Introduction
The Big Data Management (BDM) cycle begins with setting the architecture
by which large, swift, and various data forms are handled, from A to Z,
with as few human interactions as possible.
As humans’ capabilities are limited in speed, it became a necessity to
design a BDM architecture that handles various tasks
starting from data collecting, to parallel storage and Map Reducing,
until eventually reaching to the end line, which is decision making and actions.
Problem Statement
Nowadays, the rivalry among competitors in all types of businesses is at its peak.
If business owners do not keep up with the new requirements in the business world,
they will quickly be left behind and lose to other competitors.
Customer segmentation has become an essential tool in the Big data and business world,
especially with the rise of machine learning technologies and the abundance of beneficial data.
Therefore, all businesses which will not use machine learning techniques will fail in the future.
To enhance banks performance, we will build a predictive machine learning model
that uses clusterings algorithm to segment customers into categories
to help banks personalize products according to customer’s demographic and behavioral attributes.
Scope of Work - Objectives
It is challenging to direct personal ads to millions of users simultaneously.
As there will be different groups and orientations.
Therefore, advertisements personalization has become a big data problem in the marketing industry.
This is accomplished by doing the following,
A. Enhancing big data resources management in banks/firms.
by automating the annotation process of customers (Auto Labeling via clustering).
B. Enabling flexibility when handling vast records of customers.
C. Strategizing Marketing Techniques by making advertisements more accurately personalized by machine learning.
D. Minimizing the possibility of risks in future investments.
E. Keeping up with the rapid speed of customers' data expansion.
F. Detecting fraudulent/suspicious accounts (Outliers).
Current solutions -
Supervised Learning
There are many approaches which can be done to direct personal ads.
But the strongest so far is AI,
because machine learning can learn from the past (collected data)
to predict the future with high accuracy and with very short time.
As J. Chio, and K. Lim stated in their paper,
"Identifying machine learning techniques for classification of target advertising",
AI is better than traditional practices as it provides enhanced computational power,
which advances the optimization of digital advertisements.
Yet the major drawback in Supervised learning is that we annotate MANUALLY the parent for each user.
In this case (Hundred of thousands of users are annotated by humans)
to predict in the future what class the new customer is in.
Furthermore, we are limiting the number of parents (groups) from the beginning of analysis,
if new customers come with new personalizations, the system would not cast them
under a specific parent accurately.
Proposed Solution -
Unsupervised Learning
We propose a business solution that automatically clusters bank clients
based on their financial demeanor and attributes.
This solution aims to achieve a systematic customer inspection
that collects and analyzes their data unsurprisingly,
which further enhances big data resources management
as it does not require human interaction to annotate customers or classify them
under certain clusters.
Instead, the proposed algorithm gathers similar observations (customers)
under one parents clusters (group), then the marketing department can create
advertisements that directly connect with the clients based on their groups.
Simulation and Results
In this project, we created a pipeline that takes data from the database through SQL- like commands,
then descriptive and exploratory analysis is made and presented on the dashboard
to help bank business analytics understand how their customers behave.
A. Initial
Understanding about the data
Original_DF <- read.csv('/users/salahkaf/desktop/Dataset.csv')
Getting initial understanding of the data
1 - Exploring the data set head and tail.
head(Original_DF,5) #Top 5 rows
ID Gender Ever_Married Age Graduated Profession
1 462809 Male No 22 No Healthcare
2 462643 Female Yes 38 Yes Engineer
3 466315 Female Yes 67 Yes Engineer
4 461735 Male Yes 67 Yes Lawyer
5 462669 Female Yes 40 Yes Entertainment
Work_Experience Spending_Score Family_Size Var_1
1 1 Low 4 Cat_4
2 NA Average 3 Cat_4
3 1 Low 1 Cat_6
4 0 High 2 Cat_6
5 NA High 6 Cat_6
tail(Original_DF,5) #Last 5 rows
ID Gender Ever_Married Age Graduated Profession
8064 464018 Male No 22 No
8065 464685 Male No 35 No Executive
8066 465406 Female No 33 Yes Healthcare
8067 467299 Female No 27 Yes Healthcare
8068 461879 Male Yes 37 Yes Executive
Work_Experience Spending_Score Family_Size Var_1
8064 0 Low 7 Cat_1
8065 3 Low 4 Cat_4
8066 1 Low 1 Cat_6
8067 1 Low 4 Cat_6
8068 0 Average 3 Cat_4
2 - Exploring the data set dimensions and glimpse.
glimpse(Original_DF) #Glimpse about DF
Rows: 8,068
Columns: 10
$ ID <int> 462809, 462643, 466315, 461735, 462669, 4613…
$ Gender <chr> "Male", "Female", "Female", "Male", "Female"…
$ Ever_Married <chr> "No", "Yes", "Yes", "Yes", "Yes", "Yes", "No…
$ Age <int> 22, 38, 67, 67, 40, 56, 32, 33, 61, 55, 26, …
$ Graduated <chr> "No", "Yes", "Yes", "Yes", "Yes", "No", "Yes…
$ Profession <chr> "Healthcare", "Engineer", "Engineer", "Lawye…
$ Work_Experience <dbl> 1, NA, 1, 0, NA, 0, 1, 1, 0, 1, 1, 4, 0, NA,…
$ Spending_Score <chr> "Low", "Average", "Low", "High", "High", "Av…
$ Family_Size <dbl> 4, 3, 1, 2, 6, 2, 3, 3, 3, 4, 3, 4, NA, 1, 1…
$ Var_1 <chr> "Cat_4", "Cat_4", "Cat_6", "Cat_6", "Cat_6",…
3 - Exploring the data set structure and summary.
summary(Original_DF) #Summary of DF
ID Gender Ever_Married
Min. :458982 Length:8068 Length:8068
1st Qu.:461241 Class :character Class :character
Median :463472 Mode :character Mode :character
Mean :463479
3rd Qu.:465744
Max. :467974
Age Graduated Profession
Min. :18.00 Length:8068 Length:8068
1st Qu.:30.00 Class :character Class :character
Median :40.00 Mode :character Mode :character
Mean :43.47
3rd Qu.:53.00
Max. :89.00
Work_Experience Spending_Score Family_Size
Min. : 0.000 Length:8068 Min. :1.00
1st Qu.: 0.000 Class :character 1st Qu.:2.00
Median : 1.000 Mode :character Median :3.00
Mean : 2.642 Mean :2.85
3rd Qu.: 4.000 3rd Qu.:4.00
Max. :14.000 Max. :9.00
NA's :829 NA's :335
Var_1
Length:8068
Class :character
Mode :character
4 - Exploring the data set missing values.
# Total number of missing values in the data set
cat("The total number of missing values in the dataset is" , sum(is.na(Original_DF)))
The total number of missing values in the dataset is 1164
# Total number of missing values in the data set per column name
colSums(is.na(Original_DF))
ID Gender Ever_Married Age
0 0 0 0
Graduated Profession Work_Experience Spending_Score
0 0 829 0
Family_Size Var_1
335 0
Cleaning the missing values
One of the essential key points here is to decide which replacement i.e.,
imputation technique is valid to get the most effective results.
Our options here is to either:
A. To omit these values.
B. To use central tendency measurements (Mean. median, or mode).
However, option A in this case will make us lose customers data,
which opposes what we want.
Let us plot a box plot.
Box plot to analyze
the centeral tendencies
In both cases, we observe that both plots indicate that data looks to be right-skewed (long tail in the right).
Therefore it is more appropriate to use median value than the mean.
ExperienceMedian <- median(Original_DF[,7], na.rm = T)
cat("The median value for work experience is", ExperienceMedian, "year \n")
The median value for work experience is 1 year
FamilySizeMedian <- median(Original_DF[,9],na.rm = T)
cat("The median value for family size is", FamilySizeMedian, "persons \n")
The median value for family size is 3 persons
Replacing the missing values in each column with the Median of that column
Original_DF$Work_Experience[is.na(Original_DF$Work_Experience)] <- ExperienceMedian
Original_DF$Family_Size[is.na(Original_DF$Family_Size)] <- FamilySizeMedian
summary(Original_DF)
ID Gender Ever_Married
Min. :458982 Length:8068 Length:8068
1st Qu.:461241 Class :character Class :character
Median :463472 Mode :character Mode :character
Mean :463479
3rd Qu.:465744
Max. :467974
Age Graduated Profession
Min. :18.00 Length:8068 Length:8068
1st Qu.:30.00 Class :character Class :character
Median :40.00 Mode :character Mode :character
Mean :43.47
3rd Qu.:53.00
Max. :89.00
Work_Experience Spending_Score Family_Size
Min. : 0.000 Length:8068 Min. :1.000
1st Qu.: 0.000 Class :character 1st Qu.:2.000
Median : 1.000 Mode :character Median :3.000
Mean : 2.473 Mean :2.856
3rd Qu.: 4.000 3rd Qu.:4.000
Max. :14.000 Max. :9.000
Var_1
Length:8068
Class :character
Mode :character
Visualized Analysis
Bar
plot for the frequencies of spending scores of the customers
Original_DF_bar <- Original_DF[c("Spending_Score","Family_Size" )]
# setting the family size as a factor for plotting.
Original_DF_bar$Family_Size <- as.factor(Original_DF_bar$Family_Size)
ggplot(Original_DF_bar, aes(Spending_Score, fill = Family_Size)) +
geom_bar() +labs(title = "Barplot for the frequency of the spending score for customers"
, y = "Frequency", x = "The spending Scores")
We can conclude from the above bar graph the following:
1- Customers who have low spending score are more than those with a spending score of high
or average by a factor of 3 to 4.
2- Customers who have average and high spending score usually have a family size of 2
to 5 members and almost no family size of one member at all.
3- customers with a low spending score have a wider distribution of family size,
going from 1 member to 9 members with an ascending decline in the frequency according to the family size.
Barplot for the
Professions of the customers
Original_DF_bar2 <- Original_DF[c("Profession", "Family_Size", "Spending_Score")]
Original_DF_bar2$Profession[Original_DF_bar2$Profession == "Artist"] <- "Others"
# deleting rows according to the profession column that has "" as a value
Original_DF_bar2 <- filter(Original_DF_bar2, Profession != "")
Original_DF_bar2$Spending_Score <- factor(Original_DF_bar2$Spending_Score,
levels=c("High", "Average", "Low"))
Original_DF_bar2 <- group_by(Original_DF_bar2,Profession )
Original_DF_bar2 <- summarise(Original_DF_bar2, average= mean(Family_Size),
)
Original_DF_bar2
# A tibble: 9 × 2
Profession average
<chr> <dbl>
1 Doctor 2.89
2 Engineer 2.98
3 Entertainment 2.80
4 Executive 3.42
5 Healthcare 3.65
6 Homemaker 2.33
7 Lawyer 1.99
8 Marketing 3.07
9 Others 2.52
Overall, the family size for all professions has a small range of dissimilarity.
Healthcare and Executive are the highest and homemaker and lawyer are the lowest.
line
graph for Work experience average Vs the spending score
Original_DF_line <- Original_DF[c("Work_Experience", "Family_Size","Spending_Score" )]
Original_DF_line <- group_by(Original_DF_line,Spending_Score )
Original_DF_line <- summarise(Original_DF_line, average = mean(Work_Experience))
Original_DF_line <- arrange(Original_DF_line, desc(average))
Original_DF_line$Spending_Score <- factor(Original_DF_line$Spending_Score,
levels=c("Low", "Average", "High"))
Original_DF_line
# A tibble: 3 × 2
Spending_Score average
<fct> <dbl>
1 Low 2.64
2 Average 2.36
3 High 1.97
ggplot(Original_DF_line, aes(Spending_Score, average, group = 1)) +
geom_line() + geom_point() +labs(title = "Average work experience Vs the spending score",
x = "The spending score",
y = "work experience average")
We can conclude from the above bar graph the following:
The higher the number of working experience the lower the spending score.
Pie
charts for females and males spending scores frequency
# data manipulation for females
Original_DF_Pie <- Original_DF[c("Gender", "Spending_Score")]
Original_DF_Pie_F <- filter(Original_DF_Pie, Gender == "Female")
Original_DF_Pie_F <- group_by(Original_DF_Pie_F, Spending_Score)
Original_DF_Pie_F <- summarise(Original_DF_Pie_F, Female_Frequency = length(Gender))
Original_DF_Pie_F
# A tibble: 3 × 2
Spending_Score Female_Frequency
<chr> <int>
1 Average 831
2 High 490
3 Low 2330
total_females <- nrow(filter(Original_DF_Pie, Gender == "Female"))
total_males <- nrow(filter(Original_DF_Pie, Gender == "Male"))
#data manipulation for males
Original_DF_Pie_M <- filter(Original_DF_Pie, Gender == "Male")
Original_DF_Pie_M <- group_by(Original_DF_Pie_M, Spending_Score)
Original_DF_Pie_M <- summarise(Original_DF_Pie_M, Male_Frequency = length(Gender))
Original_DF_Pie_M
# A tibble: 3 × 2
Spending_Score Male_Frequency
<chr> <int>
1 Average 1143
2 High 726
3 Low 2548
F_Pie <- ggplot(Original_DF_Pie_F, aes(x="", y=Female_Frequency, fill=Spending_Score))+
geom_bar(width = 1, stat = "identity") + coord_polar("y", start=0) +
theme(plot.title = element_text(hjust = 0.5))+
geom_label(aes(label = percent(Female_Frequency/total_females)),
position = position_stack(vjust = 0.5),
show.legend = FALSE, size = 2.5) +
labs(title = "Spending scores for females")+
theme_void() # remove background, grid, numeric labels
M_Pie <- ggplot(Original_DF_Pie_M, aes(x="", y=Male_Frequency, fill=Spending_Score))+
geom_bar(width = 1, stat = "identity") + coord_polar("y", start=0) +
theme(plot.title = element_text(hjust = 0.5))+
geom_label(aes(label = percent(Male_Frequency/total_males)),
position = position_stack(vjust = 0.5),
show.legend = FALSE, size = 2.5)+
labs(title = "Spending scores for males")+
theme_void() # remove background, grid, numeric labels
grid.arrange(M_Pie, F_Pie, nrow = 1)
The above pie charts show that the percentage of males who have an average or a high
spending score is higher than the percentage of females with a high or an average
spending score..
Bar
plot for the number of people who whether have even been married or
not:
Original_DF_bar3 <- filter(Original_DF,Ever_Married != "" )
Original_DF_bar3$Spending_Score <- factor(Original_DF_bar3$Spending_Score,
levels=c("Low", "Average", "High"))
ggplot(Original_DF_bar3,aes(Ever_Married, fill = Spending_Score)) +
geom_bar()+ scale_fill_manual(values = c("dodgerblue4",
"forestgreen", "firebrick")) +
labs(title = "Marital status", x = "married or not", y = "frequency") +
theme_gray()
The bar graph above shows that peopel who are not married predominantly have a
low spending score. For married people, the spending score is normally distributed,
meaning that most values are close to the average.
Box plot for
the spending scores Vs customers age
[1] "ID" "Gender" "Ever_Married"
[4] "Age" "Graduated" "Profession"
[7] "Work_Experience" "Spending_Score" "Family_Size"
[10] "Var_1"
Original_DF_box <- Original_DF
Original_DF_box$Spending_Score <- factor(Original_DF_box$Spending_Score,
levels=c("Low", "Average", "High"))
ggplot(Original_DF_box, aes(Spending_Score, Age, fill = Spending_Score)) +
geom_boxplot()+ scale_fill_manual(values = c("dodgerblue4",
"forestgreen", "firebrick"))+
labs(title = "Box plot for age distribution Vs the spending score",
x = "The spending score", y = "Customers Age")
According to the distribution of the box plots above, there is a positive correlation
between the customers age and their spending scores, the older peopel are, the
higher their spending score is.
It is also important to mention that the low and average spending scores have many up skewed outliers
that are above the third quartile which is more than 75% of the age values for low and average spending
score.
Machine Learning Analysis
Meta data about the columns,
1 - ID >> Unique ID
2 - Gender >> Gender of the customer.
3 - Ever_Married >> Marital status of the customer.
4 - Age >> Age of the customer.
5 - Graduate >> Is the customer a graduate?
6 - Profession >> Profession of the customer.
7 - Work_Experience >> Work Experience in years.
8 - Spending_Score >> Spending score of the customer.
9 - Family_Size >> Number of family members for the customer (including the customer).
10 - Var_1 >> Anonymised Category for the customer.
We need to clarify that there are two types of clustering,
A. Hard clustering: Each data point belongs to a specific cluster.
K-means clustering is the algorithm used for hard clustering.
B. Soft clustering: Each data point exists in all the clusters with some probability.
The algorithm used for hard clustering is the k-means clustering method.
In our project, we will be using hard clustering,
which will help us in predicting which clusters are most suitable for the new customers.
K- means algorithm determines the cluster's centroid.
It is unsupervised-learning iterative technique.
Steps
1 - Specify number of clusters (K).
2 - Randomly assign each data point to a cluster.
3 - Calculate cluster centroids.
4 - Re-allocate each data point to their nearest cluster centroid.
5 - Re-figure cluster centroid.
Removing ID, and Var_1
Columns
Train <- Original_DF[,-c(1,10)]
head(Train,4)
Gender Ever_Married Age Graduated Profession Work_Experience
1 Male No 22 No Healthcare 1
2 Female Yes 38 Yes Engineer 1
3 Female Yes 67 Yes Engineer 1
4 Male Yes 67 Yes Lawyer 0
Spending_Score Family_Size
1 Low 4
2 Average 3
3 Low 1
4 High 2
Changing
charechter columns into factor column
Train$Gender <- as.factor(Train$Gender)
Train$Ever_Married <- as.factor(Train$Ever_Married)
Train$Graduated <- as.factor(Train$Graduated)
Train$Spending_Score <-as.factor(Train$Spending_Score)
Train$Profession <- as.factor(Train$Profession)
head(Train,4)
Gender Ever_Married Age Graduated Profession Work_Experience
1 Male No 22 No Healthcare 1
2 Female Yes 38 Yes Engineer 1
3 Female Yes 67 Yes Engineer 1
4 Male Yes 67 Yes Lawyer 0
Spending_Score Family_Size
1 Low 4
2 Average 3
3 Low 1
4 High 2
Apply one hot enconding
Gender_Female Gender_Male Ever_Married_ Ever_Married_No
1: 0 1 0 1
2: 1 0 0 0
3: 1 0 0 0
4: 0 1 0 0
Ever_Married_Yes Age Graduated_ Graduated_No Graduated_Yes
1: 0 22 0 1 0
2: 1 38 0 0 1
3: 1 67 0 0 1
4: 1 67 0 0 1
Profession_ Profession_Artist Profession_Doctor
1: 0 0 0
2: 0 0 0
3: 0 0 0
4: 0 0 0
Profession_Engineer Profession_Entertainment Profession_Executive
1: 0 0 0
2: 1 0 0
3: 1 0 0
4: 0 0 0
Profession_Healthcare Profession_Homemaker Profession_Lawyer
1: 1 0 0
2: 0 0 0
3: 0 0 0
4: 0 0 1
Profession_Marketing Work_Experience Spending_Score_Average
1: 0 1 0
2: 0 1 1
3: 0 1 0
4: 0 0 0
Spending_Score_High Spending_Score_Low Family_Size
1: 0 1 4
2: 0 0 3
3: 0 1 1
4: 1 0 2
Removing the duplicate
columns
Train <- Train[,-c(3,7,10)]
head(Train,4)
Gender_Female Gender_Male Ever_Married_No Ever_Married_Yes Age
1: 0 1 1 0 22
2: 1 0 0 1 38
3: 1 0 0 1 67
4: 0 1 0 1 67
Graduated_No Graduated_Yes Profession_Artist Profession_Doctor
1: 1 0 0 0
2: 0 1 0 0
3: 0 1 0 0
4: 0 1 0 0
Profession_Engineer Profession_Entertainment Profession_Executive
1: 0 0 0
2: 1 0 0
3: 1 0 0
4: 0 0 0
Profession_Healthcare Profession_Homemaker Profession_Lawyer
1: 1 0 0
2: 0 0 0
3: 0 0 0
4: 0 0 1
Profession_Marketing Work_Experience Spending_Score_Average
1: 0 1 0
2: 0 1 1
3: 0 1 0
4: 0 0 0
Spending_Score_High Spending_Score_Low Family_Size
1: 0 1 4
2: 0 0 3
3: 0 1 1
4: 1 0 2
Train the models
Gender_Female Gender_Male Ever_Married_No Ever_Married_Yes
1 0 1 1 0
2 1 0 0 1
3 1 0 0 1
4 0 1 0 1
5 1 0 0 1
6 0 1 0 1
Age Graduated_No Graduated_Yes Profession_Artist
1 0.05633803 1 0 0
2 0.28169014 0 1 0
3 0.69014085 0 1 0
4 0.69014085 0 1 0
5 0.30985915 0 1 0
6 0.53521127 1 0 1
Profession_Doctor Profession_Engineer Profession_Entertainment
1 0 0 0
2 0 1 0
3 0 1 0
4 0 0 0
5 0 0 1
6 0 0 0
Profession_Executive Profession_Healthcare Profession_Homemaker
1 0 1 0
2 0 0 0
3 0 0 0
4 0 0 0
5 0 0 0
6 0 0 0
Profession_Lawyer Profession_Marketing Work_Experience
1 0 0 0.07142857
2 0 0 0.07142857
3 0 0 0.07142857
4 1 0 0.00000000
5 0 0 0.07142857
6 0 0 0.00000000
Spending_Score_Average Spending_Score_High Spending_Score_Low
1 0 0 1
2 1 0 0
3 0 0 1
4 0 1 0
5 0 1 0
6 1 0 0
Family_Size
1 0.375
2 0.250
3 0.000
4 0.125
5 0.625
6 0.125
kmeans2 <- kmeans(Train, centers = 2, nstart = 25)
kmeans3 <- kmeans(Train, centers = 3, nstart = 25)
kmeans4 <- kmeans(Train, centers = 4, nstart = 25)
kmeans5 <- kmeans(Train, centers = 5, nstart = 25)
Interpreting the
results for K = 2, K = 3 and K = 4
K-means clustering with 2 clusters of sizes 2873, 5195
Cluster means:
Gender_Female Gender_Male Ever_Married_No Ever_Married_Yes Age
1 0.4190741 0.5809259 0.09676297 0.8840933 62.03794
2 0.4710298 0.5289702 0.57882579 0.4048123 33.19654
Graduated_No Graduated_Yes Profession_Artist Profession_Doctor
1 0.2669683 0.7225896 0.3759137 0.04803341
2 0.4340712 0.5566891 0.2764196 0.10587103
Profession_Engineer Profession_Entertainment Profession_Executive
1 0.07413853 0.1124260 0.11590672
2 0.09355149 0.1205005 0.05120308
Profession_Healthcare Profession_Homemaker Profession_Lawyer
1 0.01183432 0.01566307 0.212669683
2 0.24985563 0.03869105 0.002309913
Profession_Marketing Work_Experience Spending_Score_Average
1 0.01914375 1.594849 0.3195266
2 0.04562079 2.958614 0.2032724
Spending_Score_High Spending_Score_Low Family_Size
1 0.28611208 0.3943613 2.544379
2 0.07584216 0.7208855 3.028874
Clustering vector:
[1] 2 2 1 1 2 1 2 2 1 1 2 2 2 1 1 2 2 2 1 1 1 2 2 2 1 1 2 1 2 2 2 2
[33] 2 2 1 2 2 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2 2 1 1 2 2 2 2 1 1 1 1 1
[65] 1 2 2 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 2 1 2 2 2 2 2 1 2 1 1
[97] 2 1 1 2 1 1 1 2 2 2 2 1 2 2 1 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1
[129] 2 2 2 1 2 2 1 2 2 2 2 2 2 1 2 1 2 2 2 1 2 1 1 2 2 2 2 2 1 2 1 2
[161] 1 2 2 2 1 2 1 2 2 1 1 1 1 2 1 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2
[193] 2 1 1 2 2 1 1 2 2 2 2 2 1 2 2 1 2 1 1 2 2 1 1 2 1 2 1 1 2 2 2 2
[225] 2 1 2 2 2 2 1 2 1 2 2 2 2 2 1 1 1 1 2 1 2 2 2 2 2 2 1 2 2 1 2 1
[257] 1 2 2 2 1 2 1 2 2 1 1 1 2 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2 1 2 2
[289] 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 1 1 1 1 1 1 2 2 1 2 2 2 2
[321] 1 1 2 2 2 2 2 2 2 1 1 2 2 1 2 2 2 2 2 2 2 1 1 1 2 1 2 2 2 1 2 1
[353] 1 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 1 1 2 2 2 2 1 1 2 2 2 2 2
[385] 2 2 1 2 2 1 2 2 2 1 2 1 2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 1 1 2 1 1
[417] 1 2 2 1 2 2 2 2 1 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 2
[449] 2 2 2 2 2 1 2 1 2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 1 2 2 2 1 2 1 2 1
[481] 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 1 1 2
[513] 2 2 2 1 1 1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 1 1 2
[545] 1 2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 1 1 1
[577] 2 2 2 1 2 1 1 2 2 1 1 1 2 2 2 2 2 2 2 1 2 1 2 2 2 2 1 1 1 2 1 1
[609] 2 2 2 1 1 2 1 2 1 1 2 1 2 2 1 1 1 2 2 1 2 1 1 2 2 2 2 2 2 1 1 2
[641] 2 1 2 2 2 2 1 1 2 1 1 2 1 2 1 2 1 2 1 1 2 2 2 2 2 2 2 1 2 2 2 2
[673] 2 1 2 1 2 2 2 2 1 2 1 2 1 2 2 2 2 2 2 2 2 1 1 2 2 2 1 1 2 1 2 2
[705] 1 1 2 2 2 1 1 1 2 2 2 1 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1 2 2 1
[737] 1 2 1 1 2 2 2 2 2 1 1 2 1 1 2 2 1 1 1 1 2 1 2 1 2 1 1 2 2 1 2 2
[769] 2 1 2 2 1 2 2 1 1 2 2 1 2 1 1 2 2 2 2 2 1 2 1 2 2 2 1 2 2 1 2 1
[801] 1 1 2 1 2 2 1 1 2 1 1 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 1 2 1 1 1 2
[833] 2 1 1 2 2 2 1 2 2 2 1 2 2 1 1 1 2 2 1 2 1 1 1 1 1 1 2 2 2 1 2 2
[865] 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 1 1 1 1 2 2 2 2 2 1
[897] 2 1 1 2 1 2 1 2 2 2 1 2 2 2 2 2 1 1 2 2 1 2 1 1 1 1 2 1 2 2 2 2
[929] 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2
[961] 1 1 2 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 1 1 2 1 2 2 1 2 2 2 1 1 2
[993] 2 1 2 2 2 2 1 1 1 2 1 1 2 1 1 2 2 2 1 1 2 1 2 2 1 1 1 1 2 2 2 2
[1025] 2 2 1 1 1 1 1 1 1 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2 2
[1057] 1 2 2 2 2 2 2 2 1 2 2 1 1 2 1 1 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 1
[1089] 2 1 1 1 2 2 2 2 2 1 1 2 1 2 2 2 2 1 2 2 1 2 2 2 2 1 2 1 1 2 1 2
[1121] 1 2 1 1 2 2 2 2 1 2 2 1 2 1 2 1 2 1 2 2 2 2 2 1 1 2 1 1 2 2 1 2
[1153] 1 2 2 2 1 2 2 2 2 2 2 2 2 1 2 1 1 1 1 1 2 2 2 1 1 2 1 1 2 1 2 2
[1185] 2 2 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2 2 1 1 2 2 1 2 2 2 2 2 1 1 2 1
[1217] 1 1 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2
[1249] 1 1 1 1 2 2 2 2 2 1 1 1 2 2 2 1 1 1 2 1 2 2 2 1 2 2 1 1 2 2 2 2
[1281] 2 2 1 1 2 1 1 1 2 2 2 2 2 2 2 2 1 2 1 1 1 2 2 2 1 2 1 1 2 2 2 2
[1313] 2 1 2 2 2 2 1 2 1 2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 1 2
[1345] 2 1 2 2 2 1 2 1 1 2 2 1 2 1 2 1 2 2 2 2 2 2 2 1 2 2 1 1 2 1 1 2
[1377] 2 2 1 1 1 2 1 2 2 1 1 1 2 2 2 1 2 1 2 1 2 2 2 1 2 2 1 1 1 2 2 2
[1409] 1 1 2 1 1 1 1 2 1 2 2 2 1 2 1 1 2 1 2 1 2 2 1 2 2 1 2 2 2 2 1 2
[1441] 1 2 2 2 2 2 1 2 1 2 1 1 2 2 2 2 2 2 2 2 1 1 2 2 1 2 1 2 1 2 2 2
[1473] 1 1 1 1 2 1 2 2 1 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2
[1505] 2 1 2 1 2 2 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 2 2 2 2 2 2 1 1 1 2 2
[1537] 1 2 1 1 2 2 2 1 2 2 2 1 2 2 1 1 2 1 1 1 2 2 1 1 2 2 1 2 2 2 2 2
[1569] 2 2 1 2 1 2 2 2 2 1 2 1 1 1 1 2 1 2 2 2 2 2 2 2 1 2 2 2 1 1 1 2
[1601] 2 1 1 2 2 2 2 1 1 1 1 1 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 1
[1633] 2 2 2 2 2 2 2 2 1 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 1 1 2 1 2 2
[1665] 1 2 2 2 2 2 1 2 1 1 2 2 2 1 2 2 1 2 1 1 1 1 2 2 1 2 2 1 2 2 2 2
[1697] 2 2 1 1 1 1 2 2 2 2 2 2 2 1 2 2 1 2 2 2 1 1 2 1 2 2 1 1 2 1 2 1
[1729] 1 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 1 2 2 2 2 1 2 2 1 2 2 1 2 2 1 2
[1761] 2 1 2 2 2 1 1 2 1 2 2 1 1 2 2 2 1 1 1 2 2 2 2 2 1 2 2 1 1 1 2 2
[1793] 1 2 2 2 2 2 1 2 2 1 1 2 2 2 2 2 1 2 1 2 1 1 2 2 1 2 2 2 2 1 1 1
[1825] 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1 2 2 1 2 1 2 2 1 2
[1857] 2 2 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2
[1889] 2 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2 2 2 2 2 1 1 2 2 2 1 2 1 1 2 2 2
[1921] 2 2 1 1 2 2 2 2 2 1 2 1 1 2 2 2 2 1 1 1 1 1 2 2 2 2 2 1 1 2 2 2
[1953] 2 2 1 2 2 2 2 2 2 1 2 1 2 2 2 1 1 1 1 2 2 1 2 2 2 1 2 2 2 2 1 2
[1985] 1 2 2 2 2 1 1 2 2 2 2 1 2 2 1 1 2 1 2 1 2 2 1 2 1 1 2 2 2 2 1 2
[2017] 2 2 1 1 2 1 2 1 2 2 2 2 1 2 2 1 2 1 2 1 2 2 1 1 1 2 2 2 2 2 2 1
[2049] 2 1 1 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 1 1 1 2 2 2 2 2 2 1 2 2 2 2
[2081] 1 2 1 2 1 2 2 1 1 2 2 1 1 2 1 1 1 2 2 2 2 2 2 1 2 2 2 2 1 1 2 1
[2113] 2 2 2 1 2 1 2 2 2 2 2 2 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 1 2
[2145] 1 1 2 2 2 2 1 2 2 2 1 2 1 2 2 2 2 2 2 1 2 2 2 2 2 1 1 2 2 2 1 1
[2177] 2 1 1 2 2 2 1 2 2 2 2 2 1 1 2 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2
[2209] 2 1 1 2 2 1 2 1 1 2 1 2 1 1 2 2 2 1 2 1 2 2 1 1 1 2 1 1 2 1 1 1
[2241] 1 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 1
[2273] 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1
[2305] 2 2 2 2 2 1 2 1 1 2 1 2 2 1 1 2 2 2 2 2 1 2 2 1 1 2 2 1 2 2 1 1
[2337] 1 2 2 2 2 1 2 2 1 1 2 1 1 1 1 1 2 1 2 2 2 2 1 1 2 1 2 2 1 2 1 2
[2369] 2 2 1 2 1 2 1 2 2 2 2 1 2 1 2 2 1 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2
[2401] 2 2 2 2 2 2 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 2 1 2 2 2 2 2 2 1 2 2
[2433] 1 2 1 2 2 2 2 2 2 2 1 1 2 2 2 1 2 1 2 1 2 1 1 1 2 2 1 2 2 1 2 2
[2465] 2 1 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 2 1 2 2
[2497] 1 2 1 2 2 1 2 2 1 1 1 2 2 1 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2
[2529] 1 2 2 1 2 2 1 2 2 1 2 1 2 1 2 1 1 2 2 1 2 2 1 1 2 2 1 2 2 2 2 2
[2561] 2 1 2 2 2 1 2 2 1 2 2 1 2 1 2 2 2 2 1 1 1 1 2 2 1 2 1 1 2 2 2 2
[2593] 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 1 1 2 2 1 1 2 1 2 1 2 2 2 2 2 2 2
[2625] 2 2 1 2 2 1 2 2 1 2 2 2 2 1 1 2 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 2
[2657] 2 2 1 1 2 2 2 2 2 2 1 2 2 2 1 2 1 1 1 2 2 1 2 2 2 2 1 2 2 1 2 2
[2689] 2 1 1 2 2 1 2 2 2 1 1 2 1 1 2 1 1 2 2 2 1 2 2 1 1 1 1 1 2 1 2 2
[2721] 1 2 2 1 1 2 2 1 1 2 2 1 1 1 2 2 2 1 2 1 1 2 2 1 1 2 2 1 2 1 2 1
[2753] 2 1 1 2 2 2 1 2 1 2 2 2 1 2 2 1 2 1 1 2 2 2 1 1 1 2 2 2 2 1 2 2
[2785] 2 2 2 2 1 1 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 1 2 1 2 1 2 1
[2817] 1 2 2 1 2 2 2 2 2 2 1 2 1 1 2 1 2 1 2 2 2 1 1 2 2 1 2 2 2 2 2 2
[2849] 2 2 2 2 2 1 2 1 1 2 2 2 2 1 1 2 2 1 2 2 2 2 2 2 1 2 2 1 2 2 2 2
[2881] 2 2 1 1 1 2 1 2 2 1 2 1 2 2 1 2 1 2 1 2 2 1 1 2 1 2 2 2 1 2 2 2
[2913] 1 1 2 2 2 1 2 1 2 2 2 2 1 1 2 1 1 2 2 1 2 1 2 2 1 1 1 2 2 1 1 1
[2945] 1 1 2 2 2 2 1 2 2 1 2 2 1 2 2 2 2 2 2 1 2 2 2 1 2 2 1 2 2 1 1 2
[2977] 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 1 1 2 1 2 2 1 2 2 2 2 2 2 2
[3009] 1 2 1 2 1 2 2 2 2 1 2 1 1 2 2 2 2 1 2 2 2 2 1 1 2 1 2 2 1 2 2 2
[3041] 1 1 2 1 2 1 1 2 1 2 2 1 1 1 1 2 1 2 1 2 1 2 2 1 2 1 2 1 1 2 2 2
[3073] 2 1 2 2 2 1 2 2 1 1 1 2 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 1 2
[3105] 2 2 2 1 1 2 2 2 1 1 2 2 1 2 2 1 1 2 2 2 2 1 2 2 1 2 1 2 2 1 2 2
[3137] 2 1 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 1 2 2 1 2 2 1 2 2 2 2 1 2 1 2
[3169] 1 2 1 1 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 1 2 1 1 2 2 2 2 1 1 1 1
[3201] 1 1 1 2 1 2 2 1 2 1 1 2 2 2 1 2 1 2 2 2 2 1 2 2 1 2 1 1 2 1 1 2
[3233] 2 2 1 2 1 2 1 1 2 2 2 2 1 1 2 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2
[3265] 2 2 1 2 1 2 1 2 2 1 1 1 1 2 1 1 1 2 2 2 2 2 2 1 2 1 2 2 1 2 2 2
[3297] 1 2 2 1 1 2 1 2 2 2 1 2 2 1 1 1 1 2 2 1 2 2 2 2 2 2 1 1 1 2 2 2
[3329] 2 2 1 1 2 2 2 1 2 1 1 2 2 2 1 1 2 1 2 1 1 2 2 1 2 2 2 1 1 1 1 2
[3361] 2 2 2 2 1 2 1 1 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 1 2 2 2
[3393] 2 2 2 2 2 1 1 2 1 2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 1 1
[3425] 1 1 2 2 1 1 2 1 2 2 2 2 2 1 2 2 2 2 2 1 1 1 1 2 1 1 2 2 2 2 2 2
[3457] 1 2 2 2 2 1 2 2 2 2 1 2 1 1 1 2 1 2 1 1 2 1 2 1 1 1 2 1 2 2 1 2
[3489] 2 2 1 1 1 2 1 2 1 2 1 2 1 1 2 2 2 2 2 1 2 1 1 2 1 1 1 1 2 2 2 2
[3521] 1 2 1 1 2 2 1 1 2 2 1 2 1 2 1 2 2 1 2 2 1 1 2 2 1 1 2 2 2 2 2 1
[3553] 2 2 1 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 1 1 2 2 1 2 1 2 1 1 2 2 2
[3585] 1 2 2 2 2 2 2 1 2 1 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
[3617] 2 2 2 2 2 2 1 1 1 2 1 2 2 2 1 2 2 1 2 2 1 1 2 1 1 2 1 1 2 1 2 2
[3649] 2 1 2 2 1 1 2 2 2 2 2 2 2 2 1 1 2 1 1 2 1 1 2 1 1 2 2 1 2 2 2 1
[3681] 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 1 1 1 2 1 1 1 2 2
[3713] 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 1 1 2 2 1 2 2 2 2 2 2
[3745] 2 1 1 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 2 1 2 2
[3777] 1 1 1 2 1 2 2 2 2 1 2 1 2 2 1 1 2 2 2 1 2 1 2 2 2 2 1 1 1 2 1 1
[3809] 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 2 2 2
[3841] 1 1 1 2 1 2 1 1 2 2 2 1 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2
[3873] 1 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2
[3905] 2 1 2 1 2 1 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 2 1 2 1 2 1 2 2
[3937] 2 2 2 2 2 2 1 2 2 2 1 1 1 2 2 2 2 1 2 1 1 1 2 2 2 2 2 2 2 1 1 2
[3969] 1 1 2 1 2 1 2 1 2 2 2 2 2 1 1 2 2 2 1 1 2 1 2 2 2 2 1 2 1 2 1 1
[4001] 2 2 1 1 1 2 1 2 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 1 2 1 2 2 1 1 2 2
[4033] 1 2 2 2 2 1 2 1 1 1 1 1 1 2 2 1 1 2 2 1 2 2 2 2 2 1 1 1 1 2 1 2
[4065] 1 2 1 1 1 2 2 2 2 1 2 2 2 1 2 1 2 2 2 2 2 2 1 1 2 2 1 2 2 2 1 2
[4097] 2 2 2 2 2 1 1 1 2 2 2 1 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1
[4129] 2 1 1 2 2 1 2 1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 2 1 1 2 2 1
[4161] 1 1 2 2 2 2 1 1 1 2 2 2 1 2 2 2 1 1 2 1 2 2 2 1 1 2 2 2 2 2 2 2
[4193] 1 1 2 2 2 2 2 2 1 2 2 2 2 1 2 1 1 1 2 2 1 2 2 2 2 1 1 2 2 2 2 2
[4225] 1 2 2 2 1 2 2 2 2 2 2 2 1 1 1 1 2 2 1 2 2 1 1 2 2 2 2 2 1 2 1 2
[4257] 1 2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 1 2 1 2 1 2 2 1 1 2 2
[4289] 1 2 1 1 2 1 1 2 1 2 2 2 1 1 1 1 2 2 2 2 1 1 2 2 2 2 2 1 2 2 1 2
[4321] 2 2 2 2 1 1 2 1 1 1 1 2 2 1 2 1 2 2 2 2 2 1 1 1 2 2 1 2 2 2 2 2
[4353] 1 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 1 2 2 2 1 2 1 2 2 2 1 2 2 2
[4385] 2 2 1 2 2 2 2 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2 2 2 1 2 2 1 1 2 1 2
[4417] 2 2 1 2 1 1 1 1 2 2 2 2 2 2 2 1 1 1 2 1 2 2 1 2 2 2 1 2 2 2 2 2
[4449] 1 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 1
[4481] 1 2 1 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 1 1 2 1 1 2 2 1 1 2 2 2
[4513] 2 2 1 1 2 1 2 1 1 2 2 2 2 2 1 2 1 2 2 2 2 1 2 1 2 2 2 2 1 2 1 2
[4545] 2 2 2 2 2 2 1 2 2 2 1 2 2 1 2 1 2 2 2 2 2 2 2 1 2 1 2 1 2 2 2 2
[4577] 1 1 2 2 1 2 1 1 1 1 1 2 2 2 1 2 1 2 1 1 2 2 2 1 1 2 2 2 2 1 1 2
[4609] 1 2 1 2 1 2 1 1 1 2 1 1 1 1 2 2 1 2 2 1 1 1 2 2 1 2 2 2 1 2 2 2
[4641] 1 2 1 1 2 2 2 2 2 1 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2
[4673] 1 2 2 2 2 2 1 1 2 1 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 1 1
[4705] 1 2 2 2 2 2 2 1 2 1 2 1 2 2 1 2 2 1 1 2 2 2 2 1 2 1 2 2 1 1 2 1
[4737] 1 2 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 2 2 2 1 2 1 2 1 1 2 2 1 2 2 2
[4769] 2 2 2 2 2 1 2 2 2 2 1 1 2 2 1 1 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2
[4801] 1 1 2 2 2 1 2 1 2 2 1 1 2 2 1 2 1 1 1 2 1 1 2 2 1 1 2 2 2 2 2 2
[4833] 2 2 2 1 2 1 1 1 1 1 2 1 2 2 2 1 2 2 1 2 2 2 2 1 2 2 1 1 2 2 1 2
[4865] 2 1 1 1 2 1 2 2 1 1 2 1 2 2 2 1 1 2 1 2 2 2 1 2 1 2 1 2 1 1 2 1
[4897] 2 2 2 1 2 2 2 1 2 1 1 2 1 2 2 2 1 1 1 1 2 1 1 2 1 2 2 2 2 1 2 2
[4929] 2 1 2 1 2 2 1 2 2 2 2 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 2 2 2 2 2 2
[4961] 2 2 1 2 2 2 2 2 2 1 1 2 1 2 1 2 2 2 2 2 2 2 1 1 2 1 1 2 2 2 2 2
[4993] 2 1 2 1 1 2 2 2 1 2 1 1 2 1 2 1 2 2 1 2 2 2 1 1 1 2 1 2 2 1 2 2
[5025] 1 2 2 1 2 1 1 1 2 2 2 2 2 1 1 2 1 2 2 2 1 2 1 1 1 1 2 2 2 2 2 2
[5057] 1 2 1 1 1 1 1 1 2 1 2 1 2 1 1 2 2 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2
[5089] 2 1 1 2 1 1 2 1 2 2 1 1 1 2 2 1 1 1 2 1 2 1 1 2 1 2 1 1 2 2 1 2
[5121] 2 1 1 1 1 2 1 1 1 1 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 1 2 1 2
[5153] 1 2 2 2 1 1 2 2 1 2 1 2 2 2 2 2 1 1 2 2 2 2 2 1 1 2 1 2 2 2 2 2
[5185] 1 1 2 2 1 1 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 2 1 1 2 2 1 2 2 2 1
[5217] 2 1 2 2 2 1 2 1 1 2 2 2 1 2 2 2 1 1 2 1 1 2 2 2 1 2 2 2 2 2 1 2
[5249] 1 2 2 2 2 2 1 2 2 2 1 2 1 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 1 1 1 2
[5281] 2 1 1 1 2 2 1 2 1 1 2 2 1 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1 2 1
[5313] 1 2 1 1 2 1 2 2 1 2 2 2 2 2 1 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 2
[5345] 2 2 2 2 2 1 2 2 1 2 1 2 2 2 1 2 1 2 2 1 2 1 1 2 2 2 2 2 2 2 1 1
[5377] 1 2 1 1 2 2 1 2 1 2 2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2 2 2 2 1 2 1
[5409] 2 2 1 2 2 2 2 2 1 1 2 1 1 1 1 1 2 1 2 2 1 2 2 2 1 2 2 2 1 2 2 2
[5441] 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 1 2 2 2 2 2 1 2 2 1 2 1 1 2 2 2 1
[5473] 2 2 1 2 1 2 2 2 1 2 2 1 2 1 2 2 1 2 1 1 2 2 2 2 1 2 2 2 1 2 2 1
[5505] 2 1 1 1 1 1 1 2 2 1 2 2 2 2 2 1 2 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2
[5537] 1 2 1 1 1 2 2 1 2 2 1 2 1 2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 1 2 2 1
[5569] 1 2 1 2 2 1 1 2 2 1 1 2 2 2 2 1 2 2 1 2 2 2 2 1 1 1 2 2 1 2 2 2
[5601] 2 1 2 2 1 2 2 2 1 2 2 2 2 2 1 1 1 2 1 1 2 1 2 1 2 1 1 1 2 1 2 1
[5633] 1 2 1 2 1 1 2 2 2 1 2 2 1 2 1 2 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2 2
[5665] 1 2 1 2 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 1 1 1 2 1 2 2 1 2 2 2 1
[5697] 2 1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 1 2 1 2 2 2 1 2 1 1 1 1 2 2 2 1
[5729] 2 2 1 2 2 2 2 1 2 1 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 1
[5761] 2 1 2 2 1 1 1 2 2 1 1 1 2 2 1 1 2 2 2 2 2 1 2 1 1 2 2 1 2 1 1 1
[5793] 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 1 1 2 2 2 2 2 2 2 1
[5825] 2 2 2 2 2 1 2 1 2 2 1 2 2 1 1 1 1 2 2 2 1 2 2 2 2 2 1 1 2 2 1 2
[5857] 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 1 2 2 2 2 2 2 1 1 1
[5889] 2 2 1 2 2 2 2 1 2 1 2 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 2 2 2 2 1 2
[5921] 1 1 2 2 1 2 2 1 1 2 2 2 2 1 1 1 2 2 1 1 1 1 1 2 2 2 1 2 2 1 1 2
[5953] 2 2 2 2 2 1 2 2 1 2 1 2 1 1 2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2 1 2
[5985] 2 2 1 2 1 1 1 2 2 1 2 1 2 1 2 2 2 2 2 2 1 1 2 1 2 1 2 1 1 2 1 1
[6017] 1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 2 1 1 2 2 1 2 2 2 2 1 2 1 2 2 2 2
[6049] 2 1 1 2 2 1 2 2 1 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 1 1 1 1 2 2 2
[6081] 1 2 2 1 2 1 1 1 2 2 2 1 2 1 1 1 2 2 2 1 2 2 2 1 1 2 2 2 1 2 2 2
[6113] 2 1 1 2 2 2 1 2 1 2 1 1 1 2 2 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 1
[6145] 2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2
[6177] 1 1 1 2 1 1 1 2 1 2 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 2 2 2 2 2 1 1
[6209] 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 2
[6241] 1 2 1 2 2 2 1 2 1 1 2 2 1 2 2 2 1 2 1 1 2 2 2 2 2 2 1 1 2 2 2 2
[6273] 2 1 2 1 2 2 2 2 2 2 2 2 1 2 1 2 1 1 2 1 2 2 1 2 2 1 2 2 2 2 2 2
[6305] 2 2 2 2 2 1 2 2 1 1 2 2 1 2 2 1 2 2 1 2 1 2 2 2 2 1 2 2 2 2 2 1
[6337] 1 1 2 1 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 1 1 2 1 2
[6369] 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 1 1 1 2 2 2 2 2 1 1 1 2 2 2 2
[6401] 2 1 2 2 1 2 1 2 2 2 1 1 1 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2
[6433] 1 2 2 2 1 2 2 2 1 2 2 1 2 1 1 2 2 1 2 2 2 1 2 2 2 2 1 2 1 1 2 2
[6465] 2 1 1 2 2 1 2 2 1 1 2 1 2 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2 1 1 2 2
[6497] 2 2 1 2 2 2 1 2 1 1 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 2 2 1 2 2 2 2
[6529] 2 2 2 2 2 1 2 2 1 2 1 2 1 2 2 1 2 2 2 1 1 2 2 1 1 2 2 2 2 2 2 1
[6561] 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2 2 1 2 2 1 1 1 2 2 2 2
[6593] 2 1 2 1 2 1 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2 1 1 1 2 1 1 1 2 1 2 2
[6625] 2 1 2 2 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 1 2 2 1 1 2 1 2 1 2 1 2 2
[6657] 2 2 2 2 2 1 2 1 2 1 1 2 2 1 2 1 1 2 1 2 2 2 2 1 2 1 2 2 1 1 1 2
[6689] 2 2 2 2 1 1 2 2 2 2 2 2 2 1 1 2 1 1 2 2 1 2 2 1 1 2 1 1 2 2 1 2
[6721] 2 2 1 2 2 1 2 2 1 2 2 2 2 1 1 2 1 2 2 2 2 2 1 2 1 2 2 1 1 2 2 1
[6753] 2 2 1 2 1 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 1 2
[6785] 1 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 1 1 1 2 1 2 2 1 1 2 1 2 2 1 2 1
[6817] 2 1 1 1 2 2 2 2 2 2 1 2 1 1 1 2 1 2 2 2 2 2 2 2 1 2 2 1 1 2 2 1
[6849] 2 1 1 2 1 1 2 1 2 2 2 2 2 2 2 2 1 1 1 2 2 2 1 2 1 2 2 2 2 2 1 2
[6881] 1 1 1 1 2 1 2 1 1 1 1 1 2 2 2 1 2 2 2 2 2 2 1 2 1 2 2 2 1 1 2 1
[6913] 2 2 2 2 1 2 2 2 1 2 1 2 2 2 1 1 2 2 1 1 2 1 2 1 2 2 1 2 2 2 2 1
[6945] 1 2 2 2 2 1 2 1 1 2 2 2 2 2 1 2 2 2 1 1 2 2 2 1 1 2 1 2 2 2 1 2
[6977] 2 1 1 2 1 2 2 1 2 1 2 2 2 2 1 1 2 1 1 1 2 2 2 1 1 1 2 1 2 1 1 2
[7009] 2 2 1 2 2 2 1 2 1 2 2 2 1 1 1 2 2 1 2 2 2 1 1 2 2 1 2 1 2 1 2 1
[7041] 1 2 1 2 2 2 2 1 1 2 2 1 2 2 1 2 2 1 1 2 1 2 2 2 1 1 2 2 2 2 1 2
[7073] 1 2 1 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 2 2 2 1 2
[7105] 1 1 1 1 1 1 2 2 1 2 2 2 2 2 2 1 2 1 2 1 2 2 2 2 2 1 2 1 1 2 1 2
[7137] 1 2 2 2 2 2 2 2 1 2 2 2 1 2 2 1 2 2 1 1 1 1 2 2 2 2 1 2 1 2 1 1
[7169] 2 2 2 2 2 1 1 2 1 1 2 2 2 2 2 2 2 1 2 1 1 1 2 1 1 2 1 1 2 2 1 1
[7201] 1 2 1 2 2 2 1 2 2 2 1 2 1 1 1 1 2 1 1 2 2 1 2 2 2 1 2 1 2 1 2 1
[7233] 1 1 2 2 1 2 1 2 1 2 2 2 2 2 2 1 2 1 2 1 1 2 2 2 1 2 1 2 1 2 1 2
[7265] 2 2 2 2 2 2 2 1 2 1 1 2 1 2 1 2 1 2 2 2 2 1 1 1 2 1 2 1 1 2 1 2
[7297] 1 2 2 2 2 2 2 1 2 1 1 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 1 1 2 2 1 2
[7329] 2 1 2 2 1 2 2 2 2 1 1 2 2 1 1 2 2 1 2 1 1 2 2 1 2 2 1 2 2 1 2 2
[7361] 2 2 2 2 1 2 2 1 1 2 2 2 1 2 2 1 1 1 1 2 1 1 2 1 2 2 2 2 1 2 1 2
[7393] 2 1 2 2 2 2 1 2 1 2 1 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2
[7425] 1 1 2 2 2 1 2 1 2 1 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 2 2 2 2 2 1 1
[7457] 2 1 2 2 1 2 2 1 2 1 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 1 2
[7489] 1 1 2 1 2 2 2 1 2 2 2 2 1 1 1 2 2 2 2 2 1 1 2 1 2 1 2 2 2 2 1 2
[7521] 2 1 2 1 2 1 2 1 1 1 1 2 2 2 2 2 2 1 2 1 1 1 1 1 1 1 2 2 2 2 2 1
[7553] 2 1 2 1 1 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 1
[7585] 1 1 2 1 2 1 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 1 1 2 2 2 1 2 2 1
[7617] 2 1 2 2 1 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 1 1 2 2 1 2 2 2 2 1 1
[7649] 2 2 2 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2
[7681] 2 2 1 2 1 2 2 2 2 2 2 2 1 1 1 1 1 2 2 1 2 2 1 1 1 2 1 1 2 1 1 2
[7713] 1 1 1 2 1 2 2 1 2 1 1 2 1 1 2 2 2 1 1 1 2 2 2 2 2 2 2 1 2 1 2 2
[7745] 1 2 2 2 2 1 2 2 1 1 2 1 2 2 2 1 2 1 1 2 2 2 2 2 2 1 2 2 1 2 2 2
[7777] 2 2 1 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 1 2 1 1 2 2 1 2 2 1 1 1 1 1
[7809] 2 2 2 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 1 2 1 1 2 2 1 2 1
[7841] 2 2 2 1 2 2 2 2 1 1 2 2 1 2 1 2 1 1 1 2 1 2 2 2 1 2 1 2 2 2 2 1
[7873] 2 2 2 2 2 1 1 2 1 1 1 1 2 1 2 1 2 1 2 1 1 2 2 2 1 2 1 2 2 2 2 2
[7905] 2 2 2 2 1 1 1 2 1 1 2 2 2 2 1 2 1 1 2 1 2 2 1 2 1 2 2 1 2 2 2 1
[7937] 2 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 1 2 2 1 1 1 1 2 2 2 1 2 1 2 2
[7969] 2 2 1 1 2 2 2 2 1 2 2 2 2 2 2 2 1 2 1 1 2 1 2 2 2 2 1 2 2 2 1 2
[8001] 2 2 2 2 2 2 1 2 2 2 1 1 2 1 1 2 2 2 1 2 2 2 1 1 1 2 2 1 2 2 2 2
[8033] 2 2 1 2 2 2 1 1 2 2 2 2 1 1 1 1 2 1 1 2 2 2 1 2 1 1 2 2 1 1 2 2
[8065] 2 2 2 2
Within cluster sum of squares by cluster:
[1] 407666.6 428017.4
(between_SS / total_SS = 64.9 %)
Available components:
[1] "cluster" "centers" "totss" "withinss"
[5] "tot.withinss" "betweenss" "size" "iter"
[9] "ifault"
K-means clustering with 3 clusters of sizes 3386, 3153, 1529
Cluster means:
Gender_Female Gender_Male Ever_Married_No Ever_Married_Yes Age
1 0.4645600 0.5354400 0.71470762 0.2655050 28.48878
2 0.4636854 0.5363146 0.24421186 0.7399302 46.34443
3 0.4028777 0.5971223 0.06213211 0.9228254 70.70242
Graduated_No Graduated_Yes Profession_Artist Profession_Doctor
1 0.5372120 0.4536326 0.1813349 0.11636149
2 0.2226451 0.7687916 0.4741516 0.07897241
3 0.3276651 0.6592544 0.2661871 0.02943100
Profession_Engineer Profession_Entertainment Profession_Executive
1 0.08357944 0.11075015 0.03484938
2 0.10656518 0.13415794 0.09578180
3 0.05232178 0.09875736 0.11706998
Profession_Healthcare Profession_Homemaker Profession_Lawyer
1 0.361193148 0.04223272 0.001772002
2 0.031081510 0.02727561 0.009514748
3 0.007194245 0.01111838 0.383911053
Profession_Marketing Work_Experience Spending_Score_Average
1 0.05109273 2.950679 0.1284702
2 0.02886140 2.506502 0.3815414
3 0.01831262 1.345978 0.2197515
Spending_Score_High Spending_Score_Low Family_Size
1 0.05227407 0.8192558 3.241288
2 0.14176974 0.4766889 2.720266
3 0.38718116 0.3930674 2.284500
Clustering vector:
[1] 1 2 3 3 2 2 1 1 3 2 1 1 1 3 2 2 1 1 2 3 2 1 1 1 2 2 1 2 1 1 2 2
[33] 1 1 3 1 1 1 1 2 2 1 1 2 2 3 2 1 1 2 3 1 2 2 3 1 1 1 2 3 2 2 3 2
[65] 3 1 1 1 2 2 1 2 2 1 2 1 1 2 2 2 1 1 3 1 1 1 2 1 2 2 2 2 3 1 2 2
[97] 2 3 2 1 3 3 2 2 1 1 1 3 1 1 3 2 2 2 2 1 3 1 1 1 2 2 2 1 2 1 2 3
[129] 1 1 2 3 1 2 2 1 2 2 1 1 2 2 1 3 2 1 1 3 1 3 3 1 2 2 1 2 3 2 3 1
[161] 2 1 1 1 3 2 2 1 2 3 2 3 3 1 3 2 1 1 1 1 1 2 1 2 2 2 3 1 2 2 2 2
[193] 2 2 3 2 1 2 3 1 1 1 1 2 3 1 1 2 1 2 3 1 1 3 2 1 2 1 2 3 1 1 1 1
[225] 1 2 2 1 2 1 3 1 3 1 2 1 1 1 2 2 2 3 1 3 1 1 1 2 2 1 2 2 2 3 1 3
[257] 2 2 2 1 2 2 3 1 1 3 3 3 1 2 1 1 1 2 1 3 2 2 3 1 2 1 2 1 2 3 1 1
[289] 1 2 2 1 1 1 1 2 2 1 2 2 3 1 1 1 3 2 1 3 2 2 2 2 3 2 1 3 1 1 1 1
[321] 3 3 1 1 2 1 1 2 1 3 2 1 1 2 1 1 1 1 2 2 1 2 2 3 1 3 2 1 1 3 1 2
[353] 3 1 1 1 1 1 1 2 2 2 2 1 3 1 2 1 1 2 1 3 3 1 1 1 1 2 2 2 1 1 1 1
[385] 1 2 2 2 1 2 1 2 1 3 1 3 2 1 1 3 1 1 2 2 2 2 2 1 1 1 2 3 3 2 3 3
[417] 2 2 1 3 1 1 2 1 2 2 3 1 2 1 1 1 2 1 1 3 3 3 1 2 1 2 3 3 2 2 2 1
[449] 2 1 1 1 1 3 2 2 2 1 2 1 3 1 2 2 2 1 1 2 3 1 1 3 1 1 1 3 2 3 1 2
[481] 2 1 1 1 1 1 1 2 2 1 1 3 2 2 1 1 1 2 1 2 1 1 1 2 2 1 2 1 2 2 2 1
[513] 1 1 2 3 2 2 2 1 2 2 2 1 1 1 1 1 2 2 2 1 2 3 3 3 2 1 1 2 2 2 2 1
[545] 3 1 2 2 3 2 1 1 2 2 1 2 1 2 1 2 2 3 1 2 1 1 1 1 2 2 1 1 2 3 2 3
[577] 2 2 1 3 2 2 2 1 1 2 2 3 1 1 2 2 1 1 2 2 1 3 2 1 1 1 2 3 2 1 2 3
[609] 2 2 2 2 3 1 2 1 3 3 1 2 1 1 2 2 2 1 1 3 2 3 2 1 1 2 2 1 1 3 2 1
[641] 1 3 1 1 2 1 2 3 1 3 3 2 2 1 3 1 3 2 2 3 2 1 1 2 2 2 1 3 2 2 1 2
[673] 2 3 1 3 2 2 1 1 2 2 3 1 3 1 1 1 1 1 1 1 2 3 2 1 2 1 3 3 2 2 1 2
[705] 3 2 1 1 2 2 2 3 1 1 2 3 1 1 1 1 3 2 2 1 1 2 1 1 1 1 1 1 3 1 2 3
[737] 2 1 2 2 2 1 1 1 1 2 2 2 2 2 1 1 3 3 3 3 2 2 2 3 2 3 3 2 1 3 1 1
[769] 1 3 1 1 2 2 2 2 3 1 2 2 1 2 2 2 1 1 1 2 3 1 3 1 2 1 3 1 1 2 1 2
[801] 2 3 2 3 1 1 2 3 1 2 2 1 1 2 2 2 1 3 1 1 2 3 1 3 1 1 2 1 3 2 2 1
[833] 2 3 2 1 1 1 2 1 1 1 2 1 1 2 3 2 1 1 3 1 3 3 2 3 2 2 1 1 2 2 1 2
[865] 1 1 1 1 2 2 1 1 1 1 2 2 3 2 1 2 1 2 1 1 2 2 3 3 3 3 1 1 2 2 1 2
[897] 2 3 3 1 3 1 2 1 1 1 2 1 1 1 2 1 3 2 1 2 2 1 3 2 3 3 2 2 1 1 1 1
[929] 2 2 2 1 1 1 2 1 1 1 1 1 1 2 2 3 3 2 1 2 1 1 1 2 2 2 2 2 1 1 1 2
[961] 2 3 2 1 1 1 3 1 1 1 2 1 1 1 2 1 1 1 2 2 3 1 3 1 1 3 1 1 1 2 3 2
[993] 1 2 1 1 2 1 3 2 2 2 2 3 1 3 3 1 2 2 2 2 1 3 2 1 3 3 3 2 1 2 1 1
[1025] 1 1 2 3 3 2 2 3 3 2 1 1 1 2 3 1 1 2 1 3 2 1 2 1 1 1 2 2 3 2 1 1
[1057] 3 1 1 2 1 2 1 1 3 1 1 2 2 1 3 3 1 1 1 1 1 1 3 1 1 2 2 2 3 1 2 2
[1089] 1 2 3 3 1 2 1 1 1 2 3 2 3 1 1 1 2 3 2 1 3 1 2 1 2 3 2 2 2 1 2 1
[1121] 2 1 3 2 2 1 2 1 2 2 1 3 2 3 2 2 2 3 1 1 1 1 2 3 3 2 2 3 1 2 3 1
[1153] 2 1 2 1 3 1 1 1 2 1 1 1 1 2 2 2 3 3 3 3 2 2 2 3 2 2 2 3 2 3 1 1
[1185] 1 2 2 1 2 3 1 1 2 1 1 1 1 2 2 2 2 1 3 2 1 1 3 2 2 1 2 2 2 3 2 2
[1217] 2 3 1 2 3 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 2 2 2 1 1 2 1 2 2 3 1
[1249] 2 3 2 3 1 1 1 1 1 3 3 2 1 1 1 3 3 3 2 3 2 1 2 2 1 2 2 2 1 1 1 1
[1281] 1 2 3 3 1 2 3 3 1 1 1 2 2 2 1 2 3 1 3 3 2 1 1 2 3 1 3 3 1 1 1 1
[1313] 1 3 1 1 1 2 3 1 3 2 1 1 3 2 2 2 2 2 3 2 1 2 1 2 1 2 1 1 2 1 3 1
[1345] 1 2 1 1 1 3 1 3 2 2 1 2 1 2 2 2 1 1 1 2 1 1 1 3 2 1 3 3 2 2 3 1
[1377] 2 1 2 2 3 2 2 1 1 2 3 3 2 1 1 3 1 2 1 2 1 1 1 2 1 1 3 3 2 1 1 2
[1409] 3 3 2 2 2 2 2 1 2 2 1 1 3 1 2 3 1 2 1 3 1 1 3 1 1 3 1 1 1 1 2 1
[1441] 2 1 2 2 1 2 2 1 2 1 2 3 1 1 2 1 2 2 2 1 2 2 1 2 3 2 3 2 2 1 2 1
[1473] 2 3 2 2 2 3 2 1 2 3 1 1 1 2 1 3 2 1 1 1 2 1 1 1 2 1 1 1 2 2 2 1
[1505] 1 2 1 2 1 1 3 2 2 2 3 2 1 2 1 1 2 2 2 3 3 1 1 1 1 2 1 3 2 2 1 2
[1537] 2 1 3 2 2 1 1 3 2 1 1 2 1 1 3 3 1 2 2 3 1 2 2 3 2 1 2 2 1 1 1 1
[1569] 1 2 2 2 2 1 1 1 2 3 2 3 2 3 2 1 2 1 1 1 2 1 2 2 3 2 2 1 2 3 3 2
[1601] 1 2 2 1 1 1 1 2 2 3 3 3 2 2 3 1 2 1 2 3 1 2 1 2 1 1 1 1 1 1 1 3
[1633] 1 2 1 1 1 1 1 2 3 2 3 1 2 1 3 2 1 2 1 2 1 2 2 1 1 2 3 3 1 3 1 2
[1665] 3 1 2 2 1 2 3 2 2 2 1 1 1 2 1 1 3 1 2 3 3 2 1 2 2 2 2 3 1 1 1 1
[1697] 1 2 3 3 2 2 1 1 2 1 2 1 1 3 1 1 2 2 1 1 2 3 2 3 2 1 3 2 1 3 1 2
[1729] 3 2 2 1 2 2 1 2 1 1 2 2 1 1 3 1 3 2 1 2 2 2 2 1 2 2 1 2 2 2 2 2
[1761] 1 3 2 2 2 2 2 2 3 2 2 3 3 2 2 1 2 2 3 1 2 1 2 1 3 1 2 2 2 3 2 2
[1793] 3 1 1 1 1 1 2 2 2 3 2 2 1 2 2 1 2 2 3 1 2 3 1 2 3 1 2 1 2 2 3 3
[1825] 2 2 2 2 2 2 3 1 1 1 1 3 1 1 1 2 1 1 2 2 2 3 2 1 1 2 1 3 1 1 2 1
[1857] 2 2 1 1 1 2 1 1 2 2 1 3 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1 1
[1889] 1 3 2 2 1 1 3 2 3 3 1 2 2 1 1 1 2 2 1 2 3 3 2 2 2 3 1 2 3 1 1 1
[1921] 1 2 2 2 1 1 1 1 2 3 1 2 2 1 2 2 1 3 3 3 3 3 1 1 1 1 2 3 3 1 1 2
[1953] 1 1 3 1 1 2 2 2 2 2 1 3 1 2 1 2 3 3 3 2 2 3 1 1 2 3 2 2 2 2 3 1
[1985] 3 2 2 2 2 2 2 1 1 1 1 3 1 1 3 2 2 2 2 2 1 1 2 1 2 2 1 2 2 1 2 1
[2017] 2 1 3 3 1 3 2 2 1 1 1 1 2 2 2 3 1 3 2 3 1 1 2 3 3 2 2 2 1 1 1 3
[2049] 2 2 3 1 1 1 1 1 1 2 2 1 1 1 2 2 2 1 3 3 3 1 1 1 1 2 1 2 1 2 1 1
[2081] 3 1 2 1 2 2 1 2 3 1 1 3 3 1 2 3 3 1 1 2 1 1 1 2 1 1 2 1 3 3 2 2
[2113] 1 1 2 3 1 3 2 2 2 1 2 1 2 3 2 1 1 1 1 2 3 3 3 1 1 1 2 3 3 2 2 1
[2145] 3 3 2 2 1 2 3 1 1 2 2 2 3 2 1 2 1 1 1 3 1 2 1 1 2 3 3 1 1 1 3 3
[2177] 1 3 3 1 2 1 2 1 2 2 1 1 3 3 2 1 1 2 1 1 2 2 2 1 1 2 2 1 2 2 1 2
[2209] 2 2 2 1 1 2 1 2 3 1 3 2 2 2 2 2 1 2 1 3 2 2 2 2 3 1 3 3 2 3 3 2
[2241] 2 1 1 1 1 2 1 1 2 3 1 1 2 2 3 1 1 1 1 1 2 1 2 1 1 3 1 1 1 1 1 3
[2273] 2 1 1 2 2 3 2 3 2 1 1 1 2 2 1 1 1 2 1 1 1 2 1 2 1 2 1 1 1 3 1 2
[2305] 2 1 2 2 1 3 2 3 3 1 3 2 2 3 3 2 1 1 1 1 2 1 1 3 2 2 1 2 2 1 2 3
[2337] 2 1 2 1 2 3 1 2 3 3 1 2 2 2 2 2 2 3 1 1 1 1 3 3 2 3 1 1 2 2 3 1
[2369] 1 1 3 2 2 1 2 1 1 1 1 2 1 3 2 2 2 1 1 1 1 2 2 1 1 1 3 1 3 3 2 2
[2401] 1 2 1 1 2 2 1 2 1 3 1 2 3 1 1 2 3 2 2 2 2 1 2 1 1 1 1 1 2 2 1 2
[2433] 2 1 3 2 1 1 1 1 1 1 3 2 2 1 2 3 1 2 1 2 1 3 2 3 2 1 3 1 1 2 1 1
[2465] 1 2 2 2 2 2 2 1 1 2 2 2 1 2 1 1 1 2 2 1 1 1 2 1 3 2 2 1 1 2 2 1
[2497] 2 2 3 1 2 3 1 2 3 2 2 2 1 2 2 3 1 2 1 3 1 1 1 1 2 1 1 2 1 1 3 1
[2529] 2 2 1 3 2 2 3 2 2 3 2 3 2 2 2 2 2 1 2 3 1 2 2 2 1 2 3 2 1 1 1 1
[2561] 2 3 2 2 2 3 1 2 3 1 1 2 1 3 1 1 2 1 3 2 3 2 1 1 3 1 2 3 1 1 1 1
[2593] 2 1 1 1 2 1 2 1 1 3 3 2 3 2 2 3 2 1 1 3 2 2 3 1 2 1 1 2 2 1 1 2
[2625] 1 2 3 1 2 2 1 2 3 1 2 1 1 3 2 2 3 2 2 3 2 1 1 1 1 1 1 1 1 3 2 1
[2657] 2 1 2 2 2 1 1 1 1 1 3 1 1 1 3 2 3 2 2 1 2 3 1 1 1 2 3 1 1 3 2 1
[2689] 2 2 3 2 1 2 1 2 2 3 2 2 3 2 1 3 3 1 1 2 2 1 1 2 3 2 2 2 1 3 1 2
[2721] 3 1 1 2 3 1 1 3 3 1 1 2 2 3 2 1 1 2 1 3 2 1 2 2 3 1 1 2 1 2 1 3
[2753] 2 3 3 2 2 1 3 1 2 2 1 1 3 1 1 2 1 2 2 1 1 2 3 2 3 1 1 2 1 3 1 1
[2785] 1 1 1 1 3 2 2 2 1 1 1 1 3 1 2 1 1 2 2 2 2 2 2 2 1 3 1 2 1 2 1 2
[2817] 2 1 1 2 1 2 1 2 1 1 3 1 2 2 1 2 1 3 2 2 1 3 3 1 2 2 1 2 1 1 2 1
[2849] 1 1 1 1 2 2 2 2 3 1 2 2 2 2 2 1 2 2 1 2 1 2 2 2 3 2 2 2 1 1 1 1
[2881] 1 1 3 3 3 1 3 1 2 2 1 3 1 1 2 1 3 1 3 1 1 2 3 1 3 1 1 1 3 1 1 1
[2913] 3 3 1 1 1 2 1 3 2 1 1 1 3 2 1 3 3 2 1 3 2 3 2 1 2 2 2 1 1 2 3 2
[2945] 3 2 1 1 1 2 2 1 1 2 1 2 3 1 2 1 1 1 1 3 1 1 2 3 2 1 2 2 2 3 2 1
[2977] 2 2 2 1 2 3 1 1 1 2 1 1 1 2 2 3 1 1 2 3 1 3 1 2 2 2 2 2 1 2 2 2
[3009] 3 2 2 1 2 1 1 1 1 2 1 3 3 1 1 2 1 3 2 2 1 1 2 2 1 3 1 2 2 1 2 1
[3041] 3 2 1 2 1 2 3 1 2 2 1 2 2 2 3 1 2 2 3 2 3 1 1 3 1 3 1 2 3 1 1 2
[3073] 2 2 2 1 2 3 1 1 2 2 2 2 2 2 2 1 2 3 1 1 1 2 3 1 1 1 2 1 2 2 3 2
[3105] 2 1 1 3 3 1 1 1 3 3 1 1 3 1 2 2 3 1 2 2 1 2 1 1 2 1 3 1 1 2 2 2
[3137] 2 3 2 2 2 1 1 1 2 1 2 2 2 3 2 1 2 3 1 1 3 1 1 2 2 1 1 1 3 1 3 2
[3169] 3 1 3 3 2 2 1 2 3 2 1 1 3 1 1 3 1 1 2 2 3 2 3 2 2 2 1 1 2 2 3 3
[3201] 3 3 2 2 2 1 2 3 1 2 3 1 1 2 2 1 2 1 2 1 2 3 2 1 2 1 3 2 1 3 2 2
[3233] 1 1 2 1 3 1 2 2 1 1 2 2 3 3 1 2 3 2 1 1 2 2 1 1 2 1 1 3 2 2 1 2
[3265] 2 1 3 2 2 2 3 1 1 3 3 3 3 2 2 3 3 2 1 1 2 1 2 2 1 3 2 1 2 1 1 1
[3297] 3 2 1 2 3 1 3 2 1 1 2 1 1 2 2 2 2 2 1 3 1 1 2 2 1 2 3 2 2 2 1 2
[3329] 1 1 3 3 2 1 2 2 1 2 3 1 2 1 3 2 1 2 1 3 2 1 2 2 1 2 1 3 2 2 3 2
[3361] 1 1 1 1 3 1 2 2 2 2 1 1 3 2 2 3 1 1 1 1 1 1 1 2 2 1 2 2 3 2 1 1
[3393] 2 2 2 1 1 2 3 1 2 1 1 3 1 3 1 1 1 1 2 1 1 2 1 1 1 2 1 1 2 2 3 3
[3425] 3 2 2 2 2 3 2 3 2 1 1 2 1 3 1 2 1 2 2 2 3 3 3 2 3 2 1 1 2 1 2 2
[3457] 2 2 1 2 2 2 1 1 2 1 3 1 3 2 3 1 2 2 2 3 1 2 2 3 3 3 1 3 2 2 3 1
[3489] 1 1 3 2 3 2 2 1 2 2 2 2 2 3 1 2 1 2 1 2 1 3 3 2 3 2 2 3 2 2 1 1
[3521] 2 1 3 3 1 2 3 3 2 2 3 1 3 1 2 1 1 3 2 1 2 2 2 2 2 3 1 1 2 1 2 3
[3553] 1 1 3 1 2 3 1 1 2 1 1 1 1 1 3 1 1 3 1 3 3 2 1 2 2 2 1 3 3 2 1 2
[3585] 2 1 1 1 1 1 2 3 1 3 2 1 1 3 1 2 3 2 1 1 1 1 1 1 2 2 1 2 3 1 2 1
[3617] 1 2 1 2 1 2 2 3 2 2 3 1 1 1 3 1 1 3 2 1 3 3 2 2 2 1 2 3 1 2 1 1
[3649] 1 2 2 1 3 3 1 1 1 1 1 2 1 1 3 3 1 2 2 1 2 3 2 3 2 1 1 2 1 1 1 2
[3681] 1 3 2 2 1 2 2 1 1 1 1 1 1 2 1 1 2 2 2 1 1 1 3 3 3 2 1 2 2 3 2 1
[3713] 1 1 1 2 2 1 1 1 1 2 1 1 3 1 1 1 1 1 1 3 1 2 2 2 1 2 2 1 1 2 2 2
[3745] 1 3 3 1 2 1 1 2 1 1 2 3 2 2 1 1 1 1 1 2 2 1 1 1 3 3 2 3 2 2 2 2
[3777] 3 3 3 2 3 1 1 2 1 2 1 2 2 1 3 3 1 2 1 3 2 3 1 2 1 1 3 2 2 2 2 3
[3809] 1 1 2 2 2 1 1 1 1 2 1 1 2 1 1 1 3 3 2 2 1 2 1 1 2 1 1 2 3 2 2 1
[3841] 2 3 2 1 2 2 3 3 1 2 1 2 3 1 1 1 1 2 2 1 1 2 1 2 2 1 1 1 1 2 1 1
[3873] 2 1 1 2 1 2 3 3 2 1 1 1 2 1 2 1 3 1 1 3 2 1 1 1 1 1 2 2 1 2 1 2
[3905] 2 3 2 3 1 3 1 3 1 2 2 1 2 2 2 1 2 2 3 1 1 2 2 2 1 3 2 2 1 3 1 1
[3937] 2 1 2 1 2 1 3 2 1 1 2 2 3 2 1 1 2 2 1 3 2 2 1 2 1 2 1 2 1 2 3 2
[3969] 2 3 1 2 1 2 1 2 1 1 1 1 1 3 3 1 1 1 3 2 2 3 2 1 1 1 3 1 3 2 3 2
[4001] 1 2 3 2 2 1 3 2 1 1 2 2 1 1 3 1 1 1 3 1 3 1 2 2 1 2 1 1 3 3 1 1
[4033] 3 1 1 2 2 3 1 3 3 2 2 3 2 2 2 2 2 1 1 2 2 1 2 1 2 3 3 3 3 2 3 2
[4065] 2 1 2 3 3 2 1 1 1 3 1 2 1 3 2 3 2 2 1 1 1 2 3 2 2 1 2 2 2 1 3 1
[4097] 1 1 2 1 1 3 2 2 2 1 1 3 1 1 2 1 2 2 1 1 3 2 1 1 1 1 1 1 1 2 3 2
[4129] 1 3 2 1 2 3 2 2 3 2 1 3 3 2 1 2 1 2 3 1 2 1 1 1 1 1 2 2 3 2 2 3
[4161] 3 3 2 2 2 2 2 2 3 1 1 1 3 1 2 2 3 3 1 3 1 1 1 3 2 1 2 1 1 1 2 1
[4193] 2 3 1 1 1 1 2 1 2 1 1 2 2 2 2 3 2 3 1 1 3 1 1 2 2 3 2 2 1 1 2 1
[4225] 3 1 2 2 3 1 1 2 1 1 2 1 2 3 2 3 1 1 3 1 1 3 3 1 1 1 1 2 2 1 3 1
[4257] 3 1 1 1 3 2 1 1 1 2 2 1 1 1 1 1 1 2 1 2 2 3 1 2 1 3 1 2 3 3 1 1
[4289] 2 1 2 2 1 3 2 2 2 1 2 2 3 3 2 3 2 1 2 1 3 3 1 1 2 2 1 2 1 2 2 1
[4321] 1 1 1 2 2 2 1 3 3 3 3 1 2 2 1 3 1 2 2 2 1 2 2 3 2 2 3 1 1 1 1 2
[4353] 3 1 1 1 2 1 2 1 2 1 1 3 2 3 3 2 3 2 3 2 1 2 3 1 3 2 1 2 3 1 2 1
[4385] 1 2 3 2 2 1 2 2 1 2 1 1 2 3 1 2 3 3 2 2 2 2 1 1 3 2 1 3 3 2 2 1
[4417] 1 1 2 2 2 2 3 3 1 1 2 1 1 2 2 3 2 3 2 3 1 1 3 1 1 1 2 1 1 1 2 1
[4449] 2 2 3 3 3 2 2 3 3 1 3 3 2 1 2 1 3 2 1 1 2 1 1 2 2 3 1 2 1 1 2 3
[4481] 2 1 3 1 1 1 2 2 2 3 1 2 2 2 1 2 2 2 1 1 3 2 2 3 2 2 1 2 2 1 1 1
[4513] 1 2 2 3 2 3 2 3 2 1 1 1 1 1 3 2 2 1 2 1 2 2 1 3 1 1 1 1 3 2 3 2
[4545] 1 1 1 2 1 1 3 1 2 2 2 2 1 3 1 2 1 1 2 1 1 1 2 2 1 2 1 3 1 1 2 2
[4577] 3 2 2 2 2 2 2 2 3 3 3 1 2 2 3 1 3 2 3 3 1 1 1 3 3 1 2 1 1 3 3 1
[4609] 3 1 3 2 2 2 2 3 2 1 2 3 3 2 2 2 3 2 1 2 2 3 1 1 3 1 1 1 2 2 2 1
[4641] 3 2 2 2 1 2 1 1 1 3 3 2 2 1 3 1 1 2 1 2 1 1 1 1 1 1 1 2 2 1 3 1
[4673] 3 1 1 2 1 1 2 3 1 2 1 2 3 1 1 1 1 1 2 2 2 2 1 1 2 2 3 2 1 1 3 3
[4705] 2 2 1 1 1 2 1 2 1 2 1 2 1 1 2 1 1 3 3 1 1 1 1 2 1 2 1 2 3 3 1 2
[4737] 3 2 3 1 1 2 2 2 1 1 1 1 2 2 2 1 1 1 1 2 3 1 2 1 3 3 1 1 3 1 1 1
[4769] 1 2 1 1 1 3 1 1 1 1 3 3 1 1 3 2 1 3 1 2 2 2 2 2 1 3 1 1 2 1 2 2
[4801] 3 3 1 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 3 1 2 2 1 1 2 3 1 1 1 2 1 1
[4833] 1 1 1 2 1 2 2 3 3 2 1 2 1 1 2 2 2 2 2 2 1 1 2 2 1 2 3 3 1 1 3 2
[4865] 2 3 2 2 2 2 2 1 3 2 1 2 2 2 1 3 3 1 2 2 1 1 3 2 2 2 2 2 3 3 2 2
[4897] 2 1 2 2 2 1 1 3 1 2 2 1 3 2 1 2 3 3 3 3 1 2 2 1 2 2 2 1 1 3 1 1
[4929] 1 2 1 2 2 1 2 1 1 1 1 1 2 2 3 1 1 3 2 2 1 2 2 2 2 1 2 2 2 1 2 1
[4961] 1 2 3 1 1 1 1 1 2 3 3 1 3 2 3 1 1 2 1 1 1 1 2 2 1 3 3 1 1 2 2 2
[4993] 1 3 2 2 2 1 2 1 3 1 3 3 1 2 1 2 1 2 3 1 2 1 3 2 3 1 3 1 1 2 2 1
[5025] 3 2 1 2 1 3 2 3 2 2 1 2 2 2 2 1 2 2 1 1 3 1 3 3 3 3 2 1 2 2 2 2
[5057] 2 2 2 3 3 3 2 2 2 2 1 3 1 3 2 2 1 3 3 3 2 1 2 1 3 2 1 2 3 1 1 1
[5089] 1 3 2 2 3 2 2 3 2 2 2 3 2 1 1 3 2 2 1 2 1 3 3 2 3 2 2 3 2 1 2 2
[5121] 1 2 2 2 2 1 3 2 3 2 2 3 2 1 1 2 1 3 1 1 2 1 1 2 2 1 2 1 2 2 3 1
[5153] 2 2 2 1 2 3 2 1 2 2 3 1 2 2 1 1 2 2 1 2 1 1 1 3 3 1 2 1 1 1 2 1
[5185] 2 3 1 2 2 2 2 2 1 1 2 1 2 2 2 3 3 2 1 2 1 3 1 2 3 2 2 2 1 1 2 3
[5217] 1 2 1 1 1 3 1 3 2 1 1 1 3 2 1 1 2 3 2 2 2 1 1 1 3 1 2 1 1 2 2 2
[5249] 2 2 1 1 1 1 2 1 1 1 3 1 2 1 2 2 1 3 2 1 2 3 2 2 2 2 2 2 3 2 2 2
[5281] 1 3 2 2 1 2 3 1 3 2 1 2 2 1 2 1 2 2 2 2 1 2 2 2 1 1 2 2 1 3 1 3
[5313] 3 1 2 2 1 2 2 2 3 1 1 1 1 1 2 1 2 1 2 1 2 1 3 3 1 1 1 2 2 1 1 1
[5345] 2 1 1 1 1 2 2 1 2 1 2 2 1 1 3 1 2 1 1 3 1 3 2 1 1 1 1 1 1 1 3 2
[5377] 2 2 3 3 1 1 2 1 3 1 1 2 1 1 1 3 1 1 1 2 1 3 1 3 1 1 1 1 1 2 1 2
[5409] 1 1 2 1 1 2 1 1 3 2 1 3 3 3 2 3 2 3 2 2 2 1 2 1 3 2 1 2 3 1 1 1
[5441] 1 1 1 2 1 2 2 2 1 2 2 1 1 2 3 2 1 1 1 2 2 3 2 2 3 1 2 2 1 2 1 2
[5473] 1 1 2 1 2 2 1 1 3 1 1 2 2 3 1 1 2 1 2 3 2 1 2 1 3 2 1 2 2 1 1 2
[5505] 2 2 2 3 3 2 2 1 1 3 1 2 1 2 2 2 1 2 3 1 2 2 1 2 1 1 1 1 2 1 1 1
[5537] 3 2 3 3 2 1 1 2 1 2 3 2 2 1 1 2 1 2 1 2 1 2 2 1 2 1 3 1 2 1 1 3
[5569] 3 1 3 1 2 2 3 2 2 2 2 2 1 1 1 3 1 1 3 1 1 1 1 2 3 2 2 2 3 2 2 1
[5601] 2 2 2 1 2 1 1 1 3 1 2 2 1 1 3 2 3 1 2 2 1 3 1 2 1 3 3 2 1 3 1 2
[5633] 3 1 3 1 3 3 2 1 2 3 1 2 3 1 3 1 1 1 1 3 2 1 2 1 2 1 1 2 2 2 2 2
[5665] 3 1 3 1 2 2 1 1 3 1 2 3 1 2 1 2 1 1 1 1 2 2 2 1 3 1 1 3 1 1 2 2
[5697] 1 2 2 1 1 3 3 2 1 1 1 1 3 1 1 1 2 1 2 1 2 2 2 1 2 3 3 2 1 2 1 2
[5729] 1 1 2 1 2 1 1 2 1 2 2 2 3 1 1 3 1 1 2 1 1 2 2 2 1 3 1 3 2 1 3 3
[5761] 2 2 1 2 3 3 3 2 2 3 3 2 2 1 2 2 2 2 2 1 2 3 2 3 2 2 1 3 1 2 3 3
[5793] 1 1 2 2 1 3 2 2 1 1 1 1 1 1 2 1 1 3 1 2 1 1 2 3 2 1 1 2 1 1 1 3
[5825] 2 2 2 1 1 2 1 2 1 1 2 2 1 2 2 3 3 1 1 1 2 1 1 2 2 1 3 2 2 1 3 2
[5857] 1 1 2 2 1 2 1 1 1 2 1 1 1 1 1 2 2 1 2 1 1 2 3 1 2 1 1 2 1 3 2 2
[5889] 1 2 2 2 1 1 1 3 1 2 2 3 1 3 2 3 3 2 2 3 2 3 3 2 3 1 1 1 1 1 3 1
[5921] 2 3 2 2 3 1 1 2 2 1 2 1 1 2 3 2 1 2 2 3 3 3 3 2 1 2 2 1 2 2 2 1
[5953] 1 1 1 1 2 3 1 1 2 2 2 2 3 3 2 1 1 1 2 2 1 1 2 1 1 2 1 3 2 2 3 2
[5985] 2 2 2 1 3 2 3 2 2 3 1 2 1 3 1 1 1 1 2 1 2 2 1 3 1 2 1 2 3 1 3 2
[6017] 3 3 3 2 1 1 2 2 1 1 1 1 2 1 1 1 3 3 2 2 3 1 2 1 2 2 1 2 2 1 2 1
[6049] 1 3 2 2 1 2 1 1 2 2 2 1 2 3 1 1 3 1 1 1 2 1 1 1 1 3 2 3 3 2 1 1
[6081] 2 1 1 2 1 3 3 2 1 1 1 3 1 2 2 2 1 2 1 2 2 1 2 3 3 1 2 2 3 1 1 1
[6113] 1 3 2 1 1 1 2 1 3 1 2 3 3 2 2 1 2 2 1 2 2 1 1 1 1 3 2 2 1 2 2 3
[6145] 1 1 1 3 1 1 2 3 1 2 1 2 2 1 1 1 1 2 3 1 1 2 1 3 1 3 2 1 2 1 1 1
[6177] 3 3 3 1 2 2 3 2 3 2 2 1 1 2 2 1 1 3 3 1 1 3 3 2 2 1 2 1 1 1 2 2
[6209] 2 2 3 2 1 1 1 2 1 1 3 1 1 1 2 1 2 1 1 1 1 1 1 2 1 2 2 2 3 2 3 1
[6241] 2 2 2 2 1 2 3 1 3 2 1 1 3 1 2 1 2 2 3 3 1 1 1 1 1 2 2 2 1 1 1 1
[6273] 2 3 1 3 1 2 2 1 1 2 2 1 2 1 3 2 3 2 2 2 1 1 3 1 1 3 1 1 1 1 1 1
[6305] 2 1 2 1 2 3 2 1 3 2 1 1 3 1 1 2 2 2 3 1 3 2 1 1 1 2 2 1 1 1 2 3
[6337] 3 2 2 3 1 2 2 1 1 3 1 1 1 3 2 1 1 2 2 1 2 1 1 1 3 1 1 3 3 2 3 1
[6369] 1 2 1 1 1 2 1 1 1 2 2 1 2 1 1 1 2 3 3 2 1 1 2 1 1 3 2 3 2 2 2 1
[6401] 2 3 2 2 2 2 3 2 1 1 3 2 3 1 1 1 2 1 3 1 1 3 1 1 1 2 1 1 1 2 1 1
[6433] 2 1 1 2 3 2 2 1 2 1 1 2 1 2 2 1 2 3 1 1 1 3 1 2 1 2 3 1 3 2 2 1
[6465] 1 3 3 1 1 3 2 1 3 3 2 2 1 2 2 2 2 2 1 3 1 1 1 2 1 2 1 1 3 2 2 1
[6497] 2 1 3 1 1 2 3 1 3 2 1 2 1 1 2 2 2 3 2 1 2 2 1 2 2 2 1 3 2 2 1 1
[6529] 2 1 1 1 1 2 1 2 2 2 3 1 3 2 2 3 1 2 2 2 2 1 1 2 3 2 2 1 1 1 1 3
[6561] 2 1 1 1 2 3 1 1 1 2 2 1 1 2 1 2 2 2 3 2 2 2 2 1 1 2 2 3 1 2 2 1
[6593] 1 3 1 3 2 3 1 3 1 1 1 1 3 1 3 2 2 1 1 2 2 2 2 3 1 3 3 3 1 2 1 1
[6625] 1 2 1 1 1 2 2 2 2 1 1 1 2 2 2 1 1 2 1 2 2 1 2 3 2 3 1 3 1 2 2 1
[6657] 2 1 1 1 1 2 1 3 1 2 3 2 1 2 1 2 3 2 3 1 2 1 2 3 2 3 1 1 2 3 2 1
[6689] 1 1 1 2 2 3 1 1 2 1 1 1 2 3 2 1 3 2 2 1 2 2 1 3 2 1 3 2 1 1 2 1
[6721] 2 1 2 1 2 2 1 1 2 1 1 2 2 3 3 1 3 2 1 1 2 1 3 2 3 2 1 3 3 1 1 3
[6753] 1 2 3 1 3 2 2 2 1 1 3 2 2 2 2 1 1 1 2 1 3 1 2 1 2 2 3 2 1 1 2 1
[6785] 2 2 1 1 1 2 3 1 2 2 2 2 2 2 2 1 2 3 2 2 3 1 1 2 3 2 3 2 2 2 1 2
[6817] 1 2 2 3 2 2 2 1 1 1 3 2 2 2 2 2 3 2 1 1 1 1 1 1 3 1 2 2 2 2 1 3
[6849] 1 3 3 1 2 3 1 3 1 2 1 1 1 1 2 1 2 3 3 1 1 1 3 1 3 1 1 1 1 2 2 1
[6881] 2 3 3 3 1 2 2 2 2 2 3 3 1 2 1 3 1 2 1 1 1 1 3 1 3 1 1 2 2 2 1 3
[6913] 2 1 1 2 3 2 1 1 2 1 3 2 1 1 3 2 2 1 2 2 1 2 1 2 1 1 3 2 2 1 1 2
[6945] 2 1 2 2 2 3 1 2 2 1 1 1 1 1 3 1 1 1 3 2 1 1 1 2 2 1 2 1 1 2 3 1
[6977] 2 2 3 1 3 1 2 2 2 2 1 1 1 1 3 2 1 3 3 3 1 2 1 2 3 2 1 3 2 2 3 1
[7009] 2 1 2 1 1 2 2 2 2 1 1 1 2 3 3 1 1 3 1 1 1 3 2 2 1 3 1 3 1 2 1 3
[7041] 3 2 3 2 2 1 2 2 2 1 1 2 1 1 2 2 1 2 3 1 2 1 1 2 3 3 1 2 2 2 2 2
[7073] 2 2 2 1 1 3 1 1 1 1 3 2 2 1 2 2 1 2 2 2 2 2 1 1 2 1 1 2 1 1 3 1
[7105] 2 2 3 2 2 3 1 2 2 2 2 1 1 2 1 2 2 3 2 3 2 1 1 2 2 2 2 2 3 2 3 1
[7137] 3 2 1 1 1 1 2 1 2 1 2 2 2 1 1 2 1 1 3 3 2 3 2 1 2 2 3 2 2 1 2 2
[7169] 1 2 2 2 2 2 2 1 3 2 1 1 2 1 2 1 1 3 2 3 3 3 1 2 3 2 2 2 2 1 3 3
[7201] 3 2 3 2 2 1 3 2 1 2 2 2 2 3 2 3 2 3 2 2 2 2 2 1 1 3 1 2 2 3 1 3
[7233] 2 2 1 1 3 1 3 1 2 2 2 1 1 1 1 2 2 3 2 3 2 2 2 1 2 2 2 1 2 1 3 1
[7265] 2 1 1 1 2 1 1 3 2 2 3 1 3 1 3 1 2 1 2 1 1 3 2 2 1 2 2 3 3 2 2 1
[7297] 3 1 2 2 2 1 1 2 1 2 2 1 3 3 3 2 1 2 1 2 3 2 3 3 1 1 2 2 1 2 3 1
[7329] 1 2 1 1 3 1 1 2 2 2 2 2 2 2 2 1 1 3 2 2 3 2 1 3 2 2 2 2 1 3 1 1
[7361] 1 2 1 1 3 1 1 2 2 2 2 1 3 2 1 2 2 2 2 2 2 3 2 2 2 2 1 1 2 1 3 1
[7393] 1 2 1 1 2 1 3 2 2 1 3 1 2 2 3 1 1 2 1 1 1 2 1 2 1 2 3 1 1 1 1 2
[7425] 3 3 2 1 2 3 1 3 1 3 2 1 1 2 1 2 1 2 2 2 2 1 3 3 2 2 1 2 2 1 2 3
[7457] 2 3 2 2 3 2 1 2 2 3 2 2 1 3 3 1 1 1 2 1 1 1 1 2 1 2 2 2 3 2 3 2
[7489] 3 3 1 2 1 1 2 2 2 2 1 2 2 3 3 1 2 2 1 1 2 3 2 3 1 3 2 2 1 2 3 2
[7521] 2 2 1 3 1 2 2 3 2 3 3 2 1 2 1 1 1 3 1 3 3 3 2 3 3 2 1 2 1 2 1 2
[7553] 1 3 2 2 2 1 2 3 1 2 2 1 1 1 2 2 1 1 2 1 1 1 2 3 1 1 1 1 2 1 1 3
[7585] 3 3 1 2 2 2 1 1 2 1 1 2 1 1 3 1 1 1 2 1 1 2 2 3 3 2 2 1 3 2 1 3
[7617] 1 2 2 1 3 1 1 2 1 2 1 1 1 1 2 2 1 1 1 2 1 2 3 2 1 2 1 2 2 1 2 2
[7649] 1 2 1 1 2 2 3 1 1 2 1 2 1 2 1 1 1 1 1 3 2 2 2 1 1 1 1 2 2 1 3 1
[7681] 2 1 3 2 3 1 1 1 2 1 2 1 2 3 3 3 2 1 2 3 1 1 2 2 3 1 2 2 2 3 2 1
[7713] 3 3 3 2 2 1 1 2 1 2 3 1 3 3 1 2 1 3 2 2 2 1 2 1 1 2 1 2 1 3 1 1
[7745] 3 1 2 1 1 2 2 1 2 3 1 2 1 1 1 2 1 3 2 1 2 2 1 1 2 3 1 2 3 2 1 1
[7777] 1 1 3 2 1 1 1 3 3 3 3 2 2 2 1 2 2 1 2 1 2 2 1 1 3 1 1 3 3 3 2 3
[7809] 1 1 2 1 3 3 1 2 3 2 1 1 1 2 1 1 1 1 2 2 3 2 2 3 1 3 2 2 1 2 2 3
[7841] 2 1 1 2 1 1 1 2 3 3 1 1 3 1 2 1 3 2 2 1 3 2 1 1 3 1 3 2 1 2 1 3
[7873] 1 1 1 1 2 2 3 2 3 2 3 3 2 2 2 2 1 2 1 2 2 1 1 1 2 2 3 2 1 1 1 2
[7905] 1 2 2 1 3 2 2 2 3 2 1 1 2 2 2 1 3 3 1 3 1 1 3 1 2 1 1 3 1 1 1 3
[7937] 1 2 2 2 1 1 1 3 3 1 1 3 2 2 2 1 1 3 1 1 2 3 2 2 2 1 1 2 1 2 1 1
[7969] 2 1 3 2 1 1 1 1 2 1 1 1 1 2 1 2 3 1 2 2 1 2 2 1 1 1 3 1 1 1 3 1
[8001] 1 1 2 1 1 1 3 1 1 1 3 2 1 2 3 1 2 1 3 1 2 2 2 2 2 1 1 3 2 1 2 2
[8033] 1 2 3 1 1 1 3 3 1 1 2 2 2 2 3 2 1 3 2 2 1 1 2 1 3 3 1 2 2 3 2 1
[8065] 1 1 1 1
Within cluster sum of squares by cluster:
[1] 165701.1 154378.2 133513.6
(between_SS / total_SS = 80.9 %)
Available components:
[1] "cluster" "centers" "totss" "withinss"
[5] "tot.withinss" "betweenss" "size" "iter"
[9] "ifault"
K-means clustering with 4 clusters of sizes 1079, 2468, 2577, 1944
Cluster means:
Gender_Female Gender_Male Ever_Married_No Ever_Married_Yes Age
1 0.4179796 0.5820204 0.04819277 0.9425394 74.78962
2 0.4586710 0.5413290 0.80794165 0.1705835 25.97488
3 0.4877765 0.5122235 0.38339154 0.6049670 39.30850
4 0.4171811 0.5828189 0.12911523 0.8467078 53.80093
Graduated_No Graduated_Yes Profession_Artist Profession_Doctor
1 0.3688601 0.6200185 0.1853568 0.02409639
2 0.6329011 0.3569692 0.1126418 0.12398703
3 0.2510671 0.7411719 0.4229724 0.09235545
4 0.2134774 0.7757202 0.4876543 0.06069959
Profession_Engineer Profession_Entertainment Profession_Executive
1 0.03799815 0.06394810 0.12140871
2 0.07293355 0.09359806 0.02674230
3 0.11331005 0.14357780 0.07140085
4 0.09567901 0.14351852 0.11213992
Profession_Healthcare Profession_Homemaker Profession_Lawyer
1 0.002780352 0.009267841 0.528266914
2 0.454619125 0.041734198 0.001620746
3 0.067132324 0.036476523 0.001940241
4 0.017489712 0.020061728 0.022633745
Profession_Marketing Work_Experience Spending_Score_Average
1 0.01575533 1.164041 0.13160334
2 0.05632091 2.840357 0.07374392
3 0.03570043 3.175398 0.31548312
4 0.02263374 1.801955 0.43055556
Spending_Score_High Spending_Score_Low Family_Size
1 0.45968489 0.4087118 2.094532
2 0.03889789 0.8873582 3.468801
3 0.10671323 0.5778036 2.617385
4 0.17952675 0.3899177 2.818416
Clustering vector:
[1] 2 3 1 1 3 4 2 3 4 4 2 2 2 1 4 3 2 2 4 1 4 2 3 3 4 4 2 4 3 3 3 3
[33] 2 2 1 2 2 2 2 4 4 2 2 4 3 1 3 2 2 3 4 3 3 4 1 2 2 2 3 1 4 4 1 4
[65] 4 2 2 2 4 3 2 4 4 3 4 3 3 4 3 4 2 2 4 3 2 2 4 3 3 3 3 4 4 2 4 4
[97] 3 4 4 2 4 1 4 3 3 2 2 1 2 2 4 3 4 4 3 3 1 3 2 3 3 4 3 2 3 2 3 1
[129] 2 3 3 1 2 3 4 2 3 3 2 3 3 4 2 1 3 2 2 1 2 1 1 2 4 3 2 3 1 3 1 3
[161] 4 2 3 2 4 3 4 2 3 4 4 1 1 2 1 4 2 2 2 2 3 4 2 3 3 3 1 2 3 3 4 3
[193] 3 4 4 3 2 4 1 3 2 2 2 3 4 2 2 4 3 4 1 3 2 1 4 2 4 2 4 4 3 2 2 2
[225] 2 4 3 2 3 2 1 2 1 2 3 2 2 3 4 4 4 4 2 4 3 3 2 3 3 2 4 3 4 1 2 1
[257] 4 3 3 2 4 3 1 3 2 1 1 1 3 3 2 2 2 3 3 1 4 3 1 2 4 2 3 2 3 4 2 2
[289] 2 4 3 2 2 2 2 3 3 2 3 3 4 2 2 2 1 3 2 1 4 4 4 4 1 3 3 1 2 3 2 2
[321] 1 1 2 2 3 3 3 3 2 4 4 2 2 4 3 2 2 2 3 3 2 4 4 1 2 1 3 3 2 4 3 4
[353] 1 2 2 3 2 2 2 3 3 3 4 2 4 2 3 2 2 3 2 4 1 2 2 3 2 4 4 3 3 3 2 2
[385] 3 3 4 3 2 4 2 3 2 1 2 1 3 3 2 1 2 2 4 4 3 4 3 3 2 2 3 1 1 3 1 1
[417] 4 3 2 4 2 2 3 2 4 3 4 2 4 2 2 2 4 2 2 1 1 1 2 3 2 4 1 1 4 3 3 3
[449] 3 2 2 2 2 1 3 4 4 2 4 2 1 2 3 3 3 2 2 3 4 2 2 1 2 3 3 1 4 1 2 4
[481] 3 3 2 2 2 2 3 3 3 2 2 1 3 4 2 2 2 3 2 3 2 2 3 4 4 3 4 2 4 4 4 3
[513] 3 2 3 4 4 4 3 2 3 4 3 2 3 2 2 3 3 3 3 2 3 4 4 1 3 2 2 3 3 4 4 3
[545] 1 2 3 3 1 3 2 2 4 4 2 3 2 3 2 3 3 1 2 3 2 2 3 2 4 3 2 2 3 1 4 4
[577] 3 3 2 1 3 4 4 3 2 4 4 1 2 2 3 3 2 3 3 4 2 4 3 2 3 2 4 1 4 2 4 1
[609] 3 3 3 4 1 2 4 2 1 1 2 4 3 2 4 4 4 2 2 1 3 1 4 2 2 3 3 3 3 4 4 3
[641] 2 4 2 2 3 2 4 4 2 1 4 3 4 2 1 2 1 4 4 4 3 2 2 3 3 3 2 1 3 3 2 3
[673] 3 1 2 4 3 3 2 2 4 3 1 2 1 3 2 2 2 2 2 2 3 1 4 2 3 2 1 1 3 4 2 3
[705] 4 4 2 3 3 4 4 1 2 2 3 4 3 2 2 3 1 3 4 2 3 3 2 2 2 2 3 2 1 2 3 1
[737] 4 2 4 4 3 3 2 3 3 4 4 4 4 4 2 2 4 1 1 4 3 4 3 4 3 1 1 3 2 1 3 2
[769] 3 4 3 2 4 3 4 4 1 2 4 4 2 4 4 3 3 3 2 3 1 3 1 2 4 2 1 2 2 4 2 4
[801] 4 4 3 4 2 2 4 4 2 4 4 3 2 3 3 3 2 4 2 2 4 1 2 4 3 3 4 3 1 4 4 2
[833] 3 4 4 2 2 3 4 2 2 2 4 2 3 4 1 4 2 2 4 2 1 1 4 1 4 4 2 2 3 4 3 3
[865] 2 3 2 2 3 3 2 3 2 2 3 3 4 3 2 4 3 4 2 2 3 4 4 1 4 4 3 2 3 3 2 4
[897] 3 1 4 2 1 2 4 3 2 2 4 2 2 2 3 2 4 4 2 3 4 2 1 4 1 4 3 4 3 2 2 3
[929] 4 3 3 3 3 3 3 3 2 3 2 3 2 3 4 1 1 3 2 3 3 2 2 3 3 4 4 4 2 3 3 3
[961] 4 1 3 2 2 3 1 2 2 2 4 2 3 3 4 3 2 2 4 4 1 2 1 2 2 4 2 3 2 4 1 3
[993] 3 4 3 2 3 3 4 4 4 3 4 1 2 1 4 3 3 4 4 4 3 4 3 3 4 4 1 4 2 3 2 2
[1025] 2 3 4 4 1 4 4 4 1 3 2 2 2 4 4 2 2 3 2 4 3 2 3 2 2 2 3 4 4 3 2 2
[1057] 4 2 2 3 2 3 3 2 1 3 2 4 4 3 4 1 2 2 3 2 3 2 1 2 2 3 3 3 1 2 3 4
[1089] 2 4 1 1 2 3 2 2 2 4 1 3 4 3 2 2 3 4 3 2 1 2 3 2 3 1 3 4 4 2 4 3
[1121] 4 3 4 4 3 2 3 2 4 3 2 1 3 1 3 4 3 1 2 2 3 2 3 4 1 3 4 1 2 3 1 3
[1153] 4 2 3 2 4 2 2 2 3 2 2 2 2 4 3 4 4 1 1 1 3 3 3 4 4 3 4 1 3 1 3 2
[1185] 2 3 3 3 4 4 3 2 3 2 3 2 3 4 4 3 3 2 4 4 2 2 4 3 3 3 3 3 4 1 3 4
[1217] 4 1 2 3 1 3 2 2 3 3 2 2 2 4 2 3 2 3 3 2 2 4 3 4 2 3 3 2 3 3 1 2
[1249] 4 4 4 1 3 3 2 2 2 1 1 4 2 2 2 1 4 1 3 4 3 2 3 4 2 3 4 4 2 2 2 3
[1281] 2 3 4 4 2 4 4 1 3 3 2 3 3 3 2 3 4 2 1 1 4 2 2 3 4 2 4 1 2 2 2 3
[1313] 3 4 2 2 2 3 1 2 1 3 2 2 1 4 3 3 3 3 1 3 2 3 2 3 3 4 2 2 3 3 4 2
[1345] 2 4 2 3 2 4 2 1 4 3 2 4 3 4 3 4 2 3 2 3 2 2 2 1 3 2 1 4 3 4 1 2
[1377] 3 2 4 4 1 3 4 2 2 4 1 1 3 2 2 4 2 4 2 4 2 2 2 4 2 2 4 4 4 2 3 3
[1409] 4 4 3 4 4 4 4 2 4 3 2 2 4 2 4 1 2 4 3 1 2 2 1 2 3 1 2 2 3 2 4 2
[1441] 4 2 3 4 2 4 4 2 4 2 4 1 2 2 3 2 3 3 4 2 4 4 2 3 4 3 1 3 4 2 3 2
[1473] 4 4 4 4 3 1 3 2 4 4 3 2 2 4 3 1 3 2 2 3 3 3 2 3 4 2 3 2 4 4 4 2
[1505] 2 4 2 4 2 2 4 4 4 4 4 4 2 3 2 3 4 3 3 1 1 2 3 2 2 4 2 4 4 4 2 3
[1537] 4 2 1 4 3 2 2 1 3 3 2 4 2 2 1 1 3 4 4 1 3 4 4 1 3 3 4 3 2 2 2 2
[1569] 2 3 4 3 4 2 2 3 3 1 3 4 4 4 4 2 4 3 2 2 3 2 3 3 1 3 4 2 4 1 1 3
[1601] 2 4 4 2 2 2 3 4 4 1 1 4 3 3 1 2 3 3 3 1 2 3 2 4 2 3 2 2 2 2 3 1
[1633] 3 3 2 2 2 2 2 3 1 3 1 2 3 2 4 3 2 3 2 4 3 3 3 2 2 3 4 4 2 1 2 3
[1665] 1 3 3 3 2 3 1 3 4 4 2 3 3 4 2 3 1 2 4 1 1 4 2 3 4 3 3 4 3 2 2 2
[1697] 2 3 1 1 4 4 3 2 4 2 3 2 2 1 2 2 4 3 2 2 4 1 3 4 3 2 4 4 3 4 3 4
[1729] 4 4 3 2 4 3 2 4 3 2 4 3 2 3 1 2 1 3 2 3 3 4 3 3 4 3 2 4 3 4 4 3
[1761] 2 1 3 3 3 4 4 3 4 3 3 1 1 3 3 2 4 4 1 3 4 2 3 2 1 2 3 4 4 1 3 3
[1793] 1 2 2 3 3 2 4 3 3 1 4 3 3 3 3 2 4 3 1 2 4 1 2 3 1 2 3 3 3 4 1 1
[1825] 3 3 4 3 3 3 1 3 2 3 3 1 2 2 2 3 3 2 3 3 3 1 4 3 2 4 2 4 2 3 4 2
[1857] 3 3 3 2 2 3 3 3 4 4 2 1 2 2 3 2 3 3 2 2 2 3 3 3 2 2 4 2 3 4 2 2
[1889] 2 1 4 4 2 2 1 3 1 4 2 3 4 2 2 2 3 4 3 3 1 1 3 3 3 1 2 4 1 3 2 2
[1921] 2 3 4 4 2 3 2 2 3 1 2 4 4 2 3 3 3 4 1 1 1 1 2 3 2 2 3 4 1 2 3 4
[1953] 2 2 1 2 2 3 3 4 3 4 2 4 2 3 3 4 1 1 1 3 3 1 2 2 3 1 3 3 3 4 1 3
[1985] 1 3 3 3 3 4 4 2 3 2 3 1 2 2 1 4 3 4 3 4 3 2 4 2 4 4 2 3 3 2 4 2
[2017] 3 2 4 1 3 4 3 4 2 2 3 2 4 3 3 1 2 1 3 1 2 3 4 1 4 3 3 4 2 3 2 1
[2049] 3 4 1 3 3 2 2 3 2 3 4 2 2 2 3 4 3 3 4 1 1 2 3 2 2 3 2 4 2 3 2 2
[2081] 1 3 4 3 4 4 2 4 4 2 2 4 1 2 4 1 1 2 2 3 2 2 2 4 2 2 3 2 4 1 3 4
[2113] 2 2 3 4 2 1 3 3 3 2 3 3 4 4 4 2 2 3 2 4 1 1 1 3 2 2 3 1 1 3 4 3
[2145] 1 1 3 3 2 3 1 2 2 3 4 4 1 3 2 3 2 2 2 1 3 3 2 2 3 4 1 2 2 3 4 1
[2177] 3 1 1 2 3 3 4 2 3 3 2 2 1 1 4 2 3 3 3 2 3 4 4 2 2 4 3 3 4 3 2 3
[2209] 3 4 4 3 2 4 2 4 1 2 1 3 4 4 3 3 2 4 2 1 3 3 4 4 1 2 1 1 3 1 1 4
[2241] 4 2 2 2 2 3 3 3 3 1 3 2 3 3 1 2 2 3 2 2 3 2 4 3 2 1 2 2 2 2 2 4
[2273] 4 2 2 3 3 1 3 1 4 2 2 2 3 3 2 2 3 4 2 3 2 4 3 3 3 4 2 2 2 1 3 4
[2305] 3 2 3 3 2 1 3 4 4 2 1 4 3 1 1 3 2 2 3 2 4 2 3 1 4 3 2 4 3 3 4 1
[2337] 4 3 3 2 3 1 2 3 4 1 2 4 4 4 4 4 3 1 2 2 2 3 4 1 3 1 2 2 4 3 1 3
[2369] 2 2 1 3 4 3 4 3 2 2 2 4 3 1 3 3 4 2 2 2 2 3 3 2 2 2 1 2 1 1 3 4
[2401] 2 3 2 2 3 3 2 4 2 1 3 4 1 3 3 4 4 3 3 4 4 2 4 2 2 2 2 2 4 4 3 3
[2433] 4 2 1 4 2 2 2 3 2 2 1 4 3 2 3 1 2 4 2 4 2 1 4 1 3 2 1 2 3 4 3 3
[2465] 2 4 4 3 3 3 3 2 3 4 4 4 2 3 3 3 2 3 3 3 2 3 4 2 1 4 4 2 2 4 3 2
[2497] 4 3 1 2 3 1 3 3 1 4 4 3 2 4 3 4 2 3 2 1 2 2 3 2 3 2 2 4 2 2 1 3
[2529] 4 3 2 1 3 3 1 3 3 1 3 1 3 4 3 4 4 3 3 1 2 3 4 4 2 3 1 3 2 2 2 2
[2561] 3 4 3 3 3 1 2 3 4 3 2 4 2 1 2 3 3 2 4 4 4 4 2 2 1 3 4 1 2 2 2 2
[2593] 3 2 3 3 3 3 3 3 3 4 1 4 1 4 3 1 4 2 2 4 4 3 1 2 4 2 2 3 3 3 2 3
[2625] 3 3 1 2 3 4 3 3 1 2 3 2 3 1 4 3 1 4 4 1 4 2 2 2 2 2 2 2 2 1 4 2
[2657] 3 2 4 4 3 3 2 2 3 2 1 2 3 2 1 3 1 4 4 2 4 1 2 2 2 3 1 2 2 1 3 2
[2689] 3 4 1 3 2 4 2 3 3 1 4 3 1 4 2 1 1 3 3 3 4 2 2 4 1 4 4 4 2 4 2 3
[2721] 4 3 2 4 1 2 2 1 1 3 2 4 4 1 3 2 3 4 2 4 4 2 3 4 1 2 2 4 2 4 3 1
[2753] 3 1 4 3 3 2 4 2 4 3 2 2 1 3 2 4 2 4 4 2 3 3 1 4 1 2 2 3 2 4 2 2
[2785] 3 2 2 3 4 4 3 4 2 2 2 3 1 2 3 2 2 3 4 3 3 4 3 3 2 1 2 4 3 4 3 4
[2817] 4 2 3 4 3 3 2 3 2 2 1 2 4 4 2 4 2 1 3 3 2 1 1 2 4 4 2 3 3 2 3 2
[2849] 2 2 2 2 3 4 3 4 4 3 3 3 3 4 4 3 3 4 3 3 2 3 3 3 1 3 3 4 2 2 2 2
[2881] 3 2 1 1 4 3 1 2 3 4 2 1 2 2 4 2 1 3 4 2 3 4 4 2 1 3 2 2 1 2 3 3
[2913] 4 4 3 2 2 4 2 1 3 3 2 2 4 4 2 4 1 4 2 4 3 1 3 2 4 4 4 3 2 4 1 4
[2945] 1 4 2 2 2 3 4 3 2 4 2 3 1 2 3 3 2 3 2 4 2 2 3 1 3 3 4 3 3 4 4 2
[2977] 3 3 3 2 3 1 2 3 2 3 2 3 3 3 3 1 2 2 4 1 2 1 2 3 4 3 3 3 2 3 3 3
[3009] 1 3 4 2 4 2 2 2 2 4 2 1 4 3 2 3 2 4 3 3 2 2 4 4 3 1 3 3 4 3 3 2
[3041] 1 4 2 4 2 4 4 2 4 3 2 4 4 4 4 2 4 3 1 3 1 2 2 1 2 1 3 4 1 2 3 3
[3073] 4 4 3 2 3 1 2 2 4 4 4 3 3 3 4 2 4 4 3 2 2 4 1 2 2 2 3 3 4 3 1 3
[3105] 3 2 2 1 1 2 3 3 1 1 2 3 1 2 4 4 4 2 3 3 2 4 3 3 4 2 1 3 2 4 3 3
[3137] 3 4 3 3 3 2 2 3 3 2 3 4 3 1 3 3 4 4 2 2 1 2 3 4 3 3 3 2 1 2 4 3
[3169] 1 2 1 1 3 4 2 3 1 3 2 2 1 2 3 1 3 3 4 3 1 4 1 4 3 4 3 3 4 4 1 1
[3201] 1 4 4 3 4 2 3 4 2 4 1 2 2 3 4 2 4 3 3 2 3 1 3 2 4 2 4 4 2 1 4 3
[3233] 2 2 4 3 1 3 4 4 2 2 4 3 1 4 2 3 4 3 2 2 4 3 2 2 4 2 2 1 3 3 2 3
[3265] 3 2 4 3 4 3 1 2 2 4 4 1 4 3 4 1 1 3 2 2 3 2 3 4 2 1 3 2 4 2 2 2
[3297] 4 4 2 4 4 2 1 3 2 2 4 2 3 4 4 4 4 3 3 4 3 3 3 3 2 3 1 4 4 3 2 3
[3329] 2 2 4 1 3 2 3 4 3 4 1 2 3 2 1 4 3 4 2 1 4 2 3 4 3 3 2 1 4 4 1 3
[3361] 3 2 2 2 1 2 4 4 4 4 2 2 1 3 4 1 2 2 3 3 2 2 2 3 4 2 4 4 4 3 2 2
[3393] 3 3 3 2 2 4 1 2 4 3 2 1 2 1 3 3 2 2 3 2 3 4 2 2 2 3 3 2 4 3 4 1
[3425] 1 4 4 3 4 1 3 4 3 3 2 3 2 1 2 3 2 3 3 4 1 1 1 4 1 4 2 2 3 2 3 3
[3457] 4 3 3 3 3 4 3 3 3 2 1 2 4 4 4 2 4 3 4 1 2 4 3 1 1 1 2 1 3 3 1 3
[3489] 2 2 1 4 1 3 4 2 4 3 4 3 4 1 2 3 2 3 2 4 2 4 1 3 4 4 4 4 3 3 3 3
[3521] 4 2 1 1 2 3 1 4 4 3 1 2 1 3 4 2 2 4 3 3 4 4 3 3 4 1 3 2 3 2 3 4
[3553] 3 3 1 3 4 1 3 2 3 2 2 2 3 2 1 2 2 1 3 1 1 3 2 4 3 4 2 1 1 3 2 3
[3585] 4 2 2 2 3 2 3 4 2 1 3 3 2 4 2 4 1 3 3 3 2 2 2 2 3 3 3 3 1 2 3 2
[3617] 2 3 2 3 2 3 4 4 4 3 1 2 2 2 1 2 3 1 3 2 1 1 3 4 4 2 4 1 2 4 2 3
[3649] 2 4 3 2 1 1 2 2 3 2 2 3 3 2 1 1 2 4 4 3 4 1 3 1 4 2 2 4 2 2 2 4
[3681] 2 1 3 3 2 3 3 2 2 2 3 3 2 4 3 3 3 3 4 2 2 2 1 4 4 4 2 4 4 1 3 3
[3713] 2 2 2 3 4 2 2 3 2 4 3 2 1 2 2 2 2 2 2 1 3 4 4 3 2 4 3 3 3 3 3 3
[3745] 2 1 1 2 4 2 2 4 2 3 4 1 3 3 2 3 2 2 2 4 3 2 3 2 1 1 4 1 3 4 3 3
[3777] 1 1 4 3 1 2 2 3 2 4 2 4 3 2 4 1 3 3 3 1 3 1 2 3 2 2 4 4 4 3 4 1
[3809] 2 2 3 3 3 3 2 3 2 4 2 3 3 3 2 2 1 4 4 3 2 3 3 2 3 3 3 3 1 3 3 2
[3841] 4 4 4 2 4 3 4 1 2 3 2 4 1 2 2 2 3 3 3 2 3 4 3 3 3 2 3 3 2 4 3 2
[3873] 4 3 2 3 2 3 1 1 3 3 2 2 3 3 3 2 1 2 2 1 4 2 2 2 3 2 4 3 2 3 2 3
[3905] 3 4 3 1 2 4 3 1 2 3 3 2 3 4 4 2 3 3 4 2 2 4 3 3 2 1 3 4 2 1 2 3
[3937] 3 2 3 3 3 2 1 3 2 2 4 4 1 3 2 3 3 4 2 1 4 4 2 3 3 3 2 3 3 4 4 3
[3969] 4 1 2 4 2 4 3 4 3 2 3 2 3 1 1 2 2 2 1 4 3 4 3 3 2 2 1 2 4 3 1 4
[4001] 3 3 1 4 4 3 1 3 2 2 3 3 2 3 1 3 2 2 1 2 1 3 3 4 2 4 2 3 4 4 2 3
[4033] 1 3 2 3 3 4 2 1 1 4 4 1 4 4 3 4 4 2 2 4 3 2 3 2 3 1 1 1 4 3 1 3
[4065] 4 2 4 1 4 3 3 2 3 4 3 3 2 1 3 4 3 3 2 2 2 3 1 4 3 2 4 3 3 2 1 3
[4097] 2 3 3 3 2 1 4 4 3 2 3 1 3 3 4 2 3 3 2 3 4 3 2 2 2 2 2 2 2 3 1 4
[4129] 2 1 4 2 3 4 3 4 1 3 2 1 1 4 2 3 3 3 1 2 3 2 2 2 2 2 4 4 1 3 3 4
[4161] 4 1 4 3 3 3 4 4 1 2 3 2 1 2 3 3 1 1 2 1 2 3 3 1 4 2 3 2 2 2 3 2
[4193] 4 4 2 2 2 2 3 3 4 2 3 3 3 4 3 1 4 4 2 2 1 3 3 3 3 1 4 3 2 3 3 3
[4225] 1 3 3 4 1 2 2 3 2 3 4 3 4 1 4 4 3 2 1 2 2 1 1 2 3 2 2 3 4 2 1 2
[4257] 1 2 3 2 1 4 2 3 2 3 4 2 2 2 2 2 2 4 2 3 3 1 2 4 3 4 2 3 1 4 2 2
[4289] 4 2 4 4 2 1 4 3 4 3 3 4 4 1 4 1 3 2 3 3 4 4 2 2 3 3 2 4 2 3 4 2
[4321] 2 2 2 3 4 4 3 1 1 4 1 2 3 4 3 4 2 3 3 3 3 4 4 4 3 3 4 2 2 2 2 4
[4353] 1 2 2 2 3 3 3 3 3 2 2 1 4 1 1 4 1 3 4 3 2 3 1 2 4 4 2 3 1 2 3 2
[4385] 2 4 1 3 3 2 3 4 3 3 2 2 4 1 3 3 1 1 4 4 3 3 3 3 1 3 3 1 4 3 4 3
[4417] 2 2 4 3 4 4 1 1 2 3 3 3 3 3 3 4 4 1 3 1 2 3 4 3 2 3 4 3 2 2 3 2
[4449] 4 3 1 1 1 4 3 1 1 2 1 4 4 2 3 2 1 3 2 2 4 2 2 3 3 4 2 3 2 3 4 1
[4481] 4 2 1 2 3 2 3 3 3 1 2 3 4 3 2 3 3 3 2 2 1 4 4 1 4 3 2 4 4 2 2 2
[4513] 2 3 4 1 3 1 3 4 4 2 3 2 2 3 4 3 4 2 3 2 3 4 2 1 2 2 3 3 1 3 1 3
[4545] 3 2 2 3 2 3 4 2 3 3 4 3 2 4 2 4 3 2 4 3 3 3 3 4 3 4 2 1 3 2 3 3
[4577] 1 4 3 3 4 3 4 4 1 4 1 2 3 3 1 3 4 3 4 4 2 2 3 1 1 2 3 2 2 1 1 2
[4609] 1 2 4 3 4 3 4 1 4 2 4 1 1 4 4 4 1 3 2 4 4 1 2 3 1 2 2 2 4 3 3 2
[4641] 1 3 4 4 3 3 2 3 2 1 1 4 4 2 1 2 2 3 2 3 2 2 2 2 2 2 2 4 3 2 1 2
[4673] 1 2 3 3 2 2 4 1 3 4 2 3 4 3 2 2 2 2 3 4 3 3 2 2 3 3 1 3 3 2 1 1
[4705] 4 3 2 2 2 3 2 4 2 4 2 4 2 2 4 2 2 1 4 3 2 2 2 4 2 4 2 4 4 1 2 4
[4737] 4 3 1 3 3 4 4 3 2 2 3 3 3 4 4 2 2 2 2 3 1 2 4 2 1 1 2 2 1 2 3 2
[4769] 2 3 3 2 3 1 2 2 3 2 1 1 2 2 1 4 2 4 3 3 3 4 3 3 3 4 2 3 4 2 3 3
[4801] 1 1 3 3 3 4 3 4 3 2 4 4 2 2 4 3 4 4 1 3 4 4 2 2 4 4 2 2 3 4 2 3
[4833] 2 2 2 4 3 4 4 1 4 4 2 4 3 2 3 4 3 3 4 4 2 2 3 4 2 3 1 1 3 2 1 3
[4865] 3 1 4 4 4 4 3 3 4 4 2 4 3 3 2 4 1 2 4 3 3 2 1 3 4 3 4 3 1 4 3 4
[4897] 3 2 3 4 3 2 3 1 2 4 4 2 4 3 2 3 1 1 1 1 2 4 4 2 4 3 3 2 2 4 2 2
[4929] 3 4 2 4 3 2 4 2 3 2 2 2 4 3 1 2 2 1 3 4 2 4 3 3 4 3 3 3 3 2 3 2
[4961] 3 3 1 2 2 3 2 2 3 4 4 2 1 3 4 2 2 3 3 2 2 2 4 4 3 4 1 2 2 3 3 3
[4993] 2 1 3 4 4 2 3 2 1 3 1 4 2 4 2 4 2 3 1 3 3 2 1 4 1 3 4 2 3 4 3 2
[5025] 1 3 2 4 3 1 4 1 3 3 2 4 3 4 4 2 4 3 2 2 4 2 4 1 1 1 3 2 3 3 3 3
[5057] 4 3 4 1 1 1 4 4 3 4 2 4 2 1 4 3 3 1 1 1 3 2 4 2 1 4 3 3 1 2 2 2
[5089] 2 1 4 3 1 4 3 4 3 3 4 4 4 2 3 4 4 4 2 4 2 1 4 3 4 4 4 1 3 3 4 3
[5121] 2 4 4 4 4 2 1 4 1 4 4 4 3 2 2 3 3 1 3 3 4 3 2 3 3 2 4 3 4 4 1 2
[5153] 4 3 4 2 4 1 3 2 4 3 1 3 3 3 2 2 4 4 2 3 2 2 2 1 1 2 4 2 3 2 3 2
[5185] 4 1 2 3 4 4 4 3 2 2 3 2 3 4 3 1 4 4 2 3 3 4 3 4 4 3 3 4 2 3 3 4
[5217] 3 4 3 2 2 1 2 1 4 3 2 2 1 3 3 2 4 1 3 4 4 3 3 2 1 2 3 2 2 3 4 3
[5249] 4 3 2 2 2 3 4 2 2 3 1 3 4 2 3 4 2 4 3 2 3 1 4 3 3 4 3 3 4 4 4 3
[5281] 2 4 4 4 2 3 1 2 1 4 2 3 4 3 3 3 3 4 3 4 3 3 3 3 2 2 3 3 2 4 2 1
[5313] 4 2 4 4 3 4 3 3 4 3 2 2 2 2 4 3 3 2 3 2 4 2 1 1 2 2 2 4 4 2 2 3
[5345] 3 2 2 3 2 4 3 3 4 2 4 3 2 2 4 2 4 2 2 4 3 1 4 2 2 2 3 2 2 2 1 4
[5377] 4 3 4 1 2 3 4 2 1 2 3 3 2 2 2 1 3 3 3 3 2 1 2 4 2 2 3 2 3 4 2 4
[5409] 3 3 4 2 2 4 2 3 1 4 2 1 1 1 4 4 3 4 3 3 4 3 3 2 1 3 2 3 4 2 2 2
[5441] 3 2 2 3 2 3 3 3 2 3 4 2 3 3 1 4 2 3 3 3 3 1 3 3 4 3 4 4 2 3 2 4
[5473] 2 3 4 2 4 3 2 2 1 3 3 4 3 1 3 2 4 2 4 4 3 3 4 3 1 3 3 3 4 2 2 4
[5505] 3 4 4 1 1 4 4 2 2 4 3 4 2 3 3 4 2 4 1 2 4 3 2 4 2 2 3 3 3 3 3 2
[5537] 1 3 1 1 4 2 2 4 3 3 4 3 4 2 2 3 2 4 2 4 2 3 3 2 4 2 1 2 4 3 2 1
[5569] 1 3 1 3 3 4 1 3 4 4 4 4 2 2 2 4 2 2 4 2 2 2 3 4 1 4 4 3 1 3 3 2
[5601] 3 4 3 3 4 3 3 3 4 2 3 3 2 3 1 4 4 2 4 4 2 1 2 4 3 1 1 4 2 1 3 4
[5633] 1 2 1 2 4 1 3 2 3 4 2 3 1 2 4 2 2 2 2 1 3 2 3 3 4 2 3 4 4 3 4 3
[5665] 4 3 1 3 4 4 2 2 1 3 4 1 2 3 2 3 2 3 3 2 4 4 4 2 4 2 3 1 3 2 3 4
[5697] 3 4 4 3 3 1 4 4 2 2 3 2 1 2 2 2 4 3 4 2 3 3 4 2 4 1 4 4 2 3 2 4
[5729] 2 2 4 3 3 2 2 4 2 4 3 4 1 3 2 1 3 3 3 2 3 3 3 4 2 1 2 1 4 3 1 1
[5761] 3 4 2 3 4 1 4 3 3 1 4 4 3 2 4 4 3 3 3 2 3 1 3 1 4 3 2 4 3 4 1 1
[5793] 2 2 3 3 2 1 3 3 3 2 3 3 3 2 4 3 3 1 2 3 2 2 4 1 4 3 2 3 2 2 2 1
[5825] 3 3 3 2 2 4 2 4 2 3 4 3 2 4 4 4 4 2 2 2 4 2 2 3 3 3 1 4 3 2 1 3
[5857] 2 2 4 4 2 3 2 3 3 3 2 2 2 2 2 4 4 3 4 2 3 4 4 2 3 2 3 3 3 4 4 4
[5889] 3 3 4 3 2 3 2 1 3 4 4 4 2 1 4 1 4 3 4 1 4 1 1 4 1 3 3 3 2 2 1 2
[5921] 4 1 3 3 1 2 2 4 4 2 3 2 2 4 1 4 2 3 4 1 4 1 4 3 2 3 4 3 3 4 4 3
[5953] 2 3 2 2 3 1 2 2 4 3 4 3 4 1 3 2 2 3 4 4 2 2 3 2 2 4 2 1 3 3 4 4
[5985] 3 4 4 2 1 4 4 3 3 4 2 4 2 1 2 3 2 3 3 2 4 4 2 4 2 4 3 4 1 2 1 4
[6017] 1 1 4 3 2 2 3 4 2 3 2 2 3 2 3 3 4 1 4 3 1 2 3 2 3 4 2 4 3 2 3 2
[6049] 2 1 4 3 2 4 3 2 4 3 3 2 3 1 2 2 1 3 2 2 4 3 2 2 3 1 4 1 4 3 2 2
[6081] 4 2 3 4 2 1 1 4 2 2 2 1 2 4 4 4 2 3 2 4 3 3 3 1 1 2 3 4 4 2 3 2
[6113] 3 1 4 3 3 3 4 2 4 2 4 4 4 3 3 2 3 3 3 4 4 2 2 2 2 1 3 3 2 3 3 1
[6145] 2 2 2 1 2 2 4 1 2 3 3 3 3 2 2 2 2 3 1 2 2 3 3 1 3 1 4 2 3 2 2 2
[6177] 1 1 1 2 4 4 4 4 4 3 4 2 3 3 3 2 3 1 1 2 2 4 1 3 4 2 3 2 2 2 4 4
[6209] 3 3 1 3 2 3 2 3 2 3 1 2 2 2 3 2 3 3 3 2 2 2 3 3 3 3 3 4 4 3 4 3
[6241] 4 3 4 3 3 3 1 2 1 4 2 3 1 2 3 2 4 3 1 1 2 2 3 2 2 3 4 4 3 2 3 2
[6273] 4 4 2 1 2 3 3 2 2 3 3 3 4 2 1 3 1 4 3 4 2 3 4 2 2 4 2 2 2 2 3 2
[6305] 3 2 3 2 3 4 4 2 1 4 3 2 4 2 2 4 3 3 1 3 1 3 2 2 2 4 3 2 2 2 3 1
[6337] 1 4 4 1 2 3 3 2 3 1 2 2 2 4 3 2 2 3 3 2 3 2 2 2 1 2 2 4 1 3 1 3
[6369] 2 4 2 2 2 4 3 2 3 4 4 3 4 2 2 2 3 1 1 4 3 2 3 2 2 4 4 1 3 3 3 3
[6401] 3 1 3 3 4 3 1 3 2 3 1 4 1 2 2 3 3 2 1 2 3 1 2 3 3 4 3 2 3 3 3 2
[6433] 4 2 3 3 1 3 3 2 4 3 2 4 2 4 4 3 3 1 2 3 2 4 3 3 2 3 1 3 1 4 3 2
[6465] 3 4 4 2 2 1 3 2 1 4 3 4 3 4 3 3 3 4 3 1 3 3 3 3 2 3 2 3 4 4 3 2
[6497] 3 2 1 3 3 3 1 2 4 4 3 3 3 2 4 3 3 1 3 2 3 4 2 3 3 3 2 4 3 4 2 2
[6529] 3 3 2 2 2 4 3 3 4 3 4 3 1 3 3 4 2 3 3 4 4 3 2 4 1 3 3 2 2 3 2 1
[6561] 4 2 3 2 3 1 3 2 2 3 4 2 2 3 2 3 4 3 1 3 3 3 4 2 3 4 4 1 2 3 3 2
[6593] 3 1 3 4 3 1 3 1 2 2 3 2 1 3 4 4 3 2 3 3 3 4 4 4 3 4 1 1 3 4 2 2
[6625] 2 4 2 2 3 4 3 4 3 2 2 3 4 3 3 2 3 4 3 4 3 2 4 1 3 1 2 1 2 4 3 3
[6657] 3 3 2 3 2 4 2 4 3 4 1 3 2 4 3 4 1 3 1 2 3 2 3 1 3 4 2 2 4 1 4 2
[6689] 3 3 2 3 4 1 2 2 3 2 2 2 3 1 4 2 1 4 3 3 4 3 2 1 4 3 4 4 2 3 4 2
[6721] 3 3 4 2 3 4 3 2 4 3 2 3 3 4 1 2 1 3 3 2 3 2 4 3 4 3 2 1 1 2 2 1
[6753] 3 3 1 2 1 3 3 4 3 2 4 4 3 3 3 2 2 2 3 3 1 3 3 2 3 3 1 3 2 2 4 3
[6785] 4 3 2 2 2 3 1 2 4 3 3 3 3 3 3 2 4 1 4 3 1 2 2 4 1 3 1 3 3 4 3 4
[6817] 3 4 4 4 4 3 3 2 2 3 1 3 4 4 4 3 1 3 2 2 3 2 2 2 1 2 3 4 4 3 2 4
[6849] 2 4 1 2 4 1 2 1 3 3 3 2 3 2 3 3 4 1 4 2 2 2 1 3 1 3 2 2 3 3 4 2
[6881] 4 1 1 1 2 4 3 4 4 4 1 1 2 3 3 1 2 3 2 2 2 2 1 2 1 2 2 3 4 4 2 4
[6913] 3 3 2 3 1 3 2 3 4 2 1 3 2 3 1 4 3 2 4 4 2 4 2 4 2 3 1 3 4 2 3 4
[6945] 4 2 3 3 3 4 3 4 4 2 2 3 2 3 1 2 2 2 1 4 2 3 2 4 4 2 4 3 3 3 1 3
[6977] 3 4 4 3 1 2 3 4 3 4 3 3 2 2 1 4 2 4 1 1 2 3 3 4 1 4 3 1 4 4 1 2
[7009] 3 3 4 2 2 3 4 3 4 2 2 3 4 1 4 2 3 1 3 2 2 1 4 3 2 1 2 1 2 4 2 1
[7041] 4 3 1 4 4 2 3 4 4 2 2 4 2 2 4 3 2 4 4 2 4 2 2 3 1 4 2 3 3 3 4 3
[7073] 4 3 4 2 3 1 2 3 2 2 1 3 3 2 3 4 3 3 3 4 4 3 2 2 3 2 2 3 2 2 1 2
[7105] 4 4 1 4 4 1 3 3 4 3 3 2 2 4 3 4 3 4 3 4 4 2 2 3 3 4 3 4 1 3 1 3
[7137] 1 3 3 3 2 2 3 2 4 2 3 3 4 3 3 4 2 2 4 4 4 1 4 2 3 4 1 3 4 3 4 4
[7169] 2 3 3 3 3 4 4 2 1 4 2 2 4 2 3 3 2 4 3 4 1 4 2 4 1 3 4 4 3 3 1 4
[7201] 1 3 4 3 3 2 1 3 2 3 4 3 4 4 4 4 3 1 4 3 3 4 3 2 2 1 2 4 3 1 3 1
[7233] 4 4 2 3 1 3 4 2 4 3 4 3 2 2 2 4 3 1 3 1 4 3 3 2 4 3 4 3 4 2 1 2
[7265] 3 2 2 2 3 3 2 4 3 4 4 2 1 3 1 2 4 2 3 2 2 1 4 4 2 4 3 1 4 3 4 2
[7297] 1 2 3 3 3 2 3 4 2 4 4 2 1 1 4 4 3 3 2 3 1 3 1 1 2 2 4 4 2 4 4 3
[7329] 2 4 2 2 4 2 2 3 4 4 4 3 3 4 4 2 2 1 3 4 4 3 2 4 3 3 4 3 3 1 3 3
[7361] 2 3 3 2 1 3 2 4 4 3 3 2 4 3 3 4 4 4 4 3 4 4 3 4 3 3 2 3 4 2 4 2
[7393] 2 4 2 3 3 2 1 3 4 2 4 2 3 3 1 2 2 4 2 3 2 4 3 3 2 3 1 3 2 2 2 3
[7425] 1 1 3 2 3 1 2 1 3 1 3 2 2 3 2 3 2 4 3 3 4 2 1 1 4 3 2 3 3 2 4 4
[7457] 3 4 3 3 1 3 3 4 3 4 4 3 2 4 1 2 2 3 4 3 3 3 2 3 2 3 3 3 4 3 1 3
[7489] 1 4 2 4 2 2 3 4 3 3 2 3 4 1 1 3 3 3 2 2 4 4 3 1 2 4 3 3 2 3 1 3
[7521] 3 4 2 1 3 4 3 1 4 4 1 4 2 3 3 2 3 1 2 1 1 4 4 1 1 4 2 3 3 3 3 4
[7553] 2 4 3 4 4 3 4 1 2 4 3 3 2 3 4 3 3 2 3 2 3 2 4 1 2 2 3 2 3 2 2 1
[7585] 4 4 2 4 3 4 2 2 3 2 2 3 2 2 4 3 2 3 4 2 2 3 3 4 1 3 3 2 1 3 2 4
[7617] 2 4 4 2 4 2 3 3 2 3 3 2 2 2 4 4 2 2 2 4 3 4 1 3 2 4 2 3 3 2 4 4
[7649] 2 3 2 3 4 4 4 2 2 3 3 4 2 3 2 3 2 2 2 1 4 3 3 2 2 2 3 4 3 2 1 2
[7681] 3 2 1 3 4 3 2 3 3 2 3 2 4 1 4 1 4 2 3 1 2 2 4 4 1 2 4 4 3 1 4 2
[7713] 4 1 1 3 4 2 3 4 3 4 4 2 4 4 2 3 3 4 4 4 3 2 3 2 2 3 3 4 2 4 3 3
[7745] 4 2 3 2 2 4 3 2 4 4 2 4 2 2 2 4 2 1 4 2 3 3 3 2 3 1 2 3 4 3 2 2
[7777] 3 2 1 3 3 2 2 1 1 1 1 3 3 3 2 3 3 3 4 2 4 4 3 2 1 2 2 1 4 1 4 4
[7809] 2 2 3 2 1 1 2 3 4 3 2 2 2 3 2 2 2 2 3 4 4 3 3 4 3 1 4 3 2 4 3 1
[7841] 3 3 3 4 2 2 2 3 1 1 3 3 4 2 4 2 1 4 4 2 4 3 3 2 1 2 1 3 2 3 2 1
[7873] 2 2 3 3 3 4 4 3 1 4 1 4 3 4 3 4 2 4 2 4 4 2 2 2 4 3 1 4 2 2 3 3
[7905] 2 3 3 3 1 4 4 3 1 4 2 2 4 3 4 2 1 1 2 1 3 3 1 2 4 2 3 1 2 2 2 1
[7937] 2 3 3 3 2 2 3 4 1 3 3 4 4 3 4 2 2 4 2 2 4 1 4 4 4 3 3 4 3 4 2 2
[7969] 3 2 1 4 3 2 2 3 4 2 2 2 2 3 3 3 4 2 4 4 2 4 3 3 2 2 1 2 2 2 1 2
[8001] 2 2 3 2 2 2 4 2 2 3 1 4 2 4 1 3 3 3 1 2 3 3 4 4 4 2 2 4 3 2 3 3
[8033] 2 3 1 3 2 2 1 1 2 2 3 3 4 4 4 4 2 1 4 3 3 2 4 2 4 1 2 3 4 1 3 2
[8065] 3 3 2 3
Within cluster sum of squares by cluster:
[1] 66009.89 88622.32 81507.03 68438.78
(between_SS / total_SS = 87.2 %)
Available components:
[1] "cluster" "centers" "totss" "withinss"
[5] "tot.withinss" "betweenss" "size" "iter"
[9] "ifault"
Model Validation by Finding Best No. of Ks Using Elbow Method.
As the dataset has no truth values, i.e., classified reference values
to calculate True Positive, True Negative, False Positive, and False Negative,
Precision and Recall calculations are not feasible.
However, the most suitable number of Ks can be calculated by
identifying the total within clusters sum of squares as below.
#Elbow Method for finding the optimal number of clusters
set.seed(123)
# Compute and plot wss for k = 2 to k = 15.
k.max <- 15
data <- Train
wss <- sapply(1:k.max,
function(k){kmeans(data, k, nstart=25,iter.max = 15 )$tot.withinss})
wss
[1] 2379873.28 835684.03 453592.97 304578.03 240728.19 202412.16
[7] 172177.30 147302.78 125863.83 116599.43 108631.81 101215.44
[13] 95874.06 89783.72 85675.98
plot(1:k.max, wss,
type="b", pch = 19, frame = FALSE,
xlab="Number of clusters K",
ylab="Total within-clusters sum of squares")
Conclusion
In this project, we developed a pipeline that collects the data,
cleans it, then analyzes it visually. The pipeline also clusters observations,
i.e., customers, into groups without human interactions. These clusters are hard k-means clusters,
which annotate the observation to be in a specific parent.
thus, the project will make crowd behavior identification and understanding more efficient
as it is relativly fasterin implementation than supervised learning.
Furthermore, the project contributes in enhancing personalized advertiesments
and improving the big data management cycle.
```{.r .distill-force-highlighting-css}
