How Much do Your Friends Tell About You?
Reconstructing Private Information from the Friendship Graph
Norbert Blenn
Christian Doerr
Nasireddin Shadravan
Piet Van Mieghem
Faculty of Electrical Engineering, Mathematics and Computer Science
Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
N.Blenn@tudelft.nl, C.Doerr@tudelft.nl, N.Shadravan@student.tudelft.nl, P.F.A.VanMieghem@tudelft.nl
Abstract
After the early land rush and fast exponential growth of
online social networking platforms, concerns about how
data placed in online social networks may be exploited and
abused have begun to appear among mainstream users.
So-cial networking sites have responded to these new public
sentiments by introducing privacy filters to their site,
allow-ing users to specify which aspects of their profile are visible
to whom. In this paper, we demonstrate that such an
ap-proach to privacy and informational self-determination is
largely futile: as we form social relations and build networks
with those alike us, much of who we are and what we do can
be reconstructed from unhidden parts of the social graph.
Categories and Subject Descriptors K.4.1 [COMPUTERS
AND SOCIETY]: Public Policy Issues—Privacy
General Terms Security, Online Social Network
Keywords Privacy, OSN, Friendship Graph
1. Introduction
The recent boom of social networking platforms has lead
to a dramatic shift in how people behave, spend their time
and interact with others. The wealth of information
regis-tered users and visitors voluntarily place, curate and
main-tain within these platforms in combination with their
enor-mous market reach has however also enabled a wide set of
new applications beyond the initial usage propositions:
Ac-tivities of users and their interactions with their friends are
now analyzed to obtain personal profiles, which can be used
for marketing activities, but also help companies determine
whether a customer can be deemed “influential” and should
consequently receive a better treatment than others [13].
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5th Workshop on Social Network Systems EuroSys ’12 April 10, Bern.
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formation on relationships, personal habits and interests can
be taken into account when assessing risks and rates when
applying for health insurance [16], and face recognition
per-formed on photos stored in online social media allows the
re-identifications of persons in other contexts, such as
iden-tifying passerby’s in camera recordings to deliver targeted
billboard advertisements [17].
As such technologies are developed and applied,
con-cerns about the privacy of one’s personal data are
increas-ingly gaining track. Indeed, privacy filter usage has become
a mainstream practice: in case of the largest national social
network site in the Netherlands, hyves.nl, 63% of the users
have by now enabled privacy settings in their profile making
their details invisible to the general public.
In this paper, we demonstrate to what extent and at which
accuracy level personal information can actually be
recon-structed from a social network’s friendship graphs. The
un-derlying justification our approach is driven by is the
so-ciopsychological hypothesis, which was empirically
veri-fied for digg.com [5] and facebook.com [14], that users
form social ties with those around them who are similar in
socio-economic status, interests and opinions [15]. In
con-sequence, knowing a user’s friends can therefore to a large
degree tell us the individual tastes and choices of a social
network user even when his profile page is hidden.
The degree to which this technique can be successfully
applied varies with the overall embedding of a particular
user in the social graph as well as other attributes, such as
the user’s personal characteristics, the overall diversity of the
direct friends or the degree to which the friends are making
use of privacy settings themselves.
The remainder of this paper is structured as follows:
Sec-tion 2 overviews previous work on privacy in social
network-ing sites, section 3 outlines the platform Hyves.nl and the
data acquisition used for this study. Section 4 demonstrates
a study how hidden profile information can be extrapolated
from the social friendship graph. Section 5 summarizes our
findings and gives an outlook on future work.
2. Related Work
Two major approaches, active and passive, are possible to
access private information. Active approaches try to obtain
data by directly attacking a particular user using fake
pro-file information [2], surveys or third party applications that
access the users profile in the OSN. In this paper we will
investigate passive approaches which are based on
statis-tical analyses of users and the friendship network. These
passive approaches may be based on the profile
informa-tion a user specifies, tracking the friendship network through
third-party applications, or the combination of different data
sources.
Gross and Acquisti [7] analyzed patterns of information
revelation in OSNs and privacy implications in the “early”
stage of Facebook. An amazingly high number of 89% of
users in their dataset provided their real name. Other
at-tributes like phone number, birthday, home town, address
etc. were also given by the majority of the users. Different
techniques to infer private information like reidentification
of users by analyzing the postal code and their birthday are
presented. Face re-identification to identify users on
differ-ent sites or even iddiffer-entity theft of the users social security
number was shown to be feasible.
The role of third party sites in tracking users of OSNs
and obtaining private information is investigated by
Krish-namurthy and Wills [9, 10]. In most cases, a user has no
possibility to control all applications that track profile data.
Users are not aware which data is accessed by them and what
the different services do with this data.
Because of the knowledge about friendships in OSN and
the fact that those relations are mostly built between
individ-uals having similar interests it is still possible to infer
pri-vate attributes of a user from his friends even if the user has
a profile which is not visible to everyone. McPherson et al.
[11] discussed “homophily” as a concept that limits
individ-uals to connect only to others having similar attributes. The
strongest divisions are based on race and ethnicity followed
by age, religion, education, occupation and gender. Hence,
ties between non-similar users are either not constructed or
dissolve at a higher rate. This leads to social niches in the
social space.
He et al. [8] constructed a Bayesian network assuming
that direct neighbors have a higher overlap than users
mul-tiple hops away. It is shown that privacy can be indirectly
inferred via social relations and mathematically over
multi-ple hops. He et al. use an influence strength which is defined
as the conditional probability (P (A|B)) that user A has a
attribute given a friend (B) has the same attribute.
By using friendship information and group attendance
information, Zheleva and Getoor [19] showed for different
OSNs that it is possible to infer private attributes using group
and friendship information.
Mislove et al. [14] claim that “you are who you know”
be-cause automatic community detection for multiple attributes
of the users led them infer private attributes with an
accu-racy of 80% inside those communities. This approach needs
the knowledge of the topology of the social network in
or-der to detect communities. Because of the dynamic nature of
OSNs, standard crawling techniques take rather long to
ob-tain the whole network, it is thus unfeasible for attackers to
first crawl the network in order to detect communities.
3. Hyves.nl
Hyves.nl is the largest Dutch Online Social Network founded
in 2004 containing nearly 10.6 million accounts in 2011.
Given the total population of the Netherlands (ca. 16.5
mil-lion), a large fraction of the inhabitants are registered.
How-ever, the total number of user accounts of Hyves.nl includes
duplicates and orphan accounts as well as commercial pages.
We obtained our dataset by screen scraping Hyves.nl
us-ing multiple parallel breadth first searches. Our dataset
con-tains 2,971,261 user profiles. Out of those roughly one third
are public viewable profiles. On a profile page, users have
to define a username and a real name and they may provide
birthday, age, hometown, relationship status, living situation,
address, phone number and their email address. An example
of a typical Hyves.nl profile page is shown in fig. 1.
Figure 1. Screenshot of a
users main profile page of
Hyves.nl
Additionally, users
may join a large
selec-tion of groups. Those
groups could be real
world communities like
sport clubs, schools
or companies, famous
people, bars and
restau-rants, books, movies
etc. Groups are
or-ganized in 19 topics
namely: brands,
hang-outs, school, college,
club, company, TV shows, books, food, film, gadgets,
games, famous people, media, music, traveling, sport, TV
programs and others. It is possible to join groups without
invitation and a user may create a new group. Groups are
displayed on the user’s profile page ordered by their topic.
Every group has its own page, listing all members of
this group, additional information like events, addresses or
opening times. Friendship relations are set up by sending
a friendship request via Hyves.nl to a user. If the request
is accepted the two users are mutual friends. The average
number of friends in our dataset equals 127. Users may
also upload photos and tag people in these photos. We also
crawled 446,868 images and people tagged in them resulting
in 624,478 user names 1,311,423 relations.
In terms of privacy control, Hyves.nl allows a user to
change privacy settings to display each attribute to the
pub-lic, viewable for everyone registered at Hyves.nl, friends of
friends or only friends. Nearly one third of all profiles we
collected, are publicly viewable, which means that the real
name, groups, age, hometown and the list of friends is
dis-played. If a user has a private profile page, the real name, if
entered by the user, is still displayed.
4. Reconstructing Users’ Profiles
In order to infer private attributes of a user who has his
profile page set to private, we use statistical methods based
on different sources of information. For some OSN’s like
Hyves.nl, StudiVZ.de, Skyrock.com or Vkontakte.ru most
users belong to the population of one country. Therefore,
combining information from census bureaus of these
coun-tries constitutes a straightforward way of inferring attributes
like the age, name, phone number or relationship of the user.
We used association rule learning, trained on the dataset of
publicly available information in order to reveal relations
be-tween user’s attributes and groups a profile page lists. A third
approach is based on the theory of “birds of a feather flock
together” describing that friends have similar interests.
In general, the characteristics of a user can be classified
into two groups: intrinsic attributes (such as name, age, city
and the gender) and communities (school, college,
univer-sity, company, sport club or interests).
If a user has a private profile page it is still possible to
uncover friendship relations because they are bidirectional.
Therefore these friendships are listed on profile pages of
friends having a publicly viewable profile page. Based on
the average number of friends this indicates that on average
every user has 42 friends having a publicly viewable profile
page. As stated in Bonneau et al. [3] “eight friends are
enough” to reveal the whole network of users of a OSN.
We will show that a similarly small number of friends is
sufficient to correctly infer most of a user’s characteristics.
4.1 “Birds of a Feather”
As described by McPherson et al. [11], friends tend to have
similar interests because they know each other, live close to
each other, met physically at places where they follow their
hobbies or at places where they work together. Friendships
in Online Social Networks do not necessarily follow this
scheme as one may also create friendship relations towards
users without knowing them in person. The hypothesis that
personal preferences limit the possible number of users, still
holds as online friendships are based on common interests
as shown in [5, 11, 14, 15].
4.1.1 Age
The age distribution of users in Hyves.nl shows an
oversam-pling of young persons when comparing to the age of the
Dutch population as shown in fig. 2.
One assumption is that a user is as old as most of his
friends. Hence, for every user in our dataset providing his
age we used the most frequent age of his friends as an
estimator. The results are shown in figure 3 given by the
difference between actual age of a user to the mode of the
friend’s ages.
As indicated by multiple traces (different markers, and
colors) in fig. 3, the probability that most friends have the
same age as a user is depending on the age group the user
is in. The highest accuracy of this method (prediction rate)
is found for the group of 16 to 20 year old users where 61%
of friends of a user have exactly the same age as the user.
When allowing up to ±1 year of difference the probability
to predict the correct age of a user, by using the age of
most friends, increases to 77%. This prediction probability
decreases for older age groups.
0.3
0.2
0.1
0.0
Percentage of population
0-9
10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89
Age group
Percentage of Dutch inhabitants
Percentage of Hyves.nl users
Figure 2. Comparison of the
age of Hyves.nl users (blue) to
the population of the
Nether-lands (red)
A reason for this
high age overlap might
be based on the fact
that friendships in the
group of 10 to 20 year
old users are created in
schools where the
stu-dents are in the same
class. Later in life,
col-leagues and friends are
not exactly the same age
anymore. Another
ex-planation for this trend is the decreasing average number of
friends: In the group of 16-20 year old users 81, users at
the age of 46-50 years have on average 14 friends. We also
found a peak in the prediction error for users between 35
and 45 years which is around 20 years, indicating that quite
a number of parents are befriended with their children.
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10
8
6
4
2
0
0.6
0.5
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0.2
0.1
0.0
Probability to predict the exact age
1-5
6-10
11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50
50+
Agegroup
1-5
6-10
11-15
16-20
21-25
26-30
31-35
36-40
41-45
46-50
51-Figure 3. Prediction of the age of a user using mode of
his friends age for different age groups. Inset: Probability
to correctly guess the age of a user.
4.1.2 Location Determination
Another intrinsic value of a user is the hometown. The
sim-plest assumption is that most friends of a user live in the
same city the user lives in. Actually, based on our dataset
67% of a particular user’s friends who provided their
home-town live in the same city as the user, and 91% of all friends
live within 50 km of the users location.
As already mentioned even private profile pages list the
real name of a user. By accessing a database containing
the geographical distribution of names, for example phone
books, this information can be combined to estimate the area
or even the city of a user. Some census bureaus or
universi-ties also collect data on name distributions. In the
Nether-lands the Meertens Institute [1] lists how often and in which
municipality a particular family name or first name occurs.
Because no name is evenly geographically distributed, one
can use the name of a user to guess his location. Fig. 4 shows
the geographical distribution and the popularity of “Tim” as
first name during the last 131 years. A similar geographical
distribution can be obtained for family names. Comparing
the geographical distributions of first and family name
pro-vides a rough estimate for the city of a user.
Figure 4. The popularity of the first name Tim in the
Netherlands. Inset: Geographical distribution of the name.
Given the area distribution of names in fig. 4 and the
distribution of the surname, we deduce that a user called
“Tim Janssen”
1
lives in Amsterdam with a probability of
32%, the Hague with a probability of 19% or Utrecht with a
probability of 17% etc.
Out of the 19 topic groups in Hyves.nl, some further
strengthen location estimation. Topics like hangouts, schools,
colleges, clubs, companies, food and sport contain implicit
location information. Assuming that people like to visit bars,
restaurants, spot clubs in the same city they live and work
enables us to infer the city from these groups.
By using Bayesian analysis [18] we calculated the
prob-ability a user has joined a specific group given he lives
in a specific city. In this way we compared how many
users attend a group in different cities. If the distribution
shows no significant peaks (larger than 1 standard
devia-tion), this means that the users in this particular group are
homogeneously distributed in the Netherlands. An
over-representation of a particular group in a city however is a
good indicator that this group can be used to infer a users
city. We identified 13,512 groups that can be used to predict
the residence of a user.
By analyzing all of those 13,512 groups with more than 5
users, we found that on average 64% of the members indeed
live in the same city. This does not imply that the other 36%
reside in different cities as some users simply do not provide
their home town. When assuming that users, who did not
enter a city in their profile, would live in the same city as
1
Name is randomly chosen.
most users of this group, the average predictability increases
to 86%.
4.1.3 Different Tastes in Age Groups
Groups do not only reveal location information but also
information about the age of user. For example musical
interests have a strong relation to the age of a particular
user. We depict in figure 5 exemplarily the age of users
who like different singers or music bands. Conversely these
correlations suggest that the specified age of most users in
our dataset is accurate. We found strong relations between
interests and the age of a user for movies, music types and
game consoles.
10
20
30
40
50
60
70
80
100
0
10
20
30
40
50
60
70
80
90
Age
Percent of Interest
K3
An
d
re
Rieu
Her
m
an
Fin
ker
s
John Denver
Celine Dion
Green Day
U2
Aerosm
ith
Sting
Figure 5. Probability users have a specific taste in music to
the age of a user
Every user joined on average 26.6 groups. Homophily
suggests that friends have similar tastes which should result
in a high overlap of group memberships between a user and
his friends. Figure 6 depicts the probability the profile page
of a user’s friend lists the same groups as the user. If all
friends are taken into consideration only a small overlap
(red points) can be found. When searching for the highest
overlap of groups a user has with at least one friend we found
that most users have at least one friend who joined nearly
the same groups as the user (blue points). The difference in
groups a user is a member of compared to his friends, can
be seen as a similarity measurement between users. Based
on this metric, only a fraction of all friends are close friends,
whereas a high number of acquaintances appear in a user’s
friendship network. The fact that only a few friends in the
friendship graph are close friends is also described by [6]
as the weak and strong ties and analyzed by [12]. Thus a
way of identifying close friends could be by analyzing the
information if the users are tagged on the same image. This
would imply that the users physically know each other and
the probability they are close friends increases.
4.2 Association Rules
Association rule learning is a popular method used in data
mining in order to discover relations between attributes in
datasets. Often utilized for market basket analysis the input
dataset for association rule learning contains an item set of
things a person has bought. A typical rule created out of
a supermarket dataset could therefore be the following: If
noodles and cheese are bought then the customer will also
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
Probability friends of a user share
cg
percent of groups with the user
1.0
0.8
0.6
0.4
0.2
0.0
Predictability of a users groups based on the groups of all friends cg
average overlap with all friends
maximum overlap
f(o) = 0.011e
-14.4
Figure 6. The percentage to which extend lists of groups
be-tween friends are similar. Red, the average overlap bebe-tween
all friends of a user. Blue, the maximal overlap with at least
one of the friends.
buy bolognese sauce with a confidence of α percent where
all products appear in β percent (support) of all purchases.
The confidence α corresponds to the fraction of the support
of all items in the rule to the support of the requisites.
The naive way of calculating simple co-occurrences would
result in a very large co-occurrence matrix because of ca.
1.1 million groups in our dataset. Given the groups of all
users as input, association rule learning will still calculate
rules in a reasonable time, for a given minimum support and
confidence.
We used an implementation called apriori [4] to calculate
association rules with a given minimum support of 0.1%
and a minimum confidence of 50%. The exact number of
groups in our dataset was 1115558. The support of 0.1%
means that 1116 user profiles should list a group in order
to include the group in the rule. The calculated rules had a
maximum length of 4 resulting that at most 3 groups lead
to a consequence. Longer rules are clear subsets of shorter
ones having a higher confidence but smaller support. An
example for such a rule is the following. We found that users
that are interested in the soccer club “Ajax Amsterdam” are
also interested in the “Amsterdam Arena” with a support of
0.203% and a confidence of 58%. But if a user is interested
in “Ajax Amsterdam” and “Adidas” he is more likely to be
interested in the “Amsterdam Arena” with a confidence if
83% but the rule has a support of only 0.113%.
Because it is possible to set the privacy settings for groups
to only show groups out of selected topics, association rules
learning helps to infer others. By knowing only a few groups
of a user it is possible to directly apply a rule with a high
confidence to infer other groups of the user.
The same holds for the earlier mentioned age prediction
as shown in figure 5 based on different groups. For example
the probability to be 11 years old if a user likes the movie
“Finding Nemo” is 70%. If we know that the user
addition-ally likes “Happy Feet” this probability increases to 87% as
the rule gets more specific.
Interestingly the given example of soccer fans already
depicts that group predictions work across different topics
(sport to brands to hangouts). A graph of rules illustrating
these connections is shown in fig. 7. The colors indicate
different networks where the nodes are groups with their
corresponding id’s in our dataset.
58.8399 60.2205 50.7958 52.0901 55.4267 63.2311 59.1275 62.608 55.740158.0734 51.6586 61.4239 68.3081 57.6706 76.828977.269858.4399 51.4773 52.8242 50.0447 58.848 68.4601 61.542660.219951.926 50.6435 65.439165.7233 57.5939 66.362 57.4409 82.004680.439163.5457 52.5736 57.8979 52.176 70.075 75.300757.2264 50.7226 58.07454.2088 53.3426 54.3183 63.2967 62.897256.2103 50.1131 70.72177.5881 56.0604 53.9168 51.69263.7645 54.3194 50.1212 62.886660.0545 67.8977 66.846171.3515 52.4011 50.785353.74951.3975 50.14 63.2364 55.530954.1036 53.5372 56.9375 57.2846 50.788 50.2621 50.5693 63.4182 56.2826 56.8758 53.5078 52.2648 57.7874 60.9786 65.5455 51.5908 50.4514 54.0354 51.0327 54.3057 50.41 50.071355.4997 59.622254.043960.9787 51.8303 53.4197 51.6962 59.6744 51.9328 70.7174 65.27653.3083 56.554453.795551.283452.8161.5032 51.8276 57.82452.7298 51.3017 54.351251.8067 62.7028 50.2871 53.8325 57.744758.306 64.7068 57.9443 56.8164 58.1621 58.6964 53.67 52.6461 54.7647 52.6212 66.0039 68.5332 50.3911 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81.8015 52.8821 84.9913 81.0692 53.5919 80.7999 80.9227 71.6221 87.2574 50.59 62.6422 67.0917 55.190264.4743 63.1991 81.834 53.562165.738763.632983.3052 86.6168 52.285752.1565 53.9833 65.0173 50.3855 58.1725 63.1554 55.0978 54.877857.11163.183858.7332 68.3074 70.2167 70.641962.415962.221555.202960.0412 56.419351.5469 63.028251.261459.876956.4382 66.341862.9556 63.8665 59.968871.0401 57.523 51.2168 58.2982 56.408952.134570.112254.8442 64.3921 55.757358.329756.408 55.1402 62.9971 58.937150.946762.628761.089655.8872 55.8429 62.1456 50.878 57.237154.662251.790354.2103 76.9125 78.011260.3667 50.141559.5393 60.930952.669862.5831 69.071168.648 72.550264.951959.792564.355354.9046 71.769477.431 64.327 63.7947 57.9867 54.2808 62.842582.2377 54.082154.3944 60.5424 50.8874 53.4919 77.723576.539174.4807 60.7106 66.222959.3236 58.1624 60.5946 55.8158 65.820364.079951.5478 64.0039 57.5937 76.051976.298575.0329 60.6345 51.882 69.144669.418366.1848 56.9547 50.6545 63.59 81.9392 56.3346 58.2649 66.038980.5824 50.356150.5301 57.8889 57.7465 68.62973.1789 61.5414 51.025661.826561.7582 55.7907 62.7029 71.5653 62.3079 53.924461.18167.0415 55.336561.284652.9433 59.1936 52.7287 52.345159.2508 67.599955.1214 53.110855.8261 65.5256 70.586478.591361.8361 56.3184 76.1163 58.2561 51.4322 58.6181 58.9827 74.307 65.156258.8292 54.8198 76.9299 60.216763.0977 72.9718 65.6584 78.8854 58.5881 72.8946 76.0762 68.886 56.3978 52.5781 82.3084 55.0679 57.9549 54.0625 60.9134 62.9102 51.31152.1618 76.8363 50.7812 54.2969 63.828152.1875 69.0625 53.1741 54.161 59.5802 69.186661.355353.064653.7016 61.1655 61.1655 50.386 51.1987 53.9851 53.135 63.1893 56.3361 65.084750.708454.7868 51.34356.8413 58.6798 55.2076 58.42 53.846256.059451.5436 54.709657.142952.119357.0569 55.3884 55.5121 50.0391 53.8381 53.623261.3468 54.3435 70.9204 64.5868 83.1865 62.041 75.1499 84.0862 62.3913 51.1846 65.3977 62.9976 56.6884 54.326 51.9088 56.5217 50.5471 58.1098 52.2774 68.758653.299468.3032 54.018554.5818 50.4827 53.7698 64.352 75.0965 67.3152 77.523451.1103 52.8652 59.506455.1891 54.332 59.4462 74.065352.1276 50.0449 54.79553.8278 50.1905 63.779950.93351.7464 62.392361.7703 55.622 61.028760.9569 73.923465.5024 50.9569 62.4402 75.31172.5359 61.0526 52.177 63.732166.794364.210552.3684 51.5542 50.9611 51.4186 62.3977 53.93356.4985 50.4365 58.3284 79.0675 50.1653 54.728858.5317 65.87363.0291 70.6349 64.517264.7487 73.08265.6085 53.0423 65.5423 74.272572.552963.4921 51.8519 64.682564.715654.067566.9643 52.3603 62.3569 56.268252.055553.274653.1663 50.7818 51.552152.3137 56.956360.960658.4051 55.456755.851650.533452.999656.586851.745350.3566 78.371 63.658765.4607 56.1645 57.7379 51.8561 51.9142 50.8578 52.1401 51.259663.3599 51.612153.4134 53.374252.0151 50.149855.213754.7851.974652.9324 51.382753.0387 56.451653.1652 54.84854.6079 51.9071 54.3532 58.543755.286264.26871.573558.2627 73.054654.1099 59.3533 55.0256 53.4866 54.055551.7095 57.583253.8975 58.2638 53.5123 69.9114 56.504456.491668.845566.572557.7629 58.328 63.439151.107351.412753.4526 70.3502 57.161663.848662.070568.746655.8961 56.943450.6709 57.379750.709851.1432 53.872470.4101 53.6469 54.0735 56.541364.14654.6889 52.1114 57.693 51.930852.9243 55.025656.450751.2287 51.483556.593458.7253 73.824274.065962.0714 60.324258.9176 75.5989 53.719555.617451.6875 51.561653.492364.849562.2374 50.4259 65.0199 68.086369.278863.0892 53.0948 60.988156.2748 61.0449 72.317873.9893 52.0955 62.8077 60.9387 60.041268.209157.1099 57.002952.2273 57.5051 50.9425 52.5771 50.5716 53.2938 50.345362.804751.3796 75.456552.12770.767673.596864.4622 53.8818 54.574555.638671.223653.5136 69.459654.2134 52.9256 59.500462.248257.302462.4158 66.8284 57.9467 59.347555.588166.249655.6061 53.3972 56.0371 63.4123 57.076854.496 64.692654.7794 60.687851.0411 65.62371.880564.34455.696761.891752.2948 58.0386 65.06467.8426 54.2974 52.108564.277966.031664.311668.055957.9979 56.820264.2258 52.381 58.4842 62.9287 57.2128 51.7148 71.3936 59.6081 59.090953.2934 57.4578 61.080354.5706 57.7964 52.7577 54.3399 63.7568 62.630956.241364.56262.9376 59.4651 61.160159.9516 50.3518 61.856470.9211 50.0725 60.388656.3509 75.381865.777771.949170.2159 66.0921 75.5624 50.6323 58.336564.5185 58.0742 72.8737 58.7486 54.1401 74.7471 60.4346 55.9011 50.2061 52.1918 58.1866 84.4511 71.150275.0353 58.4208 51.9015 53.9651 59.7929 66.201466.7125 64.3856 59.159 55.4725 56.4343 64.43 69.066470.5583 53.1527 55.1675 83.1524 57.472654.5636 56.779764.6487 54.7369 59.9235 67.2401 67.459677.976470.666283.4072 56.8665 52.494552.2417 68.5757 56.5641 60.302264.0116 52.7155 51.3795 77.317469.906 50.9398 61.482758.9336 56.290951.9411 60.5239 56.2208 50.0468 73.0122 66.6954 58.3084 58.3084 59.5472 50.7903 61.0423 60.487 52.4562 72.7894 56.0584 57.5597 54.7384 61.104460.598 70.3159 51.1497 58.5557 55.043251.4521 61.5581 56.1028 50.6672 77.8454 51.3878 67.4236 52.4463 59.879359.4876 65.1566 58.989858.5403 52.245759.2006 68.334151.225352.480761.1174 55.9925 58.0481 51.039351.25 55.6994 52.5725 56.578563.077480.7901 57.7572 53.0105 56.922172.629 50.1055 55.6733 64.389 59.8005 63.790566.6334 58.8529 54.1646 70.644867.93366.8707 53.9153 63.1381 57.9276 51.1466 53.705753.9876 50.3258 54.558751.5458 60.8704 54.388650.0065 54.8154 51.2233 59.7843 60.2588 62.0169 61.3291 54.66155.7054 50.4853 51.09960.5179 63.5659 54.7744 51.051755.605553.0128 59.3944 55.6731 52.3331 66.3446 82.2968 62.071253.3774 54.1262 51.3796 62.305457.842870.226 74.0619 62.4283 81.6006 53.1289 51.5288 70.1111 67.396755.841477.168567.3604 51.4844 59.2193 58.2544 61.2009 61.0817 74.7913 59.2391 62.0155 83.5752 88.346785.439385.7554 52.2596 59.9641 56.9275 51.3611 55.1136 60.1078 51.8204 63.9099 53.1008 50.6422 56.058159.442661.7856 50.9615 55.2328 64.6147 51.2608 50.2534 50.3157 54.364951.226 57.4825 50.6084 53.255850.6779 58.666458.5512 52.6683 52.4038 53.0288 55.8654 53.2692 65.8814 51.4047 57.2917 50.0947 62.3523 50.1463 50.2298 55.782 57.7367 55.5196 66.4099 57.8313 51.5395 56.2743 50.319755.3389 50.8398 54.1346 51.1346 51.0447 53.2947 57.2049 52.281 70.239 51.8908 57.7842 60.1567 54.1418 52.436752.879772.7134 73.2656 53.1202 55.810652.5033 66.9194 58.2001 57.6431 53.7438 55.096651.7037 58.9669 74.15953.443451.005 59.8052 57.4425 54.5901 51.4034 67.1294 58.0076 61.481451.1067 50.8487 59.8893 62.1033 54.231255.7319 63.2718 71.463754.3227 50.832258.7841 67.8225 50.9949 51.4763 55.744554.2683 53.1772 54.396756.3543 58.632966.1104 68.8703 51.0041 54.4957 51.5974 58.4893 50.1141 51.1182 52.396257.4623 51.8713 57.3482 50.9356 50.0913 50.3423 54.2675 58.4665 61.1365 56.0475 56.0475 63.9206 62.779658.01 63.8521 60.5888 69.4888 51.3482 54.0557 53.2473 52.344851.7801 62.6986 50.3121 50.520252.80950.145751.747855.1186 53.1419 53.3084 54.931350.0624 58.2605 53.4124 65.314253.8512 56.3699 50.131 53.8604 59.5392 59.477652.4503 53.937455.5093 66.643656.1109 58.349 67.2277 50.6135 53.5662 61.694458.4006 51.9252 68.797960.9642 51.2154 56.2098 50.0664 56.5264 57.787858.0533 57.772461.1378 68.930750.664 54.464 50.9426 50.8652 57.3166 53.0765 56.940758.9308 54.817862.4744 70.595451.4511 59.0089 51.7182 55.192256.4737 56.738850.640754.0433 54.1759 54.1317 54.3968 53.468859.0809 56.5621 60.0088 55.6783 51.0384 64.03 59.7437 53.3805 57.5342 53.6456 50.4198 60.4065 54.2643 59.0809 54.8829 52.4525 60.05360.981 59.4344 58.8157 69.951462.0567 55.041262.9893 66.7978 58.086952.0929 54.1744 52.1425 51.0261 50.6761 55.757 53.840762.684 53.8625 58.9009 50.017450.1242 53.1592 54.7208 53.3745 50.1103 55.1364 51.4916 52.826553.9408 50.7371 66.1869 55.401153.7393 52.192 55.043 54.4455 66.109255.9798 50.7853 51.375956.0206 50.4278 62.82 57.087354.3532 53.8121 57.7281 51.9248 60.550958.7013 51.1141 64.0156 54.4333 61.4363 54.0294 62.8475 51.138 54.8135 50.373251.7955 56.1962 58.582850.130352.219861.923457.599458.0766 61.9957 61.3449 50.7881 54.157657.4693 51.554657.4403 59.0456 57.3102 64.3529 55.5556 65.6133 50.585454.047761.6822 57.8997 57.0846 61.928254.035650.3149 50.6624 51.0954 53.6476 56.328453.3653 64.7523 57.7472 57.530554.123250.5846 59.7187 58.2932 56.3864 56.786557.618 66.552 50.7624 53.262161.447151.3475 66.3942 62.8277 50.0687 50.6138 70.9187 52.0627 50.5442 55.2699 61.8425 57.7406 53.5508 58.3412 60.3891 64.7571 66.3458 57.5125 64.5626 60.6156 69.6451 56.576169.5631 51.2937 66.4452 74.2745 55.5194 70.0295 71.6235 69.3277 62.1478 67.2332 66.18462.141662.30155.0708 72.1444 72.7519 67.4974 60.849 64.5799 57.483372.7127 69.2459 60.668257.9754 68.0383 63.2235 55.6807 51.6616 69.4405 62.1914 54.0344 76.7123 74.7054 60.9062 57.0509 50.3979 71.1219 61.4037 59.4899 55.0055 72.002 51.3455 58.148 63.9101 59.8453 53.3538 62.2667 83.4153 65.3574 58.145658.6447 71.4963 51.9178 52.8781 66.470258.1626 54.9683 64.043 63.7413 56.7749 50.7655 64.7106 58.8394 58.2362 65.6019 59.3791 56.459 52.715 60.5029 50.1897 56.496 54.5993 63.6795 50.2511 50.3223 53.434854.7044 54.613460.1186 52.238153.9498 56.1338 50.4306 55.2852 61.487663.1474 50.7176 65.6932 51.1067 51.9921 55.287850.0246 50.2705 52.582459.124456.419158.9769 53.7629 50.6149 55.2878 50.0738 50.4673 52.2381 60.6001 55.435355.927254.2548 53.762955.878 61.5347 57.3045 55.878 60.108260.6985 51.5986 55.9764 60.7477 58.1407 59.9115 63.7482 57.3537 65.1746 68.371965.1254 50.5958 50.0458 52.978959.2576 52.0165 51.0999 50.412552.9789 53.5747 56.0037 55.682955.2246 52.1712 50.343 53.4444 50.0993 54.9011 57.7792 50.858353.727466.408264.962860.0558 51.3151 50.248156.098 57.655159.919450.6987 56.932751.3615 56.5486 52.8906 57.2411 50.245954.5571 52.0155 50.4013 58.4922 53.653757.8235 54.8276 51.511555.7249 50.2603 50.62750.449951.5421 52.0741 58.6704 55.8676 51.4544 53.4604 57.126752.2724 54.9238 60.560453.3344 61.728553.8403 57.6072 53.2762 51.817357.3468 51.7299 50.82450.001357.867 54.1015 54.7185 55.8214 50.7874 54.3533 56.9186 53.7946 55.567460.5557 63.0092 50.796953.3532 66.5872 59.3741 58.628957.2678 59.543 52.353352.1514 50.277 59.1829 57.2516 64.655964.6818 70.6156 69.276569.3981 59.4807 51.2814 56.267656.325661.4085 64.563862.6894 58.61852.7319 51.5785 55.667 55.9891 64.0614 59.732555.0081 57.9474 50.216977.8536 57.7426 50.4175 58.107 51.9898 52.4821 50.3326 57.4397 56.7936 55.8106 50.106 51.9996 52.5441 59.1184 73.261 53.7872 70.9091 77.145266.965 64.233 61.9803 82.2605 70.7758 62.5772 86.663462.6963 58.2294 52.8308 66.0971 60.2034 75.090251.0744 76.083172.5295 57.4423 74.8688 59.2948 74.2281 55.5899 66.8085 52.1346 57.052656.8182 60.2419 64.1177 74.3722 79.449258.611152.7843 61.3295 52.616859.1194 54.6097 73.2104 75.4461 69.765456.02350.4086 54.2734 52.7084 68.999571.7604 67.2951 69.8576 79.8973 80.4635 72.553 54.495857.3447 56.3084 69.6412 79.1076 73.5906 57.6419 55.8313 73.905675.6311 72.4784 71.1684 79.934 82.7351 62.824969.418 65.0815 58.6037 59.7916 57.8579 52.9738 63.261969.3374 52.482663.5933 60.502853.9147 53.5415 53.1657 55.352862.1993 51.5797 72.6089 67.1618 61.435 50.6238 55.636653.0388 51.712556.8756 54.044262.985580.0 61.3252 65.6359 60.2133 56.3442 51.824 52.919 54.9906 63.754450.9407 50.5781 71.699769.8055 71.1983 78.0284 74.0429 50.3906 78.9967 71.398775.984362.0197 53.2876 72.9476 61.00856.2066 61.8728 59.132264.793 50.081.6657 60.26957.759259.33453.6581 51.722454.500266.2581 64.7134 60.599956.5641 56.6374 51.724577.455461.002960.7407 70.3807 50.950459.669464.0496 66.5702 53.748451.916 53.2269 64.6117 53.9301 66.30457.509850.4729 58.9301 59.7446 58.9876 67.4077 60.6777 65.013268.1553 53.8706 52.2033 67.5665 52.044560.5993 52.2459 54.002153.1432 56.6128 66.4458 52.4942 76.4906 58.872463.1737 56.8111 50.892551.1447 52.174650.2482 51.3634 53.0757 50.7242 80.2967 52.8959 50.0728 67.5915 61.7261 52.5298 54.8544 61.6735 53.444452.8412 66.492 72.0405 73.746267.2002 58.660463.504660.113553.2435 64.2233 56.8479 66.938155.1614 58.2146 56.2082 59.3196 59.1587 69.301655.095256.952463.7619 54.9206 62.127 59.8254 51.3927 54.115 61.550555.7396 54.8258 53.0126 59.209 61.296962.0703 69.588255.799 63.2036 59.3124 58.6702 59.574556.8896 58.612 54.2047 59.5238 60.4997 50.225651.253852.0546 54.2885 58.833354.1667 54.8333 51.9915 58.499 61.5507 54.009650.823253.4785 54.8062 91.22 75.1592 50.970965.491563.0747 75.1155 57.6238 76.1282 51.286458.0339 52.966378.7797 56.821651.661 51.9044 61.114261.0314 60.5764 50.2862 54.9327 53.9167 70.0447 54.734855.961856.1106 59.407559.3709 53.7152 51.1405 59.8316 54.0316 84.8547 52.540359.472382.7390.7613 68.3095 60.2458 61.2887 62.6037 57.7064 62.434 58.0788 59.236961.7671 50.18 50.515 56.820150.224 59.1715 73.9468 65.3309 62.1909 57.0494 62.3309 75.194369.0693 57.359251.6298 57.535953.3394 51.8574 54.220452.672950.657651.704860.5796 51.3533 53.6097 67.651450.2029 68.026156.1654 56.4576 62.4148 53.349157.2856 54.6246 58.393353.2236 68.390756.0895 69.434367.6254 51.2315 61.7557 68.405256.605 60.310960.1767 57.8915 55.9896 54.5775 63.8908 50.8797 53.6745 60.3013 51.037 64.1344 51.004 56.1259 65.1916 60.1972 66.782 61.4761 55.016367.895560.753970.8236 66.7133 78.3284 72.8858 72.0776 62.2994 76.2366 79.3412 70.8118 61.4399 79.7573 76.7381 62.632 78.565573.6448 80.388172.063272.8815 66.382758.3499 56.6557 70.128 50.1834 57.2219 74.4515 64.1768 66.763258.67956.7706 51.6484 62.9763 53.2679 52.4166 51.574569.724857.2753 69.4622 55.2425 68.663665.6682 54.4547 59.9078 50.384 68.3564 68.12661.1367 63.1336 53.7634 58.8326 50.0 67.1275 59.9078 62.98 53.6098 52.4889 69.104 62.2051 70.9423 50.3325 59.05466.3099 62.4575 74.7217 68.8244 67.796959.726 68.871 57.3508 62.2047 75.396268.4379 67.274464.8955 62.975153.7442 55.179855.620161.7741 72.8082 51.761 59.60152.5384 55.8758 64.8441 58.4444 65.054254.707668.676351.8766 51.8766 60.1334 59.3828 59.5496 59.9666 57.548 50.1251 66.05565.0542 67.0559 64.6372 60.3837 59.1326 53.1276 69.0575 71.4762 59.2994 66.2219 54.243958.987260.806 59.2725 60.3067 50.2496 54.7432 66.1912 50.6063 57.20456.6334 52.95751.927858.0261 78.4332 57.2504 61.167454.5238 52.180359.3765 60.2478 51.848 61.2713 50.839 62.411860.53 75.8507 58.1151 63.791851.023752.883451.1055 56.5786 58.7242 58.3784 69.2771 55.1187 58.161859.563655.3327 58.6632 58.508 66.978157.757169.227869.238461.9747 52.6868 51.3564 54.6043 54.3181 70.2962 63.5764 58.0015 62.6516 60.516550.5534 60.6354 50.4727 59.439464.6829 62.8014 65.924 52.1048 73.4375 71.1985 50.8609 53.3142 50.1966 57.6664 64.5869 61.7685 53.0049 51.2697 51.6383 59.5935 71.9041 52.9237 58.2498 58.2956 51.764 71.6239 71.3114 51.5953 54.1254 50.6358 55.1809 56.537855.55157.730351.0373 55.036857.854963.911762.734 66.291368.655976.6252 53.475659.7516 52.4324 55.8389 67.728977.867975.492576.5933 52.8501 65.4219 67.081672.199271.1618 56.8357 69.6077 72.1323 57.483767.507767.9344 59.6951 69.6129 57.8378 71.588468.8951 74.173172.836 50.2982 58.6481 56.398351.1401 67.2638 54.8162 50.5543 64.2202 51.2193 54.1102 57.3394 51.3761 57.994850.4587 62.9751 53.843357.802254.8058 57.11 58.1898 58.8722 61.5235 51.2363 57.638 50.0 51.0387 52.6099 53.9542 58.481571.298855.5577 69.393765.376269.4668 57.3514 56.756859.2973 55.5329 60.664967.5851 62.317170.0671 51.114652.5211 59.939 66.26462.147756.5854 58.019255.1249 51.148950.073961.7517 52.3497 62.9779 57.6095 65.8065 58.27556.7233 51.5234 55.277850.5268 50.1162 51.4049 54.2233 50.0246 51.5754 50.5719 52.304751.1842 53.1548 69.7412 60.4992 52.8714 50.8305 55.1941 55.8852 57.6897 55.6776 51.6991 53.112550.999961.257250.0499 50.1451 57.2921 52.125551.5754 51.7321 60.4945 54.0811 51.7303 51.205656.347 53.9574 50.1979 68.7823 52.1589 53.8274 58.1966 50.2486 55.059660.8869 50.0422 51.896 57.194952.2031 51.8116 50.778152.3241 55.07562.2263 51.4226 54.9665 53.0356 52.3492 50.0283 56.6793 51.5749 56.1814 53.1602 53.430158.4357 66.936765.0591 57.1654 53.8144 63.1781 53.1065 70.709966.5526 64.486 60.245350.539568.433950.2005 58.6397 58.422152.924158.9716 86.5419 51.540352.924150.999257.4681 56.6103 54.0701 50.5253 54.4405 51.1614 53.0582 65.7393 66.036650.3185 55.3318 63.537453.2931 54.39151.9334 50.421 51.4602 52.183756.6164 50.8848 54.984966.7625 68.647250.177 62.436 50.093955.2652 61.9315 55.2499 55.3675 67.9183 50.7888 60.1676 50.026 57.4702 51.52659.7907 58.6946 61.1988 51.5379 64.7638 52.664354.9853 56.8486 53.214360.833351.220251.994 55.2679 50.9912 57.8928 54.613257.925462.886 51.396658.717655.755662.4947 56.027651.5495 58.212364.1341 57.988857.933 50.1676 57.877157.6353 56.4808 55.042356.9813 60.2385 56.082971.4767 50.1647 56.7179 58.8704 57.680255.274458.756158.3509 67.9943 50.0548 67.4535 51.9248 64.0093 58.1093 54.236151.554858.7716 65.4914 54.9887 63.0908 66.4237 54.0864 60.957864.3382 55.1264 67.6647 53.028956.2232 70.4043 59.7043 71.8646 50.905156.6285 55.1181 59.7384 52.023757.275866.891 68.5885 51.7579 60.4823 51.81751.9431 54.8855 65.1522 55.535356.600450.302652.3981 50.6055 50.099452.4725 60.892756.55558.945 53.1198 53.7659 52.86655.0659 52.858353.3534 74.6581 57.6984 64.0515 65.914166.6412 54.601 69.293251.1091 62.609160.8421 66.252259.0515 56.145151.8286 51.6466 71.2279 52.3641 57.4645 73.3148 50.7415 66.824570.15863.877170.825362.5728 58.535353.981351.887754.470462.8597 60.9406 57.1864 52.9182 57.805 58.4228 65.2925 51.2058 54.2348 59.5091 53.98 65.8139 52.727960.482468.4444 52.3194 58.3873 54.9025 54.0872 53.8803 55.6523 56.962 57.7886 50.862 55.9636 51.1703 61.717751.1232 52.3927 55.0914 58.637267.261569.775762.395971.98467.5568 62.867353.715855.0331 57.286862.018663.789 50.759750.7057 59.419956.4749 51.6197 56.2422 54.5046 63.849750.5299 56.1516 61.6486 57.9738 51.142 62.0644 51.881661.910759.1859.3233 60.831150.1663 76.1864 73.8533 53.289158.799 60.0991 79.2914 57.5562 65.0516 53.882 54.8554 59.242754.6667 58.4588 69.9638 54.6392 70.2762 51.2168 67.1775 59.852461.544162.436355.693459.366650.5349 51.2424 68.7065 59.1127 79.300877.1097 58.659556.8002 58.624 63.02473.599169.5287 56.7128 55.8523 65.831658.1 54.2348 57.3312 54.6654 60.3772 53.782170.842375.226 51.359460.8008 65.2572 57.9555 57.1849 56.773554.816550.6295 50.763653.5328 71.105771.2889 61.1092 66.558 56.575780.003378.6774 70.8504 77.5669 51.7314 52.9269 52.1587 75.7207 50.3369 56.850669.1601 54.0592 58.5366 64.8916 60.123859.836954.786273.4712 51.42 56.905 63.5141 74.9085 53.5072 56.3249 51.350758.1295 52.5229 50.305851.3761 56.008768.026259.177 56.4457 51.456755.3532 50.6555 18333 3300 3790 2392 918 920 237 542 584 4705 7432 59 23347 1919461 345 587782835 1764 3579 540 1082 814 4999 832 543 57 833 3301 1107590 1394 91933738 16912688 171343810 3295 834 585 13010 12312 1010 5796 2481 10741 2720 11525 1990 5410 8217 54412572 482 5412 1196 1692 50001870 2022780 1693 541 6723 2155 2544 7002 3624 576 5408 574 3296 25080 22023 1148 589 2023 8970 8500 58 4089 60 4703 577 5409 5632 1458 575 35237 591 15358 8735 141459409 4538 5061 45996 640 102 670190 82 600 55 56 11089 308097 308637309430 7591759873326 34 196404 15422529 1037 100 2496 693 741 742 42 756 738755225 101 669 30 90 85 1056 226 9128 24 1100 6402 1665 232 84 140952330 74483 911348 267 2235 504 37 2264 1535370 1389 29 40493767 36 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