Sample 60690: Computing Marginal Effects for Discrete Dependent Variable Models

Overview

Marginal effects measure the expected instantaneous change in the dependent variable as a function of a change in a certain explanatory variable while keeping all the other covariates constant. The marginal effect measurement is required to interpret the effect of the regressors on the dependent variable. This example illustrates the calculation of marginal effects by using the QLIM procedure in binary choice models and censored models.

Binary Choice Model

The first data are the binary choice (0–1) data set used by Spector and Mazzeo (1980) to study the effectiveness of a new method in teaching Economics. The data are read by the following DATA step statements.

   data greenedata;
   input gpa 1-4 tuce 6-7 psi  grade;
   datalines;
   2.66 20	0 0
   2.89 22	0 0

   ... more lines ...

   3.1  21 1 0
   2.39 19 1 1
   ;
   run;

The dependent variable $\text{[math]}$ is modeled as follows:

$y= E(y|\mb {x}) + \epsilon$

where $\text{[math]}$ is the conditional mean function, $\text{[math]}$ is the vector of explanatory variables, and $\text{[math]}$ is the error term. The conditional mean function is given by

$E(y|{\mb {x}})= F({\bbeta }’\mb {x})$

where $\text{[math]}$ denotes a cumulative distribution function and $\text{[math]}$ denotes the parameters. Therefore,

$\mr {Pr}(y=1)= F({\bbeta }’\mb {x})$

Marginal effect is a measure of the instantaneous effect that a change in a particular explanatory variable has on the predicted probability of $\text{[math]}$ , when the other covariates are kept fixed. They are obtained by computing the derivative of the conditional mean function with respect to $\text{[math]}$ given by

	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

where $\text{[math]}$ is the density function that corresponds to the cumulative function $\text{[math]}$ . The marginal effects are nonlinear functions of the parameter estimates and levels of the explanatory variables. Hence, they generally cannot be inferred directly from parameter estimates. Marginal effects for distributions such as probit and logit can be computed with PROC QLIM by using the MARGINAL option in the OUTPUT statement. The following MODEL statement fits the model equation to the endogenous variable GRADE and the covariates GPA, TUCE, and PSI. Further, you can specify the discrete nature of the endogenous variable by using the DISCRETE option. The D=PROBIT option in the MODEL statement enables you to specify the probit distribution. In the OUTPUT statement, use the OUT = option coupled with the MARGINAL option to obtain the marginal effects in the data set.

   proc qlim data=greenedata;
      model grade = gpa tuce psi / discrete(d=probit);
      output out=outme marginal;
   run;
   quit;

The following output in Figure 2.1 displays the probit model fit statistics. Figure 2.1 Parameter Estimates

The QLIM Procedure

Parameter Estimates
Parameter	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|
Intercept	1	-7.452320	2.542536	-2.93	0.0034
gpa	1	1.625810	0.693869	2.34	0.0191
tuce	1	0.051729	0.083891	0.62	0.5375
psi	1	1.426332	0.595036	2.40	0.0165

The MARGINAL option in PROC QLIM evaluates marginal effects for each observation. In the output data set, OUTME, 'Meff_P2_covariate' and 'Meff_P1_covariate' refer to the marginal effect of 'covariate' on the probability of GRADE=1 and on the probability of GRADE=0, respectively. Hence, 'Meff_P2_gpa' is the marginal effect of GPA on the probability of GRADE=1.

To evaluate the "average" or "overall" marginal effect, two approaches are frequently used. One approach is to compute the marginal effect at the sample means of the data. The other approach is to compute marginal effect at each observation and then to calculate the sample average of individual marginal effects to obtain the overall marginal effect. For large sample sizes, both the approaches yield similar results. However for smaller samples, averaging the individual marginal effects is preferred (Greene 1997, p. 876). This example uses PROC QLIM to compute the overall marginal effect by these two approaches. PROC QLIM outputs the marginal effects computed at each observation in the data set. Hence, in order to obtain overall marginal effect, you can use PROC MEANS to obtain the sample average of individual marginal effects:

   proc means data=outme n mean;
      var Meff_P2_gpa Meff_P2_tuce Meff_P2_psi;
      title 'Average of the Individual Marginal Effects';
   run;
   quit;

Figure 2.2 shows the overall marginal effects of PSI, TUCE, and GPA for the probit model fit.

Figure 2.2 Average of Individual Marginal Effects

Average of the Individual Marginal Effects

The MEANS Procedure

Meff_P2_gpa
Meff_P2_tuce
Meff_P2_psi

Marginal effect of gpa on the probability of grade=2
Marginal effect of tuce on the probability of grade=2
Marginal effect of psi on the probability of grade=2

0.3607863

0.0114793

0.3165199

Marginal effects at sample means of covariates can be obtained by adding an observation with a missing value for GRADE (endogenous variable) and the sample means of the covariates to the original dataset GREENEDATA. The following DATA step statements add the observation to the original dataset where means of GPA, TUCE, and PSI are 3.117, 21.938, and 0.4375, respectively. Because of the missing value of GRADE, model fitting does not depend on this observation. However, marginal effects and predicted probability values are obtained.

   data me_mean;
   input gpa tuce psi grade;
   datalines;
   3.117 21.938 .4375 .
   ;
   run;
      data me_mean;
         set greenedata me_mean;
      run;

Figure 2.3 shows the results of the following statements, which use the MARGINAL option in PROC QLIM on the new data set ME_MEAN:

   proc qlim data=me_mean;
      model grade = gpa tuce psi / discrete(d=probit);
      output out=outme1 marginal;
   run;
   quit;

Figure 2.3 Marginal Effects at Covariate Means

Average of the Individual Marginal Effects

Obs	gpa	tuce	psi	grade	Meff_P1_gpa	Meff_P2_gpa	Meff_P1_tuce	Meff_P2_tuce	Meff_P1_psi	Meff_P2_psi
33	3.117	21.938	0.4375	.	-0.53325	0.53325	-0.016967	0.016967	-0.46783	0.46783

There might be cases where some regressors are dummy variables. Since the MARGINAL option in PROC QLIM uses derivative calculation, marginal effect results might not be meaningful. In some cases, it might only help to provide a reasonable approximation. In such cases, analyzing the marginal effects due to dummy variables by taking the difference of estimated probabilities between the different levels of dummy covariates (PSI=1 and PSI=0) is more appropriate. Let $\text{[math]}$ denote the dummy explanatory variable and $\text{[math]}$ denote the other covariates at their means. The effect due to a change of $\text{[math]}$ on the predicted probabilities of $\text{[math]}$ is

$\mr {Pr}[y=1|x_ k=1,\mb {x}^{*}] - \mr {Pr}[y=1|x_ k=0,\mb {x}^{*}]$

The PROBALL option in the OUTPUT statement enables you to obtain the predicted probabilities of discrete endogenous variables for all responses. In order to obtain the previously described difference (when the other covariates are fixed at their means), you can append two observations with 1 and 0 as the discrete regressor’s (PSI) value, means of the other covariates, and missing values for the response variable as shown.

   data me_diff;
   input gpa tuce psi grade;
   datalines;
   3.117 21.938 1 .
   3.117 21.938 0 .
   ;
   run;

   data me_diff;
     set greenedata me_diff;
   run;
   proc qlim data=me_diff;
      model grade = gpa tuce psi / discrete(d=probit);
      output out=outme2 marginal proball;
   run;
   quit;

The marginal effect of PSI is computed as follows:

$\mr {Pr}({\mr {GRADE}}=1|{\mr {PSI}}=1,{\mr {GPA}}=3.117,{\mr {TUCE}}=21.938)-\mr {Pr}({\mr {GRADE}}=1|{\mr {PSI}}=0,{\mr {GPA}}=3.117,{\mr {TUCE}}=21.938)$

The table obtained by using the PROBALL option in PROC QLIM produces two columns labeled 'Prob2_grade' and 'Prob1_grade' which are $\text{[math]}$ and $\text{[math]}$ respectively. You can obtain the predicted probabilities required for the above computation of marginal effects from the last two observations in column 'Prob2_grade'. As shown in Figure 2.4 , you can compute the marginal effect of PSI to be $\text{[math]}$ ( $\text{[math]}$ ). Hence, the overall effect of a unit change in PSI (by introducing the new teaching method with an exposure to PSI), on the probability of GRADE=1 (an increase in the student’s grade) is $\text{[math]}$ . Figure 2.4 Estimated Probability by Using the PROBALL Option

Average of the Individual Marginal Effects

Obs	gpa	tuce	psi	grade	Meff_P1_gpa	Meff_P2_gpa	Meff_P1_tuce	Meff_P2_tuce	Meff_P1_psi	Meff_P2_psi	Prob1_grade	Prob2_grade
33	3.117	21.938	1	.	-0.63858	0.63858	-0.020318	0.020318	-0.56023	0.56023	0.42995	0.57005
34	3.117	21.938	0	.	-0.29701	0.29701	-0.009450	0.009450	-0.26057	0.26057	0.89432	0.10568

Note that although for discrete covariates the difference calculation is usually employed to obtain marginal effects, in this example you can observe that both the derivative (Meff_P2_psi= $\text{[math]}$ , from Figure 2.3) and difference calculations ( $\text{[math]}$ , by taking the difference of probabilities under 'Prob2_grade' from Figure 2.4) produce similar results. However, this might not be true for other data sets. The marginal effects plot with respect to PSI on the $\text{[math]}$ is shown in Figure 2.5 using results from the probit model fit. The marginal effects of PSI on $\text{[math]}$ are obtained as a function of the GPA, at the mean of TUCE. This allows better interpretation of results.

As shown in Figure 2.5, you can conclude that the effect of PSI is much greater on those students who have a higher GPA.

Figure 2.5 Marginal Effect of PSI on Predicted Probabilities

Similar analysis with ordered multinomial, censored, and truncated data are supported by the QLIM procedure. An example with censored data is illustrated below.

Censored Regression Model

In this section an illustration of the marginal effect calculation for censored regression model is given. The censored regression model is described as follows:

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

where $\text{[math]}$ is the latent variable and $\text{[math]}$ is the observed variable. The marginal effect in this case is as follows:

$\frac{\partial E(y|\mb {x})}{\partial \mb {x}}= \bbeta \mr {Pr}(y^{*}>0| \mb {x})$

The Mroz (1987) data set taken from the 1976 panel study of income dynamics based on data obtained for the previous year 1975, is used for analysis. The dataset is used in the study of female labor supply. A tobit model is fitted to the data. The following variables are used in the model:

WHRS = wife’s hours of work in 1975
LFP = dummy variable; LFP = 1 if woman worked in 1975; else = 0
KL6 = number of children less than 6 years old in household
K618 = number of children between ages 6 and 18 in household
WA = wife’s age
WE = wife’s educational attainment, in years
HHRS = husband’s hours worked in 1975
HA = husband’s age
HE = husband’s educational attainment, in years
HW = husband’s wage, in 1975 dollars
FAMINC = family income, in 1975 dollars

The following DATA step statements are used to read the data.

   data mroz;
   infile datalines truncover;
   input LFP WHRS KL6 K618 WA WE WW RPWG HHRS HA HE HW FAMINC MTR WMED WFED UN CIT AX;
   datalines;
   1 1610 1 0 32 12  3.3540  2.65 2708 34 12  4.0288 16310 .7215 12  7  5.0 0 14
   1 1656 0 2 30 12  1.3889  2.65 2310 30  9  8.4416 21800 .6615  7  7 11.0 1  5
   1 1980 1 3 35 12  4.5455  4.04 3072 40 12  3.5807 21040 .6915 12  7  5.0 0 15

   ... more lines ...

In this example, a tobit model is estimated. You can fit a logit or a probit model to the dummy response variable LFP, similar to the analysis shown earlier. You can append the MROZ data set with the mean values of the explanatory variables as shown in the following statements.

   /*last row has the means*/
   data add;
   input LFP WHRS KL6 K618 WA WE HHRS HA HE HW FAMINC ;
   datalines;
   1 740.5763612 0.237715803 1.353253652 42.53784861 12.28685259 2267.270916 45.12084993 12.49136786 7.482178752 23080.59495
      ;
      run;

   data mrozexsub;
   set mroz(keep=LFP WHRS KL6 K618 WA WE HHRS HA HE HW FAMINC) add;
   run;

Figure 2.6 shows the marginal effect results for a tobit model fit.


   proc qlim data=mrozexsub;
      model WHRS = KL6 K618 WA WE HHRS HA HE HW FAMINC;
      endogenous WHRS ~ censored(lb=0);
      output out=outtobit residual marginal;
   run;

   proc print data=outtobit(firstobs=754);
    var Meff_KL6 Meff_K618 Meff_WA Meff_WE Meff_HHRS Meff_HA Meff_HE Meff_HW Meff_FAMINC;
   run;

Figure 2.6 Marginal Effects for a Tobit Model Fit

Obs	Meff_KL6	Meff_K618	Meff_WA	Meff_WE	Meff_HHRS	Meff_HA	Meff_HE	Meff_HW	Meff_FAMINC
754	-579.163	-63.9936	-17.2332	52.7183	-0.43955	-10.7785	-3.79460	-127.807	0.039525

Similar analysis using the probit and logit models yield results shown in Figure 2.7 and Figure 2.8 respectively.

Figure 2.7 Marginal Effects for a Probit Model Fit

Obs	Meff_P1_KL6	Meff_P1_K618	Meff_P1_WA	Meff_P1_WE	Meff_P1_HHRS	Meff_P1_HA	Meff_P1_HE	Meff_P1_HW	Meff_P1_FAMINC
754	0.34706	0.020687	0.011396	-0.056156	.000255579	.007300417	.006522166	0.068965	-.000021673

Figure 2.8 Marginal Effects for a Logit Model Fit

Obs	Meff_P1_KL6	Meff_P1_K618	Meff_P1_WA	Meff_P1_WE	Meff_P1_HHRS	Meff_P1_HA	Meff_P1_HE	Meff_P1_HW	Meff_P1_FAMINC
754	0.35548	0.019558	0.011089	-0.058672	.000274938	.008184995	.006452848	0.074250	-.000023536

References

: Greene, W. H. (1997), Econometric Analysis, Third edition, Prentice Hall, 339–350.
: Mroz, T.A. (1987), "The Sensitivity of an Empirical Model of Married Women’s Hours of Work to Economic and Statistical Assumptions," Econometrica, 55, 765–799.
: Spector, L. and Mazzeo, M. (1980), "Probit Analysis and Economic Education," Journal of Economic Education, 11, 37–44.
: SAS Institute Inc. (2008), SAS/ETS User’s Guide, Version 9.2, Cary, NC: SAS Institute Inc.

These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

data greenedata;
input gpa 1-4 tuce 6-7 psi  grade;
datalines;
2.66 20	0 0
2.89 22	0 0
3.28 24	0 0
2.92 12	0 0
4    21 0 1
2.86 17	0 0
2.76 17	0 0
2.87 21 0 0
3.03 25 0 0
3.92 29 0 1
2.63 20 0 0
3.32 23 0 0
3.57 23 0 0
3.26 25 0 1
3.53 26 0 0
2.74 19 0 0
2.75 25 0 0
2.83 19 0 0
3.12 23 1 0
3.16 25 1 1
2.06 22 1 0
3.62 28 1 1
2.89 14 1 0
3.51 26 1 0
3.54 24 1 1
2.83 27 1 1
3.39 17 1 1
2.67 24 1 0
3.65 21 1 1
4    23 1 1
3.1  21 1 0
2.39 19 1 1
;
run;


proc qlim data=greenedata;
   model grade = gpa tuce psi / discrete(d=probit);
   output out=outme marginal;
run;
quit;

proc means data=outme n mean;
   var Meff_P2_gpa Meff_P2_tuce Meff_P2_psi;
   title 'Average of the Individual Marginal Effects';
run;
quit;

data me_mean;
input gpa tuce psi grade;
datalines;
3.117 21.938 .4375 .
;
run;
   data me_mean;
      set greenedata me_mean;
   run;


proc qlim data=me_mean;
   model grade = gpa tuce psi / discrete(d=probit);
   output out=outme1 marginal;
run;
quit;

proc print data=outme1(firstobs=33);
   run;

data me_diff;
input gpa tuce psi grade;
datalines;
3.117 21.938 1 .
3.117 21.938 0 .
;
run;


data me_diff;
  set greenedata me_diff;
run; 
proc qlim data=me_diff;
   model grade = gpa tuce psi / discrete(d=probit);
   output out=outme2 marginal proball;
run;
quit;

proc print data=outme2(firstobs=33);
run;  

   /*****graph plot*****/
proc qlim data=me_diff outest=est;
   me: model grade = gpa tuce psi / discrete(d=probit);
   output out=outme3  marginal prob proball;
   run;
quit;
   /*to get the probs at the means of tuce*/
   data nopsi;
   set outme(keep=gpa);
   if _n_ > = 1 then do;
   tuce= 21.938;
   psi=0;
   grade=.;
   end;
   if _n_ > 32 then delete;output;
run;
data yespsi;
   set outme(keep=gpa);
   if _n_ > = 1 then do;
   tuce= 21.938;
   psi=1 ;
   grade=.;
   end;
   if _n_ > 32 then delete;output;
run;
proc score data =nopsi nostd out= nopsival score=est type=parm predict;
   var gpa psi tuce;
   run;
   proc score data =yespsi nostd out= yespsival score=est type=parm predict;
   var gpa psi tuce;
run;
data yesnoval(drop=psi tuce grade);
   set yespsival(rename=(_=yes));
   set nopsival(rename=(_=no));
   yesline=cdf('normal', yes);
   noline=cdf('normal', no);
run;

   ods graphics on;
   title  'Plotting Marginal Effects';
   title2 'Effect of PSI on Predicted Probabilities';
   goptions cback=white ctitle=bl ctext=bl ftitle=centx 
         ftext=centx reset=(axis symbol);
 proc gplot data=yesnoval;
         plot yesline*gpa=1
        noline*gpa=2
        / overlay
                          haxis=axis1
                          vaxis=axis2
                          vminor=4
                          href=3.117
                          lh=2;
   
   axis1 offset=(1 cm) label=('GPA')
         order=(2.0 to 4.0 by .5);
   axis2 label=(angle=90 'Pr(Grade=1)')
         order=(0 to 1 by .2);
   symbol1  l=1 c=red;
   symbol2 l=20  c=green v=star;
   footnote1 c=r f=centx  ' +++ with psi'
             c=g f=centx  ' *** without psi'
             ;
run;
title;footnote;
quit;
ods graphics off;

data mroz;
infile datalines truncover;
input LFP WHRS KL6 K618 WA WE WW RPWG HHRS HA HE HW FAMINC MTR WMED WFED UN CIT AX;
datalines;
1 1610 1 0 32 12  3.3540  2.65 2708 34 12  4.0288 16310 .7215 12  7  5.0 0 14
1 1656 0 2 30 12  1.3889  2.65 2310 30  9  8.4416 21800 .6615  7  7 11.0 1  5
1 1980 1 3 35 12  4.5455  4.04 3072 40 12  3.5807 21040 .6915 12  7  5.0 0 15
1  456 0 3 34 12  1.0965  3.25 1920 53 10  3.5417  7300 .7815  7  7  5.0 0  6
1 1568 1 2 31 14  4.5918  3.60 2000 32 12 10.0000 27300 .6215 12 14  9.5 1  7
1 2032 0 0 54 12  4.7421  4.70 1040 57 11  6.7106 19495 .6915 14  7  7.5 1 33
1 1440 0 2 37 16  8.3333  5.95 2670 37 12  3.4277 21152 .6915 14  7  5.0 0 11
1 1020 0 0 54 12  7.8431  9.98 4120 53  8  2.5485 18900 .6915  3  3  5.0 0 35
1 1458 0 2 48 12  2.1262  0.00 1995 52  4  4.2206 20405 .7515  7  7  3.0 0 24
1 1600 0 2 39 12  4.6875  4.15 2100 43 12  5.7143 20425 .6915  7  7  5.0 0 21
1 1969 0 1 33 12  4.0630  4.30 2450 34 12  9.7959 32300 .5815 12  3  5.0 0 15
1 1960 0 1 42 11  4.5918  4.58 2375 47 14  8.0000 28700 .6215 14  7  5.0 0 14
1  240 1 2 30 12  2.0833  0.00 2830 33 16  5.3004 15500 .7215 16 16  5.0 0  0
1  997 0 2 43 12  2.2668  3.50 3317 46 12  4.3413 16860 .7215 10 10  7.5 1 14
1 1848 0 1 43 10  3.6797  3.38 2024 45 17 10.8700 31431 .5815  7  7  7.5 1  6
1 1224 0 3 35 11  1.3472  0.00 1694 38 12  9.1499 19180 .7215 16 10  7.5 1  9
1 1400 0 2 43 12  3.2143  4.00 2156 45 12  6.1224 18600 .6915 10  7  7.5 1 20
1  640 0 5 39 12  5.1750  2.25 2250 40 12  6.1498 19151 .7215 12 12  7.5 1  6
1 2000 0 0 45 12  2.0000  2.30 2024 51 11  6.9170 18100 .6915  7  7  5.0 1 23
1 1324 0 4 35 12  7.5529  3.94 2123 40 10  4.7103 20300 .6915 12  7  5.0 0  9
1 2215 0 2 42 16  3.5052  3.30 4160 48 16  3.1310 30419 .6215 10 16  7.5 0  5
1 1680 0 0 30 12  3.5714  3.80 2000 35 12  4.0000 14090 .7215 12 10  3.0 0 11
1 1600 0 0 48 13  3.2500  3.26 2420 52 17  7.2227 22679 .6615  7  3  5.0 1 18
1  800 0 0 45 12  3.2500  2.20 1150 53 17  7.9652 12160 .7215  7  7 11.0 0 15
1 1955 1 1 31 12  2.1545  2.30 2024 31 12  4.0884 12487 .7515 12  7  5.0 1  4
1  660 0 2 43 17  3.7879  0.00 1904 43 17 14.1810 29850 .5815 16 14  9.5 1 21
1  525 0 0 59 12  4.0000  3.18 2448 53 16  6.5359 18100 .6915  3  7  9.5 1 31
1 1904 0 3 32 12  4.7269  6.07 2000 33 13  8.5000 26000 .6615  3  7 11.0 1  9
1 1516 1 0 31 17  7.2559  6.00 2390 30 17  6.2762 26100 .6215 12 12  5.0 0  7
1  346 0 0 42 12  5.8671  6.39 1920 47 10  5.2083 17730 .7215 12 12  9.5 0  7
1 1040 0 0 50 11  1.5385  0.00 1840 53 10  2.7821  6719 .7515  7  7  7.5 1 32
1  732 0 0 59 16  2.4590  2.50 3360 57 17  4.9107 18550 .6915  3  3 14.0 1 11
1 1880 0 2 36 13  5.8511  5.20 2284 35 13  5.8669 24600 .6615 12 10  7.5 0 16
1 1680 0 1 51 12  3.5714  3.29 1875 50  8  7.5200 23100 .6915  7 14  5.0 1 14
1 2081 0 3 45 16  3.8068  4.19 2140 47 17  7.5449 24656 .6615 12 12  5.0 1 27
1  690 0 1 42 11  2.4638  0.00 1896 44  8  5.5380 15897 .7515 10  3  7.5 0  0
1 4210 0 0 46 12  2.3753  4.63 1040 49 16  6.9231 20320 .6915  3  3 11.0 1 17
1 2205 0 1 46 10  4.5351  4.55 2200 52 12  5.0000 21384 .6615 10  3 11.0 0 28
1 1952 0 0 51 14  5.6183  5.60 1952 58 12  7.3064 25561 .6215  7  7 14.0 0 24
1 1302 0 0 30 17 14.6310  9.53 1560 30 17 11.2180 36550 .5800 14 17  5.0 1 11
1  112 1 2 30 12  2.6786  0.00 4030 33 16  3.8462 15810 .7215 12 12  3.0 0  1
1  893 0 0 57 12  3.9194  3.50 2570 58 12  5.8366 25500 .6215  9  9  7.5 1 14
1  583 1 2 31 16  2.5729  9.98 1530 34 16 13.7250 24000 .6615 14 16  9.5 1  6
1  480 0 2 48 12  4.5375  4.65 3149 48  8  6.3493 22172 .6615  3  3  5.0 0 10
1 1900 0 3 30 12  2.0000  2.23 2690 32 12  5.2528 17930 .7215 12  7  5.0 0  6
1  576 0 2 34 12  3.4722  3.84 3096 33 12  1.3075  7000 .7815 12  7  3.0 0  4
1 2056 0 2 48 16  2.0161  0.00 2552 53 16  2.7998 25300 .7215 14 16  5.0 1 10
1 1984 0 0 45 12  4.5716  4.82 2040 47 11  2.6961 16212 .7215 10 10 11.0 0 22
1 2640 0 0 51 12  2.2727  0.00 2180 50 13  7.5688 22650 .6615  7  7  3.0 0 16
1  240 0 2 30 12  2.6375  0.00 1864 37 12  3.4077  6985 .7815 12  7 14.0 0  6
1 1173 0 1 46 12  2.2899  2.50 2068 46 12  6.5401 30000 .6915  7  7 11.0 1 12
1 3640 0 0 58 12  1.0989  0.00 2010 58 12  7.2139 18500 .6915  7  3  9.5 1 32
1  340 0 8 37 12  1.1765  0.00 2152 40 10  6.2732 16658 .7515 12  7  5.0 0 15
1  500 0 0 52  8  1.6000  0.00 1496 54 11  5.8824 10300 .7515  7  7  5.0 1 17
1 1599 0 0 52 10  1.8762  2.80 2100 47  4  3.8095 11000 .7515  7  3  7.5 0 34
1 1830 0 0 31 16  4.0437  4.20 1960 35 14  6.3776 19900 .6915 12 12  7.5 1  9
1 1920 0 0 55 14  9.6354  8.75 1985 55 15  6.0453 32500 .6400  7  7 14.0 1 37
1 2052 0 0 34 17  8.0409  8.25 2020 33 17  8.8119 37300 .5800 17 17  7.5 1 10
1 2312 0 0 55 14  4.5990  5.58 2178 56 16  8.8765 30018 .5815 17  7 11.0 1 35
1  196 0 2 39 12  2.1429  2.50 3684 39 12  3.3420 12807 .7515 12  7 14.0 1  6
1 2500 0 3 40 14  4.4000  5.50 5010 42 13  3.1836 39500 .5515 14  3  7.5 0 19
1 1980 0 4 43 12  3.5354  3.75 1880 47 12  6.9149 22050 .6915 12 12  9.5 1 10
1 1840 0 0 48  8  2.7174  4.80 1904 56  8  5.5147 15500 .7215  7  7 14.0 1 11
1  320 0 0 47 12  6.2500  6.25 2083 47 12  5.2808 13810 .7215  7  7  9.5 1 15
1  419 0 4 41 12 11.9330  6.30 2125 44 12  3.2000 11950 .7515  7  7  5.0 1 12
1 1880 0 0 36  8  3.5931  3.75 1985 37 12  5.8791 19175 .6915 12 12  7.5 0 12
1   72 0 2 46 17  6.9444  0.00 2640 48 17  6.2500 17900 .6915 12 16  7.5 0 14
1  120 0 0 34 12  2.9167  0.00 2070 51  8  7.4879 15850 .7215 12  7  5.0 1 11
1 1885 0 3 41 12  3.0769  2.90 2107 48  8  6.9767 27017 .6915  7  7  5.0 1  9
1  240 0 1 51 12  3.7500  0.00 2250 54 10  8.0000 18900 .6915 12  7  5.0 0 24
1 1729 0 0 33 12  5.7259  4.76 2880 34 16  4.1319 21800 .6915 12 12  7.5 1 12
1 1850 0 0 52 12  3.6757  3.40 1848 53 12 14.4760 33552 .5515 10 10  7.5 1 13
1 2033 0 0 58  9  5.1648  4.32 1927 53  7  5.7343 22650 .6615  7  9  7.5 1 29
1  608 2 4 34 10  8.2237  3.00 1304 38  9  3.3742 15200 .7915  0  0  7.5 1 11
1 1153 0 1 31 12  4.3365  4.52 3000 35 12  1.8333 13120 .7215  7 10  7.5 1 13
1 2208 0 1 48 12  4.9819  5.31 1892 52 12  5.6025 21660 .6615 12 14  5.0 1 19
1  252 0 2 32 12  0.3571  0.00 3644 32 12  4.2975 18190 .7215  7  7  3.0 0  2
1  337 0 0 49 17  2.9674  0.00 1430 47 17  3.9161  9600 .7515  3  3 14.0 1 24
1   90 2 2 32 15  1.0000  0.00 2350 31 14  4.8787 13755 .7515 10 12  7.5 1  9
1 1174 0 0 58 12  2.5554  4.87 1948 59 16  9.2402 35350 .6615  7 12  7.5 1  6
1  372 0 0 50  6  0.8602  2.25 1804 42 12  6.6519 12405 .7215 12  7  7.5 1 22
1   30 0 0 60 14  1.0000  0.00 2326 51 12  4.6217 12180 .7515 12 17  9.5 0 30
1 1800 0 1 50 12  2.9261  0.00 1739 55 11  9.9741 22962 .6615  7  3  7.5 1 10
1  282 0 0 56 14  3.5461  2.50 1176 57 17 20.9180 25700 .6215  7  7  9.5 1  6
1  720 0 0 51  9  1.6264  2.20 1100 55  8  1.9400  3305 .7915  7  7  3.0 0 29
1 1440 0 1 54 17  8.3333  6.00 1528 58 17  8.8351 32950 .5815  7 12  5.0 1 29
1 2100 0 0 59 13  3.0952  2.95 2250 52 15  4.6667 17000 .6915  7  7  5.0 1 36
1 1000 0 2 46  9  2.7000  2.35 1927 47 10  5.1894 13250 .7515  7  7  5.0 1 19
1  952 0 1 46 15  5.2521  0.00 2414 47 16 18.7240 50750 .4415  7 12  5.0 1  8
1 1413 1 3 39 12  1.4154  2.20  768 49  8 10.4170 15632 .7715 10 10 14.0 0 13
1 2100 0 2 44 12  4.7986  4.85 1984 43 14  8.8458 28316 .6215  7  0 11.0 1 16
1  120 2 0 33 12  1.6667  2.37 2246 36 12  7.5690 17290 .7215 12 12  9.5 1 11
1 3000 1 2 33 12  1.1217  0.00 3024 30 17  4.4507 33600 .6215 10 10  7.5 1 15
1 1000 0 2 48 12  0.5000  0.00 2921 52 12  9.3204 29200 .6215 12  7  9.0 1  6
1  336 0 4 31 12  0.7143  0.00 2045 37 17  9.1687 19870 .6915  7  7 11.0 0 13
1 1216 0 1 45 12  2.7961  2.90 1928 44 12  6.4834 16225 .7215  7  7 11.0 0 22
1  988 0 1 45 12  4.8583  4.50 1920 44 10  7.8125 28600 .6915  7  3  5.0 1 24
1 2581 0 2 32 13  1.7435  2.60 2280 37 17 11.4040 30800 .5815 14 12  7.5 1  2
1 2030 0 0 47 12  2.4631  2.80 2300 47 17  5.0870 25700 .6915  7  7  3.0 0  6
1  413 0 2 34 13  2.4213  3.00 2480 35 13  6.9758 27000 .6215 12 12  3.0 0  2
1  782 0 1 37 12  1.5345  2.30 1135 34 10  5.2863 12077 .7715 12  7  9.5 1  2
1 1388 0 1 36 12  2.8818  1.87 1384 39 12 11.5620 29612 .6615  7  7 11.0 0 14
1 1450 1 2 47 12  2.4069  3.00 1848 50 14  8.6061 24479 .6915  7 10  9.5 1  9
1 1720 0 1 48 16  5.2326  4.68 2499 46 17 12.8050 79750 .4415 14 14  7.5 1 11
1  800 0 2 42 12  3.7500  2.50 2390 43 12  6.6946 20050 .6915 12  7 11.0 0  9
1  360 0 3 33 13  1.3889  0.00 2400 44 14  8.3333 21500 .6915 10 12 11.0 1  6
1 2000 0 0 46 11  4.0000  4.61 1920 53  8  4.1667 16120 .6915  7  7  5.0 0 19
1 1176 0 3 47 12  3.2313  3.35 2301 48 13  5.4759 24686 .7215  7  7  9.5 0 26
1 2058 0 1 44 12  3.4014  3.80 1944 43 10  5.1440 24669 .6915  7 10  9.5 1 19
1  900 0 4 36 12  1.3333  2.20 2100 37 17 11.6670 26400 .6615  7  7  7.5 1  3
1  215 2 0 31 17  9.3023  9.98 1920 32 16  7.2917 16245 .7215 12 12  7.5 1  7
1 2000 0 0 55 14  4.5000  4.37 2880 55 14  4.8611 23300 .6615  7  7  9.5 1 28
1  757 0 1 45 16  4.6235  4.50 1932 48 16 12.1640 27200 .6215 12  7  9.5 1 13
1 1264 0 0 47 17  3.9557  0.00 3234 48 17 10.8230 51000 .4615 10 17  9.5 1  9
1 2064 0 3 46 12  5.8140  6.00 2805 47 12 12.4780 55000 .4615 10  7 14.0 1 15
1 1280 0 0 49 11  0.5000  0.00 2272 52  9  6.1620 15389 .7215  7  7  7.5 1 20
1 1715 0 0 49 12  4.0816  3.75 2227 52 14  7.1846 23150 .6615  7  7  9.5 1 29
1 2000 0 2 45 12  6.0000  4.95 1720 49  6  7.0930 29774 .6215  7 10 14.0 1  9
1   12 1 3 38 17  3.6667  0.00 2300 38 13 17.8260 91044 .4415 12 10 14.0 1  1
1 1528 0 0 47 10  3.8613  2.95 3410 50 12  6.3930 28200 .5815  7 12 14.0 1  8
1  561 0 3 54 13  2.7629  2.53 2304 57 16 11.7190 36150 .5515  7  7  9.5 1 19
1 2058 0 0 41 11  2.9310  2.90 1984 42 12  4.7883 15652 .7215 12 12  7.5 0 23
1 1823 0 2 43 12  4.3884  4.20 1890 33 14  4.2328 18900 .7515 14  7 11.0 0  3
1 1680 1 1 31 16  5.4167  4.70 1970 32 12  7.1066 23600 .6615 12 10  7.5 0 13
1 1440 0 0 47 17  9.8611  7.10 2400 46 12  8.3333 36200 .6100  7  7  7.5 1  8
1 4950 0 2 35 12   .1616  2.75 2504 37 12  6.9888 18700 .6915 10 10  7.5 0 17
1 1176 0 3 45 16   .3826  3.75 2398 48 17  9.5913 24125 .6615  7  7 11.0 1  4
1 1100 1 0 33 12  3.6364  3.58 1960 39 12  6.0204 15800 .7215  7  7  7.5 0 15
1 1516 0 1 54 16  2.3747  2.40 2550 55 12  2.9686 19742 .7215 12  7  3.0 0 11
1  900 0 4 35  8  4.6667  3.95 2500 41 12  7.0000 22600 .6915 10  7  9.5 0  7
1 1080 1 2 31 12  1.8519  2.25 2164 37 10  7.1627 17500 .7215  7  7  7.5 0  0
1  480 0 0 55 12  5.2000  0.00 2640 60 12  4.7364 19820 .6915  7  7  7.5 0  0
1  288 0 2 34 12  3.2986  4.62 1936 36 12  8.7810 20155 .6915 12 16 11.0 1 10
1 1875 0 1 38 13  8.5333  8.50 2136 41 12  9.8315 37300 .5800 10 12  7.5 1  8
1  630 0 1 45 11  2.0635  0.00 1955 51 10  6.6496 24860 .7215  7  7  7.5 1  2
1  234 0 1 47 12  2.5641  2.50 1980 48 10  9.8485 21450 .6615 12  3  7.5 1  4
1 1600 0 2 39 12  2.1875  0.00 2550 42 11  9.8039 29650 .6215  7  7  5.0 1  6
1  960 1 0 36 14  6.2500  0.00 2058 37 13  8.2604 23000 .6615  7  7 11.0 1 18
1  120 1 2 33 12  3.3333  0.00 2263 32 14  9.0676 21120 .6915  7  7  9.0 1  3
1 2025 0 0 50 12  4.4444  4.80 1763 54 13  8.5082 26000 .6215  7 12  5.0 1 22
1 1809 0 0 58 12  6.6335  6.45 2096 59 14  7.1565 28000 .6215  3  7  7.5 1 33
1 3087 0 0 49 17  8.4224  9.98 2059 47 13  7.0423 45500 .5200 12 12 11.0 1 28
1  910 0 2 41 14  4.3956  0.00 1820 40 17  6.5934 16000 .7215 16 12 14.0 1 23
1 1840 0 1 51 12  2.4457  2.50 2832 53  8  4.3457 18232 .6915  7 14 11.0 0 27
1  784 0 0 53  9  1.2245  2.25 1990 60 10  7.2362 28160 .7215  3  7 14.0 1 11
1  400 1 2 36 12  1.6250  0.00 2000 40  7  1.7400  5965 .8015 12  7 11.0 1  6
1 1000 0 2 46 12  3.0000  5.50 1885 46 12  6.8966 19000 .7215  7  7  9.5 1 11
1 1904 0 2 36 12  4.7269  4.20 2860 37 12  5.0455 36872 .5515 12 12 11.0 1 14
1 1771 0 1 53 14  1.1293  9.98 1913 48 16 17.2500 42000 .4915 12 12 14.0 1 17
1 1486 0 3 40 16  7.4024  6.25 1800 54 16  8.3333 26900 .6215 16 14 11.0 1 17
1  740 0 2 42 17  4.4595  1.65 2880 45 16  9.3750 30800 .5815 12 10  9.0 0 14
1 1820 1 1 33 15  2.4725  0.00 1993 32 16  8.2790 21520 .6915 12 12 11.0 1 11
1 1275 0 3 43 12  1.8824  3.00 2250 47 14  4.5000 24795 .6915  7  7  7.5 1  7
1  450 1 0 31 16  4.0000  4.00 2286 30 16  4.1995 12900 .7215 14 16 14.0 1  8
1 1221 0 0 47 17  8.1900  5.99 1880 47 16 16.0640 42700 .4915  7  7  7.5 1  6
1 1550 0 0 54 17  7.0968  6.00 2350 58 17 11.2770 38800 .5215 10 17 11.0 1  8
1  180 1 3 33 12  1.6667  0.00 3640 33 11  0.5494  2500 .9415  7  3  3.0 0  4
1 2090 0 0 43 16  3.4450  3.85 1770 47 14  9.5480 26921 .6215 14 10 11.0 1 25
1 1960 0 1 46 13  4.2347  4.20 1875 49 13  5.3333 18300 .6915  7  9  3.0 0 24
1 1440 0 3 35 12  2.7778  4.10 2200 38  9  5.4545 17200 .7215  7  7 14.0 1 11
1  794 0 3 37 11  1.8892  3.85 2033 39 12  5.9026 14209 .7515 12  3  9.5 1 19
1  993 0 2 37 16  5.0352  8.30 2739 39 17  9.8576 32300 .5815 12 16 14.0 1  9
1  160 0 3 34 14  1.2500  0.00 1626 38 14 11.6850 21400 .7215 17 12  7.5 1 19
1  105 1 0 43 16  2.8571  0.00 2248 44 17  6.2278 14700 .7215  7  7  9.5 0 14
1 1200 0 0 46 12  4.1167  4.33 2140 48 12  9.1748 25516 .6215  7  7  9.5 1 22
1  450 0 3 35  9  1.7778  2.60 1985 42 12  6.2972 13300 .7515  3  7  5.0 1  6
1  996 0 0 46 17 13.5540  9.98 1528 59 17 10.4710 31000 .5815 12 12  9.5 1 23
1 1052 0 0 46 14  4.5627  4.90 1920 48 16 14.5830 48800 .4915  7  3 11.0 1 15
1 1128 0 2 43 12  2.1277  2.40 1918 46 10  6.2143 15519 .7215  7  7 14.0 1  6
1 1840 0 0 30 12  2.9891  3.75 2112 30 12  6.6288 19500 .6915  7  7  7.5 0 11
1 1910 0 2 41 11  2.5654  2.57 2144 46  9  3.8246 14545 .7215  3  7  5.0 0  2
1  980 0 1 54 12  5.6122  5.00 1920 54 15  7.8125 22897 .6915  7  7 14.0 1 22
1 2317 0 1 31 12  2.8054  3.87 2241 41  9  3.4806 14300 .7215 10 10  7.5 1 10
1 1089 0 0 44 10  1.6070  0.00  880 47 11  5.5500 14884 .7515 10 10  9.5 1 14
1  800 0 1 32 12  2.2500  0.00 2070 31 16 11.5940 27400 .6215 12  7 11.0 1 12
1 1230 0 0 47  5  2.0325  2.82 1050 53  5  9.5238 16400 .7215  7 12 14.0 1  9
1 1158 0 1 46 17  5.5320  8.10 2635 57 17  7.2805 25704 .6215 14 17  7.5 0 13
1 2272 0 0 37 11  1.5845  3.71 3000 47  8  3.0000 12800 .7215 10 10  7.5 0 18
1  528 0 2 51 12  3.7879  0.00 2500 50 11 10.4000 40000 .6215  7  7  7.5 0  8
1 1000 0 1 49 12  3.0000  0.00 1990 49 12 10.0500 47000 .6615  7  7 14.0 1 11
1  520 0 4 36 14  8.6538  0.00 2390 37 13  8.7866 25872 .6615 10 12  9.5 1  9
1  760 0 1 39 11  4.2105  3.95 1430 44 12 10.1400 26868 .6915 12  7  9.5 1  9
1 1920 0 2 48 12  4.6875  4.30 1800 50  8  5.0000 18000 .6915 12 12  9.5 1 14
1 1220 0 2 38 14  4.0984  4.84 2103 43 17 11.8880 30200 .5815  7  7  5.0 1  9
1  200 0 2 40 12 25.0000  3.00 1350 42 12 13.3330 26220 .6615  7  7  7.5 1  2
1 2480 1 5 39 10  2.6331  4.20 2880 36 17  8.6806 40500 .5815  7  7  3.0 0 12
1 2750 0 0 37 16  6.0000  9.00 2400 43 17  7.2917 33570 .6100 12  7  7.5 1 15
1 2014 0 1 49 13  5.4126  4.05 1135 47 12  3.5242 16917 .7215  7 14 14.0 1 11
1 1355 0 3 33 12  0.6642  1.00 2750 35 17  6.1818 18000 .7215 12  7  9.5 0  7
1   80 0 0 30 12  1.2500  0.00 2085 32 16  2.9755  8337 .7515 12 12 11.0 1  9
1 1670 0 0 54 12  2.2754  2.10 2600 56  8  4.5769 17100 .7215 12  7  9.5 0 19
1  520 0 4 39 11  3.4615  3.05 3542 40 12  3.1056 17800 .7515 10  7 11.0 0 11
1  288 0 3 43 12  4.1667  3.00 1975 43 12  5.8228 13740 .7515 12 12 14.0 1  8
1 2014 0 3 31  9  4.4687  4.26 2400 32 12  7.5000 27000 .6215 10  3  9.5 1 13
1  800 0 3 33 13  1.7500  0.00 3000 37 14  8.3333 32600 .6215 12  7  7.5 1  4
1 1984 0 3 40 12  3.6694  4.25 1960 39 14  9.2347 28030 .6615 12 12 14.0 1  7
1 1823 0 1 36 12  6.5826  6.00 2000 39  9  5.5000 23100 .6615 12 12  3.0 0 19
1 1500 0 0 51 12  2.6000  2.00 3000 51 12  6.0000 24580 .6615  7  7  9.5 1 14
1 2261 0 1 44 13  4.8651  5.50 2400 43 12  6.6667 29000 .6215 12  7  9.5 1 14
1 1728 0 3 42 16  5.7870  6.25 2450 48 14 13.0610 42430 .5215 12 14  9.5 1  3
1 1960 0 1 40 12  4.5408  5.00 2423 40  8 12.7940 41800 .5215 12 12  7.5 1  9
1 1578 1 1 34 16  9.5057  7.72 2000 33 16 12.0000 39100 .5800 12 17  9.5 1  7
1 1316 0 0 30 17 10.6380  7.00 2526 41 16  6.7300 31800 .5815 16 17 11.0 1  7
1 1530 0 0 54 12  1.1111  1.13 2695 53 12  6.6790 22200 .6915  7  7 14.0 0 14
1 2220 0 0 51 12  4.0541  4.37 2048 54 12  4.3945 19500 .6915 16  7  3.0 0 29
1 1336 0 2 44  9  2.6871  2.64 1920 46 11  4.6875 14027 .7515  7 10 11.0 0 19
1 1008 0 1 43 12  2.9762  2.50 2338 42  9  7.6989 21195 .6615  7  7 11.0 1 14
1 1944 0 1 34 12  3.1728  3.23 2945 37  8  4.3287 19013 .6915 10  7  7.5 0 16
1 2000 0 0 45 13  3.5500  3.45 2047 52 12  6.7416 20900 .6615 12  7 11.0 1 10
1  258 0 0 39 12 17.9070  0.00 1668 47  7  9.3525 26820 .6215 10  3 11.0 0 12
1 1785 0 0 50 12  3.4174  5.75  175 48 10  9.1429 12800 .7515  0  0 14.0 1 24
1  480 0 0 52 12  3.3333  0.00 1798 53 12  2.6418  7850 .7515  7  7 14.0 0  6
1  772 0 2 41 12  3.8860  7.50 1222 45 12  7.3650 18600 .7215 12 12  7.5 1  9
1  900 0 0 59 10  2.3111  2.22 1820 59  7  1.4066  5380 .7715 12  7  5.0 0 14
1 1428 0 0 52 12  1.7108  2.50 1560 60  8  1.5192  6114 .7715 10  7 14.0 0 26
1  210 0 0 46 16  2.1143  4.00 2210 49 12  3.3439  8234 .7515 12 12 14.0 0  7
1  239 1 5 41 12  9.9331  4.50 2874 48 16  2.9106 20646 .7215  3  7 11.0 1  4
1 1878 0 2 33 11  3.0277  3.50 2499 35  8  4.3834 16640 .7215  7  7  9.5 0 15
1  215 0 0 45 12  1.8605  2.30 3088 38 12  4.2098 13900 .7215 12 12  5.0 1 23
1 2340 1 2 36 10  0.1282  0.00 2020 37  8  3.7129 11500 .7815 10  7  7.5 0  1
1 1960 0 1 48 12  6.6327  6.30 1980 56 10 10.6060 34000 .5515  7  7 14.0 1 29
1  532 0 1 47 12  5.6391  3.60 1968 47 11  8.6382 28700 .6615  7  3 11.0 1  9
1  394 0 0 45 12  1.5990  2.50 2100 45 12  3.8367  9563 .7515  7  7  7.5 0  6
1  675 0 2 37 12  2.6667  3.00 2651 48 17  7.1671 20960 .6915  7  7  7.5 0 11
1 1515 0 4 46 16  7.9208  6.80 1918 49 14  8.8634 38590 .6215 12 10 14.0 1 17
1 1030 0 3 43 17  5.3398  5.80 2585 46 16  7.7369 27900 .6615 12 12  5.0 1  6
1 1250 0 2 42 12  4.0000  4.00 2250 46 17  9.1702 25633 .6215  7  7  7.5 1  7
1 1158 1 2 34 17  6.0449  5.10 2480 39 17 11.2900 35200 .5515 12 12  7.5 1  2
1  112 0 0 52 12  6.2500  0.00 2924 53 12  6.3269 29500 .5815  7  7  7.5 1 24
1  336 0 3 37 12  2.9762  2.20 1896 52  9  4.7468 10000 .7515 10  7  7.5 0  4
1 1984 0 1 37 12  4.2339  4.78 2332 40 12  4.8885 19800 .6915 10  7  5.0 0 11
1  716 0 0 52  8  3.4916  2.20 3482 59  7  2.4842 12900 .7215  7  7  5.0 0 25
1 1410 1 0 30 12  4.9645  1.28 2106 30 14  8.5470 26080 .6215 12 12  7.5 0 11
1 1300 0 1 31 13  2.7692  0.00 1160 32 12  6.6379 13066 .7515 17  7 11.0 1  2
1 1640 0 1 38 12  3.6585  3.25 2040 46 12  3.1863 12500 .7215  7  7  7.5 0 19
1 1202 0 3 43 12  5.3935  0.00 2856 48 16  4.5466 35600 .5815  7  7  9.0 1  7
1  489 0 1 49  8  0.6564  2.29  950 51  8 12.7890 19424 .7515  7  7  5.0 1  2
1 2076 0 0 55 12  4.7688  4.68 2068 58 10  6.5280 26250 .6615  7  7  5.0 1 20
1  526 0 2 38 17  8.5551  4.20 1896 42 17 16.4030 36525 .5515 12 14  9.5 1 10
1 1721 0 0 52 17 10.4590  9.50 2000 56 16  7.0000 34700 .6100 14 17 14.0 1 19
1 1327 0 0 48 12  2.6375  2.57  288 51 11 13.5420  8311 .7515  7  7 11.0 1 17
1  584 0 2 32 13  6.8493  4.32 2160 33 12  6.7130 28626 .6915 12 10 11.0 1 12
1 1376 0 1 32 12  5.0872  5.00 3120 33 17  5.4487 24400 .6615  7  7  5.0 1 11
1 1040 0 2 38 12  0.9615  0.00 1944 41 17  6.6872 14025 .7215  7  7  7.5 1  6
1  548 0 3 46 12  4.3066  3.69 2046 47 12  9.0943 21367 .6915 16 12 14.0 1 10
1   15 0 3 40 12  7.0667  0.00 2005 42  9  6.5337 14136 .7515  7  7  7.5 0  4
1 1980 0 4 31  9  2.5253  2.56 2070 36 10  4.6860 19900 .7515 10  7  5.0 1  2
1 1520 0 1 43 10  7.8947  5.00 3000 50 12  8.0000 37000 .5215 12  9  9.5 1 13
1 1880 0 0 51 12  4.1489  3.90 2640 51 12  4.0530 18500 .6915  7  7  7.5 0 21
1 1260 1 0 30 16  8.1746  8.17 2450 34 17  8.1633 34550 .5515 16 14  5.0 1  9
1 1092 0 0 52 13  9.5971  0.00 1000 53 15 16.5000 49620 .4615 10  7 11.0 1  4
1 1587 1 5 30  8  2.0164  2.30 2080 33  8  3.4615 10400 .7815  3  3  7.5 0  2
1  156 0 0 51 16  7.6218  0.00 2413 51 16 11.3610 33000 .5515 16 16 11.0 1 19
1 1939 0 2 31 13  3.1975  3.43 2570 31 12  3.8911 16200 .7215  7  3  7.5 1  4
1 1250 0 4 34 12  1.6000  1.36 2030 52 12  9.6059 22660 .6915 12 16  7.5 1  9
1  610 0 0 49 11  4.0984  4.00 4684 59 17  2.6687 16000 .7215  7  7  7.5 1 14
1  270 1 3 35 13  1.4815  5.00 2802 41 17  8.8865 25780 .6615  7 16  9.5 1  6
1  660 1 0 53 12  3.6364  3.15 2090 59 12  6.3636 20675 .7215  7 12  7.5 1 24
1 1000 0 3 32 12  1.0000  0.00 2053 46 16 17.7280 40213 .5515 12  7 11.0 0  1
1 1920 0 3 38 10  2.6042  2.93 1984 42 10  5.2923 15500 .7215 12  7  7.5 1 13
1  200 0 0 54 12  1.7500  0.00 2040 54 16 15.6860 35207 .5815  7 12  9.5 1  3
1 1500 0 1 47 17  4.8000  3.60 2794 58  8  5.2423 35702 .5515 10 12 11.0 1 10
1  868 0 1 45 15  5.5300  6.00 3290 47 14  3.0395 17800 .7215 14 12  9.5 1 16
1 2318 0 1 47 16  4.0984  4.20 1911 46 16 16.7450 50900 .4915 16 16  5.0 1  9
1 2000 0 0 59 10  1.2500  0.00 2000 60 12  3.7500 17280 .6915  7  7  5.0 0 19
1   60 0 1 32 11  1.6667  0.00 2580 31 12  5.8140 15150 .7215 10  9  5.0 1  4
1 1715 0 1 45 12  3.7901  3.38 2400 49 17 10.8330 36200 .5815  7  7  7.5 1 10
1  550 0 4 40 12  2.3636  2.26 1740 47 12  9.0029 17465 .7215 14 12  5.0 1  5
1 1960 0 2 47 14 10.2040  0.00 2500 50 12  6.5400 45205 .6100 14 12  3.0 1  7
1   44 1 2 36 16  6.8182  1.36 1840 37 17  5.9783 14500 .7515 12 10  5.0 0  3
1 1920 0 0 56 14  7.2146  6.92 2036 56 14  8.6248 32011 .5815  7  7  7.5 0 38
1 2540 0 1 41  8  2.4484  0.00 3536 43 11  4.8329 35200 .6215  7 12  9.5 0 16
1  156 0 3 48  7  1.1987  0.00  880 51 11 10.9090 13579 .7515  3  7 11.0 0 13
1  780 1 2 36 12  1.6410  0.00 2007 38 12  3.8864 10455 .7515  7  7 11.0 0  1
1 3120 0 0 41 12  1.7821  0.00 2632 44 13  8.4574 32600 .5515  7  3  5.0 0  7
1 2040 0 0 41 14  2.9412  2.80 2600 43 12  5.0000 19150 .6915  7 10 11.0 1 15
1 1610 0 3 36 12  4.9689  4.25 2156 36 13  7.4212 24400 .6615 12 17  9.5 1 10
1  215 0 3 37 12  1.8605  0.00 3625 41 12  4.4938 21700 .6915 10  7  3.0 0  2
1 1120 0 0 38 12  8.0357  0.00 2420 42 12  7.0252 26201 .6215  7  3  9.5 1 19
1  846 0 2 43 14  3.9716  4.20 2080 43  9  3.2788 11920 .7515  3  3  7.5 1 25
1 3225 0 0 54 16  3.0416  0.00 3443 59 17  1.2861 16300 .7215 12 12  9.5 1 25
1 1376 0 1 38 12  2.9070  3.75 2250 41 12  5.5556 16500 .7215  7  7  5.0 1  7
1  980 1 0 30 12  3.0612  3.60 2535 34 16  7.4951 30000 .5815 12  7 11.0 1 15
1 1838 0 0 49 12  4.8966  5.00 2352 48 15 22.1090 62500 .4415  7  7  9.5 1 11
1 1494 0 1 45 13  4.0161  2.50 3036 49  6  9.0580 58500 .4415 10 10  9.5 1 25
1  450 0 0 51 13  5.5556  3.50 2600 57 14 11.5380 40900 .5215  7  7  9.5 1 19
1 1976 0 0 34 10  1.2227  2.45 2223 39  7  6.0468 16308 .6915  0 10  7.5 1  4
1 2012 0 2 34 12  2.6839  3.61 2666 34 10  1.3653  9300 .7515  7  7  7.5 1 14
1  561 0 1 41 12  2.6738  3.25 2006 41 17 16.5500 35700 .5515 10  9  7.5 1 19
1 1715 0 1 49 12  9.3294  7.05 1710 49 17  8.7719 35700 .6400  9  9 11.0 1 18
1 1912 0 0 32 12  3.1381  3.60 1920 46 14  9.6354 24500 .6615 12 12  5.0 1 14
1 3686 0 0 32 14  0.5426  0.00 1647 39 14  6.6788 13000 .7215 12 12  7.5 1 11
1 1080 0 2 32 17  8.6111  4.65 3080 35 15  7.5727 52600 .4415 12 12  5.0 0  4
1 1799 0 0 47 10  3.6687  3.25 1920 48 10  7.8125 25360 .6615  3  7  7.5 1 29
1 1984 0 1 39  9  2.3185  2.30 2420 47  4  1.9835  9400 .7515  9  9  7.5 0 21
1 1839 0 0 49 12  2.8820  3.27 2205 53 15  9.5238 26800 .6215 12 12 11.0 1 24
1 1579 0 3 37 12  3.1666  0.00 3035 39 14  6.4250 33040 .6615 12  7  7.5 1 19
1   96 0 0 59 16  3.6458  0.00 2185 60 15 10.9840 26350 .6215 14 12  7.5 1 31
1 1920 0 0 50 12  6.2500  5.47 1880 56 12 12.7660 39000 .5215  7  7 14.0 1 28
1 1688 0 1 32 17 10.2490  9.80 1863 33 17  9.5545 35100 .6100 12 12  9.5 1 15
1 1589 0 0 46 12  3.2096  5.54 2456 48 16  5.4967 22502 .6615 12 12 11.0 0 27
1  345 0 2 43 17  7.6522  5.00 1847 46 17  9.7618 21950 .6915 12 14 14.0 0 13
1 1521 0 3 37 11  1.9724  2.30 2000 42  6  5.0000 13000 .7515  7  7  7.5 0  4
1 1490 0 2 32 16  4.6980  3.90 1856 35 14  5.9995 18180 .7215 12 14  9.0 1 10
1  989 0 1 39 11  2.1234  2.76 1880 43 14  6.9149 20957 .6915 10 10  9.0 1  8
1  600 0 2 34 13  2.3333  2.90 3020 35 12  4.9669 13700 .7215 12 12  7.5 0  4
1 2646 0 1 39 11  2.3896  0.00 2646 41  8  2.3896 20000 .6915  7  7  5.0 1 18
1 2149 0 3 45  8  1.2564  2.50 1640 48  9  4.5122 12260 .7515  7  7  5.0 1  3
1  320 0 0 50 11  1.0938  0.00 1950 54 11  9.2308 24850 .6615  3 12  7.5 1 11
1 1600 0 1 40 12  3.7500  3.30 1920 39 12 11.4580 29150 .5815 12  7  7.5 1  8
1 2419 0 1 30 10  3.3072  3.90 2025 34 12  7.6993 23591 .6615  7  7 11.0 1 10
1 2005 0 0 57 17  5.1352  5.25 2470 56 17  4.1830 24717 .6615 16 12 11.0 1 33
1 1960 0 1 39 12  6.6327  3.60 1800 43 12  8.3333 30455 .6215 12 12  9.0 1 19
1 2147 0 0 53 12  4.5645  4.90 1920 56  8  5.1042 19600 .6915 12 12  7.5 1 35
1 1207 0 1 48 17 11.8480  7.15 2039 53 17  8.2271 31875 .6400  7 12  5.0 1 21
1 2000 0 1 46 14  3.7500  3.75 2570 48 16  5.6634 24055 .6615 14 14  7.5 0  7
1 1260 0 0 47 12  4.3651  4.35 1914 54 12  5.2220 18795 .7215  7 10  7.5 0 18
1   90 0 1 43 12  3.9333  4.00 1516 47 10  7.1900 12198 .7515  7  7  7.5 0  4
1 1800 0 0 47 12  3.3333  3.25 2520 47 16 13.9070 52645 .4915 12  7  7.5 1 12
1  573 0 1 47 12  3.3159  2.20 2327 48 12  6.0163 16600 .7215 10  7 14.0 0 16
1 1825 0 0 47 12  3.5616  3.00 2188 50 12  7.6782 32590 .6215  7  7  7.5 1 14
1   75 0 0 46 12  1.6000  0.00 1864 48 12  5.3112 10020 .7515  3  7  7.5 1  3
1 1348 0 4 34  9  2.2255  2.30 2183 33 10  4.1228 12048 .7515  7  7 11.0 0  1
1 1880 0 0 48 10  4.7872  4.25 1920 55 12  7.8125 39750 .6215  7  7 11.0 0 27
1 1240 0 1 30 12  5.8065  6.90 1824 31 12  4.6053 15700 .7215 10  7  7.5 1 12
1  848 0 1 51 12  2.3585  2.30 2878 54 12  3.9746 24250 .6615  7  7  3.0 0  6
1  150 0 5 52 12  2.0000  0.00 2390 54 16 15.0630 43210 .5215  7 12 14.0 1  9
1 2000 0 2 37 12  1.9000  1.85 3120 39 13  4.5064 37100 .6215 12 12  5.0 0  2
1 1952 0 2 32 12  5.1230  3.25 2040 33 12  5.8824 23820 .6615 12  7  5.0 0  6
1 1456 0 2 36 17  5.4945  6.04 2151 35 15 10.2280 31600 .5815 12 14  5.0 1  9
1 1740 0 2 35 12  6.3218  5.50 1976 37 14  6.5789 24000 .6615 10 10  7.5 1 16
1 1400 0 0 45 17  7.1429  7.14 2286 51 16  8.8145 30750 .5815 14 12  5.0 0 22
1 2000 0 0 56 12  2.3750  2.70 2032 60 10  2.9528 11050 .7515  7  7 14.0 0 26
1 1750 0 2 40 10  2.5429  2.74 1680 45  4  4.5173 12239 .7515  7  7 14.0 0 11
1 1101 1 2 45 12  2.1798  2.30 1560 49 14  5.1282 12870 .7515 14 12  7.5 1 11
1 2000 0 2 32 12  2.6000  2.50 2895 30 12  4.1451 17200 .7215 10  7  7.5 0 15
1 1877 0 0 45 12  3.7294  3.60 1820 50  8  8.7912 23980 .6615 10 10  7.5 0 13
1  160 0 2 40 12  4.3750  1.85 2450 44 12  7.3061 18600 .6915  7 12 14.0 1  6
1 1886 0 1 38 12  4.4433  4.00 1748 42  8  6.0069 23920 .6915  7 10  9.5 1 20
1 1446 0 4 49 12  4.2877  4.40 1020 45 12  8.3333 16084 .7515  7  7 14.0 1 17
1 1500 0 1 47 16  1.6667  1.50 2342 49 17 11.5290 31100 .5815 14 14 11.0 1  8
1  860 0 0 52 13  3.2558  5.83 2250 53 12  6.6667 20460 .6615  7  7 11.0 1 13
1 1848 0 1 34 13  5.4113  6.00 2880 40 16  8.6806 36000 .5515 12 12  7.5 1 15
1 1678 0 2 44 12  2.2050  2.30 2032 46 12  3.4680 17302 .7215 14 12  3.0 0 14
1  160 0 3 36 16  4.0625  0.00 3120 42 16  3.0321 16450 .7215 14  7  3.0 0 14
1  108 0 0 50 17  0.6482  0.00 1760 57 16 13.8070 41170 .5815 14 16  9.5 1  6
1 1738 0 0 45 12  5.3826  6.18 1725 47 12  6.2174 20130 .6615  0  0  7.5 1 24
1 1170 0 2 44 14  0.1709  0.00 2080 46 13  4.2308  9200 .7515 16 12  9.5 1 10
1   15 0 2 57 12 23.4670  0.00 2040 57 10 11.4700 24751 .6615  7  7 11.0 1  2
1 2088 0 0 35 17  9.5785  9.98 2940 42 17 12.2450 57300 .5000 12 17  9.5 1  9
1 2490 0 0 46 12  3.6948  3.77 2280 52 12  9.2105 37200 .5815  7  7  7.5 1 23
1  135 2 1 30 14  2.2222  0.00 2164 35 16  6.3309 14000 .7215 10 12 14.0 1 12
1 1944 0 3 42 12  1.7490  2.30 1999 44 12  7.8039 20610 .6915  7  3 14.0 0  8
1  690 0 1 34 12  1.1594  2.25 1824 36 13  7.6754 14800 .7215 10  7  7.5 1 16
1  608 0 2 45 17  6.9901  3.00 2182 47 16 15.5820 40005 .5515 10 14 14.0 1 10
1   63 1 2 35 16  3.9683  0.00 2385 37 16  9.6436 23750 .6615 14  7 14.0 1  7
1  154 0 0 40 16 21.4290  8.13 2460 44 17 12.8860 35300 .5515  7 12 14.0 1 19
1  420 0 1 32 12  0.4762  2.85 2595 35 16  6.5511 17350 .6915 12 12  7.5 1  2
1  651 0 0 54  9  2.1505  1.44 2400 57 10  8.2500 21650 .6615  7  7  7.5 1  9
1  675 0 3 38 12  1.8578  2.20 3120 42  8  1.3792  6740 .7915  7  7 14.0 0 14
1 1663 0 3 43 12  4.3295  3.60 2850 42 12  5.2632 32275 .6915 12 14  5.0 1  9
1 1680 0 0 54 16  8.9286  7.00  760 60 12 10.5260 33220 .7200 14  7  9.5 1 16
1  180 0 3 39 14  2.7778  4.00 2500 37 17 10.0000 26500 .6215 12 12  7.5 1  7
1 1581 0 1 37 12  2.6565  3.25 2630 39 14 12.5480 38700 .5215  7 12  5.0 1  6
1 1200 0 2 46 12  2.5000  3.08 2597 48  8  4.6207 15400 .7215  7  7  5.0 1 22
1  450 0 0 56 11 18.2670  0.00 2760 60 11  1.8540 19007 .6915  7  7  3.0 0  9
1  547 0 3 41 12  0.8190  2.00 2070 44  8  7.4266 16771 .7215 12  7  7.5 0  9
1  300 0 1 45 16  2.0000  0.00 2256 48 16 13.2980 31100 .5815 16  7 11.0 1 14
1  975 0 1 44 17 15.3850  8.50 1505 47 16 26.5780 66300 .5000  3  3  7.5 1 17
1 1621 0 1 50 17  6.4775  0.00 2364 52 17 13.9590 43550 .4915 16 12  5.0 0 12
1  300 0 5 37 14  8.3333  3.50 2895 38 14 13.1260 37250 .6215  7  7 11.0 0 13
1 1868 0 1 44 12  4.5503  4.25 2041 46 12  7.8883 24900 .6615 16  7 14.0 0  8
1 1803 0 2 32 14  2.4958  1.90 2195 34 17  8.6560 24200 .6615  7 14  9.5 1 10
1 2143 1 1 34 12  4.4797  4.80 1935 40 12  3.4109 16200 .7215 10 10 14.0 0 16
1 1080 0 2 32 10  2.2324  2.30 1950 35 10  4.6256 11431 .7515 10 10  7.5 0  1
1 1352 0 3 37 12  2.0710  1.80 2375 38 14  4.2105 13200 .7515 10 10 11.0 0  6
1  537 0 1 44 13  1.6760  0.00 1920 55  8  4.2708 15420 .7715 10 10  9.0 1  4
1  352 0 2 34 16  3.4091  0.00 3300 33 12  3.3424 18400 .6915 12 12 14.0 0  8
1  200 1 3 33 12  2.5000  8.00 3680 33 16  8.6359 43500 .4915 10  3  5.0 1  4
1 2045 0 3 43  7  3.9609  4.07 1968 43 12  6.7581 21972 .6915  7  7  7.5 1 15
1 1253 0 2 35 16  6.2275  3.97 2504 33 10  0.5843  7774 .7715 16 16 11.0 0  7
1 1960 0 1 43 14  3.9286  3.85 2000 45 14  5.3350 24470 .6915  7  7  7.5 0 14
1 2000 0 0 34 12  2.9000  2.50 1656 37 12  4.7101 13600 .7215  7  7  7.5 0 16
1 1960 0 3 36 10  4.0816  4.55 1968 39  7  4.9797 22500 .7215  7  0  7.5 0 15
1 2000 0 2 41 12  2.8500  4.20 2016 41 12  2.9762 13600 .7215  7  7 14.0 0 23
1 1568 0 0 41 16  7.0153  6.31 2602 44 17 12.7440 90800 .4415  7  7  7.5 0 19
1 1225 0 3 35 10  2.9388  2.40 1560 43  9  3.8462 10776 .7515 10 10  7.5 0  4
1  780 1 3 32 12  1.9231  3.25 1827 37 10  7.2233 19007 .7515 10  7  5.0 1 12
1  480 0 0 30 14  6.8750  0.00 2080 34 14  8.8077 23900 .6615 12 12 14.0 1 12
1 1923 0 0 43 12  3.9002  4.74 3390 47 12  5.3864 26060 .6215  7  7  7.5 1 25
1 2000 0 0 54  6  2.0000  0.00 2524 57  6  3.6846 13300 .7215  7  7  7.5 0 14
1 2110 0 2 35 15  4.9763  4.37 2777 34 12  1.8437 15620 .7215  7  7  7.5 0 14
1 1664 0 0 50 12  1.2019  5.00 3120 54 13  1.3013 16500 .7215  7  7  7.5 0 11
1   48 1 1 34 17 22.5000  0.00 2700 36 17  7.2222 20880 .6915 14 16  5.0 1  7
1 1791 0 0 52 14  6.8677  6.18 1904 57 12  7.3529 30600 .6615 14 12  9.5 1 18
1 1404 0 3 35 13  3.5613  5.30 2360 38 14 11.8640 39000 .6215  7 10  9.0 1  4
1 1920 0 0 55  6  1.9792  2.58 1960 58  8  5.3327 15428 .7215  7  7  7.5 0 37
1 2141 0 0 35 16  5.3713  6.00 2000 42 16  5.5000 23300 .6615  7  7  7.5 0 13
1 1720 0 1 49 14  1.7442  0.00 2600 45 16  7.2308 42100 .5215 16 16  9.5 1 14
1 3533 2 2 38 15  5.0948  8.50 2000 38  9  7.0000 36430 .6400 12  7  9.5 1 17
1 2000 0 2 42 14  2.5000  0.00 2218 45 14  7.2137 26000 .6915  7  7  9.5 1  5
1  800 0 1 48  8  3.8250  2.30 2000 52  5  4.5000 62060 .7515  7  7  7.5 0  2
1 3000 0 0 51 14  1.0000  0.00 2595 53 16  8.8632 28300 .6215 12 12  9.5 1  0
1  293 0 2 43 12  3.0717  4.00 2400 47 12  9.3333 24149 .6615 12 10  7.5 1  3
1 1872 0 1 43 12  1.7163  0.00 2856 48 12  3.8263 28141 .6615 12 10  7.5 1 21
1 2058 0 1 38 12  4.0209  4.00 2601 38 14  5.4448 23057 .6615 10 10  7.5 1 20
1 1832 0 1 44 12  5.4585  4.95 2054 48  9  8.7634 28900 .6215  3  7  7.5 1 19
1  120 1 3 36 12 25.0000  9.98 2500 35 12  8.4000 24000 .6615 12 10  9.5 1  4
1 1632 0 0 38 12  2.3897  2.30 1960 31 12  5.1020 13900 .7215 12 12  7.5 0 19
1  778 0 0 47  8  3.2134  7.25 2058 51  8  7.4101 31810 .6915 12 12  5.0 1 11
1 1984 0 2 34 12  3.3770  3.14 2410 49 10  5.3527 19840 .6915  7  7  7.5 0 14
1  225 1 2 40 17  1.7778  0.00 1278 38 17 19.5620 25490 .6615 16 17 14.0 1  8
1 1960 0 1 31 12  3.1633  3.18 2875 35 12  5.0783 20800 .6915 12 12  7.5 0 13
1  444 0 0 46 12  2.7027  0.00 2340 49 12  0.5128  2400 .8015 10 16  7.5 1 24
1  384 0 3 36 14  1.6927  0.00 3060 43 17  5.4020 32650 .5815 10 10 14.0 1  1
1 1170 1 2 39 13  0.2137  0.00 1920 47 12  7.8646 16370 .7215 12 16 11.0 1  1
1 1330 0 2 36 17  6.7669  4.50 3390 38 12  6.0531 35500 .5515  7  7 14.0 0  3
1 1350 0 4 37  8  1.7407  2.10 2400 41 12  5.0000 15100 .7515  7  7  3.0 0  4
1  480 0 4 39 12  2.5000  0.00 1640 40 11  7.6829 14100 .7515  7  9  3.0 0 21
1 1984 1 3 36 11  4.4859  3.26 1656 38  8  6.0386 19600 .7215  7  3 14.0 0 10
1 1944 0 2 49 12  2.5720  2.70 1920 53 16  5.8510 19434 .7215  7  7  5.0 1 13
1   50 1 1 45 12  3.4600  5.00 1780 46 10  6.7416 23882 .7215  7  7  9.5 1  9
1  460 2 0 32 17  4.7826  0.00 1850 31 17  8.1081 17300 .7215  7  7  7.5 0 14
1  680 0 5 36 10  2.3118  0.00 3430 43 12  5.3061 19772 .7215  7  7  7.5 0  2
1 2450 0 1 40 12  5.3061  6.50 2008 40  8  7.2709 35641 .6215  7  7  5.0 1 21
1 2144 0 2 43 13  5.8675  0.00 2140 43 11  8.1776 34220 .5815  7  7  7.5 1 22
1 1760 0 1 33 12  3.4091  3.21 3380 34 12  7.1006 30000 .5815 12 16 11.0 1 14
1  490 0 1 30 12  4.0816  2.46 2430 33 11  6.5844 18000 .6915 12 12  7.5 1  7
0  0  0  1 49 12  0.0000  0.00 2550 54 15  7.8529 21025 .6615 14 12  7.5 1  2
0  0  2  0 30 16  0.0000  0.00 1928 34 16 11.9290 23600 .6615 14  7  9.5 1  5
0  0  1  0 30 12  0.0000  0.00 1100 39 17 18.0000 22800 .6615 12 12  7.5 0 12
0  0  0  4 41 12  0.0000  0.00 3193 40 16 10.0220 35910 .5815  7  7  7.5 1  1
0  0  0  1 45 12  0.0000  0.00 2250 46 16  9.3333 21700 .6615  7  7  5.0 1 12
0  0  0  5 43 12  0.0000  0.00 2012 44 13  6.0850 21823 .7515  7  7  7.5 1  4
0  0  0  1 42 13  0.0000  0.00 3856 46 15  5.7054 31000 .6615 10  7 11.0 1  9
0  0  0  0 60 12  0.0000  0.00 1645 58 12  9.1185 15300 .7215  7  7  7.5 1  9
0  0  0  0 57 12  0.0000  0.00 1554 57 12  7.2072 12925 .7215  9  3  7.5 1  6
0  0  0  2 38 10  0.0000  0.00 2352 41  8  5.3146 15830 .7515 12  7  5.0 0  5
0  0  0  0 56 12  0.0000  0.00 1980 58 12  8.2828 30200 .6915 12 12  7.5 1  5
0  0  0  3 32 12  0.0000  0.00 2352 37  7  7.0578 16600 .7215 10  7  5.0 0  8
0  0  0  1 49  7  0.0000  0.00 1784 58  6  6.1659 11000 .7515  7  7  7.5 1  2
0  0  0  0 55 12  0.0000  0.00 2500 58 12  2.7000 15000 .7215  7 10  3.0 0  6
0  0  1  1 36  9  0.0000  0.00 2088 39 14  7.6628 20528 .7215  7  7 11.0 0  0
0  0  0  3 44 12  0.0000  0.00 4640 50 12  1.8491 13126 .7515  9  9 14.0 0  3
0  0  0  1 44 10  0.0000  0.00 3900 60 12  3.8462 15550 .7215  7 14  7.5 1  7
0  0  1  2 35 14  0.0000  0.00 1988 34 17  9.0543 18010 .7215  3 12  7.5 1  3
0  0  2  3 44 14  0.0000  0.00 1920 45 10  9.3750 18874 .7215 10 10 14.0 0 10
0  0  0  1 45 12  0.0000  0.00 2400 45 12  8.3333 24800 .6615 12 12 14.0 1  3
0  0  1  0 34 12  0.0000  0.00 1867 38 12  9.3733 17500 .6915 12 17  5.0 1  2
0  0  2  0 30 17  0.0000  0.00 3570 32 17  4.4818 16150 .7215 12 12  7.5 1 12
0  0  0  1 39  8  0.0000  0.00 2805 44 12  5.3476 15189 .7215  7  3  3.0 0 15
0  0  0  2 36 12  0.0000  0.00 1110 39 15  3.2027  6000 .7815  7  7 14.0 0  5
0  0  0  2 38 17  0.0000  0.00 2695 42 16 12.8010 37250 .5515 10 12  9.5 1  4
0  0  0  0 53 12  0.0000  0.00 1950 54 16  6.9103 27760 .6215 10 10  7.5 1 10
0  0  0  2 36 12  0.0000  0.00 2128 42 12  4.2293  9090 .7715  7  7  3.0 0  1
0  0  1  1 32 12  0.0000  0.00 3260 31 12  4.4479 14500 .7215 12  7  7.5 1  8
0  0  0  3 51  9  0.0000  0.00 1987 51 12  8.0523 19700 .7215  7  7 14.0 1 20
0  0  0  0 38 11  0.0000  0.00 2185 46 11  7.5057 16788 .6915 10  7 14.0 1  4
0  0  2  0 33 12  0.0000  0.00 2475 36 12  7.4747 18520 .6915 10 10 11.0 1  7
0  0  0  0 54 12  0.0000  0.00 2610 53 12  6.3218 20950 .6915 16 10  9.5 1 10
0  0  0  3 38  9  0.0000  0.00 1920 44 12  2.1354  7574 .8015  7  3 11.0 0  3
0  0  2  2 30 11  0.0000  0.00 2352 31 14  4.2092 10027 .7715  7  7  3.0 0  5
0  0  2  3 34 12  0.0000  0.00 3160 30 12  0.7595  5000 .9415 12 12  7.5 0 10
0  0  0  1 34  9  0.0000  0.00 1040 37 13  4.8077  7040 .7915 12  7  3.0 0  0
0  0  0  2 50 12  0.0000  0.00 3120 49 12 12.7880 40800 .5215 10  7  7.5 1  3
0  0  2  0 30 17  0.0000  0.00 2240 30 16  7.1429 16050 .7215 12 12 11.0 0 10
0  0  0  2 38 12  0.0000  0.00 1980 42 16 15.1520 33100 .5815 10  7 11.0 1  2
0  0  0  0 54 14  0.0000  0.00 1960 58 14  7.9082 33856 .7215 12 12  9.5 1 10
0  0  1  2 30 12  0.0000  3.00 2940 31 17  6.9728 20500 .6915 12 12  7.5 1  4
0  0  0  0 55 12  0.0000  0.00 2467 56 11  4.9181 28600 .5815  7  7  5.0 1  0
0  0  0  1 51 10  0.0000  0.00 2256 56 12  8.3112 18750 .6915 10 10 11.0 0 10
0  0  0  1 44 12  0.0000  0.00 1680 46 12  7.1429 20300 .7215  7  7  9.5 1  5
0  0  0  0 53 12  0.0000  0.00 2250 55 12  5.6889 13420 .7215  7  7  5.0 0  0
0  0  0  2 42 10  0.0000  0.00 2400 49  9  7.0833 18400 .7215  3  3  5.0 0  0
0  0  0  2 38 12  0.0000  0.00 2196 42 11  5.6922 16682 .7215 10  7  7.5 0 19
0  0  1  3 38 13  0.0000  0.00 2400 40 12 11.4000 32685 .6215  7  7  7.5 1  2
0  0  1  4 41 12  0.0000  0.00 3825 41 11  1.4152  7050 .8015  3  3  9.5 1 12
0  0  0  3 35  8  0.0000  0.00 2860 44  9  2.7507 10867 .7815 12  7  9.5 1  5
0  0  1  2 33 12  0.0000  2.75 2750 34 12  6.6182 18220 .7215 12 12  9.5 1  5
0  0  0  0 48 13  0.0000  0.00 2103 50 16  9.2725 26613 .6915  7  7  7.5 0  5
0  0  0  0 47 12  0.0000  0.00 1880 51 12 12.2870 25000 .6215 12 10  7.5 1 10
0  0  0  5 34 12  0.0000  0.00 3185 41 13  2.8549 15700 .7515  7  7  7.5 1  0
0  0  2  1 33 13  0.0000  0.00 2677 37 17  7.9709 40250 .5215 12 10  5.0 1  4
0  0  3  1 31 13  0.0000  0.00 3600 36 17 19.4440 73600 .4415 12 16 11.0 0  3
0  0  0  0 58  8  0.0000  0.00 4334 58  8  1.4806 10592 .7515 12  7  7.5 1  2
0  0  0  0 49 12  0.0000  0.00 2874 52  8  1.8918  8000 .7515  7  7  3.0 0  1
0  0  0  1 55  8  0.0000  0.00 1936 56  9  6.9215 13400 .7215  7  3  7.5 1  0
0  0  0  0 44 14  0.0000  1.50 1964 49  8 10.6920 23700 .6615 12 12 14.0 1  1
0  0  0  0 44  9  0.0000  0.00 1900 48  8  9.9474 18900 .6915  7  7 11.0 1  1
0  0  0  3 36 16  0.0000  0.00 2500 37 17 19.0000 48300 .4615  7 12  9.5 1  6
0  0  0  3 38 12  0.0000  0.00 3173 46 14  7.4882 24470 .6615 14 14  9.5 1 12
0  0  0  3 37 16  0.0000  0.00 2916 38 17  9.2590 28630 .6215 16  7  7.5 1  6
0  0  0  0 47 12  0.0000  0.00 2208 51 12 11.3220 25320 .6215 12  7  5.0 1  9
0  0  0  3 47 12  0.0000  0.00 2094 47 10  6.4470 13530 .7515 12 10  7.5 1 14
0  0  1  1 32 12  0.0000  0.00 2250 33 12  6.5778 14800 .7215  7  7  9.0 1 13
0  0  1  2 43 12  0.0000  0.00 2000 46 12  6.1000 17400 .7515 12  7  7.5 0  8
0  0  1  4 42 11  0.0000  0.00 2600 48 10  4.2308 15980 .7815 10 10  3.0 0  0
0  0  0  0 56 12  0.0000  0.00 4368 57  8  2.2170 16576 .7215  7  7  7.5 0  1
0  0  0  5 38 13  0.0000  2.25 3068 40 16  6.5189 21850 .6915 12  7 11.0 1  3
0  0  0  2 52 12  0.0000  0.00 2218 51 11  6.4923 14600 .7215  7  7 14.0 1 13
0  0  0  0 50 12  0.0000  0.00 1848 56 12 11.3640 21600 .6615 12 12  7.5 1  3
0  0  0  0 33 16  0.0000  0.00 2430 33 17  9.8765 24000 .6615 12 12  7.5 1  8
0  0  0  2 44 16  0.0000  0.00 2640 44 17  7.6576 20883 .6915  7  7  7.5 1  8
0  0  0  1 41 12  0.0000  0.00 2108 42 16  8.3017 19500 .6915  7  7 14.0 0 18
0  0  0  1 45 12  0.0000  0.00 1998 45 12 14.1140 42800 .6215 14 12 11.0 1  2
0  0  0  0 53 14  0.0000  0.00 2500 55 16 16.0000 41500 .5215  7  7  7.5 0  3
0  0  0  0 53 14  0.0000  0.00 1665 56 17 11.2910 18965 .6915 12 12 14.0 1  5
0  0  0  1 42 12  0.0000  0.00 2990 46 12  2.3395 16100 .7215 12 10  9.5 1  2
0  0  2  0 32 13  0.0000  0.00 1795 35 16  7.7994 14700 .7215 12 17  7.5 1 10
0  0  0  0 56 12  0.0000  0.00 2500 53 12  6.0000 18800 .7215  7  7  7.5 1 30
0  0  1  3 37 11  0.0000  0.00 2205 40 11  6.6893 14750 .7515 10  7 11.0 1  1
0  0  1  2 40 12  0.0000  0.00 2460 42 14  8.5366 21000 .6915 12  7 14.0 1  5
0  0  0  3 54 15  0.0000  0.00 1880 55 16 13.8300 35400 .6215  0  7  7.5 1  8
0  0  0  0 53  7  0.0000  0.00 3481 53  9  1.4800 10700 .7515  7  7  7.5 0  0
0  0  0  1 48 12  0.0000  0.00 2450 51 12  8.5714 24500 .6615  7  7  9.5 1  4
0  0  1  2 36 12  0.0000  0.00 2062 38 14  8.2299 17045 .7215  7  7  9.5 1  2
0  0  0  0 57 12  0.0000  0.00 2146 52 14  8.3877 18800 .6915  7  7  7.5 1 30
0  0  0  0 51 12  0.0000  0.00 1575 49  7  7.3651 14000 .7215 10  7 14.0 1 25
0  0  0  4 33 13  0.0000  0.00 3096 37 12  3.4415 18214 .7215  7  0  3.0 0  3
0  0  0  0 52 12  0.0000  0.00 3280 49 11  3.3537 20177 .7515  7  7  7.5 1 20
0  0  0  0 56 10  0.0000  0.00 1680 60  8  2.9762  8300 .7815  0  7  7.5 1 20
0  0  1  2 36 12  0.0000  0.00 2625 38 11  5.1810 14200 .7515 14  9  7.5 1  0
0  0  1  0 36 14  0.0000  0.00 1846 50 16 10.2930 21768 .6915 12 12  7.5 0 15
0  0  0  1 46 12  0.0000  0.00 2178 47 10 13.2430 29553 .5815 10  7 14.0 1 10
0  0  0  3 31 10  0.0000  0.00  960 33  9  3.6458  4350 .9415  7  7  7.5 0  4
0  0  0  0 52 11  0.0000  0.00 2210 51 12 10.4070 24000 .6615  7  7 11.0 1  3
0  0  0  2 46 12  0.0000  0.00 2192 55 12  8.2117 18300 .6915  7  7  7.5 1 10
0  0  2  0 35 12  0.0000  0.00 1960 44 16  8.6735 17200 .7215  7  3  7.5 1  9
0  0  0  0 59 12  0.0000  0.00 1920 56 10  8.3208 16476 .6915  7  7 14.0 0  7
0  0  0  1 36  8  0.0000  0.00 2286 40 12  4.2870 13400 .7515  0  0 14.0 0 12
0  0  1  3 51  7  0.0000  0.00 2000 52  7 10.5000 44988 .5215  3  3 14.0 0  0
0  0  1  0 31 16  0.0000  0.00 2256 31 12  7.9787 18200 .6915 12 12  9.0 1 16
0  0  0  2 31 14  0.0000  0.00 2370 36 17 11.8140 28000 .6215 12 12 14.0 1  4
0  0  1  1 32 12  0.0000  0.00 1800 39 13  6.1111 11550 .7515 12 12  7.5 1  7
0  0  1  2 35 16  0.0000  0.00 2250 38 16 12.5780 28450 .6215 12  7 14.0 1  7
0  0  0  3 40 12  0.0000  4.10 1080 43 12 11.2440 15096 .7515  7 10  7.5 1 14
0  0  1  2 33 10  0.0000  0.00 2840 38 12  2.7408  8009 .7815  7  7 14.0 0  2
0  0  0  0 54  7  0.0000  0.00 2250 52 11  4.4444 10040 .7515  0  0  3.0 1 20
0  0  1  1 36 12  0.0000  0.00 2746 37 12  5.8267 16700 .7215 12 12  7.5 1  5
0  0  0  1 50 10  0.0000  0.00 2300 60  8  2.3478  8400 .7815 12  7  3.0 0 10
0  0  0  0 54  8  0.0000  0.00 2860 49  8  4.4755 13000 .7215  0  0  3.0 0 20
0  0  0  1 48 11  0.0000  0.00 1765 49 12  8.4986 17970 .7215  7  7  7.5 1 10
0  0  0  4 41 15  0.0000  0.00 2520 42 16  7.1825 18450 .7215 14 17  5.0 0  8
0  0  0  4 50 12  0.0000  0.00 2208 53 12 10.8700 31000 .6615 12  7 14.0 1 11
0  0  0  2 46 12  0.0000  0.00 2119 51  8  7.1222 24135 .7215 10  7  7.5 1  3
0  0  0  1 42 13  0.0000  0.00 2580 47 17 10.6592 31700 .5815 12 12  7.5 0  6
0  0  1  2 31  9  0.0000  0.00 1984 34 12  3.2762 10190 .7915  3  3 14.0 0  4
0  0  0  0 53 12  0.0000  0.00 1880 58  8  7.7521 21574 .7215 10 10 14.0 0  4
0  0  0  1 51 12  0.0000  0.00 2185 57 12 11.9450 26680 .6215  3  3  7.5 1  9
0  0  0  1 47 12  0.0000  0.00 2080 57 12  4.6154 17700 .7515  7  9 11.0 1 10
0  0  0  1 50 12  0.0000  0.00 1920 50 12 13.0210 29400 .6215 12 12 14.0 1  3
0  0  0  1 37  6  0.0000  0.00 3000 52  5  2.6667 22159 .7515  7  7  7.5 0  2
0  0  2  2 30 12  0.0000  0.00 2100 31 12  8.8333 35000 .5815 12 12 11.0 0  2
0  0  0  0 49 12  0.0000  0.00 1690 39 12  2.3669  8630 .7915 16 16  5.0 1  0
0  0  0  2 52 12  0.0000  0.00 2600 49 16  5.0000 17080 .7515  7  0 14.0 1  8
0  0  0  2 47 12  0.0000  0.00 1984 49 16  7.4597 32500 .7215 10  7 14.0 1  6
0  0  0  0 49 12  0.0000  0.00 2064 53 12  7.7519 16000 .7215  7  7 11.0 1 15
0  0  0  4 44 12  0.0000  0.00 2553 31 16  5.4054 18850 .7515 12 10 14.0 1 15
0  0  0  0 53  8  0.0000  0.00 2776 59  9  6.1239 17500 .6915  9  9  9.5 1  9
0  0  1  0 30 12  0.0000  0.00 2315 31 13  8.3369 19392 .6915  7 12 14.0 0  8
0  0  0  2 54 12  0.0000  0.00 1880 55 12  7.1277 14450 .7215  7 10  7.5 1 18
0  0  1  1 47  7  0.0000  0.00 2160 51  7  6.1204 21800 .6915  0  0  7.5 1  3
0  0  0  0 56 15  0.0000  0.00  900 56 12  3.1111  7700 .7515  7  7 14.0 1 10
0  0  0  1 49 12  0.0000  0.00 2467 52 16 12.1610 31800 .5815  7  7 11.0 0  6
0  0  0  0 48  6  0.0000  0.00 1820 55 12  5.3846 17258 .7515  7  7  9.5 1 20
0  0  0  1 49 12  0.0000  0.00 2223 53 10  3.9838 13399 .7515 10 12  9.5 0  8
0  0  0  1 56 12  0.0000  0.00 2142 60 12  7.4697 16073 .7215 12 16 11.0 0  3
0  0  0  0 46 12  0.0000  0.00 1928 46 11 11.4110 23260 .6615  7  7  7.5 1  4
0  0  0  2 45 12  0.0000  0.00 2783 49 17 12.9360 37300 .5515 12 12 14.0 1 13
0  0  0  2 32 12  0.0000  0.00 1960 35 12  5.6122 11000 .7515 12  7 11.0 1  4
0  0  1  1 43 12  0.0000  2.70 1920 41 12  6.8099 13075 .7515  7  7 14.0 1 17
0  0  1  1 34 12  0.0000  0.00 1587 39 12  8.5066 13700 .7215  7  7  9.5 1  4
0  0  1  1 30 12  0.0000  0.00 2496 51 10  5.5080 25100 .6615  7 10  5.0 0  0
0  0  2  0 38 17  0.0000  4.80 2280 39 12  7.2285 18600 .6915 12 16  5.0 1 15
0  0  1  1 33 16  0.0000  0.00 2750 36 17  9.4545 29000 .6215 16 16  9.5 0 11
0  0  0  0 52 12  0.0000  0.00 2115 55 12  8.9835 19237 .6915  7  7  9.5 1 23
0  0  0  3 43 11  0.0000  0.00 2590 45 12  5.9846 19855 .7215 12 14  7.5 1  1
0  0  1  1 33 12  0.0000  0.00 2372 34 12  3.9629  9450 .7515 12  7  9.5 0  5
0  0  0  0 45 10  0.0000  0.00 2295 48 12  7.0575 30000 .5815  7  7  7.5 0  1
0  0  2  1 36 10  0.0000  0.00 2096 38 12  7.1565 15000 .7215 10 10 14.0 1  5
0  0  1  1 34 12  0.0000  0.00 3315 39 17  4.0145 24701 .6615 12 12  9.5 1  3
0  0  0  2 37 14  0.0000  0.00 1777 50 16  3.8829 15900 .7215 10 14 11.0 0  3
0  0  0  1 46 10  0.0000  0.00 1880 51 12  7.9787 16240 .7215  7  7 11.0 0 19
0  0  0  0 47 12  0.0000  0.00 2184 55 10  5.0366 21100 .7515 12 12  9.5 1 20
0  0  2  1 31 16  0.0000  0.00 3250 32 16  7.0769 23000 .6615 12 12  7.5 1  5
0  0  0  0 57  5  0.0000  0.00 1520 58  5  3.6184  6340 .7715  7  7 14.0 0  0
0  0  1  1 30 12  0.0000  0.00 3119 30 13 13.4660 42250 .4915 10 10  5.0 1  3
0  0  0  0 30 12  0.0000  0.00  640 43 17 14.5310 14694 .7215 12 10 11.0 1  3
0  0  0  3 44 12  0.0000  0.00 2250 45 12  6.8000 21417 .7215 12 12  9.5 1  7
0  0  0  0 53 13  0.0000  0.00 3000 53 13  6.6667 20200 .6615  7 12  7.5 1  7
0  0  0  0 51  8  0.0000  0.00 2028 54  8  5.9172 12090 .7215  7  7  9.5 1  1
0  0  1  3 39 12  0.0000  0.00 2412 36 14 10.2400 24760 .6615 12  7  5.0 1 13
0  0  0  0 52  8  0.0000  0.00 2452 54 12  8.1566 23000 .6915  7  3  3.0 0  0
0  0  0  4 46  8  0.0000  0.00 2304 50 12  6.6775 19365 .7215  3  3 11.0 1  0
0  0  0  5 47 12  0.0000  0.00 3120 49 12  0.9615  5550 .9415  7  7  3.0 0 12
0  0  0  2 52  8  0.0000  0.00 1670 54  8 16.9070 68035 .4415  7  3  7.5 1  0
0  0  0  2 45 12  0.0000  0.00 2137 46 15 13.5700 29300 .6215 10 14  7.5 1  5
0  0  0  0 60 11  0.0000  0.00 2071 52 11  8.9329 18500 .6915  7  7  7.5 1 45
0  0  0  2 41 13  0.0000  0.00 1960 54  7  4.7372 22582 .7215 17  7 11.0 0 10
0  0  0  3 39  8  0.0000  0.00 2068 45 12  8.5106 21500 .7215  7  7  7.5 1  2
0  0  0  1 49 12  0.0000  0.00 2190 51 12  5.2511 28070 .7515  7  7  7.5 0  3
0  0  1  1 32 15  0.0000  0.00 2295 37 13 21.7860 50300 .4415 12 12 14.0 1  1
0  0  1  3 33 12  0.0000  0.00 2970 34 13  7.9125 23500 .6615 12 12 14.0 1  5
0  0  0  4 36 10  0.0000  0.00 2068 37  8  7.1083 15500 .7515  7  9 14.0 0 10
0  0  3  3 37 13  0.0000  0.00 2419 39 14  5.0434 13440 .7715  7  0  5.0 0  4
0  0  1  2 30 12  0.0000  0.00 2150 34 11  2.2442  8100 .7815 12 12 11.0 0  7
0  0  1  1 44 11  0.0000  0.00 1152 37 10  8.5069  9800 .7515  7 12  9.5 1  9
0  0  0  1 48 12  0.0000  0.00 2640 49 12  7.5758 20300 .6915  7 12  5.0 1  5
0  0  0  4 40 11  0.0000  0.00 2550 45 11  5.8824 15000 .7515  7  7 14.0 1  4
0  0  0  0 47 13  0.0000  0.00 1360 49 16 40.4410 56100 .4415  9  9  5.0 1 11
0  0  0  2 36 12  0.0000  0.00 2420 40 12  6.2339 22846 .7215 12  7  5.0 1  9
0  0  0  2 40 11  0.0000  0.00 2205 42 14  9.2971 22225 .6915  7 12  5.0 1  4
0  0  0  1 46 12  0.0000  0.00 3268 46 12  0.7038 17635 .9415 12  7  7.5 1  2
0  0  0  0 52 12  0.0000  0.00 3672 54 12  2.5425 18500 .6915  3 12  7.5 0 23
0  0  0  1 44 12  0.0000  0.00 1800 45 12  5.0833 13390 .7515 12 12 11.0 0  3
0  0  0  1 45 10  0.0000  0.00 1926 46 14  7.6843 15150 .7215  7  7  7.5 1 15
0  0  2  1 30  7  0.0000  0.00 1920 35  7  4.0625 16200 .7815  7  3  7.5 0  8
0  0  1  3 40 12  0.0000  0.00 2080 44 12  6.5106 33920 .6615 12 12 14.0 1  3
0  0  0  1 43 12  0.0000  0.00 2856 43 12  2.9510 14000 .7215  7 12  7.5 0 25
0  0  0  2 49 12  0.0000  0.00 2115 53 10  5.6738 16736 .7515 12  3 11.0 1  2
0  0  1  4 46 12  0.0000  3.45 1880 48 12 12.7660 30650 .6615 12 12 11.0 1  0
0  0  0  0 52 11  0.0000  0.00 2000 52 12  6.0000 12400 .7515  7  7 11.0 0 19
0  0  1  1 31 12  0.0000  0.00 2044 33 15  9.2955 19022 .6915  7 10  9.5 1  3
0  0  1  1 42 10  0.0000  0.00 1677 47 11  5.1324 11203 .7515  7  7  5.0 0  7
0  0  0  3 33 11  0.0000  0.00 2184 38  8  9.0659 19876 .6915  7 14  7.5 1  1
0  0  0  0 57 16  0.0000  0.00 3185 57 13 11.9310 57000 .4415  7 12 14.0 1  9
0  0  0  0 49 10  0.0000  0.00 2680 51 10  6.7164 18290 .6915 10 10 11.0 1  3
0  0  0  1 45 14  0.0000  0.00 3615 47 14  4.5851 20220 .6915 14 12 11.0 1  8
0  0  0  0 56 11  0.0000  0.00 2139 56 12  9.2567 22150 .6915  7  7 14.0 1  0
0  0  1  3 41 12  0.0000  0.00 3080 43 12  8.5656 30623 .6215 10 10  7.5 1  5
0  0  0  0 56  5  0.0000  0.00 1261 53  6  6.7407  9380 .7515  3  3 14.0 1 20
0  0  0  1 48 10  0.0000  0.00 2227 48 10  9.8788 22000 .6915  7  7  5.0 1  3
0  0  0  2 52 16  0.0000  0.00 1920 53 16  9.3750 23675 .6615 12 10  7.5 1 12
0  0  0  0 51 12  0.0000  0.00 2350 55 12  6.2770 33671 .7215  7  7 14.0 1  5
0  0  0  3 35 11  0.0000  0.00 1785 39 10  6.4241 12367 .7515  7  7  7.5 0  1
0  0  0  0 45 12  0.0000  0.00 2598 51 12  8.3718 21950 .6615  7  7  5.0 0  0
0  0  0  0 54 12  0.0000  0.00 2455 58 17 12.2200 32000 .5815  7  7  9.5 1  7
0  0  0  2 54 12  0.0000  0.00 2450 54 13  3.5612 22610 .7215 10 10  9.5 1 13
0  0  1  0 31 12  0.0000  0.00 1218 32  8  8.8670 12092 .7515  7  7  3.0 0  3
0  0  0  3 53  6  0.0000  0.00 2040 54  4  1.8515  3777 .9415  7  7 11.0 0  0
0  0  2  2 35 14  0.0000  0.00 2600 34 14  8.0769 36000 .5515 16 14  3.0 0  2
0  0  1  3 36 12  0.0000  0.00 2450 40 16  8.9796 26900 .6615 12 16  7.5 0  0
0  0  0  0 59 12  0.0000  0.00 2717 60 12  6.6618 32242 .6615  7  7 11.0 1  2
0  0  0  0 54 16  0.0000  0.00 2701 54 17 11.1070 35020 .5815 16 17  5.0 1  1
0  0  1  1 37 12  0.0000  0.00 2600 47 17 14.0770 37600 .5515  7  7  9.0 1 10
0  0  0  0 44 12  0.0000  0.00 3640 54 10  0.4121  1500 .9415  7  7  7.5 1 10
0  0  1  2 34 17  0.0000  0.00 2940 40 16 23.8100 96000 .4415 12 12  5.0 1  1
0  0  0  0 49 12  0.0000  0.00 1880 50 12  9.5745 18150 .6915  7  7 11.0 0  3
0  0  0  0 49 12  0.0000  0.00 3500 51 12  1.9286 15500 .7215  7  7  3.0 0 32
0  0  0  0 60  9  0.0000  0.00 3320 60  8  2.5783 14000 .7215  7  7  3.0 0  0
0  0  0  0 51 12  0.0000  0.00 1605 55 12  7.2274 14756 .7215  7  7  7.5 1  7
0  0  1  1 30 12  0.0000  0.00 2500 30 14  8.8000 22000 .6615 12 10  5.0 1  5
0  0  0  2 47 12  0.0000  0.00 2400 49  9  7.7500 24466 .6615  7  7 11.0 1  2
0  0  0  4 36 12  0.0000  0.00 1634 45 17 14.6880 24400 .6615 12 12  7.5 1  5
0  0  1  3 35 12  0.0000  0.00 2260 38 12 10.4870 24000 .6615  7  7  9.5 1  3
0  0  0  0 58 12  0.0000  0.00 3478 53 12  4.0253 15500 .7215 12  9 11.0 0 25
0  0  1  3 41 14  0.0000  0.00 2550 42 16 11.7650 30800 .6215 14 12  7.5 0  0
0  0  0  1 51 10  0.0000  0.00  840 52  8  9.5238 10660 .7515  7  7 14.0 1  3
0  0  0  0 47 12  0.0000  0.00 1520 52 12  6.9079 13350 .7215  7  7 11.0 0 10
0  0  1  2 45  9  0.0000  0.00 1920 35  9  5.1510 10090 .7515 12  3 11.0 0 10
0  0  0  0 60 14  0.0000  0.00 2703 55 17 20.4960 55600 .4415 16 14 14.0 1  7
0  0  1  1 30 16  0.0000  2.00 1896 46 16 13.5550 25700 .6615 12 12  9.5 1  5
0  0  0  0 55 11  0.0000  0.00 1960 57 13 14.7960 29000 .5815  7  3  5.0 1 15
0  0  1  2 32 12  0.0000  0.00 3060 50  8  1.6905  7286 .7815 10  7  3.0 0  1
0  0  0  2 36 12  0.0000  0.00 2805 38 12  7.2296 37752 .5215  7  7  3.0 0  5
0  0  0  0 55 12  0.0000  0.00 1944 53  7  4.1152 13072 .7515  3  3 14.0 0  9
0  0  0  0 47 12  0.0000  0.00 1960 47 12  2.9990  7044 .7715  3  3 14.0 0 18
0  0  0  1 47 12  0.0000  0.00 2112 52  8  8.0492 18200 .6915  7  7 14.0 1  1
0  0  0  1 37 11  0.0000  0.00 2544 39 12  8.5770 27000 .6215 12  7  3.0 0  0
0  0  0  2 50 12  0.0000  0.00 1700 53 17  9.3235 30300 .5815 10 12  3.0 0  6
0  0  0  3 30 12  0.0000  0.00 2550 31 12  4.7059 12000 .7515  3  7 14.0 0  1
0  0  0  1 48 17  0.0000  0.00 2080 45 17  9.1346 31500 .6615 16 17  3.0 0  2
0  0  0  2 43 10  0.0000  0.00 2060 49 12  7.7670 27092 .7215 10 10  5.0 1 15
0  0  1  0 48 11  0.0000  0.00 1955 46  8  4.1269 20968 .7515  7  7  3.0 0 25
0  0  1  2 41 14  0.0000  0.00 2500 44 17 10.0000 27000 .6615 17  7 14.0 1  1
0  0  0  0 50 12  0.0000  0.00 2750 52 10  4.0727 11225 .7515  7 10  7.5 1  0
0  0  0  0 58  8  0.0000  0.00 2040 59  5  7.8529 37700 .5815  3  3  7.5 0  0
0  0  0  5 38 13  0.0000  0.00 3275 43 15  7.8168 28200 .6615 12 16  7.5 1  0
0  0  0  1 37 12  0.0000  0.00 2400 39 12  9.1667 34000 .6615  7 12  5.0 0  8
0  0  0  0 50 16  0.0000  0.00 2024 51 17  29.644 63200 .4415 12  7  9.5 1 22
0  0  0  4 42  8  0.0000  0.00 1840 44  6  4.0761  7500 .7915  3  3  7.5 1  5
0  0  1  3 37  9  0.0000  0.00 2033 37 17  8.3620 17410 .7215 10 10  9.5 1 10
0  0  0  2 41 16  0.0000  0.00 1946 40 17 12.0620 51000 .4415 16 17  9.0 1  1
0  0  0  2 31 12  0.0000  0.00 3660 31 12  2.3251 12916 .7515 10  7  3.0 0  1
0  0  0  0 51 12  0.0000  0.00 2088 55 11 10.0100 21900 .6615  7  7  5.0 1  6
0  0  1  2 36 12  0.0000  0.00 2048 41 12  5.2734 17640 .7515  7  7  5.0 0  4
0  0  0  0 54 15  0.0000  0.00 1920 52 15 10.4170 20000 .6915 14 16 14.0 0  6
0  0  0  0 49 12  0.0000  0.00 2000 54 12  7.5000 15000 .7215  7  7 14.0 1  0
0  0  1  1 48  9  0.0000  0.00 2204 47  8  6.3521 14060 .7215 10 12  5.0 0  1
0  0  0  2 42  9  0.0000  0.00 3157 45 10  3.8071 15825 .7215  7 14  9.5 0  3
0  0  1  2 41 12  0.0000  0.00 1665 44 14  9.9099 16510 .7215  3 16  9.5 1 15
0  0  0  0 55 16  0.0000  0.00 2304 56 11  2.6701 13000 .7215 12 12  7.5 0 33
0  0  0  0 42  9  0.0000  0.00 2275 46  8  4.3956 10000 .7515  7  7  5.0 1  2
0  0  0  1 32 15  0.0000  0.00 2760 33 17  7.9710 22000 .6615 12 12  7.5 1  1
0  0  0  2 43 12  0.0000  0.00 1750 44 14 15.4290 29800 .5815  7  7  7.5 1 10
0  0  1  3 33 12  0.0000  0.00 3366 37 13  1.9854 15000 .7215  7  7  5.0 1  0
0  0  0  1 48 15  0.0000  0.00 2205 51 16  7.2562 22300 .7215 10 14  9.5 1 14
0  0  0  2 43 12  0.0000  0.00 1990 48  9  7.0352 14550 .7215  3 16  7.5 1 15
0  0  1  3 47 17  0.0000  0.00 1930 57 16  8.1347 19730 .6915 14 12  7.5 1 15
0  0  0  0 54 12  0.0000  0.00 1350 60 12 11.9810 35000 .5515 12 12  7.5 1 10
0  0  0  1 51 12  0.0000  0.00 3340 52 12  5.9922 21014 .6615  7  3  7.5 1  6
0  0  0  1 51 10  0.0000  0.00  960 57 10  4.1458 10876 .7515 14  7  7.5 0 18
0  0  1  1 43 13  0.0000  0.00 2732 42 13  8.5102 27850 .6215 12 10  7.5 0 15
0  0  0  0 53 12  0.0000  0.00 1624 59  8  2.9631  9560 .7515  0  3  3.0 0 30
0  0  1  1 34 11  0.0000  0.00 1804 36 12  8.8149 30300 .6215  7  7  7.5 0 15
0  0  1  1 31  8  0.0000  0.00 2805 31 10  2.4955  7720 .7815  7  7  7.5 0 10
0  0  0  0 56 12  0.0000  0.00 2160 59  8  4.8843 10550 .7515 10  7  7.5 1  0
0  0  0  1 42 16  0.0000  0.00 2052 55 15 10.2000 24106 .6615 12  7  9.5 1  0
0  0  0  2 32 12  0.0000  0.00 2250 35 16 10.0000 22995 .6615 12 14  9.5 1  4
0  0  1  3 35 12  0.0000  0.00 1120 37 12  5.3571  6000 .8015 12 12  9.5 1  0
0  0  1  1 30 12  0.0000  0.00 2450 36 14  9.7959 24350 .6615 14 14  9.5 1  3
0  0  0  0 51 10  0.0000  0.00 3432 50 11  1.3741  7608 .7715  7  7  7.5 0 20
0  0  0  3 47 12  0.0000  0.00 2700 48 12  3.4630 28200 .7215  7  7  3.0 0  3
0  0  0  1 54 12  0.0000  0.00 2817 55 13  5.0408 16150 .7215  3  7  3.0 0  1
0  0  3  0 31 15  0.0000  0.00 3000 34 17 16.6670 51200 .4415  7 10  7.5 1  5
0  0  0  0 47 10  0.0000  0.00 2125 45 11  4.3294 12646 .7515  7  7  5.0 1  7
0  0  0  3 47 14  0.0000  0.00 1864 42 16 10.1930 19000 .6915  7  7 11.0 1  6
0  0  0  3 40 12  0.0000  0.00 2400 39 12  7.5833 19000 .7215  7  7  7.5 1  2
0  0  0  0 48  8  0.0000  0.00 2160 50  7  4.1204 14400 .7515  3  3  7.5 0  0
0  0  0  7 34  8  0.0000  0.00 1040 51  7  4.8077  7232 .9415  3  7 11.0 1 10
0  0  0  3 38 12  0.0000  0.00 2450 42 16  3.1531 21943 .7515  7 10  9.5 1  6
0  0  1  3 32 12  0.0000  0.00 2500 34 16 19.0000 47500 .4615  7 10  7.5 1  4
0  0  0  1 48 16  0.0000  0.00 2131 45 17  6.0535 28900 .6215 12  7  7.5 1  8
0  0  0  2 41 12  0.0000  0.00 2165 46  7  3.7875 12400 .7715  7  7  7.5 0 18
0  0  0  2 49  5  0.0000  0.00 2230 43  3  2.9287  6531 .7815  0  0  7.5 0  7
0  0  0  0 59  8  0.0000  0.00 1995 55 12  9.2972 22422 .6915  3  7 11.0 1 15
0  0  0  0 58 13  0.0000  0.00 2025 57 16  9.3827 22200 .6615  7  7 11.0 1  7
0  0  0  3 41 12  0.0000  0.00 2450 48 15 26.5310 77000 .4415  7 14 14.0 1  8
0  0  0  2 45 12  0.0000  0.00 2160 45 12 40.5090 88000 .4415 10 10 14.0 1  8
0  0  1  1 30 14  0.0000  0.00 1715 32 17 15.1600 26040 .6215 12 10 11.0 0  3
0  0  0  1 41 12  0.0000  0.00 3018 42 16 18.9640 63500 .4415  7  7  7.5 1 10
0  0  2  0 30 12  0.0000  0.00 2216 33 16  5.4152 12100 .7515 10 10  7.5 0  9
0  0  0  1 53 12  0.0000  0.00 2499 54 12  1.9988 17505 .7515 12  7  7.5 1 24
0  0  0  0 31 12  0.0000  0.00 2250 37 14  8.0000 18000 .6915 10  7  7.5 0 12
0  0  0  2 43 14  0.0000  0.00 2116 44 17 11.1530 28069 .6615 12 12 11.0 1  2
0  0  1  1 31 12  0.0000  0.00 2016 30 14  5.9524 14000 .7515 12 14 14.0 1  6
0  0  0  0 51 12  0.0000  0.00 2470 60 10  2.1194  8117 .7515 10  3  7.5 1 18
0  0  0  0 43  9  0.0000  0.00 1640 45 12  3.8384 11895 .7715  7  7  5.0 1 17
0  0  1  2 31 14  0.0000  0.00 2016 34 16 17.3610 45250 .4915 16 16  5.0 1  7
0  0  0  0 48 11  0.0000  0.00 2185 48 12  8.0092 31106 .6915  7 10  9.5 1  6
0  0  1  1 31 12  0.0000  0.00  800 33 14  3.0000  4000 .8015 12  7  9.5 1 10
0  0  0  1 44 12  0.0000  0.00 3022 46 12 10.5890 40500 .5815  7  7  7.5 1  5
0  0  0  1 48 11  0.0000  0.00 1512 50 14 10.9130 21620 .7215 10  7  7.5 1  7
0  0  0  1 53 12  0.0000  0.00 2677 53 12  5.6033 23426 .7215  0  0  7.5 1 11
0  0  0  3 42 10  0.0000  2.75 3150 44 12  7.9365 26000 .6615  3  3 11.0 1 14
0  0  2  6 39 12  0.0000  0.00 1430 34 12  2.9476  7840 .9415  7  0  9.5 1  5
0  0  1  2 32 10  0.0000  0.00 3307 36  4  2.0562  6800 .7915  7  3  7.5 0  2
0  0  0  2 36 12  0.0000  0.00 3120 39 12  1.3013  5330 .7915  7 12 14.0 0  4
0  0  0  2 40 13  0.0000  0.00 3020 43 16  9.2715 28200 .6215 10 10  9.5 1  5
0  0  2  3 31 12  0.0000  0.00 2056 33 12  4.8638 10000 .7715 12 12  7.5 0 14
0  0  0  0 43 12  0.0000  0.00 2383 43 12  1.0898  9952 .7515 10  3  7.5 0  4
0  0  0  0 60 12  0.0000  0.00 1705 55  8 12.4400 24984 .6215 12 12 14.0 1 15
0  0  0  3 39  9  0.0000  0.00 3120 48 12  6.0897 28363 .6915  7  7 11.0 1 12
;
run;


/*last row has the means*/
data add;
input LFP WHRS KL6 K618 WA WE HHRS HA HE HW FAMINC ;
datalines;
1 740.5763612 0.237715803 1.353253652 42.53784861 12.28685259 2267.270916 45.12084993 12.49136786 7.482178752 23080.59495
   ;
   run;


data mrozexsub;
set mroz(keep=LFP WHRS KL6 K618 WA WE HHRS HA HE HW FAMINC) add;
run;


proc qlim data=mrozexsub;
   model WHRS = KL6 K618 WA WE HHRS HA HE HW FAMINC; 
   endogenous WHRS ~ censored(lb=0); 
   output out=outtobit residual marginal;
run;

proc print data=outtobit(firstobs=754);
 var Meff_KL6 Meff_K618 Meff_WA Meff_WE Meff_HHRS Meff_HA Meff_HE Meff_HW Meff_FAMINC;
run;


proc qlim data=mrozexsub;
    model LFP= KL6 K618 WA WE HHRS HA HE HW FAMINC / discrete(d=probit);
  output out=outprobit residual marginal;
run;

proc print data=outprobit(firstobs=754);
   var Meff_P1_KL6 Meff_P1_K618 Meff_P1_WA Meff_P1_WE Meff_P1_HHRS Meff_P1_HA Meff_P1_HE Meff_P1_HW Meff_P1_FAMINC;
run;


proc qlim data=mrozexsub;
   model LFP= KL6 K618 WA WE HHRS HA HE HW FAMINC / discrete(d=logit);
output out=outlogit residual marginal;
run;
proc print data=outlogit(firstobs=754);
   var Meff_P1_KL6 Meff_P1_K618 Meff_P1_WA Meff_P1_WE Meff_P1_HHRS Meff_P1_HA Meff_P1_HE Meff_P1_HW Meff_P1_FAMINC;
run;

These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.

This example illustrates the calculation of marginal effects by using the QLIM procedure in binary choice models and censored models.

Type:

Sample

Date Modified:	2017-07-07 15:19:12
Date Created:	2017-06-26 15:58:10

Operating System and Release Information

Product Family	Product	Host	SAS Release
Product Family	Product	Host	Starting	Ending
SAS System	SAS/ETS	Microsoft Windows 2000 Professional
		Microsoft Windows 2000 Server
		Microsoft Windows 2000 Advanced Server
		Microsoft Windows 2000 Datacenter Server
		Microsoft Windows 95/98
		Microsoft Windows Server 2008 for x64
		Microsoft Windows Server 2008 R2
		Microsoft Windows Server 2012 Datacenter
		Microsoft Windows Server 2012 R2 Datacenter
		Microsoft Windows Server 2003 Enterprise Edition
		Microsoft Windows Server 2003 Standard Edition
		Microsoft Windows Server 2003 for x64
		Microsoft Windows Server 2008
		Microsoft Windows Server 2003 Datacenter Edition
		Microsoft Windows NT Workstation
		Microsoft Windows 8.1 Pro x64
		Microsoft Windows 10
		Microsoft Windows 8.1 Pro 32-bit
		Microsoft Windows 8.1 Enterprise x64
		Microsoft Windows 8.1 Enterprise 32-bit
		Microsoft Windows 8 Pro 32-bit
		Microsoft Windows 8 Pro x64
		Microsoft Windows 8 Enterprise x64
		Microsoft Windows 8 Enterprise 32-bit
		Microsoft® Windows® for x64
		OS/2
		Microsoft Windows XP 64-bit Edition
		Microsoft Windows Server 2003 Enterprise 64-bit Edition
		Microsoft Windows Server 2003 Datacenter 64-bit Edition
		Microsoft® Windows® for 64-Bit Itanium-based Systems
		OpenVMS VAX
		z/OS
		z/OS 64-bit
		Microsoft Windows Server 2012 R2 Std
		Microsoft Windows Server 2012 Std
		Microsoft Windows XP Professional
		Windows 7 Enterprise 32 bit
		Windows 7 Enterprise x64
		Windows 7 Home Premium 32 bit
		Windows 7 Home Premium x64
		Windows 7 Professional 32 bit
		Windows 7 Professional x64
		Windows 7 Ultimate 32 bit
		Windows 7 Ultimate x64
		Windows Millennium Edition (Me)
		Windows Vista
		Windows Vista for x64
		64-bit Enabled AIX
		64-bit Enabled HP-UX
		64-bit Enabled Solaris
		ABI+ for Intel Architecture
		AIX
		HP-UX
		HP-UX IPF
		IRIX
		Linux
		Linux for x64
		Linux on Itanium
		OpenVMS Alpha
		OpenVMS on HP Integrity
		Solaris
		Solaris for x64
		Tru64 UNIX

Support

Sample 60690: Computing Marginal Effects for Discrete Dependent Variable Models

Overview

Binary Choice Model

Censored Regression Model

References

Operating System and Release Information