Semicontinuous random variables are characterized by a continuous distribution that has point masses at one or more locations. One way to model semicontinuous data is to fit a generalized linear model by using a Tweedie distribution for the response variable. Tweedie distributions have been used in such diverse fields as actuarial science, economics, telecommunications, ecology, medicine, and meteorology. This example illustrates how to fit a Tweedie model to aggregate insurance claims payments data by using the HPGENSELECT procedure which is available in SAS/STAT 12.3, recently released with SAS 9.4.
Exponential dispersion models are the response distributions for generalized linear models. Any exponential dispersion model can be characterized by its variance function , which describes the mean-variance relationship of the distribution when the dispersion is held constant. If Y follows an exponential dispersion model distribution that has mean , variance function , and dispersion , then the variance of Y can be written as
Tweedie distributions are a special case of the exponential dispersion family for which and (Dunn and Smyth, 2005). The distribution is defined for all values of except values of in the open interval . Many important known distributions are a special case of Tweedie distributions including normal ( ), Poisson (), gamma (), and inverse Gaussian (). Apart from these special cases, the probability density unction of the Tweedie distribtion does not have an analyticl expression. For , it has the form
where for and for . The function does not have an analytical expression. It is usually evaluated by using the series expansion methods that are described in Dunn and Smyth (2005).
For , the Tweedie distribution is a compound Poisson-gamma mixture distribution, which is the distribution of defined as
where and are independently and identically distributed gamma random variables with the shape parameter and the scale parameter . At , the density is a probability mass that is governed by the Poisson distribution, and for values of , the density is a mixture of gamma variates with Poisson mixing probability. The parameters , , and are related to the natural parameters , , and of the Tweedie distribution as
The mean of a Tweedie distribution is positive for .
When modeling aggregate payments from insurance claims, if you assume that the arrival of claims follows a Poisson distribution, that the size of individual claims are independently and identically gamma distributed, and that the arrival and sizes are independent of one another, then the aggregate payments follow a Tweedie compound Poisson-gamma mixture distribution (Frees, 2010). This example uses PROC HPGENSELECT to fit a Tweedie model to the aggregate loss data from a Swedish study about third-party automobile insurance claims for 1977. The data were compiled by the Swedish Committee on the Analysis of Risk Premium in Motor Insurance (Andrews and Herzberg, 1985). The following SAS statements create the data set MotorIns
, and Table 1 describes the variables:
data motorins; input Kilometres Zone Bonus Make Insured Claims Payment; LogInsured=log(insured); Zeros=ifn(payment ne 0,1,0); datalines; 1 1 1 1 455.13 108 392491 1 1 1 2 69.17 19 46221 1 1 1 3 72.88 13 15694 1 1 1 4 1292.39 124 422201 1 1 1 5 191.01 40 119373 1 1 1 6 477.66 57 170913 ... more lines ... 5 7 7 8 13.06 0 0 5 7 7 9 384.87 16 112252 ; run;
Table 1: Example Data Set MotorIns
Variable |
Type |
Description |
---|---|---|
Kilometres |
Class |
Distance traveled |
Zone |
Class |
Geographical zone |
Make |
Class |
Make of automobile |
Bonus |
Continuous |
No-claims bonus |
Insured |
Continuous |
Number of insured drivers (years 100,000) |
LogInsured |
Continuous |
Natural logarithm of |
Claims |
Continuous |
Number of insurance claims |
Payment |
Continuous |
Sum of insurance claims payments, in Swedish kronor |
Zeros |
Binary |
Indicator variable for |
Table 2 describes the levels of the classification variable Kilometres
.
Table 2: Values and Labels of Kilometres
Value |
Label |
---|---|
1 |
Less than 1,000 km per year |
2 |
1,000–15,000 km per year |
3 |
15,000–20,000 km per year |
4 |
20,000–25,000 km per year |
5 |
More than 25,000 km per year |
Table 3 describes the levels of the classification variable Zone
. The zones are given from a detailed investigation of 100 areas in 1972 and represent combinations of traffic intensity, state of roads, climatic differences, and so on (Andrews and Herzberg, 1985).
Table 3: Values and Labels of Zone
Value |
Label |
---|---|
1 |
Stockholm, Göteborg, Malmö with surroundings |
2 |
Other large cities with surroundings |
3 |
Smaller cities with surroundings in southern Sweden |
4 |
Rural areas in southern Sweden |
5 |
Smaller cities with surroundings in northern Sweden |
6 |
Rural areas in northern Sweden |
7 |
Gotland |
The models of cars are classified into 10 premium classes, but in a special investigation for 1977 eight common pure models were chosen and the rest were put in a combined class for reference (Andrews and Herzberg, 1985). The levels 1–8 of the classification variable Make
represent the eight pure models, and level 9 is the combined class.
The variable Bonus
is a measure of individual claim history. The insured motorist starts in the class Bonus
= 1. Every year that no claim is filed, the insured moves up one class (Andrews and Herzberg, 1985).
Figure 1 shows a histogram of the response variable Payment
and the proportion of zeros. The variable Payment
exhibits a distribution that is fairly typical of semicontinuous variables: a significant density mass at zero and a continuous, right-skewed distribution elsewhere.
Figure 1: Distribution of Payment
|
|
Output 1: Frequency of Zeros
The FREQ Procedure
Zeros | Frequency | Percent | Cumulative Frequency |
Cumulative Percent |
---|---|---|---|---|
0 | 385 | 17.64 | 385 | 17.64 |
1 | 1797 | 82.36 | 2182 | 100.00 |
The following SAS statements fit a Tweedie compound Poisson-gamma mixture model to the response variable Payment
.
The CLASS statement specifies that the variables Kilometres
, Zone
, and Make
are categorical variables. The SPLIT option requests that the columns of the design matrix that correspond to any effect that contains a split classification variable be able to be selected to enter or leave a model independently of the other design columns of that effect. The PARAM= option specifies a reference cell encoding for the classification variables.
The MODEL statement specifies that the response variable have a Tweedie distribution with a log link function. The candidates for the linear predictor include the main effects and the interactions between the classification variables Kilometres
, Zone
, and Make
and the continuous variable Bonus
. The OFFSET= option specifies that the variable LogInsured
be included in the linear predictor with a coefficient of 1.
The SELECTION statement requests that stepwise selection be used and that the final model be chosen based on the AICC criterion. The DETAILS=SUMMARY option requests that only a summary of the selection process be displayed rather than the details from each step of the selection process.
The OUTPUT statement requests that the selected model’s prediction and residuals be saved to the SAS data set Tweedie
.
The ID statement requests that the variable Payment
also be included in the output data set.
proc hpgenselect data=motorins; class Kilometres Zone Make / split param=reference; model payment = Kilometres|Zone|Make|Bonus / dist=tweedie link=log offset=loginsured; selection method=stepwise(choose=aicc) details=summary; output out=tweedie P R; id payment; run;
The “Performance Information” table in Output 2 shows that the procedure executed in single-machine mode (that is, on the server where SAS is installed). When high-performance procedures run in single-machine mode, they use concurrently scheduled threads. In this case, four threads were used.
The “Model Information” table reports that a Tweedie model was fit with a log link function.
The “Selection Information” table reports that stepwise selection was used, the selection and stopping criteria are the significance level of each individual effect, the entry significance level is the default value of 0.05, and the choose criterion is AICC.
Output 2: Performance, Model, and Selection Information
The HPGENSELECT Procedure
Performance Information | |
---|---|
Execution Mode | Single-Machine |
Number of Threads | 4 |
Model Information | |
---|---|
Data Source | WORK.MOTORINS |
Response Variable | Payment |
Offset Variable | LogInsured |
Class Parameterization | Reference |
Distribution | Tweedie |
Link Function | Log |
Optimization Technique | Quasi-Newton |
Selection Information | |
---|---|
Selection Method | Stepwise |
Select Criterion | Significance Level |
Stop Criterion | Significance Level |
Choose Criterion | AICC |
Effect Hierarchy Enforced | None |
Entry Significance Level (SLE) | 0.05 |
Stay Significance Level (SLS) | 0.05 |
Stop Horizon | 1 |
Output 3 shows that the sample size is 2,182, and the “Class Level Information” table shows the number of levels and the level values of the three classification variables.
Output 3: Sample Size and Classification Variable Levels
Number of Observations Read | 2182 |
---|---|
Number of Observations Used | 2182 |
Class Level Information | ||||
---|---|---|---|---|
Class | Levels | Reference Value |
Values | |
Kilometres | 5 | * | 5 | 1 2 3 4 5 |
Zone | 7 | * | 7 | 1 2 3 4 5 6 7 |
Make | 9 | * | 9 | 1 2 3 4 5 6 7 8 9 |
* Associated Parameters Split |
The “Selection Summary” table in Output 4 reports the variables that are added at each step of the selection process. The summary shows that 30 effects plus an intercept were selected and that the selection process terminated because the sequence of effect additions and removals began cycling.
Output 4: Effect Selection Summary
Selection Summary | |||||
---|---|---|---|---|---|
Step | Effect Entered |
Effect Removed |
Number Effects In |
AICC | p Value |
0 | Intercept | 1 | 44299.3018 | . | |
1 | Bonus | 2 | 43694.2249 | <.0001 | |
2 | Zone_1 | 3 | 43576.8235 | <.0001 | |
3 | Kilometres_1 | 4 | 43414.2670 | <.0001 | |
4 | Make_4 | 5 | 43251.5268 | <.0001 | |
5 | Make_6 | 6 | 43186.2263 | <.0001 | |
6 | Bonus*Kilometres_2 | 7 | 43128.0129 | <.0001 | |
7 | Zone_5*Make_8 | 8 | 43103.4200 | <.0001 | |
8 | Bonus*Kilometres_2*Zone_1*Make_8 | 9 | 43087.3135 | <.0001 | |
9 | Zone_2 | 10 | 43057.5628 | <.0001 | |
10 | Bonus*Kilometres_3 | 11 | 43035.8693 | <.0001 | |
11 | Make_5 | 12 | 43021.0275 | <.0001 | |
12 | Kilometres_1*Make_1 | 13 | 43010.8831 | 0.0003 | |
13 | Make_8 | 14 | 43000.7509 | 0.0003 | |
14 | Make_2 | 15 | 42990.3324 | 0.0003 | |
15 | Bonus*Kilometres_4*Zone_6*Make_4 | 16 | 42987.4687 | 0.0007 | |
16 | Kilometres_1*Zone_5*Make_7 | 17 | 42981.7743 | 0.0008 | |
17 | Kilometres_1*Zone_6*Make_7 | 18 | 42976.6767 | 0.0019 | |
18 | Bonus*Zone_5 | 19 | 42969.6789 | 0.0020 | |
19 | Bonus*Zone_3 | 20 | 42961.8306 | 0.0015 | |
20 | Bonus*Kilometres_1*Make_1 | 21 | 42954.6503 | 0.0019 | |
21 | Kilometres_4 | 22 | 42945.4183 | 0.0008 | |
22 | Make_1 | 23 | 42937.8402 | 0.0017 | |
23 | Bonus*Make_5 | 24 | 42931.7907 | 0.0039 | |
24 | Bonus*Kilometres_1 | 25 | 42925.8663 | 0.0045 | |
25 | Zone_2*Make_6 | 26 | 42920.2139 | 0.0075 | |
26 | Bonus*Kilometres_1*Zone_6 | 27 | 42915.7147 | 0.0082 | |
27 | Bonus*Kilometres_3*Zone_5*Make_2 | 28 | 42913.6024 | 0.0183 | |
28 | Bonus*Kilometres_4*Zone_1*Make_5 | 29 | 42911.4418 | 0.0190 | |
29 | Zone_1*Make_2 | 30 | 42908.4035 | 0.0202 | |
30 | Bonus*Zone_1*Make_2 | 31 | 42904.3219* | 0.0099 | |
31 | Kilometres_1*Zone_6*Make_7 | 30 | 42907.6359 | 0.0534 |
* Optimal Value of Criterion |
Stepwise selection stopped because the sequence of effect additions and removals is cycling. |
The model at step 30 is selected where AICC is 42904.32. |
The “Selected Effects” note in Output 5 lists the effects that are selected for the final model. The “Dimensions” table reports that 31 effects are included in the final model and 33 parameters are estimated. The “Fit Statistics” table reports that the value of AICC for the final model is 42,904.
Output 5: Selected Effects, Dimensions, Convergence Status, and Fit Statistics
Selected Effects: | Intercept Kilometres_1 Kilometres_4 Zone_1 Zone_2 Make_1 Make_2 Make_4 Make_5 Make_6 Make_8 Kilometres_1*Make_1 Zone_1*Make_2 Zone_2*Make_6 Zone_5*Make_8 Kilometres_1*Zone_5*Make_7 Kilometres_1*Zone_6*Make_7 Bonus Bonus*Kilometres_1 Bonus*Kilometres_2 Bonus*Kilometres_3 Bonus*Zone_3 Bonus*Zone_5 Bonus*Kilometres_1*Zone_6 Bonus*Make_5 Bonus*Kilometres_1*Make_1 Bonus*Zone_1*Make_2 Bonus*Kilometres_2*Zone_1*Make_8 Bonus*Kilometres_3*Zone_5*Make_2 Bonus*Kilometres_4*Zone_1*Make_5 Bonus*Kilometres_4*Zone_6*Make_4 |
---|
Dimensions | |
---|---|
Number of Effects | 31 |
Number of Effects after Splits | 31 |
Number of Parameters | 33 |
Columns in X | 31 |
Fit Statistics | |
---|---|
-2 Log Likelihood | 42837 |
AIC (smaller is better) | 42903 |
AICC (smaller is better) | 42904 |
BIC (smaller is better) | 43091 |
Pearson Chi-Square | 1015375 |
Pearson Chi-Square/DF | 472.04777 |
Convergence criterion (GCONV=1E-8) satisfied. |
Output 6 displays the estimates of the model parameters. The estimate of the dispersion parameter, , is 349.65 and the estimate of the power, , is 1.36. The effect of using the SPLIT option in the CLASS statement is apparent. None of the classification variables have all their main effects or complete sets of interactions included in the model. The result is a more parsimonious model than you would achieve without enabling the design columns to enter and leave the model independently.
Output 6: Parameter Estimates
Parameter Estimates | |||||
---|---|---|---|---|---|
Parameter | DF | Estimate | Standard Error |
Chi-Square | Pr > ChiSq |
Intercept | 1 | 6.422717 | 0.030076 | 45604.6548 | <.0001 |
Kilometres_1 | 1 | -0.396625 | 0.050252 | 62.2944 | <.0001 |
Kilometres_4 | 1 | -0.163970 | 0.038900 | 17.7679 | <.0001 |
Zone_1 | 1 | 0.431027 | 0.028089 | 235.4780 | <.0001 |
Zone_2 | 1 | 0.234752 | 0.028513 | 67.7853 | <.0001 |
Make_1 | 1 | 0.102037 | 0.031974 | 10.1842 | 0.0014 |
Make_2 | 1 | 0.104421 | 0.048899 | 4.5601 | 0.0327 |
Make_4 | 1 | -0.676695 | 0.051711 | 171.2483 | <.0001 |
Make_5 | 1 | 0.467489 | 0.091598 | 26.0480 | <.0001 |
Make_6 | 1 | -0.200767 | 0.039391 | 25.9776 | <.0001 |
Make_8 | 1 | 0.240254 | 0.056656 | 17.9826 | <.0001 |
Kilometres_1*Make_1 | 1 | 0.443491 | 0.132307 | 11.2358 | 0.0008 |
Zone_1*Make_2 | 1 | 0.728101 | 0.202768 | 12.8939 | 0.0003 |
Zone_2*Make_6 | 1 | -0.286627 | 0.101679 | 7.9464 | 0.0048 |
Zone_5*Make_8 | 1 | 0.520894 | 0.160295 | 10.5599 | 0.0012 |
Kilometres_1*Zone_5*Make_7 | 1 | 0.736407 | 0.250920 | 8.6132 | 0.0033 |
Kilometres_1*Zone_6*Make_7 | 1 | 0.453568 | 0.230985 | 3.8558 | 0.0496 |
Bonus | 1 | -0.138215 | 0.006689 | 426.9209 | <.0001 |
Bonus*Kilometres_1 | 1 | -0.035637 | 0.010883 | 10.7225 | 0.0011 |
Bonus*Kilometres_2 | 1 | -0.069006 | 0.006272 | 121.0511 | <.0001 |
Bonus*Kilometres_3 | 1 | -0.045452 | 0.006450 | 49.6621 | <.0001 |
Bonus*Zone_3 | 1 | 0.019307 | 0.005369 | 12.9336 | 0.0003 |
Bonus*Zone_5 | 1 | 0.027528 | 0.007469 | 13.5859 | 0.0002 |
Bonus*Kilometres_1*Zone_6 | 1 | 0.031829 | 0.012152 | 6.8603 | 0.0088 |
Bonus*Make_5 | 1 | -0.055964 | 0.018012 | 9.6539 | 0.0019 |
Bonus*Kilometres_1*Make_1 | 1 | -0.063791 | 0.025037 | 6.4914 | 0.0108 |
Bonus*Zone_1*Make_2 | 1 | -0.107665 | 0.039459 | 7.4448 | 0.0064 |
Bonus*Kilometres_2*Zone_1*Make_8 | 1 | 0.166930 | 0.043453 | 14.7578 | 0.0001 |
Bonus*Kilometres_3*Zone_5*Make_2 | 1 | 0.101962 | 0.045120 | 5.1068 | 0.0238 |
Bonus*Kilometres_4*Zone_1*Make_5 | 1 | 0.098160 | 0.045496 | 4.6550 | 0.0310 |
Bonus*Kilometres_4*Zone_6*Make_4 | 1 | 0.233105 | 0.094307 | 6.1097 | 0.0134 |
Dispersion | 1 | 349.647997 | 28.740411 | . | . |
Power | 1 | 1.363043 | 0.008891 | . | . |
The following SAS statements generate a scatter plot that compares the model predictions with the observed values of the response variable.
proc sort data=tweedie out=tweedie; by payment; run;
proc sgplot data=tweedie; scatter x=payment y=pred / legendlabel="Predicted"; series x=payment y=payment / lineattrs=(pattern=solid color=red) legendlabel="45 degree line"; yaxis label="Predicted"; run;
Figure 2 shows that the predictions of the final model compare favorably with the observed responses.
Andrews, D. F. and Herzberg, A. M. (1985), A Collection of Problems from Many Fields for the Student and Research Worker, New York: Springer-Verlag.
Dunn, P. K. and Smyth, G. K. (2005), “Series Evaluation of Tweedie Exponential Dispersion Model Densities,” Statistics and Computing, 15, 267–280.
Frees, E. W. (2010), Regression Modeling with Actuarial and Financial Applications, Cambridge: Cambridge University Press.
Jørgensen, B. and Paes de Souza, M. C. (1994), “Fitting Tweedie’s Compound Poisson Model to Insurance Claims Data,” Scandinavian Actuarial Journal, 1, 69–93.
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 motorins;
input Kilometres Zone Bonus Make Insured Claims Payment;
LogInsured=log(insured);
Zeros=ifn(payment ne 0,1,0);
datalines;
1 1 1 1 455.13 108 392491
1 1 1 2 69.17 19 46221
1 1 1 3 72.88 13 15694
1 1 1 4 1292.39 124 422201
1 1 1 5 191.01 40 119373
1 1 1 6 477.66 57 170913
1 1 1 7 105.58 23 56940
1 1 1 8 32.55 14 77487
1 1 1 9 9998.46 1704 6805992
1 1 2 1 314.58 45 214011
1 1 2 2 61.82 10 65303
1 1 2 3 47.06 5 20871
1 1 2 4 782.58 48 242894
1 1 2 5 115.43 11 23545
1 1 2 6 338.06 23 39598
1 1 2 7 70.44 7 48767
1 1 2 8 15.25 2 6560
1 1 2 9 6416.19 638 2873487
1 1 3 1 309.98 24 134931
1 1 3 2 49.18 6 50908
1 1 3 3 32.02 3 4399
1 1 3 4 497.20 23 112992
1 1 3 5 73.48 6 14788
1 1 3 6 278.01 9 48713
1 1 3 7 66.36 9 52076
1 1 3 8 17.86 3 13161
1 1 3 9 5063.15 408 1707680
1 1 4 1 318.48 29 103866
1 1 4 2 57.21 7 77588
1 1 4 3 35.33 4 11839
1 1 4 4 374.28 20 98140
1 1 4 5 85.18 7 27919
1 1 4 6 199.70 7 103910
1 1 4 7 60.46 4 38065
1 1 4 8 12.74 0 0
1 1 4 9 4263.09 300 1267678
1 1 5 1 444.37 25 69203
1 1 5 2 86.65 6 14620
1 1 5 3 53.81 5 40258
1 1 5 4 361.62 22 161455
1 1 5 5 117.91 3 20011
1 1 5 6 232.55 11 57214
1 1 5 7 81.27 3 4496
1 1 5 8 18.21 0 0
1 1 5 9 4761.37 301 1116208
1 1 6 1 1016.67 61 217617
1 1 6 2 150.56 12 58099
1 1 6 3 126.69 4 12268
1 1 6 4 517.31 16 59634
1 1 6 5 246.62 13 84966
1 1 6 6 482.96 19 137005
1 1 6 7 203.60 12 33767
1 1 6 8 25.88 3 6279
1 1 6 9 9197.99 522 1939894
1 1 7 1 5430.48 214 1048698
1 1 7 2 659.54 24 143915
1 1 7 3 657.34 22 153830
1 1 7 4 2795.72 60 202413
1 1 7 5 1119.12 41 180345
1 1 7 6 2861.69 92 484604
1 1 7 7 1111.00 37 152801
1 1 7 8 166.61 6 14084
1 1 7 9 48264.64 1875 8977527
1 2 1 1 458.89 98 532092
1 2 1 2 72.78 5 9006
1 2 1 3 33.23 7 45498
1 2 1 4 1544.55 101 337480
1 2 1 5 200.90 43 191982
1 2 1 6 663.98 65 300632
1 2 1 7 124.73 10 23349
1 2 1 8 29.24 4 13581
1 2 1 9 11381.00 1326 6173598
1 2 2 1 364.78 40 211494
1 2 2 2 51.89 5 10811
1 2 2 3 29.39 4 36204
1 2 2 4 1053.01 33 135007
1 2 2 5 110.10 16 49061
1 2 2 6 470.62 30 64287
1 2 2 7 93.29 8 51080
1 2 2 8 17.88 1 600
1 2 2 9 7607.66 591 2510207
1 2 3 1 315.14 17 106975
1 2 3 2 64.53 4 16922
1 2 3 3 27.24 2 8255
1 2 3 4 726.13 29 93656
1 2 3 5 96.49 4 44966
1 2 3 6 365.81 16 43426
1 2 3 7 80.80 5 48691
1 2 3 8 13.30 1 1325
1 2 3 9 5898.98 320 1392652
1 2 4 1 320.47 16 136143
1 2 4 2 69.55 4 34137
1 2 4 3 33.37 1 2702
1 2 4 4 507.57 9 22292
1 2 4 5 72.40 7 20295
1 2 4 6 316.14 9 57404
1 2 4 7 72.05 3 8538
1 2 4 8 18.35 0 0
1 2 4 9 4957.56 269 1375988
1 2 5 1 473.63 27 136376
1 2 5 2 88.09 8 19038
1 2 5 3 46.27 2 3604
1 2 5 4 467.96 9 10597
1 2 5 5 126.88 10 26433
1 2 5 6 316.15 11 52950
1 2 5 7 101.11 7 21620
1 2 5 8 23.37 1 2680
1 2 5 9 5481.31 282 1079230
1 2 6 1 996.27 61 236220
1 2 6 2 175.14 10 25036
1 2 6 3 111.97 5 22261
1 2 6 4 601.61 16 88961
1 2 6 5 260.69 14 64368
1 2 6 6 593.18 17 65578
1 2 6 7 229.72 7 46244
1 2 6 8 46.66 7 14385
1 2 6 9 9830.72 413 1840742
1 2 7 1 6021.43 233 1086534
1 2 7 2 852.80 33 165960
1 2 7 3 751.59 24 100564
1 2 7 4 3293.99 60 201401
1 2 7 5 1289.09 53 272610
1 2 7 6 3665.27 97 524316
1 2 7 7 1369.91 35 159658
1 2 7 8 183.98 5 18603
1 2 7 9 55084.54 1744 8500391
1 3 1 1 453.06 72 329632
1 3 1 2 67.13 9 79565
1 3 1 3 35.22 5 11746
1 3 1 4 1653.17 89 338305
1 3 1 5 206.62 38 124108
1 3 1 6 859.95 64 213078
1 3 1 7 110.08 11 34844
1 3 1 8 25.92 5 25319
1 3 1 9 11436.08 1205 5173923
1 3 2 1 317.10 25 90162
1 3 2 2 54.58 8 19327
1 3 2 3 22.59 3 1209
1 3 2 4 1187.43 30 123124
1 3 2 5 129.53 13 99258
1 3 2 6 617.11 40 137828
1 3 2 7 102.50 7 14904
1 3 2 8 21.56 1 597
1 3 2 9 8351.79 425 1937445
1 3 3 1 357.43 18 37835
1 3 3 2 62.87 3 5014
1 3 3 3 18.00 0 0
1 3 3 4 849.23 25 61591
1 3 3 5 119.21 6 47495
1 3 3 6 463.60 20 53173
1 3 3 7 104.36 6 11936
1 3 3 8 14.21 1 31442
1 3 3 9 6540.44 304 1284025
1 3 4 1 338.37 19 136281
1 3 4 2 52.49 2 9253
1 3 4 3 27.97 0 0
1 3 4 4 571.94 23 142536
1 3 4 5 113.36 6 21433
1 3 4 6 406.33 21 131027
1 3 4 7 85.15 3 4079
1 3 4 8 16.16 1 1012
1 3 4 9 5123.78 217 994540
1 3 5 1 459.40 16 61958
1 3 5 2 73.51 2 5056
1 3 5 3 41.51 4 44278
1 3 5 4 517.24 8 18455
1 3 5 5 136.08 8 28248
1 3 5 6 417.71 11 15568
1 3 5 7 103.07 1 8347
1 3 5 8 26.11 1 1144
1 3 5 9 5849.14 242 1184032
1 3 6 1 1060.28 43 245621
1 3 6 2 124.82 7 12648
1 3 6 3 119.17 2 5855
1 3 6 4 639.97 12 64278
1 3 6 5 307.56 14 90310
1 3 6 6 740.33 24 117763
1 3 6 7 233.83 7 20303
1 3 6 8 53.41 3 6221
1 3 6 9 10263.04 393 2026554
1 3 7 1 7155.96 197 980780
1 3 7 2 999.32 32 168854
1 3 7 3 1049.99 19 41459
1 3 7 4 3712.23 67 229231
1 3 7 5 1862.44 74 388511
1 3 7 6 4964.00 121 622350
1 3 7 7 1785.23 58 253660
1 3 7 8 331.45 8 94395
1 3 7 9 65617.47 1865 9884008
1 4 1 1 868.60 115 627513
1 4 1 2 122.54 10 113492
1 4 1 3 55.08 3 33925
1 4 1 4 2751.70 98 578698
1 4 1 5 328.36 36 149698
1 4 1 6 1730.51 105 604161
1 4 1 7 231.91 13 55103
1 4 1 8 48.77 4 34267
1 4 1 9 20153.28 1446 6605073
1 4 2 1 622.23 41 300510
1 4 2 2 94.03 5 11936
1 4 2 3 36.73 2 6387
1 4 2 4 2037.95 48 152944
1 4 2 5 189.27 17 40047
1 4 2 6 1217.01 65 344450
1 4 2 7 155.50 16 113524
1 4 2 8 27.27 0 0
1 4 2 9 14648.20 645 3150912
1 4 3 1 613.17 32 168882
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1 4 3 4 1447.58 25 66208
1 4 3 5 168.81 8 30465
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1 4 3 7 153.11 5 38157
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1 6 3 6 294.37 15 106215
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2 1 3 4 234.48 13 65170
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2 1 3 6 318.69 21 162284
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2 7 6 4 8.68 0 0
2 7 6 5 11.99 0 0
2 7 6 6 24.08 0 0
2 7 6 7 13.38 0 0
2 7 6 8 6.54 0 0
2 7 6 9 453.04 9 81464
2 7 7 1 420.95 7 16802
2 7 7 2 126.12 1 6020
2 7 7 3 39.14 1 1012
2 7 7 4 59.08 1 3580
2 7 7 5 81.78 3 3065
2 7 7 6 193.89 3 32827
2 7 7 7 71.27 1 603
2 7 7 8 31.36 1 1021
2 7 7 9 2873.70 69 381570
3 1 1 1 213.38 53 244561
3 1 1 2 76.97 26 187544
3 1 1 3 60.42 8 18624
3 1 1 4 60.89 10 81052
3 1 1 5 53.30 10 52745
3 1 1 6 104.58 13 168471
3 1 1 7 24.92 4 5100
3 1 1 8 12.91 3 42372
3 1 1 9 2375.34 456 1911772
3 1 2 1 276.13 28 106668
3 1 2 2 73.41 14 30232
3 1 2 3 69.26 14 61941
3 1 2 4 73.29 5 66851
3 1 2 5 52.25 7 57304
3 1 2 6 139.64 9 59193
3 1 2 7 42.93 3 5646
3 1 2 8 13.03 0 0
3 1 2 9 2472.22 297 1413344
3 1 3 1 299.10 36 196119
3 1 3 2 87.60 11 55966
3 1 3 3 67.91 6 13026
3 1 3 4 65.39 2 2186
3 1 3 5 60.44 8 23091
3 1 3 6 135.85 6 74018
3 1 3 7 48.67 2 3044
3 1 3 8 16.35 3 12589
3 1 3 9 2411.79 256 1266725
3 1 4 1 336.16 29 98220
3 1 4 2 119.03 9 61145
3 1 4 3 75.71 3 16285
3 1 4 4 44.78 0 0
3 1 4 5 69.52 11 67180
3 1 4 6 115.91 10 25912
3 1 4 7 59.11 2 3783
3 1 4 8 18.65 0 0
3 1 4 9 2419.59 209 905418
3 1 5 1 480.43 41 129476
3 1 5 2 164.22 16 133759
3 1 5 3 123.44 7 48811
3 1 5 4 50.82 2 4868
3 1 5 5 102.56 3 13127
3 1 5 6 159.79 15 44864
3 1 5 7 73.37 9 56128
3 1 5 8 32.92 2 1512
3 1 5 9 3214.83 274 1088795
3 1 6 1 1110.72 84 399470
3 1 6 2 327.30 32 100742
3 1 6 3 300.23 47 234344
3 1 6 4 52.79 2 6842
3 1 6 5 209.45 23 67428
3 1 6 6 303.79 20 70487
3 1 6 7 184.93 16 90830
3 1 6 8 62.38 2 62884
3 1 6 9 6151.48 625 3050824
3 1 7 1 4918.02 236 1326307
3 1 7 2 1398.19 72 342421
3 1 7 3 2349.67 45 142660
3 1 7 4 252.36 15 25307
3 1 7 5 881.09 52 195295
3 1 7 6 1520.51 58 307753
3 1 7 7 867.16 45 110181
3 1 7 8 306.00 7 68657
3 1 7 9 26905.35 1481 6783057
3 2 1 1 230.25 30 169977
3 2 1 2 52.01 6 49480
3 2 1 3 42.02 6 19600
3 2 1 4 72.26 10 15713
3 2 1 5 63.55 10 45597
3 2 1 6 140.48 10 24925
3 2 1 7 41.12 7 29069
3 2 1 8 15.44 4 19159
3 2 1 9 2136.64 283 1188075
3 2 2 1 304.17 33 230024
3 2 2 2 74.05 9 25481
3 2 2 3 44.90 3 7212
3 2 2 4 74.01 1 700
3 2 2 5 71.95 7 12796
3 2 2 6 201.20 13 30337
3 2 2 7 49.51 4 35898
3 2 2 8 11.53 1 5716
3 2 2 9 2535.10 241 1050750
3 2 3 1 346.82 28 127469
3 2 3 2 74.87 13 71451
3 2 3 3 49.48 6 18584
3 2 3 4 67.62 4 11510
3 2 3 5 75.80 11 59922
3 2 3 6 211.42 12 52349
3 2 3 7 58.59 6 19142
3 2 3 8 21.15 1 309
3 2 3 9 2607.48 222 986926
3 2 4 1 398.70 30 121008
3 2 4 2 115.52 13 31036
3 2 4 3 61.44 5 15124
3 2 4 4 46.99 2 4809
3 2 4 5 81.79 9 79729
3 2 4 6 178.98 16 57389
3 2 4 7 73.74 4 13266
3 2 4 8 21.73 2 6506
3 2 4 9 2804.47 185 983263
3 2 5 1 577.94 44 164565
3 2 5 2 186.56 17 37312
3 2 5 3 99.25 5 70395
3 2 5 4 37.92 2 3340
3 2 5 5 114.60 12 36371
3 2 5 6 231.48 8 12793
3 2 5 7 112.71 3 7993
3 2 5 8 49.52 1 7647
3 2 5 9 3785.59 255 1135808
3 2 6 1 1204.54 64 297189
3 2 6 2 348.05 20 87441
3 2 6 3 318.67 21 132964
3 2 6 4 59.64 2 2113
3 2 6 5 233.04 14 55184
3 2 6 6 401.81 21 79575
3 2 6 7 229.04 16 63658
3 2 6 8 113.66 5 69056
3 2 6 9 7232.56 477 2168736
3 2 7 1 6206.24 291 1529817
3 2 7 2 1778.53 97 442424
3 2 7 3 1574.59 60 408143
3 2 7 4 257.82 12 34524
3 2 7 5 1214.18 67 253711
3 2 7 6 1992.86 65 250177
3 2 7 7 1295.20 52 296108
3 2 7 8 502.83 27 92809
3 2 7 9 33844.51 1504 7698320
3 3 1 1 252.96 35 165902
3 3 1 2 55.70 6 15001
3 3 1 3 42.39 5 19085
3 3 1 4 61.57 7 47058
3 3 1 5 76.42 18 103398
3 3 1 6 171.47 18 101601
3 3 1 7 37.76 5 7103
3 3 1 8 14.17 1 31442
3 3 1 9 2164.34 294 1266124
3 3 2 1 354.49 43 270211
3 3 2 2 56.21 7 45695
3 3 2 3 33.16 1 6939
3 3 2 4 72.74 5 12904
3 3 2 5 88.73 11 26769
3 3 2 6 257.15 19 67830
3 3 2 7 55.78 6 21727
3 3 2 8 26.57 2 7009
3 3 2 9 2691.01 234 1261608
3 3 3 1 388.74 25 131184
3 3 3 2 71.36 7 44201
3 3 3 3 38.48 1 4375
3 3 3 4 71.03 2 5964
3 3 3 5 86.96 11 42621
3 3 3 6 250.19 20 173266
3 3 3 7 75.00 6 39333
3 3 3 8 34.92 5 22418
3 3 3 9 2786.03 190 858717
3 3 4 1 449.50 29 195168
3 3 4 2 106.66 7 51072
3 3 4 3 50.85 3 34954
3 3 4 4 49.51 2 11339
3 3 4 5 93.52 3 4737
3 3 4 6 229.73 14 69250
3 3 4 7 93.86 6 23703
3 3 4 8 35.25 2 33142
3 3 4 9 2823.71 174 804353
3 3 5 1 623.39 41 164990
3 3 5 2 165.36 8 49197
3 3 5 3 107.24 6 9345
3 3 5 4 53.95 2 4256
3 3 5 5 115.89 13 33965
3 3 5 6 289.39 14 64812
3 3 5 7 130.94 9 58316
3 3 5 8 68.28 3 5923
3 3 5 9 3795.31 233 1102967
3 3 6 1 1211.80 55 204035
3 3 6 2 331.56 27 160170
3 3 6 3 244.41 21 112398
3 3 6 4 69.85 4 7558
3 3 6 5 285.97 13 72538
3 3 6 6 501.96 17 79132
3 3 6 7 260.81 16 66095
3 3 6 8 140.81 11 99429
3 3 6 9 6982.23 418 2296256
3 3 7 1 6637.23 243 1109910
3 3 7 2 1681.52 71 377529
3 3 7 3 1688.25 47 211505
3 3 7 4 319.83 6 49844
3 3 7 5 1402.18 55 204355
3 3 7 6 2650.35 76 436313
3 3 7 7 1414.40 56 314402
3 3 7 8 821.80 32 244466
3 3 7 9 36595.09 1462 7765626
3 4 1 1 559.52 82 333333
3 4 1 2 79.18 9 83389
3 4 1 3 52.97 5 10472
3 4 1 4 139.86 4 13468
3 4 1 5 125.06 21 139195
3 4 1 6 395.86 34 101041
3 4 1 7 65.27 4 13716
3 4 1 8 25.95 3 14203
3 4 1 9 4174.30 477 2028574
3 4 2 1 759.38 75 461748
3 4 2 2 95.99 9 12058
3 4 2 3 61.91 2 10300
3 4 2 4 162.43 7 38966
3 4 2 5 171.40 17 79870
3 4 2 6 581.13 31 233888
3 4 2 7 141.70 11 85892
3 4 2 8 33.05 3 13031
3 4 2 9 5179.78 407 2133862
3 4 3 1 882.28 67 325944
3 4 3 2 140.89 6 22634
3 4 3 3 80.68 1 3416
3 4 3 4 120.58 3 70053
3 4 3 5 168.89 12 23087
3 4 3 6 566.40 24 143467
3 4 3 7 141.85 13 34102
3 4 3 8 59.83 5 41928
3 4 3 9 5273.39 323 1769366
3 4 4 1 930.38 53 294693
3 4 4 2 186.23 13 91535
3 4 4 3 103.32 2 12215
3 4 4 4 95.19 3 36777
3 4 4 5 202.06 16 71636
3 4 4 6 507.25 21 47506
3 4 4 7 153.52 9 81848
3 4 4 8 80.05 2 7466
3 4 4 9 5361.38 290 1551046
3 4 5 1 1240.15 72 441578
3 4 5 2 271.62 16 87667
3 4 5 3 229.54 14 83355
3 4 5 4 95.75 2 8741
3 4 5 5 262.73 18 44435
3 4 5 6 575.18 17 65613
3 4 5 7 240.02 14 28430
3 4 5 8 132.37 2 7701
3 4 5 9 7316.31 332 2030248
3 4 6 1 2278.60 101 444371
3 4 6 2 587.80 31 122651
3 4 6 3 504.36 14 103196
3 4 6 4 124.82 2 31519
3 4 6 5 520.21 26 116043
3 4 6 6 969.68 40 193661
3 4 6 7 483.93 22 64380
3 4 6 8 317.12 15 150041
3 4 6 9 13375.57 616 3207923
3 4 7 1 14598.67 444 2526990
3 4 7 2 3769.94 118 775364
3 4 7 3 3657.95 104 731869
3 4 7 4 639.63 8 13695
3 4 7 5 3018.70 95 485071
3 4 7 6 6256.55 150 730785
3 4 7 7 2890.19 115 676893
3 4 7 8 2160.00 55 380519
3 4 7 9 79614.96 2548 13203616
3 5 1 1 66.18 11 86991
3 5 1 2 12.20 2 4206
3 5 1 3 10.46 0 0
3 5 1 4 12.55 1 31442
3 5 1 5 16.22 1 617
3 5 1 6 45.16 1 1606
3 5 1 7 10.26 4 8787
3 5 1 8 8.14 0 0
3 5 1 9 582.17 82 288772
3 5 2 1 95.88 4 40620
3 5 2 2 14.67 1 1234
3 5 2 3 9.10 0 0
3 5 2 4 14.04 0 0
3 5 2 5 23.38 5 10834
3 5 2 6 64.73 6 80041
3 5 2 7 15.78 0 0
3 5 2 8 7.15 0 0
3 5 2 9 682.07 66 251890
3 5 3 1 106.06 9 52060
3 5 3 2 25.79 3 5523
3 5 3 3 12.55 1 901
3 5 3 4 12.61 1 2693
3 5 3 5 28.41 1 1300
3 5 3 6 69.25 4 10121
3 5 3 7 24.06 0 0
3 5 3 8 7.05 0 0
3 5 3 9 696.56 44 270042
3 5 4 1 122.77 6 40268
3 5 4 2 28.66 1 1100
3 5 4 3 18.50 1 1855
3 5 4 4 10.00 0 0
3 5 4 5 29.15 0 0
3 5 4 6 71.37 4 11034
3 5 4 7 22.78 1 3056
3 5 4 8 10.62 2 32355
3 5 4 9 741.23 44 249540
3 5 5 1 186.40 6 97634
3 5 5 2 39.30 2 32030
3 5 5 3 31.63 2 6342
3 5 5 4 5.84 0 0
3 5 5 5 33.94 5 13825
3 5 5 6 88.30 2 32833
3 5 5 7 36.43 4 3897
3 5 5 8 29.33 1 31442
3 5 5 9 1017.94 56 268945
3 5 6 1 359.83 15 218411
3 5 6 2 79.26 10 50649
3 5 6 3 73.62 5 8906
3 5 6 4 13.33 0 0
3 5 6 5 83.20 6 49166
3 5 6 6 138.19 4 18433
3 5 6 7 79.55 3 12478
3 5 6 8 54.94 2 4486
3 5 6 9 1941.76 89 319443
3 5 7 1 1855.30 65 358790
3 5 7 2 457.25 25 217118
3 5 7 3 442.87 16 74000
3 5 7 4 61.12 2 3887
3 5 7 5 367.21 21 109371
3 5 7 6 633.37 19 145079
3 5 7 7 386.49 14 41905
3 5 7 8 252.47 13 92133
3 5 7 9 9545.23 396 1983959
3 6 1 1 187.75 35 171592
3 6 1 2 24.04 4 15092
3 6 1 3 13.61 2 32158
3 6 1 4 33.47 1 4487
3 6 1 5 41.84 8 13586
3 6 1 6 136.14 19 42561
3 6 1 7 30.60 1 556
3 6 1 8 15.77 4 4684
3 6 1 9 1238.84 140 720084
3 6 2 1 259.57 30 142441
3 6 2 2 29.78 1 2640
3 6 2 3 16.41 0 0
3 6 2 4 37.07 1 9869
3 6 2 5 58.80 4 11865
3 6 2 6 209.75 8 80833
3 6 2 7 48.04 6 17574
3 6 2 8 26.94 2 9713
3 6 2 9 1626.78 125 470051
3 6 3 1 299.91 19 169849
3 6 3 2 28.45 0 0
3 6 3 3 22.83 0 0
3 6 3 4 30.88 0 0
3 6 3 5 54.01 4 4943
3 6 3 6 181.06 11 42891
3 6 3 7 46.17 0 0
3 6 3 8 38.09 3 3450
3 6 3 9 1632.96 92 403488
3 6 4 1 300.59 17 117401
3 6 4 2 44.31 5 12173
3 6 4 3 28.00 0 0
3 6 4 4 19.33 0 0
3 6 4 5 53.55 3 5949
3 6 4 6 163.02 7 25358
3 6 4 7 58.78 5 43236
3 6 4 8 46.23 2 1803
3 6 4 9 1577.85 80 447128
3 6 5 1 385.54 16 110578
3 6 5 2 84.29 6 13624
3 6 5 3 64.25 1 1518
3 6 5 4 23.74 0 0
3 6 5 5 78.56 6 20737
3 6 5 6 198.91 7 20881
3 6 5 7 68.71 2 9151
3 6 5 8 61.13 3 18101
3 6 5 9 2017.86 112 644496
3 6 6 1 772.69 32 120917
3 6 6 2 188.97 11 69871
3 6 6 3 141.34 4 49093
3 6 6 4 35.49 0 0
3 6 6 5 160.82 7 53193
3 6 6 6 328.78 17 79488
3 6 6 7 136.87 11 36441
3 6 6 8 155.63 4 35412
3 6 6 9 3855.71 164 981465
3 6 7 1 4739.07 156 1031429
3 6 7 2 1134.37 45 235652
3 6 7 3 1078.25 32 168555
3 6 7 4 151.43 2 5982
3 6 7 5 971.01 35 95823
3 6 7 6 1928.14 45 368238
3 6 7 7 889.08 27 89649
3 6 7 8 900.56 35 228604
3 6 7 9 22985.48 799 4265828
3 7 1 1 3.39 1 303
3 7 1 2 2.34 0 0
3 7 1 3 0.80 0 0
3 7 1 4 2.49 0 0
3 7 1 5 1.34 1 906
3 7 1 6 8.71 0 0
3 7 1 7 1.63 0 0
3 7 1 8 0.15 0 0
3 7 1 9 78.57 6 66711
3 7 2 1 19.19 0 0
3 7 2 2 3.27 0 0
3 7 2 3 0.38 0 0
3 7 2 4 5.71 1 31442
3 7 2 5 4.12 1 31442
3 7 2 6 10.07 0 0
3 7 2 7 3.24 0 0
3 7 2 8 1.28 0 0
3 7 2 9 111.66 10 33310
3 7 3 1 15.14 1 1441
3 7 3 2 4.09 0 0
3 7 3 3 0.90 0 0
3 7 3 4 1.06 0 0
3 7 3 5 2.02 0 0
3 7 3 6 6.70 0 0
3 7 3 7 1.00 0 0
3 7 3 8 0.76 0 0
3 7 3 9 105.76 8 14449
3 7 4 1 14.41 0 0
3 7 4 2 1.92 1 794
3 7 4 3 0.96 0 0
3 7 4 4 1.16 0 0
3 7 4 5 3.85 0 0
3 7 4 6 5.92 0 0
3 7 4 7 1.90 3 11762
3 7 4 8 2.21 0 0
3 7 4 9 110.85 5 41333
3 7 5 1 14.35 0 0
3 7 5 2 4.57 0 0
3 7 5 3 3.34 0 0
3 7 5 4 3.56 0 0
3 7 5 5 7.44 0 0
3 7 5 6 13.81 0 0
3 7 5 7 4.92 0 0
3 7 5 8 1.16 0 0
3 7 5 9 146.21 7 49986
3 7 6 1 31.22 2 4738
3 7 6 2 14.40 0 0
3 7 6 3 4.81 0 0
3 7 6 4 6.03 0 0
3 7 6 5 4.25 2 2063
3 7 6 6 13.08 1 1769
3 7 6 7 10.27 0 0
3 7 6 8 6.33 0 0
3 7 6 9 292.33 10 22382
3 7 7 1 288.36 12 41206
3 7 7 2 84.68 1 1200
3 7 7 3 29.99 1 31442
3 7 7 4 19.07 1 3608
3 7 7 5 37.96 1 1455
3 7 7 6 113.33 2 7618
3 7 7 7 40.84 2 34979
3 7 7 8 34.87 0 0
3 7 7 9 1720.36 57 226934
4 1 1 1 49.31 11 23218
4 1 1 2 22.93 6 14940
4 1 1 3 34.01 9 101091
4 1 1 4 6.08 0 0
4 1 1 5 17.77 4 4164
4 1 1 6 18.59 1 3044
4 1 1 7 3.89 0 0
4 1 1 8 4.31 1 400
4 1 1 9 601.75 103 381138
4 1 2 1 77.53 6 16812
4 1 2 2 29.09 5 9656
4 1 2 3 36.39 6 10543
4 1 2 4 11.32 1 8231
4 1 2 5 18.74 3 4571
4 1 2 6 32.02 3 38542
4 1 2 7 13.62 1 954
4 1 2 8 3.73 0 0
4 1 2 9 735.71 86 391512
4 1 3 1 85.77 4 14451
4 1 3 2 36.08 2 3784
4 1 3 3 34.31 6 8274
4 1 3 4 12.01 1 917
4 1 3 5 19.10 4 14439
4 1 3 6 32.80 4 12608
4 1 3 7 18.59 1 900
4 1 3 8 8.54 3 4956
4 1 3 9 729.62 88 599538
4 1 4 1 105.73 15 90111
4 1 4 2 35.14 6 38663
4 1 4 3 53.38 1 3000
4 1 4 4 6.89 1 4686
4 1 4 5 18.19 3 3372
4 1 4 6 34.63 2 3178
4 1 4 7 16.77 0 0
4 1 4 8 11.75 0 0
4 1 4 9 766.14 71 430373
4 1 5 1 166.10 7 40729
4 1 5 2 66.54 5 43356
4 1 5 3 48.99 7 17562
4 1 5 4 10.91 1 993
4 1 5 5 32.50 5 47591
4 1 5 6 53.90 4 15205
4 1 5 7 17.88 2 8643
4 1 5 8 17.04 2 3314
4 1 5 9 1064.66 96 403899
4 1 6 1 344.68 32 184118
4 1 6 2 125.36 15 34894
4 1 6 3 130.03 11 66353
4 1 6 4 15.00 0 0
4 1 6 5 73.29 10 122551
4 1 6 6 95.16 4 9655
4 1 6 7 51.85 3 33098
4 1 6 8 35.32 5 12104
4 1 6 9 2154.39 173 702215
4 1 7 1 1528.57 87 483084
4 1 7 2 567.56 35 209646
4 1 7 3 563.23 34 107767
4 1 7 4 65.95 3 12950
4 1 7 5 278.46 24 93032
4 1 7 6 395.47 10 27088
4 1 7 7 230.90 5 22495
4 1 7 8 163.53 8 27401
4 1 7 9 8738.13 520 2437429
4 2 1 1 52.42 9 50023
4 2 1 2 18.13 3 33786
4 2 1 3 13.45 0 0
4 2 1 4 7.31 2 6906
4 2 1 5 17.93 7 18501
4 2 1 6 35.36 2 5317
4 2 1 7 10.18 2 1329
4 2 1 8 3.66 2 3465
4 2 1 9 510.14 83 357640
4 2 2 1 73.64 7 45054
4 2 2 2 25.83 4 12796
4 2 2 3 17.27 1 148
4 2 2 4 14.44 0 0
4 2 2 5 23.46 2 6103
4 2 2 6 58.09 5 36882
4 2 2 7 20.45 2 4383
4 2 2 8 6.65 0 0
4 2 2 9 720.52 98 456585
4 2 3 1 126.64 11 28994
4 2 3 2 35.86 4 8066
4 2 3 3 21.01 2 10160
4 2 3 4 16.24 0 0
4 2 3 5 19.53 1 6861
4 2 3 6 56.42 3 7874
4 2 3 7 26.02 3 10624
4 2 3 8 10.09 2 6237
4 2 3 9 855.76 62 303872
4 2 4 1 138.08 16 134301
4 2 4 2 41.49 3 7068
4 2 4 3 34.65 3 38011
4 2 4 4 12.24 0 0
4 2 4 5 24.21 6 25737
4 2 4 6 54.79 2 2560
4 2 4 7 34.39 2 34833
4 2 4 8 12.31 0 0
4 2 4 9 903.99 70 360223
4 2 5 1 199.99 14 66020
4 2 5 2 67.63 8 23998
4 2 5 3 44.13 1 2288
4 2 5 4 12.04 0 0
4 2 5 5 37.01 2 5688
4 2 5 6 67.39 4 5756
4 2 5 7 38.42 3 4812
4 2 5 8 20.27 4 36477
4 2 5 9 1305.83 99 321088
4 2 6 1 452.94 31 97902
4 2 6 2 166.21 17 158030
4 2 6 3 127.04 10 66279
4 2 6 4 16.52 1 1800
4 2 6 5 91.55 8 9753
4 2 6 6 135.02 3 8171
4 2 6 7 83.37 7 14223
4 2 6 8 65.80 1 4332
4 2 6 9 2702.27 157 912421
4 2 7 1 2110.59 107 595146
4 2 7 2 708.77 43 155553
4 2 7 3 717.74 28 222823
4 2 7 4 55.84 2 5417
4 2 7 5 403.75 21 52327
4 2 7 6 630.80 30 78258
4 2 7 7 410.91 26 73043
4 2 7 8 328.26 5 14963
4 2 7 9 12169.67 598 3223609
4 3 1 1 70.13 12 55595
4 3 1 2 17.58 1 8064
4 3 1 3 23.46 2 6214
4 3 1 4 11.23 1 8670
4 3 1 5 13.24 3 2138
4 3 1 6 47.61 5 12105
4 3 1 7 11.87 0 0
4 3 1 8 5.77 0 0
4 3 1 9 499.28 52 237894
4 3 2 1 112.86 11 25656
4 3 2 2 26.77 1 3915
4 3 2 3 25.69 7 41229
4 3 2 4 11.26 1 3468
4 3 2 5 23.55 3 2732
4 3 2 6 78.70 6 18099
4 3 2 7 19.31 4 8908
4 3 2 8 7.38 1 31442
4 3 2 9 784.88 74 291386
4 3 3 1 132.22 11 112977
4 3 3 2 32.33 2 5747
4 3 3 3 23.84 1 31442
4 3 3 4 12.19 1 2400
4 3 3 5 31.33 1 939
4 3 3 6 92.30 6 47618
4 3 3 7 18.55 3 10335
4 3 3 8 7.26 0 0
4 3 3 9 881.54 46 198404
4 3 4 1 181.06 9 45410
4 3 4 2 46.47 0 0
4 3 4 3 29.81 0 0
4 3 4 4 9.02 0 0
4 3 4 5 31.21 6 44195
4 3 4 6 89.92 3 10382
4 3 4 7 31.18 2 3523
4 3 4 8 17.15 3 10519
4 3 4 9 958.53 73 380081
4 3 5 1 232.21 9 86821
4 3 5 2 55.68 0 0
4 3 5 3 48.14 2 34624
4 3 5 4 12.63 0 0
4 3 5 5 52.17 2 3952
4 3 5 6 107.44 6 46145
4 3 5 7 40.18 5 11704
4 3 5 8 38.26 0 0
4 3 5 9 1404.67 95 417261
4 3 6 1 502.26 23 107693
4 3 6 2 135.72 14 84314
4 3 6 3 140.08 5 9624
4 3 6 4 17.48 0 0
4 3 6 5 107.97 5 17978
4 3 6 6 143.88 11 27311
4 3 6 7 87.39 8 42469
4 3 6 8 82.11 4 18826
4 3 6 9 2805.94 139 733705
4 3 7 1 2312.76 107 695827
4 3 7 2 676.83 29 146054
4 3 7 3 748.35 33 169849
4 3 7 4 79.77 5 42430
4 3 7 5 504.39 18 66503
4 3 7 6 862.65 25 124101
4 3 7 7 512.76 17 59311
4 3 7 8 470.40 22 121196
4 3 7 9 13951.57 584 2899470
4 4 1 1 172.47 21 105510
4 4 1 2 26.09 0 0
4 4 1 3 30.77 5 40261
4 4 1 4 13.54 0 0
4 4 1 5 30.82 3 43190
4 4 1 6 104.04 9 25652
4 4 1 7 20.72 4 7244
4 4 1 8 11.16 2 2280
4 4 1 9 944.79 90 407441
4 4 2 1 269.84 31 271937
4 4 2 2 44.88 4 18343
4 4 2 3 43.45 4 16229
4 4 2 4 35.07 2 1770
4 4 2 5 48.57 7 18027
4 4 2 6 164.27 13 55542
4 4 2 7 31.44 2 2738
4 4 2 8 21.80 2 1710
4 4 2 9 1582.15 144 690199
4 4 3 1 324.35 21 81074
4 4 3 2 67.35 5 7762
4 4 3 3 35.51 2 2184
4 4 3 4 17.58 1 1500
4 4 3 5 49.59 6 12520
4 4 3 6 164.43 15 139115
4 4 3 7 48.55 5 9487
4 4 3 8 28.33 2 34108
4 4 3 9 1687.61 120 623928
4 4 4 1 328.35 21 88706
4 4 4 2 80.47 5 6326
4 4 4 3 56.09 3 5281
4 4 4 4 20.88 0 0
4 4 4 5 64.24 4 39255
4 4 4 6 174.10 9 57665
4 4 4 7 50.19 3 7652
4 4 4 8 55.60 4 9368
4 4 4 9 1907.97 101 489424
4 4 5 1 481.30 30 86157
4 4 5 2 130.83 4 41552
4 4 5 3 93.20 4 45751
4 4 5 4 21.78 1 2193
4 4 5 5 83.41 8 27643
4 4 5 6 228.49 12 113934
4 4 5 7 90.12 5 14731
4 4 5 8 84.36 7 13308
4 4 5 9 2775.52 160 865925
4 4 6 1 978.57 44 304384
4 4 6 2 284.51 12 110861
4 4 6 3 259.23 15 36007
4 4 6 4 36.88 0 0
4 4 6 5 179.94 6 57514
4 4 6 6 398.99 18 123132
4 4 6 7 159.68 7 42550
4 4 6 8 179.44 15 135172
4 4 6 9 5553.54 255 1529493
4 4 7 1 5091.56 187 1200157
4 4 7 2 1618.34 67 364718
4 4 7 3 1710.88 74 348802
4 4 7 4 166.09 4 7563
4 4 7 5 1098.94 50 223397
4 4 7 6 2288.50 62 240148
4 4 7 7 1101.12 46 264633
4 4 7 8 1289.41 43 195629
4 4 7 9 30873.62 1186 6834531
4 5 1 1 14.14 2 2676
4 5 1 2 3.98 2 9979
4 5 1 3 1.93 0 0
4 5 1 4 0.13 0 0
4 5 1 5 5.26 1 600
4 5 1 6 12.36 2 7638
4 5 1 7 1.14 0 0
4 5 1 8 1.02 0 0
4 5 1 9 110.40 14 61788
4 5 2 1 22.43 1 1825
4 5 2 2 6.47 0 0
4 5 2 3 3.74 0 0
4 5 2 4 3.60 0 0
4 5 2 5 4.65 0 0
4 5 2 6 19.16 1 1258
4 5 2 7 3.64 1 72
4 5 2 8 2.05 0 0
4 5 2 9 184.50 17 134556
4 5 3 1 28.65 3 2343
4 5 3 2 10.98 1 5762
4 5 3 3 5.65 0 0
4 5 3 4 2.86 0 0
4 5 3 5 6.91 1 956
4 5 3 6 26.36 2 11007
4 5 3 7 3.84 1 2330
4 5 3 8 1.86 0 0
4 5 3 9 210.68 12 49731
4 5 4 1 41.28 1 4333
4 5 4 2 9.24 1 31442
4 5 4 3 9.24 1 1684
4 5 4 4 2.81 0 0
4 5 4 5 8.87 0 0
4 5 4 6 20.82 1 5368
4 5 4 7 8.46 0 0
4 5 4 8 4.40 0 0
4 5 4 9 235.24 15 106855
4 5 5 1 59.64 5 18003
4 5 5 2 13.54 0 0
4 5 5 3 9.66 1 31442
4 5 5 4 0.75 0 0
4 5 5 5 12.18 0 0
4 5 5 6 25.69 0 0
4 5 5 7 14.53 0 0
4 5 5 8 9.86 0 0
4 5 5 9 348.30 30 250211
4 5 6 1 136.90 12 96970
4 5 6 2 30.74 1 1503
4 5 6 3 38.50 3 35613
4 5 6 4 2.31 0 0
4 5 6 5 31.50 3 6302
4 5 6 6 39.79 3 34383
4 5 6 7 27.33 1 31442
4 5 6 8 26.32 2 34167
4 5 6 9 755.36 47 255811
4 5 7 1 593.04 21 123958
4 5 7 2 158.87 11 47492
4 5 7 3 196.15 9 30277
4 5 7 4 12.98 0 0
4 5 7 5 104.85 1 1978
4 5 7 6 194.90 4 10588
4 5 7 7 138.42 7 67566
4 5 7 8 149.13 3 9709
4 5 7 9 3152.35 156 768061
4 6 1 1 59.95 10 31740
4 6 1 2 8.18 0 0
4 6 1 3 7.13 1 2360
4 6 1 4 2.32 0 0
4 6 1 5 8.74 2 13931
4 6 1 6 25.54 3 32660
4 6 1 7 7.17 2 4415
4 6 1 8 3.47 0 0
4 6 1 9 282.66 22 56172
4 6 2 1 93.52 11 25417
4 6 2 2 7.56 0 0
4 6 2 3 5.70 0 0
4 6 2 4 3.57 0 0
4 6 2 5 11.91 3 41995
4 6 2 6 70.70 3 11924
4 6 2 7 10.96 1 31442
4 6 2 8 9.96 0 0
4 6 2 9 468.91 34 209378
4 6 3 1 104.27 8 51392
4 6 3 2 16.00 1 1363
4 6 3 3 9.16 2 4211
4 6 3 4 5.50 0 0
4 6 3 5 11.33 1 3759
4 6 3 6 58.02 3 10592
4 6 3 7 19.89 2 8013
4 6 3 8 11.80 1 6140
4 6 3 9 517.45 34 165960
4 6 4 1 103.11 8 23206
4 6 4 2 22.01 0 0
4 6 4 3 18.18 1 1955
4 6 4 4 3.26 0 0
4 6 4 5 15.31 2 5460
4 6 4 6 56.73 0 0
4 6 4 7 19.28 2 8463
4 6 4 8 25.32 1 2735
4 6 4 9 525.48 29 191633
4 6 5 1 129.17 5 14134
4 6 5 2 32.33 4 15546
4 6 5 3 31.20 1 2965
4 6 5 4 4.05 0 0
4 6 5 5 29.28 0 0
4 6 5 6 70.88 3 36493
4 6 5 7 26.85 5 10031
4 6 5 8 37.44 1 6323
4 6 5 9 777.52 35 203397
4 6 6 1 269.86 15 75377
4 6 6 2 82.85 3 5504
4 6 6 3 79.68 3 9347
4 6 6 4 6.70 0 0
4 6 6 5 64.77 3 13395
4 6 6 6 114.70 4 14816
4 6 6 7 52.70 5 7421
4 6 6 8 84.33 2 10085
4 6 6 9 1566.18 70 289782
4 6 7 1 1647.08 55 309988
4 6 7 2 477.62 23 155510
4 6 7 3 484.42 20 94528
4 6 7 4 35.59 1 31442
4 6 7 5 335.13 16 89775
4 6 7 6 731.98 10 57899
4 6 7 7 314.96 7 19365
4 6 7 8 568.29 24 210966
4 6 7 9 9304.84 356 2121962
4 7 1 1 2.25 0 0
4 7 1 2 0.09 0 0
4 7 1 3 0.90 0 0
4 7 1 5 0.73 0 0
4 7 1 6 3.46 0 0
4 7 1 7 0.60 0 0
4 7 1 9 25.33 2 4465
4 7 2 1 3.70 0 0
4 7 2 2 1.21 0 0
4 7 2 3 0.10 0 0
4 7 2 4 1.76 0 0
4 7 2 5 0.50 0 0
4 7 2 6 4.13 1 429
4 7 2 7 0.20 0 0
4 7 2 9 27.70 2 5216
4 7 3 1 3.23 0 0
4 7 3 2 1.61 0 0
4 7 3 3 0.40 0 0
4 7 3 5 0.70 0 0
4 7 3 6 5.43 1 1073
4 7 3 9 31.66 3 7305
4 7 4 1 4.29 1 626
4 7 4 2 3.47 0 0
4 7 4 3 1.49 0 0
4 7 4 4 0.01 0 0
4 7 4 5 3.31 0 0
4 7 4 6 3.27 0 0
4 7 4 7 0.10 0 0
4 7 4 8 1.85 0 0
4 7 4 9 36.11 3 4855
4 7 5 1 9.89 1 4125
4 7 5 2 1.50 0 0
4 7 5 3 0.20 0 0
4 7 5 4 1.36 0 0
4 7 5 5 1.77 0 0
4 7 5 6 2.74 0 0
4 7 5 8 1.28 0 0
4 7 5 9 46.95 2 2864
4 7 6 1 18.06 0 0
4 7 6 2 5.95 0 0
4 7 6 3 4.06 1 1140
4 7 6 4 2.81 0 0
4 7 6 5 2.70 1 5000
4 7 6 6 8.08 0 0
4 7 6 7 2.85 0 0
4 7 6 8 1.58 0 0
4 7 6 9 100.73 4 14546
4 7 7 1 86.76 1 913
4 7 7 2 36.79 3 6744
4 7 7 3 12.86 0 0
4 7 7 4 6.69 0 0
4 7 7 5 21.03 0 0
4 7 7 6 38.27 0 0
4 7 7 7 12.31 0 0
4 7 7 8 13.59 0 0
4 7 7 9 661.33 15 79549
5 1 1 1 39.38 8 19055
5 1 1 2 33.22 14 70516
5 1 1 3 25.94 6 12853
5 1 1 4 4.97 0 0
5 1 1 5 5.83 1 5315
5 1 1 6 10.55 2 14735
5 1 1 7 4.18 2 3699
5 1 1 8 8.91 4 2745
5 1 1 9 643.63 172 802056
5 1 2 1 40.03 7 53251
5 1 2 2 31.20 8 64325
5 1 2 3 40.44 6 51965
5 1 2 4 4.58 1 8390
5 1 2 5 10.55 0 0
5 1 2 6 20.21 2 8498
5 1 2 7 8.99 0 0
5 1 2 8 7.78 2 31442
5 1 2 9 697.77 122 505940
5 1 3 1 54.57 8 17149
5 1 3 2 36.47 8 46332
5 1 3 3 32.03 6 42364
5 1 3 4 4.03 0 0
5 1 3 5 11.06 0 0
5 1 3 6 18.96 1 1000
5 1 3 7 8.71 2 8327
5 1 3 8 14.50 5 39056
5 1 3 9 618.16 98 524453
5 1 4 1 61.37 3 67055
5 1 4 2 40.59 5 18027
5 1 4 3 32.00 0 0
5 1 4 4 2.43 0 0
5 1 4 5 16.54 1 1725
5 1 4 6 20.67 3 10781
5 1 4 7 9.94 1 3530
5 1 4 8 21.16 3 3762
5 1 4 9 617.39 81 449815
5 1 5 1 92.05 11 18385
5 1 5 2 65.64 10 47270
5 1 5 3 58.99 5 40553
5 1 5 4 1.57 0 0
5 1 5 5 18.46 2 8860
5 1 5 6 22.92 1 1845
5 1 5 7 11.36 3 36029
5 1 5 8 22.87 1 3801
5 1 5 9 820.04 111 426845
5 1 6 1 183.54 8 30510
5 1 6 2 116.62 15 66600
5 1 6 3 115.02 11 56739
5 1 6 4 4.61 0 0
5 1 6 5 42.25 4 6990
5 1 6 6 47.19 4 4778
5 1 6 7 23.47 1 2943
5 1 6 8 55.74 8 105275
5 1 6 9 1623.22 154 653118
5 1 7 1 717.63 47 208573
5 1 7 2 401.42 35 150942
5 1 7 3 439.61 30 266009
5 1 7 4 21.22 1 2000
5 1 7 5 145.24 9 53228
5 1 7 6 182.52 9 15099
5 1 7 7 102.40 5 8972
5 1 7 8 186.24 14 31626
5 1 7 9 5539.09 416 2249007
5 2 1 1 43.32 4 13238
5 2 1 2 21.67 5 8608
5 2 1 3 21.83 1 2495
5 2 1 4 6.92 2 5307
5 2 1 5 9.75 1 6866
5 2 1 6 20.25 0 0
5 2 1 7 5.50 0 0
5 2 1 8 3.68 0 0
5 2 1 9 451.09 87 438695
5 2 2 1 53.04 10 68513
5 2 2 2 26.38 4 8435
5 2 2 3 29.54 3 8813
5 2 2 4 6.84 0 0
5 2 2 5 11.94 2 3694
5 2 2 6 27.82 2 4249
5 2 2 7 11.17 1 2686
5 2 2 8 7.60 0 0
5 2 2 9 576.16 76 302181
5 2 3 1 71.90 8 51707
5 2 3 2 31.96 6 25061
5 2 3 3 28.18 3 34674
5 2 3 4 5.98 0 0
5 2 3 5 10.02 2 2855
5 2 3 6 22.94 1 8000
5 2 3 7 13.41 1 435
5 2 3 8 16.40 1 4005
5 2 3 9 612.27 64 228163
5 2 4 1 75.09 3 12022
5 2 4 2 39.02 2 3970
5 2 4 3 26.66 1 1467
5 2 4 4 4.81 0 0
5 2 4 5 14.32 0 0
5 2 4 6 38.40 1 31442
5 2 4 7 15.27 2 12253
5 2 4 8 19.66 2 7718
5 2 4 9 703.72 91 439898
5 2 5 1 122.00 2 13341
5 2 5 2 49.82 4 38056
5 2 5 3 56.86 0 0
5 2 5 4 4.69 0 0
5 2 5 5 25.10 1 31442
5 2 5 6 38.73 3 3731
5 2 5 7 18.83 2 11144
5 2 5 8 39.01 3 5673
5 2 5 9 1004.07 87 547051
5 2 6 1 276.21 24 84068
5 2 6 2 121.45 12 40273
5 2 6 3 140.30 11 72080
5 2 6 4 5.76 0 0
5 2 6 5 64.51 7 110527
5 2 6 6 71.49 3 4822
5 2 6 7 45.13 1 3571
5 2 6 8 80.96 5 38993
5 2 6 9 2109.22 172 625489
5 2 7 1 1110.45 65 373173
5 2 7 2 484.99 43 139960
5 2 7 3 611.99 34 157871
5 2 7 4 31.88 0 0
5 2 7 5 254.68 20 147025
5 2 7 6 313.88 16 102075
5 2 7 7 203.03 5 14472
5 2 7 8 389.67 20 141846
5 2 7 9 8729.83 517 2613039
5 3 1 1 62.53 6 48495
5 3 1 2 22.94 5 22703
5 3 1 3 17.73 3 15788
5 3 1 4 6.76 1 992
5 3 1 5 8.97 2 31615
5 3 1 6 25.31 3 2575
5 3 1 7 7.18 3 4422
5 3 1 8 4.46 2 7451
5 3 1 9 440.93 54 251193
5 3 2 1 74.65 12 61398
5 3 2 2 21.61 1 1450
5 3 2 3 27.40 3 5061
5 3 2 4 5.81 2 3671
5 3 2 5 13.19 2 4928
5 3 2 6 32.80 5 69277
5 3 2 7 11.21 0 0
5 3 2 8 10.80 2 2629
5 3 2 9 598.14 68 264917
5 3 3 1 94.29 13 54694
5 3 3 2 31.55 3 34055
5 3 3 3 29.43 2 1426
5 3 3 4 5.58 0 0
5 3 3 5 19.91 3 6534
5 3 3 6 44.03 0 0
5 3 3 7 16.00 2 11808
5 3 3 8 11.92 0 0
5 3 3 9 649.11 62 329058
5 3 4 1 107.13 11 94918
5 3 4 2 32.28 3 2313
5 3 4 3 33.65 4 12288
5 3 4 4 3.27 0 0
5 3 4 5 22.77 3 5911
5 3 4 6 43.27 2 10115
5 3 4 7 12.37 1 3392
5 3 4 8 21.73 0 0
5 3 4 9 729.80 63 235765
5 3 5 1 149.79 8 37006
5 3 5 2 58.08 5 37990
5 3 5 3 48.59 6 11364
5 3 5 4 6.96 0 0
5 3 5 5 34.25 4 35822
5 3 5 6 59.82 4 6347
5 3 5 7 23.38 2 6534
5 3 5 8 44.65 3 4969
5 3 5 9 1054.73 69 281281
5 3 6 1 300.28 22 76756
5 3 6 2 124.65 12 92958
5 3 6 3 145.50 5 19178
5 3 6 4 9.91 0 0
5 3 6 5 63.07 5 20281
5 3 6 6 101.73 6 43173
5 3 6 7 51.13 7 28491
5 3 6 8 116.28 4 7403
5 3 6 9 2084.66 159 771665
5 3 7 1 1291.25 41 293493
5 3 7 2 520.94 29 138830
5 3 7 3 676.38 28 235831
5 3 7 4 35.33 2 5829
5 3 7 5 299.99 23 120261
5 3 7 6 523.39 14 62013
5 3 7 7 265.89 13 36704
5 3 7 8 599.43 29 155051
5 3 7 9 9965.28 486 2560945
5 4 1 1 109.23 13 60096
5 4 1 2 31.71 3 36934
5 4 1 3 32.35 2 32365
5 4 1 4 9.88 1 3542
5 4 1 5 19.48 2 1065
5 4 1 6 50.65 5 42686
5 4 1 7 16.11 4 7357
5 4 1 8 15.57 1 9579
5 4 1 9 770.69 91 524705
5 4 2 1 180.10 26 103992
5 4 2 2 35.50 5 65836
5 4 2 3 50.22 2 32896
5 4 2 4 11.90 1 2825
5 4 2 5 36.25 6 11558
5 4 2 6 106.18 7 21782
5 4 2 7 22.34 1 7660
5 4 2 8 25.02 3 6659
5 4 2 9 1141.56 115 557417
5 4 3 1 198.57 18 70984
5 4 3 2 59.81 3 14822
5 4 3 3 46.93 2 4836
5 4 3 4 14.15 0 0
5 4 3 5 35.34 1 1985
5 4 3 6 106.79 5 40142
5 4 3 7 25.13 3 9201
5 4 3 8 34.61 1 1753
5 4 3 9 1219.62 113 506246
5 4 4 1 230.03 9 53377
5 4 4 2 59.93 4 15865
5 4 4 3 47.93 1 31442
5 4 4 4 12.54 1 800
5 4 4 5 34.38 1 2237
5 4 4 6 107.54 7 50019
5 4 4 7 31.52 5 19379
5 4 4 8 56.83 2 3886
5 4 4 9 1419.58 99 647293
5 4 5 1 317.01 15 80540
5 4 5 2 104.40 5 10570
5 4 5 3 102.93 4 5590
5 4 5 4 10.46 0 0
5 4 5 5 50.41 2 4525
5 4 5 6 122.58 5 16623
5 4 5 7 47.24 5 11325
5 4 5 8 92.60 8 43023
5 4 5 9 2014.55 125 644099
5 4 6 1 541.77 32 161900
5 4 6 2 215.82 6 14288
5 4 6 3 246.80 8 58500
5 4 6 4 11.39 0 0
5 4 6 5 133.59 13 95129
5 4 6 6 226.28 10 22795
5 4 6 7 107.83 8 25329
5 4 6 8 242.78 15 168380
5 4 6 9 4231.59 250 1304846
5 4 7 1 2946.70 122 613652
5 4 7 2 1117.96 58 255116
5 4 7 3 1396.49 53 337846
5 4 7 4 75.39 1 1962
5 4 7 5 635.91 29 196401
5 4 7 6 1291.12 50 333231
5 4 7 7 542.86 23 91399
5 4 7 8 1382.66 52 571579
5 4 7 9 21581.24 920 4847989
5 5 1 1 9.75 0 0
5 5 1 2 2.94 0 0
5 5 1 3 14.21 3 13529
5 5 1 4 0.76 0 0
5 5 1 5 3.42 1 4058
5 5 1 6 5.64 0 0
5 5 1 7 2.44 0 0
5 5 1 8 2.49 1 31442
5 5 1 9 117.39 17 121307
5 5 2 1 17.77 0 0
5 5 2 2 4.89 1 9007
5 5 2 3 4.58 0 0
5 5 2 4 0.10 0 0
5 5 2 5 6.13 1 4225
5 5 2 6 5.16 0 0
5 5 2 7 2.39 0 0
5 5 2 8 3.41 0 0
5 5 2 9 140.20 13 95879
5 5 3 1 20.03 0 0
5 5 3 2 6.06 0 0
5 5 3 3 3.24 1 779
5 5 3 4 1.16 0 0
5 5 3 5 1.52 0 0
5 5 3 6 9.01 0 0
5 5 3 7 2.63 0 0
5 5 3 8 10.94 2 6484
5 5 3 9 188.15 13 75374
5 5 4 1 20.61 3 35174
5 5 4 2 7.09 0 0
5 5 4 3 7.60 2 3611
5 5 4 5 3.31 0 0
5 5 4 6 13.00 0 0
5 5 4 7 1.37 0 0
5 5 4 8 11.07 0 0
5 5 4 9 177.36 12 61341
5 5 5 1 28.28 1 716
5 5 5 2 17.99 1 3896
5 5 5 3 21.19 1 1576
5 5 5 5 10.13 0 0
5 5 5 6 10.81 0 0
5 5 5 7 3.99 0 0
5 5 5 8 12.05 0 0
5 5 5 9 234.00 22 107065
5 5 6 1 54.72 1 3000
5 5 6 2 21.61 2 4502
5 5 6 3 42.44 2 3695
5 5 6 4 1.65 0 0
5 5 6 5 16.46 0 0
5 5 6 6 26.23 2 10259
5 5 6 7 13.65 3 5598
5 5 6 8 39.76 4 15915
5 5 6 9 568.65 42 186899
5 5 7 1 266.04 17 80318
5 5 7 2 116.75 6 48119
5 5 7 3 171.84 9 26797
5 5 7 4 2.07 0 0
5 5 7 5 61.96 4 10580
5 5 7 6 114.36 2 39981
5 5 7 7 49.37 2 5391
5 5 7 8 173.28 11 119909
5 5 7 9 2387.46 99 559278
5 6 1 1 30.80 4 8714
5 6 1 2 11.97 2 7747
5 6 1 3 3.22 1 31442
5 6 1 4 1.34 0 0
5 6 1 5 8.91 2 3112
5 6 1 6 15.68 0 0
5 6 1 7 6.17 0 0
5 6 1 8 6.94 1 994
5 6 1 9 201.95 15 120724
5 6 2 1 62.69 9 20731
5 6 2 2 8.04 0 0
5 6 2 3 10.73 0 0
5 6 2 4 1.68 0 0
5 6 2 5 15.42 1 3277
5 6 2 6 31.15 2 5291
5 6 2 7 9.18 1 4884
5 6 2 8 10.16 0 0
5 6 2 9 316.66 21 119632
5 6 3 1 63.63 2 5400
5 6 3 2 11.93 2 9525
5 6 3 3 12.55 0 0
5 6 3 4 2.30 0 0
5 6 3 5 10.67 1 31442
5 6 3 6 38.64 2 1953
5 6 3 7 13.39 3 9508
5 6 3 8 12.02 1 4581
5 6 3 9 359.57 26 139072
5 6 4 1 69.43 11 62295
5 6 4 2 13.47 1 2575
5 6 4 3 14.11 2 32158
5 6 4 4 1.05 0 0
5 6 4 5 7.50 1 31442
5 6 4 6 36.19 0 0
5 6 4 7 8.58 1 1135
5 6 4 8 22.65 1 3590
5 6 4 9 393.00 24 116662
5 6 5 1 87.44 5 17072
5 6 5 2 23.03 2 2283
5 6 5 3 23.02 0 0
5 6 5 4 1.58 0 0
5 6 5 5 10.55 2 32423
5 6 5 6 32.49 5 68672
5 6 5 7 10.74 0 0
5 6 5 8 32.78 0 0
5 6 5 9 533.49 36 186668
5 6 6 1 157.06 5 16138
5 6 6 2 49.35 3 64610
5 6 6 3 67.45 2 2977
5 6 6 4 1.15 0 0
5 6 6 5 39.60 1 1802
5 6 6 6 75.36 2 11385
5 6 6 7 25.64 1 1968
5 6 6 8 102.98 7 46010
5 6 6 9 1203.01 65 389080
5 6 7 1 889.43 34 261859
5 6 7 2 313.49 18 137743
5 6 7 3 415.78 11 79125
5 6 7 4 19.50 1 874
5 6 7 5 178.83 10 21659
5 6 7 6 389.82 17 64534
5 6 7 7 147.94 7 24026
5 6 7 8 579.49 29 130489
5 6 7 9 6392.60 317 1517683
5 7 1 1 0.90 0 0
5 7 1 2 0.04 0 0
5 7 1 5 0.70 0 0
5 7 1 9 14.77 2 8628
5 7 2 1 2.25 0 0
5 7 2 2 0.72 0 0
5 7 2 3 0.46 0 0
5 7 2 5 0.30 0 0
5 7 2 6 1.32 0 0
5 7 2 7 0.46 0 0
5 7 2 9 27.54 1 1314
5 7 3 1 4.71 0 0
5 7 3 2 1.88 0 0
5 7 3 3 0.08 0 0
5 7 3 5 0.04 0 0
5 7 3 6 1.88 0 0
5 7 3 7 0.58 0 0
5 7 3 9 23.65 2 6600
5 7 4 1 3.74 0 0
5 7 4 2 1.20 0 0
5 7 4 4 0.70 0 0
5 7 4 6 0.96 1 1231
5 7 4 7 0.03 0 0
5 7 4 9 24.61 0 0
5 7 5 1 5.98 2 6102
5 7 5 2 0.80 0 0
5 7 5 3 1.10 0 0
5 7 5 4 0.34 0 0
5 7 5 5 0.70 0 0
5 7 5 6 2.48 0 0
5 7 5 7 0.60 1 2935
5 7 5 8 1.14 0 0
5 7 5 9 38.77 1 1150
5 7 6 1 8.47 0 0
5 7 6 2 2.49 0 0
5 7 6 3 2.89 0 0
5 7 6 4 0.13 0 0
5 7 6 5 1.36 0 0
5 7 6 6 4.15 0 0
5 7 6 7 2.23 0 0
5 7 6 8 1.96 0 0
5 7 6 9 69.70 2 32275
5 7 7 1 51.24 1 31442
5 7 7 2 21.74 2 31942
5 7 7 3 9.91 0 0
5 7 7 4 2.35 0 0
5 7 7 5 8.74 0 0
5 7 7 6 16.61 0 0
5 7 7 7 2.83 1 966
5 7 7 8 13.06 0 0
5 7 7 9 384.87 16 112252
;
run;
data temp;
set motorins;
payment=payment/1000000;
run;
ods graphics on;
proc sgplot data=temp;
title "Distribution of Payment";
histogram payment / nbins=25;
xaxis label="Payment (in millions)";
run;
title ;
proc freq data=motorins;
table zeros / plots=freqplot(scale=percent);
run;
options linesize=120;
proc hpgenselect data=motorins;
class Kilometres Zone Make / split param=reference;
model payment = Kilometres|Zone|Make|Bonus /
dist=tweedie link=log offset=loginsured;
selection method=stepwise(choose=aicc) details=summary;
output out=tweedie P R;
id payment;
run;
options linesize=80;
proc sort data=tweedie out=tweedie;
by payment;
run;
proc sgplot data=tweedie;
scatter x=payment y=pred / legendlabel="Predicted";
series x=payment y=payment / lineattrs=(pattern=solid color=red)
legendlabel="45 degree line";
yaxis label="Predicted";
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.
Type: | Sample |
Topic: | SAS Reference ==> Procedures ==> HPGENSELECT |
Date Modified: | 2017-01-12 16:11:37 |
Date Created: | 2016-10-27 16:26:02 |
Product Family | Product | Host | SAS Release | |
Starting | Ending | |||
SAS System | SAS/STAT | z/OS | ||
z/OS 64-bit | ||||
OpenVMS VAX | ||||
Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||
Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||
Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||
Microsoft Windows XP 64-bit Edition | ||||
Microsoft® Windows® for x64 | ||||
OS/2 | ||||
Microsoft Windows 8 Enterprise 32-bit | ||||
Microsoft Windows 8 Enterprise x64 | ||||
Microsoft Windows 8 Pro 32-bit | ||||
Microsoft Windows 8 Pro x64 | ||||
Microsoft Windows 8.1 Enterprise 32-bit | ||||
Microsoft Windows 8.1 Enterprise x64 | ||||
Microsoft Windows 8.1 Pro 32-bit | ||||
Microsoft Windows 8.1 Pro x64 | ||||
Microsoft Windows 10 | ||||
Microsoft Windows 95/98 | ||||
Microsoft Windows 2000 Advanced Server | ||||
Microsoft Windows 2000 Datacenter Server | ||||
Microsoft Windows 2000 Server | ||||
Microsoft Windows 2000 Professional | ||||
Microsoft Windows NT Workstation | ||||
Microsoft Windows Server 2003 Datacenter Edition | ||||
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 2008 R2 | ||||
Microsoft Windows Server 2008 for x64 | ||||
Microsoft Windows Server 2012 Datacenter | ||||
Microsoft Windows Server 2012 R2 Datacenter | ||||
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 |