Final Exam
Ali Nemati
Last compiled on 19 May, 2022 , 20:36:31
# options(warn=-1) # remove warning with -1, show waring with 0
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## If necessary, install pacman package manager. ##
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## If condition. ##
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if (!require("pacman")) install.packages("pacman")## Loading required package: pacman#################################################################
## # pacman must already be installed; then load contributed ##
## # packages (including pacman) with pacman ##
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pacman::p_load(caret, magrittr, pacman, rattle, rio,
tidyverse)Question 1: Bootstrapping
Write a function that performs a simulation (with nsim iterations) to evaluate the coverage of a bootstrap confidence interval (at alpha level significance using nboot bootstrap samples) for the variance of nsamples samples from a normal distribution with mean = true_mean and variance = true_var. Your function should thus have a total of 6 arguments.
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### # SET SEED MY BIRTH DAY ###
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set.seed(1984)
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##True mean, true var, nsim, nboot, alpha, and nsamples are all included ##
##in this function. For our vairable, we can use a default number. ##
##as seen below ##
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### THE FUNCTION: ###
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Var_CI_Coverage <- function(true_mean= 0, true_var = 5, nsim = 250,
nboot = 10000, alpha = 0.05, nsamples = 100){
cover = NULL # will be assign with null
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### FOR LOOP. ###
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for(k in 1:nsim){
# k is one to nsim , our nsim in defualt equal nsim = 250 .
Var = as.numeric()
#y <- rnorm(1, mean = true_mean, sd = sqrt(true_var))
y <- rnorm(nsamples, mean = true_mean, sd = sqrt(true_var))
# add y using
# rnorm by using mean = true_mean, sd = sqrt(true_var)
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### FOR LOOP. ###
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for(i in 1:nboot){
# loop 1 to nboot , defualt is nboot = 10000
resample_y <- sample(y, size = nsamples, replace = TRUE)
# add y using
# rnorm by using size = nsamples, replace = TRUE
Var[i] <- var(resample_y) # we have result of var[i] based on var(resample_y)
}
LB <- quantile(Var, probs=c(alpha/2)) # lower bound
UB <- quantile(Var, probs=c(1 - (alpha/2))) # upper bound
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## If condition. ##
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cover[k] <- ifelse(LB <= true_var & UB >= true_var, 1, 0)
# replace cover to 1 , 0
}
return(mean(cover)) # let s return mean of cover from above line
}Example 1
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## An example: ##
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tenQ<-Var_CI_Coverage(true_mean= 0, true_var = 4, nsim = 500,
nboot = 1000, alpha = 0.05, nsamples = 10)
print(paste("our result : ", tenQ))## [1] "our result : 0.776"#################################################################
## the answer is 0.772 for the nsamples of 10 ##
#################################################################Example 2
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## An example: ##
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fiftyQ<-Var_CI_Coverage(true_mean= 0, true_var = 4, nsim = 500,
nboot = 1000, alpha = 0.05, nsamples = 50)
print(paste("our result : ", fiftyQ))## [1] "our result : 0.904"#################################################################
## the answer is 0.918 for the nsamples of 50 ##
#################################################################Example 3
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## An example: ##
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fiveHundred<-Var_CI_Coverage(true_mean= 0, true_var = 4, nsim = 500,
nboot = 1000, alpha = 0.05, nsamples = 500)
print(paste("our result : ", fiveHundred))## [1] "our result : 0.962"#################################################################
## the answer is 0.9556 for the nsamples of 500 ##
#################################################################Example 4
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## An example: ##
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ThousandQ<-Var_CI_Coverage(true_mean= 0, true_var = 4, nsim = 500,
nboot = 1000, alpha = 0.05, nsamples = 1000)
# A result
print(paste("our result : ", ThousandQ))## [1] "our result : 0.944"#################################################################
## the answer is 0.94 for the nsamples of 1000 ##
#################################################################Example 5
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## An example: ##
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#Provide an explanation for the trend we observe across these varying sample sizes
TwoThousandQ<-Var_CI_Coverage(true_mean= 0, true_var = 4,
nsim = 500, nboot = 1000, alpha = 0.05, nsamples = 2000)
# A result
print(paste("our result : ", TwoThousandQ))## [1] "our result : 0.958"#################################################################
## the answer is 0.9556 for the nsamples of 2000 ##
#################################################################Example 6
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## An example: ##
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fiveThousandQ<-Var_CI_Coverage(true_mean= 0, true_var = 4,
nsim = 500, nboot = 1000, alpha = 0.05, nsamples = 5000)
# A result
print(paste("our result : ", fiveThousandQ))## [1] "our result : 0.962"#################################################################
## the answer is 0.9556 for the nsamples of 5000 ##
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### ###
### IT SEEMS THAT THE COVERAGE OF CONFIDENCE INTERVAL ALWAYS FALLS WITHIN ###
### 95% WITH THE INCREASING OF THE NUMBER OF SAMPLES. ###
### ###
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################################################################################Question 2: Differential gene expression analysis
As an initial exploratory analysis, we will use principal components analysis to identify inherent structure/patterns in how the chicken samples cluster. Perform a PCA on the transposed gene expression data (i.e., use t() on the expression data so that samples are in the rows and genes in the columns).
How many principal components are needed to explain 50% of the variation in overall gene expression? Plot PC1 versus PC2, and color the samples according to their category. What do you observe?
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## Differential gene expression analysis. ##
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library(tidyverse)# load lib
library(cowplot)# load lib
library(mvtnorm) # load lib
library(ggplot2)
library(GGally)# load lib## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2READ CSV FILE
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### READ CSV FILE. ###
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liver_expression <- read.csv("chicken_liver_expression.csv", check.names=FALSE)
rownames(liver_expression) <- liver_expression[,1] # rename
liver_expression <- liver_expression[,-1]
group <- read.csv("chicken_liver_groups.csv")
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## If condition. ##
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#if (!requireNamespace("BiocManager", quietly = TRUE)) install.packages("BiocManager")
#BiocManager::install("mixOmics")
library(mixOmics)## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select##
## Loaded mixOmics 6.20.0
## Thank you for using mixOmics!
## Tutorials: http://mixomics.org
## Bookdown vignette: https://mixomicsteam.github.io/Bookdown
## Questions, issues: Follow the prompts at http://mixomics.org/contact-us
## Cite us: citation('mixOmics')##
## Attaching package: 'mixOmics'## The following object is masked from 'package:purrr':
##
## map## The following objects are masked from 'package:caret':
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## nearZeroVar, plsda, splsdaa<- list(rownames(liver_expression))
data(nutrimouse)
X <- t(liver_expression)
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## 1 Run the method. ##
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MyResult.pca <- pca(X)
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## 2 Plot the samples. ##
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plotIndiv(MyResult.pca) 
plotVar(MyResult.pca, cutoff = 0.5)
plotIndiv(MyResult.pca, group = group$category,
legend = TRUE)
plot(MyResult.pca)
MyResult.pca2 <- pca(X, ncomp = 3)
plotIndiv(MyResult.pca2, comp = c(1,3), legend = TRUE,
group = group$category,
title = 'Multidrug transporter, PCA comp 1 - 3')
MyResult.pca2 <- pca(X, ncomp = 4)
plotIndiv(MyResult.pca2, comp = c(1,4), legend = TRUE,
group = group$category,
title = 'Multidrug transporter, PCA comp 1 - 3')
plot(MyResult.pca2)
plotLoadings(MyResult.pca)
tune.pca(X)
screeplot(MyResult.pca2)
Question 2: Differential gene expression analysis ## Another way to apply: Load Lib
#BiocManager::install("PCAtools")
#BiocManager::install("Biobase")
#BiocManager::install("GEOquery")
library(PCAtools)## Loading required package: ggrepel##
## Attaching package: 'PCAtools'## The following object is masked from 'package:mixOmics':
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## pca## The following objects are masked from 'package:stats':
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## biplot, screeplotlibrary(Biobase)## Loading required package: BiocGenerics##
## Attaching package: 'BiocGenerics'## The following objects are masked from 'package:dplyr':
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## combine, intersect, setdiff, union## The following objects are masked from 'package:stats':
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## IQR, mad, sd, var, xtabs## The following objects are masked from 'package:base':
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## anyDuplicated, append, as.data.frame, basename, cbind, colnames,
## dirname, do.call, duplicated, eval, evalq, Filter, Find, get, grep,
## grepl, intersect, is.unsorted, lapply, Map, mapply, match, mget,
## order, paste, pmax, pmax.int, pmin, pmin.int, Position, rank,
## rbind, Reduce, rownames, sapply, setdiff, sort, table, tapply,
## union, unique, unsplit, which.max, which.min## Welcome to Bioconductor
##
## Vignettes contain introductory material; view with
## 'browseVignettes()'. To cite Bioconductor, see
## 'citation("Biobase")', and for packages 'citation("pkgname")'.library(GEOquery)## Setting options('download.file.method.GEOquery'='auto')## Setting options('GEOquery.inmemory.gpl'=FALSE)pacman::p_load( # Use p_load function from pacman
PCAtools,# PCAtools provides functions for data exploration via PCA,
#and allows the user to generate publication-ready figures.
Biobase, # Base functions for Bioconductor
GEOquery) # The NCBI Gene Expression Omnibus (GEO) is a
#public repository of microarray data.
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## Let's fit a PCA and look at the output. ##
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Q2_pca <- prcomp(X)
summary(Q2_pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.066 0.724 0.60932 0.53202 0.51609 0.50257 0.42769
## Proportion of Variance 0.243 0.112 0.07932 0.06048 0.05691 0.05396 0.03908
## Cumulative Proportion 0.243 0.355 0.43430 0.49477 0.55168 0.60565 0.64473
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.41885 0.39606 0.39056 0.3646 0.33262 0.31518 0.28465
## Proportion of Variance 0.03748 0.03351 0.03259 0.0284 0.02364 0.02122 0.01731
## Cumulative Proportion 0.68221 0.71573 0.74832 0.7767 0.80035 0.82158 0.83889
## PC15 PC16 PC17 PC18 PC19 PC20 PC21
## Standard deviation 0.2779 0.26325 0.26122 0.24446 0.23229 0.22199 0.21437
## Proportion of Variance 0.0165 0.01481 0.01458 0.01277 0.01153 0.01053 0.00982
## Cumulative Proportion 0.8554 0.87019 0.88477 0.89754 0.90907 0.91960 0.92942
## PC22 PC23 PC24 PC25 PC26 PC27 PC28
## Standard deviation 0.20025 0.18871 0.17661 0.17392 0.1662 0.15511 0.14741
## Proportion of Variance 0.00857 0.00761 0.00666 0.00646 0.0059 0.00514 0.00464
## Cumulative Proportion 0.93799 0.94560 0.95226 0.95872 0.9646 0.96976 0.97441
## PC29 PC30 PC31 PC32 PC33 PC34 PC35
## Standard deviation 0.14393 0.14054 0.13289 0.12360 0.11179 0.10584 0.09589
## Proportion of Variance 0.00443 0.00422 0.00377 0.00326 0.00267 0.00239 0.00196
## Cumulative Proportion 0.97883 0.98305 0.98683 0.99009 0.99276 0.99515 0.99712
## PC36 PC37 PC38
## Standard deviation 0.08838 0.07535 2.108e-15
## Proportion of Variance 0.00167 0.00121 0.000e+00
## Cumulative Proportion 0.99879 1.00000 1.000e+00Rotation matrix
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## Rotation matrix: loadings (sort of) represent the percent of variance. ##
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## explained by the variable. ##
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head(Q2_pca$rotation)## PC1 PC2 PC3 PC4 PC5
## gene_1 0.09847138 0.213767069 -0.09374660 -0.2130227218 0.37509261
## gene_3 -0.03953165 -0.112554441 0.04944528 -0.0968955136 -0.10843219
## gene_4 -0.19098653 -0.004084522 -0.17446667 -0.0000983641 -0.10233058
## gene_5 0.07439129 0.070774534 0.05820434 -0.0703074084 0.02581534
## gene_8 -0.06246296 -0.022168338 -0.03358737 -0.0330586422 -0.01645695
## gene_9 0.11401726 0.095876338 -0.07392398 0.0579129713 -0.02994802
## PC6 PC7 PC8 PC9 PC10
## gene_1 -0.38649725 -0.096804682 0.10984694 -0.42840798 -0.1202830419
## gene_3 0.07109343 0.003955589 0.07851050 -0.13120051 0.0009830546
## gene_4 -0.01046114 -0.026868551 -0.02701739 0.04788737 0.0774127666
## gene_5 -0.08382192 -0.050481127 -0.13365626 -0.01825075 -0.0571328839
## gene_8 -0.04661081 -0.137038964 0.06628111 -0.02755540 0.0223204705
## gene_9 -0.06802918 0.179537009 0.20704150 -0.03203401 -0.0533106540
## PC11 PC12 PC13 PC14 PC15 PC16
## gene_1 -0.04838930 -0.24878506 0.02987826 0.16913228 0.13329373 0.04126195
## gene_3 -0.03008708 -0.04908422 0.11962632 -0.09636722 0.10383820 -0.04836248
## gene_4 -0.03561987 -0.06577543 -0.04493099 -0.06658016 -0.02061142 0.05338710
## gene_5 -0.02737164 -0.07753298 -0.06345645 0.14221453 -0.05567151 -0.13144811
## gene_8 0.03555272 0.02249653 -0.04428219 0.07413043 -0.11024164 0.03885823
## gene_9 -0.08597751 0.05272996 -0.21653721 0.23661700 0.10713494 0.01398113
## PC17 PC18 PC19 PC20 PC21
## gene_1 -0.10405751 -0.105505065 0.04012491 0.0002773335 0.06781819
## gene_3 0.22425002 -0.037186873 0.03293918 -0.0082027586 0.01721992
## gene_4 -0.13262430 0.031464575 -0.02511225 -0.1421092096 0.07165713
## gene_5 0.05632945 0.220407393 0.10794418 -0.1113046092 -0.25494474
## gene_8 0.03770420 0.028281428 -0.09744944 0.0821676700 0.02051943
## gene_9 0.16164240 -0.002087269 0.04270881 0.0699787849 0.06720094
## PC22 PC23 PC24 PC25 PC26
## gene_1 -0.11561961 -0.09073958 -0.11946752 0.007809584 -0.0163792095
## gene_3 -0.03246385 -0.03153913 -0.03122655 -0.098220102 -0.1129618777
## gene_4 -0.18780899 0.04033710 -0.00825051 0.029839075 -0.0004021929
## gene_5 -0.03017181 0.01487209 0.11519015 0.018344104 -0.0763201506
## gene_8 -0.16605927 -0.06836510 0.04420817 0.186085316 -0.0557997472
## gene_9 0.11669641 0.04288313 0.10508830 -0.258748631 -0.0764176834
## PC27 PC28 PC29 PC30 PC31
## gene_1 0.074025865 0.138411875 -0.04545681 -0.05295938 -0.02271826
## gene_3 0.167627720 -0.146425343 -0.05262575 -0.03310703 -0.08053623
## gene_4 -0.021864456 0.040932855 0.09167695 -0.02102857 -0.05776633
## gene_5 0.158862480 0.007065339 -0.08080616 0.11014045 -0.26620648
## gene_8 -0.025560076 0.026867106 0.02064415 0.08062352 0.06424950
## gene_9 0.009595673 -0.101164752 0.01728375 0.03702305 0.05024024
## PC32 PC33 PC34 PC35 PC36 PC37
## gene_1 -0.08658177 0.03011449 -0.03067821 -0.11712002 0.05016861 -0.006766591
## gene_3 -0.03058803 0.10906685 0.08431935 -0.07285970 0.21475244 0.004821169
## gene_4 0.07170568 0.02978180 0.06888997 0.11358189 -0.07891347 0.107729942
## gene_5 -0.05349310 -0.08203074 -0.04209865 0.13316173 -0.11835443 0.013710773
## gene_8 -0.18649960 0.02188702 0.11510011 -0.04501977 -0.07643213 0.046450488
## gene_9 0.02106654 -0.15535767 0.13255476 -0.18483590 0.03499133 -0.088978678
## PC38
## gene_1 0.01971633
## gene_3 -0.14805733
## gene_4 0.08949939
## gene_5 0.13510137
## gene_8 0.20414051
## gene_9 0.04370603##############################################################################
## Actual principal components ##
##############################################################################
head(Q2_pca$x)## PC1 PC2 PC3 PC4 PC5 PC6
## 27255F -0.3083235 -0.4126276 0.6453056 -0.2805607 0.16614517 -0.80861663
## 27327F -0.8762894 -0.8488764 0.2617297 -0.6703358 0.08535582 0.03656693
## 27213F 4.2699938 -1.7836389 -0.4634399 -0.4140760 0.82881497 0.05023740
## 27603F -1.0571009 -0.4072185 -0.8033904 0.2268931 0.34720167 0.27966182
## 17840F -0.5493824 1.1651851 -0.5314593 -0.5442934 -0.26301724 -0.45821469
## 22980F 0.6656410 0.6384601 -0.6090438 -0.1060112 -0.28099143 -0.17728406
## PC7 PC8 PC9 PC10 PC11 PC12
## 27255F 0.6495144 -0.6521528 0.5998859 -0.44985783 0.09772059 -0.3174042
## 27327F 1.0296712 0.1342721 0.2175582 -0.09655902 0.36381938 0.0835606
## 27213F -0.6178306 0.1177914 -0.2459231 -0.40667620 0.36721545 0.4463939
## 27603F 0.1941788 -0.1299925 0.1474702 -0.29395612 -0.03920648 0.5506631
## 17840F -0.6445387 0.3546739 0.3385453 -0.61430960 0.38421369 0.2382995
## 22980F 0.3794273 0.1885406 -0.2883861 -0.17810950 -0.25896675 -0.2695801
## PC13 PC14 PC15 PC16 PC17 PC18
## 27255F 0.4407220 -0.10276289 -0.03210181 -0.08543148 -0.13592396 0.15326001
## 27327F -0.2697728 0.50651001 0.03543380 -0.17965651 -0.06506193 0.39203897
## 27213F 0.1098919 0.22482983 -0.09283756 0.16128775 -0.01790500 0.14567186
## 27603F -0.4197796 -0.06820294 0.15819502 -0.06882728 0.01516801 -0.27833396
## 17840F 0.4000419 -0.10469312 0.32620169 0.15489800 0.46359750 -0.37545518
## 22980F 0.0613767 -0.17320000 0.10706518 0.07440583 0.15974848 0.09956188
## PC19 PC20 PC21 PC22 PC23
## 27255F 0.18492202 0.03809819 -0.55083810 -0.001175751 0.34284644
## 27327F 0.05273880 -0.23391890 0.31456130 -0.038143526 -0.04995786
## 27213F -0.01828866 -0.04827600 -0.18937415 -0.037941630 -0.02134510
## 27603F 0.34432611 -0.30391368 -0.19663870 -0.164322768 0.10868522
## 17840F 0.18744189 -0.10240848 0.19371992 -0.093980099 -0.17789724
## 22980F -0.18064639 0.31604668 0.09042495 0.138470232 -0.15717209
## PC24 PC25 PC26 PC27 PC28
## 27255F 0.069955138 0.0658240336 0.044024911 0.02163421 0.10848092
## 27327F 0.070054396 -0.0175370272 -0.005465617 0.11147185 -0.12839769
## 27213F -0.015484111 -0.0726847328 0.055475965 -0.01073669 -0.02102088
## 27603F 0.005470832 0.0059664913 0.043049375 -0.01071064 -0.24140166
## 17840F 0.148903514 -0.0008606557 -0.026635917 0.10153204 0.23321422
## 22980F 0.104473983 0.0329741430 -0.003043320 0.29027229 -0.31336650
## PC29 PC30 PC31 PC32 PC33
## 27255F -0.15633287 -0.0598678705 -0.06683243 -0.003471310 -0.03923033
## 27327F 0.27864500 -0.1928517701 -0.06203451 0.052350688 0.04850764
## 27213F 0.04923392 -0.0276347968 0.07469807 -0.005059222 -0.05831152
## 27603F -0.35292133 -0.0002654399 -0.14734887 -0.187309300 0.03670447
## 17840F 0.02813427 -0.0346941536 0.09333940 0.064161053 -0.01695143
## 22980F -0.04920203 -0.3214377016 -0.17183605 -0.117838280 -0.22222404
## PC34 PC35 PC36 PC37 PC38
## 27255F 0.24537080 0.04102646 0.015254817 -0.05329805 -2.142383e-15
## 27327F -0.03639746 -0.09323527 -0.174733993 -0.10057801 -1.961972e-15
## 27213F 0.01612448 0.03254895 -0.004568568 0.01054668 -2.030494e-15
## 27603F -0.23603338 0.06651215 0.032431712 -0.06957580 -2.081234e-15
## 17840F 0.04180786 0.11003247 -0.111414100 -0.13207479 -1.531761e-15
## 22980F 0.04198156 0.15931860 -0.005688651 0.11030734 -2.037866e-15head(Q2_pca$x)## PC1 PC2 PC3 PC4 PC5 PC6
## 27255F -0.3083235 -0.4126276 0.6453056 -0.2805607 0.16614517 -0.80861663
## 27327F -0.8762894 -0.8488764 0.2617297 -0.6703358 0.08535582 0.03656693
## 27213F 4.2699938 -1.7836389 -0.4634399 -0.4140760 0.82881497 0.05023740
## 27603F -1.0571009 -0.4072185 -0.8033904 0.2268931 0.34720167 0.27966182
## 17840F -0.5493824 1.1651851 -0.5314593 -0.5442934 -0.26301724 -0.45821469
## 22980F 0.6656410 0.6384601 -0.6090438 -0.1060112 -0.28099143 -0.17728406
## PC7 PC8 PC9 PC10 PC11 PC12
## 27255F 0.6495144 -0.6521528 0.5998859 -0.44985783 0.09772059 -0.3174042
## 27327F 1.0296712 0.1342721 0.2175582 -0.09655902 0.36381938 0.0835606
## 27213F -0.6178306 0.1177914 -0.2459231 -0.40667620 0.36721545 0.4463939
## 27603F 0.1941788 -0.1299925 0.1474702 -0.29395612 -0.03920648 0.5506631
## 17840F -0.6445387 0.3546739 0.3385453 -0.61430960 0.38421369 0.2382995
## 22980F 0.3794273 0.1885406 -0.2883861 -0.17810950 -0.25896675 -0.2695801
## PC13 PC14 PC15 PC16 PC17 PC18
## 27255F 0.4407220 -0.10276289 -0.03210181 -0.08543148 -0.13592396 0.15326001
## 27327F -0.2697728 0.50651001 0.03543380 -0.17965651 -0.06506193 0.39203897
## 27213F 0.1098919 0.22482983 -0.09283756 0.16128775 -0.01790500 0.14567186
## 27603F -0.4197796 -0.06820294 0.15819502 -0.06882728 0.01516801 -0.27833396
## 17840F 0.4000419 -0.10469312 0.32620169 0.15489800 0.46359750 -0.37545518
## 22980F 0.0613767 -0.17320000 0.10706518 0.07440583 0.15974848 0.09956188
## PC19 PC20 PC21 PC22 PC23
## 27255F 0.18492202 0.03809819 -0.55083810 -0.001175751 0.34284644
## 27327F 0.05273880 -0.23391890 0.31456130 -0.038143526 -0.04995786
## 27213F -0.01828866 -0.04827600 -0.18937415 -0.037941630 -0.02134510
## 27603F 0.34432611 -0.30391368 -0.19663870 -0.164322768 0.10868522
## 17840F 0.18744189 -0.10240848 0.19371992 -0.093980099 -0.17789724
## 22980F -0.18064639 0.31604668 0.09042495 0.138470232 -0.15717209
## PC24 PC25 PC26 PC27 PC28
## 27255F 0.069955138 0.0658240336 0.044024911 0.02163421 0.10848092
## 27327F 0.070054396 -0.0175370272 -0.005465617 0.11147185 -0.12839769
## 27213F -0.015484111 -0.0726847328 0.055475965 -0.01073669 -0.02102088
## 27603F 0.005470832 0.0059664913 0.043049375 -0.01071064 -0.24140166
## 17840F 0.148903514 -0.0008606557 -0.026635917 0.10153204 0.23321422
## 22980F 0.104473983 0.0329741430 -0.003043320 0.29027229 -0.31336650
## PC29 PC30 PC31 PC32 PC33
## 27255F -0.15633287 -0.0598678705 -0.06683243 -0.003471310 -0.03923033
## 27327F 0.27864500 -0.1928517701 -0.06203451 0.052350688 0.04850764
## 27213F 0.04923392 -0.0276347968 0.07469807 -0.005059222 -0.05831152
## 27603F -0.35292133 -0.0002654399 -0.14734887 -0.187309300 0.03670447
## 17840F 0.02813427 -0.0346941536 0.09333940 0.064161053 -0.01695143
## 22980F -0.04920203 -0.3214377016 -0.17183605 -0.117838280 -0.22222404
## PC34 PC35 PC36 PC37 PC38
## 27255F 0.24537080 0.04102646 0.015254817 -0.05329805 -2.142383e-15
## 27327F -0.03639746 -0.09323527 -0.174733993 -0.10057801 -1.961972e-15
## 27213F 0.01612448 0.03254895 -0.004568568 0.01054668 -2.030494e-15
## 27603F -0.23603338 0.06651215 0.032431712 -0.06957580 -2.081234e-15
## 17840F 0.04180786 0.11003247 -0.111414100 -0.13207479 -1.531761e-15
## 22980F 0.04198156 0.15931860 -0.005688651 0.11030734 -2.037866e-15###################################################################
## ## Standard deviation of components represents the percent ##
## of variation each component explains. ##
###################################################################
Q2_pca$sdev## [1] 1.066437e+00 7.239611e-01 6.093164e-01 5.320231e-01 5.160944e-01
## [6] 5.025682e-01 4.276870e-01 4.188471e-01 3.960560e-01 3.905610e-01
## [11] 3.645624e-01 3.326163e-01 3.151798e-01 2.846522e-01 2.778866e-01
## [16] 2.632485e-01 2.612227e-01 2.444632e-01 2.322899e-01 2.219891e-01
## [21] 2.143661e-01 2.002502e-01 1.887098e-01 1.766141e-01 1.739237e-01
## [26] 1.661765e-01 1.551085e-01 1.474103e-01 1.439302e-01 1.405446e-01
## [31] 1.328869e-01 1.236031e-01 1.117914e-01 1.058433e-01 9.589424e-02
## [36] 8.837612e-02 7.535480e-02 2.107899e-15##############################################################################
## Compute variance explained: ##
##############################################################################
## Note: by definition, PC1 explains the most variation, PC2 the second most variation, ...
(Q2_pca$sdev)^2 / (sum(Q2_pca$sdev^2))## [1] 2.429914e-01 1.119828e-01 7.932435e-02 6.047581e-02 5.690876e-02
## [6] 5.396484e-02 3.908166e-02 3.748278e-02 3.351459e-02 3.259106e-02
## [11] 2.839649e-02 2.363784e-02 2.122451e-02 1.731210e-02 1.649894e-02
## [16] 1.480650e-02 1.457950e-02 1.276873e-02 1.152873e-02 1.052893e-02
## [21] 9.818224e-03 8.567749e-03 7.608690e-03 6.664562e-03 6.463061e-03
## [26] 5.900106e-03 5.140344e-03 4.642766e-03 4.426133e-03 4.220354e-03
## [31] 3.772987e-03 3.264220e-03 2.670163e-03 2.393576e-03 1.964744e-03
## [36] 1.668747e-03 1.213229e-03 9.493365e-31DOUBLE CHECK PCS.
############################################################################
############################################################################
### ###
### DOUBLE CHECK PCS. ###
### ###
############################################################################
############################################################################
PC_check <- as.matrix(scale(X, center=TRUE, scale=TRUE)) %*% Q2_pca$rotation
all.equal(PC_check, Q2_pca$x)## [1] "Mean relative difference: 0.8087177"ggplot PC1 vs PC2
## Now plot the PCs: PC1 vs PC2
pca_dat <- cbind(group, Q2_pca$x)
ggplot(pca_dat, aes(x=PC1, y=PC2, color=category)) +
geom_point() +
stat_ellipse()
ggplot PC2 vs PC3
## PC1 vs PC3
ggplot(pca_dat, aes(x=PC1, y=PC3, color=category)) +
geom_point() +
stat_ellipse()
Visualizing PCA
## Visualizing PCA: Loadings
loadings <- as.data.frame(Q2_pca$rotation)
loadings$variable <- rownames(loadings)
arrow_style <- arrow(length = unit(0.05, "inches"), type = "closed")
ggplot(loadings) +
geom_segment(x=0, y=0, aes(xend=PC1, yend=PC2), arrow=arrow_style) +
geom_text(aes(x=PC1, y=PC2, label=variable), size=3, color='red') +
xlim(-1.,1) +
ylim(-1.,1.) +
coord_fixed()
Visualizing PCA: Variance explained - ggplot
## Visualizing PCA: Variance explained
var_explained <- data.frame(value=(Q2_pca$sdev)^2 / (sum(Q2_pca$sdev^2)),
PC = colnames(Q2_pca$x))
ggplot(var_explained, aes(x = PC, y = value)) +
geom_bar(stat = "identity")
cumsum(var_explained$value)## [1] 0.2429914 0.3549742 0.4342986 0.4947744 0.5516831 0.6056480 0.6447296
## [8] 0.6822124 0.7157270 0.7483181 0.7767146 0.8003524 0.8215769 0.8388890
## [15] 0.8553879 0.8701945 0.8847740 0.8975427 0.9090714 0.9196003 0.9294186
## [22] 0.9379863 0.9455950 0.9522596 0.9587226 0.9646227 0.9697631 0.9744058
## [29] 0.9788320 0.9830523 0.9868253 0.9900895 0.9927597 0.9951533 0.9971180
## [36] 0.9987868 1.0000000 1.0000000Using a loop to iterate through each gene independently, write code to perform a permutation test (using 1000 permutations) to test the hypothesis of equal expression between the good and bad categories.Your permutation test should return a p-value for each gene.
library(devtools) ## Loading required package: usethisinstall_github("billyhw/GSALightning")## Skipping install of 'GSALightning' from a github remote, the SHA1 (4662b897) has not changed since last install.
## Use `force = TRUE` to force installationlibrary(GSALightning)
##################################################################
## permutation test should return a p-value for each gene.. ##
##################################################################
results <- permTestLight(eset = liver_expression, fac = factor(group$category),
nperm = 1000, method = 'absmean')## After gene set size filtering, there are 100 gene sets,
## containing a total of 100 genes for analysis.## Obtaining observed gene set statistics.## Permutation done. Evaluating P-values.# Show the head(results)
head(results)results$p =as.numeric(results[[1]])
results$p.bh <- p.adjust(results$p,method = "BH")
head(results)#results$BH =p.adjust(results$p-value,method = "BH")
results2 <- permTestLight(eset = liver_expression, fac = factor(group$category),
nperm = 1000, method = c("mean", "absmean"))## After gene set size filtering, there are 100 gene sets,
## containing a total of 100 genes for analysis.## Obtaining observed gene set statistics.## Permutation done. Evaluating P-values.# Show the head(results)
head(results2)Question 3. K-means clustering
The snsdata.csv data represent a random sample of 30,000 U.S. high school students who had profiles on Faceboook from 2006 to 2009.From the top 500 words appearing across all pages, 36 words were chosento represent five categories of interest (extracurricular activities, fashion, religion, romance, and antisocial behavior). The 36 words include terms like football, sexy, kissed, shopping, bible, death, and drugs. Thedata indicate, for each person, how many times each word appeared in the person’s social network profile, as well as their graduation year (gradyear), gender, and age.
Read CSV File
# Install and/or load packages with pacman
pacman::p_load( # Use p_load function from pacman
car, # For scatterplotMatrix
cluster, # Cluster analysis
datasets, # R's built-in sample datasets
factoextra, # Evaluate clusters
magrittr, # Pipes
pacman, # Load/unload packages
rio, # Import/export data
tidyverse,
broom) # So many reasons
###########################################################################
###########################################################################
### ###
### READ CSV FILE. ###
### ###
###########################################################################
###########################################################################
snsdata <- read.csv("https://raw.githubusercontent.com/brenden17/sklearnlab/master/facebook/snsdata.csv")
str(snsdata)## 'data.frame': 30000 obs. of 40 variables:
## $ gradyear : int 2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 ...
## $ gender : chr "M" "F" "M" "F" ...
## $ age : num 19 18.8 18.3 18.9 19 ...
## $ friends : int 7 0 69 0 10 142 72 17 52 39 ...
## $ basketball : int 0 0 0 0 0 0 0 0 0 0 ...
## $ football : int 0 1 1 0 0 0 0 0 0 0 ...
## $ soccer : int 0 0 0 0 0 0 0 0 0 0 ...
## $ softball : int 0 0 0 0 0 0 0 1 0 0 ...
## $ volleyball : int 0 0 0 0 0 0 0 0 0 0 ...
## $ swimming : int 0 0 0 0 0 0 0 0 0 0 ...
## $ cheerleading: int 0 0 0 0 0 0 0 0 0 0 ...
## $ baseball : int 0 0 0 0 0 0 0 0 0 0 ...
## $ tennis : int 0 0 0 0 0 0 0 0 0 0 ...
## $ sports : int 0 0 0 0 0 0 0 0 0 0 ...
## $ cute : int 0 1 0 1 0 0 0 0 0 1 ...
## $ sex : int 0 0 0 0 1 1 0 2 0 0 ...
## $ sexy : int 0 0 0 0 0 0 0 1 0 0 ...
## $ hot : int 0 0 0 0 0 0 0 0 0 1 ...
## $ kissed : int 0 0 0 0 5 0 0 0 0 0 ...
## $ dance : int 1 0 0 0 1 0 0 0 0 0 ...
## $ band : int 0 0 2 0 1 0 1 0 0 0 ...
## $ marching : int 0 0 0 0 0 1 1 0 0 0 ...
## $ music : int 0 2 1 0 3 2 0 1 0 1 ...
## $ rock : int 0 2 0 1 0 0 0 1 0 1 ...
## $ god : int 0 1 0 0 1 0 0 0 0 6 ...
## $ church : int 0 0 0 0 0 0 0 0 0 0 ...
## $ jesus : int 0 0 0 0 0 0 0 0 0 2 ...
## $ bible : int 0 0 0 0 0 0 0 0 0 0 ...
## $ hair : int 0 6 0 0 1 0 0 0 0 1 ...
## $ dress : int 0 4 0 0 0 1 0 0 0 0 ...
## $ blonde : int 0 0 0 0 0 0 0 0 0 0 ...
## $ mall : int 0 1 0 0 0 0 2 0 0 0 ...
## $ shopping : int 0 0 0 0 2 1 0 0 0 1 ...
## $ clothes : int 0 0 0 0 0 0 0 0 0 0 ...
## $ hollister : int 0 0 0 0 0 0 2 0 0 0 ...
## $ abercrombie : int 0 0 0 0 0 0 0 0 0 0 ...
## $ die : int 0 0 0 0 0 0 0 0 0 0 ...
## $ death : int 0 0 1 0 0 0 0 0 0 0 ...
## $ drunk : int 0 0 0 0 1 1 0 0 0 0 ...
## $ drugs : int 0 0 0 0 1 0 0 0 0 0 ...####################################################################################
####################################################################################
### ###
### A. ELIMINATE ALL PERSONS FOR WHOM THERE IS INSUFFICIENT DATA (NA). HOW ###
### MANY MORE OBSERVATIONS ARE THERE TO BE MADE? THE REPRESENTATIVE WORD ###
### COUNTS, WHICH INCLUDE EVERYTHING EXCEPT COLUMNS 1-4, WILL BE CENTERED AND ###
### SCALED USING SCALE(..., CENTER=TRUE,SCALE=TRUE) IN SUCH A WAY THAT THE ###
### ROWS WILL HAVE A MEAN OF 0 AND A VARIANCE OF 1. (YOU MAY HAVE TO USE A ###
### LOOP TO DO THIS). VERIFY THAT THE DATA HAVE BEEN SUITABLY CENTERED AND ###
### SCALED BY DOING A SECOND CHECK. ###
### ###
####################################################################################
####################################################################################
df <- na.omit(snsdata)
str(df)## 'data.frame': 24005 obs. of 40 variables:
## $ gradyear : int 2006 2006 2006 2006 2006 2006 2006 2006 2006 2006 ...
## $ gender : chr "M" "F" "M" "F" ...
## $ age : num 19 18.8 18.3 18.9 18.9 ...
## $ friends : int 7 0 69 0 72 17 52 39 8 21 ...
## $ basketball : int 0 0 0 0 0 0 0 0 0 0 ...
## $ football : int 0 1 1 0 0 0 0 0 0 1 ...
## $ soccer : int 0 0 0 0 0 0 0 0 0 0 ...
## $ softball : int 0 0 0 0 0 1 0 0 0 0 ...
## $ volleyball : int 0 0 0 0 0 0 0 0 0 0 ...
## $ swimming : int 0 0 0 0 0 0 0 0 0 0 ...
## $ cheerleading: int 0 0 0 0 0 0 0 0 0 0 ...
## $ baseball : int 0 0 0 0 0 0 0 0 0 0 ...
## $ tennis : int 0 0 0 0 0 0 0 0 0 0 ...
## $ sports : int 0 0 0 0 0 0 0 0 0 0 ...
## $ cute : int 0 1 0 1 0 0 0 1 0 0 ...
## $ sex : int 0 0 0 0 0 2 0 0 0 0 ...
## $ sexy : int 0 0 0 0 0 1 0 0 0 0 ...
## $ hot : int 0 0 0 0 0 0 0 1 0 0 ...
## $ kissed : int 0 0 0 0 0 0 0 0 0 0 ...
## $ dance : int 1 0 0 0 0 0 0 0 0 0 ...
## $ band : int 0 0 2 0 1 0 0 0 0 0 ...
## $ marching : int 0 0 0 0 1 0 0 0 0 0 ...
## $ music : int 0 2 1 0 0 1 0 1 0 0 ...
## $ rock : int 0 2 0 1 0 1 0 1 0 0 ...
## $ god : int 0 1 0 0 0 0 0 6 0 0 ...
## $ church : int 0 0 0 0 0 0 0 0 0 1 ...
## $ jesus : int 0 0 0 0 0 0 0 2 0 0 ...
## $ bible : int 0 0 0 0 0 0 0 0 0 0 ...
## $ hair : int 0 6 0 0 0 0 0 1 0 0 ...
## $ dress : int 0 4 0 0 0 0 0 0 0 0 ...
## $ blonde : int 0 0 0 0 0 0 0 0 0 0 ...
## $ mall : int 0 1 0 0 2 0 0 0 0 0 ...
## $ shopping : int 0 0 0 0 0 0 0 1 0 0 ...
## $ clothes : int 0 0 0 0 0 0 0 0 0 0 ...
## $ hollister : int 0 0 0 0 2 0 0 0 0 0 ...
## $ abercrombie : int 0 0 0 0 0 0 0 0 0 0 ...
## $ die : int 0 0 0 0 0 0 0 0 0 0 ...
## $ death : int 0 0 1 0 0 0 0 0 0 0 ...
## $ drunk : int 0 0 0 0 0 0 0 0 0 0 ...
## $ drugs : int 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "na.action")= 'omit' Named int [1:5995] 5 6 14 16 17 27 39 42 49 50 ...
## ..- attr(*, "names")= chr [1:5995] "5" "6" "14" "16" ...# Check data
head(df)Separate the class labels & Overwrite data frame
dfm <- df %>%
dplyr::select(c(gradyear, gender, age, friends))
df %<>% #
dplyr::select(c(-gradyear, -gender, -age, -friends))
df<-scale(df, center = TRUE, scale = TRUE)B)
Using the K-means algorithm and set.seed(12345), cluster the individuals in this dataset using thecentered/scaled representative word counts into K=5 different clusters. How many individuals are grouped into each cluster?
K-MEANS CLUSTERING
set.seed(12345)
#################################################################
## Compute three clusters. ##
#################################################################
km <- df %>%
kmeans(5) ## Warning: did not converge in 10 iterationsCompute three clusters
km <- df %>%
kmeans(5) %>% # Set the number of clusters
print() # Print output## K-means clustering with 5 clusters of sizes 17382, 544, 866, 2684, 2529
##
## Cluster means:
## basketball football soccer softball volleyball swimming
## 1 -0.18188496 -0.18897872 -0.08109067 -0.13466737 -0.12567429 -0.06716768
## 2 -0.09577802 0.06163334 -0.07917051 -0.05949619 -0.07427205 0.04392209
## 3 0.35099385 0.34994188 0.14133625 0.17165730 0.07812692 0.21454471
## 4 1.03847926 0.96887468 0.45361545 0.85513361 0.74054696 0.09773351
## 5 0.04839405 0.13752086 0.04455744 -0.02794765 0.06705753 0.27501091
## cheerleading baseball tennis sports cute sex
## 1 -0.107563668 -0.13833832 -0.040886874 -0.15806620 -0.1468812431 -0.090827690
## 2 -0.098964592 -0.12150367 0.009155917 -0.11917854 -0.0083348627 -0.032600738
## 3 0.154082425 0.27816633 0.118508441 0.76698000 0.4595774593 1.965444461
## 4 0.003084722 0.87693692 0.153706977 0.85176715 0.0006503008 -0.032782915
## 5 0.704544739 -0.04899015 0.075340840 -0.05457011 0.8532560088 -0.006952883
## sexy hot kissed dance band marching
## 1 -0.061854733 -0.12224507 -0.12616122 -0.13035816 -0.13124287 -0.11490872
## 2 -0.015222737 -0.04368477 -0.02067761 0.07671652 4.27954587 4.74876115
## 3 0.538781266 0.28035193 2.89219765 0.43304351 0.37968847 -0.01341422
## 4 -0.008966377 -0.00457371 -0.09121430 0.01892005 -0.05080476 -0.09927685
## 5 0.253428754 0.75844975 -0.02200123 0.71109318 -0.09460643 -0.12175046
## music rock god church jesus bible
## 1 -0.1231915 -0.10530757 -0.11484585 -0.13678357 -0.09070777 -0.0864724
## 2 0.5149175 0.18937515 0.06472648 0.04142814 0.04272426 0.0429554
## 3 1.1985304 1.20855926 0.37265246 0.15969993 0.07177117 0.0700527
## 4 0.1568039 0.16236815 0.57401334 0.67226222 0.57066317 0.5835465
## 5 0.1591182 0.09688719 0.03862020 0.16306171 -0.01596416 -0.0582084
## hair dress blonde mall shopping clothes
## 1 -0.183599245 -0.11075954 -0.02566085 -0.16582902 -0.18759217 -0.162303286
## 2 -0.043103798 0.09772896 -0.01382951 -0.07336383 -0.04326140 0.011623500
## 3 2.546791550 0.55809900 0.35985351 0.58835689 0.21617063 1.207685890
## 4 -0.003719602 -0.03341102 0.02166740 -0.02021921 0.02744335 0.002844062
## 5 0.403017980 0.58458652 0.03312442 0.97552440 1.19549213 0.696458320
## hollister abercrombie die death drunk drugs
## 1 -0.1643444 -0.1600079 -0.089757110 -0.07040873 -0.08390036 -0.11220146
## 2 -0.1691409 -0.1469677 -0.009798932 0.02641119 -0.08103302 -0.05576477
## 3 0.1939373 0.3159282 1.695493068 0.94473339 1.78312662 2.67669255
## 4 -0.1390213 -0.1268746 0.018059886 0.07949373 -0.04736273 -0.06540440
## 5 1.2470660 1.1578272 0.019264126 0.07037428 0.03375721 -0.06399707
##
## Clustering vector:
## 1 2 3 4 7 8 9 10 11 12 13 15 18
## 1 5 1 1 5 1 1 4 1 1 1 1 1
## 19 20 21 22 23 24 25 26 28 29 30 31 32
## 1 5 5 1 1 4 1 1 3 1 1 1 4
## 33 34 35 36 37 38 40 41 43 44 45 46 47
## 1 1 1 1 4 1 3 1 1 1 4 1 4
## 48 51 52 53 54 55 56 57 58 59 60 61 62
## 1 1 2 5 1 5 1 2 3 1 1 1 1
## 63 64 65 66 67 68 70 73 74 76 77 78 79
## 3 4 1 1 1 1 1 1 1 1 1 1 1
## 80 81 82 84 85 86 87 88 89 90 91 92 93
## 1 4 1 4 1 5 1 1 1 1 1 1 5
## 96 97 99 100 101 102 104 105 106 107 108 109 110
## 1 4 5 1 1 1 5 1 1 1 5 5 1
## 111 113 114 116 117 118 119 120 121 122 123 124 126
## 1 1 2 1 3 1 5 1 1 4 1 1 1
## 127 128 129 132 134 135 136 137 139 140 141 142 143
## 1 1 1 4 1 1 1 5 1 1 2 2 1
## 144 145 146 147 148 149 152 153 154 155 157 159 160
## 1 1 4 5 1 4 1 1 1 1 1 5 1
## 162 164 165 167 168 169 170 171 172 173 175 176 177
## 1 1 4 1 1 4 1 1 1 1 1 1 1
## 178 179 181 182 183 184 185 186 187 188 189 190 191
## 5 5 1 5 2 1 1 5 4 1 1 1 1
## 193 194 195 196 197 198 199 200 201 202 203 204 205
## 1 1 3 2 1 1 1 1 4 5 2 1 1
## 206 207 208 209 210 211 212 213 214 215 216 217 218
## 5 1 1 1 1 1 1 1 1 1 5 4 1
## 219 220 221 222 223 224 225 226 227 228 230 231 232
## 1 1 4 1 1 1 1 1 1 1 1 5 5
## 233 234 235 236 237 238 239 243 244 245 246 248 249
## 1 1 1 1 1 5 1 3 1 1 1 1 1
## 250 252 253 255 257 258 259 260 261 262 265 266 267
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 268 269 271 272 273 274 275 276 277 278 279 280 281
## 1 1 4 1 1 1 1 1 1 1 1 1 1
## 282 283 284 287 289 290 291 292 293 294 295 296 297
## 4 1 1 1 1 1 1 1 1 1 1 1 4
## 298 299 300 302 303 304 306 308 309 310 311 312 313
## 1 4 1 4 1 5 1 1 1 1 1 1 1
## 314 315 316 317 318 319 320 321 322 323 324 325 326
## 1 1 1 1 1 1 1 1 1 1 1 1 4
## 327 328 329 330 331 332 333 334 335 336 337 338 339
## 4 1 1 1 1 1 1 4 1 1 1 1 1
## 340 341 342 343 344 345 346 347 348 349 350 351 352
## 5 1 1 1 1 1 1 1 1 1 1 4 1
## 353 354 355 356 358 359 361 362 363 364 365 366 367
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 368 370 371 372 373 374 376 377 378 379 380 381 382
## 1 1 1 1 1 1 1 1 1 1 1 1 4
## 383 384 387 388 389 391 393 394 395 396 398 399 401
## 1 1 1 1 1 4 1 2 3 4 1 5 1
## 402 403 404 406 407 409 410 412 413 414 415 417 418
## 1 1 1 1 1 1 5 5 1 4 3 1 1
## 419 420 421 423 424 425 426 427 428 429 430 431 432
## 1 1 1 1 1 1 1 4 4 1 1 1 1
## 433 434 435 436 437 438 439 441 442 443 445 446 447
## 1 1 1 1 5 1 1 1 1 1 1 5 1
## 448 450 451 452 453 454 455 456 457 458 459 460 462
## 1 1 1 1 1 1 1 1 1 3 5 1 1
## 464 465 466 467 468 469 471 472 474 475 476 477 478
## 1 1 1 4 1 1 1 1 1 1 1 5 1
## 479 480 481 483 484 485 486 489 491 492 493 494 495
## 5 1 1 1 1 4 5 2 2 2 1 5 2
## 497 498 499 500 501 502 503 504 505 506 508 509 511
## 1 2 1 1 1 1 4 1 4 1 1 1 1
## 512 513 514 517 518 519 520 521 522 523 525 527 528
## 1 1 1 1 1 4 1 1 1 4 4 1 1
## 529 530 532 533 534 535 536 537 538 539 540 541 542
## 1 5 4 1 1 1 4 1 4 5 1 5 5
## 543 544 545 546 547 548 549 552 554 555 556 557 558
## 1 4 1 1 4 1 1 1 1 1 1 1 1
## 559 560 562 563 565 566 568 569 570 571 573 574 575
## 1 1 4 1 1 1 1 1 1 1 1 1 1
## 576 578 579 580 581 582 583 584 586 587 588 591 592
## 1 1 1 1 1 3 1 1 1 1 4 4 1
## 593 594 595 596 597 598 599 600 601 602 603 604 605
## 1 1 1 1 1 1 4 1 1 1 1 4 1
## 606 607 608 609 611 612 613 615 616 617 619 620 622
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 623 625 626 627 628 629 630 631 632 633 636 637 638
## 1 1 1 1 1 1 1 1 1 4 1 4 1
## 639 640 641 642 643 644 645 646 647 648 649 650 652
## 1 1 1 1 1 1 1 1 4 1 1 1 1
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## 1 1 1 1 1 4 1 5 1 5 1 1 4
## 9449 9450 9451 9453 9454 9455 9456 9458 9459 9460 9461 9462 9463
## 1 1 1 1 1 1 5 1 5 1 1 4 1
## 9464 9465 9466 9467 9468 9469 9470 9471 9472 9473 9474 9478 9479
## 1 5 4 1 1 4 1 1 1 1 1 1 1
## 9481 9482 9483 9484 9485 9486 9488 9489 9491 9492 9493 9494 9496
## 5 5 4 1 1 1 4 1 4 1 1 1 1
## 9497 9498 9499 9500 9501 9503 9505 9506 9507 9508 9510 9511 9513
## 1 1 1 1 1 1 1 1 1 4 1 2 3
## 9515 9516 9518 9519 9520 9521 9526 9527 9529 9531 9532 9533 9534
## 1 4 4 1 1 1 1 1 1 3 1 1 1
## 9536 9537 9538 9540 9541 9542 9543 9546 9547 9549 9550 9551 9552
## 1 1 5 1 1 1 1 1 1 1 1 3 1
## 9553 9554 9555 9556 9557 9558 9559 9560 9561 9562 9563 9565 9566
## 1 1 1 1 1 5 1 1 3 1 1 1 1
## 9567 9569 9571 9572 9576 9577 9578 9579 9581 9582 9583 9584 9585
## 4 1 1 2 1 1 1 1 1 1 1 1 4
## 9586 9588 9590 9591 9592 9594 9595 9596 9597 9598 9599 9600 9601
## 1 4 1 1 1 1 5 5 1 1 1 1 1
## 9603 9604 9605 9606 9607 9608 9610 9611 9612 9613 9615 9617 9618
## 3 1 3 1 3 1 1 1 4 1 1 1 1
## 9619 9620 9622 9623 9624 9625 9627 9628 9629 9630 9631 9634 9635
## 1 1 1 4 4 1 1 5 1 1 1 1 1
## 9636 9637 9638 9641 9642 9643 9644 9645 9646 9647 9649 9650 9651
## 1 1 1 5 2 1 4 2 5 1 5 1 5
## 9652 9653 9654 9655 9656 9657 9658 9660 9661 9662 9663 9664 9665
## 1 1 1 1 1 1 1 5 1 1 1 5 1
## 9666 9667 9668 9670 9671 9672 9673 9674 9676 9677 9678 9679 9680
## 4 1 1 1 1 4 3 1 1 1 1 1 1
## 9681 9683 9684 9685 9686 9687 9688 9689 9690 9691 9694 9695 9696
## 1 1 1 1 3 5 1 1 5 1 1 1 4
## 9697 9698 9700 9701 9702 9703 9704 9705 9706 9707 9708 9709 9710
## 1 5 1 1 1 1 4 1 1 1 1 4 3
## 9711 9712 9714 9715 9716 9719 9720 9721 9722 9724 9725 9726 9727
## 1 1 1 1 4 1 1 1 4 5 1 1 1
## 9728 9731 9732 9733 9736 9737 9739 9740 9742 9743 9744 9746 9747
## 4 1 1 1 1 1 1 1 1 1 1 1 1
## 9748 9749 9750 9751 9753 9754 9755 9756 9757 9758 9760 9761 9762
## 1 1 1 1 4 4 5 1 4 1 1 1 1
## 9763 9765 9766 9767 9769 9770 9771 9772 9773 9775 9776 9778 9779
## 1 1 1 1 3 3 4 1 5 1 1 3 1
## 9780 9781 9782 9783 9784 9785 9786 9787 9788 9789 9790 9791 9792
## 1 4 1 1 2 1 1 1 1 5 1 1 1
## 9793 9794 9795 9796 9797 9798 9799 9800 9802 9803 9804 9807 9808
## 1 1 1 1 1 5 1 1 5 1 1 4 1
## 9809 9810 9811 9813 9814 9815 9816 9817 9818 9819 9820 9821 9822
## 1 1 1 1 1 1 1 1 4 1 3 3 1
## 9823 9824 9825 9826 9827 9828 9829 9830 9831 9832 9834 9835 9836
## 1 1 2 1 1 1 1 1 4 1 2 5 1
## 9837 9838 9839 9841 9842 9844 9847 9848 9849 9850 9851 9854 9855
## 1 1 1 1 1 1 4 1 1 1 1 4 1
## 9857 9858 9859 9862 9863 9865 9866 9867 9868 9869 9870 9871 9872
## 1 1 1 1 1 1 1 5 4 1 1 1 1
## 9873 9874 9875 9877 9878 9879 9880 9883 9884 9885 9886 9887 9888
## 1 1 4 1 1 1 4 1 1 1 1 1 1
## 9889 9890 9891 9892 9893 9894 9895 9896 9897 9898 9899 9900 9901
## 1 5 5 5 5 1 5 4 1 1 4 5 1
## 9902 9903 9904 9905 9906 9907 9908 9909 9910 9912 9913 9914 9915
## 1 4 1 1 4 1 1 5 4 3 1 1 4
## 9916 9917 9918 9920 9921 9923 9924 9925 9926 9927 9928 9929 9930
## 1 1 1 1 1 1 4 4 4 1 1 1 1
## 9931 9932 9933 9935 9936 9937 9938 9939 9940 9941 9942 9943 9944
## 1 4 1 5 5 5 1 1 1 3 4 1 1
## 9946 9947 9948 9949 9950 9951 9952 9953 9954 9955 9956 9957 9958
## 1 4 5 1 4 3 1 1 1 1 1 4 1
## 9959 9960 9961 9962 9963 9964 9965 9966 9969 9970 9971 9972 9975
## 1 5 1 5 4 1 1 1 1 5 1 5 1
## 9976 9978 9980 9981 9982 9983 9984 9985 9986 9987 9988 9990 9991
## 1 1 1 4 1 1 1 5 1 1 5 1 1
## 9992 9993 9994 9995 9996 9997 9999 10000 10001 10002 10003 10004 10005
## 4 1 1 1 1 1 1 5 1 1 1 1 1
## 10006 10007 10008 10009 10011 10012 10013 10015 10016 10018 10019 10020 10021
## 1 4 1 1 1 1 1 1 4 1 1 5 1
## 10022 10023 10024 10025 10026 10027 10029 10031 10034 10035 10036 10037 10039
## 1 2 1 1 5 1 1 1 5 5 1 1 1
## 10040 10041 10042 10044 10045 10046 10047 10048 10049 10051 10052 10055 10056
## 4 1 1 3 1 1 1 1 5 1 1 1 1
## 10059 10060 10062 10063 10064 10065 10066 10067 10068 10069 10070 10071 10072
## 1 1 1 4 1 1 1 1 1 5 5 1 1
## 10073 10074 10075 10077 10078 10079 10080 10082 10083 10084 10085 10086 10090
## 5 4 1 1 1 5 4 3 1 1 1 1 1
## 10091 10092 10093 10094 10096 10097 10100 10101 10103 10105 10106 10108 10110
## 1 1 4 1 1 5 1 1 1 4 1 5 1
## 10111 10112 10114 10115 10116 10119 10120 10121 10123 10124 10125 10127 10128
## 1 1 1 1 2 1 1 1 1 2 1 1 1
## 10129 10130 10132 10133 10134 10135 10136 10137 10138 10139 10140 10141 10146
## 3 1 1 1 1 1 4 1 1 1 1 2 1
## 10148 10150 10151 10152 10153 10154 10155 10156 10158 10159 10160 10161 10162
## 1 5 1 1 1 2 1 1 1 1 1 1 1
## 10165 10166 10167 10168 10169 10170 10171 10172 10173 10174 10175 10177 10178
## 1 1 2 1 4 1 4 5 1 1 1 1 1
## 10179 10180 10182 10184 10185 10186 10187 10189 10190 10191 10192 10193 10194
## 2 1 1 1 5 1 1 1 1 1 1 1 1
## 10195 10196 10197 10198 10199 10201 10202 10203 10207 10208 10209 10211 10212
## 5 1 1 1 5 1 1 1 1 1 1 1 1
## 10213 10214 10217 10218 10219 10221 10222 10223 10224 10225 10227 10228 10229
## 1 1 1 1 1 1 1 1 1 1 1 5 1
## 10232 10233 10235 10236 10237 10238 10239 10241 10242 10243 10244 10245 10246
## 1 1 1 1 1 1 3 1 1 4 1 1 5
## 10247 10248 10250 10251 10252 10253 10254 10257 10258 10259 10260 10262 10263
## 1 1 4 1 1 1 1 1 1 1 1 3 1
## 10264 10265 10266 10267 10268 10269 10270 10271 10272 10273 10274 10275 10276
## 1 1 1 1 4 1 1 1 1 1 4 1 4
## 10277 10279 10280 10281 10282 10283 10284 10285 10286 10287 10288 10290 10293
## 1 5 1 1 1 1 1 4 1 1 2 1 2
## 10294 10295 10296 10298 10299 10300 10301 10302 10303 10304 10305 10306 10307
## 1 4 1 5 1 1 1 1 4 2 5 1 1
## 10308 10309 10310 10311 10312 10313 10315 10316 10318 10319 10320 10321 10322
## 5 5 1 4 5 1 1 1 1 1 1 1 1
## 10323 10324 10326 10327 10328 10329 10331 10333 10334 10336 10338 10339 10340
## 5 4 1 1 1 3 1 1 4 1 1 1 1
## 10341 10343 10344 10345 10346 10347 10348 10349 10352 10353 10355 10358 10359
## 2 5 4 1 1 1 1 1 4 1 1 1 1
## 10360 10361 10362 10363 10364 10365 10366 10367 10368 10369 10371 10372 10374
## 4 1 1 1 1 1 4 1 1 1 1 1 1
## 10375 10376 10377 10378 10379 10380 10381 10382 10383 10384 10385 10386 10387
## 1 1 1 3 1 1 1 1 5 4 1 1 4
## 10388 10391 10392 10393 10394 10395 10396 10397 10398 10399 10400 10401 10402
## 1 4 1 4 1 1 1 4 1 1 1 5 3
## 10403 10404 10405 10406 10407 10408 10409 10410 10411 10412 10413 10415 10416
## 1 4 1 1 1 1 1 1 1 1 1 4 1
## 10417 10419 10420 10421 10422 10423 10424 10425 10426 10427 10428 10429 10431
## 5 1 1 1 5 1 3 4 1 5 1 1 1
## 10432 10433 10435 10436 10437 10438 10439 10440 10441 10442 10443 10444 10445
## 5 4 5 1 1 1 1 1 1 1 1 1 5
## 10447 10449 10450 10451 10452 10453 10454 10455 10456 10457 10458 10459 10460
## 1 1 1 1 1 1 1 1 1 5 1 1 1
## 10462 10463 10465 10466 10468 10469 10470 10471 10474 10476 10477 10479 10480
## 1 1 1 1 1 1 1 1 1 4 5 1 1
## 10481 10482 10484 10486 10487 10488 10489 10490 10491 10492 10493 10494 10495
## 1 1 2 1 5 1 1 1 1 1 1 5 1
## 10496 10498 10500 10501 10502 10503 10504 10505 10506 10508 10510 10511 10512
## 1 1 5 1 1 1 1 1 1 3 4 1 1
## 10513 10514 10515 10517 10519 10520 10521 10522 10523 10526 10527 10528 10530
## 1 5 1 1 5 1 1 1 4 1 1 1 1
## 10531 10532 10534 10535 10536 10537 10541 10542 10543 10544 10545 10546 10547
## 1 2 1 1 1 1 4 5 5 4 1 5 1
## 10548 10550 10551 10552 10553 10554 10555 10556 10557 10558 10559 10560 10561
## 1 1 4 4 1 5 1 1 2 1 1 1 1
## 10562 10563 10564 10565 10567 10568 10570 10572 10573 10574 10575 10576 10577
## 1 4 1 1 5 1 4 1 1 1 1 1 1
## 10578 10579 10580 10581 10582 10583 10584 10585 10586 10587 10588 10589 10592
## 1 2 1 1 4 1 1 1 4 1 1 1 1
## 10593 10594 10595 10596 10597 10598 10599 10600 10601 10602 10604 10605 10607
## 1 1 1 1 4 1 1 1 1 1 1 1 5
## 10608 10609 10610 10612 10613 10614 10615 10616 10617 10618 10619 10620 10621
## 5 4 2 1 1 4 1 1 1 1 1 1 1
## 10623 10624 10625 10626 10627 10628 10629 10630 10631 10632 10633 10634 10636
## 1 1 1 1 1 1 1 1 1 3 1 1 1
## 10638 10639 10641 10642 10643 10644 10645 10646 10647 10648 10649 10650 10652
## 4 1 1 1 3 1 1 1 1 1 5 1 1
## 10653 10655 10656 10657 10658 10659 10660 10661 10662 10663 10664 10666 10667
## 1 4 4 1 1 3 1 1 1 1 1 1 1
## 10668 10669 10670 10671 10672 10673 10674 10676 10677 10678 10679 10680 10681
## 5 1 1 1 1 1 1 1 1 4 1 1 1
## 10683 10684 10685 10686 10687 10688 10689 10690 10691 10693 10694 10695 10696
## 1 1 2 1 1 1 1 4 1 1 1 2 1
## 10697 10698 10699 10700 10701 10702 10703 10704 10705 10706 10707 10708 10709
## 1 1 1 1 1 5 1 4 1 1 4 1 1
## 10710 10711 10712 10713 10714 10715 10717 10718 10719 10720 10721 10722 10723
## 1 1 1 1 3 1 4 1 1 1 1 4 2
## 10724 10725 10726 10727 10728 10729 10730 10731 10732 10733 10734 10735 10736
## 5 1 4 1 1 5 1 1 1 1 1 5 1
## 10737 10741 10743 10744 10745 10746 10747 10748 10749 10751 10754 10755 10756
## 4 3 1 4 1 4 1 1 4 4 1 2 1
## 10758 10759 10760 10761 10763 10764 10765 10766 10767 10768 10769 10770 10771
## 4 4 4 3 5 1 1 1 1 4 5 1 4
## 10774 10775 10776 10777 10779 10780 10781 10783 10784 10785 10786 10787 10788
## 5 2 1 1 1 1 1 1 1 1 1 1 1
## 10789 10790 10791 10792 10793 10794 10795 10796 10797 10799 10800 10803 10804
## 1 1 1 1 1 1 1 1 1 1 1 4 1
## 10806 10807 10808 10811 10812 10814 10816 10817 10818 10820 10821 10822 10823
## 1 1 1 1 1 1 4 1 1 5 1 1 1
## 10824 10825 10826 10827 10828 10829 10830 10831 10832 10833 10834 10835 10836
## 3 1 5 5 1 1 1 1 1 1 1 1 1
## 10837 10838 10839 10840 10841 10842 10843 10845 10846 10847 10848 10849 10850
## 1 1 2 1 1 1 1 1 3 1 1 1 4
## 10851 10852 10853 10854 10856 10857 10858 10860 10861 10863 10866 10867 10868
## 1 4 1 1 1 4 1 1 1 1 1 1 1
## 10869 10870 10871 10872 10873 10874 10875 10876 10877 10879 10880 10882 10883
## 1 3 5 1 4 5 1 1 4 1 1 1 4
## 10886 10887 10888 10889 10890 10891 10893 10894 10895 10896 10897 10899 10901
## 5 5 1 1 1 1 4 1 1 4 1 1 4
## 10902 10904 10905 10906 10907 10908 10909 10910 10911 10912 10914 10915 10916
## 1 3 1 4 1 1 1 1 4 1 1 1 5
## 10917 10918 10919 10920 10921 10922 10923 10924 10926 10927 10928 10929 10930
## 1 1 1 5 1 1 1 1 1 1 4 1 2
## 10931 10932 10933 10934 10935 10936 10937 10938 10940 10941 10942 10943 10944
## 1 1 1 1 1 1 1 1 1 1 1 5 1
## 10945 10946 10947 10948 10952 10953 10954 10955 10956 10957 10958 10959 10960
## 1 1 5 1 1 1 1 1 4 1 1 1 1
## 10961 10962 10963 10964 10965 10966 10968 10969 10971 10972 10973 10975 10976
## 5 1 1 1 1 4 5 1 1 1 1 5 4
## 10980 10981 10982 10983 10985 10986 10987 10988 10989 10991 10992 10993 10994
## 3 1 1 1 1 5 1 1 1 1 5 1 5
## 10995 10996 10997 10998 10999 11000 11001 11002 11003 11004 11005 11006 11008
## 4 2 1 5 1 4 1 1 4 1 1 1 4
## 11009 11010 11011 11012 11013 11015 11016 11017 11018 11019 11020 11021 11022
## 1 5 4 1 1 5 4 1 1 1 4 4 5
## 11023 11024 11026 11027 11029 11030 11031 11033 11036 11037 11038 11039 11041
## 1 5 1 5 1 1 1 1 1 1 1 5 3
## 11042 11043 11044 11045 11046 11047 11048 11049 11051 11052 11053 11054 11055
## 4 1 1 1 3 1 1 5 4 1 1 1 1
## 11056 11057 11058 11059 11060 11061 11063 11064 11065 11066 11067 11069 11071
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 11072 11073 11075 11076 11077 11078 11079 11080 11081 11082 11083 11084 11085
## 1 1 1 1 4 4 1 1 1 1 5 1 1
## 11086 11087 11089 11090 11091 11092 11093 11094 11095 11096 11097 11098 11099
## 1 1 4 1 4 1 1 5 1 1 1 1 1
## 11101 11102 11103 11104 11105 11106 11107 11109 11110 11112 11113 11114 11115
## 1 1 1 1 1 1 1 1 1 1 5 1 4
## 11116 11117 11119 11120 11122 11123 11124 11125 11126 11128 11129 11131 11132
## 1 1 1 4 4 1 1 1 1 1 1 4 5
## 11133 11136 11138 11140 11141 11142 11143 11144 11146 11147 11148 11149 11151
## 1 4 1 3 1 1 5 1 1 1 1 1 4
## 11153 11154 11155 11156 11157 11158 11159 11160 11161 11162 11163 11164 11165
## 5 1 1 1 1 1 1 5 1 4 1 1 1
## 11166 11168 11169 11170 11171 11172 11174 11176 11177 11178 11179 11180 11181
## 1 1 1 1 4 1 4 3 1 4 1 1 4
## 11182 11183 11184 11185 11186 11189 11190 11191 11192 11193 11194 11197 11198
## 3 1 4 5 4 1 1 1 1 1 3 1 1
## 11199 11200 11201 11202 11203 11205 11206 11207 11208 11209 11210 11211 11212
## 1 4 1 1 1 1 1 1 1 1 1 3 1
## 11213 11214 11215 11216 11217 11218 11219 11220 11222 11223 11225 11226 11227
## 1 3 5 1 1 1 1 4 1 1 1 1 1
## 11228 11229 11230 11231 11232 11233 11234 11235 11236 11237 11238 11240 11241
## 5 1 1 1 3 1 1 1 4 1 2 1 4
## 11243 11244 11247 11248 11249 11250 11252 11253 11255 11256 11257 11258 11259
## 5 1 1 1 1 1 1 5 1 1 1 1 1
## 11261 11262 11263 11264 11265 11266 11267 11268 11269 11270 11272 11273 11274
## 1 1 1 3 3 1 3 1 1 1 1 1 1
## 11277 11279 11280 11281 11282 11283 11284 11285 11286 11287 11288 11289 11290
## 1 1 4 4 1 1 1 1 1 1 1 1 1
## 11292 11294 11295 11300 11301 11304 11305 11306 11307 11308 11312 11313 11314
## 1 1 1 3 5 5 1 5 1 1 5 1 1
## 11315 11316 11317 11320 11321 11323 11326 11327 11328 11329 11331 11332 11333
## 1 1 1 4 1 1 4 1 1 1 1 1 1
## 11334 11335 11337 11340 11342 11343 11344 11346 11347 11348 11349 11352 11353
## 1 5 5 1 1 1 1 1 1 3 1 4 1
## 11354 11355 11357 11359 11360 11361 11363 11364 11365 11366 11367 11368 11369
## 5 4 3 1 1 4 5 1 1 2 1 4 1
## 11371 11372 11373 11374 11375 11376 11377 11378 11379 11381 11382 11384 11385
## 1 4 1 1 5 1 1 5 1 1 1 1 4
## 11386 11387 11388 11389 11391 11392 11393 11394 11395 11396 11397 11398 11399
## 1 4 4 2 1 1 1 4 1 5 1 5 4
## 11400 11401 11402 11403 11404 11405 11407 11408 11409 11410 11413 11414 11415
## 1 4 1 1 1 1 1 1 1 4 1 5 1
## 11416 11418 11419 11420 11421 11423 11424 11425 11426 11427 11428 11429 11430
## 1 1 1 1 1 3 1 1 4 1 1 1 1
## 11431 11432 11433 11434 11435 11436 11437 11438 11440 11441 11442 11444 11445
## 1 1 1 1 1 1 1 1 4 4 1 1 1
## 11446 11447 11448 11449 11450 11451 11452 11454 11456 11457 11459 11460 11461
## 1 1 1 4 1 1 1 1 1 1 1 5 1
## 11462 11464 11465 11466 11467 11468 11470 11472 11474 11475 11476 11477 11478
## 1 1 3 1 5 1 1 1 5 5 4 4 2
## 11479 11481 11482 11483 11484 11485 11487 11488 11489 11490 11491 11494 11495
## 1 5 3 4 1 5 1 1 1 1 1 1 5
## 11496 11497 11498 11499 11500 11501 11502 11503 11504 11505 11506 11507 11508
## 4 1 1 1 1 1 1 1 1 1 1 1 1
## 11509 11510 11512 11513 11514 11515 11516 11517 11518 11519 11520 11521 11522
## 2 5 3 1 1 3 1 1 1 1 1 1 1
## 11523 11524 11526 11527 11528 11529 11530 11531 11533 11534 11535 11536 11537
## 1 1 1 4 1 1 4 4 1 5 4 1 5
## 11538 11539 11540 11541 11543 11544 11545 11547 11548 11551 11552 11553 11554
## 1 1 1 1 1 4 3 1 4 1 1 1 2
## 11555 11556 11558 11559 11560 11562 11563 11564 11565 11566 11567 11568 11569
## 1 1 5 1 1 1 1 5 1 1 4 1 1
## 11572 11573 11574 11575 11576 11578 11579 11580 11581 11584 11585 11586 11587
## 5 1 4 3 1 1 3 1 1 1 5 1 1
## 11588 11589 11590 11591 11592 11593 11597 11599 11600 11601 11602 11604 11606
## 1 5 5 2 2 3 2 1 1 1 5 1 1
## 11608 11609 11610 11612 11613 11614 11615 11616 11617 11619 11620 11621 11622
## 1 1 1 1 1 1 1 1 1 1 4 1 1
## 11623 11624 11625 11626 11629 11631 11632 11633 11634 11636 11638 11639 11640
## 4 1 1 1 1 2 1 1 1 1 1 1 4
## 11641 11642 11643 11645 11646 11647 11648 11649 11650 11651 11652 11653 11655
## 1 1 1 1 5 1 1 1 1 1 1 4 1
## 11657 11658 11660 11661 11662 11663 11666 11668 11670 11671 11672 11673 11674
## 1 1 1 1 1 1 1 1 1 1 1 1 5
## 11675 11677 11678 11679 11680 11681 11682 11683 11684 11685 11686 11687 11688
## 1 1 1 1 1 1 1 1 1 4 1 1 1
## 11689 11690 11691 11692 11693 11694 11695 11698 11699 11700 11701 11702 11703
## 1 1 1 1 1 1 4 1 1 1 3 1 4
## 11704 11705 11707 11708 11709 11711 11712 11714 11715 11716 11717 11718 11719
## 1 1 1 1 1 4 5 4 4 1 1 1 5
## 11720 11721 11722 11723 11724 11726 11727 11730 11731 11732 11733 11735 11736
## 1 1 1 1 4 1 4 5 1 1 1 4 1
## 11737 11738 11739 11740 11742 11743 11744 11745 11746 11747 11748 11751 11753
## 1 5 1 4 1 1 4 4 1 1 5 1 4
## 11754 11755 11756 11757 11758 11759 11760 11761 11762 11763 11765 11766 11767
## 4 4 5 1 3 1 1 5 1 4 1 1 1
## 11768 11770 11771 11772 11773 11774 11775 11776 11777 11778 11779 11780 11781
## 1 1 5 1 1 5 3 1 5 1 5 1 1
## 11782 11784 11785 11786 11787 11789 11791 11792 11793 11794 11795 11796 11797
## 1 1 1 1 1 1 1 5 1 3 1 1 2
## 11799 11800 11801 11802 11803 11804 11805 11806 11807 11808 11809 11811 11812
## 1 1 5 1 4 1 1 1 1 1 1 4 1
## 11814 11815 11816 11817 11818 11819 11820 11821 11823 11824 11825 11829 11830
## 1 4 1 4 1 1 1 1 3 1 1 2 1
## 11831 11832 11833 11835 11836 11837 11840 11842 11843 11844 11845 11846 11847
## 1 1 1 1 1 1 1 3 1 1 4 1 1
## 11848 11849 11850 11851 11853 11855 11856 11857 11858 11859 11860 11861 11862
## 1 4 1 1 1 1 1 1 1 5 1 1 1
## 11863 11864 11865 11866 11867 11868 11870 11871 11872 11873 11874 11875 11876
## 1 1 1 1 1 1 1 1 1 3 1 1 1
## 11879 11880 11881 11882 11884 11885 11886 11887 11888 11891 11893 11894 11896
## 1 1 1 5 1 1 1 1 1 1 1 1 1
## 11897 11898 11899 11900 11902 11903 11904 11906 11907 11908 11910 11911 11912
## 1 5 1 1 4 1 1 1 4 1 1 1 3
## 11913 11914 11915 11916 11919 11920 11922 11923 11924 11925 11926 11927 11928
## 5 1 4 1 1 1 1 1 1 1 1 1 1
## 11930 11933 11934 11935 11936 11937 11938 11940 11941 11942 11943 11944 11945
## 1 3 3 1 1 5 1 5 1 1 1 1 1
## 11946 11947 11948 11949 11952 11953 11954 11955 11957 11959 11960 11964 11965
## 4 1 1 1 1 1 1 1 1 1 1 1 1
## 11966 11967 11968 11969 11970 11971 11972 11973 11975 11978 11979 11980 11981
## 1 1 1 4 1 1 5 1 1 1 1 1 1
## 11982 11983 11984 11985 11986 11987 11988 11989 11990 11991 11992 11993 11994
## 1 1 1 1 1 1 1 4 1 1 1 4 4
## 11996 11997 11998 11999 12003 12004 12005 12007 12008 12010 12012 12014 12016
## 1 1 1 1 1 1 3 4 1 1 1 4 1
## 12017 12018 12019 12020 12021 12022 12023 12024 12026 12028 12029 12030 12031
## 1 3 4 1 5 1 1 5 1 1 1 1 1
## 12032 12033 12034 12035 12036 12037 12038 12039 12040 12041 12042 12043 12045
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 12046 12047 12048 12049 12052 12053 12054 12056 12057 12058 12059 12060 12061
## 5 1 4 1 1 2 1 1 4 1 2 1 1
## 12062 12063 12065 12066 12067 12068 12070 12071 12072 12076 12077 12078 12079
## 1 1 1 1 1 1 1 5 1 1 5 5 1
## 12080 12081 12083 12084 12085 12087 12089 12090 12092 12093 12097 12098 12099
## 4 1 4 1 1 5 1 1 4 1 1 5 1
## 12100 12101 12102 12103 12105 12106 12107 12108 12109 12110 12111 12112 12113
## 1 4 5 1 5 1 3 1 1 2 1 4 4
## 12114 12115 12116 12117 12118 12119 12120 12121 12122 12123 12124 12125 12126
## 1 1 5 1 1 1 1 1 1 1 1 1 1
## 12127 12129 12131 12132 12133 12134 12136 12137 12138 12140 12141 12142 12143
## 1 1 1 1 1 1 1 1 1 1 1 1 4
## 12144 12145 12146 12147 12148 12149 12151 12154 12156 12157 12158 12159 12160
## 1 1 1 1 3 1 1 1 1 1 1 4 1
## 12161 12162 12163 12165 12166 12168 12169 12170 12171 12174 12177 12179 12182
## 1 2 1 1 1 1 1 2 5 1 1 1 1
## 12183 12184 12185 12188 12189 12190 12191 12192 12194 12198 12199 12202 12205
## 1 2 4 1 5 1 1 5 2 1 5 1 1
## 12207 12208 12210 12211 12212 12213 12214 12215 12216 12217 12218 12219 12220
## 1 5 1 1 1 1 5 1 1 5 1 1 1
## 12221 12223 12224 12225 12226 12227 12228 12229 12230 12231 12232 12233 12234
## 1 1 3 1 2 1 1 5 1 1 3 1 1
## 12235 12236 12237 12239 12240 12241 12242 12243 12244 12245 12246 12247 12249
## 2 1 1 5 5 1 1 5 5 1 1 1 1
## 12250 12251 12252 12253 12254 12255 12256 12258 12260 12261 12262 12263 12264
## 3 4 1 1 1 3 1 2 1 5 1 5 1
## 12265 12266 12267 12268 12269 12270 12271 12272 12273 12275 12276 12277 12278
## 3 1 1 3 1 1 5 1 1 1 1 1 5
## 12279 12280 12281 12282 12284 12285 12286 12288 12289 12290 12292 12293 12295
## 1 1 1 1 1 4 4 1 3 1 3 4 1
## 12297 12298 12299 12300 12301 12302 12303 12304 12305 12306 12307 12309 12310
## 4 1 4 5 2 1 1 1 1 4 1 1 1
## 12311 12312 12313 12314 12315 12316 12317 12318 12319 12321 12322 12323 12324
## 5 1 1 1 1 1 1 1 5 5 1 1 1
## 12325 12326 12327 12328 12329 12330 12331 12332 12333 12334 12335 12337 12338
## 4 3 1 1 1 1 1 1 1 1 1 1 5
## 12339 12340 12341 12342 12343 12344 12345 12346 12347 12348 12349 12350 12351
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## 12366 12367 12368 12369 12370 12372 12373 12374 12376 12377 12378 12379 12380
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## 12381 12382 12383 12384 12385 12386 12387 12390 12391 12392 12394 12395 12396
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## 12397 12398 12399 12400 12401 12402 12404 12405 12407 12408 12409 12410 12411
## 1 1 1 1 4 1 1 1 1 1 1 1 1
## 12412 12413 12414 12415 12416 12417 12418 12420 12421 12423 12424 12425 12426
## 1 1 1 1 1 1 5 1 1 1 1 5 5
## 12428 12431 12433 12434 12436 12437 12438 12440 12441 12442 12443 12444 12445
## 1 3 1 4 1 1 1 1 1 1 1 1 4
## 12446 12448 12449 12450 12452 12453 12454 12455 12458 12459 12460 12461 12462
## 1 1 2 1 1 4 3 1 4 4 1 1 1
## 12463 12465 12466 12467 12468 12469 12470 12471 12472 12473 12474 12475 12476
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## 12477 12478 12479 12480 12481 12482 12483 12485 12486 12487 12488 12489 12490
## 1 1 1 1 1 1 5 3 1 5 1 1 1
## 12491 12492 12493 12494 12495 12496 12498 12500 12502 12503 12504 12505 12506
## 1 1 1 1 1 1 1 1 4 1 2 4 1
## 12507 12508 12509 12510 12511 12512 12515 12516 12519 12520 12521 12522 12523
## 1 4 1 4 1 1 1 1 1 1 1 1 1
## 12525 12526 12527 12528 12529 12530 12531 12532 12533 12534 12537 12538 12539
## 1 1 1 4 1 3 4 1 1 1 1 1 1
## 12541 12542 12544 12546 12547 12548 12550 12551 12552 12553 12554 12555 12556
## 4 4 1 5 1 1 1 4 1 1 1 1 3
## 12557 12558 12559 12560 12561 12562 12563 12564 12565 12568 12570 12571 12572
## 1 1 1 1 4 1 1 1 1 5 4 1 5
## 12574 12575 12576 12577 12578 12579 12580 12581 12582 12583 12585 12587 12588
## 1 1 5 1 4 3 1 3 1 1 1 2 1
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## 12604 12605 12607 12608 12609 12610 12611 12612 12613 12614 12615 12616 12617
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## 12618 12619 12622 12623 12624 12625 12627 12629 12630 12631 12632 12633 12634
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## 12695 12696 12698 12700 12701 12702 12703 12704 12705 12706 12707 12708 12710
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## 12923 12924 12926 12927 12928 12929 12930 12931 12932 12934 12935 12937 12939
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## 12974 12975 12977 12978 12980 12981 12982 12983 12987 12988 12989 12990 12992
## 1 1 1 5 1 1 1 1 1 1 1 1 1
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## 1 1 5 1 4 1 1 1 1 1 1 1 1
## 13012 13013 13014 13015 13017 13018 13019 13020 13021 13022 13024 13025 13026
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## 13027 13028 13029 13030 13031 13032 13033 13034 13035 13036 13038 13040 13041
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## 13042 13043 13044 13046 13047 13048 13049 13050 13051 13053 13054 13055 13056
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## 13057 13058 13059 13060 13061 13062 13065 13066 13067 13068 13069 13070 13071
## 1 1 1 5 1 1 1 4 1 1 1 1 1
## 13073 13074 13075 13076 13078 13079 13080 13081 13082 13083 13084 13085 13086
## 1 4 1 1 4 1 1 1 1 1 1 1 1
## 13087 13088 13089 13090 13091 13092 13093 13094 13095 13096 13097 13098 13099
## 1 1 1 1 4 1 1 5 2 1 1 1 1
## 13100 13101 13102 13104 13107 13108 13110 13112 13113 13114 13115 13116 13117
## 1 1 4 4 1 5 1 1 4 1 1 1 4
## 13118 13119 13121 13122 13124 13125 13126 13127 13128 13129 13130 13131 13132
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## 13165 13167 13168 13169 13170 13172 13173 13174 13175 13176 13177 13178 13179
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## 13196 13198 13200 13201 13203 13204 13205 13207 13208 13209 13212 13214 13215
## 4 1 1 1 4 1 1 1 1 1 1 1 1
## 13216 13218 13219 13220 13222 13223 13224 13226 13227 13228 13229 13230 13233
## 1 1 1 4 5 5 1 1 5 1 1 1 1
## 13234 13235 13236 13237 13238 13239 13240 13241 13242 13243 13244 13245 13246
## 1 1 1 1 1 1 1 2 1 1 1 3 1
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## 1 1 1 1 1 3 1 1 1 1 1 1 1
## 13264 13265 13266 13268 13269 13270 13271 13272 13273 13274 13275 13276 13277
## 1 1 4 1 1 5 1 1 1 4 1 1 1
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## 1 1 1 5 1 1 1 1 3 1 5 1 1
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## 1 5 1 1 1 1 1 1 3 1 1 1 1
## 13309 13310 13311 13312 13313 13315 13316 13317 13318 13319 13320 13321 13322
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## 13323 13325 13326 13327 13328 13329 13330 13331 13332 13333 13334 13335 13336
## 1 1 1 1 1 5 1 5 4 1 1 1 1
## 13337 13338 13339 13340 13341 13342 13343 13345 13348 13349 13352 13353 13354
## 1 1 4 1 1 1 1 1 5 1 5 2 4
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## 1 4 4 5 1 1 1 3 1 1 4 1 1
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## 13404 13405 13407 13409 13410 13411 13412 13413 13414 13415 13417 13419 13420
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## 1 1 2 1 4 4 1 1 5 1 1 1 1
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## 2 1 1 1 1 1 1 1 1 1 1 1 1
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## 1 1 5 1 3 1 4 1 1 1 1 1 1
## 13920 13921 13922 13923 13924 13925 13926 13927 13929 13930 13931 13932 13933
## 1 1 1 1 1 5 1 1 1 1 1 1 1
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## 1 1 1 1 1 1 4 4 2 5 1 1 1
## 13950 13951 13952 13953 13954 13955 13956 13958 13959 13960 13961 13962 13963
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## 1 5 1 1 1 1 1 1 1 1 1 1 1
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## 1 4 1 1 1 1 1 1 5 1 1 4 1
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## 1 1 1 2 1 1 1 1 1 5 1 1 1
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## 5 2 1 1 1 1 1 1 4 4 4 1 1
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## 1 5 1 5 1 4 1 1 5 1 1 1 1
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## 4 4 1 1 1 1 1 1 1 3 4 1 1
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## 5 1 1 5 1 5 1 1 1 1 1 1 1
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## 5 1 1 1 1 1 1 5 1 1 1 1 1
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## 1 4 1 1 1 1 1 1 1 1 1 1 4
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## 1 1 1 1 1 1 1 1 1 1 1 1 4
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## 1 1 1 5 5 1 5 4 1 1 1 1 1
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## 14450 14451 14452 14453 14454 14456 14458 14459 14462 14464 14466 14467 14468
## 5 1 1 1 5 2 1 1 1 1 1 1 1
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## 1 4 1 1 1 4 1 1 3 1 1 1 1
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## 1 1 1 1 1 1 1 1 1 5 1 1 1
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## 1 1 3 1 5 1 1 5 1 5 1 3 1
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## 1 5 5 2 1 1 5 1 5 1 1 5 5
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## 1 1 1 1 1 1 1 1 1 1 1 1 1
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## 1 1 1 5 1 1 1 1 1 1 1 1 1
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## 1 1 1 5 5 1 1 4 1 1 1 1 5
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## 1 1 1 1 5 1 1 1 1 1 1 1 1
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## 5 1 5 1 1 1 1 1 1 1 1 1 1
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## 1 1 5 5 1 5 1 4 1 4 1 1 1
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## 1 1 5 5 1 1 1 1 1 5 1 1 5
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## 1 1 1 5 5 5 1 1 1 1 4 1 1
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## 4 1 1 1 1 1 1 1 1 1 1 1 5
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## 5 5 5 5 1 3 1 1 1 1 1 1 5
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## 1 1 1 1 1 1 5 1 1 1 1 1 1
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## 5 1 1 4 5 1 4 5 3 1 1 1 1
## 14854 14855 14856 14859 14860 14861 14862 14863 14864 14865 14866 14867 14868
## 1 1 1 1 1 1 1 1 3 1 1 1 1
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## 1 4 1 1 5 1 1 1 1 1 1 1 1
## 14885 14886 14888 14889 14890 14892 14893 14894 14895 14896 14897 14898 14899
## 1 4 1 1 1 1 1 1 1 1 1 1 1
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## 1 1 1 5 4 4 1 1 1 3 1 1 1
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## 1 4 1 1 1 1 5 1 1 1 4 1 1
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## 1 1 1 1 1 1 1 1 4 5 1 1 1
## 14949 14951 14952 14953 14954 14956 14958 14959 14960 14961 14962 14963 14964
## 4 1 5 4 1 3 5 1 4 4 4 1 1
## 14965 14966 14967 14968 14969 14971 14972 14973 14974 14975 14976 14977 14978
## 5 1 4 5 1 1 1 1 1 1 3 1 1
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## 1 1 1 2 1 1 1 1 1 1 1 4 3
## 14996 14997 14998 14999 15000 15002 15004 15005 15006 15007 15008 15009 15012
## 1 1 1 2 1 1 1 5 1 1 1 1 1
## 15013 15014 15016 15017 15019 15020 15021 15022 15023 15027 15029 15030 15032
## 1 1 3 1 4 1 3 4 1 4 5 5 5
## 15035 15036 15037 15038 15041 15042 15043 15044 15045 15048 15049 15050 15051
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 15052 15053 15055 15056 15058 15060 15062 15063 15064 15065 15068 15069 15070
## 1 5 1 5 1 1 2 1 1 5 1 4 5
## 15071 15072 15074 15075 15076 15077 15078 15079 15080 15081 15082 15083 15084
## 1 4 4 4 3 5 1 4 1 1 5 1 3
## 15085 15086 15087 15088 15089 15090 15091 15092 15094 15095 15096 15097 15098
## 1 3 1 1 1 1 3 1 1 1 1 1 1
## 15099 15101 15102 15103 15104 15105 15106 15107 15108 15109 15110 15111 15112
## 5 4 5 5 1 4 1 1 1 1 1 1 1
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## 5 5 4 5 4 1 1 1 1 3 1 1 4
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## 1 5 1 3 1 1 3 1 1 5 5 1 1
## 15146 15147 15149 15150 15152 15153 15154 15155 15156 15157 15158 15159 15160
## 1 1 1 1 5 5 1 5 5 1 1 1 1
## 15161 15162 15163 15164 15166 15167 15168 15169 15170 15171 15173 15174 15175
## 1 3 2 1 1 1 1 4 1 1 4 1 1
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## 3 1 1 1 5 1 4 1 1 1 5 1 2
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## 1 1 1 1 1 2 1 1 1 1 1 1 4
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## 1 4 1 2 1 1 2 1 5 1 1 5 1
## 15231 15232 15233 15234 15235 15236 15237 15238 15239 15240 15241 15242 15243
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## 21115 21116 21119 21121 21122 21123 21124 21125 21126 21129 21130 21131 21132
## 1 5 1 1 5 4 5 1 5 1 1 1 4
## 21135 21136 21137 21138 21141 21142 21143 21145 21147 21148 21149 21150 21151
## 5 5 1 3 2 1 1 1 1 1 1 5 5
## 21152 21153 21156 21157 21159 21160 21162 21165 21166 21167 21168 21170 21172
## 1 5 1 4 4 1 1 1 1 1 1 1 4
## 21173 21174 21176 21177 21178 21180 21181 21183 21185 21186 21188 21189 21190
## 1 4 1 1 1 4 1 1 4 4 5 2 5
## 21191 21192 21193 21194 21195 21196 21197 21198 21199 21200 21201 21202 21203
## 4 3 1 1 1 4 1 1 1 5 4 1 1
## 21204 21205 21207 21208 21209 21210 21211 21212 21213 21214 21215 21216 21217
## 1 1 1 1 1 4 1 5 1 1 1 1 1
## 21219 21222 21223 21224 21225 21226 21228 21229 21230 21231 21232 21233 21234
## 2 4 1 1 1 4 1 1 1 1 1 1 1
## 21235 21236 21237 21238 21239 21241 21242 21243 21245 21246 21248 21249 21250
## 1 1 1 4 1 1 1 1 2 1 1 5 1
## 21251 21253 21254 21255 21256 21258 21259 21260 21261 21262 21263 21264 21265
## 1 4 5 1 1 5 1 4 2 1 4 1 1
## 21267 21268 21270 21271 21272 21273 21274 21275 21276 21277 21278 21280 21281
## 1 5 5 1 1 1 4 1 1 1 1 4 1
## 21283 21284 21285 21286 21287 21288 21289 21290 21291 21292 21293 21294 21295
## 1 2 3 4 3 1 1 1 1 1 1 1 1
## 21296 21297 21298 21299 21301 21302 21303 21306 21307 21308 21309 21311 21312
## 1 3 1 1 1 1 2 1 1 4 1 1 1
## 21313 21314 21315 21316 21317 21318 21319 21322 21324 21326 21327 21328 21329
## 1 1 4 1 3 1 1 1 5 1 1 1 1
## 21330 21331 21332 21334 21335 21338 21339 21340 21341 21343 21345 21347 21348
## 4 4 3 4 1 1 1 1 1 4 4 5 3
## 21349 21350 21351 21353 21355 21356 21357 21358 21359 21360 21361 21362 21363
## 1 4 1 1 1 1 1 1 1 1 4 1 1
## 21364 21365 21366 21367 21368 21370 21372 21374 21375 21377 21378 21379 21381
## 1 1 1 1 1 1 1 5 1 5 5 1 1
## 21382 21383 21385 21386 21387 21388 21389 21390 21391 21392 21394 21395 21396
## 1 1 1 5 1 1 1 5 1 5 1 1 1
## 21397 21401 21402 21403 21404 21407 21408 21409 21410 21411 21412 21413 21415
## 1 1 4 5 4 1 1 1 1 1 1 5 1
## 21416 21417 21419 21420 21421 21424 21425 21426 21428 21429 21430 21431 21432
## 4 1 1 5 4 1 4 1 1 1 1 1 1
## 21433 21434 21435 21436 21437 21438 21439 21440 21441 21442 21443 21444 21445
## 1 1 1 1 1 1 1 1 1 4 1 1 1
## 21446 21448 21449 21450 21451 21452 21453 21454 21456 21457 21458 21459 21460
## 1 1 1 4 1 1 1 1 1 5 1 5 1
## 21462 21463 21464 21465 21466 21467 21468 21469 21470 21471 21472 21473 21474
## 5 4 1 1 1 4 4 4 1 1 4 1 1
## 21475 21476 21477 21478 21480 21482 21484 21485 21486 21487 21488 21489 21491
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 21492 21494 21495 21496 21497 21498 21499 21500 21501 21502 21504 21505 21509
## 1 1 1 2 1 4 1 1 1 1 1 5 1
## 21510 21511 21512 21514 21515 21516 21517 21521 21522 21523 21524 21525 21526
## 1 1 4 4 1 1 1 1 5 1 1 1 3
## 21527 21528 21529 21531 21532 21533 21534 21535 21536 21539 21541 21542 21543
## 1 1 1 5 1 1 3 2 1 1 2 4 1
## 21544 21545 21546 21547 21548 21549 21550 21551 21552 21553 21554 21555 21556
## 1 4 1 1 1 5 1 5 4 4 1 1 4
## 21557 21558 21559 21560 21561 21562 21564 21566 21567 21569 21572 21573 21574
## 4 1 5 1 1 2 1 1 1 1 1 1 5
## 21577 21579 21580 21581 21582 21584 21585 21586 21587 21588 21589 21590 21591
## 1 1 1 1 1 1 4 5 1 1 1 5 4
## 21592 21593 21594 21595 21596 21597 21598 21599 21600 21601 21602 21604 21605
## 2 3 1 5 1 4 4 1 4 1 1 1 1
## 21606 21607 21608 21609 21610 21611 21612 21613 21614 21615 21616 21621 21622
## 1 1 1 4 1 1 1 1 1 1 1 1 4
## 21623 21624 21626 21627 21628 21629 21630 21631 21632 21633 21635 21636 21637
## 2 4 3 1 1 4 1 1 1 1 1 1 1
## 21638 21639 21640 21641 21642 21643 21644 21645 21646 21649 21652 21653 21654
## 1 1 1 1 4 1 1 3 4 1 1 5 1
## 21655 21659 21660 21661 21663 21664 21665 21666 21667 21668 21669 21672 21673
## 5 1 1 3 1 1 5 5 1 3 4 1 4
## 21674 21675 21678 21679 21681 21682 21685 21687 21688 21689 21691 21693 21695
## 1 1 1 5 1 4 1 1 1 1 1 1 1
## 21696 21697 21698 21699 21701 21702 21705 21706 21707 21708 21709 21710 21711
## 3 1 1 1 1 1 1 4 1 2 5 1 5
## 21712 21713 21714 21715 21717 21719 21721 21722 21723 21726 21728 21729 21730
## 1 1 1 4 1 1 5 5 1 1 4 1 1
## 21731 21732 21733 21736 21737 21738 21739 21740 21741 21742 21744 21749 21750
## 5 1 5 1 1 1 1 4 1 1 5 5 4
## 21751 21752 21754 21755 21756 21757 21758 21759 21760 21761 21762 21763 21765
## 1 4 1 1 1 4 4 1 1 4 1 1 1
## 21766 21768 21770 21771 21774 21775 21776 21780 21782 21784 21785 21786 21788
## 1 4 5 1 5 1 1 1 1 1 1 1 5
## 21789 21790 21793 21795 21797 21798 21800 21803 21804 21805 21807 21809 21810
## 1 1 1 4 1 5 5 1 1 1 1 1 1
## 21811 21812 21813 21814 21816 21817 21818 21819 21820 21821 21822 21823 21825
## 1 1 1 1 1 1 1 4 1 5 1 1 1
## 21826 21827 21828 21829 21830 21831 21832 21833 21834 21835 21836 21837 21838
## 1 1 1 1 1 1 4 3 1 1 1 5 1
## 21840 21841 21843 21844 21846 21847 21848 21849 21850 21851 21852 21854 21856
## 1 1 5 1 1 5 1 1 1 1 1 1 1
## 21857 21859 21860 21862 21865 21866 21867 21869 21870 21871 21872 21873 21874
## 4 5 1 1 1 2 1 1 1 1 5 3 1
## 21875 21876 21877 21879 21880 21881 21882 21883 21884 21885 21886 21887 21888
## 5 1 1 5 1 1 1 1 1 4 5 1 1
## 21889 21892 21893 21894 21895 21896 21899 21900 21903 21904 21908 21909 21910
## 1 1 1 1 1 1 1 1 3 5 5 5 3
## 21911 21913 21916 21918 21919 21920 21921 21922 21923 21924 21925 21926 21927
## 4 1 1 1 5 1 5 1 5 4 1 1 1
## 21928 21929 21930 21931 21932 21933 21934 21937 21939 21940 21941 21942 21944
## 5 1 1 1 5 1 1 1 1 1 3 1 5
## 21945 21946 21947 21948 21950 21951 21952 21953 21954 21955 21956 21957 21958
## 4 2 1 3 1 5 4 1 1 5 1 1 5
## 21959 21962 21963 21964 21966 21967 21968 21971 21972 21973 21974 21976 21977
## 1 1 1 1 5 1 4 1 5 1 1 4 5
## 21978 21980 21981 21982 21983 21984 21985 21986 21987 21988 21989 21990 21991
## 5 3 5 5 1 1 1 1 1 1 5 1 1
## 21992 21993 21994 21996 21997 21999 22000 22001 22002 22003 22004 22005 22006
## 1 1 1 5 1 1 1 1 5 1 1 1 4
## 22007 22008 22010 22012 22013 22014 22015 22016 22017 22020 22021 22022 22023
## 5 5 1 4 1 5 1 3 1 5 1 5 1
## 22024 22025 22026 22027 22030 22031 22032 22033 22035 22036 22037 22038 22044
## 1 4 1 4 1 1 1 1 1 5 1 1 4
## 22045 22046 22049 22051 22052 22053 22054 22055 22056 22057 22058 22059 22060
## 1 1 5 3 1 1 5 1 2 5 1 5 1
## 22061 22062 22063 22064 22065 22067 22068 22070 22071 22072 22073 22074 22075
## 1 1 1 1 3 5 1 1 5 4 1 5 5
## 22076 22078 22079 22082 22083 22084 22085 22086 22087 22088 22089 22090 22091
## 1 1 1 1 4 1 4 5 1 1 4 1 5
## 22092 22093 22094 22095 22096 22098 22099 22100 22102 22103 22104 22105 22106
## 5 4 1 1 1 1 5 1 1 4 5 1 1
## 22107 22108 22109 22110 22111 22113 22114 22116 22117 22119 22120 22121 22122
## 5 1 5 1 1 3 3 4 5 5 5 1 1
## 22123 22124 22125 22126 22127 22128 22129 22130 22132 22133 22134 22135 22136
## 1 1 1 1 1 4 5 1 1 5 1 1 4
## 22137 22140 22141 22142 22143 22144 22146 22147 22150 22152 22153 22154 22155
## 1 1 5 5 4 1 3 4 1 1 1 5 5
## 22156 22157 22158 22159 22160 22161 22163 22164 22167 22169 22171 22172 22175
## 1 1 4 1 1 1 1 1 1 4 1 1 1
## 22178 22179 22180 22182 22183 22184 22185 22186 22187 22189 22190 22191 22192
## 1 1 1 1 1 1 5 4 1 5 1 1 1
## 22193 22195 22196 22197 22198 22199 22200 22201 22202 22204 22205 22206 22207
## 5 1 1 5 1 1 1 1 1 1 1 1 1
## 22208 22209 22210 22211 22212 22213 22214 22216 22218 22219 22220 22221 22222
## 1 1 1 5 2 1 5 1 1 5 1 1 1
## 22223 22224 22225 22226 22227 22228 22229 22230 22232 22233 22234 22235 22236
## 1 1 1 1 1 1 1 5 3 1 1 1 1
## 22237 22239 22240 22242 22244 22245 22247 22248 22249 22250 22251 22252 22254
## 1 1 1 1 4 1 1 1 1 5 1 5 1
## 22255 22256 22257 22258 22259 22260 22262 22265 22266 22267 22268 22269 22270
## 1 1 2 1 1 4 1 5 5 1 1 1 5
## 22272 22275 22277 22278 22279 22280 22281 22282 22283 22284 22286 22287 22288
## 1 5 3 1 5 1 1 1 4 1 1 2 3
## 22291 22292 22293 22295 22296 22297 22298 22299 22300 22301 22302 22303 22304
## 4 2 4 1 1 1 1 1 5 1 2 1 1
## 22305 22306 22307 22308 22309 22310 22311 22312 22314 22317 22318 22319 22320
## 1 1 1 1 1 1 1 3 1 3 5 1 1
## 22322 22323 22324 22325 22326 22327 22329 22330 22331 22332 22333 22335 22336
## 1 5 1 1 1 1 1 1 1 3 3 4 5
## 22337 22338 22339 22340 22341 22342 22343 22344 22345 22347 22348 22349 22350
## 5 1 1 1 5 1 1 1 1 5 1 1 4
## 22352 22353 22354 22356 22358 22359 22361 22364 22365 22366 22367 22368 22369
## 1 1 1 3 5 1 3 1 5 1 4 1 4
## 22370 22371 22373 22374 22375 22376 22378 22379 22380 22381 22382 22383 22384
## 1 1 1 1 5 1 1 1 1 1 1 1 5
## 22387 22388 22389 22391 22393 22394 22395 22396 22397 22398 22400 22401 22402
## 1 1 5 1 1 1 1 1 1 1 1 1 1
## 22403 22404 22405 22406 22407 22408 22409 22410 22411 22415 22416 22417 22418
## 1 1 1 3 1 1 1 4 1 1 1 3 1
## 22420 22421 22422 22423 22424 22425 22426 22427 22428 22429 22430 22434 22436
## 1 1 1 1 4 1 1 4 1 4 3 1 1
## 22437 22438 22439 22440 22441 22442 22443 22444 22445 22446 22449 22450 22451
## 4 1 4 4 1 1 1 1 5 1 1 1 1
## 22452 22453 22455 22456 22457 22458 22459 22461 22462 22463 22464 22466 22467
## 5 1 1 1 1 1 1 2 5 1 1 1 1
## 22468 22469 22470 22471 22472 22474 22476 22477 22478 22479 22480 22481 22482
## 1 5 5 1 5 1 1 1 1 4 1 1 5
## 22483 22484 22485 22486 22487 22488 22489 22490 22491 22493 22494 22496 22498
## 5 4 1 1 1 1 1 4 3 3 1 1 1
## 22500 22502 22504 22506 22507 22508 22509 22510 22511 22512 22513 22515 22517
## 1 1 1 1 4 1 1 1 1 5 1 5 5
## 22518 22519 22521 22522 22523 22524 22525 22526 22529 22530 22531 22532 22533
## 1 5 3 5 5 5 5 5 1 3 1 3 1
## 22534 22535 22536 22537 22538 22539 22540 22541 22542 22543 22545 22547 22550
## 1 1 1 1 1 1 1 4 1 4 1 5 1
## 22551 22552 22553 22554 22555 22556 22561 22562 22563 22564 22565 22567 22569
## 1 1 5 1 1 5 1 1 1 4 5 4 4
## 22570 22571 22572 22573 22574 22575 22577 22578 22580 22581 22582 22583 22585
## 1 4 4 5 1 1 1 1 3 4 1 5 1
## 22586 22587 22588 22589 22592 22593 22594 22595 22596 22597 22599 22600 22601
## 1 1 1 4 1 5 4 1 1 1 1 5 1
## 22602 22603 22604 22605 22606 22607 22608 22612 22613 22614 22615 22616 22617
## 5 1 3 1 1 1 1 1 5 5 1 1 4
## 22619 22620 22621 22624 22625 22626 22628 22631 22632 22634 22635 22636 22637
## 5 4 1 1 1 1 4 1 1 1 1 1 1
## 22638 22640 22641 22642 22643 22644 22645 22646 22647 22648 22650 22651 22652
## 1 1 1 1 1 5 4 1 1 5 4 1 1
## 22653 22654 22656 22657 22658 22660 22664 22665 22666 22670 22671 22672 22673
## 1 1 1 1 1 4 4 5 1 4 1 5 4
## 22674 22675 22676 22677 22678 22679 22680 22681 22682 22683 22684 22685 22686
## 1 1 1 5 4 1 1 4 2 1 1 3 3
## 22687 22688 22691 22692 22693 22695 22697 22699 22701 22703 22706 22707 22708
## 1 1 5 5 1 1 1 1 1 2 1 5 5
## 22710 22711 22713 22714 22716 22717 22720 22721 22722 22723 22724 22725 22726
## 1 1 1 1 5 2 1 1 1 1 1 1 1
## 22727 22728 22729 22730 22731 22732 22733 22734 22736 22738 22739 22740 22742
## 1 2 1 3 1 1 1 1 4 2 1 1 1
## 22743 22744 22746 22747 22748 22749 22750 22751 22752 22753 22754 22755 22757
## 1 1 1 4 1 1 1 1 1 1 1 4 1
## 22758 22759 22760 22761 22762 22763 22767 22768 22769 22771 22772 22773 22774
## 4 1 1 1 1 5 1 5 4 1 5 1 1
## 22775 22776 22777 22778 22779 22780 22781 22782 22783 22784 22785 22787 22788
## 4 1 1 3 5 4 4 1 3 1 1 1 4
## 22789 22791 22792 22793 22794 22795 22796 22797 22798 22799 22800 22801 22802
## 1 5 1 1 1 1 1 1 1 1 1 1 1
## 22803 22804 22805 22806 22807 22808 22809 22812 22813 22814 22815 22816 22818
## 1 1 4 1 1 1 1 1 5 1 1 1 1
## 22819 22820 22821 22823 22824 22825 22826 22827 22828 22830 22832 22833 22834
## 1 1 1 4 1 1 1 1 4 1 1 1 5
## 22835 22836 22838 22839 22840 22841 22842 22843 22844 22845 22846 22848 22849
## 1 5 4 1 1 1 1 1 4 1 1 1 5
## 22850 22851 22852 22853 22854 22855 22861 22862 22863 22864 22865 22866 22867
## 1 1 1 1 5 1 1 1 3 1 4 1 1
## 22868 22870 22871 22872 22873 22874 22875 22877 22878 22879 22880 22882 22883
## 5 1 5 4 1 1 1 1 1 1 1 4 5
## 22884 22885 22886 22887 22888 22889 22890 22891 22892 22894 22895 22896 22897
## 1 1 1 1 1 1 4 1 5 1 1 1 5
## 22898 22899 22900 22901 22902 22903 22904 22905 22906 22908 22909 22911 22912
## 4 1 4 1 4 5 2 1 1 4 1 1 5
## 22913 22914 22915 22916 22917 22918 22919 22920 22921 22923 22924 22927 22929
## 1 1 4 4 1 3 1 1 1 4 1 4 5
## 22930 22931 22932 22933 22934 22935 22936 22938 22939 22941 22942 22943 22944
## 5 1 4 5 1 1 1 1 4 5 1 3 1
## 22945 22946 22948 22949 22950 22951 22952 22953 22956 22957 22958 22959 22960
## 4 1 1 1 4 1 1 1 1 1 1 1 5
## 22961 22962 22965 22966 22967 22968 22969 22970 22971 22973 22974 22975 22977
## 1 1 2 2 1 5 1 1 1 2 1 4 1
## 22978 22979 22980 22981 22982 22984 22985 22988 22989 22990 22991 22992 22993
## 4 4 4 4 4 4 4 1 1 4 4 5 1
## 22994 22995 22996 22998 23000 23001 23003 23004 23006 23007 23008 23009 23010
## 1 1 1 5 1 4 1 1 1 1 1 5 1
## 23012 23014 23015 23017 23018 23019 23020 23021 23023 23024 23025 23026 23028
## 4 4 4 4 1 1 1 1 1 2 5 1 1
## 23029 23030 23031 23032 23033 23034 23036 23037 23039 23041 23042 23043 23044
## 3 5 1 5 1 1 1 5 1 1 4 1 2
## 23049 23050 23051 23052 23054 23055 23056 23057 23059 23060 23062 23063 23065
## 4 1 5 1 1 3 1 1 1 1 1 1 4
## 23066 23067 23068 23069 23071 23073 23074 23076 23077 23078 23079 23080 23081
## 1 1 1 1 1 1 5 4 1 5 4 1 5
## 23082 23083 23084 23085 23086 23087 23088 23089 23090 23091 23092 23093 23094
## 1 3 1 1 1 1 5 5 1 1 2 1 1
## 23095 23097 23098 23099 23100 23101 23102 23104 23107 23108 23109 23110 23111
## 4 1 1 4 1 1 5 1 1 1 5 4 5
## 23112 23114 23117 23118 23121 23123 23124 23127 23128 23129 23130 23132 23133
## 1 1 1 1 1 1 1 1 5 4 1 1 1
## 23135 23137 23139 23140 23142 23143 23144 23145 23147 23148 23149 23150 23151
## 1 1 4 1 1 4 1 1 1 1 1 1 4
## 23152 23153 23155 23156 23158 23160 23161 23162 23165 23166 23167 23168 23169
## 1 5 1 1 1 1 1 1 1 4 1 1 1
## 23171 23172 23173 23174 23175 23176 23178 23179 23180 23182 23184 23186 23189
## 5 1 1 1 1 1 4 5 4 4 1 1 1
## 23190 23191 23192 23195 23196 23197 23198 23199 23201 23202 23203 23204 23205
## 1 1 1 4 1 5 1 4 3 4 5 1 1
## 23207 23209 23210 23211 23212 23213 23214 23215 23216 23217 23219 23220 23222
## 1 5 1 1 1 5 1 1 5 1 1 1 1
## 23223 23224 23225 23226 23227 23228 23229 23230 23231 23233 23234 23235 23236
## 1 5 1 1 1 1 1 4 1 3 1 1 1
## 23238 23239 23240 23241 23242 23243 23244 23246 23248 23249 23250 23252 23253
## 1 1 1 1 1 1 1 4 1 4 1 1 1
## 23254 23255 23256 23257 23258 23259 23260 23261 23263 23264 23265 23266 23267
## 1 1 1 1 4 5 1 1 1 1 1 1 1
## 23268 23269 23271 23272 23274 23275 23276 23277 23278 23281 23282 23283 23284
## 1 1 1 1 4 1 1 1 4 1 1 3 1
## 23285 23286 23290 23291 23292 23293 23294 23295 23297 23298 23299 23300 23301
## 1 1 5 1 2 1 1 1 1 1 1 1 1
## 23302 23303 23304 23306 23307 23308 23309 23310 23311 23313 23314 23316 23317
## 1 1 1 1 1 1 1 4 1 1 1 1 4
## 23318 23319 23320 23322 23323 23324 23325 23326 23327 23328 23329 23330 23331
## 1 1 4 1 1 1 2 2 1 5 5 1 3
## 23332 23334 23335 23337 23338 23340 23341 23344 23346 23348 23349 23350 23351
## 1 5 2 4 1 1 1 4 5 1 1 1 1
## 23352 23353 23354 23356 23357 23358 23359 23360 23361 23362 23363 23364 23365
## 1 1 1 1 4 5 1 4 1 1 4 4 4
## 23366 23367 23368 23370 23371 23372 23373 23374 23375 23376 23377 23379 23380
## 1 5 1 1 1 1 1 5 1 1 1 1 1
## 23381 23382 23383 23384 23386 23388 23391 23392 23393 23394 23397 23398 23399
## 1 5 1 5 1 1 1 1 5 1 5 1 4
## 23400 23402 23403 23404 23405 23406 23407 23408 23409 23411 23412 23414 23415
## 3 1 1 5 4 1 5 1 1 1 5 1 5
## 23416 23419 23420 23422 23424 23425 23426 23427 23428 23430 23431 23432 23433
## 4 1 1 1 1 5 1 1 1 1 1 1 1
## 23434 23435 23436 23437 23438 23439 23441 23442 23444 23446 23447 23449 23450
## 5 1 1 1 5 1 1 1 4 1 1 1 4
## 23451 23453 23454 23455 23456 23458 23459 23460 23461 23462 23463 23465 23467
## 4 1 1 1 4 1 1 1 1 1 5 1 1
## 23468 23469 23470 23471 23473 23475 23476 23478 23479 23480 23481 23482 23483
## 1 1 1 1 1 5 1 1 1 4 4 5 1
## 23484 23485 23486 23487 23488 23489 23491 23494 23495 23497 23498 23499 23500
## 3 1 1 1 1 5 4 1 2 5 5 5 1
## 23501 23503 23504 23505 23506 23507 23509 23512 23513 23514 23515 23516 23517
## 4 4 1 1 1 1 1 1 1 1 1 1 1
## 23518 23519 23520 23521 23522 23523 23525 23526 23528 23529 23530 23532 23533
## 1 3 1 1 1 1 1 4 1 1 3 1 4
## 23534 23535 23536 23537 23538 23539 23540 23541 23542 23543 23544 23545 23546
## 1 4 1 1 4 5 5 1 1 1 5 5 1
## 23547 23548 23549 23550 23551 23552 23553 23555 23556 23557 23558 23559 23560
## 5 1 1 1 1 1 1 1 1 1 1 4 1
## 23561 23562 23563 23564 23565 23566 23567 23568 23569 23570 23571 23572 23573
## 1 1 5 1 1 5 1 1 1 1 1 1 5
## 23578 23580 23581 23582 23583 23584 23585 23586 23587 23588 23589 23590 23591
## 1 1 1 1 1 1 1 4 1 4 5 1 5
## 23592 23593 23594 23595 23596 23599 23600 23601 23602 23603 23604 23605 23607
## 4 1 5 1 1 1 1 1 5 1 5 1 2
## 23610 23612 23613 23614 23615 23616 23617 23619 23620 23621 23622 23623 23624
## 1 5 4 1 1 4 5 2 4 1 5 5 1
## 23625 23626 23627 23628 23631 23632 23633 23634 23635 23636 23637 23638 23639
## 1 1 4 1 1 1 1 5 3 1 1 1 1
## 23642 23643 23644 23645 23646 23647 23648 23649 23650 23651 23652 23654 23655
## 4 1 1 1 1 1 1 1 1 5 1 1 1
## 23656 23657 23658 23659 23660 23662 23663 23664 23671 23672 23675 23676 23677
## 1 2 1 1 1 1 1 1 1 1 1 1 1
## 23678 23679 23680 23681 23682 23683 23685 23686 23687 23688 23689 23690 23691
## 1 1 1 1 1 1 4 1 1 1 5 4 4
## 23693 23695 23696 23698 23699 23700 23701 23702 23703 23704 23705 23706 23707
## 1 1 1 1 1 1 1 1 1 1 4 1 1
## 23708 23709 23710 23711 23712 23713 23714 23715 23716 23717 23718 23719 23720
## 1 5 1 1 4 1 1 1 1 1 1 1 1
## 23724 23727 23728 23729 23730 23731 23732 23733 23734 23735 23736 23738 23740
## 3 5 4 1 1 1 4 1 5 5 1 1 5
## 23741 23743 23744 23745 23746 23747 23750 23751 23753 23754 23755 23757 23758
## 5 3 2 4 1 1 1 1 1 1 1 1 1
## 23759 23760 23761 23763 23765 23766 23767 23769 23771 23772 23773 23774 23775
## 1 1 1 1 1 1 1 5 1 1 1 1 1
## 23776 23778 23779 23780 23781 23782 23783 23784 23785 23789 23790 23792 23793
## 1 1 1 1 5 1 4 5 1 1 1 1 1
## 23794 23796 23797 23798 23799 23801 23802 23804 23805 23807 23809 23810 23811
## 1 1 4 1 4 1 5 1 5 1 1 1 4
## 23813 23814 23817 23818 23819 23820 23822 23823 23824 23825 23826 23827 23829
## 1 1 4 4 1 1 1 1 4 1 1 4 1
## 23830 23831 23832 23833 23834 23835 23836 23837 23838 23839 23840 23841 23843
## 2 1 4 1 4 2 1 1 1 1 2 5 1
## 23844 23845 23847 23848 23849 23850 23851 23853 23854 23855 23856 23857 23858
## 1 1 4 1 4 4 1 1 1 4 1 1 1
## 23859 23860 23861 23863 23865 23866 23868 23870 23871 23874 23875 23876 23877
## 1 5 1 1 1 4 3 1 4 1 1 1 1
## 23878 23879 23880 23882 23883 23884 23885 23886 23887 23889 23890 23892 23893
## 5 1 1 5 1 4 1 1 5 1 1 1 1
## 23895 23896 23897 23898 23899 23900 23901 23902 23903 23904 23905 23906 23907
## 1 1 5 2 1 5 5 1 1 1 4 1 3
## 23908 23909 23912 23913 23914 23916 23917 23919 23923 23924 23925 23926 23927
## 1 1 1 5 1 2 1 5 1 1 4 4 1
## 23928 23930 23931 23932 23933 23935 23936 23937 23938 23939 23940 23941 23942
## 1 1 1 1 1 1 4 1 1 1 4 1 4
## 23943 23944 23945 23946 23947 23948 23951 23952 23953 23957 23958 23959 23960
## 5 5 1 1 2 4 1 1 1 1 1 1 1
## 23963 23964 23965 23966 23967 23969 23970 23971 23972 23973 23975 23977 23978
## 1 1 1 1 1 1 1 1 1 4 1 1 4
## 23979 23980 23981 23982 23984 23985 23986 23987 23988 23989 23990 23991 23992
## 1 3 1 1 4 5 1 1 1 1 1 1 4
## 23993 23994 23995 23996 23997 23998 23999 24001 24002 24004 24005 24006 24007
## 1 1 1 4 1 1 1 1 1 1 1 1 5
## 24008 24009 24011 24014 24015 24016 24017 24019 24020 24021 24023 24027 24029
## 5 1 1 4 5 1 1 1 1 1 1 1 1
## 24030 24031 24032 24033 24035 24036 24037 24040 24042 24046 24047 24048 24049
## 1 1 3 1 1 3 1 1 1 5 1 1 1
## 24051 24052 24053 24054 24055 24056 24057 24059 24060 24061 24062 24063 24064
## 4 5 1 5 1 1 1 1 1 1 4 1 1
## 24065 24066 24067 24068 24069 24070 24071 24073 24074 24075 24076 24077 24078
## 1 1 1 4 1 3 1 1 1 4 1 1 1
## 24080 24081 24082 24083 24084 24086 24087 24088 24090 24091 24092 24093 24094
## 1 1 1 1 1 1 1 1 1 5 1 1 1
## 24095 24097 24098 24099 24101 24102 24103 24107 24109 24110 24111 24112 24113
## 1 5 1 1 1 1 4 4 1 1 4 1 1
## 24114 24115 24116 24117 24119 24120 24121 24122 24123 24124 24125 24126 24128
## 2 1 1 1 1 1 4 1 4 2 4 1 4
## 24129 24131 24132 24133 24134 24137 24138 24139 24140 24141 24142 24143 24145
## 5 4 4 1 1 1 1 1 1 1 3 4 2
## 24146 24147 24148 24149 24150 24151 24153 24155 24157 24158 24159 24160 24161
## 1 1 1 1 1 1 1 3 1 1 1 1 1
## 24162 24163 24164 24167 24168 24170 24173 24174 24175 24176 24177 24179 24180
## 1 1 5 4 1 4 1 4 1 3 3 1 1
## 24181 24184 24185 24186 24187 24188 24189 24190 24192 24193 24195 24197 24198
## 4 1 1 1 3 5 3 1 4 1 1 1 1
## 24199 24200 24201 24202 24203 24204 24205 24206 24207 24208 24209 24210 24211
## 1 1 2 1 1 2 1 4 1 1 5 1 5
## 24215 24217 24218 24220 24222 24223 24224 24225 24226 24227 24229 24230 24232
## 1 1 1 1 1 1 1 1 1 3 4 1 1
## 24233 24234 24235 24236 24237 24238 24240 24241 24242 24244 24245 24247 24248
## 1 1 1 5 1 3 1 1 1 1 1 1 1
## 24249 24250 24251 24253 24254 24255 24257 24258 24259 24261 24265 24266 24267
## 1 1 5 1 4 1 1 1 1 1 5 1 2
## 24268 24269 24270 24271 24272 24273 24274 24275 24276 24277 24278 24279 24280
## 1 1 5 1 1 4 1 1 1 1 1 3 1
## 24283 24284 24285 24286 24287 24288 24289 24290 24292 24293 24294 24295 24296
## 1 1 1 1 1 5 1 1 1 1 1 4 1
## 24297 24298 24301 24302 24303 24304 24305 24307 24308 24309 24311 24312 24313
## 1 1 1 1 1 1 1 1 5 1 4 1 1
## 24314 24315 24316 24317 24319 24320 24322 24323 24324 24325 24326 24327 24329
## 1 1 4 5 1 4 1 5 1 1 1 1 1
## 24330 24331 24332 24333 24335 24336 24339 24342 24343 24344 24345 24347 24348
## 1 1 1 1 1 1 1 1 1 4 1 1 1
## 24349 24350 24351 24352 24353 24354 24356 24357 24358 24359 24360 24362 24363
## 1 1 1 3 5 4 1 1 1 4 5 4 1
## 24364 24365 24366 24368 24369 24371 24372 24373 24374 24375 24376 24377 24378
## 1 1 3 4 1 1 1 1 1 1 1 1 1
## 24379 24380 24381 24382 24383 24384 24385 24386 24388 24389 24390 24393 24394
## 4 1 4 1 1 4 1 1 1 1 5 4 1
## 24395 24396 24397 24398 24399 24400 24402 24404 24405 24406 24408 24409 24411
## 1 1 1 1 4 4 1 1 1 1 1 5 1
## 24412 24413 24414 24415 24416 24417 24421 24423 24425 24426 24427 24428 24429
## 1 1 5 4 1 1 4 1 1 5 1 5 5
## 24432 24433 24435 24436 24437 24440 24441 24442 24443 24444 24445 24446 24447
## 1 1 1 1 1 1 4 2 1 5 1 1 4
## 24448 24449 24450 24451 24452 24453 24454 24456 24457 24458 24459 24462 24467
## 4 1 1 1 1 1 5 1 4 5 3 1 1
## 24468 24469 24470 24471 24472 24475 24477 24478 24479 24480 24481 24482 24483
## 1 1 1 1 4 2 5 1 1 4 1 1 1
## 24485 24486 24487 24489 24490 24491 24493 24495 24496 24497 24499 24500 24502
## 1 1 5 1 1 1 5 1 1 1 1 1 1
## 24503 24504 24506 24507 24509 24510 24511 24512 24513 24514 24515 24516 24517
## 5 1 5 1 1 1 1 3 1 1 1 3 5
## 24518 24520 24521 24522 24523 24525 24526 24527 24528 24530 24532 24533 24535
## 4 1 4 4 1 4 4 4 1 1 1 5 1
## 24536 24537 24538 24539 24541 24542 24543 24544 24545 24547 24548 24549 24550
## 1 1 3 1 3 5 1 1 1 1 1 5 5
## 24551 24552 24553 24554 24555 24557 24559 24560 24562 24563 24564 24565 24566
## 1 1 5 1 1 1 1 1 3 4 4 1 1
## 24567 24568 24569 24570 24571 24572 24574 24576 24578 24579 24580 24582 24583
## 1 1 1 1 1 4 1 1 1 1 1 4 2
## 24584 24585 24586 24587 24588 24589 24590 24593 24595 24597 24598 24600 24602
## 1 1 5 1 1 2 1 1 1 1 5 1 1
## 24604 24605 24606 24607 24608 24609 24610 24611 24612 24613 24614 24615 24616
## 4 1 5 5 1 3 1 1 1 2 1 5 1
## 24617 24619 24620 24621 24623 24624 24625 24628 24629 24632 24633 24634 24635
## 1 1 1 5 3 1 1 1 1 1 1 1 1
## 24636 24637 24638 24639 24640 24641 24642 24643 24644 24645 24647 24648 24649
## 1 2 1 4 5 5 1 1 1 1 1 4 1
## 24650 24651 24652 24653 24655 24656 24658 24659 24660 24661 24662 24664 24665
## 1 1 4 1 2 1 1 4 1 1 4 1 5
## 24666 24667 24668 24669 24670 24671 24672 24674 24677 24678 24679 24682 24686
## 1 1 5 5 4 1 1 1 4 4 3 1 1
## 24687 24688 24689 24690 24691 24692 24694 24695 24696 24697 24699 24700 24701
## 1 1 5 4 1 1 4 5 1 1 1 1 1
## 24702 24703 24704 24705 24706 24707 24708 24709 24710 24711 24712 24714 24716
## 1 1 1 1 1 5 3 1 1 4 1 1 1
## 24718 24719 24720 24721 24722 24723 24724 24725 24726 24727 24728 24730 24731
## 1 1 1 1 1 1 4 4 1 1 1 1 1
## 24732 24733 24734 24735 24736 24737 24738 24739 24740 24741 24742 24743 24744
## 1 1 5 1 1 1 1 5 1 4 1 1 1
## 24745 24746 24747 24748 24751 24752 24754 24755 24756 24757 24758 24759 24760
## 1 1 1 5 1 1 1 1 1 5 1 1 1
## 24761 24762 24763 24765 24766 24767 24768 24769 24770 24771 24772 24773 24774
## 1 1 1 1 1 1 3 1 1 5 3 4 1
## 24775 24776 24777 24779 24781 24782 24784 24785 24786 24787 24788 24789 24790
## 1 1 1 4 1 1 4 4 1 1 4 1 1
## 24792 24793 24794 24795 24796 24797 24798 24800 24801 24802 24803 24804 24807
## 5 1 1 1 1 5 1 1 4 5 5 1 1
## 24808 24810 24812 24814 24817 24818 24819 24821 24822 24823 24824 24825 24826
## 1 1 1 4 1 1 1 3 1 1 4 5 1
## 24828 24830 24831 24832 24833 24834 24835 24836 24837 24838 24839 24841 24842
## 1 1 1 5 1 4 1 5 5 1 4 1 1
## 24844 24845 24846 24850 24852 24853 24854 24855 24856 24858 24859 24860 24863
## 1 1 1 1 1 1 1 4 1 1 4 1 1
## 24864 24865 24866 24867 24869 24870 24871 24872 24875 24876 24877 24878 24879
## 1 5 1 1 1 1 1 1 1 1 1 1 1
## 24880 24882 24883 24884 24887 24888 24891 24892 24893 24894 24895 24896 24897
## 1 1 1 1 1 5 1 1 4 5 1 1 1
## 24899 24900 24901 24902 24903 24904 24906 24907 24908 24909 24910 24911 24912
## 1 1 1 5 5 1 1 1 1 1 1 1 1
## 24913 24914 24915 24916 24917 24920 24923 24925 24926 24927 24928 24929 24930
## 1 3 4 1 1 5 1 5 5 5 5 1 5
## 24931 24932 24933 24934 24936 24937 24939 24940 24941 24943 24945 24946 24947
## 1 1 1 5 5 4 5 5 1 4 1 1 1
## 24948 24949 24951 24952 24953 24954 24955 24956 24957 24958 24960 24961 24962
## 1 1 1 1 1 1 1 1 1 5 2 1 1
## 24964 24965 24966 24969 24971 24972 24973 24974 24975 24977 24978 24979 24982
## 4 1 4 1 1 4 3 4 4 1 1 1 1
## 24983 24984 24985 24987 24988 24989 24990 24992 24993 24994 24995 24996 24997
## 1 4 4 1 1 1 1 1 1 5 1 1 4
## 24998 24999 25001 25002 25005 25006 25007 25009 25011 25012 25013 25014 25016
## 4 1 2 1 5 1 1 5 1 5 1 1 1
## 25017 25018 25022 25023 25025 25026 25030 25031 25032 25033 25034 25035 25036
## 1 5 1 1 1 5 1 1 5 1 1 1 1
## 25037 25038 25039 25040 25041 25042 25043 25046 25049 25051 25053 25055 25056
## 1 5 1 1 1 1 1 3 1 4 5 1 5
## 25057 25058 25059 25060 25063 25065 25066 25067 25068 25069 25070 25071 25072
## 1 4 5 1 4 1 5 1 1 1 1 5 1
## 25074 25075 25076 25079 25082 25083 25084 25085 25086 25089 25093 25094 25095
## 1 4 4 1 1 4 5 1 1 1 1 1 1
## 25096 25097 25098 25099 25100 25101 25102 25103 25104 25105 25106 25107 25108
## 1 1 1 1 1 1 1 2 1 1 1 1 1
## 25110 25111 25112 25113 25114 25115 25116 25117 25118 25119 25120 25121 25123
## 4 1 1 1 1 1 1 1 1 1 1 1 1
## 25124 25125 25126 25127 25128 25129 25130 25131 25132 25133 25134 25135 25137
## 5 3 1 1 1 1 1 1 1 1 4 1 1
## 25138 25139 25141 25142 25144 25145 25146 25147 25148 25150 25152 25153 25154
## 4 1 1 1 1 5 1 5 4 1 4 5 1
## 25155 25156 25157 25158 25159 25160 25163 25164 25165 25168 25169 25170 25171
## 1 1 1 1 1 4 5 1 4 1 3 1 1
## 25174 25175 25176 25177 25179 25180 25181 25182 25183 25185 25186 25187 25188
## 5 5 1 1 1 2 4 1 1 1 1 4 1
## 25189 25190 25191 25192 25193 25194 25195 25196 25197 25198 25199 25201 25202
## 5 1 1 3 1 1 1 1 1 5 1 4 1
## 25203 25204 25205 25206 25208 25209 25210 25211 25212 25213 25214 25215 25216
## 5 1 1 1 4 1 4 1 5 1 1 2 1
## 25217 25218 25219 25221 25222 25224 25225 25226 25227 25228 25229 25230 25231
## 1 1 1 1 1 5 1 4 1 1 4 4 1
## 25232 25233 25237 25238 25239 25240 25241 25242 25243 25244 25245 25246 25247
## 1 1 1 1 1 1 2 5 1 2 1 4 3
## 25248 25249 25250 25251 25252 25253 25254 25255 25256 25257 25258 25259 25261
## 1 1 4 1 3 1 1 1 5 1 1 1 4
## 25262 25264 25265 25266 25267 25269 25270 25271 25272 25273 25275 25276 25277
## 5 4 1 5 1 4 5 1 1 4 1 5 1
## 25278 25279 25281 25282 25283 25285 25287 25288 25289 25291 25292 25293 25295
## 5 1 1 1 4 1 4 1 1 1 1 5 1
## 25296 25297 25298 25299 25300 25301 25303 25305 25306 25307 25308 25310 25311
## 4 4 1 1 1 1 1 1 1 4 2 1 1
## 25312 25313 25314 25315 25316 25317 25318 25319 25320 25322 25324 25325 25326
## 1 1 1 1 5 1 1 1 1 1 1 2 4
## 25327 25329 25330 25331 25332 25333 25334 25336 25337 25338 25340 25342 25343
## 5 1 4 1 1 4 1 1 1 1 1 1 2
## 25344 25345 25347 25348 25349 25350 25354 25355 25356 25357 25358 25359 25360
## 1 4 4 5 1 1 2 1 1 5 1 1 4
## 25361 25362 25363 25365 25366 25367 25368 25369 25370 25371 25373 25374 25375
## 4 4 1 1 4 1 1 3 4 1 1 1 3
## 25376 25377 25378 25379 25380 25381 25382 25383 25384 25385 25386 25387 25388
## 1 5 1 4 5 4 5 5 1 2 5 5 5
## 25389 25391 25392 25393 25394 25396 25397 25398 25399 25400 25401 25402 25403
## 4 1 3 4 1 1 1 1 1 1 5 4 1
## 25404 25405 25406 25407 25409 25410 25412 25413 25414 25416 25418 25419 25420
## 1 2 1 1 2 4 4 4 1 1 1 1 1
## 25421 25422 25423 25427 25428 25429 25430 25431 25432 25433 25434 25435 25436
## 4 4 1 4 1 1 4 1 1 1 1 1 2
## 25437 25438 25439 25440 25441 25442 25443 25444 25445 25447 25448 25449 25450
## 1 1 4 5 1 1 1 4 4 1 1 5 1
## 25452 25453 25454 25455 25456 25457 25458 25459 25460 25461 25462 25463 25464
## 1 1 1 1 1 1 4 1 1 1 5 1 1
## 25465 25466 25467 25469 25471 25472 25474 25475 25476 25477 25478 25479 25480
## 1 4 1 5 5 4 1 1 1 4 5 1 1
## 25481 25482 25483 25484 25485 25486 25488 25491 25492 25493 25494 25495 25498
## 1 1 1 1 1 1 1 1 1 4 5 1 4
## 25499 25500 25503 25504 25507 25508 25509 25511 25512 25513 25514 25515 25517
## 1 1 1 1 1 1 1 1 1 1 1 2 4
## 25519 25520 25523 25524 25525 25526 25527 25529 25531 25532 25533 25534 25536
## 1 5 1 1 1 3 1 1 1 1 1 1 1
## 25539 25540 25541 25542 25544 25545 25546 25548 25549 25550 25551 25552 25553
## 1 1 4 1 4 3 1 1 1 1 1 4 1
## 25554 25555 25557 25558 25560 25561 25562 25563 25564 25567 25569 25570 25571
## 1 1 1 3 1 1 1 1 1 1 5 1 1
## 25572 25573 25574 25576 25577 25578 25579 25581 25582 25583 25584 25585 25586
## 1 1 1 4 1 1 5 1 1 1 4 1 5
## 25587 25588 25589 25590 25591 25592 25593 25594 25595 25596 25598 25599 25601
## 1 1 1 5 4 1 1 1 1 4 4 1 1
## 25602 25603 25605 25606 25607 25609 25611 25612 25615 25616 25617 25618 25619
## 1 1 5 1 4 1 1 1 1 1 2 1 4
## 25620 25622 25625 25626 25627 25628 25630 25631 25632 25633 25634 25636 25637
## 3 1 5 4 5 1 1 4 1 1 5 5 5
## 25638 25639 25647 25649 25651 25652 25653 25654 25655 25656 25657 25658 25660
## 1 5 1 1 1 1 1 1 1 1 1 4 1
## 25661 25662 25663 25664 25667 25668 25670 25672 25673 25674 25675 25676 25677
## 1 1 4 1 1 1 2 1 3 1 4 1 1
## 25679 25681 25683 25685 25686 25687 25688 25689 25691 25693 25694 25695 25696
## 5 1 1 1 5 5 1 4 1 1 4 5 5
## 25697 25698 25699 25700 25702 25704 25705 25706 25707 25708 25710 25712 25713
## 1 1 5 1 5 1 1 1 1 1 3 1 5
## 25714 25715 25716 25718 25719 25720 25721 25722 25723 25724 25725 25726 25727
## 1 1 1 1 1 1 5 4 1 1 1 4 1
## 25728 25729 25730 25731 25732 25734 25736 25737 25738 25739 25740 25743 25744
## 1 1 5 1 1 1 1 5 5 1 1 1 5
## 25745 25746 25747 25748 25749 25750 25751 25752 25753 25754 25755 25756 25757
## 1 5 1 1 1 1 4 1 1 5 1 3 1
## 25758 25759 25760 25761 25762 25763 25765 25766 25767 25768 25769 25770 25771
## 5 5 1 1 1 1 5 1 1 1 1 1 1
## 25772 25773 25774 25775 25776 25777 25778 25779 25780 25781 25782 25783 25784
## 1 4 1 1 1 5 1 1 5 1 1 1 1
## 25785 25787 25788 25789 25790 25791 25792 25794 25795 25797 25798 25799 25801
## 1 1 1 1 1 5 5 4 1 1 1 3 1
## 25802 25803 25806 25808 25809 25810 25811 25812 25813 25814 25815 25816 25817
## 1 4 4 1 1 1 1 3 1 1 5 1 1
## 25818 25819 25820 25821 25822 25823 25824 25826 25827 25828 25829 25831 25833
## 3 5 3 4 5 1 1 3 1 4 1 1 1
## 25835 25836 25837 25838 25839 25840 25841 25843 25844 25846 25847 25848 25850
## 4 1 1 4 1 1 1 5 4 1 4 1 1
## 25851 25852 25853 25854 25856 25857 25858 25860 25861 25862 25863 25864 25865
## 4 1 1 4 1 1 1 1 1 1 1 1 5
## 25866 25867 25868 25870 25871 25872 25873 25875 25876 25877 25879 25880 25881
## 1 1 5 1 1 1 5 1 1 1 1 1 1
## 25882 25883 25884 25885 25886 25887 25888 25889 25890 25891 25892 25895 25896
## 1 3 1 1 1 1 1 1 1 4 1 1 1
## 25898 25899 25901 25903 25905 25906 25907 25910 25911 25913 25914 25915 25916
## 1 1 1 1 1 3 1 1 1 5 1 1 1
## 25920 25923 25924 25925 25926 25927 25929 25931 25932 25933 25934 25935 25936
## 5 2 1 1 2 1 5 1 1 5 1 5 1
## 25937 25938 25939 25940 25941 25943 25945 25946 25947 25948 25949 25950 25951
## 3 1 5 5 1 5 1 5 4 1 1 1 1
## 25954 25956 25957 25959 25960 25961 25963 25964 25965 25967 25968 25969 25970
## 1 4 1 1 1 1 1 1 1 1 1 5 1
## 25971 25972 25973 25974 25975 25976 25977 25978 25979 25981 25982 25984 25985
## 1 1 1 1 1 1 5 1 1 1 1 1 1
## 25986 25987 25988 25989 25991 25993 25994 25995 25996 25997 25998 26000 26001
## 3 1 1 1 1 4 4 1 1 1 5 1 1
## 26002 26003 26004 26005 26006 26007 26008 26009 26010 26014 26015 26016 26017
## 1 1 1 4 1 1 5 1 4 5 1 1 1
## 26018 26019 26020 26021 26022 26023 26024 26027 26028 26029 26030 26031 26032
## 1 1 1 1 1 1 4 1 1 1 4 1 3
## 26033 26034 26035 26036 26037 26038 26041 26042 26043 26044 26045 26048 26050
## 1 1 1 1 5 1 1 1 3 1 1 5 1
## 26051 26053 26054 26056 26057 26058 26059 26060 26061 26062 26063 26064 26065
## 1 1 4 1 1 1 1 5 4 1 1 1 1
## 26066 26067 26068 26069 26071 26072 26074 26075 26076 26077 26078 26079 26080
## 1 5 1 1 1 5 5 1 4 1 5 1 1
## 26082 26083 26084 26085 26086 26087 26088 26090 26092 26094 26095 26096 26098
## 1 1 3 5 1 1 4 1 1 4 1 1 1
## 26099 26100 26101 26102 26104 26105 26106 26107 26108 26109 26110 26111 26112
## 1 5 5 3 1 5 1 1 2 1 1 1 4
## 26113 26114 26116 26117 26118 26121 26122 26123 26124 26125 26126 26127 26128
## 1 1 4 1 1 1 1 1 1 1 5 4 4
## 26129 26130 26131 26133 26134 26135 26136 26137 26138 26139 26140 26142 26143
## 1 5 4 1 5 4 1 1 1 1 1 1 1
## 26144 26146 26148 26149 26150 26151 26152 26153 26155 26156 26157 26158 26159
## 1 1 1 5 1 1 5 1 5 3 1 1 5
## 26160 26161 26162 26163 26164 26166 26167 26168 26169 26170 26171 26172 26173
## 1 3 1 2 4 4 5 1 1 1 4 1 1
## 26174 26175 26176 26178 26179 26180 26182 26183 26184 26185 26186 26187 26188
## 1 1 4 5 1 1 1 1 3 1 5 1 1
## 26189 26190 26191 26193 26194 26195 26196 26197 26198 26201 26202 26204 26205
## 1 1 1 1 4 1 4 1 5 1 1 1 1
## 26207 26208 26209 26212 26213 26215 26217 26219 26220 26221 26222 26223 26224
## 1 1 1 1 1 1 1 1 1 1 4 4 3
## 26227 26229 26231 26232 26234 26235 26236 26237 26238 26239 26241 26242 26243
## 1 1 1 4 1 1 5 1 1 1 4 3 5
## 26245 26247 26249 26252 26253 26255 26258 26260 26262 26263 26264 26265 26266
## 1 1 5 5 1 4 4 1 1 5 1 5 5
## 26267 26269 26270 26271 26272 26273 26274 26275 26276 26277 26278 26280 26281
## 1 1 1 1 1 1 5 5 3 1 4 1 4
## 26282 26285 26286 26290 26291 26293 26294 26295 26296 26297 26298 26299 26301
## 3 1 1 1 1 1 1 1 4 4 1 5 4
## 26303 26304 26305 26306 26308 26309 26310 26311 26312 26313 26314 26317 26319
## 1 1 1 1 1 5 1 1 1 1 1 3 1
## 26320 26323 26324 26325 26326 26328 26329 26330 26332 26334 26335 26337 26338
## 1 1 1 1 1 1 4 1 1 5 1 1 1
## 26339 26340 26341 26343 26344 26345 26346 26347 26348 26351 26352 26353 26354
## 1 1 3 4 1 1 4 5 1 5 1 1 1
## 26355 26356 26357 26358 26359 26360 26361 26365 26366 26368 26369 26370 26371
## 1 5 4 1 1 1 1 5 1 1 1 4 1
## 26373 26374 26375 26376 26377 26378 26380 26381 26382 26383 26384 26385 26386
## 1 1 1 1 1 3 1 1 1 1 5 5 3
## 26387 26388 26390 26391 26392 26393 26394 26396 26397 26398 26399 26400 26401
## 4 3 1 1 5 1 5 1 1 4 1 1 1
## 26402 26403 26404 26405 26406 26408 26409 26410 26411 26412 26413 26414 26415
## 1 1 1 1 3 1 1 1 4 1 1 1 1
## 26416 26417 26418 26419 26420 26422 26423 26424 26425 26426 26427 26428 26429
## 3 1 1 1 1 1 1 1 4 5 5 1 1
## 26430 26431 26432 26434 26435 26437 26438 26439 26440 26441 26442 26443 26444
## 1 1 1 5 1 5 1 1 1 1 4 4 1
## 26445 26446 26447 26448 26451 26452 26453 26454 26455 26456 26457 26458 26459
## 1 4 4 1 1 1 1 3 1 1 1 4 1
## 26460 26461 26462 26464 26465 26466 26467 26468 26470 26472 26473 26474 26475
## 1 4 1 1 5 1 1 1 2 1 1 1 1
## 26477 26478 26479 26480 26481 26482 26483 26484 26485 26486 26487 26488 26489
## 5 1 4 5 4 1 4 5 1 1 1 5 1
## 26490 26491 26492 26494 26498 26499 26500 26501 26503 26504 26505 26506 26507
## 5 1 1 1 1 1 1 5 1 1 4 1 1
## 26508 26509 26510 26511 26512 26513 26514 26515 26517 26518 26519 26521 26522
## 5 1 1 1 2 1 1 1 1 1 1 4 4
## 26523 26524 26525 26526 26527 26528 26529 26530 26531 26532 26533 26535 26536
## 1 1 1 1 1 5 1 4 1 5 1 1 1
## 26537 26538 26539 26540 26541 26542 26543 26544 26545 26546 26547 26549 26550
## 4 1 4 1 3 1 1 1 1 1 4 1 5
## 26551 26552 26553 26554 26555 26556 26557 26558 26560 26561 26563 26564 26565
## 4 1 1 4 1 1 2 1 1 1 1 5 1
## 26566 26567 26568 26569 26570 26571 26572 26574 26575 26576 26578 26579 26580
## 1 1 5 1 1 5 1 1 1 1 1 5 1
## 26582 26584 26587 26588 26591 26592 26593 26594 26597 26598 26599 26600 26602
## 1 1 5 1 1 5 5 1 4 1 1 4 1
## 26603 26605 26606 26607 26609 26610 26612 26614 26616 26617 26618 26619 26620
## 3 5 4 1 4 1 4 4 1 1 1 1 1
## 26622 26624 26625 26627 26628 26629 26630 26631 26632 26633 26634 26635 26637
## 1 4 1 3 1 1 1 4 5 1 1 3 4
## 26639 26640 26642 26643 26644 26645 26647 26650 26651 26652 26654 26655 26656
## 1 1 5 1 5 5 1 1 1 1 5 1 1
## 26657 26658 26659 26660 26661 26662 26664 26665 26666 26667 26669 26670 26671
## 1 4 1 1 4 1 1 1 2 1 5 4 1
## 26672 26673 26674 26676 26677 26678 26679 26680 26681 26682 26683 26685 26686
## 4 1 1 4 1 3 4 1 1 3 1 1 1
## 26687 26689 26691 26692 26693 26694 26695 26696 26697 26698 26699 26700 26701
## 1 4 4 1 4 3 1 1 4 1 5 4 5
## 26702 26704 26705 26706 26708 26710 26711 26712 26713 26715 26716 26717 26718
## 1 1 5 5 5 1 1 4 4 1 1 1 4
## 26719 26720 26721 26722 26723 26725 26726 26727 26728 26729 26730 26731 26732
## 1 5 5 5 1 1 1 1 1 1 1 1 1
## 26734 26735 26736 26737 26738 26739 26741 26743 26744 26745 26746 26747 26748
## 1 1 1 1 1 1 1 1 1 1 5 4 5
## 26752 26753 26754 26755 26756 26757 26759 26760 26761 26762 26763 26764 26765
## 5 4 1 1 1 1 1 1 5 4 1 4 1
## 26767 26768 26769 26770 26771 26772 26773 26774 26776 26777 26778 26779 26780
## 1 5 1 1 5 1 5 4 4 1 1 1 1
## 26781 26782 26783 26784 26785 26786 26787 26788 26789 26790 26791 26792 26793
## 1 1 1 1 1 1 1 1 1 1 4 4 2
## 26794 26795 26796 26797 26798 26800 26801 26802 26803 26804 26805 26806 26807
## 1 1 4 3 1 1 1 4 4 1 1 1 1
## 26808 26809 26810 26812 26815 26816 26818 26819 26821 26822 26823 26825 26826
## 1 1 3 1 1 1 4 1 1 1 1 3 1
## 26827 26828 26830 26831 26833 26835 26836 26838 26839 26841 26842 26843 26845
## 1 4 1 1 1 1 1 1 1 5 1 1 1
## 26847 26848 26849 26850 26851 26852 26853 26855 26856 26857 26858 26859 26860
## 1 1 1 1 1 1 1 1 1 1 1 1 5
## 26862 26864 26865 26866 26868 26869 26871 26873 26875 26876 26877 26879 26880
## 1 1 1 5 1 1 1 1 4 1 1 1 5
## 26882 26883 26884 26886 26888 26889 26890 26891 26892 26895 26896 26897 26899
## 4 4 1 1 1 1 1 3 1 5 4 1 1
## 26900 26901 26902 26905 26906 26907 26908 26909 26911 26914 26915 26917 26919
## 1 1 4 2 1 2 4 1 5 1 1 1 1
## 26922 26924 26925 26926 26927 26929 26930 26931 26933 26934 26935 26937 26939
## 5 1 1 1 5 5 1 1 1 1 1 1 5
## 26940 26941 26942 26943 26944 26945 26947 26948 26949 26951 26952 26955 26956
## 1 1 1 1 3 1 1 1 1 1 1 5 1
## 26957 26958 26959 26960 26961 26962 26963 26964 26965 26966 26967 26968 26969
## 1 4 4 1 1 1 1 1 1 1 4 5 1
## 26970 26971 26972 26973 26974 26975 26976 26977 26978 26979 26980 26981 26984
## 4 1 1 1 1 5 1 4 1 1 1 1 1
## 26985 26987 26988 26993 26994 26995 26996 26997 26999 27000 27002 27003 27005
## 1 5 1 1 5 1 1 1 1 1 1 5 3
## 27007 27009 27010 27012 27014 27018 27019 27020 27021 27022 27023 27026 27027
## 4 1 1 5 1 1 4 1 4 4 1 3 1
## 27028 27029 27030 27031 27032 27033 27034 27035 27036 27037 27038 27039 27041
## 5 1 3 1 5 1 1 1 1 5 3 1 1
## 27042 27043 27044 27046 27047 27048 27049 27054 27055 27056 27057 27058 27059
## 1 1 4 5 3 5 1 5 4 1 4 1 1
## 27060 27061 27062 27063 27065 27066 27067 27069 27070 27071 27073 27074 27075
## 5 1 1 5 1 3 1 1 1 1 1 1 1
## 27076 27078 27079 27080 27084 27085 27086 27087 27088 27089 27090 27091 27092
## 1 1 1 4 4 1 1 1 1 1 1 4 1
## 27093 27094 27095 27097 27098 27099 27100 27102 27103 27104 27106 27107 27108
## 5 1 1 1 4 1 3 1 1 1 4 4 1
## 27110 27112 27115 27116 27117 27118 27119 27120 27121 27122 27123 27124 27125
## 1 1 1 1 1 1 1 3 1 1 5 1 1
## 27127 27128 27131 27132 27133 27134 27137 27138 27139 27140 27142 27143 27144
## 4 1 2 1 1 1 5 3 1 1 1 1 1
## 27145 27146 27148 27150 27151 27152 27153 27154 27155 27156 27157 27159 27162
## 1 1 4 1 5 1 1 1 1 4 1 1 1
## 27163 27164 27165 27166 27167 27170 27171 27172 27173 27174 27175 27176 27177
## 1 1 5 5 1 1 4 1 1 5 1 1 1
## 27178 27179 27180 27181 27182 27183 27184 27185 27186 27187 27190 27191 27196
## 5 1 1 4 1 1 1 1 4 1 4 1 1
## 27197 27198 27199 27200 27201 27202 27203 27204 27205 27206 27207 27209 27210
## 4 1 1 1 5 5 1 1 4 1 1 1 1
## 27211 27212 27213 27215 27216 27217 27218 27219 27220 27222 27223 27224 27225
## 1 1 1 1 1 3 1 1 1 1 1 1 4
## 27226 27227 27228 27229 27231 27232 27234 27236 27237 27238 27239 27240 27242
## 1 3 1 1 1 1 1 1 5 4 1 5 1
## 27243 27244 27245 27247 27248 27250 27251 27252 27253 27254 27255 27256 27258
## 1 1 1 1 5 5 1 4 3 1 1 1 4
## 27259 27260 27261 27262 27264 27265 27266 27268 27269 27270 27271 27272 27273
## 1 3 1 4 3 1 5 1 4 1 4 1 5
## 27275 27276 27277 27279 27280 27283 27284 27285 27286 27287 27291 27293 27294
## 1 1 1 1 1 1 1 1 5 1 1 1 4
## 27296 27297 27298 27299 27300 27301 27302 27303 27304 27306 27307 27308 27309
## 1 1 1 4 5 4 2 1 1 1 1 1 1
## 27311 27312 27313 27316 27317 27319 27320 27321 27322 27323 27325 27326 27327
## 5 1 1 1 1 1 1 1 1 1 1 1 1
## 27329 27331 27332 27333 27334 27336 27337 27338 27340 27341 27342 27343 27344
## 4 1 1 4 1 1 1 1 1 1 4 1 5
## 27345 27348 27349 27350 27351 27352 27354 27355 27356 27357 27358 27359 27360
## 1 1 1 1 1 1 1 1 1 1 1 1 5
## 27361 27362 27365 27366 27367 27368 27370 27372 27373 27374 27375 27376 27377
## 5 1 1 1 1 1 1 1 1 4 5 4 1
## 27378 27381 27383 27386 27387 27388 27390 27391 27392 27394 27395 27396 27397
## 4 5 5 4 1 1 1 1 1 1 2 1 1
## 27398 27400 27401 27402 27403 27404 27405 27406 27407 27408 27410 27411 27412
## 1 1 1 1 4 1 4 1 1 1 1 1 1
## 27413 27415 27416 27417 27418 27419 27420 27421 27422 27423 27424 27427 27428
## 1 1 1 1 1 5 1 1 1 1 4 1 1
## 27429 27430 27432 27433 27434 27435 27436 27438 27439 27441 27442 27443 27444
## 1 1 1 1 5 1 1 1 1 4 1 1 1
## 27445 27446 27448 27449 27450 27452 27453 27454 27455 27456 27457 27458 27459
## 1 5 1 5 4 2 1 1 1 1 1 1 1
## 27463 27464 27465 27466 27467 27468 27469 27471 27472 27473 27474 27475 27476
## 1 1 5 1 5 4 4 1 1 1 5 1 4
## 27478 27480 27481 27482 27483 27484 27485 27486 27487 27488 27489 27490 27491
## 5 1 1 4 1 1 4 1 5 3 1 1 1
## 27492 27493 27494 27495 27496 27497 27499 27501 27502 27503 27504 27506 27507
## 1 2 1 5 1 1 1 1 1 1 1 1 1
## 27508 27509 27510 27511 27512 27513 27516 27517 27518 27519 27520 27522 27523
## 5 4 1 1 5 1 1 1 1 4 1 4 1
## 27524 27525 27529 27530 27531 27532 27533 27534 27535 27536 27537 27538 27539
## 1 4 1 4 1 4 4 4 1 1 1 1 4
## 27540 27543 27545 27546 27547 27549 27550 27551 27552 27553 27555 27557 27558
## 1 1 1 1 4 5 1 1 3 1 1 1 1
## 27559 27560 27561 27563 27564 27565 27567 27568 27569 27570 27571 27572 27573
## 1 4 5 1 1 1 1 1 5 5 1 1 5
## 27574 27575 27576 27578 27579 27580 27581 27582 27583 27584 27585 27586 27587
## 1 1 1 1 5 1 1 1 1 1 5 4 5
## 27588 27589 27590 27591 27592 27593 27594 27598 27599 27601 27602 27603 27605
## 1 1 5 1 5 1 4 1 5 1 1 1 1
## 27606 27608 27609 27610 27611 27612 27613 27614 27615 27616 27617 27618 27619
## 1 1 1 1 4 1 4 3 1 1 4 1 1
## 27620 27621 27622 27623 27624 27625 27626 27627 27628 27629 27630 27631 27632
## 1 4 1 4 1 1 4 1 5 4 1 5 1
## 27633 27635 27636 27637 27639 27642 27643 27644 27645 27649 27650 27652 27654
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 27655 27656 27657 27658 27659 27660 27661 27662 27663 27664 27665 27666 27668
## 1 1 1 1 1 4 1 1 1 1 1 1 3
## 27669 27671 27673 27675 27678 27679 27680 27681 27682 27683 27684 27685 27686
## 1 5 1 1 1 4 1 1 1 1 1 5 4
## 27688 27689 27690 27691 27692 27693 27694 27695 27696 27697 27698 27700 27701
## 1 1 1 1 1 1 1 1 3 1 1 5 4
## 27702 27703 27704 27705 27706 27707 27709 27710 27711 27712 27713 27715 27716
## 1 5 5 1 1 1 1 4 1 1 1 1 1
## 27717 27718 27719 27720 27721 27722 27724 27725 27726 27727 27728 27729 27731
## 1 3 1 1 1 1 5 1 4 1 1 3 1
## 27732 27733 27734 27735 27736 27737 27738 27739 27740 27742 27743 27745 27746
## 5 1 1 1 4 4 1 1 4 1 1 1 4
## 27747 27748 27749 27750 27751 27752 27753 27754 27755 27756 27757 27758 27759
## 1 1 1 1 3 1 3 5 1 1 1 3 1
## 27760 27761 27762 27763 27764 27765 27767 27768 27769 27770 27772 27773 27774
## 1 1 1 1 5 1 1 4 2 4 1 1 1
## 27775 27776 27777 27778 27780 27782 27786 27788 27791 27792 27793 27794 27795
## 5 1 1 1 1 1 5 5 4 1 4 1 5
## 27797 27798 27799 27800 27802 27803 27804 27805 27807 27808 27809 27810 27811
## 1 1 4 1 5 4 5 1 1 4 1 2 1
## 27812 27815 27816 27817 27818 27819 27820 27821 27823 27824 27826 27827 27828
## 1 1 1 1 3 1 1 2 1 1 1 4 1
## 27829 27831 27832 27834 27835 27836 27837 27839 27840 27841 27842 27843 27844
## 4 1 1 1 1 1 4 1 5 1 5 1 1
## 27845 27847 27849 27850 27852 27853 27855 27856 27857 27861 27863 27864 27865
## 4 1 1 4 1 5 1 1 4 1 4 1 4
## 27866 27867 27869 27870 27871 27872 27873 27875 27876 27877 27878 27879 27880
## 1 3 4 1 1 1 1 1 1 1 1 1 3
## 27882 27883 27884 27886 27887 27888 27889 27890 27891 27892 27893 27894 27896
## 1 4 1 1 1 1 1 1 1 1 1 1 1
## 27897 27898 27900 27901 27902 27903 27904 27905 27906 27907 27908 27910 27914
## 1 1 1 1 1 4 1 1 1 4 1 1 1
## 27915 27916 27917 27918 27919 27922 27923 27924 27925 27926 27927 27929 27930
## 1 1 1 1 1 1 1 5 3 1 4 5 4
## 27931 27932 27933 27935 27936 27937 27938 27939 27940 27941 27942 27943 27945
## 1 3 1 1 5 1 1 5 1 4 1 1 1
## 27946 27948 27949 27951 27952 27953 27955 27956 27957 27960 27961 27962 27964
## 1 4 5 1 1 1 1 1 1 1 1 1 1
## 27965 27966 27967 27968 27969 27970 27972 27973 27975 27976 27977 27978 27980
## 1 1 1 1 1 1 1 1 1 1 1 5 4
## 27981 27982 27983 27984 27985 27987 27988 27989 27990 27991 27992 27993 27994
## 1 1 4 1 1 1 1 1 1 1 1 4 1
## 27995 27996 27998 27999 28000 28001 28003 28004 28005 28006 28007 28008 28012
## 1 2 3 1 5 4 4 4 4 4 4 4 4
## 28017 28018 28020 28022 28024 28025 28026 28027 28029 28030 28031 28032 28034
## 4 4 1 4 1 5 4 4 1 1 4 1 4
## 28035 28036 28037 28038 28039 28040 28044 28046 28047 28048 28049 28050 28051
## 1 1 2 1 1 1 1 1 1 4 1 1 4
## 28052 28053 28054 28055 28056 28057 28058 28059 28060 28061 28062 28063 28064
## 4 1 1 1 1 1 1 1 4 1 1 1 1
## 28065 28066 28067 28068 28069 28070 28073 28074 28076 28077 28078 28079 28081
## 1 1 5 1 3 1 1 1 1 1 5 1 1
## 28083 28084 28086 28087 28088 28089 28090 28091 28092 28093 28094 28095 28096
## 1 1 4 3 1 1 1 1 4 1 4 3 4
## 28097 28098 28099 28100 28101 28102 28103 28104 28105 28106 28107 28108 28111
## 4 4 4 4 1 1 4 1 1 5 1 1 1
## 28112 28113 28115 28116 28118 28119 28120 28123 28124 28126 28128 28129 28130
## 1 1 1 5 1 1 1 1 5 1 1 1 1
## 28131 28132 28133 28134 28135 28136 28137 28138 28139 28141 28142 28143 28144
## 1 1 1 2 1 4 1 1 1 1 5 1 1
## 28145 28147 28148 28149 28150 28151 28152 28153 28155 28157 28158 28159 28160
## 4 4 1 5 1 1 1 1 1 5 1 1 1
## 28161 28162 28163 28164 28166 28168 28169 28170 28171 28172 28173 28174 28175
## 1 1 4 1 1 1 1 1 4 1 1 4 1
## 28176 28177 28178 28179 28182 28183 28185 28186 28189 28190 28192 28193 28194
## 4 1 1 1 1 5 5 1 5 1 1 1 1
## 28195 28196 28197 28201 28202 28203 28204 28205 28206 28207 28209 28210 28211
## 1 1 1 5 1 1 1 5 1 1 1 1 1
## 28212 28213 28214 28215 28216 28217 28224 28226 28227 28228 28229 28230 28231
## 1 3 1 1 1 1 1 1 1 4 5 5 5
## 28232 28233 28234 28235 28236 28240 28241 28242 28244 28245 28247 28249 28250
## 1 5 5 5 5 1 3 3 1 1 1 3 1
## 28251 28252 28253 28254 28255 28256 28257 28258 28259 28260 28261 28264 28265
## 5 1 1 1 4 1 2 1 4 5 4 2 1
## 28269 28270 28271 28272 28273 28274 28275 28276 28278 28279 28280 28282 28283
## 1 4 3 1 1 5 1 1 1 4 5 1 1
## 28284 28286 28287 28288 28289 28290 28291 28292 28293 28294 28295 28296 28297
## 1 1 4 5 1 1 1 1 4 1 1 1 1
## 28298 28299 28300 28301 28305 28306 28307 28308 28310 28311 28312 28313 28314
## 1 1 1 3 1 1 1 1 1 1 1 1 1
## 28315 28317 28318 28319 28320 28321 28322 28325 28326 28327 28329 28330 28332
## 1 1 1 5 1 5 1 1 5 1 5 1 1
## 28333 28334 28336 28337 28338 28339 28340 28341 28343 28344 28345 28346 28347
## 1 1 1 5 1 1 5 1 5 1 1 1 1
## 28348 28350 28351 28354 28355 28356 28358 28359 28360 28361 28362 28363 28364
## 1 4 5 1 1 1 4 5 5 4 5 1 1
## 28365 28366 28367 28370 28371 28372 28373 28374 28375 28376 28378 28379 28380
## 1 1 1 5 4 1 1 1 1 1 5 1 1
## 28382 28384 28387 28388 28389 28390 28392 28393 28394 28395 28396 28397 28398
## 1 1 1 1 1 3 1 1 1 1 4 1 5
## 28399 28400 28402 28404 28405 28406 28408 28409 28410 28413 28414 28415 28416
## 1 1 5 4 3 3 1 1 3 5 1 4 1
## 28417 28419 28421 28424 28425 28426 28427 28428 28429 28430 28431 28432 28434
## 3 5 1 4 1 1 5 1 1 4 1 1 4
## 28435 28436 28437 28439 28440 28441 28442 28443 28444 28445 28446 28447 28448
## 4 1 1 1 4 1 1 1 4 1 5 1 1
## 28449 28452 28454 28456 28457 28459 28461 28462 28463 28464 28465 28466 28467
## 1 4 5 1 5 4 1 1 1 1 2 1 5
## 28468 28469 28470 28471 28472 28474 28476 28477 28478 28479 28480 28482 28483
## 2 1 1 1 5 1 1 1 1 4 1 1 1
## 28484 28485 28486 28487 28489 28490 28491 28492 28493 28494 28495 28496 28497
## 3 1 1 5 1 1 1 1 4 1 1 4 3
## 28499 28500 28501 28502 28504 28506 28507 28508 28509 28510 28513 28516 28517
## 1 1 1 4 1 1 1 1 1 1 1 1 1
## 28519 28521 28522 28523 28524 28526 28527 28528 28529 28531 28532 28533 28534
## 1 1 1 1 1 1 1 1 1 4 4 1 1
## 28535 28536 28540 28541 28542 28543 28545 28547 28549 28550 28551 28552 28554
## 1 1 5 4 1 1 3 3 1 1 1 5 1
## 28555 28556 28557 28558 28560 28561 28562 28563 28564 28565 28568 28569 28570
## 4 1 1 1 1 4 1 1 1 1 1 5 1
## 28572 28573 28574 28576 28577 28578 28579 28581 28582 28583 28585 28587 28588
## 4 1 1 4 1 1 2 1 5 1 1 1 1
## 28589 28590 28593 28594 28595 28596 28597 28598 28599 28600 28601 28602 28604
## 1 4 4 1 1 1 4 1 4 1 5 1 1
## 28605 28606 28607 28609 28610 28611 28612 28613 28614 28615 28616 28617 28618
## 1 5 4 1 5 1 1 1 1 1 1 1 1
## 28619 28620 28622 28623 28624 28626 28627 28628 28629 28630 28632 28633 28634
## 1 4 1 1 2 1 1 1 4 1 1 5 1
## 28635 28636 28637 28638 28640 28641 28642 28643 28644 28645 28646 28647 28649
## 5 5 1 1 1 1 1 1 1 4 1 5 1
## 28650 28651 28652 28653 28654 28656 28657 28658 28659 28660 28661 28662 28663
## 1 1 1 5 1 1 2 1 1 1 1 1 1
## 28664 28665 28666 28668 28669 28670 28671 28672 28673 28674 28676 28678 28679
## 1 1 1 5 4 4 1 1 1 5 1 1 1
## 28680 28681 28684 28685 28686 28688 28689 28690 28691 28692 28693 28694 28696
## 1 5 1 1 1 4 1 1 5 1 1 1 1
## 28697 28698 28699 28700 28702 28703 28705 28706 28710 28711 28712 28713 28714
## 1 1 1 1 5 1 2 1 1 2 1 5 1
## 28715 28716 28717 28720 28721 28722 28723 28724 28725 28726 28727 28728 28729
## 1 1 1 1 1 1 1 1 1 1 1 1 1
## 28730 28731 28732 28733 28734 28735 28736 28737 28738 28739 28740 28742 28743
## 1 1 1 1 4 1 4 1 1 1 1 1 1
## 28744 28745 28746 28748 28749 28750 28752 28754 28755 28756 28757 28758 28759
## 1 1 3 1 1 1 4 4 1 1 1 1 1
## 28761 28762 28765 28767 28769 28771 28772 28773 28775 28776 28777 28778 28780
## 5 4 1 4 1 1 5 1 1 1 5 1 3
## 28781 28783 28784 28785 28786 28787 28789 28790 28791 28792 28793 28794 28795
## 4 1 2 1 1 1 1 5 1 1 5 4 4
## 28796 28797 28799 28800 28801 28802 28803 28804 28805 28806 28808 28811 28812
## 1 1 1 1 4 1 1 1 1 5 1 1 1
## 28814 28815 28817 28818 28819 28821 28822 28823 28824 28825 28826 28827 28828
## 1 5 5 1 1 1 1 1 1 4 5 1 4
## 28829 28832 28833 28834 28836 28837 28838 28839 28841 28842 28843 28844 28845
## 1 1 4 1 4 4 1 1 1 1 1 1 1
## 28846 28848 28850 28852 28853 28856 28857 28858 28859 28860 28862 28863 28864
## 3 1 2 4 5 1 1 1 1 1 4 1 1
## 28866 28867 28868 28869 28870 28871 28873 28874 28875 28876 28877 28878 28879
## 2 1 4 4 1 1 1 1 1 4 5 1 1
## 28880 28881 28884 28885 28886 28888 28889 28890 28891 28892 28893 28894 28896
## 1 1 1 1 1 3 1 1 1 1 4 1 1
## 28897 28898 28900 28901 28903 28904 28905 28906 28907 28908 28909 28910 28911
## 5 1 4 5 1 1 1 1 1 1 3 1 4
## 28913 28914 28915 28916 28918 28920 28921 28922 28923 28924 28925 28927 28928
## 1 4 5 1 1 1 3 1 1 1 1 1 1
## 28929 28931 28932 28933 28934 28935 28936 28937 28938 28940 28941 28942 28943
## 1 1 1 1 4 1 1 1 1 5 1 1 1
## 28945 28946 28947 28948 28949 28950 28951 28952 28953 28954 28955 28957 28958
## 1 4 3 4 1 5 1 4 1 1 3 3 5
## 28960 28961 28962 28965 28966 28967 28968 28969 28970 28971 28972 28973 28974
## 1 1 5 4 4 3 4 1 1 1 1 5 4
## 28975 28977 28978 28979 28981 28982 28983 28984 28985 28986 28988 28992 28993
## 5 3 1 4 1 1 5 5 1 1 1 1 5
## 28996 28998 28999 29000 29001 29002 29003 29005 29007 29009 29010 29011 29012
## 1 4 3 5 1 1 1 1 5 3 5 3 5
## 29014 29015 29016 29017 29018 29020 29022 29024 29025 29026 29030 29032 29033
## 1 1 1 1 1 1 5 1 1 1 5 5 4
## 29034 29035 29036 29037 29038 29039 29040 29041 29043 29044 29045 29046 29047
## 5 5 1 5 1 1 3 1 1 1 1 1 1
## 29048 29049 29050 29051 29053 29054 29055 29056 29057 29058 29059 29060 29061
## 1 1 1 5 4 1 4 3 1 1 5 1 1
## 29062 29063 29065 29066 29067 29068 29069 29070 29071 29074 29075 29076 29078
## 1 4 5 1 5 4 5 1 1 1 4 1 1
## 29079 29080 29082 29083 29087 29088 29089 29091 29092 29093 29094 29095 29096
## 1 1 4 1 5 1 1 5 1 1 5 1 4
## 29098 29099 29100 29103 29104 29105 29107 29109 29110 29111 29112 29113 29114
## 2 1 5 3 1 1 1 1 1 4 5 1 4
## 29115 29116 29117 29118 29119 29121 29122 29124 29125 29126 29127 29128 29129
## 4 1 1 5 1 3 1 1 1 5 5 5 1
## 29130 29131 29132 29133 29134 29135 29136 29137 29138 29139 29142 29143 29144
## 1 5 3 5 5 1 1 1 1 1 4 4 1
## 29146 29147 29149 29151 29152 29158 29159 29160 29161 29162 29163 29164 29165
## 1 1 1 1 1 1 1 1 1 4 2 3 5
## 29166 29167 29168 29169 29170 29171 29172 29173 29175 29176 29179 29180 29181
## 4 2 3 1 1 5 1 1 2 1 1 4 1
## 29182 29183 29184 29185 29186 29187 29189 29191 29192 29193 29194 29196 29197
## 1 1 1 5 1 4 1 1 1 5 1 1 4
## 29198 29199 29200 29201 29202 29203 29205 29206 29207 29208 29209 29211 29212
## 4 1 5 1 2 1 1 3 4 1 1 1 1
## 29213 29214 29216 29217 29218 29219 29220 29221 29222 29223 29224 29225 29226
## 1 1 1 1 1 1 4 1 5 1 5 1 5
## 29227 29228 29229 29230 29231 29232 29233 29235 29236 29237 29238 29239 29240
## 1 1 1 1 3 5 5 4 1 1 1 1 1
## 29241 29242 29243 29244 29246 29248 29250 29252 29253 29254 29256 29258 29259
## 1 5 5 1 4 5 1 5 1 1 1 1 1
## 29260 29261 29263 29264 29265 29267 29269 29270 29272 29273 29275 29276 29277
## 4 1 5 1 1 1 5 1 1 1 1 1 1
## 29280 29282 29283 29284 29285 29286 29289 29290 29292 29293 29294 29296 29298
## 1 3 3 1 5 1 4 5 1 5 1 1 1
## 29299 29300 29301 29302 29303 29304 29306 29307 29308 29309 29312 29313 29314
## 5 4 5 4 1 1 5 1 1 4 1 5 1
## 29315 29317 29318 29319 29323 29324 29325 29328 29329 29330 29331 29332 29333
## 4 1 1 1 1 1 1 1 4 1 1 1 1
## 29334 29337 29338 29339 29340 29341 29342 29343 29344 29345 29346 29347 29348
## 1 4 1 1 1 1 4 5 1 5 1 1 4
## 29349 29350 29351 29352 29353 29354 29355 29356 29357 29358 29359 29361 29362
## 1 5 1 3 1 1 1 5 5 1 1 1 3
## 29363 29364 29366 29367 29368 29370 29371 29372 29373 29374 29375 29376 29377
## 1 1 5 1 1 3 5 1 4 1 1 4 5
## 29378 29379 29380 29381 29382 29383 29384 29385 29386 29387 29388 29390 29391
## 4 5 1 1 1 1 1 5 5 4 1 1 1
## 29392 29394 29395 29397 29398 29399 29400 29401 29402 29403 29404 29406 29408
## 1 1 1 5 1 1 1 1 1 5 1 1 5
## 29409 29410 29411 29412 29414 29415 29416 29417 29418 29419 29421 29422 29423
## 1 1 1 1 5 4 1 1 5 1 5 1 4
## 29425 29426 29427 29428 29429 29430 29431 29432 29433 29434 29435 29436 29437
## 1 1 3 1 1 1 1 1 1 1 1 5 1
## 29438 29439 29440 29442 29443 29444 29445 29446 29447 29449 29450 29451 29452
## 1 1 1 5 1 1 1 5 5 5 1 1 1
## 29453 29455 29456 29458 29460 29461 29463 29464 29465 29466 29467 29468 29469
## 5 1 5 5 1 5 1 1 5 1 5 5 4
## 29470 29471 29473 29474 29475 29477 29478 29481 29483 29484 29485 29486 29487
## 5 1 1 1 5 3 4 5 5 1 1 5 3
## 29488 29491 29492 29493 29495 29498 29499 29501 29502 29504 29505 29506 29508
## 4 4 2 1 1 1 1 4 1 5 1 1 5
## 29511 29512 29514 29516 29517 29518 29519 29520 29521 29522 29524 29525 29526
## 1 1 1 1 4 1 3 5 1 1 1 1 5
## 29527 29529 29530 29531 29533 29534 29535 29536 29537 29538 29539 29540 29541
## 1 1 1 1 4 1 1 1 1 1 5 1 1
## 29546 29548 29550 29551 29552 29553 29555 29556 29557 29558 29559 29561 29562
## 5 5 4 2 5 1 1 4 1 1 5 1 5
## 29563 29564 29566 29569 29570 29571 29572 29573 29574 29576 29577 29579 29582
## 1 1 1 5 5 4 1 5 5 1 5 1 1
## 29583 29584 29585 29590 29592 29593 29594 29596 29597 29598 29599 29601 29602
## 1 3 5 1 5 5 1 1 1 1 1 1 1
## 29603 29605 29607 29608 29609 29610 29611 29612 29613 29615 29616 29617 29618
## 1 5 1 1 1 4 4 1 1 1 1 1 1
## 29619 29620 29623 29625 29629 29630 29633 29634 29635 29636 29637 29638 29639
## 1 1 1 1 1 1 1 2 4 1 4 4 1
## 29640 29641 29642 29643 29644 29645 29646 29647 29648 29649 29651 29652 29653
## 5 4 1 4 1 5 4 1 1 1 4 1 1
## 29655 29656 29658 29659 29660 29661 29662 29663 29665 29666 29667 29668 29670
## 4 1 5 5 4 1 5 1 1 4 1 1 4
## 29671 29672 29675 29676 29677 29678 29679 29680 29681 29683 29685 29688 29689
## 1 4 1 1 4 1 1 1 1 1 4 3 5
## 29690 29691 29692 29693 29694 29695 29696 29697 29698 29700 29701 29703 29704
## 1 5 1 4 4 4 1 5 4 1 1 5 5
## 29705 29707 29708 29710 29711 29713 29714 29715 29716 29718 29719 29720 29721
## 1 5 3 5 4 1 1 1 1 1 5 5 1
## 29723 29726 29727 29728 29730 29731 29732 29733 29734 29735 29736 29737 29739
## 1 5 1 5 4 1 5 1 1 1 1 1 1
## 29743 29744 29745 29746 29747 29748 29749 29750 29752 29755 29756 29757 29758
## 3 1 1 1 1 4 2 1 1 3 1 1 1
## 29759 29761 29762 29763 29764 29765 29766 29767 29768 29769 29771 29772 29773
## 5 1 1 1 1 4 1 1 1 5 3 1 1
## 29775 29778 29781 29782 29783 29784 29786 29787 29788 29790 29791 29792 29793
## 1 1 1 4 1 1 1 3 5 1 5 3 1
## 29795 29796 29797 29801 29802 29803 29804 29805 29806 29808 29809 29810 29812
## 4 1 1 5 1 1 1 5 1 5 1 1 2
## 29813 29814 29815 29816 29817 29818 29820 29821 29824 29825 29826 29827 29828
## 1 5 1 1 4 5 4 1 5 4 5 1 3
## 29830 29832 29833 29834 29836 29837 29838 29840 29841 29842 29843 29845 29846
## 1 1 4 1 4 1 1 1 1 1 1 1 4
## 29847 29848 29849 29850 29851 29852 29853 29854 29855 29856 29857 29858 29859
## 1 1 4 1 1 1 1 1 1 1 1 1 1
## 29860 29861 29863 29864 29865 29866 29867 29868 29869 29870 29871 29872 29873
## 1 1 4 1 1 1 1 5 1 1 5 1 1
## 29874 29875 29876 29877 29878 29879 29880 29882 29883 29887 29888 29889 29890
## 1 1 4 1 3 1 1 1 1 1 1 4 4
## 29891 29893 29895 29896 29897 29898 29899 29901 29902 29903 29905 29907 29908
## 4 1 1 1 1 1 5 5 1 1 1 5 5
## 29909 29910 29912 29914 29915 29916 29918 29919 29920 29921 29923 29924 29925
## 1 1 4 1 3 3 1 1 1 1 1 5 1
## 29927 29930 29931 29933 29934 29936 29939 29940 29941 29942 29943 29944 29945
## 1 1 1 5 1 4 4 1 1 5 1 1 5
## 29946 29947 29948 29949 29951 29952 29953 29954 29955 29956 29957 29959 29960
## 1 1 1 1 4 1 1 1 1 1 1 1 1
## 29961 29962 29963 29964 29965 29966 29967 29968 29969 29970 29973 29974 29975
## 1 1 1 1 1 5 4 1 1 1 5 1 1
## 29976 29977 29978 29979 29980 29982 29983 29984 29985 29986 29987 29988 29989
## 1 1 1 1 3 1 1 1 4 1 5 1 1
## 29991 29995 29996 29997 29998 29999 30000
## 1 1 1 1 1 1 1
##
## Within cluster sum of squares by cluster:
## [1] 217125.1 29708.3 147779.1 194440.8 167559.1
## (between_SS / total_SS = 12.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"km$size## [1] 17382 544 866 2684 2529#####################################################################
## K-means clustering with 5 clusters of sizes 548, 2203, 3206, ##
## 17213, 835. ##
#####################################################################Visualize the clusters
km %>% fviz_cluster(
data = df,
geom = c("point")
) +
geom_text(
vjust = 1.5, # Color points according to cluster
aes(
color = as.factor(km$cluster),
label = dfm$gradyear # label according to gradyear
)
)
km %>% fviz_cluster(
data = df,
geom = c("point")
) +
geom_text(
vjust = 1.5, # Color points according to cluster
aes(
color = as.factor(km$cluster),
label = dfm$gender # label according to gender
)
)
km %>% fviz_cluster(
data = df,
geom = c("point")
) +
geom_text(
vjust = 1.5, # Color points according to cluster
aes(
color = as.factor(km$cluster),
label = dfm$age # label according to age
)
)
Examine the estimated cluster centroids using the $centers output from the K-means algorithm, andplot them as a heatmap using either the heatmap function (base plotting) or geom_tile from ggplot2.Can you give a broad “name” to every cluster to summarize the interests of individuals in that cluster?Note: we did not make heatmaps in class so you may need to look at the help pages for ?heatmap or?geom_tile to see what arguments are needed. If you use the ggplot2 function, you will need to first tidy the estimated cluster centroids into a long format
heatmap(km$centers)
-cluster 1 is about the marching, “basket case”
-cluster 2 is about the sports, “Brains”
-cluster 3 is about the dance,mall,cheerleading “princesses”
-cluster 4 is about the sexy,soccer,jesus ,swimming “Athletes”
-cluster 5 is about the drugs and die “Criminals
Recode the gender variable in your data so that 0 represents F and 1 represents M, and convert yourK-means cluster labels in the $cluster output into a factor. Fit a logistic regression for gender ~cluster to determine whether there are any significant associations between cluster labels and self identified gender. Interpret two of the coefficients of your logistic regression model; do you think your results make sense in light of your cluster “names” from part c?
df1 <- na.omit(snsdata)
#################################################################
## If condition. ##
#################################################################
df1$gender <- ifelse(df1$gender == "F" &!is.na(df1$gender), 0, 1)
km$cluster<- factor(km$cluster,
levels = c(1,2,3,4,5),
labels = c("basket case", "Brains", "princesses","Athletes","Criminals"))
df1$cluster <- km$clusterCompute model
fit <- glm(
gender ~ cluster,
data = df1,
family = "binomial"
)Summarize regression model
fit %>% summary() # Standard output##
## Call:
## glm(formula = gender ~ cluster, family = "binomial", data = df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7638 -0.6870 -0.6870 -0.2826 2.5458
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.32362 0.01861 -71.105 < 2e-16 ***
## clusterBrains 0.14496 0.10278 1.410 0.158
## clusterprincesses -0.37433 0.09579 -3.908 9.31e-05 ***
## clusterAthletes 0.24084 0.04815 5.002 5.67e-07 ***
## clusterCriminals -1.87691 0.10418 -18.017 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 23725 on 24004 degrees of freedom
## Residual deviance: 23089 on 24000 degrees of freedom
## AIC: 23099
##
## Number of Fisher Scoring iterations: 5fit %>% tidy() # Tidy output# Confidence intervals for coefficients
fit %>% confint()## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) -1.36022964 -1.2872581
## clusterBrains -0.06000343 0.3432164
## clusterprincesses -0.56597517 -0.1901956
## clusterAthletes 0.14594732 0.3347022
## clusterCriminals -2.08738594 -1.6784654Predicted Values
# Predicted propobability are in "fitted values"
fit %>% view()Question 4: Monte Carlo simulations for the Monty Hall problem
The Monty Hall problem is a brain teaser based on the American game show Let’s Make a Deal. Write a Monte Carlo simulation to confirm that contestants who switch doors have a 2/3 chance of winning the car, while those who stay with their initial choice have only a 1/3 chance of winning.
library(ggplot2)
# number of times to repeat the experiment
iter<- 10000
# defining the doors
doors <- c("goat","goat","car")
# initialize dataframe to store the result per iteration
###########################################################################
###########################################################################
### ###
### THE FUNCTION: ###
### ###
###########################################################################
###########################################################################
monte_hall <- function(iteration){
contestant_door <- sample(doors, size = iteration, replace = TRUE)
i=1:iteration
#stick_win which is equal to 1 if the contestant_door in current i is car, 0 otherwise.
#switch_win which is equal to 0 if the contestant_door is equal to car, 1 otherwise.
#################################################################
## If condition. ##
#################################################################
stick_win <- ifelse(contestant_door == 'car',1,0)
#################################################################
## If condition. ##
#################################################################
switch_win <- ifelse(contestant_door == 'car',0,1)
stick_prob <- cumsum(stick_win)/i
switch_prob <- cumsum(switch_win)/i
#
#################################################################
## store result in a dataframe ##
#################################################################
results <- data.frame(i=i, contestant_door=contestant_door,
stick_win=stick_win, switch_win=switch_win,
stick_prob=stick_prob, switch_prob=switch_prob)
return(results)
}
monte_hall_results <- monte_hall(iter)
# show head of monte_hall_results
head(monte_hall_results)summary <- table(monte_hall_results$contestant_door)print summary
print(summary)##
## car goat
## 3346 6654df_summary <- data.frame(label = names(summary), count = matrix(summary))
print(df_summary)## label count
## 1 car 3346
## 2 goat 6654head(monte_hall_results)print(paste("Chance of winning if we always stick from our first choice: ",
sum(monte_hall_results$stick_win)/iter))## [1] "Chance of winning if we always stick from our first choice: 0.3346"###########################################################################
## Chance of winning if we always stick from our first choice: 0.3388 ##
###########################################################################print(paste("Chance of winning if we switch from our first choice: ",
sum(monte_hall_results$switch_win)/iter))## [1] "Chance of winning if we switch from our first choice: 0.6654"#####################################################################
## Chance of winning if we switch from our first choice: 0.6612 ##
#####################################################################Monte Carlo simulations for the Monty Hall problem - ggplot
g <- ggplot(monte_hall_results, mapping = aes(x=i, y=stick_prob))
g + geom_line(color="#3333ff") +
geom_hline(yintercept = 1/3, color = '#8080ff') +
geom_line(aes(y=switch_prob), color= "#ff751a") +
geom_hline(yintercept = 2/3, color = '#ff944d') +
ylab('Est.Probability')+xlab('Iteration') +
geom_label(data = data.frame(label = c('switch', 'stick'), i = c(10000,10000),
stick_prob = c(0.75,0.25)),
aes(label = label, color=label),
show.legend = FALSE
)+
scale_color_manual(values = c("#3333ff", "#ff751a"))+
ggtitle("Estimated Probability of Winning")
Refrence
In-class
- Dr. Kourosh Ravvaz content, UWM, Spring 2022.
Webpage
https://bookdown.org/yihui/rmarkdown-cookbook/update-date.html
https://www.rdocumentation.org/packages/ggplot2/versions/1.0.1/topics/geom_bar
https://www.rdocumentation.org/packages/olsrr/versions/0.5.3
https://cran.r-project.org/web/packages/olsrr/vignettes/variable_selection.html
https://www.machinelearningplus.com/machine-learning/complete-introduction-linear-regression-r/
https://www.machinelearningplus.com/machine-learning/complete-introduction-linear-regression-r/
https://www.geeksforgeeks.org/applying-a-function-over-an-object-in-r-programming-sapply-function/
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
https://bookdown.org/yihui/rmarkdown-cookbook/update-date.html
The best way to predict the future is to create it.” Abraham Lincoln.
End of Document.