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advances.sciencemag.org/cgi/content/full/5/1/eaav0042/DC1
Supplementary Materials for
Urban scaling and the regional divide
Marc Keuschnigg*, Selcan Mutgan, Peter Hedström
*Corresponding author. Email: marc.keuschnigg@liu.se
Published 30 January 2019, Sci. Adv. 5, eaav0042 (2019)
DOI: 10.1126/sciadv.aav0042
This PDF file includes:
Section S1. Full population data, metropolitan areas, and regional composition
Section S2. Outlier analysis of urban scaling parameters
Section S3. Replication of the scaling relation’s decomposition with U.S. data
Section S4. Wage data and measures of individual productivity
Section S5. Full tabulation of cross-sectional results
Section S6. Full tabulation of the urban wage premium
Fig. S1. Scaling relations of urban indicators excluding the three largest labor market areas.
Fig. S2. Decomposition of the total scaling relation for wages across U.S. Metropolitan
Statistical Areas.
Fig. S3. Complementary analyses of the urban wage premium.
Table S1. Description of Sweden’s full working-age population.
Table S2. Creative jobs and the corresponding occupational codes.
Table S3. Composition effects on the scaling of wage income.
Table S4. Urban wage premium following a move from one of Sweden’s smaller labor market
areas to one of the four largest.
Statistics Sweden, the country’s central statistical office, assembled longitudinal geocoded
micro-data for us on Sweden’s entire population by merging administrative population reg-
isters. In Sweden, all register-based information for each individual and each organization
gets filed under a unique ID number. The quality of these data is generally very high, with
missing data virtually nonexistent.
(A) Differences in population means
among Sweden’s 71 smaller labor market areas (2,673–234,449 inhabitants), its four largest labor market
areas (Stockholm [2.51 million inhabitants], Malmö [1.09], Gothenburg [1.08] and Linköping [0.26]), and its
capital Stockholm in 2012. Total population aged 18–60 (in millions); mean age (in years); mean education
(in years); mean cognitive ability (as measured in a standardized conscription test [z-std.], for males only);
employees in creative jobs (as a fraction of the total labor force). All differences between the smaller and
larger labor market areas (LMAs) are significant at p<0.001 in two-sided t-tests. (B) Stayers (4.77 millions,
excluding Stockholm) and those who have left smaller for relatively larger labor market areas (503,274
one-time movers between 1990 and 2012) differ strongly, on average, in education (in years) and cognitive
ability (z-std., for males only). Moreover, those with more education tend to self-select into the biggest
labor markets, thus passing larger population differences between their native and target labor market areas
(pop. diff. in millions). All differences are significant at p<0.001 in two-sided t-tests.
A71 smaller 4 largest Stockholm B
LMAs LMAs LMA Stayers Movers
Population 2.47 2.85 1.47 Education 11.16 12.94
Age 39.16 38.35 38.34 Cognitive ability –0.15 0.26
Education 12.03 12.58 12.67 Pop. diff. | Educ. 11 0.92
Cognitive ability –0.14 0.13 0.19 Pop. diff. | Educ. 12–13 1.08
Creative jobs 26.10 35.55 38.65 Pop. diff. | Educ. 14 1.12
Analyses of urban scaling rely on functional rather than administrative boundaries of
cities (3,33). Similar to the construction of Metropolitan Statistical Areas in the United
States, which are frequently used in the urban-scaling literature, Statistics Sweden groups
the country’s municipalities into unified labor markets based on commuting patterns of local
work forces (27 ). These labor market areas cluster around local centers in which <20% of
the working population commute to other municipalities and <7.5% commute to any single
Section S1. Full population data, metropolitan areas, and regional composition
Table S1. Description of Sweden’s full working-age population.
neighboring municipality. Each remaining municipality is then assigned to the local center
receiving the largest share of its commuters. In 2012, this procedure resulted in the de-
marcation of 75 highly-modular labor market areas (see https://tinyurl.com/ycnjj4ew),
which we use as a functional definition for metropolitan areas. Table S1 summarizes com-
position differences across relevant groupings of labor market areas and highlights movers’
contributions to urban labor forces’ productivity.
From the smallest (2,673 inhabitants) to the largest labor market area (2.51 million in-
habitants) the scaling relationships reported in Fig. 1 span four orders of magnitude. One
could consider the three biggest labor markets, Stockholm (2.51 million inhabitants), Malmö
(1.09), and Gothenburg (1.08), outliers in Sweden’s urban system. Still, scaling parameters
are robust to the exclusion of those three labor market areas (Fig. S1).
Excluding, further, the mining areas Gällivare and Kiruna has little effect on the
estimated scaling parameters for company turnover (β= 1.194 ±0.054), property tax
(β= 1.170 ±0.042), and the total number of residential moves (β= 1.134 ±0.024), divorces
(β= 1.162±0.062), college graduates (β= 1.108 ±0.024), and creatives (β= 1.113±0.018).
101
102
103
104
105
106
107
Economic output
103104105106107
Population
Company turnover
β = 1.191, R2 = 0.929
Property tax
β = 1.171, R2 = 0.976
β = 1
A
100
101
102
103
104
105
106
Pace of life
103104105106107
Population
Residential moves
β = 1.134, R2 = 0.994
Divorces
β = 1.161, R2 = 0.970
β = 1
B
102
103
104
105
106
Composition
103104105106107
Population
C
College graduates
β = 1.109, R2 = 0.994
Creatives
= 1.112, R2 = 0.994
= 1
β
β
Fig. S1. Scaling relations of urban indicators excluding the three largest labor market areas.
(A) In this artificially-shrunk urban system, the scaling parameters for company turnover (blue: β= 1.191
±0.056 [95% confidence interval], R2= 0.929) and collected property tax (red: β= 1.171 ±0.042,R2=
0.976) remain within the range of βw1.15. (B) The same holds for the total numbers of residential moves
(blue: β= 1.134 ±0.024,R2= 0.994) and of divorces (red: β= 1.161 ±0.062,R2= 0.970) as well as (C)
the total numbers of college graduates (blue: β= 1.109 ±0.024,R2= 0.994) and of employees in creative
jobs (red: β= 1.112 ±0.021,R2= 0.994). The colored lines show estimates of βfrom the linearized model
(Eq. 1 in Materials and Methods); M= 72.
Section S2. Outlier analysis of urban scaling parameters
In Fig. S2 we replicate our decomposition of the total scaling relation (Fig. 3) with wage
and employment data from the 382 Metropolitan Statistical Areas (MSAs) of the United
States. Similar to the Swedish case, the scaling relation for total wages (β= 1.110 ±0.022)
is due partly to a higher labor force participation in bigger cities (β= 1.026 ±0.011).
Metropolitan Statistical Areas’ average wages carry the remaining part of the scaling relation
(β= 0.084 ±0.014). Note that further analyses controlling for labor-market productivity
related characteristics require full-population micro-data unavailable for the United States.
109
1010
1011
1012
104105106107108
Population
Total wages, 382 MSAs
β = 1.110, R2 = 0.961
β = 1
A
104
105
106
107
104105106107108
Population
Total employment, 382 MSAs
β = 1.026, R2 = 0.983
β = 1
B
20K
40K
60K
80K
100K
104105106107108
Population
Average wage, 382 MSAs
β = 0.084, R2 = 0.300
β = 0
C
Fig. S2. Decomposition of the total scaling relation for wages across U.S. Metropolitan Statistical
Areas. (A) The total scaling relation for wages, measured in thousands of US$ in 2015, amounts to β= 1.110
±0.022,R2= 0.961. (B) Also, the total number of employees scales superlinearly with β= 1.026 ±0.011,
R2= 0.983. Both colored lines show estimates of βfrom the linearized model (Eq. 1 in Materials and
Methods). (C) With β= 0.084 ±0.014,R2= 0.300, per-capita wage carries the remaining part of the total
scaling relation (β= 1.026 + 0.084 = 1.110). Here, we fit Eq. 2 and the gray line indicates a proportional
per-capita relation (β= 0). Data for 2015 obtained from U.S. Bureau of Economic Analysis (www.bea.gov).
Our main analyses (Figs. 3–5) focus on wage earnings as a local source of income. To isolate
composition effects, we restrict our complete population data to fully-employed Swedish-born
males aged 18–60 who took a compulsory conscription test during 1970–2006 (see below).
Instead of giving a description of the entire Swedish population, we thus give priority to clean
estimates of the scaling parameter unaffected by, for example, variations in female labor force
participation or ethnic discrimination between urban areas of different sizes (see 24 for similar
sample restrictions). In our individual-level analyses we also exclude employees in Gällivare
and Kiruna (mining areas in the far north), as their economies depend almost exclusively on
the extraction of natural resources. In our cross-sectional (2012) and longitudinal analyses
(1993–2012) we scrutinize the same set of 1.29 million individuals nested in 73 labor market
areas.
Section S3. Replication of the scaling relation’s decomposition with U.S. data
Section S4. Wage data and measures of individual productivity
The strong norm of equality that prevails in Sweden places bounds on income differences.
This is most likely the explanation for why β= 1.082 <1.15 for Swedish wages (Fig. 3A).
Payment regulations cap the dispersion of wages between regions and may weaken the su-
perlinearity of total wages across Sweden’s labor market areas. Recall that our aim lies not
in demonstrating βw1.15 for Swedish wages but in exploring how much of βis independent
from direct composition effects and thus consistent with the interconnectivity explanation.
Although we look at a relatively small economy, the interconnectivity explanation is a general
theory that should also hold for Sweden.
In our cross-sectional analysis we partial out composition effects on the scaling of wages,
first by considering the human capital earnings function (34,35), which models individual
log(wage) as the sum of years of education and a quadratic function of years of work experi-
ence. Both education (12.5 years on average, min=9, max=20, sd=2.3) and work experience
(17.1 years on average, min=0, max=22, sd=6.0) are directly observable in the register data.
Second, unlike seminal net-agglomeration studies from regional economics (24,25 ), our data
permit inclusion of a measure of cognitive ability and thus crucially extend the vector of
observed individual characteristics. Third, as an additional feature of urban composition
we include a binary variable measuring each employee’s innovativeness. In the following, we
describe these measures in detail.
We draw on standardized test results of cognitive ability among male conscripts. The
Swedish military enlistment procedure consisted of a series of physical, psychological, and
intellectual tests all men had to take at age 18–19 until its abolition in 2010. The enlistment
procedure included an assessment of cognitive ability similar to the Armed Forces Qualifying
Test (AFQT) used in the United States ( ). There were separate paper and pencil tests
for verbal understanding, technical comprehension, spatial ability, and logic. Each test
consisted of 40 items presented in order of increasing difficulty and speed. With only minor
revisions implemented over the years, this procedure evaluated the same four underlying
abilities throughout the entire period (29). Motivation for participation in military service
was explicitly not a factor for evaluation and avoiding enlistment by obtaining low-ability
scores was not possible. Our data combine the test results with a normally distributed scale
ranging from 1–9, which has been found to be a good measure of general intelligence ( ).
Enlistment became less comprehensive after 2006 and the numbers dropped substantially.
We thus restrict our analyses to men who went through the enlistment procedure between
1970 and 2006, which, for the year 2012, leaves us with a 81.6% coverage of Swedish men
in the relevant age bracket 18–60. To account for test revisions over time, we z-standardize
each year’s scores. This results in a bell-shaped distribution of cognitive ability for the years
1970–2006 with mean 0 and standard deviation 1.
28
30
in the sense of Florida (18 ), relying on the International Classification of Occupations (ISCO-88) codes
provided in ( ) which permit an almost 1:1 mapping to the Swedish Standard Classification of Occupations
(SSYK96) available in our data (3).
Creative core SSYK96
Physicists, chemists, and related professionals 211
Mathematicians, statisticians, and related professionals 212
Computing professionals 213
Architects, engineers, and related professionals 214
Life science professionals 221
Health professionals (except nursing) 222
College, university, higher education teaching professionals 231
Secondary education teaching professionals 232
Primary and preprimary education teaching professionals 233
Special-education teaching professionals 234
Other teaching professionals 235
Archivists, librarians, and related information professionals 243
Social sciences and related professionals 224 + 249
Public service administrative professionals 247
Creative professionals
Legislators, senior officials, and managers 1
Nursing and midwifery professionals 223
Business professionals 241 + 248
Legal professionals 242
Physical and engineering science associate professionals 31
Life science and health associate professionals 32 + 5135
Finance and sales associate professionals 341
Business services agents and trade brokers 342
Administrative associate professionals 343
Social work associate professionals 346
Bohemians
Writers, musicians, creative or performing artists 245
Photographers, image/sound recording equipment operators 3131
Artistic, entertainment, sports associate professionals, journalists 347
Fashion and other models 521
In line with our composition argument, Florida (18 ) stresses the role of highly-skilled
creative workers for urban productivity. Following his classification, we define creative em-
ployees as “people in science and engineering, architecture and design, education, arts, music,
and entertainment whose economic function is to create new ideas, new technology, and new
creative content” as well as those with occupations in “business and finance, law, health
care, and related fields [...] engaging in complex problem solving” (p. 8). We capture these
individuals utilizing the International Classification of Occupations (ISCO-88) codes pro-
vided in (37) which permit an almost 1:1 mapping to the Swedish Standard Classification
of Occupations (SSYK96; 38) available in our data (Table S2). We assign the value 1 to
Table S2. Creative jobs and the corresp onding o ccupational codes. We capture creative employees
37
8
each employee in a creative occupational category (0 for employees in all other occupations).
In our restricted data, 47.1% work in creative jobs. The number of creatives scales with
β= 1.112 ±0.017 across Sweden’s labor market areas (see Fig. 1C; note that Fig. 1 refers to
the full population of Sweden).
Alternately, one may interpret the number of individuals in creative jobs as an approx-
imation of a city’s relative position in an urban system of occupational location (21,32).
Correspondingly, the share of creatives in the full working-age population is larger in Stock-
holm (38.7%) than in the four largest labor markets combined (35.6%) and substantially
with the “theory of central places” (21 ) according to which specialist industries with high
economic returns locate in central places where they can distribute fixed costs over larger
catchment areas.
To arrive at a net-agglomeration effect for Swedish wages (Fig. 3C), we estimate individual-
level log(wage) regressions and include our proxies for individual productivity (see Eq. 3 in
Materials and Methods). Table S3 summarizes our results.
Two-level random-effects regressions
(Eq. 3 in Materials and Methods) with 1.29 million individuals (level 1) nested in 73 labor market areas
(level 2) in 2012. N= labor market population. Cluster-robust standard errors in parentheses. Individuals
working in the mining areas Gällivare and Kiruna are excluded. All estimates are significant at p<0.001.
(1) (2) (3) (4) (5)
Human Cognitive Creative Central Population
capital ability job industries density
log(N).0382 (.004) .0364 (.004) .0283 (.005) .0346 (.004)
×high density .1046 (.011)
×low density .0271 (.005)
Education .0765 (.004) .0644 (.003) .0353 (.003) .0615 (.002) .0336 (.002)
Experience .0340 (.003) .0365 (.003) .0322 (.002) .0364 (.002) .0322 (.002)
Experience2.0004 (.000) .0005 (.000) .0005 (.000) .0005 (.000) .0005 (.000)
Ability .0549 (.005) .0238 (.002) .0489 (.003) .0228 (.002)
Creative job .3320 (.023) .3241 (.016)
Central industry .1222 (.033)
R2.086 .091 .127 .095 .130
The control variables carry the expected weights, with education, experience, ability,
and creative job characteristics correlating positively with log(wage). Further, in line with
the expectation of the human capital earnings function, the negative sign of the quadratic
Section S5. Full tabulation of cross-sectional results
Table S3. Composition effects on the scaling of wage income.
term of experience implies a bound on the returns to professional experience. All estimates
are significant at p<0.001. The step-wise inclusion of the controls increases the explained
variance of log(wage) from 8.6 (model 1) to 12.7% (model 3), indicating that each control adds
to the prediction of individual wage notwithstanding their collinearity: The linear correlation
between education and cognitive ability is ρ= 0.496 and each variable correlates with the
binary indicator of creative job characteristics at ρ= 0.481 and ρ= 0.396, respectively
(p<0.001 for all pairwise correlations). Most importantly, the inclusion of observable worker
characteristics associated with individual productivity reduces the elasticity between wage
and city size to 0.0283 (model 3). This net-agglomeration effect is well in line with studies
from regional economics controlling for characteristics of local industries and workforces
(24,25,36) and matches—based on a continuous indicator—the per-capita increase to size
(β= 0.028, yet insignificant) reported for U.S. patenting activity (47).
Additional model specifications substantiate our results: In model 4, we demonstrate
that substituting our measure of creative job characteristics with a binary variable for central
industries—1 for employees in finance, consulting, computation and telecommunication, and
media (we follow the classification in [32])—adds little to the prediction of log(wage) (+0.4%
variance explained compared to +3.6% for the creatives dummy). When further controlling
for a creative job title (not tabulated) employment in a central industry shows no significant
correlation with log(wage). Hence, the scale effects of central industries appear of lesser
importance than individual-level measures of occupational characteristics. Model 5, finally,
demonstrates it is not population size per se but population density that drives agglomer-
ation effects. Elasticities are much stronger for employees in dense (β= 0.1046 ±0.0207)
than in sparse (β= 0.0271 ±0.0010) environments. This finding suggests that density has
important effects on individual productivity and corroborates an important assumption of
urban-scaling research. This result is based on analyses in which we constructed square
catchment areas 500 meters on a side (0.25km2) surrounding each individual’s workplace
and counted all other employees therein. We then split the count at the 75% percentile
(4,031 employees) and assigned the focal employee to either a low-density (4,031 proxi-
mate employees) or a high-density environment (>4,031 proximate employees). We sized
these catchment areas based on the prior finding that networking effects attenuate quickly
and that inadequately disaggregated data may underestimate location benefits (45,46). We
follow a similar modeling approach (log(N)×factorial dummy) to estimate urban scaling’s
social gradients (Fig. 5), splitting the study population in three groups consisting of those
with relatively little (<25th percentile), intermediate (25–75th percentile), or high (>75th
percentile) education or ability, respectively.
Our estimation of the urban wage premium rests on the wage trajectories of individuals
who—between 1993 and 2012—left their native labor market areas to work in relatively
larger labor markets. We scrutinize the same set of 1.29 million individuals as in the cross-
sectional analysis but restrict the estimation of the urban wage premium to individuals
who moved only once and had been fully-employed for at least one year both prior and
following migration. On average, we observe individual wage trajectories for 14 years, but
our unbalanced panel data include individuals with shorter and longer employment histories.
areas to one of the four largest. Movers’ relative wage change against the counterfactual wage they
would have received had they stayed in their native labor markets (Eq. 4 in Materials and Methods). Cluster-
robust standard errors in parentheses. Individuals working in the mining areas Gällivare and Kiruna are
excluded. All estimates are significant at p<0.001.
(1) (2) (3) (4)
Stockholm Malmö Gothenburg Linköping
(2.51 million) (1.09 million) (1.08 million) (0.26 million)
–6 years .0109 (.009) .0118 (.015) .0022 (.010) .0133 (.020)
–5 years .0211 (.010) .0227 (.016) .0084 (.011) .0178 (.023)
–4 years .0216 (.010) .0310 (.016) .0067 (.012) .0111 (.025)
–3 years .0069 (.010) .0079 (.017) .0004 (.012) .0082 (.024)
–2 years .0184 (.011) .0005 (.017) .0363 (.012) .0384 (.024)
–1 year .0714 (.011) .0725 (.018) .0978 (.013) .1055 (.025)
Move .1676 (.011) .0437 (.018) .0650 (.012) .0428 (.024)
+1 year .2981 (.011) .1549 (.017) .1428 (.012) .1160 (.024)
+2 years .3119 (.011) .1628 (.018) .1630 (.012) .1047 (.025)
+3 years .3366 (.011) .1720 (.018) .1608 (.012) .1271 (.025)
+4 years .3466 (.011) .1719 (.018) .1671 (.012) .1239 (.025)
+5 years .3491 (.011) .1910 (.018) .1706 (.013) .1266 (.026)
+6 years .3605 (.011) .1978 (.018) .1701 (.013) .1184 (.027)
+7 years .3622 (.011) .2065 (.018) .1680 (.013) .1154 (.028)
+8 years .3607 (.011) .2201 (.019) .1641 (.013) .1309 (.027)
+9 years .3658 (.011) .2075 (.019) .1585 (.013) .1176 (.029)
+10 years .3715 (.012) .2261 (.020) .1582 (.014) .1134 (.028)
Education .2549 (.002) .2569 (.002) .2571 (.002) .2579 (.002)
Experience .0662 (.000) .0660 (.000) .0659 (.000) .0658 (.000)
Experience2.0019 (.000) .0019 (.000) .0019 (.000) .0019 (.000)
Fully-employed .6886 (.002) .6796 (.002) .6818 (.002) .6774 (.002)
Regional GDP .0022 (.000) .0022 (.000) .0022 (.000) .0022 (.000)
R2within .347 .339 .342 .339
Table S4 summarizes the results of our within-person distributed fixed-effects regressions.
We display the “distributed effects” (3 , ) on log(wage) following a move from one of Swe-
den’s smaller labor markets to one of the four largest (see Eq. 4 in Materials and Methods).
Section S . Full tabulation of
Table S4. Urban wage premium following a move from one of Sweden’s smaller labor market
6 the urban wage premium
9 40
Both the immediate (γt=1) and the long-term urban wage premium (γt=10) relate positively
to the target area’s population size and are most pronounced for those settling into Stock-
holm’s labor market (+29.8% ±2.1at t= 1 and +37.2% ±2.3at t= 10). The control
variables show the expected average effects: An additional year of education increases wages
by approximately 26%, each year of work experience raises wages by almost 7% (the effect
plateaus, as indicated by the negative sign of experience2), individuals earn around 32% less
in years they are not fully-employed, and GDP growth translates into higher wages. Inter-
estingly, many movers experience a slight drop in relative wages shortly before migration, a
common finding in the literature (24 ) which may be among the reasons movers choose to
leave.
To approximate the interconnectivity effect on individual wages, we are interested in the
urban wage premium conditional on population differences between native and target labor
market areas. We focus on the long-term urban wage premium (γt=10), which includes post-
migration earning paths, capturing not only immediate wage benefits of big-city employment
but also the accumulation of learning effects in high-density urban environments over time
(24 ). In Sweden, moving from any labor market area to a relatively larger area results in
(72 ×73)/2 = 2,628 possible combinations of origin and target labor market areas (again,
excluding the two mining areas). For the scaling analysis displayed in Fig. 4B—connecting
γt=10 to log(population difference)—we estimated Eq. 4 (see Materials and Methods) for the
100 labor-market combinations with 200 movers in 1993–2012. This yields, for each combi-
nation, a separate mean urban wage premium based on respective movers’ wage trajectories.
0 .1 .2 .3 .4
Density
102103104105106
Population difference
A
Urban wage premium
-.3 -.2 -.1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
103104105106107
Population difference
N movers >=100
β = 0.0499, R2 = 0.273
N movers >=50
β = 0.0486, R2 = 0.186
B
-.2 -.1 0 .1 .2 .3 .4 .5 .6
Urban wage premium
.25 .5 1 2 4 8 16 32 64
Density difference
N movers >=200
β = 0.0582, R2 = 0.241
β= 0
C
Fig. S3. Complementary analyses of the urban wage premium. (A) The distribution of population
differences between movers’ native and target labor market areas. The hump to the right indicates moves
from small places into the three largest labor markets Stockholm, Malmö, and Gothenburg. (B) Reducing the
necessary number of movers between labor-market combinations leads to parameter estimates very similar
to that reported in Fig. 4B: For 165 combinations (blue dots) with at least 100 movers β= 0.050 ±0.013,
R2= 0.273 (blue line); for 260 combinations (blue and red dots) with at least 50 movers β= 0.049 ±0.012,
R2= 0.186 (red line). (C) Replacing differences in population size with differences in population density
reveals stronger superlinearity as compared to Fig. 4B. The urban wage premium now scales at β= 0.058
±0.023,R2= 0.241.
To demonstrate the robustness of the reported scaling parameter (β= 0.050 ±0.014),
we perform a similar analysis for origin-and-target combinations sharing at least 50 or
100 movers in 1993–2012 (Fig.S3). The estimates of βare equal to 0.049 ±0.012 and
0.050 ±0.013, respectively. Fig. S3C, again, demonstrates that social density rather than
population size drives agglomeration effects: Mean urban wage premiums plotted against
the difference in population density between native and target labor market areas (measured
as the difference in the number of inhabitants per km2; mean=5.7, min=–40, max=58)
reveals stronger superlinearity (β= 0.058 ±0.023) as compared to the baseline in Fig. 4B.

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