Evaluation of Haitian
with the Use of Principal Components
Ronald WV Ward and Ahmed Zahalka *
Considerable experimental agricultural development
efforts have been undertaken in Haiti (Zurekas, pp. 80-120).
Many of the Haitian programs have been direc-ted toward
development through intensive extension efforts with the
primary purpose to provide local producers with improved
production and management techniques. Frequently such
experiments are localized and designed to emphasize the
development methods while giving less consideration to
evaluating the overall project performance. The Haitian Bas
Boen region development project is a case in point (Prires,
In this paper the Eas Doen project is considered with
the primary objective to show the relationship between
production responses to intensive agricultural development
programs. A statistical technique using principal
components is used to link production responses to those
inputs changed through the extension efforts.
Ronald W. Ward is a professor in the Food and Resource
Economics Department, University of Florida. Mr. Ahmed
Zahalka is a market development consultant in Barbados.
The authors acknowledge the comments from the journal
Florida Agricultural Experimen-t Station Journal Series
-l l. r ... .
Bas Soen Project
The Bas Boen project began in 1969 with an agreement
signed by the Organization of American States, Israel and
Haiti (La Gra, p. 4). It was a pilot project with the major
objective to enhance rural farm incomes through improved
production and management practices. Between 1969 and 1973
experiments in collective farming using a variety of
nontraditional commodities were considered with little
apparent success. Because of crop failures and changes in
government policies toward exports,- the project was
redirected back to the production of traditional crops such
as corn, sorghum, beans, cane, and tobacco.
The role of agriculture in Haiti's economy has received
increasing attention in recent years, reflecting a growing
awareness that the country's economic problems cannot be
solved without a solution to the problem of agricultural
stagnation. Zurekas advocated the necessity of a farm-level
study in Haiti where the study would help determine the
productivity increases obtainable from purchased inputs and
new production practices (p. 342). Gislason noted the
important potential impact the Bas Boen project could have
on productivity by training small producers to adopt new
technologies to small plots of land (p. 38). Prires
describes the Bas Boen project's gradual approach in
achieving the goal of improving the welfare of the farmers
through intensive extension efforts (p. 76). Finally, La
Gra documented the changes at Bas Boen that were felt to be
a result of the project between 1969 and 1972. Each of
these studies emphasis the need to have better empirical
analysis of the work completed
In 1.974 an intensive extension system using para-
extension personnel was integrated into the project.
Because of the changes between 1969 to 1973, the early
stages of the development efforts have little relevance to
the subsequent production gains except to redirect the
overall emphasis. Hence, the analytical focus of this
research is for the periods 1974-78 (Gislason, p. 10).
The overall project consists of seven villages,
including the Bas Boen area which received the initial
intensive extension assistance. The educational levels,
incomes, family characteristics, and cultural and religious
practices differ little among the local farmers. Hence, for
statistical purposes the population studied can be
considered homogeneous. A test later in the analysis will
provide support for the homogeneity assumption.
While a total of 597 producers were in some way
exposed to the extension input over the four years, data
were collected on.a continuous basis for a random sample of
30 producers. The professional extension staff recorded
production data from the outset of the project. Hence for
those randomly selected producers monitored, the information
recorded should be highly reliable since it was coded by
trained extension personnel. The analysis is limited to the
small number of producers where the'extension programs were
overseen on a continuous bases (Zahalka, pp. 53-56).
Information on a wide range of crops was documented;
however, cane, corn, beans, sorghum and tobacco accounted
for over 90 percent of the acreage and resulting'income.
The subsequent analysis is limited to these five crops.
The analysis includes data pooled over cross sections
of producers and time series over production periods. The
producers differed primarily by the size of their operations
and were very similar with respect to demographic
characteristics. If a data pooling problem exists it would
most probably be related to size differences. Hence, a test
for pooling bias will be made later in the analysis by
defining the cross sections by size of the land farmed.
Table 1 provides a description of the data collected
during the project life. Production yields (YD) are
expressed in output per hectare for each of the five crops.
Guidance in the use of each of the variables in Table 1 was
provided on a continuous basis by the resident extension
specialist. A large part of the changes in the use of these
input variables can be attributed to the extension efforts.
This is especially true when compared to earlier uses of
these inputs. The first six input variables (SD through CL)
represent physical inputs where continuous levels can be
applied. Whereas, the remaining variables are discrete in
that they either were or were not used (eg., they can be
expressed as dummy variables). Variables (ML, CL, VY, IN,
SR, CL, MD) were measured as discrete management practice
Table 1. List of variables and unit of measurement.
Variable Symbol Unit of Measurement
Yield YD Yields in kilograms per hectare
Seeds SD Founds of seeds per hectare
Fertilizers FZ Pounds of basic fertilizer
Nitrogen NG Pounds of urea 46% per hectare
Water WR Hours of irrigation per hectare
Labor LR Day-work of manpower per hectare
Cleaning CL Times of cleaning with units of
1, 2, 3,and 4 times per crop season
Multiple ML Number of crops planted in the
Cropping same field per year
Rotation RN Crop rotation plan (code with 1=
recommended rotation, and 0=
Variety VY Variety of seeds (code with 1=
hybrid seeds, and O=Iocal seeds)
Insecticide IN Code with 1=insecticide applies
and 0=no application
Supervision SR Code with l=under supervision
and 0=no supervision
Method MD Method of planting (code with
1=planted on rows and 0=planted
in square or pockets)
Entries below the dash line are discrete type management
type inputs in contrast to the varying levels of the other
The variables in Table 1 include those major inputs
that should theoretically influence the yields for each of
the five commodities. Furthermore, complementarity probably
exists among some of the inputs. For example, the gains
from cleaning probably depend on irrigation efforts,
fertilizer use, etc. Such complementarity points to the use
of a multiplicative type production function. If X. is
defined to be those continuous input variables and X. the
discrete inputs, then the multiplicative function in
equation (1) can be adapted to the current problem.
(1) B. (Bo + j XK. + e)
YD = IX. exp J J
Each input should have a positive effect on yields such that
3YD / a X. = B.YDIX. > 0 AND 2 YD/~X. 9Xk B. B YD/X. X > 0
I I I I k 1 k I k
where k j j. Likewise, for the discrete variables, the
yield adjustment from some level YD due to using one or
more of the inputs follows as in (2):
E am m
(2) YDI = YD0 (exp 1) > 0
where m is a subset of the j discrete variables that have
been changed. The gains in both cases depend on the levels
of the other inputs.
The time and cross sectional notational has not been
included in (2). Using the variables discussed earlier for
this model requires the pooling of cross sectional and time
series data. A explicit test for the appropriateness of
pooling the data will be addressed in the empirical
analysis. Clearly, equation (1) can be transformed into a
linear estimable function as shown in (3).
(3) log(YD) = Bi log(X.) + ABjXj + Bg + e.
Define the vector Y as the transformed yields in
equation (3) and X as a matrix of the transformed inputs,
then yields are related to the inputs where
(4) Y = X B + E.
Clearly if the vector B is known, the effect of each input
on production can be measured.
Development efforts in the Bas Boen project were
designed to influence the values of X. If the extension
efforts were completely successful in stimulating the
sampled producers to respond to the recommendations, then it
is likely that the levels of various inputs would be highly
correlated. Estimation problems associated with
multicollinearity are well known and principal components
procedures provide a useful way for dealing with the data
Theoretically there exists some vector of weights
applied to the exogenous variables such that
(5) (X'X hI)W = 0, and W'W = I.
Note that the latter product matrix assumes the vectors of W
to be orthogonal and h is a vector of eigenvalues and W is
a matrix of weights or eigenvectors. In then follows that
W'X'XW = hi or P'P=hl where P = XW. P represents the
principal components of X and are orthogonal since P'P is a
diagonal matrix. Hence, there exist a matrix W such that X
can be transformed into a set of orthogonal vectors. The
vector of the first principal component is defined as F1 =
XW1. The variability among the independent variables is
equal to tr(X'X). Furthermore, tr(P'P) = tr(W'X'XW)
tr(X'XW'W) = tr(X'X). That is, the variance of the input
variables can be explained by a set of orthogonal vectors P.
For the present problem, the values of h and W are of
Estimates of Principal Components
Equation (3) differs slightly with each of the five
crops since some of the inputs were not present or did not
change for a particular crop. Hence, selected B's are
restricted to zero for different crops as will be shown
subsequently. For the variables included in each crop, the
correlations ranged from near zero up to .97.
Given the correlations and the results from equation
For a detailed discussion of principal components see
Dhrymes, pp.53-65. The above discussion of the trace of X'X
assumes that the vectors of X have been first normalized.
Subsequent regression estimates wil', however, be for the
original values of X.
(4), both h and W are shown in Tables 2 and 3. The
eigenvalues for the principal component of each crop are
shown in Table 2. The sum of the eigenvalues equals the
variance of the normalized X and the ratio of each
eigenvalue to this total shows the contribution of each
principal component in representing the variability of the
initial input variables (X). For example, over 75 percent
of the variability of corn inputs can be explained with the
first three principal components (see the % columns).
Similarly over 90 percent of the cane-- input variability is
explained with the first three components. Hence, for most
of the commodities it is possible to estimate the
relationships between the yields and inputs by using a
limited number of orthogonal vectors to represent the input
The eigenvectors W give a weighted contributed of each
input variable in calculating the principal components,
recalling that P=XW. These weights represent loading factors
useful for showing the importance of each input to .the
principal components. The weights of the first component
are usually easy to interpret, while values for the higher
components are more difficult to explain.
Consider in Table 3, the weights for the first
principal component for. the commodities point to the
importance of each input. For cane, WR, LR, RN, and SR are
The correlations are not reported in this paper but are
available upon written request to the authors.
Table 2. Eigenvalues (EV) and cumulative percentage of variance.
PC I Corn 1 Sorghum Beans I Cane 1 Tobacco
SEV % I EV % EV % EV % EV %
----------+----+------4----- -----+---------- ---+--------------
1 5.83 .53 7.43 .68 5.20 .58 4.20 .70 2.32 .39
2 1.46 .66 1.10 .78 .92 .68 .88 .85 1.73 .68
3 .93 .75 .80 .85 .82 .77 .40 .91 .90 .83
4 .73 .82 .53 .90 .80 .86 .36 .97 .72 .95
5 .51 .87 .37 .93 .50 .92 .20 1.00 .33 1.00
6 .45 .91 .31 .96 .40 .96
7 .36 .94 .24 .98 .21 .99
8 .29 .96 .13 .99 .13 1.00
9 .24 .98 .09 1.00
10 .18 .99
11 .02 1.00
First 3 PC for the five basic crops.
Crop Var Principal 1 Principal 2 Principal 3
Corn FZ 0.28950
Beans SD 0.40305 -0.18764
WR 0.33562 0.06775
LR 0.24755 -0.00865
ML 0.30149 0.37215
RN 0.37777 -0.44569
IN 0.22478 0.42501
SR 0.38931 -0.39782
CL 0.39444 0.07228
MD 0.26896 0.52808
Tobacco FZ 0.36294 0.44544
NG 0.57102 -0.34881
WR 0.58554 -0.31123
LR 0.24094 0.42583
ML 0.33911 0.04305
CL 0.16218 b.63235
weighted almost equally while ML and CL are slightly less.
Each input for corn is weighted very close except for
insecticides, that is they have similar loading factors for
calculating the first principal component. The remaining
weights for the other commodities lead to a similar
observation that the inputs are of relative close importance
with only a few exceptions. The weight of nitrogen use for
sorghum was low relative to the other factors. Possibly
part of this low value results because some of the nitrogen
inputs were included in FZ. Data on -specific FZ analyses
were not available.
The second principal component and the resulting
weights (col. 2 of Table 3) are used to show the importance
of the inputs to explaining the residual variability in X
not explained by the first component. If the first
principal component explains a large portion of the
variability of X, then the interpretation of the remaining
components become much more tentative. What is generally
seen in both the second and third components is that only a
few of the inputs are of major importance and that no
consistent weighting is apparent across the commodities.
Given the different biological requirements of these
commodities, the resulting differences in weights beyond the
first principal component would be expected.
The most important aspect of the weights in Table 3 is
that they are used to calculate the principal components.
The parameters of (4) can then be estimated using a limited
set of principal components, say up to the first r
(6) Y = Pr A + E
=X Wr A + E
where B = WrA, Wr is (k x r), A is (r x 1), and Pr =X Wr,
assuming there are k variables and r components (i.e., r <=
k). Recall that the vectors of P are orthogonal, hence A
can be estimated in (6). Given A and W, then B of (4)
The final regression results using the above procedures
are reported in Table 4 for each crop. The parameters
correspond to the multiplicative function set forth in
equation (1). The values were calculated by multiplying
the weights of W in Table 3 by the principal component
parameters (A). The A parameters are not shown since their
values alone are of limited interest. Standard errors are
reported in parenthesis and the R2 values apply to YD
relative to YD. The signs of all parameters but one are
correct and the significance levels are acceptable. The
impact of nitrogen on sorghum is negative but statistically
insignificant. Where parameter values are missing, that
variable did not enter a particular crop model.
For those continuous variables (SD, FZ, NG, WR, LR, CL)
the parameters can be readily interpreted as the percentage
yield adjustment resulting from a percentage increase in
each particular input. The actual effect of each input
differs considerably across commodities as will be shown
Table 4. Estimated coefficients using principal components.
Corn Sorghum Beans Cane Tobacco
cept 2.486 3.101 1.954 7.921 -8.223
FZ .0127 .0093 .3534
(.0013) (.0004) (.1776)
NG .0158 -.0158 .0-066
(.0008) (.0125) (.0160)
WR .3771 .0199 .2804 .0123 .2691
(.0263) (.0000) (.0208) (.0000) (.3750)
LR .7140 .8344 .2475 .5599 2.0732
(.0618) (.2895) (.0282) (.0000) (.5712)
ML .2344 .1840 .2071 .0894 .4310
(.0145) (.0085) (.0264) (.0634) (.2718)
RN .1662 .1444 .0756 .0535
(.0148) (.0055) (.0177) (.0064)
VY .1287 .1512
IN .1192 .1512 .0995
(.0460) (.0070) (.0473)
SR .1680 .1509 .0782 .1141
(.0153) (.0074) (.0153) (.0128)
CL .1342 .1446 .1334 .2453 .5868
(.0198) (.0162) (.0067) (.1474) (.1771)
MD .1376 .1353 .1260
(.0115) (.0040) (.0200)
RE .8592 .9140 .7185 .6958 .3882
# PC 3 3 3 3 3
SSE 2.5114 1.1002 1.9162 .3960 2.6202
MSE .0230 .0154 .0183 .0073 .1007
# OBS 113 75 109 58 30
G TEST .0291 5.6709 20.9444 8.7470 1.2063
F TEST .2427 .3935 .6406 .0848 .3283
later. The explanatory power of the estimates were
reasonable except for the tobacco equation where the R =
.38. The lower value is of importance to tobacco producers
in that considerable more variability in yields could be
expected even with well planned use of those inputs included
in the tobacco equation.
Three principal components (i.e., r=3) were used in
each equation. Estimates with more principal components
were nearly identical to those reported in Table 4.
The potential problem from pooling the producers over
the production years was recognized earlier. If there are
differences among the cross sections, the error sums of
squares should differ among the cross sections. Breusch and
Pagan provide one test of this difference where their
weights of the errors (see E in equation (4)) follows a Chi-
Square distribution. The G-test values shown in Table 4 are
the weighted errors over cross sections and without
exception they are less than the table Chi-Square values,
assuming a .05 significance level. One further test of the
homogeneity property is to adjust the equations in Table 4
by using a covariance model accounting for both cross
sectional and time series effects. Pindyck and Rubinfeld
(p.252) outline a well known F test procedure comparing the
difference in the error sums of squares from the covariance
and fixed parameters models. If the F value is not
significant, then the error structures are statistically no
different with the adjustments for either cross sections and
time series. These F values shown at the bottom of Table 4
are statistically insignificant for each commodity. With
these results using size of the farm as the pooling
criteria, the homogeneity assumption cannot be rejected and
pooling presents no particular estimation problem. Given
these parameter values, the problem of evaluating the
success of the Bas Boen project can be addressed.
Discrete Variable Responses
A number of the input variables were discrete as noted
in Table 1. If YDo is defined as the level of yields
without some particular discrete input and YD1 as the level
with that input, then the percentage adjustment by adding
that input is easily shown (Halvorsen and Palmquist, p.
(7) ((YD YD )/YD ) = exp 1
These percentage adjustments are given in Table 5 for the
four crops where the discrete variables were present. Both
corn and sorghum included all five discrete inputs. The
last column in Table 5 shows the total gain expected if all
discrete variables were added. For corn and sorghum, nearly
a 78 percent increase in yields would be expected over the
level YD while the gain would be considerably less for
beans and cane. The importance of crop rotation (RN) and
supervision (SR) by the extension specialist is seen where a
15-18 percent increase in yields would be projected with
each of these inputs. Gains resulting from planting in rows
Table 5. Response of crop yields to the discrete inputs.
RN % VY % IN % SR % MD % TOTAL %
Corn 18.08 13.74 12.66 18.30 14.75 77.53
Sorghum 15.54 16.30 16.29 16.28 13.35 78.16
Beans 7.86 10.46 8.13 13.43 39.88
Cane 5.50 12.09 17.59
The variables are: RN = rotation, VY = variety, IN = insecticide,
SR = supervision, and MD = method of planting.
See Table 1 for a complete definition of variables.
versus squares or pockets are nearly equal for the three
crops where a change in the planting method (MD) occurred.
Overall what is evidence in Table 5 is the significant
productivity improvements that can be realized with those
inputs characterized with the discrete variables. The
expected gains among the four major crops provide guidelines
for redirecting the extension emphasis.
Adjustments Among the Continuous Inputs
The effects among the continuous input variables
differed considerably across the crops. In order to
illustrate these responses, the yields are again indexed
where YD is the predicted yields over values of the Xi and
YD0 is the yield with the lowest level of that input, say Xi
(8) IN = YD /YD0
= ( X. I X.(low) )
thus showing the predicted percentage gain relative to the
lowest predicted yield for that input. The following
figures illustrate the index over selected continuous
variable initially identified in Table 1.
Figure 1 shows the indexed values as irrigation (WR) is
measured from a low of 10 hours per hectare to a high of 25
hours. Corn, beans and tobacco show large yield
improvements over this range of irrigation. Corn production
responded with nearly a 40 percent increase while beans and
tobacco yields increased around 25 percent. Both sorghum
10 12 14 16 18 20 22 2
WRTER HOURS PER HECTARE
FIGURE 1. INDEX OF PRODUCTION RESPONSE
TO IRRIGATION USRGE (WR).
and cane were primarily rain-fed crops and hence did not
show the same levels of response to irrigation.
Yield changes in response to more labor input are
recorded in Figure 2. Tobacco showed the greatest gain
since it is a labor intensive crop. Output increased 120
percent over the data range considered. The positive
response among the other crop remained considerably below
that of tobacco.
Indexed production gains for both multiple cropping and
cleaning are shown in Figures 3 and 4. Multiple cropping
represented the number of crops grown on the same land
within a season. A positive response was expected since
land fertility and overall management skills are likely to
improve through the multiple cropping practices. The
positive adjustments to both cleaning and multiple cropping
followed similar relative patterns. In each of these
figures, the index, represents the expected gain from changes
in one or more inputs. The index should not, however, be
interpreted as a prediction of yields since in each figure
all variables are held fixed except for the one being
analyzed. Rather it is an index of gains that can be
expected with adjustments in one particular input.
Finally, responses to fertilizer and nitrogen are not
shown since tobacco was the only crop showing large
production gains. The levels of application were generally
low for both corn and sorghum and this possibly attributed
to low but significant yield responses reported in Table 4.
1. 0 4
I1.0 ..... l" ..... 'I '''" '' I"......I" '...... ....... ''' '' I
80 85 90 95 100 105 i10 115 120
LRBOR DOTS PER HECTFRE
FIGURE 2. INDEX OF PRODUCTION PD-JUSTMENTS
TO LRBOR INTENSITY (LR: .
CROPS PER FIELD
FIGURE 3. INDEX OF PRODUCTION ADJUSTMENTS
TO MULTIPLE CROPPING PRACTICES (ML3 .
CLERNINGS PER SEASON
FIGURE 4. INDEX OF PRODUCTION ADJUSTMENTS
TO FIELD CLEANING PRACTICES (CL .
Predicted Production Gains
The prior results established a strong analytical
production relationship with inputs, yet it the actual gains
realized over the four years of the Bas Boen project were
not shown. While actual yields are known, it is necessary
to calculate the predicted yields in order to show the
effects from those input variables most directly influenced
by the intensive extension efforts. As pointed out earlier,
the input variables were of two types: physical inputs (SD,
FZ, NG, WR, LR) and general management practice variables
(CL, ML, RN, VY, SR, MD). Both variables clearly require
management decisions. The decision as to how much of the
physical inputs to use must be made. Second, the use of
different production practices must be considered. The
project goal was to provide guidelines for influencing both
types of decisions. The specified model (eq. (1))
facilitates separating the effects of these two variable
types given the above distinction.
To calculate the expected gains two indices are
developed. Define YD1 now to be the predicted yield based
on the average values of all input for each of the four
years. The yield YD2 represents the predicted production
with the annual average level of all management practice
variables while holding all other inputs at the 1974 level.
Finally, YD0 is the predicted value for 1974 using average
input levels for that year. Then:
(8) IT = YDI /YD0,
and (9) IL = YD2/YD,.
Index IT shows the yield gains relative to the 1974 initial
period of the experiment. Whereas, IL shows the gains
predicted given changes only in the management practice
variables. This index remains the same if it is calculated
relative to the base period of 1974 as shown in equation (9)
or it is calculated relative to what the difference would be
each year if management practices where added relative to
that used in 1974 letting the other inputs change. That is,
YD3 is the predicted yield holding all-management practices
at the 1974 level, then YD1 / YD3 is equivalent to YD2 /
These indices are estimated by crop in Table 6.
Estimated corn yields are shown to increase by nearly 170
percent from the 1974 level. To the extent that the
increase use of the inputs resulted from the extension
efforts, then this index provides strong evidence of the
success of the' efforts. The effects of changing only the
management practice variables while holding the other
variables fixed are also shown in Table 6. By 1978
approximately 60 percent of the corn production gains were
from the management practice variables. Between 1974 and
1975 the management variables were the only inputs changed
for sorghum. By 1978 estimated sorghum gains exceeded 200
percent and the management practice variables accounted for
nearly 80 percent of this gain. Production gains for beans
showed similar improvements resulting from increases in both
Table 6. Estimated yield responses over time.
Years Corn : Sorghum I Beans I Cane I Tobacco
IT IL I IT IL I IT IL : IT IL 1 IT IL
1974 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1975 2.017 1.647 1.185 1.185 1.551 1.327 1.024 1.024 1.346 1.026
1976 2.428 1.852 2.602 2.340 1.809 1.560 1.044 1.044 1.640 1.129
1977 2.689 2.001 3.035 2.570 1.989 1.645 1.394 1.214 1.569 1.151
See equations (8) and (9) for definitions of IT and IL.
The cane crop was cultivated under traditional farming
practices without significant intervention from the project
management until 1977. The response in productivity
following 1976 is readily seen where a 40 percent gain over
the base period is observed. Again a large share of the
increase was due to improved management practices.
Finally, tobacco required considerable physical inputs
where FZ, NG, WR, and LR were changed. Hence, most of the
predicted gains are attributable to these inputs.
The analytical model set forth provides a direct
measure of the productivity gains that were realized in Das
Boen region of Haiti. Using principal component procedures,
both the effects for changing management practices and
applications of physical inputs were measured. In most
crops, over 60 percent of the productivity gains are related
to improved management practices. Such results are of
paramount importance in that it points to the potential
gains that can be achieved through extension guidance.
Furthermore, the model clearly shows the strong
complementarity among the inputs and the overall gains
achieveable through coordinated management of all inputs.
These results were based on a sample of farmers within
a small study area. The question of the applicability of
the empirical estimates to a broader base is logically
raised. Given the homogeneous nature of the producers and
the similarity of resource distribution throughout the
region, the results should have useful applications to other
agricultural efforts in the country. It is ,however, again
emphasized that the estimates are based on a small subset of
farmers within the region. Clearly, additional empirical
research is needed on a broader scale. Also, follow up
efforts are needed to judge the continued use of the
production technology in subsequent years after the project
The experimental extension program-is one of a number of
development plans designed to assist the LDC's. The results
of this analysis do not provide data for judging the
relative merits of alternative development methods. Rather,
they illustrate the gains that can be realized when both
capital investments are coordinated with direct personalized
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Gislason, Conrad. The Bas Doen Project--The Lessons
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