34 9 6 24 44 54 26 25 23 20 17 14 83 64 54 31
## [3889] 26 40 36 11 29 28 23 34 29 3 39 14 55 54 24 65 22 19 21 22 59 55 26 25
## [3913] 60 57 34 4 29 17 56 25 25 0 13 70 18 45 41 17 16 11 57 50 29 20 2 25
## [3937] 27 31 3 19 30 25 0 74 50 42 45 53 23 22 22 17 28 25 10 5 40 43 18 44
## [3961] 49 19 50 52 26 27 47 20 17 14 75 71 37 30 1 50 46 30 25 5 17 57 51 16
## [3985] 14 35 25 3 53 48 18 44 19 16 12 25 25 6 29 29 5 23 6 1 32 30 9 7
## [4009] 17 60 40 20 10 47 22 30 25 5 25 22 0 50 31 27 23 38 30 12 3 48 37 16
## [4033] 13 86 53 48 24 16 28 7 4 80 18 15 22 38 25 16 15 5 45 42 20 27 23 2
## [4057] 1 30 25 3 23 50 48 22 20 47 37 8 27 9 2 70 62 25 22 22 19 1 49 37
## [4081] 46 42 22 20 39 20 16 27 4 46 38 14 12 8 25 32 7 1 52 65 57 18 86 82
## [4105] 20 21 1 16 30 26 10 8 65 68 28 27 26 23 18 35 37 10 6 32 41 8 3 45
## [4129] 38 16 14 12 11 9 46 45 50 13 46 44 21 35 57 58 33 30 2 0 16 72 66 48
## [4153] 52 46 15 11 41 34 18 8 65 53 35 20 56 56 27 25 24 23 48 48 22 39 16 44
## [4177] 41 20 16 38 28 12 45 15 13 84 34 26 37 31 15 13 11 10 58 19 34 28 1 45
## [4201] 41 14 8 21 19 71 30 18 17 39 35 15 9 7 36 26 4 30 24 4 0 62 55 25
## [4225] 51 51 14 46 38 19 12 39 28 6 55 31 26 8 1 63 56 16 65 32 29 2 50 38
## [4249] 21 17 38 34 12 6 22 18 26 23 3 52 56 25 6 3 21 3 72 35 23 2 78 72
## [4273] 50 22 28 28 11 7 5 25 22 65 50 15 13 12 90 32 24 29 25 3 44 39 14 10
## [4297] 54 45 25 21 36 32 11 10 33 39 10 7 2 30 23 7 5 32 27 9 5 2 19 17
## [4321] 51 47 29 26 4 23 51 39 22 33 32 11 5 35 23 3 18 29 36 12 9 26 27 5
## [4345] 20 17 43 31 6 1 38 23 31 7 4 30 12 10 7 27 24 1 19 71 61 22 17 25
## [4369] 42 38 22 18 16 15 0 12 31 25 11 6 2 16 21 6 3 51 35 31 10 43 48 13
## [4393] 10 6 75 75 32 24 5 4 27 23 28 9 1 11 22 19 26 22 20 18 15 71 59 33
## [4417] 35 7 49 48 25 23 10 55 46 25 23 40 13 9 19 21 30 24 23 25 21 20 20 24
## [4441] 20 26 27 20 39 32 11 3 37 32 5 2 27 25 26 21 19 82 58 52 32 15 41 34
## [4465] 17 11 81 58 11 45 40 19 17 15 26 21 77 35 11 11 29 10 47 45 18 15 68 17
## [4489] 17 17 45 39 19 18 48 48 18 16 28 23 0 32 29 1 13 40 60 60 17 31 29 4
## [4513] 2 23 21 19 25 33 31 8 4 24 22 16 41 22 0 68 60 33 29 67 65 39 35 13
## [4537] 11 34 56 55 31 26 1 25 20 17 50 21 16 35 14 4 38 35 18 11 53 51 23 75
## [4561] 40 36 14 11 60 42 30 10 5 30 22 33 28 26 40 31 80 50 48 41 24 18 16 48
## [4585] 41 21 17 35 32 30 8 0 57 59 35 34 15 41 41 15 12 8 45 43 24 22 17 73
## [4609] 43 36 36 10 2 56 29 24 6 1 50 29 2 32 27 25 20 48 26 12 25 44 16 74
## [4633] 51 47 22 41 39 18 30 26 0 36 30 9 8 0 58 53 29 23 56 56 78 52 45 20
## [4657] 18 47 45 20 16 13 75 81 40 35 17 15 12 36 26 1 51 42 15 72 68 32 0 37
## [4681] 28 3 56 48 30 22 25 23 4 16 68 59 38 30 11 9 35 30 9 4 28 25 7 5
## [4705] 22 21 21 26 60 45 23 21 82 72 70 68 29 25 69 46 41 7 1 40 33 6 3 51
## [4729] 24 20 22 54 51 26 24 23 55 48 19 19 33 24 2 22 20 19 22 52 58 48 28 27
## [4753] 28 52 48 22 31 5 24 21 25 0 20 32 24 2 34 38 25 24 5 0 29 34 33 12
## [4777] 9 1 34 29 6 0 27 23 15 32 19 22 29 21 17 38 40 17 15 34 39 14 9 72
## [4801] 60 30 9 28 4 38 36 18 14 23 25 4 22 35 32 14 12 8 44 26 24 21 84 42
## [4825] 35 13 65 66 36 24 8 2 86 73 43 23 21 18 58 52 13 30 29 3 44 44 21 14
## [4849] 40 35 15 12 4 73 31 17 73 61 40 38 15 10 32 33 28 7 42 42 16 13 70 44
## [4873] 40 17 15 11 87 52 25 14 25 22 52 52 29 24 22 55 40 35 11 68 62 43 35 13
## [4897] 30 39 31 14 13 9 45 39 15 14 66 64 29 6 2 37 36 11 5 32 26 23 22 53
## [4921] 51 35 26 31 26 0 25 55 56 53 31 80 58 58 30 24 83 52 44 22 48 49 20 26
## [4945] 24 28 47 59 53 35 28 6 3 27 37 28 41 38 15 13 69 55 32 30 6 4 23 30
## [4969] 34 14 10 7 6 45 40 21 19 12 32 29 10 40 28 9 6 3 45 41 21 19 9 40
## [4993] 35 8 2 53 53 21 20 17 30 39 7 22 32 28 13 8 38 37 17 9 11 14 44 43
## [5017] 17 14 2 52 57 26 26 1 55 45 16 10 56 43 29 11 45 40 23 20 17 52 49 21
## [5041] 18 16 40 44 12 82 79 54 26 26 5 60 18 24 59 50 31 26 3 11 67 64 32 26
## [5065] 3 54 85 22 20 20 19 59 55 20 25 24 21 10 7 31 28 12 65 55 34 23 1 38
## [5089] 31 11 9 27 3 65 24 12 18 15 22 42 30 7 3 57 50 20 51 51 24 34 29 11
## [5113] 4 28 25 28 28 27 6 24 4 55 28 4 82 37 28 11 7 60 57 33 30 1 28 26
## [5137] 41 12 27 24 5 4 0 52 46 25 24 5 21 73 17 13 36 30 2 57 32 30 59 36
## [5161] 34 17 16 46 12 11 65 96 21 54 50 23 9 49 44 16 15 45 41 13 25 23 1 58
## [5185] 54 28 22 36 32 17 15 19 40 21 7 0 46 40 16 11 74 62 27 36 44 24 11 78
## [5209] 73 54 52 52 50 19 43 19 17 44 19 17 55 48 15 82 42 40 19 17 12 37 17 55
## [5233] 54 30 22 16 62 58 58 28 25 4 53 51 20 51 40 22 20 14 6 42 46 21 19 62
## [5257] 56 30 10 7 58 51 19 15 88 70 43 12 31 28 8 5 1 40 39 19 17 53 43 22
## [5281] 25 28 25 3 1 0 22 22 31 30 7 2 43 38 29 20 16 14 10 36 30 9 7 28
## [5305] 32 20 27 52 42 24 18 28 24 35 35 17 13 25 4 56 53 28 19 0 30 6 23 26
## [5329] 24 6 4 20 70 60 32 26 2 52 47 21 18 51 38 22 14 42 36 5 3 18 40 32
## [5353] 14 12 47 45 37 66 35 33 42 40 79 9 41 38 14 6 60 55 28 25 27 22 40 36
## [5377] 19 18 67 62 8 28 23 0 20 16 22 4 28 54 15 56 50 25 6 60 14 33 13 10
## [5401] 9 5 18 14 33 59 57 16 51 28 24 22 58 38 30 22 20 14 6 47 45 22 21 1
## [5425] 48 42 40 6 79 23 35 33 9 22 56 73 65 37 33 20 18 7 31 41 20 49 48 78
## [5449] 58 62 22 23 12 48 47 16 45 24 85 43 23 50 48 21 18 22 18 51 42 22 20 17
## [5473] 26 28 65 62 54 29 26 23 11 35 35 17 47 40 14 45 45 55 27 25 22 20 48 46
## [5497] 20 17 9 75 32 16 14 8 6 84 65 27 26 7 25 23 0 50 24 23 22 2 11 57
## [5521] 47 26 22 65 59 20 30 28 7 33 30 12 9 25 6 4 19 37 37 14 7 28 26 20
## [5545] 52 27 21 19 34 15 11 59 52 28 23 23 52 44 7 38 32 7 4 66 11 13 8 36
## [5569] 30 12 6 55 40 17 11 4 42 48 23 12 47 28 13 31 51 47 72 12 46 20 18 64
## [5593] 31 28 3 17 39 32 15 13 32 22 31 13 59 62 35 34 6 1 22 18 16 35 28 8
## [5617] 6 5 2 30 20 5 2 24 7 29 26 36 1 38 17 15 12 43 37 13 10 7 37 13
## [5641] 10 63 42 22 20 19 46 22 20 81 76 78 45 33 29 37 26 5 2 30 38 40 12 6
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## [5689] 27 4 25 25 6 5 46 16 15 33 33 9 4 36 27 7 56 20 56 43 26 25 44 43
## [5713] 11 46 41 38 32 25 2 30 25 23 27 25 6 4 3 2 50 47 26 25 14 37 37 11
## [5737] 10 41 15 49 45 26 19 17 37 42 14 33 28 4 21 32 26 3 0 43 17 15 13 9
## [5761] 30 17 17 38 34 4 65 34 32 20 24 44 41 21 17 40 29 8 1 33 32 15 12 10
## [5785] 50 46 22 18 15 42 42 17 11 8 8 85 34 34 14 11 35 35 18 10 43 35 18 12
## [5809] 54 50 22 23 52 46 26 58 35 27 0 33 28 69 68 47 37 17 14 7 62 40 39 16
## [5833] 14 6 22 48 27 15 8 5 26 52 47 43 39 16 12 45 43 16 15 86 36 34 20 65
## [5857] 61 40 9 8 52 57 31 22 4 27 83 60 55 31 31 7 39 35 10 6 77 32 8 6
## [5881] 46 43 46 38 18 39 32 29 4 56 36 35 15 32 35 12 9 44 50 18 19 11 41 49
## [5905] 21 18 71 47 47 18 15 41 18 33 34 5 28 24 23 30 24 3 3 38 41 13 8 39
## [5929] 35 16 14 17 27 25 7 23 37 35 8 0 29 29 29 11 7 4 56 33 9 7 74 61
## [5953] 37 13 12 31 27 7 0 63 56 44 41 21 17 67 62 19 23 3 58 23 21 0 27 5
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## [6073] 27 25 20 68 63 39 37 14 10 93 45 38 19 13 29 29 8 5 3 34 44 19 16 14
## [6097] 37 32 4 0 75 57 46 43 36 43 30 39 29 38 30 6 5 3 1 1 16 33 28 4
## [6121] 27 6 37 40 18 12 28 24 35 31 11 2 31 24 1 29 6 0 24 21 21 19 19 41
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## [6865] 11 9 6 36 51 39 12 74 57 39 38 7 28 26 8 4 2 30 11 6 1 46 40 18
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## [11785] 58 32 8 2 33 14 10 6 61 58 46 23 19 17 4 41 36 15 53 54 29 26 6 2
## [11809] 30 11 9 2 43 46 22 22 4 1 16 13 11 50 32 10 37 13 10 10 51 47 53 52
## [11833] 21 19 25 7 3 40 33 11 6 63 59 53 27 19 35 37 14 12 10 38 34 13 9 7
## [11857] 3 65 42 32 9 6 14 69 59 46 17 12 35 16 14 11 9 33 42 41 17 14 12 63
## [11881] 51 45 22 18 21 16 32 26 4 0 55 48 22 17 14 30 38 11 9 2 75 55 30 27
## [11905] 8 6 35 28 11 9 1 30 29 12 8 5 35 30 5 40 32 6 14 72 17 38 36 31
## [11929] 27 8 2 57 50 58 56 23 17 13 11 35 32 12 7 25 23 6 44 38 19 12 30 25
## [11953] 5 38 36 14 8 4 45 42 19 17 15 50 45 18 16 8 41 35 12 6 0 60 56 20
## [11977] 20 2 0 15 10 50 39 24 2 17 50 48 30 47 46 22 17 5 49 51 55 51 23 12
## [12001] 7 35 18 16 11 74 72 59 76 79 53 55 24 1 25 83 35 10 40 40 20 18 1 21
## [12025] 2 64 53 23 27 3 14 41 19 16 35 32 14 10 1 37 16 13 6 48 48 25 21 1
## [12049] 19 49 46 11 8 6 39 40 11 7 4 3 27 26 5 0 73 72 52 47 15 10 46 29
## [12073] 18 16 7 62 15 35 32 15 11 7 47 47 22 21 18 16 59 65 62 36 32 6 5 3
## [12097] 84 51 48 16 14 22 4 2 3 41 34 13 11 6 15 38 34 12 7 7 3 42 16 13
## [12121] 10 72 61 35 32 13 9 4 64 63 31 28 2 76 75 15 11 9 2 67 42 14 9 21
## [12145] 24 18 42 15 46 50 12 75 61 58 57 17 38 80 76 70 53 51 16 14 38 13 8 62
## [12169] 61 41 32 14 6 63 61 29 9 3 27 25 0 25 43 34 7 4 61 60 11 66 34 30
## [12193] 22 61 60 27 4 2 0 66 37 33 14 11 7 6 48 40 18 16 16 13 11 36 9 7
## [12217] 4 33 32 10 7 70 39 33 8 43 15 12 10 46 42 17 15 12 23 5 3 0 41 39
## [12241] 16 13 10 6 3 40 39 15 12 10 8 4 72 68 69 65 25 22 3 1 22 18 39 32
## [12265] 14 12 7 6 69 73 68 38 38 13 10 37 34 11 7 55 54 21 10 64 59 33 11 7
## [12289] 58 58 28 20 8 47 39 19 15 34 31 1 63 64 25 3 32 14 11 2 28 18 52 21
## [12313] 53 51 21 18 14 11 33 20 30 26 43 35 19 18 16 24 22 6 3 40 38 6 2 36
## [12337] 34 11 7 21 3 35 58 7 36 30 10 9 7 3 36 32 18 15 7 5 36 36 16 11
## [12361] 60 56 26 76 40 21 16 35 31 3 50 46 21 18 30 30 4 2 66 55 50 27 6 2
## [12385] 30 25 4 2 24 21 70 50 39 22 35 32 14 12 10 77 58 52 33 29 9 7 28 23
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## [12481] 13 35 12 7 38 13 70 55 52 24 21 14 52 51 30 34 12 7 5 37 30 14 12 57
## [12505] 56 42 35 13 19 59 65 18 13 48 44 21 18 16 71 33 31 9 6 22 34 16 14 12
## [12529] 7 47 38 9 3 81 17 17 14 12 7 33 33 10 7 53 52 23 0 9 60 52 24 20
## [12553] 15 29 7 36 17 15 28 10 8 28 6 4 30 35 11 8 64 57 35 10 7 39 40 17
## [12577] 10 3 66 51 29 22 10 50 17 15 10 29 10 7 66 47 45 24 21 20 40 37 16 13
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## [12625] 60 45 40 17 15 13 11 7 45 14 61 35 24 5 1 19 16 21 30 13 10 28 25 9
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## [12673] 9 48 42 16 24 6 2 66 35 27 12 10 8 32 30 9 5 3 43 47 21 18 96 76
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## [12721] 13 8 51 24 22 28 27 6 5 1 37 32 16 14 5 52 50 25 17 21 18 16 38 15
## [12745] 12 47 45 17 15 11 5 25 22 0 50 55 51 32 16 14 35 8 5 1 44 21 17 11
## [12769] 62 57 19 15 78 38 32 12 10 8 3 75 65 29 3 0 58 51 13 40 22 13 52 50
## [12793] 25 8 3 0 21 18 71 55 28 26 7 3 20 3 0 71 68 31 10 8 29 9 7 6
## [12817] 21 67 55 42 37 12 6 22 5 39 37 15 12 11 9 66 34 30 14 10 8 2 67 66
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## [12865] 40 18 16 16 14 12 10 8 2 69 67 21 33 11 7 5 65 63 27 25 6 3 2 45
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## [12913] 24 3 55 50 15 9 8 6 33 30 8 7 6 5 4 3 52 50 30 28 10 7 6 60
## [12937] 55 62 57 35 33 8 6 3 30 12 10 8 4 60 55 51 13 35 32 66 63 44 40 9
## [12961] 6 45 40 15 6 70 65 41 20 0 16 13 66 64 29 27 6 5 2 23 5 3 0 43
## [12985] 40 17 15 8 6 70 68 32 12 7 5 35 32 12 9 6 30 10 24 4 60 45 42 7
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## [13033] 11 72 22 1 21 43 41 13 10 56 28 26 3 0 18 2 65 63 20 72 55 32 9 6
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## [13153] 35 7 3 45 43 18 16 10 57 52 40 17 15 12 7 5 58 55 47 36 7 4 57 50
## [13177] 23 24 1 8 34 33 8 2 75 44 42 18 15 53 51 16 21 14 14 31 3 1 45 40
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## [13489] 39 15 12 40 32 14 12 10 8 65 55 28 26 10 23 6 3 48 40 18 59 56 33 31
## [13513] 10 5 3 27 21 15 46 38 14 11 8 72 25 5 1 19 40 35 23 21 16 6 2 80
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## [13729] 52 25 40 45 21 2 14 11 72 38 35 15 12 10 64 60 42 36 14 12 25 50 35 13
## [13753] 10 8 45 42 17 60 45 30 28 9 14 11 11 55 23 5 1 19 60 45 24 9 16 10
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## [13801] 5 19 2 34 32 10 6 31 13 11 4 60 52 21 17 12 57 52 30 27 6 4 2 47
## [13825] 42 16 12 11 10 75 55 52 16 10 80 76 55 50 24 5 2 20 77 76 65 55 31 27
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## [13873] 8 66 62 32 31 12 10 8 6 2 61 55 51 27 25 10 7 5 2 23 6 4 2 65
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## [13969] 35 40 13 11 60 25 9 5 2 65 60 37 26 22 0 53 51 30 24 6 3 62 30 28
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## [14065] 25 13 4 1 48 22 17 0 18 17 61 18 37 13 10 65 50 40 16 11 6 2 52 28
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## [14569] 30 12 9 7 5 3 55 53 26 5 3 17 55 60 52 24 21 0 19 26 8 3 1 35
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## [18025] 15 10 7 21 1 41 72 65 79 75 35 30 15 11 7 1 68 43 18 16 14 12 10 8
## [18049] 4 59 50 25 22 6 3 65 56 27 21 3 0 78 17 0 21 3 0 26 24 8 6 3
## [18073] 1 27 25 4 2 66 74 45 19 17 15 12 11 9 43 15 12 10 47 50 24 22 14 44
## [18097] 7 44 42 25 28 9 8 4 2 0 11 30 34 17 17 11 41 7 51 46 18 43 45 16
## [18121] 9 6 40 34 10 26 7 5 2 51 42 11 6 2 0 60 59 27 25 8 6 3 25 25
## [18145] 7 5 19 60 59 50 31 15 13 59 44 16 61 49 70 23 5 40 38 16 14 10 7 5
## [18169] 52 52 20 14 78 32 4 72 31 61 66 60 12 29 27 7 4 60 55 26 5 4 17 35
## [18193] 16 11 34 13 11 43 36 47 41 18 15 12 10 39 39 36 16 13 10 7 63 56 55 50
## [18217] 13 56 51 17 10 24 21 5 3 34 38 10 2 80 59 56 67 27 23 22 45 37 13 9
## [18241] 39 28 12 10 7 5 4 34 52 14 9 45 50 19 18 75 37 30 10 9 3 68 66 50
## [18265] 19 81 51 52 18 16 13 28 0 55 18 23 1 31 29 6 78 68 30 6 3 66 42 26
## [18289] 7 5 2 71 57 51 28 5 1 11 8 14 63 63 22 2 27 7 2 47 40 19 16 14
## [18313] 11 60 55 27 3 1 19 12 25 26 6 4 2 33 33 12 8 4 65 70 39 34 8 5
## [18337] 32 35 9 7 5 15 78 63 39 25 26 24 40 33 14 12 10 47 30 16 12 9 8 6
## [18361] 3 52 40 13 10 6 3 46 48 22 16 72 41 81 82 37 46 15 11 9 6 48 53 26
## [18385] 24 7 24 24 4 2 16 16 30 9 9 12 48 48 28 25 4 3 0 24 25 3 0 17
## [18409] 15 12 10 4 39 39 18 13 11 11 5 66 21 1 0 42 38 16 14 12 8 5 38 32
## [18433] 16 15 14 12 10 46 45 19 17 14 11 8 5 48 40 31 31 12 8 4 0 44 43 9
## [18457] 2 36 34 14 11 8 5 43 37 12 17 15 19 11 10 4 1 25 22 1 58 57 45 40
## [18481] 22 12 39 33 16 14 65 60 38 32 15 13 73 40 44 18 15 14 10 50 50 25 20 18
## [18505] 15 12 10 50 47 28 22 21 6 49 46 26 25 3 30 26 4 46 45 23 21 19 44 40
## [18529] 24 20 20 17 15 29 28 11 8 6 34 30 10 6 5 61 70 37 35 12 64 64 58 49
## [18553] 30 19 15 13 27 30 5 0 20 18 6 40 35 11 9 4 50 45 25 18 1 12 10 6
## [18577] 3 28 22 10 5 2 51 39 16 13 8 5 5 3 37 36 13 10 6 4 35 27 5 4
## [18601] 3 0 67 48 45 12 9 7 4 34 33 17 16 7 4 2 1 50 35 15 9 3 30 11
## [18625] 8 5 50 48 21 17 14 68 27 26 23 17 58 22 26 5 42 45 22 3 56 48 22 18
## [18649] 15 90 38 30 10 7 4 1 53 40 12 32 31 13 10 27 26 6 5 56 14 34 10 65
## [18673] 65 29 0 49 51 17 14 11 92 38 49 11 5 74 70 13 63 63 20 66 66 39 11 8
## [18697] 53 48 20 15 12 49 43 14 4 61 33 27 7 5 57 54 9 39 17 17 15 13 43 40
## [18721] 17 7 77 76 50 40 6 57 55 12 52 57 20 17 15 33 34 12 9 7 76 33 31 13
## [18745] 10 3 2 74 52 30 29 6 1 76 76 63 50 16 13 37 39 19 14 13 11 76 29 8
## [18769] 6 5 2 35 35 14 12 9 7 3 30 9 6 3 34 34 10 8 4 54 40 21 18 15
## [18793] 14 65 59 28 10 7 64 44 18 38 13 9 6 3 47 50 21 16 35 38 14 12 10 7
## [18817] 50 45 61 48 19 16 13 10 24 19 65 60 22 16 13 33 33 11 8 5 47 15 14 13
## [18841] 83 83 74 29 29 6 52 51 52 15 59 47 15 60 60 26 18 68 71 70 12 74 62 60
## [18865] 61 32 31 29 11 8 65 10 6 34 14 11 27 8 5 46 46 63 45 22 29 29 5 1
## [18889] 66 50 20 16 11 32 26 4 28 48 40 17 50 58 19 29 33 10 7 4 77 68 64 34
## [18913] 8 66 35 32 35 12 9 6 30 29 10 8 0 70 59 27 7 4 40 40 16 15 11 39
## [18937] 42 21 12 28 30 25 10 8 48 44 16 53 55 62 9 30 8 4 37 37 15 11 9 7
## [18961] 56 55 17 60 47 43 20 0 21 35 32 13 10 8 40 35 15 12 9 7 3 73 28 11
## [18985] 7 76 31 10 8 44 49 17 15 12 60 60 24 1 39 35 15 11 9 5 33 33 12 5
## [19009] 64 58 20 19 15 61 59 26 79 76 59 43 18 14 72 62 47 18 15 52 38 14 12 62
## [19033] 55 50 19 13 11 55 51 14 39 11 36 34 13 11 9 4 2 65 69 49 23 17 42 38
## [19057] 16 14 12 45 42 17 14 12 37 14 12 10 50 17 25 5 2 28 62 41 18 15 13 11
## [19081] 43 16 12 69 33 8 6 4 0 31 13 8 6 60 56 26 6 23 16 12 75 81 81 76
## [19105] 39 36 10 8 2 67 54 24 20 30 27 16 51 51 18 15 11 29 30 6 6 4 0 35
## [19129] 65 65 23 20 47 44 15 12 9 45 45 19 34 34 11 6 31 25 0 32 25 6 2 42
## [19153] 42 18 15 10 6 0 33 12 9 83 46 62 19 22 19 40 53 13 11 5 0 42 17 14
## [19177] 9 3 33 14 10 79 70 21 19 2 0 44 36 15 73 52 68 50 17 13 11 44 29 12
## [19201] 11 10 44 15 13 81 53 49 67 73 36 13 10 6 4 1 18 11 54 51 21 16 51 56
## [19225] 27 91 52 45 14 55 19 30 30 14 7 2 16 51 41 10 6 36 32 11 9 7 1 29
## [19249] 8 5 2 0 55 53 34 13 8 5 64 32 9 7 4 36 28 54 52 24 5 4 23 21
## [19273] 1 41 19 12 87 35 27 12 9 27 23 8 5 2 35 15 13 11 8 6 32 9 7 44
## [19297] 44 23 18 65 58 50 30 5 2 18 37 42 15 12 10 7 5 44 47 10 32 30 3 77
## [19321] 55 33 8 7 5 26 31 8 5 55 56 26 8 5 44 44 13 52 45 25 18 0 18 7
## [19345] 58 48 75 55 26 5 2 61 27 25 7 6 19 81 43 39 18 15 84 44 35 11 10 8
## [19369] 6 37 34 11 10 6 42 39 17 16 12 32 28 11 8 41 40 17 15 13 11 40 38 13
## [19393] 10 61 43 4 49 40 17 13 9 76 71 70 72 23 5 35 22 12 10 2 14 0 65 43
## [19417] 51 54 16 15 78 46 39 17 13 11 59 26 7 4 48 44 71 30 8 1 77 62 37 29
## [19441] 1 59 48 20 2 0 18 26 7 2 49 15 42 41 20 14 54 51 22 6 4 17 35 24
## [19465] 7 4 42 29 22 2 70 39 30 13 8 60 51 17 79 68 28 31 11 10 7 3 60 59
## [19489] 73 70 31 32 69 44 37 14 80 57 24 44 39 18 15 87 66 68 67 42 44 54 51 29
## [19513] 31 23 17 11 7 7 0 0 33 30 10 4 82 37 64 64 31 32 36 32 13 10 8 60
## [19537] 57 19 17 15 25 5 1 64 65 38 15 11 37 36 14 12 10 7 5 3 44 39 21 9
## [19561] 40 42 15 12 69 67 67 55 21 30 4 2 25 2 50 48 19 14 22 4 18 1 12 56
## [19585] 55 30 12 9 5 35 33 15 9 8 66 66 47 45 17 16 57 47 23 1 52 53 26 9
## [19609] 7 23 21 4 2 0 47 17 15 11 72 64 44 56 26 18 1 35 19 17 13 12 10 65
## [19633] 55 56 45 20 50 50 20 2 74 60 20 15 16 66 34 37 75 37 12 45 15 42 33 12
## [19657] 7 30 34 10 6 71 70 36 36 14 13 12 76 55 47 42 19 13 12 9 59 51 21 16
## [19681] 13 22 4 21 1 72 66 30 11 8 4 43 54 50 8 28 31 10 9 8 31 12 9 6
## [19705] 38 28 17 51 49 11 45 41 41 41 16 25 28 4 46 46 17 76 26 26 6 6 5 27
## [19729] 9 45 28 12 8 4 1 80 56 47 21 22 44 44 23 15 15 53 47 57 11 45 44 21
## [19753] 19 14 11 81 53 45 19 15 56 39 10 82 32 12 5 68 68 24 10 5 35 15 12 9
## [19777] 31 33 29 10 8 5 66 29 60 53 52 42 13 60 49 59 59 49 25 3 0 22 26 1
## [19801] 63 72 54 35 25 18 12 28 9 6 52 52 33 61 59 33 24 4 21 40 16 7 5 25
## [19825] 39 35 17 13 4 76 47 42 16 13 8 7 5 66 52 45 23 21 19 17 15 14 65 61
## [19849] 35 36 13 12 11 42 21 0 19 16 67 62 25 2 0 45 13 10 8 8 48 27 4 1
## [19873] 14 14 66 65 45 17 15 60 60 86 62 14 34 9 47 47 32 7 1 22 28 41 18 13
## [19897] 68 60 29 4 26 2 17 58 47 19 17 14 56 51 14 25 7 2 19 4 61 50 22 2
## [19921] 21 13 36 30 14 11 3 2 60 58 27 9 8 1 47 39 12 9 7 4 28 10 9 8
## [19945] 45 38 26 0 14 55 29 7 5 0 74 32 7 6 5 79 67 20 1 30 31 11 8 45
## [19969] 15 13 31 11 8 49 48 22 71 58 52 21 67 52 25 3 17 16 65 62 23 18 16 10
## [19993] 5 31 28 2 1 64 40 36 13 11 8 5 62 59 62 51 16 14 11 9 46 35 15 10
## [20017] 6 70 45 12 65 55 19 22 20 18 53 48 22 2 16 75 67 25 60 15 47 19 18 8
## [20041] 59 55 44 40 18 16 13 33 12 8 58 52 9 46 15 72 33 12 9 5 51 18 15 34
## [20065] 31 14 13 31 14 12 8 60 41 58 60 28 27 8 2 74 65 22 3 7 55 17 72 61
## [20089] 22 23 8 37 14 8 5 83 81 14 53 38 26 22 1 21 17 14 12 9 5 65 58 18
## [20113] 56 51 15 13 11 8 2 65 66 53 59 75 64 26 22 2 48 37 11 10 8 5 2 60
## [20137] 55 13 53 40 50 3 2 0 38 39 6 3 24 35 36 16 13 11 5 3 55 41 14 6
## [20161] 4 2 76 64 65 30 2 14 58 56 63 38 36 40 38 15 10 54 45 16 8 53 54 30
## [20185] 2 42 48 65 26 4 2 48 45 9 85 60 61 58 20 18 79 37 11 64 62 23 0 79
## [20209] 67 25 24 8 6 21 21 3 0 43 40 18 15 12 8 1 57 55 35 18 15 55 53 27
## [20233] 20 4 0 40 12 10 7 4 74 31 23 9 73 55 48 28 26 11 10 6 2 1 75 48
## [20257] 45 28 56 7 4 2 1 42 14 13 11 10 4 1 35 12 10 8 5 43 15 52 37 15
## [20281] 13 49 40 21 0 55 48 28 43 38 22 75 48 48 13 44 10 9 4 44 35 16 13 12
## [20305] 10 6 38 37 17 14 9 28 27 9 7 5 29 25 7 5 2 33 15 11 8 46 39 16
## [20329] 10 6 4 32 3 38 6 2 0 30 26 5 60 50 42 25 19 15 11 72 70 47 30 62
## [20353] 55 13 36 38 12 8 57 52 19 6 38 17 15 26 24 4 0 34 31 13 10 8 6 35
## [20377] 32 13 10 3 0 44 37 16 13 11 9 6 29 9 7 2 66 59 36 67 66 28 9 3
## [20401] 1 36 35 16 11 4 1 68 67 52 55 19 69 61 29 7 28 7 6 40 55 51 62 52
## [20425] 30 5 4 17 15 10 8 6 71 58 77 28 8 6 2 54 26 67 69 66 32 26 3 68
## [20449] 61 11 23 0 29 23 2 20 2 1 51 46 20 16 11 75 46 60 50 21 12 8 71 61
## [20473] 57 26 20 57 42 0 82 13 31 27 8 3 44 51 19 0 15 66 22 2 50 82 48 41
## [20497] 17 12 58 15 10 65 61 27 9 0 29 25 1 31 28 1 39 17 9 48 15 10 7 3
## [20521] 57 21 3 19 48 49 19 59 39 19 17 15 11 9 35 13 11 8 34 29 11 8 6 64
## [20545] 48 45 18 15 13 11 8 71 40 33 15 12 10 8 40 36 13 8 5 2 62 16 82 67
## [20569] 63 42 22 7 15 23 3 30 28 9 6 4 2 46 77 59 56 60 34 13 48 51 15 13
## [20593] 25 8 3 0 49 52 24 5 15 12 76 34 14 17 66 55 44 8 36 14 11 25 26 7
## [20617] 3 41 19 16 11 38 35 13 11 7 25 5 39 18 16 14 24 5 3 58 19 19 15 10
## [20641] 20 23 51 47 20 18 16 8 27 23 2 35 30 13 11 9 18 18 50 59 25 29 8 5
## [20665] 0 26 21 3 1 19 14 18 20 19 63 70 58 52 41 16 12 10 27 9 4 43 38 15
## [20689] 10 7 53 49 27 6 4 11 61 22 15 40 16 50 49 26 5 2 65 13 47 45 20 18
## [20713] 12 9 40 17 14 9 7 55 50 25 15 9 78 34 3 52 29 23 53 56 15 75 37 13
## [20737] 10 60 26 7 1 17 21 0 37 48 17 14 11 10 8 71 70 16 15 45 28 9 8 5
## [20761] 4 25 7 5 2 68 64 19 18 38 10 5 2 26 7 5 2 48 22 5 17 19 28 8
## [20785] 6 4 47 41 23 19 1 0 18 14 12 10 2 55 52 14 12 59 58 30 6 15 59 52
## [20809] 24 5 3 76 59 56 77 32 39 11 8 58 53 24 8 3 48 31 65 22 4 0 65 59
## [20833] 26 5 2 12 11 51 48 23 6 4 17 29 10 7 40 18 12 80 54 12 48 12 60 44
## [20857] 31 10 4 2 66 18 15 20 1 18 35 34 17 14 83 69 22 22 6 4 3 40 19 18
## [20881] 17 13 11 76 65 30 23 23 6 3 26 6 33 32 14 11 78 55 28 24 4 2 40 17
## [20905] 12 10 40 21 17 10 6 0 74 62 44 30 7 5 69 54 60 14 75 51 47 23 60 55
## [20929] 26 4 1 17 19 17 33 39 13 10 56 53 24 29 9 7 5 58 56 39 41 13 11 85
## [20953] 28 4 3 31 11 10 7 3 1 31 10 9 3 70 65 18 13 28 11 26 4 76 68 21
## [20977] 2 58 30 12 10 4 66 35 15 23 54 53 26 13 47 49 23 5 2 19 55 59 45 38
## [21001] 13 41 36 16 12 10 58 56 32 27 5 2 25 19 35 8 6 24 8 40 20 16 6 76
## [21025] 70 38 17 16 12 48 43 47 41 19 14 38 35 14 12 30 25 7 4 0 60 56 18 16
## [21049] 76 59 21 1 26 28 9 4 2 59 50 13 66 56 15 23 22 3 27 9 8 16 52 59
## [21073] 17 13 42 36 18 16 14 12 9 29 68 59 38 30 12 8 38 16 11 70 46 22 1 18
## [21097] 8 48 23 19 38 35 12 8 39 33 14 12 10 6 61 59 90 66 57 20 64 51 20 78
## [21121] 76 57 22 7 0 44 15 13 75 71 38 37 13 10 8 63 63 25 21 5 3 0 45 15
## [21145] 51 51 21 1 39 16 12 9 65 57 66 36 77 41 36 17 14 10 36 17 16 14 8 26
## [21169] 8 14 13 46 38 15 11 81 71 62 73 31 27 6 4 65 65 34 11 8 5 30 22 35
## [21193] 16 14 30 25 9 3 0 50 50 10 32 10 8 19 4 0 14 68 45 41 12 10 35 16
## [21217] 13 11 8 36 19 16 13 9 7 60 48 19 16 14 10 26 5 25 23 6 4 34 30 11
## [21241] 7 58 52 37 35 11 5 66 65 50 43 17 14 17 50 50 24 24 6 3 20 14 2 28
## [21265] 8 4 65 43 39 15 9 8 44 37 22 19 18 12 80 60 32 29 26 19 0 55 25 20
## [21289] 72 26 34 4 38 19 60 59 50 29 1 50 50 45 46 45 14 9 30 12 8 62 35 17
## [21313] 13 36 15 10 26 10 7 28 10 6 34 32 13 11 58 56 58 24 19 16 59 55 34 15
## [21337] 13 12 10 25 5 22 20 0 77 47 43 26 25 6 1 19 13 30 28 12 10 46 42 15
## [21361] 13 11 8 34 17 16 14 33 12 10 42 41 20 16 12 10 45 37 19 17 40 34 12 45
## [21385] 44 21 18 60 13 9 57 55 20 18 56 51 47 41 19 18 15 60 42 41 15 11 8 70
## [21409] 65 10 8 6 52 41 24 22 7 3 18 24 20 1 75 44 24 22 1 20 18 18 16 15
## [21433] 66 56 50 27 25 6 25 22 2 21 39 37 7 5 53 38 32 13 9 42 42 17 16 12
## [21457] 50 50 50 35 15 13 11 32 27 7 6 3 1 53 59 34 15 14 57 55 38 20 18 14
## [21481] 31 14 13 4 30 28 10 7 2 29 25 8 5 2 47 46 19 16 8 37 36 14 13 10
## [21505] 62 45 29 30 13 12 3 27 28 9 6 3 26 18 54 52 13 35 12 9 6 4 1 52
## [21529] 45 17 13 33 31 14 10 8 46 43 11 40 17 13 38 35 10 8 6 5 4 48 44 21
## [21553] 14 8 52 50 14 23 3 0 30 28 5 3 60 57 55 18 16 10 5 29 13 11 10 69
## [21577] 67 26 7 5 14 12 46 37 18 16 14 13 27 4 67 14 59 45 21 10 66 63 49 33
## [21601] 29 11 48 21 17 27 1 30 24 2 0 30 2 10 32 26 9 5 62 36 12 10 79 47
## [21625] 43 37 17 15 57 13 52 45 14 62 62 35 30 27 56 16 14 10 9 59 56 17 11 11
## [21649] 62 39 15 13 11 55 53 20 1 73 71 36 9 7 5 46 45 11 9 84 74 70 68 27
## [21673] 6 19 39 37 17 15 13 10 7 55 23 4 2 42 37 15 10 8 60 58 48 17 15 11
## [21697] 51 59 22 20 1 37 18 15 50 52 25 10 8 3 21 2 26 16 26 7 17 38 35 16
## [21721] 14 65 57 22 20 55 50 81 60 52 57 21 24 20 7 76 65 39 20 16 11 68 64 43
## [21745] 19 61 55 36 42 16 28 21 24 1 52 49 32 20 25 56 56 29 24 15 29 40 27 16
## [21769] 26 28 30 13 11 23 21 50 36 13 12 36 15 12 8 70 32 11 5 0 54 53 48 47
## [21793] 25 19 18 15 35 14 6 4 1 42 41 18 13 72 70 46 44 22 4 2 19 16 50 40
## [21817] 17 14 42 45 11 32 29 10 7 15 54 51 30 7 3 1 22 43 40 21 3 1 8 6
## [21841] 57 52 26 9 7 0 51 50 26 8 5 20 20 23 5 2 27 26 9 6 37 17 14 10
## [21865] 77 64 76 58 27 8 6 25 54 24 18 0 14 11 8 54 54 13 40 13 38 16 14 9
## [21889] 6 57 20 16 55 52 22 16 13 9 51 47 22 14 25 20 17 51 49 48 45 17 14 12
## [21913] 10 8 6 43 15 10 7 4 44 18 14 11 6 30 27 10 8 6 3 0 42 44 12 10
## [21937] 5 80 37 37 17 15 14 11 9 7 60 58 26 7 44 43 21 19 16 14 10 8 73 44
## [21961] 40 13 11 10 9 7 50 49 15 14 58 57 17 44 42 18 15 12 10 70 60 35 10 7
## [21985] 28 27 10 9 8 6 5 25 23 22 2 0 19 14 48 47 19 0 12 10 7 2 46 44
## [22009] 25 23 12 9 9 82 62 51 30 29 8 4 1 26 20 56 48 28 28 11 11 9 7 3
## [22033] 2 27 22 7 3 2 23 11 35 11 9 5 56 54 28 10 5 34 32 12 10 8 80 40
## [22057] 40 16 13 10 7 1 54 54 21 16 13 35 34 15 11 8 6 60 58 30 10 5 30 28
## [22081] 26 5 0 18 16 37 32 12 10 6 3 73 5 56 56 25 24 22 33 16 11 67 62 44
## [22105] 17 14 11 24 7 82 59 46 24 21 18 16 61 53 34 18 26 22 30 4 66 55 33 5
## [22129] 2 48 40 12 76 60 39 24 4 35 15 13 37 12 11 8 67 26 2 18 14 38 34 14
## [22153] 10 6 55 51 34 30 9 8 7 3 25 2 18 12 37 39 18 14 12 7 45 24 21 1
## [22177] 20 16 13 67 66 43 30 9 6 2 58 52 25 5 0 18 60 58 38 28 16 51 50 32
## [22201] 5 3 0 15 13 80 43 55 50 35 7 30 28 7 25 23 1 15 13 44 43 19 8 6
## [22225] 54 55 28 9 3 0 28 26 4 0 25 23 64 62 39 37 16 13 13 40 34 9 7 70
## [22249] 71 40 15 10 27 4 24 2 55 44 22 18 1 17 76 30 27 8 3 26 4 47 46 13
## [22273] 76 57 5 45 58 41 18 16 14 33 28 7 65 75 70 22 1 12 70 58 37 17 15 2
## [22297] 66 60 30 8 7 5 1 42 13 11 9 6 55 31 29 46 42 14 29 27 9 34 29 10
## [22321] 7 4 26 20 4 19 1 57 35 16 12 10 75 60 52 23 18 13 32 30 54 48 18 12
## [22345] 9 52 12 10 65 60 58 35 32 6 4 2 1 25 22 2 47 44 20 18 14 10 80 50
## [22369] 33 30 13 10 6 38 36 7 4 0 60 38 30 10 7 5 3 70 50 26 23 3 1 18
## [22393] 16 72 72 46 42 17 15 13 10 14 6 8 28 26 9 7 4 27 25 7 4 46 45 24
## [22417] 17 14 11 38 76 43 34 14 11 44 17 75 40 21 19 14 10 80 4 8 41 22 13 4
## [22441] 40 35 12 9 47 46 27 21 20 38 15 11 50 47 19 75 33 14 13 10 71 31 27 11
## [22465] 9 7 5 22 21 18 55 25 25 2 0 68 65 64 53 28 10 7 17 76 67 30 23 2
## [22489] 51 50 55 58 21 1 0 20 36 35 19 17 16 52 50 29 6 1 25 23 2 19 17 16
## [22513] 8 60 55 20 18 1 17 70 40 33 12 10 8 27 23 4 0 35 27 10 6 55 52 33
## [22537] 32 16 14 13 11 10 8 28 27 8 6 4 2 26 25 5 2 61 51 35 43 40 20 14
## [22561] 55 45 27 5 2 13 11 61 58 72 48 17 14 10 8 4 38 15 10 3 71 45 43 16
## [22585] 14 11 10 8 37 12 9 3 35 33 10 7 4 1 65 62 40 38 14 12 10 8 55 50
## [22609] 32 25 22 15 11 7 4 60 47 31 28 11 9 5 4 0 20 17 15 8 46 42 21 19
## [22633] 16 13 11 9 7 5 65 12 60 50 30 27 7 5 3 27 26 10 6 5 22 5 2 14
## [22657] 67 65 32 29 9 7 38 15 12 10 70 60 45 42 20 16 13 5 74 65 13 51 46 25
## [22681] 24 5 40 35 16 12 10 8 2 45 37 9 2 0 42 14 10 47 40 18 17 14 12 7
## [22705] 3 62 56 31 27 11 9 6 1 18 21 75 60 25 3 18 69 65 29 25 8 4 2 38
## [22729] 35 16 11 40 38 20 18 1 14 12 10 8 6 50 35 40 12 7 5 3 0 40 18 10
## [22753] 51 18 16 12 10 8 3 1 30 29 3 0 42 40 10 61 31 28 12 4 30 27 7 3
## [22777] 3 29 27 4 1 50 45 17 13 64 63 35 33 3 55 50 22 18 14 12 8 58 55 35
## [22801] 30 0 28 2 56 48 16 18 3 2 36 30 10 6 29 23 20 43 19 15 12 65 25 21
## [22825] 1 30 27 11 5 17 65 63 54 52 29 29 12 24 22 20 48 44 16 13 11 78 27 6
## [22849] 2 68 64 18 0 26 0 24 0 37 13 11 6 3 40 17 12 9 48 42 18 13 30 26
## [22873] 10 8 6 3 55 42 40 16 12 70 55 50 26 10 7 3 16 14 10 18 16 41 35 16
## [22897] 9 48 38 20 17 14 4 34 19 17 15 12 60 43 28 22 21 0 17 15 13 50 40 15
## [22921] 12 7 4 1 53 52 23 9 7 26 23 10 1 70 53 57 54 26 4 21 85 31 11 9
## [22945] 50 47 26 3 1 55 52 28 7 4 14 39 38 16 12 8 6 4 1 66 25 22 68 36
## [22969] 17 14 12 10 7 4 33 30 13 10 8 6 5 2 36 14 11 9 7 2 65 50 45 21
## [22993] 65 62 34 15 13 9 7 5 1 20 19 36 30 6 1 48 46 15 12 9 30 27 8 4
## [23017] 29 27 8 5 3 0 62 60 16 30 2 59 48 14 10 8 32 15 11 8 4 50 19 18
## [23041] 16 14 46 45 19 18 16 13 10 70 50 47 28 25 3 0 18 15 8 6 34 13 10 8
## [23065] 5 3 80 71 69 46 22 18 14 24 19 28 26 8 5 1 38 32 15 9 7 3 72 35
## [23089] 16 11 6 2 43 41 40 38 20 14 36 34 8 7 70 65 35 32 15 12 10 8 6 3
## [23113] 65 60 34 32 15 12 11 8 75 66 50 40 19 17 15 13 8 4 40 30 6 3 2 23
## [23137] 60 59 35 20 18 16 12 52 50 31 30 13 11 9 6 3 66 60 21 20 6 4 0 54
## [23161] 40 10 8 2 55 52 40 38 18 16 14 11 6 45 20 19 1 50 48 13 12 8 6 57
## [23185] 50 16 10 13 9 55 53 16 14 12 8 25 6 2 31 11 8 3 54 65 22 76 62 22
## [23209] 21 5 3 55 41 23 20 35 35 7 0 85 75 62 49 4 46 44 82 18 5 8 26 13
## [23233] 11 9 6 2 57 44 38 34 9 6 32 22 0 50 22 4 31 12 9 57 41 22 18 15
## [23257] 11 5 32 32 16 12 8 7 27 8 4 3 49 44 23 4 0 19 1 19 37 31 11 8
## [23281] 7 1 38 15 10 7 17 51 16 0 13 11 67 66 36 14 10 8 40 20 79 64 27 27
## [23305] 8 7 4 1 23 1 77 63 22 14 33 28 8 3 3 27 3 61 61 21 17 77 29 29
## [23329] 3 2 39 34 14 36 16 34 17 10 44 43 18 17 37 37 14 14 12 54 46 26 24 22
## [23353] 50 49 18 16 14 10 42 39 19 17 12 50 51 51 23 23 5 18 3 17 9 53 56 25
## [23377] 26 7 5 4 19 17 15 11 64 55 32 24 4 0 78 66 34 30 12 9 5 3 36 11
## [23401] 9 6 2 75 34 12 11 7 59 51 26 21 15 8 6 9 36 14 12 9 6 57 42 38
## [23425] 15 12 47 45 15 12 11 9 3 70 66 20 59 44 19 0 14 12 9 4 4 42 42 17
## [23449] 13 11 6 57 27 8 5 50 20 35 34 10 7 19 55 47 26 11 5 27 20 23 17 40
## [23473] 15 12 39 19 17 14 78 35 16 14 42 55 60 8 18 44 38 19 16 9 5 27 8 6
## [23497] 50 40 28 10 7 65 33 33 13 12 10 6 38 35 16 13 11 7 3 51 31 30 12 9
## [23521] 56 51 31 26 7 4 26 6 3 18 31 27 3 26 24 21 67 57 39 38 16 14 12 38
## [23545] 37 14 14 16 68 54 22 20 18 16 62 60 18 27 6 4 33 31 15 12 4 2 32 30
## [23569] 9 7 2 0 47 41 20 0 15 47 42 16 25 6 4 3 27 40 41 12 10 45 21 3
## [23593] 1 17 17 46 16 17 22 5 0 52 53 16 45 33 14 12 12 8 5 25 8 51 50 18
## [23617] 15 57 50 59 15 29 27 4 16 21 46 24 1 39 38 12 17 30 25 3 1 48 50 66
## [23641] 63 30 10 7 57 53 34 14 11 6 4 32 25 1 58 30 14 10 7 54 40 14 11 9
## [23665] 25 23 4 0 30 13 10 14 64 42 6 4 1 39 12 0 66 63 53 35 13 72 39 21
## [23689] 0 18 17 15 75 65 43 31 9 6 67 23 3 0 10 70 29 5 42 22 4 15 37 15
## [23713] 13 36 17 14 12 52 45 19 17 4 67 39 41 7 5 69 74 39 17 14 60 48 30 8
## [23737] 6 2 22 0 60 50 21 14 63 36 16 44 38 21 19 17 13 8 58 35 8 5 30 10
## [23761] 6 4 37 17 13 8 73 69 40 34 13 8 42 37 15 13 46 20 4 17 9 25 7 3
## [23785] 60 22 34 16 12 11 9 0 58 36 18 16 13 34 29 13 11 9 7 40 35 3 1 35
## [23809] 30 13 9 7 1 59 32 26 10 8 7 50 46 22 1 21 16 13 10 7 42 12 35 30
## [23833] 12 8 6 75 36 33 15 8 58 48 22 18 15 12 9 48 43 25 23 0 8 5 72 70
## [23857] 30 13 7 56 50 25 26 8 3 20 8 11 10 6 22 38 18 16 13 61 50 19 12 33
## [23881] 12 43 40 18 15 9 50 35 22 16 13 11 19 13 8 34 40 14 10 7 0 35 25 1
## [23905] 17 57 49 24 15 27 22 0 37 33 14 13 9 30 7 2 15 41 22 20 18 16 10 40
## [23929] 34 14 16 49 45 18 16 44 34 14 12 31 27 6 5 3 60 40 21 0 37 47 20 17
## [23953] 20 18 17 54 36 14 12 10 50 45 21 17 60 51 16 15 14 8 42 36 12 10 8 5
## [23977] 2 45 40 14 3 75 70 55 46 30 16 15 10 8 4 2 75 70 26 19 30 25 7 5
## [24001] 1 35 31 14 11 9 7 5 3 50 12 9 5 22 5 1 27 21 32 12 7 36 30 8
## [24025] 6 4 2 27 28 6 0 60 52 22 20 16 31 31 11 7 52 65 36 35 11 6 44 39
## [24049] 7 5 26 24 9 50 27 12 10 24 1 40 32 17 15 12 10 30 10 6 50 45 13 8
## [24073] 5 30 13 11 9 7 40 26 2 37 17 13 8 55 55 61 50 29 25 4 0 87 55 48
## [24097] 50 29 11 8 4 65 23 3 11 6 4 42 46 46 34 17 16 13 10 4 43 38 15 17
## [24121] 50 23 1 24 10 6 75 30 13 7 26 10 5 68 42 39 13 51 44 58 30 22 1 71
## [24145] 54 38 36 14 30 27 10 8 6 4 40 39 21 19 15 13 22 5 2 23 23 1 45 45
## [24169] 16 38 33 15 11 40 12 11 38 18 9 3 30 4 6 43 40 15 12 10 29 11 9 5
## [24193] 2 66 83 35 12 25 23 2 54 47 35 16 11 9 7 27 7 5 0 47 78 75 69 5
## [24217] 45 40 27 24 5 34 24 4 3 38 15 14 74 32 31 14 10 7 6 55 52 47 16 13
## [24241] 71 47 32 13 5 67 59 38 24 9 6 4 62 61 23 6 27 26 3 25 26 10 8 3
## [24265] 41 53 21 15 34 28 7 5 34 36 13 9 48 46 16 15 12 10 25 3 68 60 63 20
## [24289] 18 10 50 43 18 14 10 51 22 5 0 16 27 29 12 10 7 15 43 40 22 21 19 33
## [24313] 15 12 65 61 23 27 7 4 52 15 11 34 29 9 6 2 39 38 18 16 33 31 13 8
## [24337] 38 16 14 11 36 14 11 49 61 25 22 5 15 26 23 2 45 17 15 12 55 45 28 64
## [24361] 58 20 18 15 21 0 39 35 16 14 12 8 7 2 4 39 35 11 9 5 1 58 49 12
## [24385] 9 7 2 1 82 53 53 25 18 2 15 11 27 7 79 79 75 63 26 11 1 30 64 60
## [24409] 19 17 67 25 22 3 1 47 47 11 6 2 65 21 19 0 48 16 37 15 12 7 6 46
## [24433] 14 6 38 32 14 11 6 45 12 6 35 29 9 7 4 31 27 7 4 65 60 26 8 6
## [24457] 0 20 40 16 14 6 40 34 15 9 41 18 14 9 7 5 30 28 11 9 7 5 52 14
## [24481] 31 28 6 2 73 67 30 28 8 6 3 38 31 13 8 6 45 36 17 17 11 11 8 8
## [24505] 38 36 15 11 10 7 57 24 17 33 8 6 71 43 25 21 0 22 41 35 13 12 23 4
## [24529] 0 21 1 52 15 38 34 11 9 51 32 15 11 9 6 4 38 15 10 3 44 43 24 4
## [24553] 3 20 18 0 17 12 9 4 51 14 12 9 7 31 8 33 32 15 10 8 6 26 6 2
## [24577] 0 50 50 29 12 9 7 25 3 0 22 3 0 16 12 47 40 17 12 10 34 32 12 9
## [24601] 6 4 34 28 13 10 6 4 72 70 52 48 16 15 13 11 7 4 57 57 34 13 11 9
## [24625] 8 21 9 54 27 3 51 45 20 1 18 16 60 35 26 9 5 42 16 12 8 7 66 55
## [24649] 25 26 5 0 0 22 50 41 18 14 12 12 8 5 31 30 10 8 6 2 60 55 69 60
## [24673] 32 32 11 9 5 37 16 13 10 7 55 52 36 35 58 32 11 16 5 51 50 18 15 10
## [24697] 40 39 16 14 12 40 63 16 50 18 16 47 70 66 35 13 9 5 0 66 64 80 64 63
## [24721] 39 31 33 2 0 33 77 38 21 13 40 35 11 5 18 35 37 12 3 0 39 42 15 9
## [24745] 68 60 59 32 34 8 3 39 16 11 6 17 0 53 56 24 21 7 42 11 7 38 14 12
## [24769] 83 59 57 19 15 13 68 10 8 6 29 12 10 6 24 26 6 4 1 27 27 9 3 62
## [24793] 52 50 51 48 18 15 13 9 59 54 26 27 5 14 11 41 41 17 13 8 46 50 21 17
## [24817] 14 11 83 82 76 78 69 73 70 22 16 46 7 72 59 64 19 49 42 15 3 12 8 5
## [24841] 67 40 44 14 8 5 64 22 3 1 56 59 41 17 12 8 7 1 66 40 13 10 6 3
## [24865] 63 56 14 11 33 26 9 5 2 67 64 21 20 3 53 51 24 19 20 3 17 49 46 18
## [24889] 14 11 49 45 23 16 12 4 22 5 1 75 21 52 21 28 18 4 58 53 22 2 16 13
## [24913] 11 8 40 39 16 13 9 3 7 3 65 39 38 18 15 11 9 32 26 9 7 4 42 45
## [24937] 17 15 12 10 8 49 41 15 13 11 5 64 60 25 9 22 6 35 29 13 9 4 2 60
## [24961] 46 6 53 17 37 34 15 10 9 5 1 47 49 21 7 51 56 52 24 22 5 2 65 60
## [24985] 23 22 20 0 18 16 15 39 31 15 4 2 52 45 25 17 2 0 17 13 6 21 17 13
## [25009] 10 8 6 56 51 22 21 19 12 7 44 37 16 13 10 8 80 39 34 16 13 11 9 6
## [25033] 5 4 2 27 8 6 0 52 26 13 11 10 25 24 2 54 22 21 5 15 12 45 39 18
## [25057] 16 14 10 8 29 12 10 8 6 53 25 23 2 0 16 9 40 36 21 19 16 14 11 7
## [25081] 5 2 36 35 14 10 66 44 38 6 20 10 1 52 48 15 13 9 6 2 80 81 46 44
## [25105] 15 10 7 4 0 22 3 17 28 30 8 3 0 50 28 24 2 71 36 33 16 12 10 7
## [25129] 5 26 30 9 7 6 22 6 49 40 19 15 12 8 39 23 18 15 16 14 5 41 36 10
## [25153] 9 66 28 11 9 7 3 62 56 40 37 12 21 2 30 9 7 5 3 0 59 14 22 1
## [25177] 68 40 15 12 41 41 18 57 23 6 3 0 60 61 21 25 23 3 0 29 27 9 5 1
## [25201] 51 49 30 32 7 4 0 31 30 8 6 4 2 62 60 73 67 29 4 1 25 45 40 18
## [25225] 14 20 19 2 85 70 41 35 17 16 8 6 26 28 32 30 11 8 35 32 13 12 9 65
## [25249] 51 50 20 20 1 17 9 39 39 15 12 9 9 1 74 59 53 15 11 9 8 34 33 14
## [25273] 11 5 2 28 25 10 5 28 11 9 4 37 34 16 13 10 63 45 39 22 14 11 21 4
## [25297] 0 67 58 17 17 1 65 61 32 31 13 5 24 5 3 48 48 19 13 8 70 50 47 19
## [25321] 55 55 24 21 17 13 35 34 11 8 5 32 28 11 6 3 78 28 10 7 3 1 26 31
## [25345] 33 11 7 71 52 23 17 40 36 13 11 54 53 18 13 11 49 40 14 42 37 18 16 17
## [25369] 14 9 44 50 17 14 12 7 21 1 78 40 16 13 50 40 16 71 69 39 15 45 12 9
## [25393] 38 18 15 12 32 9 5 75 52 45 25 14 33 26 5 0 20 18 3 29 29 10 7 28
## [25417] 10 6 1 35 25 5 2 0 19 31 30 7 4 2 65 64 36 34 11 7 4 1 57 52
## [25441] 15 28 8 2 0 35 35 16 14 11 64 45 16 40 35 15 13 12 11 6 3 42 40 14
## [25465] 11 3 19 31 26 9 7 5 54 41 36 10 7 2 66 30 27 7 3 0 60 34 17 14
## [25489] 10 24 5 0 36 4 2 63 22 20 25 42 36 11 82 78 42 49 49 21 17 45 33 21
## [25513] 19 13 53 44 27 24 19 1 22 65 49 24 4 0 32 29 4 1 42 33 17 13 17 80
## [25537] 36 16 14 11 32 25 7 53 51 15 39 40 15 12 10 6 3 69 60 42 40 52 62 34
## [25561] 13 55 54 26 25 3 40 17 52 17 35 29 11 10 4 42 17 80 74 13 70 66 53 40
## [25585] 22 18 21 2 22 22 3 54 50 26 5 22 5 1 22 8 5 20 25 7 4 1 20 45
## [25609] 41 20 18 17 39 35 14 10 8 6 25 8 3 37 29 7 5 0 36 32 13 11 7 3
## [25633] 37 17 14 11 9 7 3 34 13 11 9 64 24 20 3 1 82 31 26 11 7 5 32 11
## [25657] 10 7 3 22 59 23 22 21 19 10 52 51 88 54 52 15 13 48 43 20 0 34 28 12
## [25681] 9 6 45 40 20 19 1 51 18 1 15 86 33 32 15 12 9 5 37 13 1 40 36 18
## [25705] 16 14 12 10 33 34 10 8 4 1 63 41 21 4 14 64 60 20 7 19 19 53 17 22
## [25729] 2 55 54 21 16 14 12 10 8 70 28 1 36 17 15 11 8 60 48 14 12 9 7 1
## [25753] 25 3 0 65 50 45 16 11 6 70 72 63 35 13 7 60 47 41 20 19 17 14 53 50
## [25777] 23 26 8 6 42 35 12 9 6 65 31 28 6 3 2 26 22 4 3 1 49 45 23 18
## [25801] 14 12 8 26 4 55 53 55 53 20 17 14 12 52 45 7 5 3 57 55 26 22 5 3
## [25825] 0 22 9 52 35 12 8 6 0 30 27 5 3 56 55 22 18 15 28 25 5 3 0 28
## [25849] 22 1 70 63 23 22 1 52 55 17 17 16 13 33 28 10 7 5 25 70 43 11 3 57
## [25873] 16 11 8 30 30 13 11 3 67 49 49 20 18 15 12 51 32 12 10 8 6 3 1 18
## [25897] 0 59 70 65 36 18 17 11 10 8 7 6 62 50 20 13 8 59 45 22 2 0 19 14
## [25921] 11 46 40 14 9 7 3 66 46 56 23 21 3 0 18 75 30 12 10 7 3 26 3 0
## [25945] 60 36 16 13 25 4 1 26 7 6 2 40 38 16 13 10 6 2 0 33 32 12 10 7
## [25969] 5 3 1 60 60 31 30 2 0 55 54 12 58 47 19 10 6 34 30 9 6 4 1 23
## [25993] 26 9 1 20 21 36 15 8 6 6 58 27 32 11 7 5 23 30 28 7 3 0 53 14
## [26017] 61 51 21 18 0 16 9 18 34 28 12 9 6 0 45 18 18 65 40 36 11 9 5 0
## [26041] 26 23 4 60 35 36 13 10 4 4 52 50 55 48 30 28 10 2 17 15 12 66 62 40
## [26065] 38 21 21 1 12 15 9 65 55 25 21 0 20 18 0 6 54 50 29 26 11 6 2 0
## [26089] 21 21 2 0 17 35 33 14 11 8 1 26 30 10 9 7 0 61 53 31 10 9 9 3
## [26113] 1 41 31 12 10 8 1 36 29 13 11 6 3 61 55 24 22 1 15 39 35 13 12 11
## [26137] 8 4 1 24 21 0 56 18 51 41 21 20 14 11 7 0 24 20 3 22 16 39 18 13
## [26161] 11 9 7 3 50 45 19 17 15 13 10 7 7 15 30 28 8 7 4 38 38 18 14 10
## [26185] 9 6 2 65 67 51 35 22 18 14 12 7 6 34 34 12 11 10 9 5 3 40 39 18
## [26209] 14 11 10 4 80 60 45 45 22 21 1 17 12 9 7 74 60 25 18 21 40 35 9 6
## [26233] 4 48 36 16 13 11 36 16 21 0 40 15 10 8 5 2 18 2 59 20 21 2 0 56
## [26257] 52 40 17 18 13 6 54 45 18 16 13 11 45 30 10 6 3 1 35 34 16 13 10 6
## [26281] 4 2 66 60 18 30 22 30 26 6 3 1 50 49 23 20 16 13 10 6 2 25 20 2
## [26305] 58 46 38 18 15 13 9 6 2 60 56 30 9 8 6 2 4 47 40 20 16 8 6 4
## [26329] 45 35 11 6 4 70 67 60 27 22 2 55 52 21 16 11 8 18 0 75 56 22 24 2
## [26353] 19 22 13 75 35 11 8 5 2 24 22 3 1 18 33 30 9 7 4 2 65 55 21 18
## [26377] 15 30 6 2 0 45 15 14 11 22 0 39 37 14 11 7 5 3 67 43 42 17 15 10
## [26401] 5 2 66 39 38 15 12 9 5 3 35 30 11 9 8 0 65 40 35 20 19 3 0 12
## [26425] 8 4 2 0 52 35 18 14 12 6 0 42 42 22 18 0 16 5 30 26 9 7 3 2
## [26449] 60 60 25 24 2 18 12 60 50 35 17 7 12 30 26 2 6 0 27 22 1 65 22 26
## [26473] 7 4 0 60 33 30 6 0 35 27 9 3 1 65 36 32 14 10 7 70 62 24 21 4
## [26497] 1 19 19 0 12 67 65 65 30 25 18 15 14 12 9 27 23 5 4 58 55 26 25 4
## [26521] 1 22 22 1 10 61 58 13 26 18 65 43 42 18 15 13 85 35 13 11 9 7 3 60
## [26545] 6 35 21 0 13 38 61 48 24 0 42 36 15 7 4 1 40 38 16 14 4 2 50 51
## [26569] 23 24 4 1 16 50 45 15 11 7 50 21 19 19 16 14 70 63 50 10 5 13 12 7
## [26593] 60 55 20 18 13 54 27 26 19 39 18 12 55 88 12 33 13 11 6 1 61 53 29 34
## [26617] 6 14 33 7 5 1 60 56 13 10 50 49 15 13 21 25 5 3 39 20 20 15 58 55
## [26641] 37 28 11 18 4 1 24 18 2 33 21 60 53 50 7 67 64 33 31 10 7 3 10 61
## [26665] 13 22 13 11 48 20 15 11 54 39 39 20 16 9 52 49 13 9 38 36 18 16 12 10
## [26689] 7 4 46 43 44 39 17 14 12 66 54 17 42 39 14 36 8 6 4 2 77 55 31 27
## [26713] 8 4 2 43 40 18 15 12 9 65 51 29 24 6 2 26 22 4 19 33 33 15 12 47
## [26737] 14 84 40 38 14 12 8 6 2 75 29 27 7 4 1 47 39 16 14 56 60 45 18 1
## [26761] 15 13 34 32 11 9 5 2 0 39 10 0 35 33 13 10 8 6 3 59 57 36 16 13
## [26785] 11 0 62 56 9 19 19 15 43 14 7 22 48 37 15 13 8 75 65 31 30 28 9 5
## [26809] 3 1 59 20 18 15 80 55 52 15 12 18 42 16 11 8 21 1 62 52 22 60 12 34
## [26833] 9 6 62 63 55 20 0 13 46 45 17 14 12 53 46 35 16 25 9 5 2 35 30 15
## [26857] 13 11 10 5 2 58 50 20 14 9 0 40 35 14 10 3 2 31 25 2 0 85 48 45
## [26881] 17 15 12 8 27 26 4 3 38 32 15 10 7 80 54 42 18 16 11 7 46 38 19 16
## [26905] 10 75 46 30 10 6 28 9 63 39 33 11 8 34 15 9 3 50 18 60 25 1 45 60
## [26929] 19 6 15 12 36 50 50 20 1 18 16 56 51 13 9 55 40 28 18 13 12 49 8 9
## [26953] 29 24 7 1 52 13 9 72 60 77 45 16 44 6 11 50 24 3 1 13 8 4 38 16
## [26977] 13 10 85 80 9 40 39 13 8 4 0 27 15 11 5 25 42 10 40 14 9 18 34 5
## [27001] 80 75 35 17 17 14 12 2 37 35 13 12 7 72 66 24 20 2 25 24 47 46 23 0
## [27025] 21 8 28 25 6 2 71 14 69 60 26 9 5 24 22 2 0 36 35 18 15 13 78 6
## [27049] 16 13 44 23 21 4 1 52 50 22 21 1 69 51 61 43 48 39 14 12 6 47 44 7
## [27073] 3 1 43 11 5 79 76 18 15 50 23 4 0 12 24 4 9 47 45 14 11 2 31 13
## [27097] 10 7 70 85 73 61 19 1 19 35 14 54 52 49 50 23 4 2 47 45 14 45 40 23
## [27121] 16 15 14 13 9 53 50 16 10 18 17 15 36 17 35 33 9 7 5 0 70 35 16 12
## [27145] 10 75 72 30 35 15 15 35 12 8 5 75 51 23 18 35 29 10 8 4 75 69 23 0
## [27169] 10 55 18 24 2 38 36 10 7 5 26 25 4 1 61 19 48 16 12 77 39 17 13 10
## [27193] 9 6 67 77 79 34 18 13 5 72 26 2 60 20 16 13 10 7 53 42 12 9 6 19
## [27217] 12 7 5 22 2 35 13 9 7 5 1 25 0 52 12 18 28 6 3 45 50 15 45 15
## [27241] 22 3 27 5 1 32 8 6 1 32 30 13 11 8 4 61 25 3 1 43 41 22 20 68
## [27265] 50 20 18 40 38 19 2 59 28 6 3 1 27 7 5 2 0 76 65 60 31 28 9 6
## [27289] 4 61 40 35 14 10 4 33 12 2 55 51 18 18 15 13 11 33 30 5 2 70 35 9
## [27313] 3 35 34 16 12 10 8 5 3 58 30 28 22 20 0 18 16 14 6 52 46 21 20 18
## [27337] 15 10 34 33 13 11 5 66 45 40 21 23 0 12 10 7 18 37 35 18 15 7 5 59
## [27361] 30 25 9 7 4 0 48 44 25 23 16 11 8 6 35 32 13 11 7 50 46 22 20 4
## [27385] 1 75 38 36 17 14 12 56 36 17 12 9 2 57 53 20 19 1 14 8 65 60 21 20
## [27409] 1 55 50 24 18 42 40 20 18 15 20 1 42 37 18 16 9 7 34 11 9 3 1 35
## [27433] 15 11 9 6 3 33 31 12 9 6 4 61 61 27 22 2 60 40 19 16 10 22 20 4
## [27457] 0 16 56 34 25 16 74 71 50 22 23 5 4 42 18 12 81 38 34 17 15 13 11 61
## [27481] 31 11 8 5 2 1 62 19 2 62 26 21 0 48 21 20 1 69 68 26 7 5 41 20
## [27505] 17 15 65 36 17 15 12 54 51 14 12 24 5 57 27 4 2 30 12 8 1 65 44 14
## [27529] 25 46 75 38 21 19 17 3 38 32 14 11 9 5 65 58 60 54 26 23 2 22 4 0
## [27553] 36 8 52 40 19 17 13 8 43 38 18 15 12 9 70 60 55 50 20 20 15 12 10 21
## [27577] 2 20 30 11 7 4 1 42 41 17 14 10 24 23 2 0 63 38 34 15 12 9 5 58
## [27601] 33 11 5 35 28 4 45 16 14 11 9 7 76 35 31 12 9 6 3 1 63 35 32 12
## [27625] 7 3 42 16 3 27 11 2 62 22 4 0 18 35 13 11 8 6 22 3 2 0 70 25
## [27649] 18 18 37 35 11 7 4 1 52 48 17 12 9 7 4 46 33 13 11 9 7 5 1 1
## [27673] 37 29 3 24 21 21 61 60 58 16 12 80 40 12 10 8 5 0 27 25 8 5 36 16
## [27697] 14 10 6 4 1 65 57 32 28 1 0 50 42 18 15 13 11 8 6 4 40 38 15 12
## [27721] 10 5 3 87 35 30 9 7 5 3 70 64 19 0 69 55 26 6 65 50 15 40 35 16
## [27745] 14 10 8 76 55 46 69 45 16 29 10 8 3 50 16 25 22 3 0 24 23 0 60 25
## [27769] 1 21 0 70 35 16 12 10 7 40 20 16 10 6 65 20 21 14 12 0 42 42 16 13
## [27793] 8 5 45 40 18 13 10 6 3 0 21 6 30 28 6 3 2 44 37 16 13 6 3 2
## [27817] 25 4 1 62 60 35 33 14 18 10 8 2 60 55 35 7 3 14 15 67 62 36 34 16
## [27841] 14 12 10 8 27 6 3 69 60 30 12 9 7 40 41 19 17 15 10 8 39 13 10 6
## [27865] 20 18 41 21 20 18 45 43 23 20 0 16 8 32 11 8 7 5 13 39 35 16 14 12
## [27889] 49 43 17 11 9 44 39 34 30 70 20 18 16 14 12 10 9 6 1 53 45 17 15 71
## [27913] 35 6 2 29 9 6 4 65 19 19 64 62 21 15 39 34 16 10 1 36 26 7 5 3
## [27937] 22 20 21 2 62 25 23 5 3 48 40 20 16 9 35 35 15 12 4 39 17 13 23 24
## [27961] 7 4 2 0 21 20 53 52 30 25 11 5 3 0 37 30 13 11 9 6 62 61 16 40
## [27985] 23 22 5 2 18 9 14 26 6 4 30 24 9 3 1 34 14 12 8 32 14 12 10 45
## [28009] 18 16 14 24 1 18 79 45 43 21 23 4 0 29 33 10 3 58 23 5 3 22 3 2
## [28033] 74 62 28 10 8 17 30 11 9 46 55 25 18 12 26 10 40 42 14 11 10 7 3 0
## [28057] 44 40 16 14 11 6 2 73 34 18 13 44 18 13 9 6 26 8 5 2 75 43 15 29
## [28081] 8 6 2 32 10 5 26 9 4 3 52 57 30 27 8 4 18 14 10 60 59 33 27 4
## [28105] 2 62 58 57 50 24 1 35 34 3 49 45 16 17 14 11 8 71 60 26 31 25 3 57
## [28129] 29 23 21 25 15 11 63 46 49 19 17 16 13 63 46 34 30 6 0 21 1 20 50 45
## [28153] 39 45 18 15 22 60 30 11 4 29 32 12 9 59 54 30 25 9 39 18 17 13 10 52
## [28177] 50 16 12 63 57 36 31 12 9 6 65 35 36 15 10 41 35 16 14 14 62 65 34 34
## [28201] 15 10 30 32 14 8 6 40 39 16 12 9 45 40 16 11 75 50 52 29 28 13 7 21
## [28225] 18 35 29 6 11 20 15 70 67 66 42 8 6 2 20 48 16 14 10 7 5 38 36 14
## [28249] 12 8 6 1 67 50 16 67 19 0 70 65 99 63 54 40 36 14 10 23 2 25 25 5
## [28273] 2 0 23 0 21 17 15 82 30 29 12 9 7 5 25 20 1 42 20 0 18 45 50 55
## [28297] 21 0 22 25 6 2 53 49 18 16 35 30 15 13 10 7 51 48 14 11 17 54 24 5
## [28321] 3 0 16 11 24 3 1 18 14 79 69 28 27 9 8 51 71 70 56 51 29 24 2 25
## [28345] 22 60 57 14 73 44 43 21 20 18 68 58 55 6 4 32 31 13 10 38 18 14 42 15
## [28369] 8 42 36 18 15 15 52 35 14 8 35 16 14 11 7 4 70 70 28 21 5 52 42 20
## [28393] 16 18 58 58 25 24 5 0 48 26 24 3 62 53 28 22 19 16 14 11 0 45 19 14
## [28417] 12 50 11 50 40 17 14 12 30 25 5 2 59 51 19 18 0 19 17 15 13 40 36 15
## [28441] 13 60 51 44 20 0 20 38 41 19 18 15 9 48 40 23 20 35 30 8 6 60 17 18
## [28465] 1 0 48 19 17 16 25 30 7 3 59 67 63 27 20 17 22 3 1 13 40 35 13 12
## [28489] 7 74 60 37 30 7 25 25 2 35 33 13 9 9 50 23 19 0 65 54 25 11 5 1
## [28513] 20 59 56 78 40 35 12 9 6 26 6 16 31 30 7 3 29 10 5 3 56 16 57 50
## [28537] 32 14 12 40 16 57 52 14 11 9 53 45 38 35 11 9 2 55 39 36 17 14 12 9
## [28561] 49 45 22 20 19 1 0 42 38 19 18 0 15 50 44 19 16 0 12 44 39 14 12 8
## [28585] 42 19 18 14 40 17 12 7 33 33 14 11 4 99 58 50 18 15 21 40 32 13 10 5
## [28609] 3 0 42 32 13 10 9 6 35 18 16 14 62 45 16 12 35 15 13 10 5 0 50 46
## [28633] 42 16 12 11 30 10 6 2 0 60 40 21 20 13 53 43 24 22 0 18 14 12 50 49
## [28657] 19 18 40 39 18 15 8 6 0 31 27 9 8 5
## attr(,"label")
## [1] "1.03 age"
## attr(,"format.stata")
## [1] "%8.0g"…we see the different values that are stored here. Every single one of those numbers represents the age of one person who was in a household that was surveyed.
To make our code easier to read and to save us from typing a bunch of complicated numbers and symbols over and over again, we’re going to save our list of ages to a variable with an easier name:
ages <- s01$v01_03Doing Analysis
We can immediately start performing calculations on these values if we want:
mean(ages)
## [1] 26.92707
median(ages)
## [1] 22(Side note: we could also use the pipe here if we wanted. The
command ages |> mean() is exactly the same thing as
mean(ages). Use whichever you prefer.)
Basic Visualization
Mean and median are interesting here (and it’s very interesting that mean and median are so far apart!), but to really understand this data we can use different kinds of graphical visualizations.
Using ggplot
You’ve probably already seen ggplot in action. It is a great library. There are other visualization libraries out there that can do more, and there are other libraries that are easier to learn, but I believe that ggplot strikes the perfect balance for 95% of use cases.
I won’t go into too much detail about ggplot syntax here (check out Hadley Wickham’s book for that), but getting started is relatively straight forward. Creating a graph in ggplot usually involves three steps: - Input your data into ggplot, - Assign variables to aesthetic mappings, and - Add visual “layers” to the output
In our case, a very common way to visualize a variable like age would be a histogram. A histogram separates a numerical value into “bins” of different sizes, plots those bins on the x-axis and then plots the frequency counts of each bin on the y-axis. So, moving left to right, each bar represents an age range, and the bar height represents the number of people who are that age.
s01 |>
ggplot(mapping = aes(x = v01_03)) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Not a bad start, but it could definitely be easier to read. Since we didn’t tell geom_histogram how many different “bins” we wanted, it decided by default to break to total range into 30 different bins. For age, we might want to create a separate bar for each value. We’ll also add tweak the colors to make things easier to read:
s01 |>
ggplot(mapping = aes(x = v01_03)) +
geom_histogram(binwidth=1, color="black", fill="lightgray")
There are several interesting thigns here in their own right, but it’s potentially a bit misleading. As we talked about last week, the NLSS uses a stratified sampling strategy. This gives us much more useful data about regions with low population densities, but it also means that our sample is not representative of the country as a whole. If we just use the data as it is, we’ll under-represent some parts of the country and over-represent other parts.
Re-weighting our analysis
To fix this problem, we need to “weight” our observations. In very
concrete terms, this means that each household in our survey will
represent a different number of other households from the same strata in
Nepal. This information is provided for us in the
sample.dta file. We’ll load it in, just like we did with
the section 1 data, and we’ll save it as a data frame named
weights.
weights <- read_dta("nlss2011/data/sample.dta") |> as_factor()Table joins
You can take a look at the weights table by clicking on the variable
name in R Studio’s “environment” window. By itself, this file won’t do
much. We need to combine it somehow with the data in our
s01 table to make it useful. We’ll do that by “joining” the
tables. Joins can be very intimidating at first glance, but they’re
fairly straightforward once you get familiar.
To join two tables, we need to identify one or more linking
variables. These variables allow us to figure out which values in table
A should correspond to which values in table B. In the NLSS, we’ll
always use the same linking variables: xhpsu and/or
xhnum. - The xhpsu variable represents our
“primary sampling unit”. To conduct this survey, the team picked a
number of different VDC wards, and each ward selected this way was given
a number. - Within these PSUs, each house selected was also given a
number, listed as xhnum. - For individual data, we can also
match the individual’s person id number idc, but we won’t
worry about that now.
In any table, you can join tables by matching these values.
The code to combine tables might look something like this:
s01_with_weights <- s01 |>
left_join(weights, by="xhpsu")Joins can be very confusing at first, but the idea is pretty simple.
Here, we’re just saying: create Use our existing s01 data
frame as a base, and look up data from the data frame
weights using the variable xhpsu as a key.
Combine all the columns from both tables together as a new data frame
called s01_with_weights.
There are many types of joins, and this is where a lot of the
confusion comes from. The difference between them is just what to do
when there are either multiple matches or no matches. We’re using a
left_join here, which basically just means to keep all of
the observations in our “left” side table (s01). We don’t need to worry
about this stuff too much at this point.
Checking our weights
Now, we can see that our section 1 data is now combined with the
household weights. The variable from weights we are interested in is
called wt_hh.
s01$wt_hh[1:80]
## Warning: Unknown or uninitialised column: `wt_hh`.
## NULL
s01_with_weights$wt_hh[1:80] # show just the first 80 rows
## [1] 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574
## [9] 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574
## [17] 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574
## [25] 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574
## [33] 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574
## [41] 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 293.0574 280.3486
## [49] 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486
## [57] 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486
## [65] 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486
## [73] 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486 280.3486If things worked correctly, our new s01_with_weights
data frame should have the same number of rows as the original
s01 data frame.
nrow(s01)
## [1] 28670
nrow(s01_with_weights)
## [1] 28670Sure enough, they both have the same length: 28670. That number is
the number of people living in the households that were surveyed as part
of this study. Each person now has a wt_hh value, which
represents how many different households in Nepal their household stands
for as part of a representative sample.
This has an interesting effect. If we add the value of
wt_hh for each of these people, we should get a value very
close to the population of Nepal when the survey was taken.
sum(s01_with_weights$wt_hh)
## [1] 28208617Sure enough, we get 28,208,617.
Using our weights
Now that we’ve got our household weightings, we need to use
them. Exactly how we use weights will depend on the kind of analysis
we’re doing, but many common graphs and analyses have the ability to use
weighted observations automatically. With ggplot, it’s as simple as
using the weight aesthetic mapping.
s01_with_weights |>
ggplot(mapping = aes(x = v01_03, weight = wt_hh)) +
geom_histogram(binwidth=1, color="black", fill="lightgray")
I can’t say it looks very different to the naked eye, but we can plot
the two versions together to better see how much of an effect the
weights have. For this, rather than using a histogram, we’d be better
off using a density estimate. A density estimate is effectively a
histogram turned into a continuous line. This makes it a bit harder to
see exact values but gives us a better sense of the over all shape for
comparison.
s01_with_weights |>
ggplot(mapping = aes(x = v01_03)) +
geom_density(color="red") +
geom_density(mapping = aes(weight = wt_hh), color="blue")
It’s definitely not a dramatic difference, but once we get into
regression analysis these weights can have real impact that changes our
findings. Here, the unweighted version tends to underrepresent the
number of young people (0-15) and overrepresent the older population
(16-50).
More visualizations
Plotting the age of Nepal’s population is interesting, but things
start getting much more interesting when we start comparing different
variables. Our sample.dta file gives us lots of information
about the geographic distribution of our primary sampling units, and we
can use that to make some interesting observations. We can also bring in
variables from other sections of the survey.
Before we go further, though, we have to fix a small glitch with our
s01_with_weights table. Because of a minor quirk in the
sample.dta table, our xhnum column is getting
renamed to xhnum.x. This will create a problem when we
start trying to join in other tables. There are a few ways to fix it,
but the easiest is just to rename the column:
s01_with_weights <- s01 |>
left_join(weights, by="xhpsu") |>
rename(xhnum = xhnum.x)Anyway, on with the show…
Age and Settlement Type
s01_with_weights |>
ggplot(aes(x = v01_03, weight = wt_hh, color = urbrur)) +
geom_density() +
labs(color = "Settlement type", x = "Age (years)", y = "Relative Density")
Age and Region
s01_with_weights |>
ggplot(aes(x = v01_03, weight = wt_hh, color = region)) +
geom_density() +
labs(color = "Geographic Region", x = "Age (years)", y = "Relative Density")
Age and Sex
s01_with_weights |>
mutate(v01_02 = fct_relevel(v01_02, c("female", "male"))) |> # let's reorder this just because
ggplot(aes(x = v01_03, weight = wt_hh, color = v01_02)) +
geom_density() +
labs(color = "Designated Sex", x = "Age (years)", y = "Relative Density")
Age and Literacy
# why stop there? Let's start including new tables. Section 7 has interesting educational data for individuals
s07 <- read_dta("nlss2011/data/xh10_s07.dta") |> as_factor()
# we'll start with our s01_with_weights data frame as a base
s01_with_weights |>
# we'll do another join to the s07 table
# (nb: v01_idc and v07_idc both refer to the individual's household id and should match)
left_join(s07, by=c("xhpsu", "xhnum", "v01_idc" = "v07_idc")) |>
# values are not recorded as 'NA' for children under 3, but let's treat that as a "no"
mutate(v07_02 = replace_na(v07_02, 'no')) |>
# and visualize!
ggplot(aes(x = v01_03, weight = wt_hh, color = v07_02)) +
geom_density() +
labs(color = "Can Read a Letter?", x = "Age (years)", y = "Relative Density")
Age and Health Status
# one last one! health status...
s08 <- read_dta("nlss2011/data/xh11_s08.dta") |> as_factor()
# we'll start with our s01_with_weights data frame as a base
s01_with_weights |>
# we'll do another join to the s07 table
# (nb: v01_idc and v08_idc both refer to the individual's household id and should match)
left_join(s08, by=c("xhpsu", "xhnum", "v01_idc" = "v08a_idc")) |>
# there are some variables marked NA.
# For now, let's just remove them, though we should figure out why they're there
filter(!is.na(v08_10)) |>
# and visualize!
ggplot(aes(x = v01_03, weight = wt_hh, color = v08_10)) +
geom_density() +
labs(color = "Present Health Status", x = "Age (years)", y = "Relative Density")
That’s it for now! As you start to explore on your own, post any questions you have to the chat.