MachineLearningPractice1

The below code is for Rmarkdown to generate output even if there are errors

knitr::opts_chunk$set(error = TRUE,cache.extra = knitr::rand_seed)

Lets Install Package

library("caret", "skimr")

## Loading required package: lattice

## Loading required package: ggplot2

## Registered S3 methods overwritten by 'ggplot2':
##   method         from 
##   [.quosures     rlang
##   c.quosures     rlang
##   print.quosures rlang

library("RANN", "randomForest", "fastAdaboost")

## Warning: package 'RANN' was built under R version 3.6.1

## Warning in library("RANN", "randomForest", "fastAdaboost"): 'fastAdaboost'
## not found on search path, using pos = 2

library("gbm", "xgboost")

## Warning: package 'gbm' was built under R version 3.6.1

## Loaded gbm 2.1.5

library("caretEnsemble", "C50")

## Warning: package 'caretEnsemble' was built under R version 3.6.3

## 
## Attaching package: 'caretEnsemble'

## The following object is masked from 'package:ggplot2':
## 
##     autoplot

library("earth")

## Warning: package 'earth' was built under R version 3.6.3

## Loading required package: Formula

## Loading required package: plotmo

## Warning: package 'plotmo' was built under R version 3.6.3

## Loading required package: plotrix

## Loading required package: TeachingDemos

## Warning: package 'TeachingDemos' was built under R version 3.6.3

Import Dataset

orange <- read.csv('https://raw.githubusercontent.com/selva86/datasets/master/orange_juice_withmissing.csv')

Lets see the Structure of the dataframe

str(orange)

## 'data.frame':    1070 obs. of  18 variables:
##  $ Purchase      : Factor w/ 2 levels "CH","MM": 1 1 1 2 1 1 1 1 1 1 ...
##  $ WeekofPurchase: int  237 239 245 227 228 230 232 234 235 238 ...
##  $ StoreID       : int  1 1 1 1 7 7 7 7 7 7 ...
##  $ PriceCH       : num  1.75 1.75 1.86 1.69 1.69 1.69 1.69 1.75 1.75 1.75 ...
##  $ PriceMM       : num  1.99 1.99 2.09 1.69 1.69 1.99 1.99 1.99 1.99 1.99 ...
##  $ DiscCH        : num  0 0 0.17 0 0 0 0 0 0 0 ...
##  $ DiscMM        : num  0 0.3 0 0 0 0 0.4 0.4 0.4 0.4 ...
##  $ SpecialCH     : int  0 0 0 0 0 0 1 1 0 0 ...
##  $ SpecialMM     : int  0 1 0 0 0 1 1 0 0 0 ...
##  $ LoyalCH       : num  0.5 0.6 0.68 0.4 0.957 ...
##  $ SalePriceMM   : num  1.99 1.69 2.09 1.69 1.69 1.99 1.59 1.59 1.59 1.59 ...
##  $ SalePriceCH   : num  1.75 1.75 1.69 1.69 1.69 1.69 1.69 1.75 1.75 1.75 ...
##  $ PriceDiff     : num  0.24 -0.06 0.4 0 0 0.3 -0.1 -0.16 -0.16 -0.16 ...
##  $ Store7        : Factor w/ 2 levels "No","Yes": 1 1 1 1 2 2 2 2 2 2 ...
##  $ PctDiscMM     : num  0 0.151 0 0 0 ...
##  $ PctDiscCH     : num  0 0 0.0914 0 0 ...
##  $ ListPriceDiff : num  0.24 0.24 0.23 0 0 0.3 0.3 0.24 0.24 0.24 ...
##  $ STORE         : int  1 1 1 1 0 0 0 0 0 0 ...

See top 6 rows and 10 columns

head(orange[, 1:10])

##   Purchase WeekofPurchase StoreID PriceCH PriceMM DiscCH DiscMM SpecialCH
## 1       CH            237       1    1.75    1.99   0.00    0.0         0
## 2       CH            239       1    1.75    1.99   0.00    0.3         0
## 3       CH            245       1    1.86    2.09   0.17    0.0         0
## 4       MM            227       1    1.69    1.69   0.00    0.0         0
## 5       CH            228       7    1.69    1.69   0.00    0.0         0
## 6       CH            230       7    1.69    1.99   0.00    0.0         0
##   SpecialMM  LoyalCH
## 1         0 0.500000
## 2         1 0.600000
## 3         0 0.680000
## 4         0 0.400000
## 5         0 0.956535
## 6         1 0.965228

Data Preparation and Preprocessing

How to Split the dataset into training and Test set

We will split it into training(80%) and test (20%) using caret’s createdatapartition() method It preserves the proportion of the categories in Y variable. In the argument, we need to give the column of our Y variable.
Setting the seed

set.seed(100)

Step 1: Get row numbers for the training data

trainRowNumbers <- createDataPartition(orange$Purchase, p=0.8, list=FALSE)

createDataPartition() takes as input the Y variable in the source dataset and the percentage data that should go into training as the p argument. It returns the rownumbers that should form the training dataset.Plus, you need to set list=F, to prevent returning the result as a list.

Step 2: Create the training dataset

trainData <- orange[trainRowNumbers,]

Step 3: Create the test dataset

testData <- orange[-trainRowNumbers,]

Store X and Y for later use.

x = trainData[, 2:18]
y = trainData$Purchase

Lets see a data summary

library(skimr)

## Warning: package 'skimr' was built under R version 3.6.3

skimmed <- skim(trainData)
a <- skimmed[, c(1:4,6,8,9:10,12,14:15)]
a

Data summary
Name	trainData
Number of rows	857
Number of columns	18
_______________________
Column type frequency:
factor	2
numeric	16
________________________
Group variables	None

Variable type: factor

skim_variable	n_missing	complete_rate	n_unique
Purchase	0	1	2
Store7	0	1	2

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p50	p100	hist
WeekofPurchase	0	1.00	254.16	15.64	227.00	256.00	278.00	▇▅▅▇▇
StoreID	1	1.00	4.01	2.33	1.00	3.00	7.00	▇▅▃▁▇
PriceCH	0	1.00	1.87	0.10	1.69	1.86	2.09	▅▂▇▆▁
PriceMM	2	1.00	2.08	0.14	1.69	2.09	2.29	▂▁▃▇▆
DiscCH	1	1.00	0.05	0.12	0.00	0.00	0.50	▇▁▁▁▁
DiscMM	4	1.00	0.13	0.22	0.00	0.00	0.80	▇▁▁▁▁
SpecialCH	2	1.00	0.15	0.36	0.00	0.00	1.00	▇▁▁▁▂
SpecialMM	5	0.99	0.17	0.37	0.00	0.00	1.00	▇▁▁▁▂
LoyalCH	3	1.00	0.56	0.31	0.00	0.60	1.00	▅▃▆▆▇
SalePriceMM	5	0.99	1.96	0.26	1.19	2.09	2.29	▁▂▂▂▇
SalePriceCH	1	1.00	1.81	0.15	1.39	1.86	2.09	▂▁▇▇▅
PriceDiff	0	1.00	0.14	0.27	-0.67	0.23	0.64	▁▂▃▇▂
PctDiscMM	4	1.00	0.06	0.10	0.00	0.00	0.40	▇▁▁▁▁
PctDiscCH	2	1.00	0.03	0.06	0.00	0.00	0.25	▇▁▁▁▁
ListPriceDiff	0	1.00	0.22	0.11	0.00	0.24	0.44	▂▃▅▇▁
STORE	2	1.00	1.59	1.43	0.00	2.00	4.00	▇▃▅▅▃

How to Impute missing values using preprocess()

Lets impute the missing values using knn impute

To predict the missing values with k-Nearest Neighbors using preProcess():

You need to set the method=knnImpute for k-Nearest Neighbors and apply it on the training data. This creates a preprocess model. Then use predict() on the created preprocess model by setting the newdata argument on the same training data.

# Create the knn imputation model on the training data
preProcess_missingdata_model <- preProcess(trainData, method='knnImpute')
preProcess_missingdata_model

## Created from 827 samples and 18 variables
## 
## Pre-processing:
##   - centered (16)
##   - ignored (2)
##   - 5 nearest neighbor imputation (16)
##   - scaled (16)

The above output shows the various preprocessing steps done in the process of knn imputation.

That is, it has centered (subtract by mean) 16 variables, ignored 2, used k=5 (considered 5 nearest neighbors) to predict the missing values and finally scaled (divide by standard deviation) 16 variables.

Let’s now use this model to predict the missing values in trainData.

# Use the imputation model to predict the values of missing data points
library(RANN)  # required for knnInpute
trainData <- predict(preProcess_missingdata_model, newdata = trainData)
anyNA(trainData)

## [1] FALSE

All the missing values are successfully imputed.

Lets create one hot encoding of the dummy Variables. you should ensure the dummyVars model is built on the training data alone and that model is in turn used to create the dummy vars on the test data.

In caret, one-hot-encodings can be created using dummyVars(). Lets do the one hot encoding

dummies_model <- dummyVars(Purchase ~ ., data=trainData)

Create the dummy variables using predict. The Y variable (Purchase) will not be present in trainData_mat.

trainData_mat <- predict(dummies_model, newdata = trainData)

## Warning in model.frame.default(Terms, newdata, na.action = na.action, xlev
## = object$lvls): variable 'Purchase' is not a factor

Converting to dataframed

trainData <- data.frame(trainData_mat)

See the structure of the new dataset

str(trainData)

## 'data.frame':    857 obs. of  18 variables:
##  $ WeekofPurchase: num  -1.097 -0.969 -0.586 -1.737 -1.673 ...
##  $ StoreID       : num  -1.29 -1.29 -1.29 -1.29 1.29 ...
##  $ PriceCH       : num  -1.1422 -1.1422 -0.0592 -1.7329 -1.7329 ...
##  $ PriceMM       : num  -0.6795 -0.6795 0.0498 -2.8676 -2.8676 ...
##  $ DiscCH        : num  -0.444 -0.444 0.981 -0.444 -0.444 ...
##  $ DiscMM        : num  -0.578 0.793 -0.578 -0.578 -0.578 ...
##  $ SpecialCH     : num  -0.425 -0.425 -0.425 -0.425 -0.425 ...
##  $ SpecialMM     : num  -0.447 2.235 -0.447 -0.447 -0.447 ...
##  $ LoyalCH       : num  -0.211 0.116 0.378 -0.539 1.284 ...
##  $ SalePriceMM   : num  0.13 -1.037 0.519 -1.037 -1.037 ...
##  $ SalePriceCH   : num  -0.432 -0.432 -0.843 -0.843 -0.843 ...
##  $ PriceDiff     : num  0.352 -0.744 0.936 -0.525 -0.525 ...
##  $ Store7.No     : num  1 1 1 1 0 0 0 0 0 0 ...
##  $ Store7.Yes    : num  0 0 0 0 1 1 1 1 1 1 ...
##  $ PctDiscMM     : num  -0.587 0.861 -0.587 -0.587 -0.587 ...
##  $ PctDiscCH     : num  -0.44 -0.44 1 -0.44 -0.44 ...
##  $ ListPriceDiff : num  0.21 0.21 0.118 -2.012 -2.012 ...
##  $ STORE         : num  -0.412 -0.412 -0.412 -0.412 -1.111 ...

In above case, we had one categorical variable, Store7 with 2 categories. It was one-hot-encoded to produce two new columns – Store7.No and Store7.Yes.

Preprocessing to Transform the data

The following are the Transformations available in Caret

range: Normalize values so it ranges between 0 and 1 center: Subtract Mean scale: Divide by standard deviation BoxCox: Remove skewness leading to normality. Values must be > 0 YeoJohnson: Like BoxCox, but works for negative values. expoTrans: Exponential transformation, works for negative values. pca: Replace with principal components ica: Replace with independent components spatialSign: Project the data to a unit circle

For our problem, let’s convert all the numeric variables to range between 0 and 1, by setting method=range in preProcess()

preProcess_range_model <- preProcess(trainData, method='range')
trainData <- predict(preProcess_range_model, newdata = trainData)

Lets append the y Variable. Remember we have created two variables y and x above

trainData$Purchase <- y
str(trainData)

## 'data.frame':    857 obs. of  19 variables:
##  $ WeekofPurchase: num  0.1961 0.2353 0.3529 0 0.0196 ...
##  $ StoreID       : num  0 0 0 0 1 1 1 1 1 1 ...
##  $ PriceCH       : num  0.15 0.15 0.425 0 0 ...
##  $ PriceMM       : num  0.5 0.5 0.667 0 0 ...
##  $ DiscCH        : num  0 0 0.34 0 0 0 0 0 0 0.54 ...
##  $ DiscMM        : num  0 0.375 0 0 0 0 0.5 0.5 0.5 0 ...
##  $ SpecialCH     : num  0 0 0 0 0 0 1 0 0 0 ...
##  $ SpecialMM     : num  0 1 0 0 0 1 0 0 0 0 ...
##  $ LoyalCH       : num  0.5 0.6 0.68 0.4 0.957 ...
##  $ SalePriceMM   : num  0.727 0.455 0.818 0.455 0.455 ...
##  $ SalePriceCH   : num  0.514 0.514 0.429 0.429 0.429 ...
##  $ PriceDiff     : num  0.695 0.466 0.817 0.511 0.511 ...
##  $ Store7.No     : num  1 1 1 1 0 0 0 0 0 0 ...
##  $ Store7.Yes    : num  0 0 0 0 1 1 1 1 1 1 ...
##  $ PctDiscMM     : num  0 0.375 0 0 0 ...
##  $ PctDiscCH     : num  0 0 0.362 0 0 ...
##  $ ListPriceDiff : num  0.545 0.545 0.523 0 0 ...
##  $ STORE         : num  0.25 0.25 0.25 0.25 0 0 0 0 0 0 ...
##  $ Purchase      : Factor w/ 2 levels "CH","MM": 1 1 1 2 1 1 1 1 1 1 ...

apply(trainData[, 1:10], 2, FUN=function(x){c('min'=min(x), 'max'=max(x))}) ## WHY 1st 10, why not all

##     WeekofPurchase StoreID PriceCH PriceMM DiscCH DiscMM SpecialCH
## min              0       0       0       0      0      0         0
## max              1       1       1       1      1      1         1
##     SpecialMM LoyalCH SalePriceMM
## min         0       0           0
## max         1       1           1

How to visualize the feature importance

A simple common sense approach is, if you group the X variable by the categories of Y, a significant mean shift amongst the X’s groups is a strong indicator (if not the only indicator) that X will have a significant role to help predict Y.

It is possible to watch this shift visually using box plots and density plots.

In fact, caret’s featurePlot() function makes it so convenient.

Simply set the X and Y parameters and set plot=‘box’. You can additionally adjust the label font size (using strip) and the scales to be free as I have done in the below plot.

featurePlot(x = trainData[, 1:18], 
            y = trainData$Purchase, 
            plot = "box",
            strip=strip.custom(par.strip.text=list(cex=.7)),
            scales = list(x = list(relation="free"), 
                          y = list(relation="free")))

Consider for example, LoyalCHs subplot, which measures the loyalty score of the customer to the CH brand. The mean and the placement of the two boxes are glaringly different.

Just by seeing that, I am pretty sure, LoyalCH is going to be a significant predictor of Y.

Let’s do a similar exercise with density plots.

In this case, For a variable to be important, I would expect the density curves to be significantly different for the 2 classes, both in terms of the height (kurtosis) and placement (skewness).

featurePlot(x = trainData[, 1:18], 
            y = trainData$Purchase, 
            plot = "density",
            strip=strip.custom(par.strip.text=list(cex=.7)),
            scales = list(x = list(relation="free"), 
                          y = list(relation="free")))

Take a look at the density curves of the two categories for ‘LoyalCH’, ‘STORE’, ‘StoreID’, ‘WeekofPurchase’. Are they different?

Having visualised the relationships between X and Y, We can only say which variables are likely to be important to predict Y. It may not be wise to conclude which variables are NOT important.

Because sometimes, variables with uninteresting pattern can help explain certain aspects of Y that the visually important variables may not.

So to be safe, let’s not arrive at conclusions about excluding variables prematurely.

Recursive Feature Elimination usie rfe()

A good choice of selecting the important features is the recursive feature elimination (RFE).

So how does recursive feature elimination work?

RFE works in 3 broad steps:

Step 1: Build a ML model on a training dataset and estimate the feature importances on the test dataset.

Step 2: Keeping priority to the most important variables, iterate through by building models of given subset sizes, that is, subgroups of most important predictors determined from step 1. Ranking of the predictors is recalculated in each iteration.

Step 3: The model performances are compared across different subset sizes to arrive at the optimal number and list of final predictors.

It can be implemented using the rfe() function and you have the flexibility to control what algorithm rfe uses and how it cross validates by defining the rfeControl().

set.seed(100)
options(warn=-1)

subsets <- c(1:5, 10, 15, 18)

ctrl <- rfeControl(functions = rfFuncs,
                   method = "repeatedcv",
                   repeats = 5,
                   verbose = FALSE)

lmProfile <- rfe(x=trainData[, 1:18], y=trainData$Purchase,
                 sizes = subsets,
                 rfeControl = ctrl)

lmProfile

## 
## Recursive feature selection
## 
## Outer resampling method: Cross-Validated (10 fold, repeated 5 times) 
## 
## Resampling performance over subset size:
## 
##  Variables Accuracy  Kappa AccuracySD KappaSD Selected
##          1   0.7815 0.5340    0.03321 0.07347         
##          2   0.8210 0.6219    0.04125 0.08631         
##          3   0.8243 0.6296    0.04133 0.08696        *
##          4   0.8112 0.6036    0.04315 0.09059         
##          5   0.8119 0.6048    0.04300 0.09022         
##         10   0.8131 0.6050    0.04039 0.08581         
##         15   0.8133 0.6048    0.03993 0.08518         
##         18   0.8115 0.6017    0.04319 0.09164         
## 
## The top 3 variables (out of 3):
##    LoyalCH, PriceDiff, StoreID

Apart from the x and y datasets, RFE also takes two important parameters.

sizes rfeControl The sizes determines what all model sizes (the number of most important features) the rfe should consider. In above case, it iterates models of size 1 to 5, 10, 15 and 18.

From the above output, a model size of 3 with LoyalCH, PriceDiff and StoreID seems to achieve the optimal accuracy.

That means, out of 18 other features, a model with just 3 features outperformed many other larger model. Interesting isn’t it! Can you explain why?

However, it is not a mandate that only including these 3 variables will always give high accuracy over larger sized models.

Thats because, the rfe() we just implemented is particular to random forest based rfFuncs

Since ML algorithms have their own way of learning the relationship between the x and y, it is not wise to neglect the other predictors, especially when there is evidence that there is information contained in rest of the variables to explain the relationship between x and y.

Plus also, since the training dataset isn’t large enough, the other predictors may not have had the chance to show its worth.

In the next step, we will build the actual randomForest model on trainData.

Training and Tuning the Model

Let’s train a Multivariate Adaptive Regression Splines (MARS) model by setting the method=‘earth’.

The MARS algorithm was named as ‘earth’ in R because of a possible trademark conflict with Salford Systems. May be a rumor. Or not.

modelLookup('earth')

##   model parameter          label forReg forClass probModel
## 1 earth    nprune         #Terms   TRUE     TRUE      TRUE
## 2 earth    degree Product Degree   TRUE     TRUE      TRUE

Set the seed for reproducibility

  set.seed(100)

Train the model using earth and predict on the training data itself

model_mars = train(Purchase ~ ., data=trainData, method='earth')
fitted <- predict(model_mars)

But you may ask how is using train() different from using the algorithm’s function directly?

The difference is, besides building the model train() does multiple other things like:

Cross validating the model Tune the hyper parameters for optimal model performance Choose the optimal model based on a given evaluation metric Preprocess the predictors (what we did so far using preProcess()) The train function also accepts the arguments used by the algorithm specified in the method argument.

Now let’s see what the train() has generated.

model_mars

## Multivariate Adaptive Regression Spline 
## 
## 857 samples
##  18 predictor
##   2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 857, 857, 857, 857, 857, 857, ... 
## Resampling results across tuning parameters:
## 
##   nprune  Accuracy   Kappa    
##    2      0.8116999  0.5969106
##    9      0.8234148  0.6245781
##   17      0.8105738  0.5975440
## 
## Tuning parameter 'degree' was held constant at a value of 1
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were nprune = 9 and degree = 1.

You can see what is the Accuracy and Kappa for various combinations of the hyper parameters – interaction.depth and n.trees. And it says ‘Resampling: Bootstrapped (25 reps)’ with a summary of sample sizes.

Looks like train() has already done a basic cross validation and hyper parameter tuning. And that is the default behaviour.

The chosen model and its parameters is reported in the last 2 lines of the output.

When we used model_mars to predict the Y, this final model was automatically used by predict() to compute the predictions.

Plotting the model shows how the various iterations of hyperparameter search performed.

plot(model_mars, main="Model Accuracies with MARS")

How to compute variable importance

Excellent, since MARS supports computing variable importances, let’s extract the variable importances using varImp() to understand which variables came out to be useful.

varimp_mars <- varImp(model_mars)
plot(varimp_mars, main="Variable Importance with MARS")

As suspected, LoyalCH was the most used variable, followed by PriceDiff and StoreID.

Prepare the test dataset and Predict

A default MARS model has been selected.

Now in order to use the model to predict on new data, the data has to be preprocessed and transformed just the way we did on the training data.

Thanks to caret, all the information required for pre-processing is stored in the respective preProcess model and dummyVar model.

If you recall, we did the pre-processing in the following sequence:

Missing Value imputation –> One-Hot Encoding –> Range Normalization

You need to pass the testData through these models in the same sequence:

preProcess_missingdata_model –> dummies_model –> preProcess_range_model

# Step 1: Impute missing values 
testData2 <- predict(preProcess_missingdata_model, testData)  

# Step 2: Create one-hot encodings (dummy variables)
testData3 <- predict(dummies_model, testData2)

# Step 3: Transform the features to range between 0 and 1
testData4 <- predict(preProcess_range_model, testData3)

# View
head(testData4[, 1:10])

##    WeekofPurchase   StoreID PriceCH   PriceMM DiscCH DiscMM SpecialCH
## 7      0.09803922 1.0000000   0.000 0.5000000      0    0.5         1
## 11     0.25490196 1.0000000   0.425 0.6666667      0    0.0         0
## 18     0.80392157 0.1666667   0.425 0.8166667      0    0.0         0
## 21     0.58823529 1.0000000   0.425 0.8166667      0    0.0         0
## 33     0.94117647 0.1666667   0.675 0.8166667      0    1.0         0
## 35     0.47058824 0.3333333   0.750 0.9000000      0    0.0         0
##    SpecialMM   LoyalCH SalePriceMM
## 7          1 0.9722332   0.3636364
## 11         0 0.9886583   0.8181818
## 18         1 0.4000146   0.9000000
## 21         0 0.6000274   0.9000000
## 33         1 0.6800325   0.1727273
## 35         0 0.5440238   0.9454545

Predict on the Testdata

# Predict on testData
predicted <- predict(model_mars, testData4)
head(predicted)

## [1] CH CH CH CH MM CH
## Levels: CH MM

Confusion Matrix

The confusion matrix is a tabular representation to compare the predictions (data) vs the actuals (reference). By setting mode=‘everything’ pretty much most classification evaluation metrics are computed.

# Compute the confusion matrix
confusionMatrix(reference = testData$Purchase, data = predicted, mode='everything', positive='MM')

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  CH  MM
##         CH 114  26
##         MM  16  57
##                                         
##                Accuracy : 0.8028        
##                  95% CI : (0.743, 0.854)
##     No Information Rate : 0.6103        
##     P-Value [Acc > NIR] : 1.281e-09     
##                                         
##                   Kappa : 0.5762        
##                                         
##  Mcnemar's Test P-Value : 0.1649        
##                                         
##             Sensitivity : 0.6867        
##             Specificity : 0.8769        
##          Pos Pred Value : 0.7808        
##          Neg Pred Value : 0.8143        
##               Precision : 0.7808        
##                  Recall : 0.6867        
##                      F1 : 0.7308        
##              Prevalence : 0.3897        
##          Detection Rate : 0.2676        
##    Detection Prevalence : 0.3427        
##       Balanced Accuracy : 0.7818        
##                                         
##        'Positive' Class : MM            
##

You have an overall accuracy of 80.28%.

hyperparameter tuning to optimize the model for better performance

There are two main ways to do hyper parameter tuning using the train():

Set the tuneLength
Define and set the tuneGrid

tuneLength corresponds to the number of unique values for the tuning parameters caret will consider while forming the hyper parameter combinations.

Caret will automatically determine the values each parameter should take.

Alternately, if you want to explicitly control what values should be considered for each parameter, then, you can define the tuneGrid and pass it to train().

Let’s see an example of both these approaches but first let’s setup the trainControl().

Setting up the traincontrol

The train() function takes a trControl argument that accepts the output of trainControl().

Inside trainControl() you can control how the train() will:

Cross validation method to use. How the results should be summarised using a summary function Cross validation method can be one amongst:

‘boot’: Bootstrap sampling ‘boot632’: Bootstrap sampling with 63.2% bias correction applied ‘optimism_boot’: The optimism bootstrap estimator ‘boot_all’: All boot methods. ‘cv’: k-Fold cross validation ‘repeatedcv’: Repeated k-Fold cross validation ‘oob’: Out of Bag cross validation ‘LOOCV’: Leave one out cross validation ‘LGOCV’: Leave group out cross validation The summaryFunction can be twoClassSummary if Y is binary class or multiClassSummary if the Y has more than 2 categories.

By settiung the classProbs=T the probability scores are generated instead of directly predicting the class based on a predetermined cutoff of 0.5.

# Define the training control
fitControl <- trainControl(
    method = 'cv',                   # k-fold cross validation
    number = 5,                      # number of folds
    savePredictions = 'final',       # saves predictions for optimal tuning parameter
    classProbs = T,                  # should class probabilities be returned
    summaryFunction=twoClassSummary  # results summary function
)

Hyperparameter tuning using tunelength

Let’s take the train() function we used before, plus, additionally set the tuneLength, trControl and metric.

# Step 1: Tune hyper parameters by setting tuneLength
set.seed(100)
model_mars2 = train(Purchase ~ ., data=trainData, method='earth', tuneLength = 5, metric='ROC', trControl = fitControl)
model_mars2

## Multivariate Adaptive Regression Spline 
## 
## 857 samples
##  18 predictor
##   2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 685, 686, 685, 686, 686 
## Resampling results across tuning parameters:
## 
##   nprune  ROC        Sens       Spec     
##    2      0.8837092  0.8757143  0.7094075
##    5      0.9025000  0.8795421  0.7513795
##    9      0.8929800  0.8719048  0.7423338
##   13      0.8930665  0.8719048  0.7393035
##   17      0.8930665  0.8719048  0.7393035
## 
## Tuning parameter 'degree' was held constant at a value of 1
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were nprune = 5 and degree = 1.

# Step 2: Predict on testData and Compute the confusion matrix
predicted2 <- predict(model_mars2, testData4)
confusionMatrix(reference = testData$Purchase, data = predicted2, mode='everything', positive='MM')

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  CH  MM
##         CH 113  27
##         MM  17  56
##                                           
##                Accuracy : 0.7934          
##                  95% CI : (0.7328, 0.8457)
##     No Information Rate : 0.6103          
##     P-Value [Acc > NIR] : 8.319e-09       
##                                           
##                   Kappa : 0.556           
##                                           
##  Mcnemar's Test P-Value : 0.1748          
##                                           
##             Sensitivity : 0.6747          
##             Specificity : 0.8692          
##          Pos Pred Value : 0.7671          
##          Neg Pred Value : 0.8071          
##               Precision : 0.7671          
##                  Recall : 0.6747          
##                      F1 : 0.7179          
##              Prevalence : 0.3897          
##          Detection Rate : 0.2629          
##    Detection Prevalence : 0.3427          
##       Balanced Accuracy : 0.7720          
##                                           
##        'Positive' Class : MM              
##

Hyperparamete training using Tunegrid()

# Step 1: Define the tuneGrid
marsGrid <-  expand.grid(nprune = c(2, 4, 6, 8, 10), 
                        degree = c(1, 2, 3))

# Step 2: Tune hyper parameters by setting tuneGrid
set.seed(100)
model_mars3 = train(Purchase ~ ., data=trainData, method='earth', metric='ROC', tuneGrid = marsGrid, trControl = fitControl)
model_mars3

## Multivariate Adaptive Regression Spline 
## 
## 857 samples
##  18 predictor
##   2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 685, 686, 685, 686, 686 
## Resampling results across tuning parameters:
## 
##   degree  nprune  ROC        Sens       Spec     
##   1        2      0.8837092  0.8757143  0.7094075
##   1        4      0.9011512  0.8718315  0.7633198
##   1        6      0.9022966  0.8795421  0.7424242
##   1        8      0.8986413  0.8757143  0.7483492
##   1       10      0.8938458  0.8719048  0.7453641
##   2        2      0.8212388  0.8663553  0.6260968
##   2        4      0.9028221  0.8776374  0.7693351
##   2        6      0.9001307  0.8565201  0.7782451
##   2        8      0.8942283  0.8546520  0.7812754
##   2       10      0.8941091  0.8546337  0.7753053
##   3        2      0.8773872  0.8297802  0.7604251
##   3        4      0.9034469  0.8776007  0.7753053
##   3        6      0.9026720  0.8660806  0.7631389
##   3        8      0.8997006  0.8603846  0.7601085
##   3       10      0.8983994  0.8584982  0.7780642
## 
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were nprune = 4 and degree = 3.

# Step 3: Predict on testData and Compute the confusion matrix
predicted3 <- predict(model_mars3, testData4)
confusionMatrix(reference = testData$Purchase, data = predicted3, mode='everything', positive='MM')

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  CH  MM
##         CH 113  27
##         MM  17  56
##                                           
##                Accuracy : 0.7934          
##                  95% CI : (0.7328, 0.8457)
##     No Information Rate : 0.6103          
##     P-Value [Acc > NIR] : 8.319e-09       
##                                           
##                   Kappa : 0.556           
##                                           
##  Mcnemar's Test P-Value : 0.1748          
##                                           
##             Sensitivity : 0.6747          
##             Specificity : 0.8692          
##          Pos Pred Value : 0.7671          
##          Neg Pred Value : 0.8071          
##               Precision : 0.7671          
##                  Recall : 0.6747          
##                      F1 : 0.7179          
##              Prevalence : 0.3897          
##          Detection Rate : 0.2629          
##    Detection Prevalence : 0.3427          
##       Balanced Accuracy : 0.7720          
##                                           
##        'Positive' Class : MM              
##

How to evaluate performance of Multiple Machine Learning Algorithms

Caret provides the resamples() function where you can provide multiple machine learning models and collectively evaluate them.

Let’s first train some more algorithms.

Training Adaboost

set.seed(100)

# Train the model using adaboost
model_adaboost = train(Purchase ~ ., data=trainData, method='adaboost', tuneLength=2, trControl = fitControl)
model_adaboost

## AdaBoost Classification Trees 
## 
## 857 samples
##  18 predictor
##   2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 685, 686, 685, 686, 686 
## Resampling results across tuning parameters:
## 
##   nIter  method         ROC        Sens       Spec     
##    50    Adaboost.M1    0.8783495  0.8298535  0.7543193
##    50    Real adaboost  0.6881750  0.8412454  0.7363636
##   100    Adaboost.M1    0.8768766  0.8317399  0.7602895
##   100    Real adaboost  0.6831206  0.8393407  0.7393487
## 
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were nIter = 50 and method
##  = Adaboost.M1.

Training Random Forest

set.seed(100)

# Train the model using rf
model_rf = train(Purchase ~ ., data=trainData, method='rf', tuneLength=5, trControl = fitControl)
model_rf

## Random Forest 
## 
## 857 samples
##  18 predictor
##   2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 685, 686, 685, 686, 686 
## Resampling results across tuning parameters:
## 
##   mtry  ROC        Sens       Spec     
##    2    0.8711563  0.8660989  0.6615106
##    6    0.8871323  0.8565751  0.7333333
##   10    0.8867648  0.8527656  0.7573496
##   14    0.8862704  0.8565751  0.7602895
##   18    0.8850728  0.8508608  0.7723202
## 
## ROC was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 6.

Training XGBoost

set.seed(100)

# Train the model using MARS
model_xgbDART = train(Purchase ~ ., data=trainData, method='xgbDART', tuneLength=5, trControl = fitControl, verbose=F)
model_xgbDART

## eXtreme Gradient Boosting 
## 
## 857 samples
##  18 predictor
##   2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 685, 686, 685, 686, 686 
## Resampling results across tuning parameters:
## 
##   max_depth  eta  rate_drop  skip_drop  subsample  colsample_bytree
##   1          0.3  0.01       0.05       0.500      0.6             
##   1          0.3  0.01       0.05       0.500      0.6             
##   1          0.3  0.01       0.05       0.500      0.6             
##   1          0.3  0.01       0.05       0.500      0.6             
##   1          0.3  0.01       0.05       0.500      0.6             
##   1          0.3  0.01       0.05       0.500      0.8             
##   1          0.3  0.01       0.05       0.500      0.8             
##   1          0.3  0.01       0.05       0.500      0.8             
##   1          0.3  0.01       0.05       0.500      0.8             
##   1          0.3  0.01       0.05       0.500      0.8             
##   1          0.3  0.01       0.05       0.625      0.6             
##   1          0.3  0.01       0.05       0.625      0.6             
##   1          0.3  0.01       0.05       0.625      0.6             
##   1          0.3  0.01       0.05       0.625      0.6             
##   1          0.3  0.01       0.05       0.625      0.6             
##   1          0.3  0.01       0.05       0.625      0.8             
##   1          0.3  0.01       0.05       0.625      0.8             
##   1          0.3  0.01       0.05       0.625      0.8             
##   1          0.3  0.01       0.05       0.625      0.8             
##   1          0.3  0.01       0.05       0.625      0.8             
##   1          0.3  0.01       0.05       0.750      0.6             
##   1          0.3  0.01       0.05       0.750      0.6             
##   1          0.3  0.01       0.05       0.750      0.6             
##   1          0.3  0.01       0.05       0.750      0.6             
##   1          0.3  0.01       0.05       0.750      0.6             
##   1          0.3  0.01       0.05       0.750      0.8             
##   1          0.3  0.01       0.05       0.750      0.8             
##   1          0.3  0.01       0.05       0.750      0.8             
##   1          0.3  0.01       0.05       0.750      0.8             
##   1          0.3  0.01       0.05       0.750      0.8             
##   1          0.3  0.01       0.05       0.875      0.6             
##   1          0.3  0.01       0.05       0.875      0.6             
##   1          0.3  0.01       0.05       0.875      0.6             
##   1          0.3  0.01       0.05       0.875      0.6             
##   1          0.3  0.01       0.05       0.875      0.6             
##   1          0.3  0.01       0.05       0.875      0.8             
##   1          0.3  0.01       0.05       0.875      0.8             
##   1          0.3  0.01       0.05       0.875      0.8             
##   1          0.3  0.01       0.05       0.875      0.8             
##   1          0.3  0.01       0.05       0.875      0.8             
##   1          0.3  0.01       0.05       1.000      0.6             
##   1          0.3  0.01       0.05       1.000      0.6             
##   1          0.3  0.01       0.05       1.000      0.6             
##   1          0.3  0.01       0.05       1.000      0.6             
##   1          0.3  0.01       0.05       1.000      0.6             
##   1          0.3  0.01       0.05       1.000      0.8             
##   1          0.3  0.01       0.05       1.000      0.8             
##   1          0.3  0.01       0.05       1.000      0.8             
##   1          0.3  0.01       0.05       1.000      0.8             
##   1          0.3  0.01       0.05       1.000      0.8             
##   1          0.3  0.01       0.95       0.500      0.6             
##   1          0.3  0.01       0.95       0.500      0.6             
##   1          0.3  0.01       0.95       0.500      0.6             
##   1          0.3  0.01       0.95       0.500      0.6             
##   1          0.3  0.01       0.95       0.500      0.6             
##   1          0.3  0.01       0.95       0.500      0.8             
##   1          0.3  0.01       0.95       0.500      0.8             
##   1          0.3  0.01       0.95       0.500      0.8             
##   1          0.3  0.01       0.95       0.500      0.8             
##   1          0.3  0.01       0.95       0.500      0.8             
##   1          0.3  0.01       0.95       0.625      0.6             
##   1          0.3  0.01       0.95       0.625      0.6             
##   1          0.3  0.01       0.95       0.625      0.6             
##   1          0.3  0.01       0.95       0.625      0.6             
##   1          0.3  0.01       0.95       0.625      0.6             
##   1          0.3  0.01       0.95       0.625      0.8             
##   1          0.3  0.01       0.95       0.625      0.8             
##   1          0.3  0.01       0.95       0.625      0.8             
##   1          0.3  0.01       0.95       0.625      0.8             
##   1          0.3  0.01       0.95       0.625      0.8             
##   1          0.3  0.01       0.95       0.750      0.6             
##   1          0.3  0.01       0.95       0.750      0.6             
##   1          0.3  0.01       0.95       0.750      0.6             
##   1          0.3  0.01       0.95       0.750      0.6             
##   1          0.3  0.01       0.95       0.750      0.6             
##   1          0.3  0.01       0.95       0.750      0.8             
##   1          0.3  0.01       0.95       0.750      0.8             
##   1          0.3  0.01       0.95       0.750      0.8             
##   1          0.3  0.01       0.95       0.750      0.8             
##   1          0.3  0.01       0.95       0.750      0.8             
##   1          0.3  0.01       0.95       0.875      0.6             
##   1          0.3  0.01       0.95       0.875      0.6             
##   1          0.3  0.01       0.95       0.875      0.6             
##   1          0.3  0.01       0.95       0.875      0.6             
##   1          0.3  0.01       0.95       0.875      0.6             
##   1          0.3  0.01       0.95       0.875      0.8             
##   1          0.3  0.01       0.95       0.875      0.8             
##   1          0.3  0.01       0.95       0.875      0.8             
##   1          0.3  0.01       0.95       0.875      0.8             
##   1          0.3  0.01       0.95       0.875      0.8             
##   1          0.3  0.01       0.95       1.000      0.6             
##   1          0.3  0.01       0.95       1.000      0.6             
##   1          0.3  0.01       0.95       1.000      0.6             
##   1          0.3  0.01       0.95       1.000      0.6             
##   1          0.3  0.01       0.95       1.000      0.6             
##   1          0.3  0.01       0.95       1.000      0.8             
##   1          0.3  0.01       0.95       1.000      0.8             
##   1          0.3  0.01       0.95       1.000      0.8             
##   1          0.3  0.01       0.95       1.000      0.8             
##   1          0.3  0.01       0.95       1.000      0.8             
##   1          0.3  0.50       0.05       0.500      0.6             
##   1          0.3  0.50       0.05       0.500      0.6             
##   1          0.3  0.50       0.05       0.500      0.6             
##   1          0.3  0.50       0.05       0.500      0.6             
##   1          0.3  0.50       0.05       0.500      0.6             
##   1          0.3  0.50       0.05       0.500      0.8             
##   1          0.3  0.50       0.05       0.500      0.8             
##   1          0.3  0.50       0.05       0.500      0.8             
##   1          0.3  0.50       0.05       0.500      0.8             
##   1          0.3  0.50       0.05       0.500      0.8             
##   1          0.3  0.50       0.05       0.625      0.6             
##   1          0.3  0.50       0.05       0.625      0.6             
##   1          0.3  0.50       0.05       0.625      0.6             
##   1          0.3  0.50       0.05       0.625      0.6             
##   1          0.3  0.50       0.05       0.625      0.6             
##   1          0.3  0.50       0.05       0.625      0.8             
##   1          0.3  0.50       0.05       0.625      0.8             
##   1          0.3  0.50       0.05       0.625      0.8             
##   1          0.3  0.50       0.05       0.625      0.8             
##   1          0.3  0.50       0.05       0.625      0.8             
##   1          0.3  0.50       0.05       0.750      0.6             
##   1          0.3  0.50       0.05       0.750      0.6             
##   1          0.3  0.50       0.05       0.750      0.6             
##   1          0.3  0.50       0.05       0.750      0.6             
##   1          0.3  0.50       0.05       0.750      0.6             
##   1          0.3  0.50       0.05       0.750      0.8             
##   1          0.3  0.50       0.05       0.750      0.8             
##   1          0.3  0.50       0.05       0.750      0.8             
##   1          0.3  0.50       0.05       0.750      0.8             
##   1          0.3  0.50       0.05       0.750      0.8             
##   1          0.3  0.50       0.05       0.875      0.6             
##   1          0.3  0.50       0.05       0.875      0.6             
##   1          0.3  0.50       0.05       0.875      0.6             
##   1          0.3  0.50       0.05       0.875      0.6             
##   1          0.3  0.50       0.05       0.875      0.6             
##   1          0.3  0.50       0.05       0.875      0.8             
##   1          0.3  0.50       0.05       0.875      0.8             
##   1          0.3  0.50       0.05       0.875      0.8             
##   1          0.3  0.50       0.05       0.875      0.8             
##   1          0.3  0.50       0.05       0.875      0.8             
##   1          0.3  0.50       0.05       1.000      0.6             
##   1          0.3  0.50       0.05       1.000      0.6             
##   1          0.3  0.50       0.05       1.000      0.6             
##   1          0.3  0.50       0.05       1.000      0.6             
##   1          0.3  0.50       0.05       1.000      0.6             
##   1          0.3  0.50       0.05       1.000      0.8             
##   1          0.3  0.50       0.05       1.000      0.8             
##   1          0.3  0.50       0.05       1.000      0.8             
##   1          0.3  0.50       0.05       1.000      0.8             
##   1          0.3  0.50       0.05       1.000      0.8             
##   1          0.3  0.50       0.95       0.500      0.6             
##   1          0.3  0.50       0.95       0.500      0.6             
##   1          0.3  0.50       0.95       0.500      0.6             
##   1          0.3  0.50       0.95       0.500      0.6             
##   1          0.3  0.50       0.95       0.500      0.6             
##   1          0.3  0.50       0.95       0.500      0.8             
##   1          0.3  0.50       0.95       0.500      0.8             
##   1          0.3  0.50       0.95       0.500      0.8             
##   1          0.3  0.50       0.95       0.500      0.8             
##   1          0.3  0.50       0.95       0.500      0.8             
##   1          0.3  0.50       0.95       0.625      0.6             
##   1          0.3  0.50       0.95       0.625      0.6             
##   1          0.3  0.50       0.95       0.625      0.6             
##   1          0.3  0.50       0.95       0.625      0.6             
##   1          0.3  0.50       0.95       0.625      0.6             
##   1          0.3  0.50       0.95       0.625      0.8             
##   1          0.3  0.50       0.95       0.625      0.8             
##   1          0.3  0.50       0.95       0.625      0.8             
##   1          0.3  0.50       0.95       0.625      0.8             
##   1          0.3  0.50       0.95       0.625      0.8             
##   1          0.3  0.50       0.95       0.750      0.6             
##   1          0.3  0.50       0.95       0.750      0.6             
##   1          0.3  0.50       0.95       0.750      0.6             
##   1          0.3  0.50       0.95       0.750      0.6             
##   1          0.3  0.50       0.95       0.750      0.6             
##   1          0.3  0.50       0.95       0.750      0.8             
##   1          0.3  0.50       0.95       0.750      0.8             
##   1          0.3  0.50       0.95       0.750      0.8             
##   1          0.3  0.50       0.95       0.750      0.8             
##   1          0.3  0.50       0.95       0.750      0.8             
##   1          0.3  0.50       0.95       0.875      0.6             
##   1          0.3  0.50       0.95       0.875      0.6             
##   1          0.3  0.50       0.95       0.875      0.6             
##   1          0.3  0.50       0.95       0.875      0.6             
##   1          0.3  0.50       0.95       0.875      0.6             
##   1          0.3  0.50       0.95       0.875      0.8             
##   1          0.3  0.50       0.95       0.875      0.8             
##   1          0.3  0.50       0.95       0.875      0.8             
##   1          0.3  0.50       0.95       0.875      0.8             
##   1          0.3  0.50       0.95       0.875      0.8             
##   1          0.3  0.50       0.95       1.000      0.6             
##   1          0.3  0.50       0.95       1.000      0.6             
##   1          0.3  0.50       0.95       1.000      0.6             
##   1          0.3  0.50       0.95       1.000      0.6             
##   1          0.3  0.50       0.95       1.000      0.6             
##   1          0.3  0.50       0.95       1.000      0.8             
##   1          0.3  0.50       0.95       1.000      0.8             
##   1          0.3  0.50       0.95       1.000      0.8             
##   1          0.3  0.50       0.95       1.000      0.8             
##   1          0.3  0.50       0.95       1.000      0.8             
##   1          0.4  0.01       0.05       0.500      0.6             
##   1          0.4  0.01       0.05       0.500      0.6             
##   1          0.4  0.01       0.05       0.500      0.6             
##   1          0.4  0.01       0.05       0.500      0.6             
##   1          0.4  0.01       0.05       0.500      0.6             
##   1          0.4  0.01       0.05       0.500      0.8             
##   1          0.4  0.01       0.05       0.500      0.8             
##   1          0.4  0.01       0.05       0.500      0.8             
##   1          0.4  0.01       0.05       0.500      0.8             
##   1          0.4  0.01       0.05       0.500      0.8             
##   1          0.4  0.01       0.05       0.625      0.6             
##   1          0.4  0.01       0.05       0.625      0.6             
##   1          0.4  0.01       0.05       0.625      0.6             
##   1          0.4  0.01       0.05       0.625      0.6             
##   1          0.4  0.01       0.05       0.625      0.6             
##   1          0.4  0.01       0.05       0.625      0.8             
##   1          0.4  0.01       0.05       0.625      0.8             
##   1          0.4  0.01       0.05       0.625      0.8             
##   1          0.4  0.01       0.05       0.625      0.8             
##   1          0.4  0.01       0.05       0.625      0.8             
##   1          0.4  0.01       0.05       0.750      0.6             
##   1          0.4  0.01       0.05       0.750      0.6             
##   1          0.4  0.01       0.05       0.750      0.6             
##   1          0.4  0.01       0.05       0.750      0.6             
##   1          0.4  0.01       0.05       0.750      0.6             
##   1          0.4  0.01       0.05       0.750      0.8             
##   1          0.4  0.01       0.05       0.750      0.8             
##   1          0.4  0.01       0.05       0.750      0.8             
##   1          0.4  0.01       0.05       0.750      0.8             
##   1          0.4  0.01       0.05       0.750      0.8             
##   1          0.4  0.01       0.05       0.875      0.6             
##   1          0.4  0.01       0.05       0.875      0.6             
##   1          0.4  0.01       0.05       0.875      0.6             
##   1          0.4  0.01       0.05       0.875      0.6             
##   1          0.4  0.01       0.05       0.875      0.6             
##   1          0.4  0.01       0.05       0.875      0.8             
##   1          0.4  0.01       0.05       0.875      0.8             
##   1          0.4  0.01       0.05       0.875      0.8             
##   1          0.4  0.01       0.05       0.875      0.8             
##   1          0.4  0.01       0.05       0.875      0.8             
##   1          0.4  0.01       0.05       1.000      0.6             
##   1          0.4  0.01       0.05       1.000      0.6             
##   1          0.4  0.01       0.05       1.000      0.6             
##   1          0.4  0.01       0.05       1.000      0.6             
##   1          0.4  0.01       0.05       1.000      0.6             
##   1          0.4  0.01       0.05       1.000      0.8             
##   1          0.4  0.01       0.05       1.000      0.8             
##   1          0.4  0.01       0.05       1.000      0.8             
##   1          0.4  0.01       0.05       1.000      0.8             
##   1          0.4  0.01       0.05       1.000      0.8             
##   1          0.4  0.01       0.95       0.500      0.6             
##   1          0.4  0.01       0.95       0.500      0.6             
##   1          0.4  0.01       0.95       0.500      0.6             
##   1          0.4  0.01       0.95       0.500      0.6             
##   1          0.4  0.01       0.95       0.500      0.6             
##   1          0.4  0.01       0.95       0.500      0.8             
##   1          0.4  0.01       0.95       0.500      0.8             
##   1          0.4  0.01       0.95       0.500      0.8             
##   1          0.4  0.01       0.95       0.500      0.8             
##   1          0.4  0.01       0.95       0.500      0.8             
##   1          0.4  0.01       0.95       0.625      0.6             
##   1          0.4  0.01       0.95       0.625      0.6             
##   1          0.4  0.01       0.95       0.625      0.6             
##   1          0.4  0.01       0.95       0.625      0.6             
##   1          0.4  0.01       0.95       0.625      0.6             
##   1          0.4  0.01       0.95       0.625      0.8             
##   1          0.4  0.01       0.95       0.625      0.8             
##   1          0.4  0.01       0.95       0.625      0.8             
##   1          0.4  0.01       0.95       0.625      0.8             
##   1          0.4  0.01       0.95       0.625      0.8             
##   1          0.4  0.01       0.95       0.750      0.6             
##   1          0.4  0.01       0.95       0.750      0.6             
##   1          0.4  0.01       0.95       0.750      0.6             
##   1          0.4  0.01       0.95       0.750      0.6             
##   1          0.4  0.01       0.95       0.750      0.6             
##   1          0.4  0.01       0.95       0.750      0.8             
##   1          0.4  0.01       0.95       0.750      0.8             
##   1          0.4  0.01       0.95       0.750      0.8             
##   1          0.4  0.01       0.95       0.750      0.8             
##   1          0.4  0.01       0.95       0.750      0.8             
##   1          0.4  0.01       0.95       0.875      0.6             
##   1          0.4  0.01       0.95       0.875      0.6             
##   1          0.4  0.01       0.95       0.875      0.6             
##   1          0.4  0.01       0.95       0.875      0.6             
##   1          0.4  0.01       0.95       0.875      0.6             
##   1          0.4  0.01       0.95       0.875      0.8             
##   1          0.4  0.01       0.95       0.875      0.8             
##   1          0.4  0.01       0.95       0.875      0.8             
##   1          0.4  0.01       0.95       0.875      0.8             
##   1          0.4  0.01       0.95       0.875      0.8             
##   1          0.4  0.01       0.95       1.000      0.6             
##   1          0.4  0.01       0.95       1.000      0.6             
##   1          0.4  0.01       0.95       1.000      0.6             
##   1          0.4  0.01       0.95       1.000      0.6             
##   1          0.4  0.01       0.95       1.000      0.6             
##   1          0.4  0.01       0.95       1.000      0.8             
##   1          0.4  0.01       0.95       1.000      0.8             
##   1          0.4  0.01       0.95       1.000      0.8             
##   1          0.4  0.01       0.95       1.000      0.8             
##   1          0.4  0.01       0.95       1.000      0.8             
##   1          0.4  0.50       0.05       0.500      0.6             
##   1          0.4  0.50       0.05       0.500      0.6             
##   1          0.4  0.50       0.05       0.500      0.6             
##   1          0.4  0.50       0.05       0.500      0.6             
##   1          0.4  0.50       0.05       0.500      0.6             
##   1          0.4  0.50       0.05       0.500      0.8             
##   1          0.4  0.50       0.05       0.500      0.8             
##   1          0.4  0.50       0.05       0.500      0.8             
##   1          0.4  0.50       0.05       0.500      0.8             
##   1          0.4  0.50       0.05       0.500      0.8             
##   1          0.4  0.50       0.05       0.625      0.6             
##   1          0.4  0.50       0.05       0.625      0.6             
##   1          0.4  0.50       0.05       0.625      0.6             
##   1          0.4  0.50       0.05       0.625      0.6             
##   1          0.4  0.50       0.05       0.625      0.6             
##   1          0.4  0.50       0.05       0.625      0.8             
##   1          0.4  0.50       0.05       0.625      0.8             
##   1          0.4  0.50       0.05       0.625      0.8             
##   1          0.4  0.50       0.05       0.625      0.8             
##   1          0.4  0.50       0.05       0.625      0.8             
##   1          0.4  0.50       0.05       0.750      0.6             
##   1          0.4  0.50       0.05       0.750      0.6             
##   1          0.4  0.50       0.05       0.750      0.6             
##   1          0.4  0.50       0.05       0.750      0.6             
##   1          0.4  0.50       0.05       0.750      0.6             
##   1          0.4  0.50       0.05       0.750      0.8             
##   1          0.4  0.50       0.05       0.750      0.8             
##   1          0.4  0.50       0.05       0.750      0.8             
##   1          0.4  0.50       0.05       0.750      0.8             
##   1          0.4  0.50       0.05       0.750      0.8             
##   1          0.4  0.50       0.05       0.875      0.6             
##   1          0.4  0.50       0.05       0.875      0.6             
##   1          0.4  0.50       0.05       0.875      0.6             
##   1          0.4  0.50       0.05       0.875      0.6             
##   1          0.4  0.50       0.05       0.875      0.6             
##   1          0.4  0.50       0.05       0.875      0.8             
##   1          0.4  0.50       0.05       0.875      0.8             
##   1          0.4  0.50       0.05       0.875      0.8             
##   1          0.4  0.50       0.05       0.875      0.8             
##   1          0.4  0.50       0.05       0.875      0.8             
##   1          0.4  0.50       0.05       1.000      0.6             
##   1          0.4  0.50       0.05       1.000      0.6             
##   1          0.4  0.50       0.05       1.000      0.6             
##   1          0.4  0.50       0.05       1.000      0.6             
##   1          0.4  0.50       0.05       1.000      0.6             
##   1          0.4  0.50       0.05       1.000      0.8             
##   1          0.4  0.50       0.05       1.000      0.8             
##   1          0.4  0.50       0.05       1.000      0.8             
##   1          0.4  0.50       0.05       1.000      0.8             
##   1          0.4  0.50       0.05       1.000      0.8             
##   1          0.4  0.50       0.95       0.500      0.6             
##   1          0.4  0.50       0.95       0.500      0.6             
##   1          0.4  0.50       0.95       0.500      0.6             
##   1          0.4  0.50       0.95       0.500      0.6             
##   1          0.4  0.50       0.95       0.500      0.6             
##   1          0.4  0.50       0.95       0.500      0.8             
##   1          0.4  0.50       0.95       0.500      0.8             
##   1          0.4  0.50       0.95       0.500      0.8             
##   1          0.4  0.50       0.95       0.500      0.8             
##   1          0.4  0.50       0.95       0.500      0.8             
##   1          0.4  0.50       0.95       0.625      0.6             
##   1          0.4  0.50       0.95       0.625      0.6             
##   1          0.4  0.50       0.95       0.625      0.6             
##   1          0.4  0.50       0.95       0.625      0.6             
##   1          0.4  0.50       0.95       0.625      0.6             
##   1          0.4  0.50       0.95       0.625      0.8             
##   1          0.4  0.50       0.95       0.625      0.8             
##   1          0.4  0.50       0.95       0.625      0.8             
##   1          0.4  0.50       0.95       0.625      0.8             
##   1          0.4  0.50       0.95       0.625      0.8             
##   1          0.4  0.50       0.95       0.750      0.6             
##   1          0.4  0.50       0.95       0.750      0.6             
##   1          0.4  0.50       0.95       0.750      0.6             
##   1          0.4  0.50       0.95       0.750      0.6             
##   1          0.4  0.50       0.95       0.750      0.6             
##   1          0.4  0.50       0.95       0.750      0.8             
##   1          0.4  0.50       0.95       0.750      0.8             
##   1          0.4  0.50       0.95       0.750      0.8             
##   1          0.4  0.50       0.95       0.750      0.8             
##   1          0.4  0.50       0.95       0.750      0.8             
##   1          0.4  0.50       0.95       0.875      0.6             
##   1          0.4  0.50       0.95       0.875      0.6             
##   1          0.4  0.50       0.95       0.875      0.6             
##   1          0.4  0.50       0.95       0.875      0.6             
##   1          0.4  0.50       0.95       0.875      0.6             
##   1          0.4  0.50       0.95       0.875      0.8             
##   1          0.4  0.50       0.95       0.875      0.8             
##   1          0.4  0.50       0.95       0.875      0.8             
##   1          0.4  0.50       0.95       0.875      0.8             
##   1          0.4  0.50       0.95       0.875      0.8             
##   1          0.4  0.50       0.95       1.000      0.6             
##   1          0.4  0.50       0.95       1.000      0.6             
##   1          0.4  0.50       0.95       1.000      0.6             
##   1          0.4  0.50       0.95       1.000      0.6             
##   1          0.4  0.50       0.95       1.000      0.6             
##   1          0.4  0.50       0.95       1.000      0.8             
##   1          0.4  0.50       0.95       1.000      0.8             
##   1          0.4  0.50       0.95       1.000      0.8             
##   1          0.4  0.50       0.95       1.000      0.8             
##   1          0.4  0.50       0.95       1.000      0.8             
##   2          0.3  0.01       0.05       0.500      0.6             
##   2          0.3  0.01       0.05       0.500      0.6             
##   2          0.3  0.01       0.05       0.500      0.6             
##   2          0.3  0.01       0.05       0.500      0.6             
##   2          0.3  0.01       0.05       0.500      0.6             
##   2          0.3  0.01       0.05       0.500      0.8             
##   2          0.3  0.01       0.05       0.500      0.8             
##   2          0.3  0.01       0.05       0.500      0.8             
##   2          0.3  0.01       0.05       0.500      0.8             
##   2          0.3  0.01       0.05       0.500      0.8             
##   2          0.3  0.01       0.05       0.625      0.6             
##   2          0.3  0.01       0.05       0.625      0.6             
##   2          0.3  0.01       0.05       0.625      0.6             
##   2          0.3  0.01       0.05       0.625      0.6             
##   2          0.3  0.01       0.05       0.625      0.6             
##   2          0.3  0.01       0.05       0.625      0.8             
##   2          0.3  0.01       0.05       0.625      0.8             
##   2          0.3  0.01       0.05       0.625      0.8             
##   2          0.3  0.01       0.05       0.625      0.8             
##   2          0.3  0.01       0.05       0.625      0.8             
##   2          0.3  0.01       0.05       0.750      0.6             
##   2          0.3  0.01       0.05       0.750      0.6             
##   2          0.3  0.01       0.05       0.750      0.6             
##   2          0.3  0.01       0.05       0.750      0.6             
##   2          0.3  0.01       0.05       0.750      0.6             
##   2          0.3  0.01       0.05       0.750      0.8             
##   2          0.3  0.01       0.05       0.750      0.8             
##   2          0.3  0.01       0.05       0.750      0.8             
##   2          0.3  0.01       0.05       0.750      0.8             
##   2          0.3  0.01       0.05       0.750      0.8             
##   2          0.3  0.01       0.05       0.875      0.6             
##   2          0.3  0.01       0.05       0.875      0.6             
##   2          0.3  0.01       0.05       0.875      0.6             
##   2          0.3  0.01       0.05       0.875      0.6             
##   2          0.3  0.01       0.05       0.875      0.6             
##   2          0.3  0.01       0.05       0.875      0.8             
##   2          0.3  0.01       0.05       0.875      0.8             
##   2          0.3  0.01       0.05       0.875      0.8             
##   2          0.3  0.01       0.05       0.875      0.8             
##   2          0.3  0.01       0.05       0.875      0.8             
##   2          0.3  0.01       0.05       1.000      0.6             
##   2          0.3  0.01       0.05       1.000      0.6             
##   2          0.3  0.01       0.05       1.000      0.6             
##   2          0.3  0.01       0.05       1.000      0.6             
##   2          0.3  0.01       0.05       1.000      0.6             
##   2          0.3  0.01       0.05       1.000      0.8             
##   2          0.3  0.01       0.05       1.000      0.8             
##   2          0.3  0.01       0.05       1.000      0.8             
##   2          0.3  0.01       0.05       1.000      0.8             
##   2          0.3  0.01       0.05       1.000      0.8             
##   2          0.3  0.01       0.95       0.500      0.6             
##   2          0.3  0.01       0.95       0.500      0.6             
##   2          0.3  0.01       0.95       0.500      0.6             
##   2          0.3  0.01       0.95       0.500      0.6             
##   2          0.3  0.01       0.95       0.500      0.6             
##   2          0.3  0.01       0.95       0.500      0.8             
##   2          0.3  0.01       0.95       0.500      0.8             
##   2          0.3  0.01       0.95       0.500      0.8             
##   2          0.3  0.01       0.95       0.500      0.8             
##   2          0.3  0.01       0.95       0.500      0.8             
##   2          0.3  0.01       0.95       0.625      0.6             
##   2          0.3  0.01       0.95       0.625      0.6             
##   2          0.3  0.01       0.95       0.625      0.6             
##   2          0.3  0.01       0.95       0.625      0.6             
##   2          0.3  0.01       0.95       0.625      0.6             
##   2          0.3  0.01       0.95       0.625      0.8             
##   2          0.3  0.01       0.95       0.625      0.8             
##   2          0.3  0.01       0.95       0.625      0.8             
##   2          0.3  0.01       0.95       0.625      0.8             
##   2          0.3  0.01       0.95       0.625      0.8             
##   2          0.3  0.01       0.95       0.750      0.6             
##   2          0.3  0.01       0.95       0.750      0.6             
##   2          0.3  0.01       0.95       0.750      0.6             
##   2          0.3  0.01       0.95       0.750      0.6             
##   2          0.3  0.01       0.95       0.750      0.6             
##   2          0.3  0.01       0.95       0.750      0.8             
##   2          0.3  0.01       0.95       0.750      0.8             
##   2          0.3  0.01       0.95       0.750      0.8             
##   2          0.3  0.01       0.95       0.750      0.8             
##   2          0.3  0.01       0.95       0.750      0.8             
##   2          0.3  0.01       0.95       0.875      0.6             
##   2          0.3  0.01       0.95       0.875      0.6             
##   2          0.3  0.01       0.95       0.875      0.6             
##   2          0.3  0.01       0.95       0.875      0.6             
##   2          0.3  0.01       0.95       0.875      0.6             
##   2          0.3  0.01       0.95       0.875      0.8             
##   2          0.3  0.01       0.95       0.875      0.8             
##   2          0.3  0.01       0.95       0.875      0.8             
##   2          0.3  0.01       0.95       0.875      0.8             
##   2          0.3  0.01       0.95       0.875      0.8             
##   2          0.3  0.01       0.95       1.000      0.6             
##   2          0.3  0.01       0.95       1.000      0.6             
##   2          0.3  0.01       0.95       1.000      0.6             
##   2          0.3  0.01       0.95       1.000      0.6             
##   2          0.3  0.01       0.95       1.000      0.6             
##   2          0.3  0.01       0.95       1.000      0.8             
##   2          0.3  0.01       0.95       1.000      0.8             
##   2          0.3  0.01       0.95       1.000      0.8             
##   2          0.3  0.01       0.95       1.000      0.8             
##   2          0.3  0.01       0.95       1.000      0.8             
##   2          0.3  0.50       0.05       0.500      0.6             
##   2          0.3  0.50       0.05       0.500      0.6             
##   2          0.3  0.50       0.05       0.500      0.6             
##   2          0.3  0.50       0.05       0.500      0.6             
##   2          0.3  0.50       0.05       0.500      0.6             
##   2          0.3  0.50       0.05       0.500      0.8             
##   2          0.3  0.50       0.05       0.500      0.8             
##   2          0.3  0.50       0.05       0.500      0.8             
##   2          0.3  0.50       0.05       0.500      0.8             
##   2          0.3  0.50       0.05       0.500      0.8             
##   2          0.3  0.50       0.05       0.625      0.6             
##   2          0.3  0.50       0.05       0.625      0.6             
##   2          0.3  0.50       0.05       0.625      0.6             
##   2          0.3  0.50       0.05       0.625      0.6             
##   2          0.3  0.50       0.05       0.625      0.6             
##   2          0.3  0.50       0.05       0.625      0.8             
##   2          0.3  0.50       0.05       0.625      0.8             
##   2          0.3  0.50       0.05       0.625      0.8             
##   2          0.3  0.50       0.05       0.625      0.8             
##   2          0.3  0.50       0.05       0.625      0.8             
##   2          0.3  0.50       0.05       0.750      0.6             
##   2          0.3  0.50       0.05       0.750      0.6             
##   2          0.3  0.50       0.05       0.750      0.6             
##   2          0.3  0.50       0.05       0.750      0.6             
##   2          0.3  0.50       0.05       0.750      0.6             
##   2          0.3  0.50       0.05       0.750      0.8             
##   2          0.3  0.50       0.05       0.750      0.8             
##   2          0.3  0.50       0.05       0.750      0.8             
##   2          0.3  0.50       0.05       0.750      0.8             
##   2          0.3  0.50       0.05       0.750      0.8             
##   2          0.3  0.50       0.05       0.875      0.6             
##   2          0.3  0.50       0.05       0.875      0.6             
##   2          0.3  0.50       0.05       0.875      0.6             
##   2          0.3  0.50       0.05       0.875      0.6             
##   2          0.3  0.50       0.05       0.875      0.6             
##   2          0.3  0.50       0.05       0.875      0.8             
##   2          0.3  0.50       0.05       0.875      0.8             
##   2          0.3  0.50       0.05       0.875      0.8             
##   2          0.3  0.50       0.05       0.875      0.8             
##   2          0.3  0.50       0.05       0.875      0.8             
##   2          0.3  0.50       0.05       1.000      0.6             
##   2          0.3  0.50       0.05       1.000      0.6             
##   2          0.3  0.50       0.05       1.000      0.6             
##   2          0.3  0.50       0.05       1.000      0.6             
##   2          0.3  0.50       0.05       1.000      0.6             
##   2          0.3  0.50       0.05       1.000      0.8             
##   2          0.3  0.50       0.05       1.000      0.8             
##   2          0.3  0.50       0.05       1.000      0.8             
##   2          0.3  0.50       0.05       1.000      0.8             
##   2          0.3  0.50       0.05       1.000      0.8             
##   2          0.3  0.50       0.95       0.500      0.6             
##   2          0.3  0.50       0.95       0.500      0.6             
##   2          0.3  0.50       0.95       0.500      0.6             
##   2          0.3  0.50       0.95       0.500      0.6             
##   2          0.3  0.50       0.95       0.500      0.6             
##   2          0.3  0.50       0.95       0.500      0.8             
##   2          0.3  0.50       0.95       0.500      0.8             
##   2          0.3  0.50       0.95       0.500      0.8             
##   2          0.3  0.50       0.95       0.500      0.8             
##   2          0.3  0.50       0.95       0.500      0.8             
##   2          0.3  0.50       0.95       0.625      0.6             
##   2          0.3  0.50       0.95       0.625      0.6             
##   2          0.3  0.50       0.95       0.625      0.6             
##   2          0.3  0.50       0.95       0.625      0.6             
##   2          0.3  0.50       0.95       0.625      0.6             
##   2          0.3  0.50       0.95       0.625      0.8             
##   2          0.3  0.50       0.95       0.625      0.8             
##   2          0.3  0.50       0.95       0.625      0.8             
##   2          0.3  0.50       0.95       0.625      0.8             
##   2          0.3  0.50       0.95       0.625      0.8             
##   2          0.3  0.50       0.95       0.750      0.6             
##   2          0.3  0.50       0.95       0.750      0.6             
##   2          0.3  0.50       0.95       0.750      0.6             
##   2          0.3  0.50       0.95       0.750      0.6             
##   2          0.3  0.50       0.95       0.750      0.6             
##   2          0.3  0.50       0.95       0.750      0.8             
##   2          0.3  0.50       0.95       0.750      0.8             
##   2          0.3  0.50       0.95       0.750      0.8             
##   2          0.3  0.50       0.95       0.750      0.8             
##   2          0.3  0.50       0.95       0.750      0.8             
##   2          0.3  0.50       0.95       0.875      0.6             
##   2          0.3  0.50       0.95       0.875      0.6             
##   2          0.3  0.50       0.95       0.875      0.6             
##   2          0.3  0.50       0.95       0.875      0.6             
##   2          0.3  0.50       0.95       0.875      0.6             
##   2          0.3  0.50       0.95       0.875      0.8             
##   2          0.3  0.50       0.95       0.875      0.8             
##   2          0.3  0.50       0.95       0.875      0.8             
##   2          0.3  0.50       0.95       0.875      0.8             
##   2          0.3  0.50       0.95       0.875      0.8             
##   2          0.3  0.50       0.95       1.000      0.6             
##   2          0.3  0.50       0.95       1.000      0.6             
##   2          0.3  0.50       0.95       1.000      0.6             
##   2          0.3  0.50       0.95       1.000      0.6             
##   2          0.3  0.50       0.95       1.000      0.6             
##   2          0.3  0.50       0.95       1.000      0.8             
##   2          0.3  0.50       0.95       1.000      0.8             
##   2          0.3  0.50       0.95       1.000      0.8             
##   2          0.3  0.50       0.95       1.000      0.8             
##   2          0.3  0.50       0.95       1.000      0.8             
##   2          0.4  0.01       0.05       0.500      0.6             
##   2          0.4  0.01       0.05       0.500      0.6             
##   2          0.4  0.01       0.05       0.500      0.6             
##   2          0.4  0.01       0.05       0.500      0.6             
##   2          0.4  0.01       0.05       0.500      0.6             
##   2          0.4  0.01       0.05       0.500      0.8             
##   2          0.4  0.01       0.05       0.500      0.8             
##   2          0.4  0.01       0.05       0.500      0.8             
##   2          0.4  0.01       0.05       0.500      0.8             
##   2          0.4  0.01       0.05       0.500      0.8             
##   2          0.4  0.01       0.05       0.625      0.6             
##   2          0.4  0.01       0.05       0.625      0.6             
##   2          0.4  0.01       0.05       0.625      0.6             
##   2          0.4  0.01       0.05       0.625      0.6             
##   2          0.4  0.01       0.05       0.625      0.6             
##   2          0.4  0.01       0.05       0.625      0.8             
##   2          0.4  0.01       0.05       0.625      0.8             
##   2          0.4  0.01       0.05       0.625      0.8             
##   2          0.4  0.01       0.05       0.625      0.8             
##   2          0.4  0.01       0.05       0.625      0.8             
##   2          0.4  0.01       0.05       0.750      0.6             
##   2          0.4  0.01       0.05       0.750      0.6             
##   2          0.4  0.01       0.05       0.750      0.6             
##   2          0.4  0.01       0.05       0.750      0.6             
##   2          0.4  0.01       0.05       0.750      0.6             
##   2          0.4  0.01       0.05       0.750      0.8             
##   2          0.4  0.01       0.05       0.750      0.8             
##   2          0.4  0.01       0.05       0.750      0.8             
##   2          0.4  0.01       0.05       0.750      0.8             
##   2          0.4  0.01       0.05       0.750      0.8             
##   2          0.4  0.01       0.05       0.875      0.6             
##   2          0.4  0.01       0.05       0.875      0.6             
##   2          0.4  0.01       0.05       0.875      0.6             
##   2          0.4  0.01       0.05       0.875      0.6             
##   2          0.4  0.01       0.05       0.875      0.6             
##   2          0.4  0.01       0.05       0.875      0.8             
##   2          0.4  0.01       0.05       0.875      0.8             
##   2          0.4  0.01       0.05       0.875      0.8             
##   2          0.4  0.01       0.05       0.875      0.8             
##   2          0.4  0.01       0.05       0.875      0.8             
##   2          0.4  0.01       0.05       1.000      0.6             
##   2          0.4  0.01       0.05       1.000      0.6             
##   2          0.4  0.01       0.05       1.000      0.6             
##   2          0.4  0.01       0.05       1.000      0.6             
##   2          0.4  0.01       0.05       1.000      0.6             
##   2          0.4  0.01       0.05       1.000      0.8             
##   2          0.4  0.01       0.05       1.000      0.8             
##   2          0.4  0.01       0.05       1.000      0.8             
##   2          0.4  0.01       0.05       1.000      0.8             
##   2          0.4  0.01       0.05       1.000      0.8             
##   2          0.4  0.01       0.95       0.500      0.6             
##   2          0.4  0.01       0.95       0.500      0.6             
##   2          0.4  0.01       0.95       0.500      0.6             
##   2          0.4  0.01       0.95       0.500      0.6             
##   2          0.4  0.01       0.95       0.500      0.6             
##   2          0.4  0.01       0.95       0.500      0.8             
##   2          0.4  0.01       0.95       0.500      0.8             
##   2          0.4  0.01       0.95       0.500      0.8             
##   2          0.4  0.01       0.95       0.500      0.8             
##   2          0.4  0.01       0.95       0.500      0.8             
##   2          0.4  0.01       0.95       0.625      0.6             
##   2          0.4  0.01       0.95       0.625      0.6             
##   2          0.4  0.01       0.95       0.625      0.6             
##   2          0.4  0.01       0.95       0.625      0.6             
##   2          0.4  0.01       0.95       0.625      0.6             
##   2          0.4  0.01       0.95       0.625      0.8             
##   2          0.4  0.01       0.95       0.625      0.8             
##   2          0.4  0.01       0.95       0.625      0.8             
##   2          0.4  0.01       0.95       0.625      0.8             
##   2          0.4  0.01       0.95       0.625      0.8             
##   2          0.4  0.01       0.95       0.750      0.6             
##   2          0.4  0.01       0.95       0.750      0.6             
##   2          0.4  0.01       0.95       0.750      0.6             
##   2          0.4  0.01       0.95       0.750      0.6             
##   2          0.4  0.01       0.95       0.750      0.6             
##   2          0.4  0.01       0.95       0.750      0.8             
##   2          0.4  0.01       0.95       0.750      0.8             
##   2          0.4  0.01       0.95       0.750      0.8             
##   2          0.4  0.01       0.95       0.750      0.8             
##   2          0.4  0.01       0.95       0.750      0.8             
##   2          0.4  0.01       0.95       0.875      0.6             
##   2          0.4  0.01       0.95       0.875      0.6             
##   2          0.4  0.01       0.95       0.875      0.6             
##   2          0.4  0.01       0.95       0.875      0.6             
##   2          0.4  0.01       0.95       0.875      0.6             
##   2          0.4  0.01       0.95       0.875      0.8             
##   2          0.4  0.01       0.95       0.875      0.8             
##   2          0.4  0.01       0.95       0.875      0.8             
##   2          0.4  0.01       0.95       0.875      0.8             
##   2          0.4  0.01       0.95       0.875      0.8             
##   2          0.4  0.01       0.95       1.000      0.6             
##   2          0.4  0.01       0.95       1.000      0.6             
##   2          0.4  0.01       0.95       1.000      0.6             
##   2          0.4  0.01       0.95       1.000      0.6             
##   2          0.4  0.01       0.95       1.000      0.6             
##   2          0.4  0.01       0.95       1.000      0.8             
##   2          0.4  0.01       0.95       1.000      0.8             
##   2          0.4  0.01       0.95       1.000      0.8             
##   2          0.4  0.01       0.95       1.000      0.8             
##   2          0.4  0.01       0.95       1.000      0.8             
##   2          0.4  0.50       0.05       0.500      0.6             
##   2          0.4  0.50       0.05       0.500      0.6             
##   2          0.4  0.50       0.05       0.500      0.6             
##   2          0.4  0.50       0.05       0.500      0.6             
##   2          0.4  0.50       0.05       0.500      0.6             
##   2          0.4  0.50       0.05       0.500      0.8             
##   2          0.4  0.50       0.05       0.500      0.8             
##   2          0.4  0.50       0.05       0.500      0.8             
##   2          0.4  0.50       0.05       0.500      0.8             
##   2          0.4  0.50       0.05       0.500      0.8             
##   2          0.4  0.50       0.05       0.625      0.6             
##   2          0.4  0.50       0.05       0.625      0.6             
##   2          0.4  0.50       0.05       0.625      0.6             
##   2          0.4  0.50       0.05       0.625      0.6             
##   2          0.4  0.50       0.05       0.625      0.6             
##   2          0.4  0.50       0.05       0.625      0.8             
##   2          0.4  0.50       0.05       0.625      0.8             
##   2          0.4  0.50       0.05       0.625      0.8             
##   2          0.4  0.50       0.05       0.625      0.8             
##   2          0.4  0.50       0.05       0.625      0.8             
##   2          0.4  0.50       0.05       0.750      0.6             
##   2          0.4  0.50       0.05       0.750      0.6             
##   2          0.4  0.50       0.05       0.750      0.6             
##   2          0.4  0.50       0.05       0.750      0.6             
##   2          0.4  0.50       0.05       0.750      0.6             
##   2          0.4  0.50       0.05       0.750      0.8             
##   2          0.4  0.50       0.05       0.750      0.8             
##   2          0.4  0.50       0.05       0.750      0.8             
##   2          0.4  0.50       0.05       0.750      0.8             
##   2          0.4  0.50       0.05       0.750      0.8             
##   2          0.4  0.50       0.05       0.875      0.6             
##   2          0.4  0.50       0.05       0.875      0.6             
##   2          0.4  0.50       0.05       0.875      0.6             
##   2          0.4  0.50       0.05       0.875      0.6             
##   2          0.4  0.50       0.05       0.875      0.6             
##   2          0.4  0.50       0.05       0.875      0.8             
##   2          0.4  0.50       0.05       0.875      0.8             
##   2          0.4  0.50       0.05       0.875      0.8             
##   2          0.4  0.50       0.05       0.875      0.8             
##   2          0.4  0.50       0.05       0.875      0.8             
##   2          0.4  0.50       0.05       1.000      0.6             
##   2          0.4  0.50       0.05       1.000      0.6             
##   2          0.4  0.50       0.05       1.000      0.6             
##   2          0.4  0.50       0.05       1.000      0.6             
##   2          0.4  0.50       0.05       1.000      0.6             
##   2          0.4  0.50       0.05       1.000      0.8             
##   2          0.4  0.50       0.05       1.000      0.8             
##   2          0.4  0.50       0.05       1.000      0.8             
##   2          0.4  0.50       0.05       1.000      0.8             
##   2          0.4  0.50       0.05       1.000      0.8             
##   2          0.4  0.50       0.95       0.500      0.6             
##   2          0.4  0.50       0.95       0.500      0.6             
##   2          0.4  0.50       0.95       0.500      0.6             
##   2          0.4  0.50       0.95       0.500      0.6             
##   2          0.4  0.50       0.95       0.500      0.6             
##   2          0.4  0.50       0.95       0.500      0.8             
##   2          0.4  0.50       0.95       0.500      0.8             
##   2          0.4  0.50       0.95       0.500      0.8             
##   2          0.4  0.50       0.95       0.500      0.8             
##   2          0.4  0.50       0.95       0.500      0.8             
##   2          0.4  0.50       0.95       0.625      0.6             
##   2          0.4  0.50       0.95       0.625      0.6             
##   2          0.4  0.50       0.95       0.625      0.6             
##   2          0.4  0.50       0.95       0.625      0.6             
##   2          0.4  0.50       0.95       0.625      0.6             
##   2          0.4  0.50       0.95       0.625      0.8             
##   2          0.4  0.50       0.95       0.625      0.8             
##   2          0.4  0.50       0.95       0.625      0.8             
##   2          0.4  0.50       0.95       0.625      0.8             
##   2          0.4  0.50       0.95       0.625      0.8             
##   2          0.4  0.50       0.95       0.750      0.6             
##   2          0.4  0.50       0.95       0.750      0.6             
##   2          0.4  0.50       0.95       0.750      0.6             
##   2          0.4  0.50       0.95       0.750      0.6             
##   2          0.4  0.50       0.95       0.750      0.6             
##   2          0.4  0.50       0.95       0.750      0.8             
##   2          0.4  0.50       0.95       0.750      0.8             
##   2          0.4  0.50       0.95       0.750      0.8             
##   2          0.4  0.50       0.95       0.750      0.8             
##   2          0.4  0.50       0.95       0.750      0.8             
##   2          0.4  0.50       0.95       0.875      0.6             
##   2          0.4  0.50       0.95       0.875      0.6             
##   2          0.4  0.50       0.95       0.875      0.6             
##   2          0.4  0.50       0.95       0.875      0.6             
##   2          0.4  0.50       0.95       0.875      0.6             
##   2          0.4  0.50       0.95       0.875      0.8             
##   2          0.4  0.50       0.95       0.875      0.8             
##   2          0.4  0.50       0.95       0.875      0.8             
##   2          0.4  0.50       0.95       0.875      0.8             
##   2          0.4  0.50       0.95       0.875      0.8             
##   2          0.4  0.50       0.95       1.000      0.6             
##   2          0.4  0.50       0.95       1.000      0.6             
##   2          0.4  0.50       0.95       1.000      0.6             
##   2          0.4  0.50       0.95       1.000      0.6             
##   2          0.4  0.50       0.95       1.000      0.6             
##   2          0.4  0.50       0.95       1.000      0.8             
##   2          0.4  0.50       0.95       1.000      0.8             
##   2          0.4  0.50       0.95       1.000      0.8             
##   2          0.4  0.50       0.95       1.000      0.8             
##   2          0.4  0.50       0.95       1.000      0.8             
##   3          0.3  0.01       0.05       0.500      0.6             
##   3          0.3  0.01       0.05       0.500      0.6             
##   3          0.3  0.01       0.05       0.500      0.6             
##   3          0.3  0.01       0.05       0.500      0.6             
##   3          0.3  0.01       0.05       0.500      0.6             
##   3          0.3  0.01       0.05       0.500      0.8             
##   3          0.3  0.01       0.05       0.500      0.8             
##   3          0.3  0.01       0.05       0.500      0.8             
##   3          0.3  0.01       0.05       0.500      0.8             
##   3          0.3  0.01       0.05       0.500      0.8             
##   3          0.3  0.01       0.05       0.625      0.6             
##   3          0.3  0.01       0.05       0.625      0.6             
##   3          0.3  0.01       0.05       0.625      0.6             
##   3          0.3  0.01       0.05       0.625      0.6             
##   3          0.3  0.01       0.05       0.625      0.6             
##   3          0.3  0.01       0.05       0.625      0.8             
##   3          0.3  0.01       0.05       0.625      0.8             
##   3          0.3  0.01       0.05       0.625      0.8             
##   3          0.3  0.01       0.05       0.625      0.8             
##   3          0.3  0.01       0.05       0.625      0.8             
##   3          0.3  0.01       0.05       0.750      0.6             
##   3          0.3  0.01       0.05       0.750      0.6             
##   3          0.3  0.01       0.05       0.750      0.6             
##   3          0.3  0.01       0.05       0.750      0.6             
##   3          0.3  0.01       0.05       0.750      0.6             
##   3          0.3  0.01       0.05       0.750      0.8             
##   3          0.3  0.01       0.05       0.750      0.8             
##   3          0.3  0.01       0.05       0.750      0.8             
##   3          0.3  0.01       0.05       0.750      0.8             
##   3          0.3  0.01       0.05       0.750      0.8             
##   3          0.3  0.01       0.05       0.875      0.6             
##   3          0.3  0.01       0.05       0.875      0.6             
##   3          0.3  0.01       0.05       0.875      0.6             
##   3          0.3  0.01       0.05       0.875      0.6             
##   3          0.3  0.01       0.05       0.875      0.6             
##   3          0.3  0.01       0.05       0.875      0.8             
##   3          0.3  0.01       0.05       0.875      0.8             
##   3          0.3  0.01       0.05       0.875      0.8             
##   3          0.3  0.01       0.05       0.875      0.8             
##   3          0.3  0.01       0.05       0.875      0.8             
##   3          0.3  0.01       0.05       1.000      0.6             
##   3          0.3  0.01       0.05       1.000      0.6             
##   3          0.3  0.01       0.05       1.000      0.6             
##   3          0.3  0.01       0.05       1.000      0.6             
##   3          0.3  0.01       0.05       1.000      0.6             
##   3          0.3  0.01       0.05       1.000      0.8             
##   3          0.3  0.01       0.05       1.000      0.8             
##   3          0.3  0.01       0.05       1.000      0.8             
##   3          0.3  0.01       0.05       1.000      0.8             
##   3          0.3  0.01       0.05       1.000      0.8             
##   3          0.3  0.01       0.95       0.500      0.6             
##   3          0.3  0.01       0.95       0.500      0.6             
##   3          0.3  0.01       0.95       0.500      0.6             
##   3          0.3  0.01       0.95       0.500      0.6             
##   3          0.3  0.01       0.95       0.500      0.6             
##   3          0.3  0.01       0.95       0.500      0.8             
##   3          0.3  0.01       0.95       0.500      0.8             
##   3          0.3  0.01       0.95       0.500      0.8             
##   3          0.3  0.01       0.95       0.500      0.8             
##   3          0.3  0.01       0.95       0.500      0.8             
##   3          0.3  0.01       0.95       0.625      0.6             
##   3          0.3  0.01       0.95       0.625      0.6             
##   3          0.3  0.01       0.95       0.625      0.6             
##   3          0.3  0.01       0.95       0.625      0.6             
##   3          0.3  0.01       0.95       0.625      0.6             
##   3          0.3  0.01       0.95       0.625      0.8             
##   3          0.3  0.01       0.95       0.625      0.8             
##   3          0.3  0.01       0.95       0.625      0.8             
##   3          0.3  0.01       0.95       0.625      0.8             
##   3          0.3  0.01       0.95       0.625      0.8             
##   3          0.3  0.01       0.95       0.750      0.6             
##   3          0.3  0.01       0.95       0.750      0.6             
##   3          0.3  0.01       0.95       0.750      0.6             
##   3          0.3  0.01       0.95       0.750      0.6             
##   3          0.3  0.01       0.95       0.750      0.6             
##   3          0.3  0.01       0.95       0.750      0.8             
##   3          0.3  0.01       0.95       0.750      0.8             
##   3          0.3  0.01       0.95       0.750      0.8             
##   3          0.3  0.01       0.95       0.750      0.8             
##   3          0.3  0.01       0.95       0.750      0.8             
##   3          0.3  0.01       0.95       0.875      0.6             
##   3          0.3  0.01       0.95       0.875      0.6             
##   3          0.3  0.01       0.95       0.875      0.6             
##   3          0.3  0.01       0.95       0.875      0.6             
##   3          0.3  0.01       0.95       0.875      0.6             
##   3          0.3  0.01       0.95       0.875      0.8             
##   3          0.3  0.01       0.95       0.875      0.8             
##   3          0.3  0.01       0.95       0.875      0.8             
##   3          0.3  0.01       0.95       0.875      0.8             
##   3          0.3  0.01       0.95       0.875      0.8             
##   3          0.3  0.01       0.95       1.000      0.6             
##   3          0.3  0.01       0.95       1.000      0.6             
##   3          0.3  0.01       0.95       1.000      0.6             
##   3          0.3  0.01       0.95       1.000      0.6             
##   3          0.3  0.01       0.95       1.000      0.6             
##   3          0.3  0.01       0.95       1.000      0.8             
##   3          0.3  0.01       0.95       1.000      0.8             
##   3          0.3  0.01       0.95       1.000      0.8             
##   3          0.3  0.01       0.95       1.000      0.8             
##   3          0.3  0.01       0.95       1.000      0.8             
##   3          0.3  0.50       0.05       0.500      0.6             
##   3          0.3  0.50       0.05       0.500      0.6             
##   3          0.3  0.50       0.05       0.500      0.6             
##   3          0.3  0.50       0.05       0.500      0.6             
##   3          0.3  0.50       0.05       0.500      0.6             
##   3          0.3  0.50       0.05       0.500      0.8             
##   3          0.3  0.50       0.05       0.500      0.8             
##   3          0.3  0.50       0.05       0.500      0.8             
##   3          0.3  0.50       0.05       0.500      0.8             
##   3          0.3  0.50       0.05       0.500      0.8             
##   3          0.3  0.50       0.05       0.625      0.6             
##   3          0.3  0.50       0.05       0.625      0.6             
##   3          0.3  0.50       0.05       0.625      0.6             
##   3          0.3  0.50       0.05       0.625      0.6             
##   3          0.3  0.50       0.05       0.625      0.6             
##   3          0.3  0.50       0.05       0.625      0.8             
##   3          0.3  0.50       0.05       0.625      0.8             
##   3          0.3  0.50       0.05       0.625      0.8             
##   3          0.3  0.50       0.05       0.625      0.8             
##   3          0.3  0.50       0.05       0.625      0.8             
##   3          0.3  0.50       0.05       0.750      0.6             
##   3          0.3  0.50       0.05       0.750      0.6             
##   3          0.3  0.50       0.05       0.750      0.6             
##   3          0.3  0.50       0.05       0.750      0.6             
##   3          0.3  0.50       0.05       0.750      0.6             
##   3          0.3  0.50       0.05       0.750      0.8             
##   3          0.3  0.50       0.05       0.750      0.8             
##   3          0.3  0.50       0.05       0.750      0.8             
##   3          0.3  0.50       0.05       0.750      0.8             
##   3          0.3  0.50       0.05       0.750      0.8             
##   3          0.3  0.50       0.05       0.875      0.6             
##   3          0.3  0.50       0.05       0.875      0.6             
##   3          0.3  0.50       0.05       0.875      0.6             
##   3          0.3  0.50       0.05       0.875      0.6             
##   3          0.3  0.50       0.05       0.875      0.6             
##   3          0.3  0.50       0.05       0.875      0.8             
##   3          0.3  0.50       0.05       0.875      0.8             
##   3          0.3  0.50       0.05       0.875      0.8             
##   3          0.3  0.50       0.05       0.875      0.8             
##   3          0.3  0.50       0.05       0.875      0.8             
##   3          0.3  0.50       0.05       1.000      0.6             
##   3          0.3  0.50       0.05       1.000      0.6             
##   3          0.3  0.50       0.05       1.000      0.6             
##   3          0.3  0.50       0.05       1.000      0.6             
##   3          0.3  0.50       0.05       1.000      0.6             
##   3          0.3  0.50       0.05       1.000      0.8             
##   3          0.3  0.50       0.05       1.000      0.8             
##   3          0.3  0.50       0.05       1.000      0.8             
##   3          0.3  0.50       0.05       1.000      0.8             
##   3          0.3  0.50       0.05       1.000      0.8             
##   3          0.3  0.50       0.95       0.500      0.6             
##   3          0.3  0.50       0.95       0.500      0.6             
##   3          0.3  0.50       0.95       0.500      0.6             
##   3          0.3  0.50       0.95       0.500      0.6             
##   3          0.3  0.50       0.95       0.500      0.6             
##   3          0.3  0.50       0.95       0.500      0.8             
##   3          0.3  0.50       0.95       0.500      0.8             
##   3          0.3  0.50       0.95       0.500      0.8             
##   3          0.3  0.50       0.95       0.500      0.8             
##   3          0.3  0.50       0.95       0.500      0.8             
##   3          0.3  0.50       0.95       0.625      0.6             
##   3          0.3  0.50       0.95       0.625      0.6             
##   3          0.3  0.50       0.95       0.625      0.6             
##   3          0.3  0.50       0.95       0.625      0.6             
##   3          0.3  0.50       0.95       0.625      0.6             
##   3          0.3  0.50       0.95       0.625      0.8             
##   3          0.3  0.50       0.95       0.625      0.8             
##   3          0.3  0.50       0.95       0.625      0.8             
##   3          0.3  0.50       0.95       0.625      0.8             
##   3          0.3  0.50       0.95       0.625      0.8             
##   3          0.3  0.50       0.95       0.750      0.6             
##   3          0.3  0.50       0.95       0.750      0.6             
##   3          0.3  0.50       0.95       0.750      0.6             
##   3          0.3  0.50       0.95       0.750      0.6             
##   3          0.3  0.50       0.95       0.750      0.6             
##   3          0.3  0.50       0.95       0.750      0.8             
##   3          0.3  0.50       0.95       0.750      0.8             
##   3          0.3  0.50       0.95       0.750      0.8             
##   3          0.3  0.50       0.95       0.750      0.8             
##   3          0.3  0.50       0.95       0.750      0.8             
##   3          0.3  0.50       0.95       0.875      0.6             
##   3          0.3  0.50       0.95       0.875      0.6             
##   3          0.3  0.50       0.95       0.875      0.6             
##   3          0.3  0.50       0.95       0.875      0.6             
##   3          0.3  0.50       0.95       0.875      0.6             
##   3          0.3  0.50       0.95       0.875      0.8             
##   3          0.3  0.50       0.95       0.875      0.8             
##   3          0.3  0.50       0.95       0.875      0.8             
##   3          0.3  0.50       0.95       0.875      0.8             
##   3          0.3  0.50       0.95       0.875      0.8             
##   3          0.3  0.50       0.95       1.000      0.6             
##   3          0.3  0.50       0.95       1.000      0.6             
##   3          0.3  0.50       0.95       1.000      0.6             
##   3          0.3  0.50       0.95       1.000      0.6             
##   3          0.3  0.50       0.95       1.000      0.6             
##   3          0.3  0.50       0.95       1.000      0.8             
##   3          0.3  0.50       0.95       1.000      0.8             
##   3          0.3  0.50       0.95       1.000      0.8             
##   3          0.3  0.50       0.95       1.000      0.8             
##   3          0.3  0.50       0.95       1.000      0.8             
##   3          0.4  0.01       0.05       0.500      0.6             
##   3          0.4  0.01       0.05       0.500      0.6             
##   3          0.4  0.01       0.05       0.500      0.6             
##   3          0.4  0.01       0.05       0.500      0.6             
##   3          0.4  0.01       0.05       0.500      0.6             
##   3          0.4  0.01       0.05       0.500      0.8             
##   3          0.4  0.01       0.05       0.500      0.8             
##   3          0.4  0.01       0.05       0.500      0.8             
##   3          0.4  0.01       0.05       0.500      0.8             
##   3          0.4  0.01       0.05       0.500      0.8             
##   3          0.4  0.01       0.05       0.625      0.6             
##   3          0.4  0.01       0.05       0.625      0.6             
##   3          0.4  0.01       0.05       0.625      0.6             
##   3          0.4  0.01       0.05       0.625      0.6             
##   3          0.4  0.01       0.05       0.625      0.6             
##   3          0.4  0.01       0.05       0.625      0.8             
##   3          0.4  0.01       0.05       0.625      0.8             
##   3          0.4  0.01       0.05       0.625      0.8             
##   3          0.4  0.01       0.05       0.625      0.8             
##   3          0.4  0.01       0.05       0.625      0.8             
##   3          0.4  0.01       0.05       0.750      0.6             
##   3          0.4  0.01       0.05       0.750      0.6             
##   3          0.4  0.01       0.05       0.750      0.6             
##   3          0.4  0.01       0.05       0.750      0.6             
##   3          0.4  0.01       0.05       0.750      0.6             
##   3          0.4  0.01       0.05       0.750      0.8             
##   3          0.4  0.01       0.05       0.750      0.8             
##   3          0.4  0.01       0.05       0.750      0.8             
##   3          0.4  0.01       0.05       0.750      0.8             
##   3          0.4  0.01       0.05       0.750      0.8             
##   3          0.4  0.01       0.05       0.875      0.6             
##   3          0.4  0.01       0.05       0.875      0.6             
##   3          0.4  0.01       0.05       0.875      0.6             
##   3          0.4  0.01       0.05       0.875      0.6             
##   3          0.4  0.01       0.05       0.875      0.6             
##   3          0.4  0.01       0.05       0.875      0.8             
##   3          0.4  0.01       0.05       0.875      0.8             
##   3          0.4  0.01       0.05       0.875      0.8             
##   3          0.4  0.01       0.05       0.875      0.8             
##   3          0.4  0.01       0.05       0.875      0.8             
##   3          0.4  0.01       0.05       1.000      0.6             
##   3          0.4  0.01       0.05       1.000      0.6             
##   3          0.4  0.01       0.05       1.000      0.6             
##   3          0.4  0.01       0.05       1.000      0.6             
##   3          0.4  0.01       0.05       1.000      0.6             
##   3          0.4  0.01       0.05       1.000      0.8             
##   3          0.4  0.01       0.05       1.000      0.8             
##   3          0.4  0.01       0.05       1.000      0.8             
##   3          0.4  0.01       0.05       1.000      0.8             
##   3          0.4  0.01       0.05       1.000      0.8             
##   3          0.4  0.01       0.95       0.500      0.6             
##   3          0.4  0.01       0.95       0.500      0.6             
##   3          0.4  0.01       0.95       0.500      0.6             
##   3          0.4  0.01       0.95       0.500      0.6             
##   3          0.4  0.01       0.95       0.500      0.6             
##   3          0.4  0.01       0.95       0.500      0.8             
##   3          0.4  0.01       0.95       0.500      0.8             
##   3          0.4  0.01       0.95       0.500      0.8             
##   3          0.4  0.01       0.95       0.500      0.8             
##   3          0.4  0.01       0.95       0.500      0.8             
##   3          0.4  0.01       0.95       0.625      0.6             
##   3          0.4  0.01       0.95       0.625      0.6             
##   3          0.4  0.01       0.95       0.625      0.6             
##   3          0.4  0.01       0.95       0.625      0.6             
##   3          0.4  0.01       0.95       0.625      0.6             
##   3          0.4  0.01       0.95       0.625      0.8             
##   3          0.4  0.01       0.95       0.625      0.8             
##   3          0.4  0.01       0.95       0.625      0.8             
##   3          0.4  0.01       0.95       0.625      0.8             
##   3          0.4  0.01       0.95       0.625      0.8             
##   3          0.4  0.01       0.95       0.750      0.6             
##   3          0.4  0.01       0.95       0.750      0.6             
##   3          0.4  0.01       0.95       0.750      0.6             
##   3          0.4  0.01       0.95       0.750      0.6             
##   3          0.4  0.01       0.95       0.750      0.6             
##   3          0.4  0.01       0.95       0.750      0.8             
##   3          0.4  0.01       0.95       0.750      0.8             
##   3          0.4  0.01       0.95       0.750      0.8             
##   3          0.4  0.01       0.95       0.750      0.8             
##   3          0.4  0.01       0.95       0.750      0.8             
##   3          0.4  0.01       0.95       0.875      0.6             
##   3          0.4  0.01       0.95       0.875      0.6             
##   3          0.4  0.01       0.95       0.875      0.6             
##   3          0.4  0.01       0.95       0.875      0.6             
##   3          0.4  0.01       0.95       0.875      0.6             
##   3          0.4  0.01       0.95       0.875      0.8             
##   3          0.4  0.01       0.95       0.875      0.8             
##   3          0.4  0.01       0.95       0.875      0.8             
##   3          0.4  0.01       0.95       0.875      0.8             
##   3          0.4  0.01       0.95       0.875      0.8             
##   3          0.4  0.01       0.95       1.000      0.6             
##   3          0.4  0.01       0.95       1.000      0.6             
##   3          0.4  0.01       0.95       1.000      0.6             
##   3          0.4  0.01       0.95       1.000      0.6             
##   3          0.4  0.01       0.95       1.000      0.6             
##   3          0.4  0.01       0.95       1.000      0.8             
##   3          0.4  0.01       0.95       1.000      0.8             
##   3          0.4  0.01       0.95       1.000      0.8             
##   3          0.4  0.01       0.95       1.000      0.8             
##   3          0.4  0.01       0.95       1.000      0.8             
##   3          0.4  0.50       0.05       0.500      0.6             
##   3          0.4  0.50       0.05       0.500      0.6             
##   3          0.4  0.50       0.05       0.500      0.6             
##   3          0.4  0.50       0.05       0.500      0.6             
##   3          0.4  0.50       0.05       0.500      0.6             
##   3          0.4  0.50       0.05       0.500      0.8             
##   3          0.4  0.50       0.05       0.500      0.8             
##   3          0.4  0.50       0.05       0.500      0.8             
##   3          0.4  0.50       0.05       0.500      0.8             
##   3          0.4  0.50       0.05       0.500      0.8             
##   3          0.4  0.50       0.05       0.625      0.6             
##   3          0.4  0.50       0.05       0.625      0.6             
##   3          0.4  0.50       0.05       0.625      0.6             
##   3          0.4  0.50       0.05       0.625      0.6             
##   3          0.4  0.50       0.05       0.625      0.6             
##   3          0.4  0.50       0.05       0.625      0.8             
##   3          0.4  0.50       0.05       0.625      0.8             
##   3          0.4  0.50       0.05       0.625      0.8             
##   3          0.4  0.50       0.05       0.625      0.8             
##   3          0.4  0.50       0.05       0.625      0.8             
##   3          0.4  0.50       0.05       0.750      0.6             
##   3          0.4  0.50       0.05       0.750      0.6             
##   3          0.4  0.50       0.05       0.750      0.6             
##   3          0.4  0.50       0.05       0.750      0.6             
##   3          0.4  0.50       0.05       0.750      0.6             
##   3          0.4  0.50       0.05       0.750      0.8             
##   3          0.4  0.50       0.05       0.750      0.8             
##   3          0.4  0.50       0.05       0.750      0.8             
##   3          0.4  0.50       0.05       0.750      0.8             
##   3          0.4  0.50       0.05       0.750      0.8             
##   3          0.4  0.50       0.05       0.875      0.6             
##   3          0.4  0.50       0.05       0.875      0.6             
##   3          0.4  0.50       0.05       0.875      0.6             
##   3          0.4  0.50       0.05       0.875      0.6             
##   3          0.4  0.50       0.05       0.875      0.6             
##   3          0.4  0.50       0.05       0.875      0.8             
##   3          0.4  0.50       0.05       0.875      0.8             
##   3          0.4  0.50       0.05       0.875      0.8             
##   3          0.4  0.50       0.05       0.875      0.8             
##   3          0.4  0.50       0.05       0.875      0.8             
##   3          0.4  0.50       0.05       1.000      0.6             
##   3          0.4  0.50       0.05       1.000      0.6             
##   3          0.4  0.50       0.05       1.000      0.6             
##   3          0.4  0.50       0.05       1.000      0.6             
##   3          0.4  0.50       0.05       1.000      0.6             
##   3          0.4  0.50       0.05       1.000      0.8             
##   3          0.4  0.50       0.05       1.000      0.8             
##   3          0.4  0.50       0.05       1.000      0.8             
##   3          0.4  0.50       0.05       1.000      0.8             
##   3          0.4  0.50       0.05       1.000      0.8             
##   3          0.4  0.50       0.95       0.500      0.6             
##   3          0.4  0.50       0.95       0.500      0.6             
##   3          0.4  0.50       0.95       0.500      0.6             
##   3          0.4  0.50       0.95       0.500      0.6             
##   3          0.4  0.50       0.95       0.500      0.6             
##   3          0.4  0.50       0.95       0.500      0.8             
##   3          0.4  0.50       0.95       0.500      0.8             
##   3          0.4  0.50       0.95       0.500      0.8             
##   3          0.4  0.50       0.95       0.500      0.8             
##   3          0.4  0.50       0.95       0.500      0.8             
##   3          0.4  0.50       0.95       0.625      0.6             
##   3          0.4  0.50       0.95       0.625      0.6             
##   3          0.4  0.50       0.95       0.625      0.6             
##   3          0.4  0.50       0.95       0.625      0.6             
##   3          0.4  0.50       0.95       0.625      0.6             
##   3          0.4  0.50       0.95       0.625      0.8             
##   3          0.4  0.50       0.95       0.625      0.8             
##   3          0.4  0.50       0.95       0.625      0.8             
##   3          0.4  0.50       0.95       0.625      0.8             
##   3          0.4  0.50       0.95       0.625      0.8             
##   3          0.4  0.50       0.95       0.750      0.6             
##   3          0.4  0.50       0.95       0.750      0.6             
##   3          0.4  0.50       0.95       0.750      0.6             
##   3          0.4  0.50       0.95       0.750      0.6             
##   3          0.4  0.50       0.95       0.750      0.6             
##   3          0.4  0.50       0.95       0.750      0.8             
##   3          0.4  0.50       0.95       0.750      0.8             
##   3          0.4  0.50       0.95       0.750      0.8             
##   3          0.4  0.50       0.95       0.750      0.8             
##   3          0.4  0.50       0.95       0.750      0.8             
##   3          0.4  0.50       0.95       0.875      0.6             
##   3          0.4  0.50       0.95       0.875      0.6             
##   3          0.4  0.50       0.95       0.875      0.6             
##   3          0.4  0.50       0.95       0.875      0.6             
##   3          0.4  0.50       0.95       0.875      0.6             
##   3          0.4  0.50       0.95       0.875      0.8             
##   3          0.4  0.50       0.95       0.875      0.8             
##   3          0.4  0.50       0.95       0.875      0.8             
##   3          0.4  0.50       0.95       0.875      0.8             
##   3          0.4  0.50       0.95       0.875      0.8             
##   3          0.4  0.50       0.95       1.000      0.6             
##   3          0.4  0.50       0.95       1.000      0.6             
##   3          0.4  0.50       0.95       1.000      0.6             
##   3          0.4  0.50       0.95       1.000      0.6             
##   3          0.4  0.50       0.95       1.000      0.6             
##   3          0.4  0.50       0.95       1.000      0.8             
##   3          0.4  0.50       0.95       1.000      0.8             
##   3          0.4  0.50       0.95       1.000      0.8             
##   3          0.4  0.50       0.95       1.000      0.8             
##   3          0.4  0.50       0.95       1.000      0.8             
##   4          0.3  0.01       0.05       0.500      0.6             
##   4          0.3  0.01       0.05       0.500      0.6             
##   4          0.3  0.01       0.05       0.500      0.6             
##   4          0.3  0.01       0.05       0.500      0.6             
##   4          0.3  0.01       0.05       0.500      0.6             
##   4          0.3  0.01       0.05       0.500      0.8             
##   4          0.3  0.01       0.05       0.500      0.8             
##   4          0.3  0.01       0.05       0.500      0.8             
##   4          0.3  0.01       0.05       0.500      0.8             
##   4          0.3  0.01       0.05       0.500      0.8             
##   4          0.3  0.01       0.05       0.625      0.6             
##   4          0.3  0.01       0.05       0.625      0.6             
##   4          0.3  0.01       0.05       0.625      0.6             
##   4          0.3  0.01       0.05       0.625      0.6             
##   4          0.3  0.01       0.05       0.625      0.6             
##   4          0.3  0.01       0.05       0.625      0.8             
##   4          0.3  0.01       0.05       0.625      0.8             
##   4          0.3  0.01       0.05       0.625      0.8             
##   4          0.3  0.01       0.05       0.625      0.8             
##   4          0.3  0.01       0.05       0.625      0.8             
##   4          0.3  0.01       0.05       0.750      0.6             
##   4          0.3  0.01       0.05       0.750      0.6             
##   4          0.3  0.01       0.05       0.750      0.6             
##   4          0.3  0.01       0.05       0.750      0.6             
##   4          0.3  0.01       0.05       0.750      0.6             
##   4          0.3  0.01       0.05       0.750      0.8             
##   4          0.3  0.01       0.05       0.750      0.8             
##   4          0.3  0.01       0.05       0.750      0.8             
##   4          0.3  0.01       0.05       0.750      0.8             
##   4          0.3  0.01       0.05       0.750      0.8             
##   4          0.3  0.01       0.05       0.875      0.6             
##   4          0.3  0.01       0.05       0.875      0.6             
##   4          0.3  0.01       0.05       0.875      0.6             
##   4          0.3  0.01       0.05       0.875      0.6             
##   4          0.3  0.01       0.05       0.875      0.6             
##   4          0.3  0.01       0.05       0.875      0.8             
##   4          0.3  0.01       0.05       0.875      0.8             
##   4          0.3  0.01       0.05       0.875      0.8             
##   4          0.3  0.01       0.05       0.875      0.8             
##   4          0.3  0.01       0.05       0.875      0.8             
##   4          0.3  0.01       0.05       1.000      0.6             
##   4          0.3  0.01       0.05       1.000      0.6             
##   4          0.3  0.01       0.05       1.000      0.6             
##   4          0.3  0.01       0.05       1.000      0.6             
##   4          0.3  0.01       0.05       1.000      0.6             
##   4          0.3  0.01       0.05       1.000      0.8             
##   4          0.3  0.01       0.05       1.000      0.8             
##   4          0.3  0.01       0.05       1.000      0.8             
##   4          0.3  0.01       0.05       1.000      0.8             
##   4          0.3  0.01       0.05       1.000      0.8             
##   4          0.3  0.01       0.95       0.500      0.6             
##   4          0.3  0.01       0.95       0.500      0.6             
##   4          0.3  0.01       0.95       0.500      0.6             
##   4          0.3  0.01       0.95       0.500      0.6             
##   4          0.3  0.01       0.95       0.500      0.6             
##   4          0.3  0.01       0.95       0.500      0.8             
##   4          0.3  0.01       0.95       0.500      0.8             
##   4          0.3  0.01       0.95       0.500      0.8             
##   4          0.3  0.01       0.95       0.500      0.8             
##   4          0.3  0.01       0.95       0.500      0.8             
##   4          0.3  0.01       0.95       0.625      0.6             
##   4          0.3  0.01       0.95       0.625      0.6             
##   4          0.3  0.01       0.95       0.625      0.6             
##   4          0.3  0.01       0.95       0.625      0.6             
##   4          0.3  0.01       0.95       0.625      0.6             
##   4          0.3  0.01       0.95       0.625      0.8             
##   4          0.3  0.01       0.95       0.625      0.8             
##   4          0.3  0.01       0.95       0.625      0.8             
##   4          0.3  0.01       0.95       0.625      0.8             
##   4          0.3  0.01       0.95       0.625      0.8             
##   4          0.3  0.01       0.95       0.750      0.6             
##   4          0.3  0.01       0.95       0.750      0.6             
##   4          0.3  0.01       0.95       0.750      0.6             
##   4          0.3  0.01       0.95       0.750      0.6             
##   4          0.3  0.01       0.95       0.750      0.6             
##   4          0.3  0.01       0.95       0.750      0.8             
##   4          0.3  0.01       0.95       0.750      0.8             
##   4          0.3  0.01       0.95       0.750      0.8             
##   4          0.3  0.01       0.95       0.750      0.8             
##   4          0.3  0.01       0.95       0.750      0.8             
##   4          0.3  0.01       0.95       0.875      0.6             
##   4          0.3  0.01       0.95       0.875      0.6             
##   4          0.3  0.01       0.95       0.875      0.6             
##   4          0.3  0.01       0.95       0.875      0.6             
##   4          0.3  0.01       0.95       0.875      0.6             
##   4          0.3  0.01       0.95       0.875      0.8             
##   4          0.3  0.01       0.95       0.875      0.8             
##   4          0.3  0.01       0.95       0.875      0.8             
##   4          0.3  0.01       0.95       0.875      0.8             
##   4          0.3  0.01       0.95       0.875      0.8             
##   4          0.3  0.01       0.95       1.000      0.6             
##   4          0.3  0.01       0.95       1.000      0.6             
##   4          0.3  0.01       0.95       1.000      0.6             
##   4          0.3  0.01       0.95       1.000      0.6             
##   4          0.3  0.01       0.95       1.000      0.6             
##   4          0.3  0.01       0.95       1.000      0.8             
##   4          0.3  0.01       0.95       1.000      0.8             
##   4          0.3  0.01       0.95       1.000      0.8             
##   4          0.3  0.01       0.95       1.000      0.8             
##   4          0.3  0.01       0.95       1.000      0.8             
##   4          0.3  0.50       0.05       0.500      0.6             
##   4          0.3  0.50       0.05       0.500      0.6             
##   4          0.3  0.50       0.05       0.500      0.6             
##   4          0.3  0.50       0.05       0.500      0.6             
##   4          0.3  0.50       0.05       0.500      0.6             
##   4          0.3  0.50       0.05       0.500      0.8             
##   4          0.3  0.50       0.05       0.500      0.8             
##   4          0.3  0.50       0.05       0.500      0.8             
##   4          0.3  0.50       0.05       0.500      0.8             
##   4          0.3  0.50       0.05       0.500      0.8             
##   4          0.3  0.50       0.05       0.625      0.6             
##   4          0.3  0.50       0.05       0.625      0.6             
##   4          0.3  0.50       0.05       0.625      0.6             
##   4          0.3  0.50       0.05       0.625      0.6             
##   4          0.3  0.50       0.05       0.625      0.6             
##   4          0.3  0.50       0.05       0.625      0.8             
##   4          0.3  0.50       0.05       0.625      0.8             
##   4          0.3  0.50       0.05       0.625      0.8             
##   4          0.3  0.50       0.05       0.625      0.8             
##   4          0.3  0.50       0.05       0.625      0.8             
##   4          0.3  0.50       0.05       0.750      0.6             
##   4          0.3  0.50       0.05       0.750      0.6             
##   4          0.3  0.50       0.05       0.750      0.6             
##   4          0.3  0.50       0.05       0.750      0.6             
##   4          0.3  0.50       0.05       0.750      0.6             
##   4          0.3  0.50       0.05       0.750      0.8             
##   4          0.3  0.50       0.05       0.750      0.8             
##   4          0.3  0.50       0.05       0.750      0.8             
##   4          0.3  0.50       0.05       0.750      0.8             
##   4          0.3  0.50       0.05       0.750      0.8             
##   4          0.3  0.50       0.05       0.875      0.6             
##   4          0.3  0.50       0.05       0.875      0.6             
##   4          0.3  0.50       0.05       0.875      0.6             
##   4          0.3  0.50       0.05       0.875      0.6             
##   4          0.3  0.50       0.05       0.875      0.6             
##   4          0.3  0.50       0.05       0.875      0.8             
##   4          0.3  0.50       0.05       0.875      0.8             
##   4          0.3  0.50       0.05       0.875      0.8             
##   4          0.3  0.50       0.05       0.875      0.8             
##   4          0.3  0.50       0.05       0.875      0.8             
##   4          0.3  0.50       0.05       1.000      0.6             
##   4          0.3  0.50       0.05       1.000      0.6             
##   4          0.3  0.50       0.05       1.000      0.6             
##   4          0.3  0.50       0.05       1.000      0.6             
##   4          0.3  0.50       0.05       1.000      0.6             
##   4          0.3  0.50       0.05       1.000      0.8             
##   4          0.3  0.50       0.05       1.000      0.8             
##   4          0.3  0.50       0.05       1.000      0.8             
##   4          0.3  0.50       0.05       1.000      0.8             
##   4          0.3  0.50       0.05       1.000      0.8             
##   4          0.3  0.50       0.95       0.500      0.6             
##   4          0.3  0.50       0.95       0.500      0.6             
##   4          0.3  0.50       0.95       0.500      0.6             
##   4          0.3  0.50       0.95       0.500      0.6             
##   4          0.3  0.50       0.95       0.500      0.6             
##   4          0.3  0.50       0.95       0.500      0.8             
##   4          0.3  0.50       0.95       0.500      0.8             
##   4          0.3  0.50       0.95       0.500      0.8             
##   4          0.3  0.50       0.95       0.500      0.8             
##   4          0.3  0.50       0.95       0.500      0.8             
##   4          0.3  0.50       0.95       0.625      0.6             
##   4          0.3  0.50       0.95       0.625      0.6             
##   4          0.3  0.50       0.95       0.625      0.6             
##   4          0.3  0.50       0.95       0.625      0.6             
##   4          0.3  0.50       0.95       0.625      0.6             
##   4          0.3  0.50       0.95       0.625      0.8             
##   4          0.3  0.50       0.95       0.625      0.8             
##   4          0.3  0.50       0.95       0.625      0.8             
##   4          0.3  0.50       0.95       0.625      0.8             
##   4          0.3  0.50       0.95       0.625      0.8             
##   4          0.3  0.50       0.95       0.750      0.6             
##   4          0.3  0.50       0.95       0.750      0.6             
##   4          0.3  0.50       0.95       0.750      0.6             
##   4          0.3  0.50       0.95       0.750      0.6             
##   4          0.3  0.50       0.95       0.750      0.6             
##   4          0.3  0.50       0.95       0.750      0.8             
##   4          0.3  0.50       0.95       0.750      0.8             
##   4          0.3  0.50       0.95       0.750      0.8             
##   4          0.3  0.50       0.95       0.750      0.8             
##   4          0.3  0.50       0.95       0.750      0.8             
##   4          0.3  0.50       0.95       0.875      0.6             
##   4          0.3  0.50       0.95       0.875      0.6             
##   4          0.3  0.50       0.95       0.875      0.6             
##   4          0.3  0.50       0.95       0.875      0.6             
##   4          0.3  0.50       0.95       0.875      0.6             
##   4          0.3  0.50       0.95       0.875      0.8             
##   4          0.3  0.50       0.95       0.875      0.8             
##   4          0.3  0.50       0.95       0.875      0.8             
##   4          0.3  0.50       0.95       0.875      0.8             
##   4          0.3  0.50       0.95       0.875      0.8             
##   4          0.3  0.50       0.95       1.000      0.6             
##   4          0.3  0.50       0.95       1.000      0.6             
##   4          0.3  0.50       0.95       1.000      0.6             
##   4          0.3  0.50       0.95       1.000      0.6             
##   4          0.3  0.50       0.95       1.000      0.6             
##   4          0.3  0.50       0.95       1.000      0.8             
##   4          0.3  0.50       0.95       1.000      0.8             
##   4          0.3  0.50       0.95       1.000      0.8             
##   4          0.3  0.50       0.95       1.000      0.8             
##   4          0.3  0.50       0.95       1.000      0.8             
##   4          0.4  0.01       0.05       0.500      0.6             
##   4          0.4  0.01       0.05       0.500      0.6             
##   4          0.4  0.01       0.05       0.500      0.6             
##   4          0.4  0.01       0.05       0.500      0.6             
##   4          0.4  0.01       0.05       0.500      0.6             
##   4          0.4  0.01       0.05       0.500      0.8             
##   4          0.4  0.01       0.05       0.500      0.8             
##   4          0.4  0.01       0.05       0.500      0.8             
##   4          0.4  0.01       0.05       0.500      0.8             
##   4          0.4  0.01       0.05       0.500      0.8             
##   4          0.4  0.01       0.05       0.625      0.6             
##   4          0.4  0.01       0.05       0.625      0.6             
##   4          0.4  0.01       0.05       0.625      0.6             
##   4          0.4  0.01       0.05       0.625      0.6             
##   4          0.4  0.01       0.05       0.625      0.6             
##   4          0.4  0.01       0.05       0.625      0.8             
##   4          0.4  0.01       0.05       0.625      0.8             
##   4          0.4  0.01       0.05       0.625      0.8             
##   4          0.4  0.01       0.05       0.625      0.8             
##   4          0.4  0.01       0.05       0.625      0.8             
##   4          0.4  0.01       0.05       0.750      0.6             
##   4          0.4  0.01       0.05       0.750      0.6             
##   4          0.4  0.01       0.05       0.750      0.6             
##   4          0.4  0.01       0.05       0.750      0.6             
##   4          0.4  0.01       0.05       0.750      0.6             
##   4          0.4  0.01       0.05       0.750      0.8             
##   4          0.4  0.01       0.05       0.750      0.8             
##   4          0.4  0.01       0.05       0.750      0.8             
##   4          0.4  0.01       0.05       0.750      0.8             
##   4          0.4  0.01       0.05       0.750      0.8             
##   4          0.4  0.01       0.05       0.875      0.6             
##   4          0.4  0.01       0.05       0.875      0.6             
##   4          0.4  0.01       0.05       0.875      0.6             
##   4          0.4  0.01       0.05       0.875      0.6             
##   4          0.4  0.01       0.05       0.875      0.6             
##   4          0.4  0.01       0.05       0.875      0.8             
##   4          0.4  0.01       0.05       0.875      0.8             
##   4          0.4  0.01       0.05       0.875      0.8             
##   4          0.4  0.01       0.05       0.875      0.8             
##   4          0.4  0.01       0.05       0.875      0.8             
##   4          0.4  0.01       0.05       1.000      0.6             
##   4          0.4  0.01       0.05       1.000      0.6             
##   4          0.4  0.01       0.05       1.000      0.6             
##   4          0.4  0.01       0.05       1.000      0.6             
##   4          0.4  0.01       0.05       1.000      0.6             
##   4          0.4  0.01       0.05       1.000      0.8             
##   4          0.4  0.01       0.05       1.000      0.8             
##   4          0.4  0.01       0.05       1.000      0.8             
##   4          0.4  0.01       0.05       1.000      0.8             
##   4          0.4  0.01       0.05       1.000      0.8             
##   4          0.4  0.01       0.95       0.500      0.6             
##   4          0.4  0.01       0.95       0.500      0.6             
##   4          0.4  0.01       0.95       0.500      0.6             
##   4          0.4  0.01       0.95       0.500      0.6             
##   4          0.4  0.01       0.95       0.500      0.6             
##   4          0.4  0.01       0.95       0.500      0.8             
##   4          0.4  0.01       0.95       0.500      0.8             
##   4          0.4  0.01       0.95       0.500      0.8             
##   4          0.4  0.01       0.95       0.500      0.8             
##   4          0.4  0.01       0.95       0.500      0.8             
##   4          0.4  0.01       0.95       0.625      0.6             
##   4          0.4  0.01       0.95       0.625      0.6             
##   4          0.4  0.01       0.95       0.625      0.6             
##   4          0.4  0.01       0.95       0.625      0.6             
##   4          0.4  0.01       0.95       0.625      0.6             
##   4          0.4  0.01       0.95       0.625      0.8             
##   4          0.4  0.01       0.95       0.625      0.8             
##   4          0.4  0.01       0.95       0.625      0.8             
##   4          0.4  0.01       0.95       0.625      0.8             
##   4          0.4  0.01       0.95       0.625      0.8             
##   4          0.4  0.01       0.95       0.750      0.6             
##   4          0.4  0.01       0.95       0.750      0.6             
##   4          0.4  0.01       0.95       0.750      0.6             
##   4          0.4  0.01       0.95       0.750      0.6             
##   4          0.4  0.01       0.95       0.750      0.6             
##   4          0.4  0.01       0.95       0.750      0.8             
##   4          0.4  0.01       0.95       0.750      0.8             
##   4          0.4  0.01       0.95       0.750      0.8             
##   4          0.4  0.01       0.95       0.750      0.8             
##   4          0.4  0.01       0.95       0.750      0.8             
##   4          0.4  0.01       0.95       0.875      0.6             
##   4          0.4  0.01       0.95       0.875      0.6             
##   4          0.4  0.01       0.95       0.875      0.6             
##   4          0.4  0.01       0.95       0.875      0.6             
##   4          0.4  0.01       0.95       0.875      0.6             
##   4          0.4  0.01       0.95       0.875      0.8             
##   4          0.4  0.01       0.95       0.875      0.8             
##   4          0.4  0.01       0.95       0.875      0.8             
##   4          0.4  0.01       0.95       0.875      0.8             
##   4          0.4  0.01       0.95       0.875      0.8             
##   4          0.4  0.01       0.95       1.000      0.6             
##   4          0.4  0.01       0.95       1.000      0.6             
##   4          0.4  0.01       0.95       1.000      0.6             
##   4          0.4  0.01       0.95       1.000      0.6             
##   4          0.4  0.01       0.95       1.000      0.6             
##   4          0.4  0.01       0.95       1.000      0.8             
##   4          0.4  0.01       0.95       1.000      0.8             
##   4          0.4  0.01       0.95       1.000      0.8             
##   4          0.4  0.01       0.95       1.000      0.8             
##   4          0.4  0.01       0.95       1.000      0.8             
##   4          0.4  0.50       0.05       0.500      0.6             
##   4          0.4  0.50       0.05       0.500      0.6             
##   4          0.4  0.50       0.05       0.500      0.6             
##   4          0.4  0.50       0.05       0.500      0.6             
##   4          0.4  0.50       0.05       0.500      0.6             
##   4          0.4  0.50       0.05       0.500      0.8             
##   4          0.4  0.50       0.05       0.500      0.8             
##   4          0.4  0.50       0.05       0.500      0.8             
##   4          0.4  0.50       0.05       0.500      0.8             
##   4          0.4  0.50       0.05       0.500      0.8             
##   4          0.4  0.50       0.05       0.625      0.6             
##   4          0.4  0.50       0.05       0.625      0.6             
##   4          0.4  0.50       0.05       0.625      0.6             
##   4          0.4  0.50       0.05       0.625      0.6             
##   4          0.4  0.50       0.05       0.625      0.6             
##   4          0.4  0.50       0.05       0.625      0.8             
##   4          0.4  0.50       0.05       0.625      0.8             
##   4          0.4  0.50       0.05       0.625      0.8             
##   4          0.4  0.50       0.05       0.625      0.8             
##   4          0.4  0.50       0.05       0.625      0.8             
##   4          0.4  0.50       0.05       0.750      0.6             
##   4          0.4  0.50       0.05       0.750      0.6             
##   4          0.4  0.50       0.05       0.750      0.6             
##   4          0.4  0.50       0.05       0.750      0.6             
##   4          0.4  0.50       0.05       0.750      0.6             
##   4          0.4  0.50       0.05       0.750      0.8             
##   4          0.4  0.50       0.05       0.750      0.8             
##   4          0.4  0.50       0.05       0.750      0.8             
##   4          0.4  0.50       0.05       0.750      0.8             
##   4          0.4  0.50       0.05       0.750      0.8             
##   4          0.4  0.50       0.05       0.875      0.6             
##   4          0.4  0.50       0.05       0.875      0.6             
##   4          0.4  0.50       0.05       0.875      0.6             
##   4          0.4  0.50       0.05       0.875      0.6             
##   4          0.4  0.50       0.05       0.875      0.6             
##   4          0.4  0.50       0.05       0.875      0.8             
##   4          0.4  0.50       0.05       0.875      0.8             
##   4          0.4  0.50       0.05       0.875      0.8             
##   4          0.4  0.50       0.05       0.875      0.8             
##   4          0.4  0.50       0.05       0.875      0.8             
##   4          0.4  0.50       0.05       1.000      0.6             
##   4          0.4  0.50       0.05       1.000      0.6             
##   4          0.4  0.50       0.05       1.000      0.6             
##   4          0.4  0.50       0.05       1.000      0.6             
##   4          0.4  0.50       0.05       1.000      0.6             
##   4          0.4  0.50       0.05       1.000      0.8             
##   4          0.4  0.50       0.05       1.000      0.8             
##   4          0.4  0.50       0.05       1.000      0.8             
##   4          0.4  0.50       0.05       1.000      0.8             
##   4          0.4  0.50       0.05       1.000      0.8             
##   4          0.4  0.50       0.95       0.500      0.6             
##   4          0.4  0.50       0.95       0.500      0.6             
##   4          0.4  0.50       0.95       0.500      0.6             
##   4          0.4  0.50       0.95       0.500      0.6             
##   4          0.4  0.50       0.95       0.500      0.6             
##   4          0.4  0.50       0.95       0.500      0.8             
##   4          0.4  0.50       0.95       0.500      0.8             
##   4          0.4  0.50       0.95       0.500      0.8             
##   4          0.4  0.50       0.95       0.500      0.8             
##   4          0.4  0.50       0.95       0.500      0.8             
##   4          0.4  0.50       0.95       0.625      0.6             
##   4          0.4  0.50       0.95       0.625      0.6             
##   4          0.4  0.50       0.95       0.625      0.6             
##   4          0.4  0.50       0.95       0.625      0.6             
##   4          0.4  0.50       0.95       0.625      0.6             
##   4          0.4  0.50       0.95       0.625      0.8             
##   4          0.4  0.50       0.95       0.625      0.8             
##   4          0.4  0.50       0.95       0.625      0.8             
##   4          0.4  0.50       0.95       0.625      0.8             
##   4          0.4  0.50       0.95       0.625      0.8             
##   4          0.4  0.50       0.95       0.750      0.6             
##   4          0.4  0.50       0.95       0.750      0.6             
##   4          0.4  0.50       0.95       0.750      0.6             
##   4          0.4  0.50       0.95       0.750      0.6             
##   4          0.4  0.50       0.95       0.750      0.6             
##   4          0.4  0.50       0.95       0.750      0.8             
##   4          0.4  0.50       0.95       0.750      0.8             
##   4          0.4  0.50       0.95       0.750      0.8             
##   4          0.4  0.50       0.95       0.750      0.8             
##   4          0.4  0.50       0.95       0.750      0.8             
##   4          0.4  0.50       0.95       0.875      0.6             
##   4          0.4  0.50       0.95       0.875      0.6             
##   4          0.4  0.50       0.95       0.875      0.6             
##   4          0.4  0.50       0.95       0.875      0.6             
##   4          0.4  0.50       0.95       0.875      0.6             
##   4          0.4  0.50       0.95       0.875      0.8             
##   4          0.4  0.50       0.95       0.875      0.8             
##   4          0.4  0.50       0.95       0.875      0.8             
##   4          0.4  0.50       0.95       0.875      0.8             
##   4          0.4  0.50       0.95       0.875      0.8             
##   4          0.4  0.50       0.95       1.000      0.6             
##   4          0.4  0.50       0.95       1.000      0.6             
##   4          0.4  0.50       0.95       1.000      0.6             
##   4          0.4  0.50       0.95       1.000      0.6             
##   4          0.4  0.50       0.95       1.000      0.6             
##   4          0.4  0.50       0.95       1.000      0.8             
##   4          0.4  0.50       0.95       1.000      0.8             
##   4          0.4  0.50       0.95       1.000      0.8             
##   4          0.4  0.50       0.95       1.000      0.8             
##   4          0.4  0.50       0.95       1.000      0.8             
##   5          0.3  0.01       0.05       0.500      0.6             
##   5          0.3  0.01       0.05       0.500      0.6             
##   5          0.3  0.01       0.05       0.500      0.6             
##   5          0.3  0.01       0.05       0.500      0.6             
##   5          0.3  0.01       0.05       0.500      0.6             
##   5          0.3  0.01       0.05       0.500      0.8             
##   5          0.3  0.01       0.05       0.500      0.8             
##   5          0.3  0.01       0.05       0.500      0.8             
##   5          0.3  0.01       0.05       0.500      0.8             
##   5          0.3  0.01       0.05       0.500      0.8             
##   5          0.3  0.01       0.05       0.625      0.6             
##   5          0.3  0.01       0.05       0.625      0.6             
##   5          0.3  0.01       0.05       0.625      0.6             
##   5          0.3  0.01       0.05       0.625      0.6             
##   5          0.3  0.01       0.05       0.625      0.6             
##   5          0.3  0.01       0.05       0.625      0.8             
##   5          0.3  0.01       0.05       0.625      0.8             
##   5          0.3  0.01       0.05       0.625      0.8             
##   5          0.3  0.01       0.05       0.625      0.8             
##   5          0.3  0.01       0.05       0.625      0.8             
##   5          0.3  0.01       0.05       0.750      0.6             
##   5          0.3  0.01       0.05       0.750      0.6             
##   5          0.3  0.01       0.05       0.750      0.6             
##   5          0.3  0.01       0.05       0.750      0.6             
##   5          0.3  0.01       0.05       0.750      0.6             
##   5          0.3  0.01       0.05       0.750      0.8             
##   5          0.3  0.01       0.05       0.750      0.8             
##   5          0.3  0.01       0.05       0.750      0.8             
##   5          0.3  0.01       0.05       0.750      0.8             
##   5          0.3  0.01       0.05       0.750      0.8             
##   5          0.3  0.01       0.05       0.875      0.6             
##   5          0.3  0.01       0.05       0.875      0.6             
##   5          0.3  0.01       0.05       0.875      0.6             
##   5          0.3  0.01       0.05       0.875      0.6             
##   5          0.3  0.01       0.05       0.875      0.6             
##   5          0.3  0.01       0.05       0.875      0.8             
##   5          0.3  0.01       0.05       0.875      0.8             
##   5          0.3  0.01       0.05       0.875      0.8             
##   5          0.3  0.01       0.05       0.875      0.8             
##   5          0.3  0.01       0.05       0.875      0.8             
##   5          0.3  0.01       0.05       1.000      0.6             
##   5          0.3  0.01       0.05       1.000      0.6             
##   5          0.3  0.01       0.05       1.000      0.6             
##   5          0.3  0.01       0.05       1.000      0.6             
##   5          0.3  0.01       0.05       1.000      0.6             
##   5          0.3  0.01       0.05       1.000      0.8             
##   5          0.3  0.01       0.05       1.000      0.8             
##   5          0.3  0.01       0.05       1.000      0.8             
##   5          0.3  0.01       0.05       1.000      0.8             
##   5          0.3  0.01       0.05       1.000      0.8             
##   5          0.3  0.01       0.95       0.500      0.6             
##   5          0.3  0.01       0.95       0.500      0.6             
##   5          0.3  0.01       0.95       0.500      0.6             
##   5          0.3  0.01       0.95       0.500      0.6             
##   5          0.3  0.01       0.95       0.500      0.6             
##   5          0.3  0.01       0.95       0.500      0.8             
##   5          0.3  0.01       0.95       0.500      0.8             
##   5          0.3  0.01       0.95       0.500      0.8             
##   5          0.3  0.01       0.95       0.500      0.8             
##   5          0.3  0.01       0.95       0.500      0.8             
##   5          0.3  0.01       0.95       0.625      0.6             
##   5          0.3  0.01       0.95       0.625      0.6             
##   5          0.3  0.01       0.95       0.625      0.6             
##   5          0.3  0.01       0.95       0.625      0.6             
##   5          0.3  0.01       0.95       0.625      0.6             
##   5          0.3  0.01       0.95       0.625      0.8             
##   5          0.3  0.01       0.95       0.625      0.8             
##   5          0.3  0.01       0.95       0.625      0.8             
##   5          0.3  0.01       0.95       0.625      0.8             
##   5          0.3  0.01       0.95       0.625      0.8             
##   5          0.3  0.01       0.95       0.750      0.6             
##   5          0.3  0.01       0.95       0.750      0.6             
##   5          0.3  0.01       0.95       0.750      0.6             
##   5          0.3  0.01       0.95       0.750      0.6             
##   5          0.3  0.01       0.95       0.750      0.6             
##   5          0.3  0.01       0.95       0.750      0.8             
##   5          0.3  0.01       0.95       0.750      0.8             
##   5          0.3  0.01       0.95       0.750      0.8             
##   5          0.3  0.01       0.95       0.750      0.8             
##   5          0.3  0.01       0.95       0.750      0.8             
##   5          0.3  0.01       0.95       0.875      0.6             
##   5          0.3  0.01       0.95       0.875      0.6             
##   5          0.3  0.01       0.95       0.875      0.6             
##   5          0.3  0.01       0.95       0.875      0.6             
##   5          0.3  0.01       0.95       0.875      0.6             
##   5          0.3  0.01       0.95       0.875      0.8             
##   5          0.3  0.01       0.95       0.875      0.8             
##   5          0.3  0.01       0.95       0.875      0.8             
##   5          0.3  0.01       0.95       0.875      0.8             
##   5          0.3  0.01       0.95       0.875      0.8             
##   5          0.3  0.01       0.95       1.000      0.6             
##   5          0.3  0.01       0.95       1.000      0.6             
##   5          0.3  0.01       0.95       1.000      0.6             
##   5          0.3  0.01       0.95       1.000      0.6             
##   5          0.3  0.01       0.95       1.000      0.6             
##   5          0.3  0.01       0.95       1.000      0.8             
##   5          0.3  0.01       0.95       1.000      0.8             
##   5          0.3  0.01       0.95       1.000      0.8             
##   5          0.3  0.01       0.95       1.000      0.8             
##   5          0.3  0.01       0.95       1.000      0.8             
##   5          0.3  0.50       0.05       0.500      0.6             
##   5          0.3  0.50       0.05       0.500      0.6             
##   5          0.3  0.50       0.05       0.500      0.6             
##   5          0.3  0.50       0.05       0.500      0.6             
##   5          0.3  0.50       0.05       0.500      0.6             
##   5          0.3  0.50       0.05       0.500      0.8             
##   5          0.3  0.50       0.05       0.500      0.8             
##   5          0.3  0.50       0.05       0.500      0.8             
##   5          0.3  0.50       0.05       0.500      0.8             
##   5          0.3  0.50       0.05       0.500      0.8             
##   5          0.3  0.50       0.05       0.625      0.6             
##   5          0.3  0.50       0.05       0.625      0.6             
##   5          0.3  0.50       0.05       0.625      0.6             
##   5          0.3  0.50       0.05       0.625      0.6             
##   5          0.3  0.50       0.05       0.625      0.6             
##   5          0.3  0.50       0.05       0.625      0.8             
##   5          0.3  0.50       0.05       0.625      0.8             
##   5          0.3  0.50       0.05       0.625      0.8             
##   5          0.3  0.50       0.05       0.625      0.8             
##   5          0.3  0.50       0.05       0.625      0.8             
##   5          0.3  0.50       0.05       0.750      0.6             
##   5          0.3  0.50       0.05       0.750      0.6             
##   5          0.3  0.50       0.05       0.750      0.6             
##   5          0.3  0.50       0.05       0.750      0.6             
##   5          0.3  0.50       0.05       0.750      0.6             
##   5          0.3  0.50       0.05       0.750      0.8             
##   5          0.3  0.50       0.05       0.750      0.8             
##   5          0.3  0.50       0.05       0.750      0.8             
##   5          0.3  0.50       0.05       0.750      0.8             
##   5          0.3  0.50       0.05       0.750      0.8             
##   5          0.3  0.50       0.05       0.875      0.6             
##   5          0.3  0.50       0.05       0.875      0.6             
##   5          0.3  0.50       0.05       0.875      0.6             
##   5          0.3  0.50       0.05       0.875      0.6             
##   5          0.3  0.50       0.05       0.875      0.6             
##   5          0.3  0.50       0.05       0.875      0.8             
##   5          0.3  0.50       0.05       0.875      0.8             
##   5          0.3  0.50       0.05       0.875      0.8             
##   5          0.3  0.50       0.05       0.875      0.8             
##   5          0.3  0.50       0.05       0.875      0.8             
##   5          0.3  0.50       0.05       1.000      0.6             
##   5          0.3  0.50       0.05       1.000      0.6             
##   5          0.3  0.50       0.05       1.000      0.6             
##   5          0.3  0.50       0.05       1.000      0.6             
##   5          0.3  0.50       0.05       1.000      0.6             
##   5          0.3  0.50       0.05       1.000      0.8             
##   5          0.3  0.50       0.05       1.000      0.8             
##   5          0.3  0.50       0.05       1.000      0.8             
##   5          0.3  0.50       0.05       1.000      0.8             
##   5          0.3  0.50       0.05       1.000      0.8             
##   5          0.3  0.50       0.95       0.500      0.6             
##   5          0.3  0.50       0.95       0.500      0.6             
##   5          0.3  0.50       0.95       0.500      0.6             
##   5          0.3  0.50       0.95       0.500      0.6             
##   5          0.3  0.50       0.95       0.500      0.6             
##   5          0.3  0.50       0.95       0.500      0.8             
##   5          0.3  0.50       0.95       0.500      0.8             
##   5          0.3  0.50       0.95       0.500      0.8             
##   5          0.3  0.50       0.95       0.500      0.8             
##   5          0.3  0.50       0.95       0.500      0.8             
##   5          0.3  0.50       0.95       0.625      0.6             
##   5          0.3  0.50       0.95       0.625      0.6             
##   5          0.3  0.50       0.95       0.625      0.6             
##   5          0.3  0.50       0.95       0.625      0.6             
##   5          0.3  0.50       0.95       0.625      0.6             
##   5          0.3  0.50       0.95       0.625      0.8             
##   5          0.3  0.50       0.95       0.625      0.8             
##   5          0.3  0.50       0.95       0.625      0.8             
##   5          0.3  0.50       0.95       0.625      0.8             
##   5          0.3  0.50       0.95       0.625      0.8             
##   5          0.3  0.50       0.95       0.750      0.6             
##   5          0.3  0.50       0.95       0.750      0.6             
##   5          0.3  0.50       0.95       0.750      0.6             
##   5          0.3  0.50       0.95       0.750      0.6             
##   5          0.3  0.50       0.95       0.750      0.6             
##   5          0.3  0.50       0.95       0.750      0.8             
##   5          0.3  0.50       0.95       0.750      0.8             
##   5          0.3  0.50       0.95       0.750      0.8             
##   5          0.3  0.50       0.95       0.750      0.8             
##   5          0.3  0.50       0.95       0.750      0.8             
##   5          0.3  0.50       0.95       0.875      0.6             
##   5          0.3  0.50       0.95       0.875      0.6             
##   5          0.3  0.50       0.95       0.875      0.6             
##   5          0.3  0.50       0.95       0.875      0.6             
##   5          0.3  0.50       0.95       0.875      0.6             
##   5          0.3  0.50       0.95       0.875      0.8             
##   5          0.3  0.50       0.95       0.875      0.8             
##   5          0.3  0.50       0.95       0.875      0.8             
##   5          0.3  0.50       0.95       0.875      0.8             
##   5          0.3  0.50       0.95       0.875      0.8             
##   5          0.3  0.50       0.95       1.000      0.6             
##   5          0.3  0.50       0.95       1.000      0.6             
##   5          0.3  0.50       0.95       1.000      0.6             
##   5          0.3  0.50       0.95       1.000      0.6             
##   5          0.3  0.50       0.95       1.000      0.6             
##   5          0.3  0.50       0.95       1.000      0.8             
##   5          0.3  0.50       0.95       1.000      0.8             
##   5          0.3  0.50       0.95       1.000      0.8             
##   5          0.3  0.50       0.95       1.000      0.8             
##   5          0.3  0.50       0.95       1.000      0.8             
##   5          0.4  0.01       0.05       0.500      0.6             
##   5          0.4  0.01       0.05       0.500      0.6             
##   5          0.4  0.01       0.05       0.500      0.6             
##   5          0.4  0.01       0.05       0.500      0.6             
##   5          0.4  0.01       0.05       0.500      0.6             
##   5          0.4  0.01       0.05       0.500      0.8             
##   5          0.4  0.01       0.05       0.500      0.8             
##   5          0.4  0.01       0.05       0.500      0.8             
##   5          0.4  0.01       0.05       0.500      0.8             
##   5          0.4  0.01       0.05       0.500      0.8             
##   5          0.4  0.01       0.05       0.625      0.6             
##   5          0.4  0.01       0.05       0.625      0.6             
##   5          0.4  0.01       0.05       0.625      0.6             
##   5          0.4  0.01       0.05       0.625      0.6             
##   5          0.4  0.01       0.05       0.625      0.6             
##   5          0.4  0.01       0.05       0.625      0.8             
##   5          0.4  0.01       0.05       0.625      0.8             
##   5          0.4  0.01       0.05       0.625      0.8             
##   5          0.4  0.01       0.05       0.625      0.8             
##   5          0.4  0.01       0.05       0.625      0.8             
##   5          0.4  0.01       0.05       0.750      0.6             
##   5          0.4  0.01       0.05       0.750      0.6             
##   5          0.4  0.01       0.05       0.750      0.6             
##   5          0.4  0.01       0.05       0.750      0.6             
##   5          0.4  0.01       0.05       0.750      0.6             
##   5          0.4  0.01       0.05       0.750      0.8             
##   5          0.4  0.01       0.05       0.750      0.8             
##   5          0.4  0.01       0.05       0.750      0.8             
##   5          0.4  0.01       0.05       0.750      0.8             
##   5          0.4  0.01       0.05       0.750      0.8             
##   5          0.4  0.01       0.05       0.875      0.6             
##   5          0.4  0.01       0.05       0.875      0.6             
##   5          0.4  0.01       0.05       0.875      0.6             
##   5          0.4  0.01       0.05       0.875      0.6             
##   5          0.4  0.01       0.05       0.875      0.6             
##   5          0.4  0.01       0.05       0.875      0.8             
##   5          0.4  0.01       0.05       0.875      0.8             
##   5          0.4  0.01       0.05       0.875      0.8             
##   5          0.4  0.01       0.05       0.875      0.8             
##   5          0.4  0.01       0.05       0.875      0.8             
##   5          0.4  0.01       0.05       1.000      0.6             
##   5          0.4  0.01       0.05       1.000      0.6             
##   5          0.4  0.01       0.05       1.000      0.6             
##   5          0.4  0.01       0.05       1.000      0.6             
##   5          0.4  0.01       0.05       1.000      0.6             
##   5          0.4  0.01       0.05       1.000      0.8             
##   5          0.4  0.01       0.05       1.000      0.8             
##   5          0.4  0.01       0.05       1.000      0.8             
##   5          0.4  0.01       0.05       1.000      0.8             
##   5          0.4  0.01       0.05       1.000      0.8             
##   5          0.4  0.01       0.95       0.500      0.6             
##   5          0.4  0.01       0.95       0.500      0.6             
##   5          0.4  0.01       0.95       0.500      0.6             
##   5          0.4  0.01       0.95       0.500      0.6             
##   5          0.4  0.01       0.95       0.500      0.6             
##   5          0.4  0.01       0.95       0.500      0.8             
##   5          0.4  0.01       0.95       0.500      0.8             
##   5          0.4  0.01       0.95       0.500      0.8             
##   5          0.4  0.01       0.95       0.500      0.8             
##   5          0.4  0.01       0.95       0.500      0.8             
##   5          0.4  0.01       0.95       0.625      0.6             
##   5          0.4  0.01       0.95       0.625      0.6             
##   5          0.4  0.01       0.95       0.625      0.6             
##   5          0.4  0.01       0.95       0.625      0.6             
##   5          0.4  0.01       0.95       0.625      0.6             
##   5          0.4  0.01       0.95       0.625      0.8             
##   5          0.4  0.01       0.95       0.625      0.8             
##   5          0.4  0.01       0.95       0.625      0.8             
##   5          0.4  0.01       0.95       0.625      0.8             
##   5          0.4  0.01       0.95       0.625      0.8             
##   5          0.4  0.01       0.95       0.750      0.6             
##   5          0.4  0.01       0.95       0.750      0.6             
##   5          0.4  0.01       0.95       0.750      0.6             
##   5          0.4  0.01       0.95       0.750      0.6             
##   5          0.4  0.01       0.95       0.750      0.6             
##   5          0.4  0.01       0.95       0.750      0.8             
##   5          0.4  0.01       0.95       0.750      0.8             
##   5          0.4  0.01       0.95       0.750      0.8             
##   5          0.4  0.01       0.95       0.750      0.8             
##   5          0.4  0.01       0.95       0.750      0.8             
##   5          0.4  0.01       0.95       0.875      0.6             
##   5          0.4  0.01       0.95       0.875      0.6             
##   5          0.4  0.01       0.95       0.875      0.6             
##   5          0.4  0.01       0.95       0.875      0.6             
##   5          0.4  0.01       0.95       0.875      0.6             
##   5          0.4  0.01       0.95       0.875      0.8             
##   5          0.4  0.01       0.95       0.875      0.8             
##   5          0.4  0.01       0.95       0.875      0.8             
##   5          0.4  0.01       0.95       0.875      0.8             
##   5          0.4  0.01       0.95       0.875      0.8             
##   5          0.4  0.01       0.95       1.000      0.6             
##   5          0.4  0.01       0.95       1.000      0.6             
##   5          0.4  0.01       0.95       1.000      0.6             
##   5          0.4  0.01       0.95       1.000      0.6             
##   5          0.4  0.01       0.95       1.000      0.6             
##   5          0.4  0.01       0.95       1.000      0.8             
##   5          0.4  0.01       0.95       1.000      0.8             
##   5          0.4  0.01       0.95       1.000      0.8             
##   5          0.4  0.01       0.95       1.000      0.8             
##   5          0.4  0.01       0.95       1.000      0.8             
##   5          0.4  0.50       0.05       0.500      0.6             
##   5          0.4  0.50       0.05       0.500      0.6             
##   5          0.4  0.50       0.05       0.500      0.6             
##   5          0.4  0.50       0.05       0.500      0.6             
##   5          0.4  0.50       0.05       0.500      0.6             
##   5          0.4  0.50       0.05       0.500      0.8             
##   5          0.4  0.50       0.05       0.500      0.8             
##   5          0.4  0.50       0.05       0.500      0.8             
##   5          0.4  0.50       0.05       0.500      0.8             
##   5          0.4  0.50       0.05       0.500      0.8             
##   5          0.4  0.50       0.05       0.625      0.6             
##   5          0.4  0.50       0.05       0.625      0.6             
##   5          0.4  0.50       0.05       0.625      0.6             
##   5          0.4  0.50       0.05       0.625      0.6             
##   5          0.4  0.50       0.05       0.625      0.6             
##   5          0.4  0.50       0.05       0.625      0.8             
##   5          0.4  0.50       0.05       0.625      0.8             
##   5          0.4  0.50       0.05       0.625      0.8             
##   5          0.4  0.50       0.05       0.625      0.8             
##   5          0.4  0.50       0.05       0.625      0.8             
##   5          0.4  0.50       0.05       0.750      0.6             
##   5          0.4  0.50       0.05       0.750      0.6             
##   5          0.4  0.50       0.05       0.750      0.6             
##   5          0.4  0.50       0.05       0.750      0.6             
##   5          0.4  0.50       0.05       0.750      0.6             
##   5          0.4  0.50       0.05       0.750      0.8             
##   5          0.4  0.50       0.05       0.750      0.8             
##   5          0.4  0.50       0.05       0.750      0.8             
##   5          0.4  0.50       0.05       0.750      0.8             
##   5          0.4  0.50       0.05       0.750      0.8             
##   5          0.4  0.50       0.05       0.875      0.6             
##   5          0.4  0.50       0.05       0.875      0.6             
##   5          0.4  0.50       0.05       0.875      0.6             
##   5          0.4  0.50       0.05       0.875      0.6             
##   5          0.4  0.50       0.05       0.875      0.6             
##   5          0.4  0.50       0.05       0.875      0.8             
##   5          0.4  0.50       0.05       0.875      0.8             
##   5          0.4  0.50       0.05       0.875      0.8             
##   5          0.4  0.50       0.05       0.875      0.8             
##   5          0.4  0.50       0.05       0.875      0.8             
##   5          0.4  0.50       0.05       1.000      0.6             
##   5          0.4  0.50       0.05       1.000      0.6             
##   5          0.4  0.50       0.05       1.000      0.6             
##   5          0.4  0.50       0.05       1.000      0.6             
##   5          0.4  0.50       0.05       1.000      0.6             
##   5          0.4  0.50       0.05       1.000      0.8             
##   5          0.4  0.50       0.05       1.000      0.8             
##   5          0.4  0.50       0.05       1.000      0.8             
##   5          0.4  0.50       0.05       1.000      0.8             
##   5          0.4  0.50       0.05       1.000      0.8             
##   5          0.4  0.50       0.95       0.500      0.6             
##   5          0.4  0.50       0.95       0.500      0.6             
##   5          0.4  0.50       0.95       0.500      0.6             
##   5          0.4  0.50       0.95       0.500      0.6             
##   5          0.4  0.50       0.95       0.500      0.6             
##   5          0.4  0.50       0.95       0.500      0.8             
##   5          0.4  0.50       0.95       0.500      0.8             
##   5          0.4  0.50       0.95       0.500      0.8             
##   5          0.4  0.50       0.95       0.500      0.8             
##   5          0.4  0.50       0.95       0.500      0.8             
##   5          0.4  0.50       0.95       0.625      0.6             
##   5          0.4  0.50       0.95       0.625      0.6             
##   5          0.4  0.50       0.95       0.625      0.6             
##   5          0.4  0.50       0.95       0.625      0.6             
##   5          0.4  0.50       0.95       0.625      0.6             
##   5          0.4  0.50       0.95       0.625      0.8             
##   5          0.4  0.50       0.95       0.625      0.8             
##   5          0.4  0.50       0.95       0.625      0.8             
##   5          0.4  0.50       0.95       0.625      0.8             
##   5          0.4  0.50       0.95       0.625      0.8             
##   5          0.4  0.50       0.95       0.750      0.6             
##   5          0.4  0.50       0.95       0.750      0.6             
##   5          0.4  0.50       0.95       0.750      0.6             
##   5          0.4  0.50       0.95       0.750      0.6             
##   5          0.4  0.50       0.95       0.750      0.6             
##   5          0.4  0.50       0.95       0.750      0.8             
##   5          0.4  0.50       0.95       0.750      0.8             
##   5          0.4  0.50       0.95       0.750      0.8             
##   5          0.4  0.50       0.95       0.750      0.8             
##   5          0.4  0.50       0.95       0.750      0.8             
##   5          0.4  0.50       0.95       0.875      0.6             
##   5          0.4  0.50       0.95       0.875      0.6             
##   5          0.4  0.50       0.95       0.875      0.6             
##   5          0.4  0.50       0.95       0.875      0.6             
##   5          0.4  0.50       0.95       0.875      0.6             
##   5          0.4  0.50       0.95       0.875      0.8             
##   5          0.4  0.50       0.95       0.875      0.8             
##   5          0.4  0.50       0.95       0.875      0.8             
##   5          0.4  0.50       0.95       0.875      0.8             
##   5          0.4  0.50       0.95       0.875      0.8             
##   5          0.4  0.50       0.95       1.000      0.6             
##   5          0.4  0.50       0.95       1.000      0.6             
##   5          0.4  0.50       0.95       1.000      0.6             
##   5          0.4  0.50       0.95       1.000      0.6             
##   5          0.4  0.50       0.95       1.000      0.6             
##   5          0.4  0.50       0.95       1.000      0.8             
##   5          0.4  0.50       0.95       1.000      0.8             
##   5          0.4  0.50       0.95       1.000      0.8             
##   5          0.4  0.50       0.95       1.000      0.8             
##   5          0.4  0.50       0.95       1.000      0.8             
##   nrounds  ROC        Sens       Spec     
##    50      0.9022676  0.8623443  0.7753053
##   100      0.9005646  0.8680769  0.7604251
##   150      0.8966960  0.8623077  0.7602895
##   200      0.8997248  0.8604212  0.7692899
##   250      0.9010432  0.8699634  0.7663501
##    50      0.9041983  0.8700183  0.7602895
##   100      0.9023155  0.8680403  0.7872004
##   150      0.9015020  0.8603846  0.7871551
##   200      0.8990032  0.8584982  0.7782451
##   250      0.9012306  0.8661722  0.7782451
##    50      0.9052504  0.8661355  0.7843510
##   100      0.9023994  0.8680586  0.7843510
##   150      0.9024170  0.8699634  0.7663953
##   200      0.9007762  0.8737729  0.7723654
##   250      0.9032855  0.8641941  0.7843057
##    50      0.9048888  0.8680586  0.7931705
##   100      0.9027491  0.8680952  0.7692447
##   150      0.9010945  0.8680586  0.7722750
##   200      0.8999018  0.8699817  0.7752601
##   250      0.8993197  0.8661722  0.7603347
##    50      0.9078411  0.8738462  0.7782451
##   100      0.9066537  0.8776374  0.7812754
##   150      0.9021321  0.8699451  0.7842605
##   200      0.9024339  0.8661355  0.7753053
##   250      0.9020776  0.8680769  0.7663501
##    50      0.9068755  0.8738828  0.7783356
##   100      0.9032355  0.8814835  0.7663048
##   150      0.9018840  0.8718498  0.7692899
##   200      0.9030443  0.8757143  0.7603347
##   250      0.9021518  0.8642308  0.7693351
##    50      0.9070927  0.8814835  0.7722298
##   100      0.9065635  0.8795604  0.7692447
##   150      0.9058188  0.8833516  0.7693351
##   200      0.9043542  0.8852564  0.7633198
##   250      0.9046956  0.8738095  0.7543645
##    50      0.9098692  0.8757143  0.7843510
##   100      0.9073198  0.8757143  0.7783808
##   150      0.9063468  0.8757143  0.7693804
##   200      0.9036276  0.8757143  0.7723202
##   250      0.9039602  0.8757143  0.7693351
##    50      0.9087301  0.8795238  0.7843510
##   100      0.9073448  0.8833333  0.7783356
##   150      0.9068763  0.8795238  0.7753957
##   200      0.9066650  0.8795238  0.7782904
##   250      0.9053662  0.8795238  0.7663501
##    50      0.9085491  0.8776190  0.7872908
##   100      0.9089542  0.8852381  0.7723202
##   150      0.9079738  0.8891026  0.7753053
##   200      0.9069267  0.8814469  0.7663501
##   250      0.9067969  0.8814469  0.7693351
##    50      0.9054168  0.8680037  0.7932157
##   100      0.9038869  0.8680586  0.7902307
##   150      0.9008164  0.8604212  0.7782904
##   200      0.8993926  0.8661538  0.7692899
##   250      0.8955649  0.8604212  0.7633650
##    50      0.9063073  0.8718498  0.7752601
##   100      0.8994780  0.8584799  0.7633650
##   150      0.8979538  0.8623443  0.7693351
##   200      0.8974015  0.8547070  0.7752601
##   250      0.8982230  0.8566117  0.7753053
##    50      0.9033659  0.8718681  0.7513342
##   100      0.9013492  0.8718498  0.7632745
##   150      0.9024644  0.8661172  0.7632745
##   200      0.8986170  0.8642308  0.7603347
##   250      0.8967286  0.8546703  0.7753053
##    50      0.9058008  0.8738278  0.7872456
##   100      0.9041101  0.8719048  0.7782451
##   150      0.9019721  0.8661722  0.7663048
##   200      0.8985708  0.8661905  0.7692899
##   250      0.8968676  0.8565934  0.7513342
##    50      0.9048621  0.8833883  0.7842605
##   100      0.9039819  0.8775824  0.7542741
##   150      0.9019719  0.8700000  0.7663048
##   200      0.9007339  0.8719048  0.7573496
##   250      0.8997800  0.8681136  0.7543645
##    50      0.9084151  0.8852381  0.7842605
##   100      0.9033719  0.8757143  0.7692447
##   150      0.9000253  0.8795604  0.7573496
##   200      0.9004665  0.8680952  0.7692899
##   250      0.8983765  0.8757692  0.7543645
##    50      0.9065543  0.8700000  0.7872004
##   100      0.9039118  0.8756960  0.7663048
##   150      0.9038778  0.8757143  0.7723202
##   200      0.9017226  0.8699817  0.7603347
##   250      0.9001209  0.8623260  0.7663048
##    50      0.9088488  0.8852564  0.7781999
##   100      0.9054435  0.8795238  0.7692899
##   150      0.9034113  0.8738095  0.7693351
##   200      0.9025696  0.8718681  0.7573948
##   250      0.9000941  0.8642308  0.7543645
##    50      0.9080730  0.8776374  0.7901854
##   100      0.9078667  0.8795421  0.7753053
##   150      0.9057658  0.8795238  0.7693351
##   200      0.9037351  0.8757326  0.7573948
##   250      0.9016852  0.8757326  0.7543645
##    50      0.9093954  0.8852564  0.7872908
##   100      0.9083317  0.8814469  0.7812754
##   150      0.9062356  0.8795238  0.7693351
##   200      0.9042338  0.8795421  0.7573496
##   250      0.9024334  0.8776374  0.7543645
##    50      0.8879504  0.8527289  0.7542741
##   100      0.8942538  0.8566117  0.7632293
##   150      0.8983109  0.8680220  0.7512890
##   200      0.9017720  0.8718132  0.7632293
##   250      0.9015823  0.8737912  0.7722750
##    50      0.8907219  0.8585531  0.7483492
##   100      0.8913431  0.8508425  0.7513342
##   150      0.8942319  0.8546703  0.7543645
##   200      0.8962255  0.8566300  0.7603347
##   250      0.8977244  0.8547253  0.7722298
##    50      0.8905757  0.8546703  0.7632745
##   100      0.8955690  0.8623260  0.7543645
##   150      0.8986385  0.8699451  0.7513795
##   200      0.9010710  0.8738095  0.7662144
##   250      0.9040072  0.8795421  0.7872456
##    50      0.8902237  0.8604212  0.7393487
##   100      0.8937125  0.8546886  0.7573044
##   150      0.8964202  0.8642308  0.7603347
##   200      0.8977319  0.8565934  0.7752601
##   250      0.8983456  0.8642308  0.7633198
##    50      0.8885477  0.8718681  0.7512438
##   100      0.8947193  0.8642125  0.7601990
##   150      0.9018620  0.8719048  0.7661692
##   200      0.9034513  0.8681136  0.7632293
##   250      0.9062509  0.8719048  0.7781999
##    50      0.8901906  0.8681136  0.7453641
##   100      0.8976159  0.8566667  0.7513342
##   150      0.8983248  0.8604579  0.7602895
##   200      0.9001597  0.8604579  0.7662596
##   250      0.9041905  0.8680952  0.7601990
##    50      0.8850880  0.8604579  0.7483492
##   100      0.8961961  0.8585348  0.7483492
##   150      0.8987060  0.8546886  0.7722298
##   200      0.8979397  0.8661538  0.7513342
##   250      0.9059467  0.8661538  0.7692899
##    50      0.8923440  0.8566117  0.7543193
##   100      0.8978202  0.8566117  0.7543193
##   150      0.8990410  0.8546886  0.7602895
##   200      0.9004537  0.8546886  0.7632745
##   250      0.9007437  0.8546337  0.7603347
##    50      0.8899870  0.8584982  0.7453189
##   100      0.8995396  0.8547436  0.7602895
##   150      0.9003307  0.8489560  0.7543193
##   200      0.9033594  0.8661905  0.7781999
##   250      0.9046985  0.8642857  0.7811850
##    50      0.8930593  0.8508974  0.7602895
##   100      0.8928750  0.8585165  0.7572592
##   150      0.8972564  0.8585165  0.7602895
##   200      0.9007453  0.8585165  0.7602895
##   250      0.9020615  0.8547070  0.7662596
##    50      0.9053313  0.8680769  0.7692447
##   100      0.9039519  0.8719048  0.7842153
##   150      0.9008117  0.8661905  0.7722750
##   200      0.8996893  0.8680769  0.7663048
##   250      0.8967822  0.8623260  0.7602895
##    50      0.9057881  0.8681136  0.7781999
##   100      0.9037329  0.8680586  0.7841248
##   150      0.8998823  0.8584615  0.7782904
##   200      0.8979340  0.8565934  0.7662596
##   250      0.8978426  0.8566300  0.7843057
##    50      0.9048513  0.8604212  0.7781999
##   100      0.9035530  0.8738095  0.7752148
##   150      0.9026441  0.8642857  0.7573044
##   200      0.8983414  0.8719048  0.7603347
##   250      0.9002137  0.8604396  0.7633198
##    50      0.9051540  0.8737912  0.7753957
##   100      0.9033610  0.8661722  0.7784261
##   150      0.9000343  0.8661905  0.7723654
##   200      0.8982681  0.8604579  0.7663048
##   250      0.8985869  0.8546703  0.7603347
##    50      0.9065177  0.8738278  0.7842605
##   100      0.9047790  0.8700000  0.7782904
##   150      0.9025776  0.8718498  0.7663048
##   200      0.9007881  0.8604212  0.7633198
##   250      0.9000698  0.8643223  0.7573496
##    50      0.9066271  0.8795604  0.7812754
##   100      0.9031075  0.8661538  0.7693351
##   150      0.9016151  0.8604029  0.7812302
##   200      0.8987956  0.8604396  0.7663048
##   250      0.8991241  0.8546703  0.7543193
##    50      0.9083097  0.8681136  0.7812302
##   100      0.9050127  0.8814469  0.7753053
##   150      0.9042135  0.8661538  0.7633198
##   200      0.9017229  0.8642491  0.7543645
##   250      0.9006857  0.8623443  0.7543645
##    50      0.9084298  0.8852930  0.7901854
##   100      0.9039157  0.8852564  0.7633198
##   150      0.9038962  0.8756960  0.7692899
##   200      0.9016164  0.8699634  0.7573496
##   250      0.8997535  0.8699817  0.7573496
##    50      0.9098845  0.8852930  0.7842153
##   100      0.9089133  0.8833700  0.7693351
##   150      0.9069257  0.8776374  0.7633650
##   200      0.9045070  0.8738278  0.7663501
##   250      0.9029447  0.8795604  0.7603347
##    50      0.9089806  0.8814103  0.7902759
##   100      0.9080955  0.8833516  0.7843057
##   150      0.9063624  0.8795238  0.7693351
##   200      0.9042191  0.8814469  0.7663501
##   250      0.9030430  0.8795421  0.7513795
##    50      0.9010686  0.8776557  0.7603347
##   100      0.8983736  0.8643040  0.7663048
##   150      0.9003956  0.8738095  0.7663048
##   200      0.9007426  0.8719048  0.7873360
##   250      0.8990577  0.8604396  0.7722750
##    50      0.9042606  0.8660989  0.7902759
##   100      0.9054047  0.8565568  0.7842605
##   150      0.9029739  0.8661722  0.7663048
##   200      0.9005089  0.8718498  0.7692899
##   250      0.8999050  0.8623077  0.7663048
##    50      0.9032973  0.8699634  0.7782904
##   100      0.9011054  0.8737912  0.7634102
##   150      0.9016595  0.8718864  0.7813207
##   200      0.9021820  0.8603846  0.7753053
##   250      0.9031113  0.8699817  0.7633198
##    50      0.9034396  0.8737729  0.7842605
##   100      0.9018871  0.8661722  0.7781999
##   150      0.8998271  0.8585348  0.7781999
##   200      0.9007546  0.8623443  0.7752148
##   250      0.9018390  0.8737912  0.7722750
##    50      0.9053361  0.8794872  0.7722750
##   100      0.9025271  0.8775641  0.7692899
##   150      0.8997762  0.8718498  0.7692899
##   200      0.8982032  0.8603846  0.7692899
##   250      0.9006025  0.8642308  0.7752601
##    50      0.9022052  0.8661538  0.7783356
##   100      0.9040286  0.8680586  0.7692899
##   150      0.9015592  0.8699634  0.7543645
##   200      0.9027290  0.8680952  0.7603347
##   250      0.9001754  0.8604029  0.7633198
##    50      0.9052421  0.8871795  0.7692899
##   100      0.9061441  0.8872161  0.7603799
##   150      0.9045213  0.8814469  0.7663048
##   200      0.9034776  0.8757509  0.7753053
##   250      0.9031956  0.8738095  0.7723202
##    50      0.9065999  0.8737546  0.7872456
##   100      0.9047499  0.8737363  0.7902307
##   150      0.9020541  0.8718681  0.7782904
##   200      0.9006113  0.8680403  0.7722750
##   250      0.9015136  0.8718864  0.7692899
##    50      0.9091564  0.8814469  0.7902759
##   100      0.9090086  0.8756777  0.7991859
##   150      0.9070532  0.8776190  0.7842605
##   200      0.9053203  0.8795238  0.7663501
##   250      0.9051349  0.8814469  0.7693351
##    50      0.9084964  0.8776007  0.7872908
##   100      0.9089261  0.8814469  0.7812754
##   150      0.9081562  0.8833333  0.7753053
##   200      0.9055797  0.8814286  0.7723202
##   250      0.9050593  0.8814469  0.7693351
##    50      0.9020361  0.8680769  0.7782451
##   100      0.8976646  0.8680220  0.7692899
##   150      0.8963780  0.8604212  0.7455450
##   200      0.8996597  0.8623260  0.7663501
##   250      0.8983261  0.8661355  0.7513342
##    50      0.9040714  0.8680769  0.7841701
##   100      0.9016495  0.8757326  0.7752601
##   150      0.8984407  0.8565568  0.7692447
##   200      0.8958574  0.8604029  0.7632745
##   250      0.8965393  0.8584982  0.7691995
##    50      0.9007628  0.8680586  0.7692447
##   100      0.8986793  0.8622711  0.7633198
##   150      0.8972550  0.8622711  0.7663048
##   200      0.8948672  0.8584982  0.7633198
##   250      0.8932691  0.8470330  0.7483492
##    50      0.9034036  0.8661538  0.7782904
##   100      0.8992968  0.8585165  0.7603347
##   150      0.8964062  0.8508974  0.7663048
##   200      0.8946353  0.8528388  0.7752601
##   250      0.8948680  0.8528022  0.7602895
##    50      0.9029285  0.8642674  0.7781999
##   100      0.9032366  0.8661722  0.7633650
##   150      0.9009903  0.8680952  0.7603799
##   200      0.8989271  0.8584982  0.7603347
##   250      0.8949377  0.8565934  0.7573044
##    50      0.9044684  0.8719231  0.7752601
##   100      0.9009212  0.8661722  0.7513795
##   150      0.8983076  0.8584615  0.7663501
##   200      0.8960173  0.8642308  0.7573496
##   250      0.8940870  0.8661905  0.7453641
##    50      0.9076558  0.8853114  0.7782451
##   100      0.9017858  0.8700000  0.7513795
##   150      0.8998788  0.8642125  0.7663048
##   200      0.8970054  0.8623443  0.7603347
##   250      0.8966085  0.8642308  0.7573496
##    50      0.9047604  0.8852564  0.7752148
##   100      0.9044659  0.8814286  0.7633198
##   150      0.9012340  0.8718864  0.7722750
##   200      0.8987540  0.8680586  0.7752601
##   250      0.8963874  0.8642125  0.7633198
##    50      0.9082818  0.8852747  0.7872456
##   100      0.9061535  0.8795238  0.7723202
##   150      0.9040242  0.8776374  0.7543645
##   200      0.9024282  0.8757143  0.7483944
##   250      0.9012711  0.8719048  0.7573496
##    50      0.9083539  0.8852747  0.7811850
##   100      0.9068210  0.8814469  0.7812754
##   150      0.9041919  0.8814469  0.7603799
##   200      0.9025561  0.8795421  0.7483944
##   250      0.9014427  0.8738095  0.7543645
##    50      0.8912763  0.8604212  0.7422886
##   100      0.8965421  0.8603846  0.7452736
##   150      0.9002968  0.8623260  0.7514247
##   200      0.8996676  0.8623810  0.7543645
##   250      0.9004867  0.8681319  0.7513795
##    50      0.8922793  0.8527656  0.7632745
##   100      0.8973533  0.8527473  0.7602442
##   150      0.9005156  0.8642308  0.7542741
##   200      0.9022925  0.8642491  0.7721845
##   250      0.9011011  0.8642125  0.7753053
##    50      0.8869523  0.8546886  0.7662596
##   100      0.8980648  0.8604945  0.7633650
##   150      0.9024075  0.8642674  0.7781999
##   200      0.9028713  0.8680769  0.7871551
##   250      0.9036017  0.8623443  0.7841701
##    50      0.8875819  0.8450733  0.7752148
##   100      0.8942195  0.8469963  0.7632745
##   150      0.8969938  0.8488828  0.7783356
##   200      0.9007576  0.8470696  0.7753505
##   250      0.9031619  0.8661355  0.7782451
##    50      0.8904642  0.8565568  0.7571687
##   100      0.8949366  0.8623443  0.7572139
##   150      0.8982968  0.8661538  0.7542289
##   200      0.8986697  0.8623443  0.7662596
##   250      0.9038191  0.8718864  0.7662596
##    50      0.8939029  0.8546886  0.7632745
##   100      0.8983416  0.8470513  0.7752148
##   150      0.9035202  0.8565751  0.7632745
##   200      0.9063372  0.8680403  0.7781095
##   250      0.9040589  0.8622894  0.7872004
##    50      0.8909871  0.8546886  0.7542741
##   100      0.9008819  0.8604396  0.7453641
##   150      0.9004125  0.8604029  0.7512438
##   200      0.9046567  0.8680403  0.7662596
##   250      0.9067170  0.8699634  0.7573044
##    50      0.8921164  0.8604212  0.7453189
##   100      0.8893067  0.8508608  0.7602895
##   150      0.8983298  0.8565385  0.7452736
##   200      0.9019512  0.8623077  0.7512438
##   250      0.9051631  0.8699634  0.7512438
##    50      0.8928775  0.8604212  0.7512438
##   100      0.8939421  0.8623260  0.7422886
##   150      0.8995515  0.8661355  0.7422886
##   200      0.9029082  0.8642491  0.7542289
##   250      0.9017424  0.8623810  0.7542289
##    50      0.8952134  0.8508974  0.7543193
##   100      0.8990305  0.8470513  0.7543193
##   150      0.9017287  0.8584982  0.7512890
##   200      0.9039039  0.8603846  0.7513342
##   250      0.9059321  0.8642308  0.7602895
##    50      0.9025658  0.8680037  0.7603347
##   100      0.9002367  0.8718864  0.7691995
##   150      0.8926962  0.8508059  0.7811850
##   200      0.8889385  0.8508974  0.7602442
##   250      0.8931577  0.8489744  0.7752148
##    50      0.9071037  0.8776557  0.7813207
##   100      0.9005123  0.8641758  0.7632745
##   150      0.8975269  0.8508608  0.7602895
##   200      0.8971918  0.8547070  0.7424242
##   250      0.8920236  0.8527656  0.7693351
##    50      0.9063702  0.8852747  0.7632293
##   100      0.9025287  0.8719231  0.7633650
##   150      0.8994624  0.8661722  0.7603347
##   200      0.9001853  0.8681136  0.7603347
##   250      0.8984118  0.8642491  0.7573496
##    50      0.9026840  0.8699817  0.7723654
##   100      0.9011493  0.8718864  0.7692899
##   150      0.8998512  0.8757143  0.7573044
##   200      0.8945072  0.8527473  0.7722750
##   250      0.8955089  0.8604212  0.7693351
##    50      0.9076372  0.8737912  0.7961104
##   100      0.9035794  0.8718681  0.7782904
##   150      0.9006147  0.8700000  0.7753053
##   200      0.8980620  0.8680769  0.7633198
##   250      0.8966717  0.8680769  0.7843057
##    50      0.9050664  0.8776557  0.7811850
##   100      0.9028321  0.8699817  0.7782904
##   150      0.8992577  0.8661722  0.7573496
##   200      0.8996474  0.8603663  0.7722750
##   250      0.8996301  0.8661722  0.7692447
##    50      0.9075162  0.8852564  0.7633198
##   100      0.9045496  0.8718864  0.7692899
##   150      0.9026312  0.8699817  0.7603347
##   200      0.9002211  0.8584982  0.7543193
##   250      0.8981094  0.8584799  0.7573496
##    50      0.9080130  0.8833516  0.7603799
##   100      0.9030983  0.8699817  0.7723202
##   150      0.9012063  0.8700000  0.7573496
##   200      0.8982501  0.8604212  0.7543645
##   250      0.8965661  0.8623260  0.7663048
##    50      0.9081150  0.8833700  0.7962460
##   100      0.9059549  0.8795055  0.7782904
##   150      0.9039903  0.8795421  0.7722750
##   200      0.9022148  0.8680769  0.7722750
##   250      0.9010296  0.8680769  0.7513795
##    50      0.9090857  0.8871795  0.7872004
##   100      0.9065775  0.8852564  0.7753053
##   150      0.9042735  0.8795421  0.7663501
##   200      0.9021286  0.8795421  0.7573496
##   250      0.9010002  0.8738095  0.7483944
##    50      0.8996523  0.8566300  0.7631841
##   100      0.9010853  0.8624359  0.7752601
##   150      0.8962712  0.8642125  0.7722298
##   200      0.8950299  0.8623443  0.7723202
##   250      0.8935103  0.8546886  0.7781999
##    50      0.9001969  0.8642857  0.7693351
##   100      0.8973503  0.8604212  0.7693804
##   150      0.8924551  0.8584799  0.7512890
##   200      0.8885554  0.8584799  0.7633198
##   250      0.8914155  0.8527656  0.7751696
##    50      0.8985851  0.8565934  0.7543193
##   100      0.8951723  0.8584982  0.7601990
##   150      0.8920640  0.8584982  0.7602442
##   200      0.8904996  0.8565934  0.7752148
##   250      0.8890228  0.8585165  0.7661692
##    50      0.8960850  0.8450733  0.7513342
##   100      0.8924389  0.8508242  0.7723202
##   150      0.8904439  0.8565568  0.7693804
##   200      0.8898548  0.8565568  0.7722298
##   250      0.8881334  0.8546154  0.7662144
##    50      0.9027050  0.8622894  0.7812302
##   100      0.8954513  0.8565568  0.7632745
##   150      0.8939122  0.8527289  0.7724107
##   200      0.8932279  0.8584799  0.7662596
##   250      0.8914750  0.8584615  0.7603347
##    50      0.9046807  0.8680952  0.7572592
##   100      0.9005279  0.8642674  0.7721845
##   150      0.8965284  0.8566117  0.7601990
##   200      0.8909262  0.8546520  0.7661239
##   250      0.8908060  0.8584799  0.7631841
##    50      0.9032686  0.8585165  0.7812302
##   100      0.8981250  0.8489194  0.7871551
##   150      0.8965853  0.8508608  0.7782451
##   200      0.8944058  0.8566117  0.7691542
##   250      0.8928263  0.8527473  0.7691542
##    50      0.9035565  0.8642308  0.7722298
##   100      0.8971731  0.8603663  0.7662596
##   150      0.8951893  0.8565385  0.7574401
##   200      0.8926010  0.8508608  0.7693351
##   250      0.8913755  0.8622894  0.7602442
##    50      0.9011534  0.8604579  0.7633198
##   100      0.8966576  0.8547253  0.7633650
##   150      0.8943969  0.8546703  0.7543645
##   200      0.8921734  0.8508608  0.7512438
##   250      0.8888073  0.8470147  0.7483039
##    50      0.9053781  0.8756960  0.7842153
##   100      0.9008878  0.8622894  0.7662596
##   150      0.8957956  0.8603846  0.7662596
##   200      0.8928457  0.8565568  0.7632293
##   250      0.8923464  0.8546703  0.7632745
##    50      0.9020322  0.8680403  0.7482135
##   100      0.8927013  0.8680586  0.7422433
##   150      0.8892981  0.8603846  0.7422886
##   200      0.8852182  0.8527839  0.7661692
##   250      0.8784423  0.8527473  0.7332429
##    50      0.8991020  0.8700000  0.7753505
##   100      0.8955951  0.8527106  0.7662596
##   150      0.8845969  0.8488645  0.7602442
##   200      0.8816468  0.8489377  0.7332881
##   250      0.8779028  0.8489194  0.7393035
##    50      0.8985352  0.8642308  0.7603347
##   100      0.8932766  0.8565934  0.7633650
##   150      0.8895575  0.8565751  0.7601538
##   200      0.8857798  0.8585348  0.7722750
##   250      0.8834784  0.8527473  0.7752601
##    50      0.9035270  0.8719048  0.7812754
##   100      0.8970561  0.8565934  0.7961556
##   150      0.8923977  0.8604029  0.7692447
##   200      0.8870459  0.8508059  0.7753505
##   250      0.8845430  0.8604396  0.7691995
##    50      0.9015228  0.8661722  0.7663048
##   100      0.8920295  0.8546886  0.7662144
##   150      0.8877767  0.8489377  0.7782451
##   200      0.8838582  0.8489377  0.7632293
##   250      0.8826473  0.8546520  0.7602442
##    50      0.8982302  0.8604396  0.7662596
##   100      0.8905759  0.8565934  0.7722750
##   150      0.8880344  0.8546337  0.7634555
##   200      0.8797759  0.8469963  0.7544098
##   250      0.8799788  0.8469597  0.7723202
##    50      0.9016387  0.8623626  0.7633198
##   100      0.8969768  0.8680220  0.7602895
##   150      0.8919042  0.8584615  0.7631389
##   200      0.8869075  0.8623077  0.7722750
##   250      0.8830613  0.8527473  0.7723202
##    50      0.9008609  0.8718864  0.7603347
##   100      0.8921477  0.8547070  0.7661692
##   150      0.8902467  0.8565568  0.7541836
##   200      0.8870292  0.8507875  0.7691542
##   250      0.8837628  0.8507875  0.7662144
##    50      0.9022080  0.8680952  0.7812302
##   100      0.8965354  0.8585531  0.7573496
##   150      0.8900197  0.8527656  0.7512890
##   200      0.8858470  0.8451099  0.7572592
##   250      0.8827235  0.8412821  0.7572139
##    50      0.9048067  0.8719048  0.7812754
##   100      0.8991053  0.8661722  0.7573044
##   150      0.8936166  0.8661355  0.7543193
##   200      0.8896667  0.8546337  0.7513342
##   250      0.8884508  0.8469963  0.7512890
##    50      0.9009942  0.8738278  0.7600633
##   100      0.9058072  0.8814652  0.7603799
##   150      0.9049592  0.8795604  0.7633198
##   200      0.9038808  0.8738278  0.7663048
##   250      0.9053169  0.8757143  0.7663501
##    50      0.9011966  0.8776374  0.7691995
##   100      0.9037573  0.8738462  0.7722298
##   150      0.9049324  0.8719048  0.7872004
##   200      0.9045263  0.8738095  0.7901854
##   250      0.9032117  0.8738095  0.7901854
##    50      0.9022607  0.8776190  0.7333333
##   100      0.9066515  0.8833700  0.7483039
##   150      0.9047431  0.8815201  0.7602442
##   200      0.9058454  0.8814835  0.7663048
##   250      0.9067864  0.8795788  0.7722298
##    50      0.9026588  0.8546886  0.7871099
##   100      0.9024755  0.8642308  0.7841701
##   150      0.9031764  0.8699634  0.7782904
##   200      0.9048949  0.8814652  0.7692899
##   250      0.9057026  0.8757326  0.7812302
##    50      0.8983991  0.8890842  0.7333786
##   100      0.9010027  0.8833883  0.7573044
##   150      0.9010767  0.8680952  0.7752148
##   200      0.9029305  0.8700000  0.7722298
##   250      0.9043636  0.8623810  0.7692447
##    50      0.9040393  0.8642857  0.7663048
##   100      0.9078095  0.8795604  0.7841701
##   150      0.9069061  0.8776190  0.7871551
##   200      0.9069596  0.8776007  0.7781547
##   250      0.9065437  0.8756410  0.7781999
##    50      0.9059985  0.8756960  0.7632293
##   100      0.9041884  0.8814835  0.7572592
##   150      0.9060650  0.8661355  0.7750791
##   200      0.9064908  0.8738095  0.7781095
##   250      0.9054331  0.8833883  0.7810945
##    50      0.9035145  0.8547436  0.7812302
##   100      0.9040186  0.8584799  0.7930801
##   150      0.9020966  0.8700183  0.7781999
##   200      0.9048260  0.8680952  0.7811850
##   250      0.9042521  0.8718864  0.7811850
##    50      0.8986996  0.8814652  0.7273632
##   100      0.9064294  0.8738278  0.7691995
##   150      0.9077320  0.8700000  0.7781547
##   200      0.9083372  0.8719048  0.7781999
##   250      0.9079190  0.8699634  0.7752148
##    50      0.9076847  0.8547070  0.7931705
##   100      0.9063275  0.8585897  0.7931705
##   150      0.9061952  0.8700000  0.7842153
##   200      0.9065482  0.8795421  0.7842153
##   250      0.9073973  0.8776557  0.7781999
##    50      0.9030097  0.8700000  0.7513795
##   100      0.8971860  0.8622894  0.7721845
##   150      0.8926586  0.8585165  0.7572592
##   200      0.8877514  0.8489011  0.7662144
##   250      0.8871529  0.8450916  0.7692899
##    50      0.9032824  0.8738278  0.7662144
##   100      0.8896950  0.8469780  0.7542289
##   150      0.8875065  0.8508242  0.7392583
##   200      0.8836898  0.8489377  0.7481682
##   250      0.8785969  0.8451099  0.7572139
##    50      0.9037358  0.8680769  0.7752148
##   100      0.8981060  0.8623443  0.7662596
##   150      0.8907622  0.8585531  0.7631841
##   200      0.8861673  0.8451282  0.7752601
##   250      0.8850198  0.8546886  0.7661692
##    50      0.9035952  0.8681136  0.7752601
##   100      0.8934247  0.8623260  0.7543645
##   150      0.8862634  0.8527106  0.7513342
##   200      0.8810515  0.8412637  0.7573948
##   250      0.8793130  0.8565751  0.7604251
##    50      0.9007926  0.8642491  0.7752601
##   100      0.8969704  0.8527839  0.7602442
##   150      0.8885894  0.8584615  0.7692899
##   200      0.8866311  0.8508425  0.7632745
##   250      0.8807332  0.8526923  0.7632745
##    50      0.9070847  0.8680769  0.7902307
##   100      0.8969295  0.8527289  0.7843057
##   150      0.8934638  0.8470147  0.7752601
##   200      0.8875646  0.8547070  0.7602442
##   250      0.8861075  0.8565751  0.7573496
##    50      0.9029131  0.8699817  0.7781999
##   100      0.8955220  0.8622711  0.7722298
##   150      0.8934289  0.8565751  0.7782904
##   200      0.8892017  0.8604029  0.7603347
##   250      0.8873061  0.8642125  0.7722750
##    50      0.9015310  0.8622894  0.7662144
##   100      0.8945263  0.8642308  0.7662596
##   150      0.8887995  0.8489011  0.7812302
##   200      0.8849294  0.8527473  0.7541836
##   250      0.8817175  0.8622894  0.7601990
##    50      0.9011464  0.8546886  0.7752601
##   100      0.8981553  0.8585165  0.7692899
##   150      0.8923908  0.8527289  0.7542741
##   200      0.8887276  0.8431685  0.7542741
##   250      0.8864583  0.8393407  0.7572139
##    50      0.9039217  0.8718864  0.7782451
##   100      0.8966711  0.8623443  0.7602895
##   150      0.8910055  0.8508059  0.7513342
##   200      0.8875998  0.8527106  0.7483039
##   250      0.8845248  0.8488828  0.7542289
##    50      0.8987723  0.8565751  0.7722750
##   100      0.8947292  0.8604212  0.7662144
##   150      0.8875730  0.8546886  0.7453641
##   200      0.8907365  0.8547436  0.7543193
##   250      0.8879146  0.8661355  0.7483039
##    50      0.8954191  0.8623626  0.7692899
##   100      0.8847690  0.8604396  0.7722298
##   150      0.8853020  0.8508242  0.7722750
##   200      0.8814946  0.8527656  0.7542289
##   250      0.8784898  0.8451099  0.7572592
##    50      0.9001250  0.8603297  0.7483039
##   100      0.8902727  0.8565751  0.7363636
##   150      0.8886088  0.8680037  0.7483039
##   200      0.8877478  0.8660989  0.7602442
##   250      0.8837225  0.8412454  0.7632293
##    50      0.8956801  0.8584982  0.7663048
##   100      0.8921371  0.8508059  0.7783356
##   150      0.8908350  0.8622894  0.7722750
##   200      0.8861551  0.8603846  0.7632293
##   250      0.8879956  0.8604029  0.7753505
##    50      0.8998085  0.8604396  0.7723202
##   100      0.8933796  0.8432784  0.7663048
##   150      0.8927378  0.8469963  0.7782451
##   200      0.8925973  0.8622894  0.7812302
##   250      0.8875859  0.8546703  0.7751696
##    50      0.9030733  0.8565751  0.8081411
##   100      0.8924247  0.8489377  0.7752148
##   150      0.8904497  0.8469780  0.7511986
##   200      0.8899488  0.8546337  0.7631841
##   250      0.8872759  0.8450733  0.7601538
##    50      0.8994844  0.8585714  0.7602442
##   100      0.8954504  0.8547070  0.7512890
##   150      0.8928139  0.8585165  0.7692899
##   200      0.8901413  0.8451465  0.7782451
##   250      0.8891110  0.8547070  0.7752148
##    50      0.9037491  0.8623810  0.7963365
##   100      0.8941735  0.8508425  0.7902307
##   150      0.8937563  0.8604029  0.7782904
##   200      0.8911112  0.8603846  0.7902759
##   250      0.8891834  0.8584799  0.7783356
##    50      0.8970032  0.8680769  0.7484848
##   100      0.8919703  0.8565934  0.7544098
##   150      0.8894024  0.8488828  0.7393487
##   200      0.8882589  0.8565385  0.7632745
##   250      0.8878253  0.8546337  0.7601990
##    50      0.8993907  0.8661355  0.7543645
##   100      0.8956058  0.8565568  0.7692899
##   150      0.8917271  0.8546520  0.7692447
##   200      0.8899483  0.8489011  0.7572592
##   250      0.8892347  0.8450733  0.7632293
##    50      0.9012311  0.8719231  0.7631841
##   100      0.8957128  0.8624176  0.7721393
##   150      0.8854754  0.8566300  0.7692899
##   200      0.8857922  0.8623260  0.7661692
##   250      0.8754879  0.8508791  0.7573044
##    50      0.8891436  0.8546703  0.7454093
##   100      0.8823714  0.8527289  0.7572592
##   150      0.8807710  0.8565385  0.7632293
##   200      0.8793074  0.8546886  0.7511986
##   250      0.8788026  0.8546337  0.7422433
##    50      0.8976688  0.8662088  0.7693351
##   100      0.8935291  0.8624176  0.7722750
##   150      0.8874823  0.8585531  0.7632293
##   200      0.8866949  0.8546703  0.7661692
##   250      0.8791487  0.8546520  0.7511986
##    50      0.8977067  0.8622894  0.7752148
##   100      0.8876899  0.8565568  0.7482587
##   150      0.8825931  0.8431136  0.7633198
##   200      0.8795617  0.8412637  0.7542741
##   250      0.8778153  0.8393956  0.7453189
##    50      0.9001361  0.8585165  0.7602895
##   100      0.8926184  0.8623077  0.7692447
##   150      0.8847519  0.8508425  0.7692447
##   200      0.8798155  0.8604029  0.7453189
##   250      0.8775972  0.8584799  0.7513795
##    50      0.8994560  0.8718498  0.7663048
##   100      0.8911481  0.8661722  0.7692899
##   150      0.8845845  0.8699634  0.7572592
##   200      0.8839895  0.8584615  0.7631841
##   250      0.8777563  0.8527656  0.7572139
##    50      0.8983123  0.8622894  0.7632745
##   100      0.8895428  0.8546886  0.7691995
##   150      0.8875118  0.8508608  0.7813207
##   200      0.8836481  0.8508791  0.7723654
##   250      0.8814924  0.8508425  0.7663048
##    50      0.8980753  0.8642308  0.7572592
##   100      0.8901145  0.8546703  0.7542289
##   150      0.8841774  0.8699817  0.7512438
##   200      0.8799413  0.8546520  0.7542741
##   250      0.8756733  0.8604029  0.7572592
##    50      0.9011454  0.8584799  0.7752601
##   100      0.8932129  0.8412454  0.7753053
##   150      0.8876969  0.8374176  0.7512438
##   200      0.8848637  0.8431502  0.7542289
##   250      0.8812595  0.8374176  0.7512438
##    50      0.9013477  0.8661172  0.7723202
##   100      0.8921936  0.8527839  0.7512890
##   150      0.8888899  0.8489194  0.7512890
##   200      0.8848338  0.8489194  0.7482587
##   250      0.8802561  0.8450916  0.7512438
##    50      0.9016274  0.8852747  0.7363184
##   100      0.9036703  0.8871429  0.7634102
##   150      0.9046586  0.8814652  0.7603347
##   200      0.9019597  0.8737546  0.7843057
##   250      0.9034095  0.8756777  0.7663953
##    50      0.9038896  0.8604396  0.7871551
##   100      0.9002104  0.8757326  0.7782451
##   150      0.9014874  0.8719048  0.7752601
##   200      0.8990855  0.8719231  0.7781999
##   250      0.9007381  0.8756960  0.7692447
##    50      0.8981202  0.8814103  0.7573044
##   100      0.9010429  0.8757326  0.7513795
##   150      0.9020122  0.8756960  0.7423338
##   200      0.9001581  0.8719231  0.7573044
##   250      0.9015759  0.8662454  0.7633650
##    50      0.9019524  0.8661538  0.7602442
##   100      0.9026889  0.8699084  0.7811850
##   150      0.9024015  0.8813370  0.7722298
##   200      0.9036910  0.8852381  0.7722298
##   250      0.9034620  0.8757143  0.7662596
##    50      0.9065613  0.8776374  0.7752148
##   100      0.9042385  0.8700000  0.7931253
##   150      0.9057812  0.8700366  0.7932157
##   200      0.9045264  0.8699451  0.7842153
##   250      0.9031298  0.8699267  0.7632293
##    50      0.9019811  0.8623260  0.7872456
##   100      0.9058235  0.8661722  0.7812302
##   150      0.9067543  0.8737912  0.7752601
##   200      0.9078134  0.8738095  0.7782904
##   250      0.9068956  0.8700000  0.7872456
##    50      0.9052593  0.8852381  0.7483039
##   100      0.9041528  0.8757326  0.7602442
##   150      0.9043131  0.8700000  0.7692447
##   200      0.9043977  0.8604396  0.7722298
##   250      0.9046922  0.8681319  0.7722298
##    50      0.9076331  0.8680769  0.7841701
##   100      0.9057736  0.8737912  0.7902307
##   150      0.9060457  0.8776374  0.7782451
##   200      0.9066803  0.8757143  0.7872004
##   250      0.9064750  0.8814469  0.7723202
##    50      0.9008101  0.8719414  0.7363184
##   100      0.9058576  0.8834249  0.7542741
##   150      0.9094714  0.8814652  0.7752148
##   200      0.9078385  0.8795421  0.7752601
##   250      0.9067102  0.8757143  0.7842153
##    50      0.9052444  0.8662271  0.7751696
##   100      0.9067612  0.8757143  0.7722750
##   150      0.9070021  0.8757143  0.7811850
##   200      0.9070889  0.8852747  0.7783356
##   250      0.9067735  0.8814835  0.7783808
##    50      0.9039815  0.8565385  0.7691542
##   100      0.8913395  0.8527473  0.7632745
##   150      0.8873544  0.8450733  0.7632745
##   200      0.8879844  0.8604029  0.7423338
##   250      0.8832386  0.8565385  0.7303483
##    50      0.8932172  0.8623443  0.7602442
##   100      0.8845888  0.8527656  0.7603347
##   150      0.8780528  0.8489377  0.7722750
##   200      0.8790390  0.8336630  0.7693351
##   250      0.8694526  0.8355495  0.7573496
##    50      0.8974845  0.8528022  0.7842605
##   100      0.8917888  0.8470147  0.7573044
##   150      0.8826997  0.8469963  0.7662144
##   200      0.8777017  0.8469780  0.7424242
##   250      0.8781822  0.8489377  0.7692447
##    50      0.8929350  0.8622711  0.7724107
##   100      0.8786087  0.8469963  0.7663048
##   150      0.8762758  0.8527289  0.7513795
##   200      0.8710725  0.8526923  0.7424242
##   250      0.8724859  0.8470147  0.7453641
##    50      0.8981101  0.8546886  0.7753053
##   100      0.8935861  0.8432234  0.7781999
##   150      0.8860451  0.8336081  0.7782451
##   200      0.8841966  0.8432051  0.7781547
##   250      0.8807164  0.8489011  0.7512438
##    50      0.9010507  0.8623443  0.7751244
##   100      0.8921987  0.8603846  0.7601538
##   150      0.8856579  0.8565934  0.7511986
##   200      0.8831130  0.8661538  0.7392130
##   250      0.8801557  0.8604029  0.7451832
##    50      0.9025911  0.8623077  0.7842605
##   100      0.8913135  0.8489560  0.7842153
##   150      0.8873488  0.8527289  0.7663501
##   200      0.8825922  0.8508242  0.7543645
##   250      0.8813028  0.8470147  0.7663048
##    50      0.8994301  0.8661355  0.7720941
##   100      0.8892917  0.8565751  0.7631389
##   150      0.8841694  0.8584799  0.7631841
##   200      0.8820053  0.8584799  0.7691995
##   250      0.8766149  0.8469963  0.7633198
##    50      0.8976497  0.8680586  0.7781999
##   100      0.8928143  0.8603480  0.7632293
##   150      0.8887382  0.8584799  0.7512438
##   200      0.8850743  0.8584982  0.7542289
##   250      0.8832767  0.8565934  0.7482587
##    50      0.9017022  0.8623077  0.7841701
##   100      0.8927448  0.8604212  0.7542289
##   150      0.8897813  0.8546703  0.7601990
##   200      0.8858438  0.8489377  0.7511533
##   250      0.8836891  0.8470147  0.7511986
##    50      0.8951064  0.8527656  0.7782904
##   100      0.8885361  0.8393956  0.7931705
##   150      0.8871490  0.8584615  0.7602895
##   200      0.8789801  0.8642125  0.7603799
##   250      0.8792568  0.8603846  0.7573948
##    50      0.8912889  0.8450916  0.7782451
##   100      0.8862182  0.8565201  0.7632293
##   150      0.8842854  0.8526923  0.7663048
##   200      0.8835099  0.8584432  0.7692447
##   250      0.8821631  0.8603663  0.7691995
##    50      0.8933790  0.8585165  0.7933062
##   100      0.8855968  0.8547253  0.7453189
##   150      0.8877231  0.8412821  0.7753053
##   200      0.8830139  0.8489377  0.7603347
##   250      0.8796349  0.8565934  0.7692899
##    50      0.8916226  0.8489560  0.7602442
##   100      0.8785866  0.8413187  0.7601538
##   150      0.8760319  0.8393590  0.7722750
##   200      0.8753720  0.8527106  0.7572592
##   250      0.8768319  0.8527473  0.7453641
##    50      0.8945898  0.8642491  0.7812302
##   100      0.8884387  0.8604212  0.7841701
##   150      0.8841504  0.8508425  0.7842605
##   200      0.8845497  0.8508059  0.7782451
##   250      0.8825976  0.8527106  0.7752601
##    50      0.8943278  0.8584799  0.7661692
##   100      0.8866563  0.8546703  0.7512438
##   150      0.8833146  0.8450733  0.7632745
##   200      0.8812530  0.8489011  0.7543193
##   250      0.8817983  0.8546337  0.7602895
##    50      0.8977597  0.8527839  0.7722750
##   100      0.8928935  0.8584249  0.7782451
##   150      0.8901484  0.8545971  0.7782904
##   200      0.8864524  0.8584066  0.7812754
##   250      0.8845046  0.8527106  0.7812754
##    50      0.8952368  0.8642308  0.7693804
##   100      0.8888513  0.8527289  0.7513342
##   150      0.8861552  0.8546703  0.7572592
##   200      0.8845189  0.8546337  0.7602442
##   250      0.8834301  0.8527473  0.7632745
##    50      0.8963655  0.8604212  0.7452736
##   100      0.8905856  0.8622711  0.7393487
##   150      0.8882560  0.8584432  0.7542741
##   200      0.8841910  0.8526923  0.7542741
##   250      0.8813249  0.8488462  0.7512438
##    50      0.8957051  0.8699817  0.7602895
##   100      0.8887429  0.8584615  0.7572592
##   150      0.8851786  0.8546337  0.7542741
##   200      0.8834418  0.8527106  0.7572592
##   250      0.8811000  0.8508059  0.7482587
##    50      0.8923999  0.8566117  0.7572592
##   100      0.8846507  0.8642491  0.7363184
##   150      0.8782088  0.8527473  0.7482587
##   200      0.8727905  0.8470513  0.7452736
##   250      0.8755993  0.8565751  0.7483944
##    50      0.8914390  0.8700000  0.7602442
##   100      0.8809877  0.8565934  0.7601990
##   150      0.8714182  0.8469780  0.7722750
##   200      0.8728648  0.8412821  0.7752601
##   250      0.8726736  0.8546886  0.7693351
##    50      0.8922463  0.8508425  0.7811850
##   100      0.8808406  0.8546337  0.7631841
##   150      0.8777764  0.8431136  0.7452284
##   200      0.8754632  0.8469780  0.7632293
##   250      0.8709370  0.8412454  0.7602895
##    50      0.8961866  0.8527656  0.7632293
##   100      0.8850736  0.8527473  0.7692447
##   150      0.8815276  0.8584249  0.7783356
##   200      0.8770541  0.8527473  0.7633650
##   250      0.8759557  0.8527473  0.7603799
##    50      0.8984948  0.8470513  0.7601538
##   100      0.8929711  0.8527473  0.7752148
##   150      0.8853408  0.8508425  0.7631389
##   200      0.8800651  0.8546703  0.7692447
##   250      0.8793314  0.8546703  0.7633198
##    50      0.8963168  0.8603846  0.7752601
##   100      0.8852772  0.8546337  0.7753053
##   150      0.8802687  0.8508059  0.7572592
##   200      0.8766413  0.8431868  0.7543193
##   250      0.8755225  0.8451465  0.7483492
##    50      0.8946247  0.8546337  0.7692899
##   100      0.8859513  0.8585531  0.7752601
##   150      0.8788196  0.8489194  0.7722750
##   200      0.8761971  0.8470147  0.7633198
##   250      0.8738559  0.8431502  0.7573496
##    50      0.8922631  0.8489011  0.7692447
##   100      0.8873546  0.8508242  0.7691542
##   150      0.8806679  0.8527473  0.7631389
##   200      0.8788328  0.8470330  0.7662596
##   250      0.8757568  0.8489194  0.7752148
##    50      0.8963413  0.8642308  0.7752148
##   100      0.8871961  0.8546520  0.7601990
##   150      0.8823717  0.8527473  0.7392583
##   200      0.8766180  0.8431502  0.7512438
##   250      0.8736270  0.8431502  0.7453189
##    50      0.8958121  0.8603846  0.7572592
##   100      0.8889433  0.8527106  0.7542289
##   150      0.8829527  0.8469963  0.7452284
##   200      0.8793505  0.8546337  0.7543193
##   250      0.8777454  0.8507692  0.7573044
##    50      0.9014029  0.8719048  0.7393487
##   100      0.9057907  0.8661905  0.7662596
##   150      0.9067420  0.8776374  0.7633198
##   200      0.9063387  0.8681319  0.7632745
##   250      0.9056374  0.8700183  0.7782904
##    50      0.9043467  0.8757326  0.7602895
##   100      0.9057327  0.8756960  0.7723202
##   150      0.9057941  0.8699267  0.7842153
##   200      0.9057562  0.8737912  0.7722298
##   250      0.9040369  0.8623626  0.7872004
##    50      0.9020455  0.8834066  0.7481682
##   100      0.9064803  0.8814469  0.7661692
##   150      0.9079998  0.8833700  0.7752148
##   200      0.9047554  0.8737912  0.7781999
##   250      0.9042908  0.8680769  0.7692447
##    50      0.9063203  0.8833516  0.7872456
##   100      0.9105354  0.8680952  0.7962913
##   150      0.9055989  0.8681136  0.7812302
##   200      0.9068125  0.8680952  0.7812302
##   250      0.9044994  0.8719231  0.7782451
##    50      0.9028033  0.8814469  0.7483944
##   100      0.9046564  0.8776190  0.7514247
##   150      0.9064157  0.8719048  0.7693351
##   200      0.9055778  0.8757326  0.7722750
##   250      0.9028380  0.8604029  0.7663048
##    50      0.9049296  0.8871978  0.7753053
##   100      0.9060946  0.8757326  0.7752148
##   150      0.9054661  0.8738095  0.7812302
##   200      0.9037400  0.8718864  0.7782451
##   250      0.9020370  0.8737729  0.7781999
##    50      0.9046361  0.8738095  0.7483944
##   100      0.9055536  0.8757143  0.7513342
##   150      0.9062790  0.8738278  0.7663501
##   200      0.9052312  0.8738095  0.7663953
##   250      0.9025589  0.8719231  0.7692899
##    50      0.9019149  0.8814652  0.7663048
##   100      0.9033784  0.8776374  0.7722750
##   150      0.9042343  0.8776923  0.7723654
##   200      0.9051507  0.8738462  0.7722750
##   250      0.9048360  0.8757509  0.7723202
##    50      0.8987154  0.8776740  0.7393035
##   100      0.9051770  0.8776740  0.7812754
##   150      0.9061157  0.8757692  0.7753505
##   200      0.9048055  0.8738645  0.7813207
##   250      0.9051275  0.8680769  0.7902759
##    50      0.9037164  0.8834066  0.7782904
##   100      0.9035712  0.8795604  0.7932610
##   150      0.9036987  0.8757326  0.7873360
##   200      0.9042342  0.8757509  0.7843057
##   250      0.9023537  0.8719231  0.7872456
##    50      0.8886373  0.8527289  0.7512438
##   100      0.8843333  0.8489011  0.7511986
##   150      0.8788514  0.8393407  0.7753053
##   200      0.8726672  0.8393590  0.7662596
##   250      0.8688701  0.8278755  0.7513342
##    50      0.8912983  0.8585165  0.7662596
##   100      0.8770703  0.8508608  0.7633650
##   150      0.8763964  0.8546703  0.7543193
##   200      0.8719815  0.8527656  0.7663048
##   250      0.8733837  0.8412637  0.7483492
##    50      0.8970443  0.8413187  0.7662144
##   100      0.8856779  0.8623260  0.7632745
##   150      0.8811856  0.8546703  0.7482135
##   200      0.8800375  0.8451099  0.7542741
##   250      0.8751373  0.8374542  0.7572592
##    50      0.8866683  0.8508425  0.7632745
##   100      0.8793307  0.8565751  0.7572592
##   150      0.8772693  0.8508425  0.7572592
##   200      0.8729576  0.8412821  0.7573496
##   250      0.8674468  0.8469963  0.7453189
##    50      0.8957153  0.8642125  0.7632293
##   100      0.8870295  0.8565751  0.7632293
##   150      0.8799249  0.8527473  0.7634102
##   200      0.8769179  0.8546703  0.7633650
##   250      0.8753701  0.8412637  0.7543193
##    50      0.8939400  0.8680403  0.7454093
##   100      0.8855220  0.8489194  0.7752148
##   150      0.8802581  0.8527106  0.7692899
##   200      0.8721584  0.8411905  0.7662596
##   250      0.8698814  0.8431136  0.7454093
##    50      0.8956893  0.8641941  0.7423338
##   100      0.8880378  0.8527473  0.7573044
##   150      0.8850304  0.8489194  0.7602895
##   200      0.8809376  0.8412637  0.7632745
##   250      0.8754761  0.8336081  0.7663048
##    50      0.8949885  0.8584982  0.7513342
##   100      0.8865440  0.8565751  0.7512890
##   150      0.8809755  0.8527656  0.7482135
##   200      0.8767875  0.8527289  0.7513342
##   250      0.8755378  0.8431868  0.7453189
##    50      0.8970250  0.8642125  0.7603799
##   100      0.8897231  0.8623077  0.7542289
##   150      0.8848989  0.8526923  0.7542741
##   200      0.8817817  0.8527289  0.7632745
##   250      0.8770224  0.8431685  0.7632293
##    50      0.8952683  0.8699634  0.7632745
##   100      0.8868673  0.8584615  0.7542741
##   150      0.8823517  0.8642125  0.7483039
##   200      0.8794621  0.8469780  0.7513342
##   250      0.8773153  0.8450733  0.7543193
##    50      0.8900919  0.8604396  0.7811850
##   100      0.8812344  0.8489560  0.7542289
##   150      0.8808785  0.8489194  0.7752601
##   200      0.8742125  0.8354579  0.7722298
##   250      0.8734197  0.8393223  0.7781547
##    50      0.8784033  0.8393407  0.7481230
##   100      0.8765038  0.8374359  0.7512438
##   150      0.8705244  0.8412271  0.7513342
##   200      0.8746766  0.8527839  0.7513342
##   250      0.8741763  0.8565751  0.7423790
##    50      0.8887991  0.8603480  0.7332881
##   100      0.8772524  0.8565201  0.7334690
##   150      0.8799630  0.8641941  0.7454093
##   200      0.8805642  0.8527473  0.7544098
##   250      0.8787634  0.8547070  0.7573948
##    50      0.8913117  0.8585165  0.7663048
##   100      0.8815842  0.8546703  0.7602442
##   150      0.8805052  0.8489194  0.7542289
##   200      0.8762391  0.8451099  0.7721845
##   250      0.8763450  0.8489194  0.7542741
##    50      0.8863470  0.8584249  0.7423790
##   100      0.8814835  0.8585165  0.7453189
##   150      0.8805925  0.8565568  0.7543193
##   200      0.8772595  0.8566300  0.7572592
##   250      0.8769479  0.8470696  0.7632293
##    50      0.8897641  0.8489744  0.7813659
##   100      0.8808908  0.8584799  0.7693351
##   150      0.8769263  0.8603480  0.7542741
##   200      0.8775046  0.8584799  0.7632293
##   250      0.8804301  0.8642125  0.7543193
##    50      0.8927520  0.8604396  0.7542289
##   100      0.8866877  0.8546154  0.7751244
##   150      0.8826159  0.8565568  0.7573044
##   200      0.8782982  0.8431502  0.7633198
##   250      0.8781474  0.8508425  0.7632745
##    50      0.8895559  0.8642308  0.7452284
##   100      0.8818590  0.8527473  0.7511986
##   150      0.8801838  0.8546703  0.7573044
##   200      0.8778894  0.8508425  0.7602895
##   250      0.8757715  0.8450916  0.7573044
##    50      0.8877414  0.8470330  0.7632745
##   100      0.8846326  0.8470147  0.7572592
##   150      0.8809462  0.8546337  0.7512890
##   200      0.8792321  0.8469780  0.7542289
##   250      0.8775981  0.8489377  0.7542289
##    50      0.8928489  0.8527473  0.7602895
##   100      0.8856138  0.8584982  0.7483039
##   150      0.8824219  0.8412821  0.7512438
##   200      0.8818684  0.8527473  0.7392583
##   250      0.8791472  0.8527656  0.7422886
##    50      0.8890225  0.8470147  0.7572592
##   100      0.8831233  0.8603480  0.7513795
##   150      0.8768519  0.8469780  0.7334690
##   200      0.8726718  0.8469963  0.7364541
##   250      0.8704253  0.8431502  0.7424242
##    50      0.8860038  0.8604762  0.7602442
##   100      0.8756685  0.8374176  0.7483944
##   150      0.8692305  0.8317033  0.7633198
##   200      0.8656254  0.8412454  0.7453641
##   250      0.8658771  0.8316850  0.7483944
##    50      0.8859798  0.8584615  0.7603347
##   100      0.8781492  0.8392857  0.7513342
##   150      0.8759609  0.8393040  0.7573496
##   200      0.8712627  0.8451099  0.7573496
##   250      0.8681694  0.8470330  0.7543193
##    50      0.8863604  0.8604212  0.7662596
##   100      0.8778141  0.8623077  0.7424242
##   150      0.8714625  0.8489011  0.7424695
##   200      0.8667616  0.8546154  0.7454093
##   250      0.8690850  0.8527473  0.7424242
##    50      0.8885438  0.8776740  0.7542741
##   100      0.8836776  0.8585165  0.7602442
##   150      0.8771611  0.8526923  0.7543193
##   200      0.8737143  0.8469780  0.7633198
##   250      0.8713235  0.8393223  0.7632745
##    50      0.8808934  0.8565751  0.7573496
##   100      0.8765657  0.8565751  0.7393939
##   150      0.8741980  0.8508608  0.7483039
##   200      0.8704876  0.8431685  0.7483944
##   250      0.8685941  0.8374725  0.7513342
##    50      0.8889830  0.8565751  0.7722750
##   100      0.8816603  0.8622527  0.7722298
##   150      0.8754828  0.8431685  0.7692899
##   200      0.8723021  0.8469780  0.7633198
##   250      0.8716049  0.8412454  0.7573496
##    50      0.8871544  0.8584432  0.7572592
##   100      0.8779673  0.8489011  0.7601990
##   150      0.8757220  0.8545971  0.7543193
##   200      0.8736745  0.8565751  0.7483492
##   250      0.8700821  0.8527473  0.7453641
##    50      0.8925941  0.8565385  0.7482135
##   100      0.8826698  0.8432051  0.7572592
##   150      0.8799777  0.8489560  0.7632745
##   200      0.8759904  0.8432234  0.7543193
##   250      0.8735034  0.8412821  0.7572592
##    50      0.8916015  0.8584799  0.7572592
##   100      0.8837756  0.8642125  0.7603347
##   150      0.8791715  0.8508242  0.7602442
##   200      0.8766093  0.8584615  0.7662596
##   250      0.8720530  0.8488828  0.7572139
##    50      0.8989426  0.8718864  0.7393487
##   100      0.9000381  0.8776374  0.7781999
##   150      0.8979999  0.8661722  0.7811398
##   200      0.8984003  0.8623443  0.7722750
##   250      0.8985796  0.8661905  0.7633198
##    50      0.9055431  0.8642491  0.7813207
##   100      0.9054220  0.8718681  0.7722750
##   150      0.9031344  0.8776190  0.7692899
##   200      0.9030008  0.8661722  0.7781547
##   250      0.9030296  0.8642308  0.7722298
##    50      0.9062409  0.8852564  0.7573948
##   100      0.9064552  0.8776374  0.7512890
##   150      0.9063123  0.8737912  0.7514247
##   200      0.9038202  0.8757143  0.7603799
##   250      0.9054796  0.8661722  0.7812302
##    50      0.9037062  0.8814652  0.7813659
##   100      0.9016744  0.8757326  0.7783808
##   150      0.9041861  0.8681136  0.7843510
##   200      0.9049163  0.8699817  0.7692447
##   250      0.9055121  0.8585531  0.7691995
##    50      0.9005515  0.8680586  0.7393939
##   100      0.9011278  0.8738095  0.7513342
##   150      0.9009682  0.8719414  0.7544098
##   200      0.8995403  0.8661722  0.7543645
##   250      0.9011842  0.8661355  0.7573044
##    50      0.9046325  0.8718864  0.7663048
##   100      0.9013882  0.8756777  0.7573496
##   150      0.9014438  0.8776557  0.7692899
##   200      0.9027194  0.8814286  0.7663048
##   250      0.9017595  0.8756593  0.7692899
##    50      0.9043265  0.8795055  0.7573496
##   100      0.9020824  0.8718498  0.7513795
##   150      0.9026756  0.8718681  0.7751696
##   200      0.9032253  0.8756593  0.7692447
##   250      0.9030990  0.8660989  0.7722750
##    50      0.9044820  0.8795421  0.7603799
##   100      0.9023841  0.8776557  0.7632745
##   150      0.9025300  0.8757875  0.7662596
##   200      0.9018402  0.8738828  0.7692899
##   250      0.9013715  0.8719231  0.7722750
##    50      0.9051852  0.8871978  0.7663501
##   100      0.9039248  0.8776374  0.7723202
##   150      0.9064993  0.8699817  0.7842605
##   200      0.9055792  0.8699634  0.7842605
##   250      0.9040388  0.8642125  0.7842605
##    50      0.9037330  0.8814103  0.7663048
##   100      0.9048765  0.8795055  0.7722750
##   150      0.9024496  0.8718681  0.7782451
##   200      0.9025541  0.8757143  0.7782451
##   250      0.9015541  0.8738278  0.7782451
##    50      0.8919482  0.8489560  0.7721845
##   100      0.8778024  0.8469414  0.7513795
##   150      0.8728197  0.8393773  0.7483039
##   200      0.8711981  0.8355311  0.7393939
##   250      0.8689293  0.8374725  0.7423790
##    50      0.8835833  0.8355128  0.7632745
##   100      0.8765139  0.8527656  0.7603799
##   150      0.8752542  0.8489011  0.7453641
##   200      0.8775431  0.8469780  0.7544098
##   250      0.8792401  0.8508425  0.7603347
##    50      0.8872311  0.8566484  0.7572592
##   100      0.8792590  0.8470330  0.7692447
##   150      0.8743964  0.8451465  0.7662596
##   200      0.8693502  0.8469963  0.7723202
##   250      0.8699554  0.8431502  0.7573948
##    50      0.8903448  0.8584615  0.7721393
##   100      0.8848256  0.8565751  0.7662596
##   150      0.8819107  0.8488828  0.7781999
##   200      0.8707319  0.8316667  0.7662144
##   250      0.8718247  0.8412821  0.7453189
##    50      0.8900381  0.8565934  0.7541836
##   100      0.8809140  0.8604029  0.7543193
##   150      0.8741797  0.8451099  0.7603347
##   200      0.8682944  0.8489194  0.7573496
##   250      0.8662013  0.8508059  0.7573496
##    50      0.8915678  0.8565201  0.7722750
##   100      0.8817129  0.8546337  0.7483492
##   150      0.8778763  0.8508242  0.7632745
##   200      0.8751543  0.8393407  0.7572592
##   250      0.8719228  0.8374176  0.7512890
##    50      0.8866928  0.8546703  0.7601990
##   100      0.8795376  0.8316850  0.7691995
##   150      0.8746141  0.8412271  0.7782451
##   200      0.8728071  0.8393590  0.7662596
##   250      0.8732301  0.8393590  0.7662596
##    50      0.8935613  0.8527656  0.7632293
##   100      0.8803338  0.8508242  0.7692447
##   150      0.8771587  0.8546520  0.7573044
##   200      0.8725200  0.8470147  0.7602895
##   250      0.8706603  0.8489011  0.7453189
##    50      0.8906950  0.8565751  0.7572592
##   100      0.8845555  0.8623443  0.7632293
##   150      0.8800773  0.8546337  0.7601538
##   200      0.8747896  0.8450183  0.7602442
##   250      0.8707223  0.8431136  0.7542289
##    50      0.8919754  0.8641758  0.7721845
##   100      0.8838793  0.8489011  0.7662144
##   150      0.8769868  0.8508242  0.7512438
##   200      0.8735857  0.8451099  0.7662596
##   250      0.8707503  0.8489194  0.7692899
##    50      0.8888194  0.8412637  0.7602442
##   100      0.8874671  0.8565934  0.7663048
##   150      0.8806617  0.8489377  0.7692447
##   200      0.8820639  0.8546886  0.7602895
##   250      0.8780724  0.8565568  0.7512438
##    50      0.8797186  0.8604396  0.7333786
##   100      0.8768057  0.8527289  0.7243781
##   150      0.8759925  0.8450549  0.7513342
##   200      0.8751595  0.8527473  0.7574401
##   250      0.8741172  0.8507875  0.7454093
##    50      0.8907242  0.8585165  0.7423338
##   100      0.8832072  0.8527473  0.7572592
##   150      0.8807545  0.8508425  0.7602895
##   200      0.8797619  0.8489377  0.7633198
##   250      0.8758855  0.8412637  0.7603347
##    50      0.8901194  0.8508425  0.7783356
##   100      0.8846228  0.8584615  0.7633650
##   150      0.8781091  0.8642125  0.7573948
##   200      0.8780487  0.8604212  0.7573496
##   250      0.8742555  0.8623443  0.7424242
##    50      0.8871096  0.8546154  0.7572592
##   100      0.8826730  0.8470330  0.7603347
##   150      0.8759945  0.8489011  0.7633198
##   200      0.8725763  0.8451282  0.7603347
##   250      0.8741795  0.8413004  0.7663048
##    50      0.8878480  0.8566300  0.7661692
##   100      0.8791040  0.8451099  0.7692899
##   150      0.8771921  0.8374176  0.7692899
##   200      0.8749290  0.8413004  0.7543645
##   250      0.8739550  0.8355495  0.7573496
##    50      0.8903441  0.8527289  0.7722750
##   100      0.8825686  0.8508425  0.7633650
##   150      0.8789874  0.8565934  0.7663048
##   200      0.8764304  0.8393773  0.7633650
##   250      0.8767079  0.8432051  0.7722750
##    50      0.8881585  0.8623077  0.7572592
##   100      0.8796982  0.8508425  0.7453641
##   150      0.8767766  0.8470330  0.7483492
##   200      0.8754835  0.8527289  0.7483039
##   250      0.8748248  0.8489194  0.7483944
##    50      0.8922152  0.8527289  0.7632745
##   100      0.8855003  0.8412637  0.7602895
##   150      0.8811104  0.8431502  0.7422886
##   200      0.8787900  0.8469963  0.7483039
##   250      0.8769939  0.8508425  0.7423338
##    50      0.8953328  0.8642308  0.7662144
##   100      0.8867430  0.8546520  0.7602442
##   150      0.8830603  0.8469780  0.7572139
##   200      0.8786514  0.8469963  0.7543645
##   250      0.8774226  0.8412271  0.7453189
##    50      0.8897409  0.8680220  0.7602895
##   100      0.8768703  0.8508242  0.7631841
##   150      0.8770454  0.8489011  0.7544098
##   200      0.8739825  0.8469780  0.7573948
##   250      0.8708040  0.8336630  0.7782904
##    50      0.8866858  0.8642491  0.7541836
##   100      0.8783295  0.8527473  0.7452736
##   150      0.8743873  0.8470330  0.7363184
##   200      0.8737080  0.8431319  0.7303935
##   250      0.8709281  0.8393223  0.7393939
##    50      0.8859216  0.8488828  0.7603347
##   100      0.8793205  0.8451099  0.7423338
##   150      0.8717163  0.8450549  0.7662596
##   200      0.8734390  0.8488462  0.7573044
##   250      0.8710569  0.8469597  0.7393487
##    50      0.8846685  0.8641941  0.7573496
##   100      0.8715969  0.8584799  0.7483492
##   150      0.8694763  0.8527473  0.7394392
##   200      0.8675972  0.8508242  0.7573044
##   250      0.8671734  0.8470330  0.7483039
##    50      0.8944017  0.8604212  0.7541836
##   100      0.8798579  0.8547070  0.7453189
##   150      0.8797917  0.8470147  0.7602442
##   200      0.8755086  0.8374359  0.7572592
##   250      0.8727125  0.8374542  0.7512438
##    50      0.8904027  0.8603846  0.7662144
##   100      0.8796541  0.8565385  0.7393939
##   150      0.8741908  0.8431319  0.7512890
##   200      0.8707887  0.8374542  0.7483492
##   250      0.8688357  0.8431502  0.7543193
##    50      0.8891390  0.8603663  0.7542289
##   100      0.8800915  0.8641941  0.7661692
##   150      0.8729973  0.8546337  0.7542289
##   200      0.8700464  0.8412454  0.7482587
##   250      0.8658977  0.8450733  0.7452736
##    50      0.8875487  0.8489377  0.7601990
##   100      0.8768144  0.8566117  0.7573044
##   150      0.8728485  0.8584799  0.7543193
##   200      0.8726744  0.8508425  0.7543645
##   250      0.8688960  0.8432234  0.7513342
##    50      0.8894893  0.8565934  0.7542289
##   100      0.8813171  0.8470147  0.7512890
##   150      0.8775589  0.8431685  0.7542289
##   200      0.8730319  0.8450733  0.7423790
##   250      0.8701966  0.8450733  0.7513342
##    50      0.8924847  0.8604029  0.7631841
##   100      0.8832363  0.8489377  0.7511533
##   150      0.8792281  0.8489194  0.7362280
##   200      0.8765903  0.8469963  0.7422886
##   250      0.8734428  0.8489194  0.7362732
##    50      0.8970404  0.8680037  0.7393035
##   100      0.9004187  0.8699817  0.7423338
##   150      0.8984220  0.8680220  0.7483039
##   200      0.8966519  0.8565751  0.7662144
##   250      0.8963005  0.8565751  0.7542289
##    50      0.9058860  0.8680220  0.7662596
##   100      0.9022618  0.8622894  0.7631841
##   150      0.9002770  0.8661172  0.7631389
##   200      0.9007463  0.8603846  0.7511533
##   250      0.8989982  0.8622894  0.7542741
##    50      0.8924444  0.8680769  0.7363184
##   100      0.8959743  0.8680769  0.7603347
##   150      0.8957327  0.8699634  0.7633198
##   200      0.8958560  0.8642308  0.7663048
##   250      0.8995072  0.8660989  0.7633198
##    50      0.9022862  0.8738278  0.7752148
##   100      0.9028077  0.8604579  0.7722298
##   150      0.9039749  0.8699817  0.7691995
##   200      0.9017711  0.8584982  0.7721845
##   250      0.9013106  0.8623260  0.7722750
##    50      0.9000986  0.8699634  0.7453189
##   100      0.8975419  0.8661905  0.7602895
##   150      0.8968892  0.8604029  0.7602895
##   200      0.8988841  0.8642674  0.7602442
##   250      0.8991782  0.8661905  0.7632745
##    50      0.9004727  0.8738462  0.7632293
##   100      0.9022661  0.8623443  0.7722298
##   150      0.9017958  0.8642125  0.7781999
##   200      0.8997614  0.8661355  0.7751696
##   250      0.9010833  0.8718498  0.7632293
##    50      0.8979430  0.8738645  0.7332429
##   100      0.9014116  0.8738278  0.7483039
##   150      0.8995188  0.8662271  0.7722750
##   200      0.8986310  0.8661722  0.7573044
##   250      0.8983972  0.8680952  0.7663048
##    50      0.9036091  0.8795788  0.7572592
##   100      0.9025644  0.8757326  0.7662144
##   150      0.9010122  0.8719048  0.7782451
##   200      0.9014008  0.8718864  0.7692899
##   250      0.9006846  0.8718864  0.7722750
##    50      0.8952945  0.8775641  0.7334690
##   100      0.8967264  0.8776190  0.7424242
##   150      0.9010812  0.8680403  0.7573948
##   200      0.9000211  0.8699634  0.7513795
##   250      0.9001154  0.8680586  0.7513795
##    50      0.9002607  0.8680769  0.7692447
##   100      0.9004769  0.8642491  0.7722750
##   150      0.8993697  0.8604029  0.7692447
##   200      0.8998830  0.8584615  0.7753053
##   250      0.8985949  0.8565385  0.7812754
##    50      0.8916821  0.8470330  0.7631841
##   100      0.8792006  0.8431685  0.7542289
##   150      0.8765462  0.8412821  0.7543193
##   200      0.8722590  0.8431685  0.7692447
##   250      0.8716735  0.8451099  0.7662596
##    50      0.8873113  0.8566117  0.7783356
##   100      0.8788868  0.8317216  0.7782451
##   150      0.8704513  0.8508242  0.7483039
##   200      0.8721783  0.8412454  0.7453641
##   250      0.8684489  0.8393407  0.7423790
##    50      0.8866495  0.8527656  0.7692447
##   100      0.8819730  0.8451099  0.7632745
##   150      0.8768193  0.8451465  0.7663048
##   200      0.8714877  0.8431868  0.7572592
##   250      0.8718520  0.8393773  0.7632293
##    50      0.8888100  0.8508608  0.7722298
##   100      0.8811921  0.8508608  0.7572592
##   150      0.8768332  0.8470330  0.7483944
##   200      0.8711288  0.8450916  0.7423338
##   250      0.8668104  0.8431502  0.7422886
##    50      0.8877303  0.8470147  0.7661692
##   100      0.8783352  0.8451465  0.7572139
##   150      0.8736950  0.8431502  0.7692447
##   200      0.8746923  0.8470147  0.7663048
##   250      0.8717939  0.8393590  0.7512890
##    50      0.8815308  0.8546337  0.7663048
##   100      0.8781544  0.8450916  0.7662596
##   150      0.8751599  0.8450733  0.7603347
##   200      0.8707283  0.8450916  0.7573044
##   250      0.8705534  0.8431868  0.7453189
##    50      0.8901825  0.8565018  0.7722750
##   100      0.8837577  0.8507875  0.7483492
##   150      0.8790613  0.8488828  0.7542741
##   200      0.8740440  0.8526923  0.7542741
##   250      0.8728066  0.8412637  0.7542741
##    50      0.8867965  0.8565568  0.7601990
##   100      0.8785130  0.8450916  0.7632745
##   150      0.8737038  0.8413004  0.7513342
##   200      0.8702877  0.8432234  0.7602895
##   250      0.8684581  0.8431868  0.7572139
##    50      0.8892420  0.8566117  0.7512890
##   100      0.8849944  0.8546703  0.7392583
##   150      0.8793574  0.8450916  0.7452736
##   200      0.8752137  0.8508425  0.7452284
##   250      0.8717114  0.8450916  0.7452284
##    50      0.8930991  0.8680403  0.7632293
##   100      0.8816946  0.8565568  0.7512438
##   150      0.8769190  0.8527106  0.7572592
##   200      0.8736829  0.8431685  0.7482587
##   250      0.8715129  0.8393590  0.7512438
##    50      0.8784170  0.8470147  0.7813207
##   100      0.8742641  0.8373993  0.7573496
##   150      0.8688575  0.8335714  0.7363636
##   200      0.8705020  0.8431685  0.7482587
##   250      0.8655376  0.8374359  0.7393487
##    50      0.8742191  0.8566484  0.7573948
##   100      0.8812693  0.8546703  0.7872456
##   150      0.8757881  0.8603663  0.7633198
##   200      0.8772089  0.8469780  0.7512438
##   250      0.8788544  0.8546154  0.7453189
##    50      0.8775910  0.8488645  0.7393035
##   100      0.8755816  0.8393590  0.7661692
##   150      0.8720395  0.8508242  0.7572139
##   200      0.8694513  0.8469963  0.7572139
##   250      0.8673287  0.8450549  0.7573044
##    50      0.8778399  0.8565751  0.7363636
##   100      0.8744992  0.8508242  0.7571687
##   150      0.8754400  0.8450916  0.7453641
##   200      0.8759045  0.8545971  0.7483039
##   250      0.8748757  0.8527106  0.7602895
##    50      0.8826453  0.8508791  0.7662144
##   100      0.8794444  0.8431136  0.7692899
##   150      0.8767193  0.8412088  0.7662596
##   200      0.8758361  0.8316850  0.7573044
##   250      0.8744058  0.8355311  0.7602442
##    50      0.8898352  0.8546337  0.7933062
##   100      0.8858517  0.8565568  0.7752148
##   150      0.8823154  0.8546520  0.7662596
##   200      0.8799322  0.8527473  0.7602442
##   250      0.8767385  0.8489194  0.7572592
##    50      0.8856128  0.8584432  0.7573496
##   100      0.8814342  0.8680586  0.7663501
##   150      0.8754125  0.8489744  0.7633198
##   200      0.8731248  0.8546703  0.7573044
##   250      0.8726722  0.8527656  0.7573496
##    50      0.8805634  0.8392674  0.7483492
##   100      0.8732768  0.8393223  0.7423790
##   150      0.8713660  0.8393590  0.7484396
##   200      0.8707312  0.8317033  0.7424695
##   250      0.8712700  0.8317399  0.7513795
##    50      0.8830609  0.8565751  0.7512890
##   100      0.8803246  0.8527839  0.7333786
##   150      0.8769465  0.8604029  0.7363184
##   200      0.8766005  0.8489377  0.7363184
##   250      0.8746223  0.8508425  0.7422886
##    50      0.8910715  0.8527289  0.7511081
##   100      0.8823130  0.8546520  0.7573044
##   150      0.8797159  0.8546520  0.7422433
##   200      0.8773686  0.8546520  0.7483039
##   250      0.8779464  0.8489377  0.7632745
##    50      0.8837347  0.8489011  0.7662596
##   100      0.8775324  0.8393223  0.7273632
##   150      0.8674268  0.8373993  0.7392583
##   200      0.8654540  0.8412088  0.7245138
##   250      0.8637086  0.8316667  0.7393939
##    50      0.8823099  0.8432234  0.7632293
##   100      0.8741839  0.8546520  0.7663501
##   150      0.8724687  0.8527473  0.7692899
##   200      0.8682513  0.8469780  0.7573044
##   250      0.8678432  0.8336264  0.7603347
##    50      0.8770281  0.8622894  0.7572139
##   100      0.8705788  0.8450916  0.7451832
##   150      0.8693476  0.8508425  0.7482135
##   200      0.8660866  0.8642125  0.7423338
##   250      0.8656446  0.8527473  0.7662596
##    50      0.8763387  0.8565751  0.7542289
##   100      0.8699971  0.8470330  0.7483492
##   150      0.8734221  0.8508608  0.7483944
##   200      0.8704181  0.8450733  0.7573496
##   250      0.8684326  0.8412637  0.7574401
##    50      0.8856893  0.8604212  0.7514247
##   100      0.8768567  0.8527106  0.7453641
##   150      0.8714320  0.8450916  0.7334238
##   200      0.8673499  0.8374359  0.7424695
##   250      0.8659422  0.8298168  0.7453641
##    50      0.8814734  0.8431868  0.7541836
##   100      0.8788953  0.8507875  0.7452736
##   150      0.8732835  0.8374359  0.7632293
##   200      0.8707823  0.8393040  0.7572592
##   250      0.8693743  0.8374359  0.7423338
##    50      0.8801832  0.8489011  0.7752148
##   100      0.8738248  0.8565568  0.7423338
##   150      0.8693021  0.8412637  0.7393487
##   200      0.8660255  0.8355495  0.7422886
##   250      0.8662843  0.8431685  0.7513342
##    50      0.8795277  0.8470147  0.7632745
##   100      0.8746376  0.8508242  0.7541836
##   150      0.8728819  0.8565568  0.7752601
##   200      0.8669284  0.8431868  0.7633198
##   250      0.8665962  0.8412637  0.7632745
##    50      0.8868094  0.8489560  0.7602895
##   100      0.8787609  0.8584799  0.7452736
##   150      0.8764190  0.8565751  0.7632745
##   200      0.8728396  0.8508425  0.7512890
##   250      0.8712629  0.8451099  0.7543193
##    50      0.8872138  0.8584799  0.7573496
##   100      0.8813231  0.8489377  0.7572139
##   150      0.8755630  0.8450733  0.7483039
##   200      0.8724714  0.8393407  0.7423338
##   250      0.8714968  0.8432051  0.7423338
##    50      0.9023953  0.8757326  0.7573044
##   100      0.9013012  0.8737912  0.7601990
##   150      0.8999264  0.8757326  0.7691995
##   200      0.8982393  0.8738462  0.7781999
##   250      0.8947661  0.8661355  0.7662144
##    50      0.8998515  0.8757143  0.7661692
##   100      0.9018768  0.8795055  0.7662596
##   150      0.8972140  0.8737729  0.7632293
##   200      0.8954167  0.8623626  0.7572592
##   250      0.8921756  0.8642857  0.7692447
##    50      0.8994746  0.8680769  0.7573948
##   100      0.8987952  0.8699817  0.7573496
##   150      0.8978289  0.8623077  0.7603799
##   200      0.8969905  0.8738095  0.7573948
##   250      0.8969031  0.8699634  0.7542289
##    50      0.9008577  0.8661538  0.7753053
##   100      0.9000727  0.8623260  0.7752601
##   150      0.9007949  0.8680586  0.7662596
##   200      0.8991649  0.8661538  0.7722750
##   250      0.8977139  0.8680220  0.7782451
##    50      0.8995552  0.8661722  0.7602442
##   100      0.8924869  0.8584982  0.7512438
##   150      0.8976685  0.8565751  0.7512890
##   200      0.8973497  0.8680769  0.7481682
##   250      0.8970828  0.8623443  0.7572139
##    50      0.9001187  0.8795421  0.7573948
##   100      0.8978692  0.8700000  0.7812302
##   150      0.8958599  0.8623077  0.7722750
##   200      0.8964532  0.8565568  0.7693351
##   250      0.8953355  0.8603846  0.7631841
##    50      0.8969620  0.8642491  0.7512890
##   100      0.8990333  0.8623626  0.7602442
##   150      0.8982202  0.8661355  0.7513342
##   200      0.8992106  0.8623260  0.7752601
##   250      0.8975997  0.8623260  0.7602442
##    50      0.9042504  0.8776190  0.7721845
##   100      0.9011750  0.8661172  0.7632745
##   150      0.8993297  0.8660806  0.7631841
##   200      0.8981778  0.8622711  0.7512890
##   250      0.8990055  0.8681136  0.7662144
##    50      0.9013858  0.8718864  0.7483944
##   100      0.9010850  0.8623443  0.7603347
##   150      0.8989393  0.8700000  0.7753053
##   200      0.8984954  0.8642491  0.7692899
##   250      0.8992685  0.8585165  0.7663048
##    50      0.9026289  0.8699451  0.7722298
##   100      0.9002446  0.8546703  0.7872908
##   150      0.8994478  0.8642308  0.7752601
##   200      0.8980593  0.8604029  0.7752601
##   250      0.8990062  0.8565751  0.7781999
##    50      0.8830761  0.8431319  0.7723202
##   100      0.8774863  0.8508242  0.7603347
##   150      0.8643435  0.8374542  0.7514247
##   200      0.8652907  0.8431502  0.7633198
##   250      0.8647798  0.8431868  0.7483944
##    50      0.8873341  0.8508425  0.7721393
##   100      0.8681256  0.8451282  0.7542289
##   150      0.8723909  0.8412821  0.7573496
##   200      0.8687951  0.8393407  0.7632745
##   250      0.8649716  0.8355495  0.7573496
##    50      0.8762144  0.8584982  0.7693351
##   100      0.8730275  0.8316850  0.7602895
##   150      0.8709469  0.8374908  0.7483039
##   200      0.8739240  0.8316667  0.7632745
##   250      0.8701430  0.8393223  0.7542741
##    50      0.8811414  0.8527839  0.7602895
##   100      0.8696061  0.8279487  0.7543193
##   150      0.8675381  0.8317399  0.7573044
##   200      0.8657860  0.8278571  0.7662596
##   250      0.8627527  0.8259890  0.7632745
##    50      0.8778467  0.8604396  0.7273180
##   100      0.8710884  0.8489560  0.7543193
##   150      0.8668517  0.8393407  0.7393487
##   200      0.8649527  0.8412271  0.7303483
##   250      0.8638634  0.8335714  0.7274084
##    50      0.8833469  0.8566117  0.7573044
##   100      0.8780638  0.8470513  0.7512890
##   150      0.8715818  0.8336264  0.7542289
##   200      0.8688697  0.8317399  0.7393487
##   250      0.8709504  0.8374908  0.7513342
##    50      0.8837397  0.8565934  0.7751696
##   100      0.8764221  0.8527289  0.7752148
##   150      0.8728472  0.8432234  0.7692447
##   200      0.8699599  0.8450916  0.7602895
##   250      0.8643902  0.8374725  0.7483492
##    50      0.8868684  0.8584615  0.7541384
##   100      0.8755817  0.8565385  0.7363184
##   150      0.8691344  0.8527289  0.7363184
##   200      0.8678363  0.8489011  0.7184532
##   250      0.8646672  0.8470147  0.7244686
##    50      0.8884235  0.8527839  0.7631841
##   100      0.8780903  0.8451099  0.7632293
##   150      0.8740795  0.8565751  0.7512890
##   200      0.8690316  0.8489194  0.7393487
##   250      0.8679314  0.8508059  0.7483492
##    50      0.8848396  0.8622894  0.7512438
##   100      0.8769898  0.8489011  0.7421981
##   150      0.8744224  0.8546337  0.7453189
##   200      0.8695859  0.8469963  0.7423338
##   250      0.8669502  0.8450733  0.7423338
##    50      0.8877291  0.8623443  0.7663048
##   100      0.8793624  0.8585348  0.7693804
##   150      0.8798835  0.8622894  0.7513342
##   200      0.8771280  0.8469963  0.7513795
##   250      0.8792331  0.8489377  0.7603347
##    50      0.8894063  0.8642125  0.7631389
##   100      0.8818900  0.8546703  0.7603347
##   150      0.8779751  0.8527473  0.7721845
##   200      0.8742383  0.8412454  0.7633650
##   250      0.8721525  0.8374176  0.7542289
##    50      0.8814247  0.8546154  0.7692899
##   100      0.8732408  0.8431868  0.7692447
##   150      0.8676809  0.8508242  0.7393939
##   200      0.8681098  0.8470147  0.7423790
##   250      0.8688881  0.8508242  0.7542741
##    50      0.8830222  0.8622527  0.7602442
##   100      0.8805080  0.8641941  0.7782451
##   150      0.8755291  0.8565201  0.7573948
##   200      0.8755339  0.8545788  0.7513795
##   250      0.8750112  0.8527656  0.7483944
##    50      0.8822973  0.8508425  0.7602895
##   100      0.8773947  0.8565751  0.7662144
##   150      0.8735756  0.8489011  0.7572592
##   200      0.8735622  0.8412454  0.7632745
##   250      0.8723373  0.8412637  0.7663048
##    50      0.8887761  0.8489744  0.7662144
##   100      0.8790819  0.8393590  0.7601538
##   150      0.8778854  0.8374542  0.7572592
##   200      0.8753661  0.8450916  0.7632293
##   250      0.8741763  0.8470147  0.7662144
##    50      0.8823064  0.8527656  0.7542289
##   100      0.8783611  0.8546520  0.7691542
##   150      0.8757730  0.8507875  0.7512438
##   200      0.8745122  0.8489194  0.7512890
##   250      0.8730258  0.8508242  0.7512890
##    50      0.8789902  0.8450549  0.7632293
##   100      0.8739803  0.8527289  0.7543193
##   150      0.8737517  0.8565018  0.7513342
##   200      0.8703914  0.8507875  0.7542741
##   250      0.8698497  0.8488828  0.7513342
##    50      0.8876901  0.8470330  0.7542289
##   100      0.8806994  0.8470147  0.7602442
##   150      0.8753201  0.8469780  0.7483039
##   200      0.8732224  0.8393407  0.7512438
##   250      0.8729004  0.8469963  0.7512890
##    50      0.8836256  0.8507875  0.7602442
##   100      0.8786395  0.8507692  0.7512890
##   150      0.8770907  0.8450733  0.7632293
##   200      0.8758617  0.8450549  0.7512438
##   250      0.8741077  0.8450733  0.7542289
##    50      0.8834266  0.8584982  0.7573044
##   100      0.8741377  0.8374359  0.7602442
##   150      0.8701130  0.8489011  0.7513342
##   200      0.8720321  0.8489194  0.7602895
##   250      0.8709490  0.8412821  0.7483492
##    50      0.8780693  0.8527473  0.7393487
##   100      0.8741685  0.8470330  0.7454093
##   150      0.8715532  0.8470513  0.7483944
##   200      0.8686566  0.8412454  0.7334690
##   250      0.8655891  0.8431685  0.7453641
##    50      0.8890524  0.8565568  0.7663048
##   100      0.8776407  0.8546886  0.7513342
##   150      0.8752446  0.8393407  0.7633650
##   200      0.8709428  0.8412454  0.7513795
##   250      0.8666706  0.8374359  0.7573496
##    50      0.8774660  0.8450916  0.7632745
##   100      0.8715580  0.8470147  0.7513342
##   150      0.8674038  0.8317033  0.7364089
##   200      0.8672951  0.8431685  0.7364541
##   250      0.8639214  0.8393773  0.7423790
##    50      0.8824590  0.8508059  0.7573496
##   100      0.8736536  0.8508425  0.7513795
##   150      0.8709980  0.8508425  0.7424242
##   200      0.8693420  0.8451099  0.7454545
##   250      0.8672711  0.8451099  0.7364541
##    50      0.8794360  0.8527473  0.7573948
##   100      0.8737919  0.8412454  0.7453641
##   150      0.8676873  0.8431685  0.7513795
##   200      0.8659551  0.8355128  0.7543645
##   250      0.8631998  0.8354945  0.7423338
##    50      0.8811973  0.8508425  0.7393487
##   100      0.8760425  0.8469780  0.7453189
##   150      0.8705412  0.8297802  0.7453189
##   200      0.8672588  0.8317033  0.7423338
##   250      0.8632150  0.8374359  0.7363184
##    50      0.8803065  0.8488828  0.7512438
##   100      0.8742372  0.8508059  0.7542741
##   150      0.8705745  0.8470330  0.7632745
##   200      0.8674182  0.8451282  0.7602442
##   250      0.8657279  0.8470147  0.7573044
##    50      0.8831349  0.8604396  0.7481682
##   100      0.8744576  0.8489377  0.7453189
##   150      0.8702501  0.8393407  0.7452736
##   200      0.8683797  0.8431868  0.7333333
##   250      0.8670860  0.8431685  0.7393487
##    50      0.8865179  0.8508242  0.7752601
##   100      0.8809430  0.8488828  0.7632293
##   150      0.8745882  0.8450733  0.7543193
##   200      0.8712932  0.8412821  0.7543193
##   250      0.8678527  0.8431868  0.7453641
##    50      0.8994716  0.8852747  0.7453189
##   100      0.8985598  0.8738095  0.7604251
##   150      0.8999706  0.8642125  0.7723654
##   200      0.8979904  0.8718498  0.7692899
##   250      0.8958586  0.8584615  0.7632745
##    50      0.8989618  0.8719048  0.7602442
##   100      0.8986877  0.8661722  0.7572139
##   150      0.8984534  0.8661538  0.7542289
##   200      0.8948263  0.8603846  0.7542741
##   250      0.8927468  0.8565568  0.7631389
##    50      0.8922353  0.8585348  0.7542289
##   100      0.8920457  0.8604029  0.7362732
##   150      0.8929866  0.8566484  0.7661692
##   200      0.8940779  0.8604579  0.7722298
##   250      0.8931889  0.8680586  0.7722298
##    50      0.9005604  0.8699817  0.7571687
##   100      0.9004037  0.8738095  0.7572139
##   150      0.9007259  0.8757326  0.7512438
##   200      0.9001792  0.8718864  0.7601538
##   250      0.8994765  0.8699817  0.7572139
##    50      0.8979247  0.8642308  0.7753957
##   100      0.8950762  0.8661722  0.7663048
##   150      0.8936211  0.8604029  0.7692899
##   200      0.8919832  0.8604212  0.7722298
##   250      0.8918582  0.8584982  0.7631389
##    50      0.8999869  0.8623626  0.7692447
##   100      0.8985092  0.8662088  0.7632293
##   150      0.8964042  0.8642857  0.7692899
##   200      0.8977175  0.8642857  0.7752601
##   250      0.8936792  0.8642491  0.7543645
##    50      0.8899471  0.8661905  0.7213930
##   100      0.8940986  0.8661355  0.7602895
##   150      0.8929632  0.8719048  0.7573044
##   200      0.8933486  0.8776374  0.7483492
##   250      0.8941339  0.8719048  0.7573496
##    50      0.8971047  0.8566300  0.7691995
##   100      0.8940891  0.8528205  0.7632293
##   150      0.8967497  0.8508242  0.7751696
##   200      0.8951255  0.8546520  0.7662596
##   250      0.8934843  0.8507692  0.7721845
##    50      0.8961759  0.8623443  0.7573496
##   100      0.8968755  0.8585165  0.7453641
##   150      0.8967732  0.8547253  0.7483039
##   200      0.8954391  0.8565934  0.7632293
##   250      0.8961738  0.8546886  0.7572592
##    50      0.9004084  0.8700366  0.7842153
##   100      0.8976826  0.8604212  0.7901854
##   150      0.9005504  0.8565934  0.7932157
##   200      0.8982233  0.8603846  0.7872456
##   250      0.8982713  0.8565385  0.7872456
##    50      0.8797413  0.8375092  0.7542741
##   100      0.8695472  0.8469780  0.7633198
##   150      0.8734476  0.8393773  0.7542289
##   200      0.8699895  0.8336630  0.7543193
##   250      0.8683112  0.8393773  0.7633198
##    50      0.8814818  0.8508791  0.7543645
##   100      0.8755894  0.8508791  0.7603347
##   150      0.8715152  0.8374359  0.7483039
##   200      0.8693438  0.8374176  0.7484396
##   250      0.8691852  0.8335897  0.7514247
##    50      0.8873517  0.8565934  0.7752601
##   100      0.8783835  0.8603114  0.7602895
##   150      0.8757367  0.8507875  0.7543193
##   200      0.8725937  0.8526923  0.7453641
##   250      0.8695096  0.8431319  0.7393939
##    50      0.8704465  0.8374725  0.7331524
##   100      0.8678792  0.8374725  0.7452736
##   150      0.8650683  0.8450916  0.7393035
##   200      0.8645129  0.8374725  0.7304387
##   250      0.8630957  0.8393773  0.7304387
##    50      0.8850824  0.8546337  0.7632745
##   100      0.8777037  0.8565385  0.7482135
##   150      0.8735050  0.8527656  0.7542289
##   200      0.8695435  0.8469780  0.7542289
##   250      0.8681773  0.8489011  0.7542289
##    50      0.8796711  0.8604212  0.7513795
##   100      0.8749532  0.8527656  0.7722750
##   150      0.8701555  0.8508425  0.7513342
##   200      0.8665724  0.8432051  0.7603347
##   250      0.8659603  0.8546703  0.7573496
##    50      0.8833842  0.8565385  0.7512890
##   100      0.8754564  0.8450733  0.7453189
##   150      0.8727099  0.8470513  0.7422886
##   200      0.8693073  0.8489194  0.7482135
##   250      0.8673301  0.8450916  0.7363184
##    50      0.8818488  0.8412637  0.7602442
##   100      0.8765453  0.8412454  0.7662596
##   150      0.8727144  0.8355861  0.7632293
##   200      0.8687754  0.8355678  0.7572592
##   250      0.8663143  0.8317033  0.7542289
##    50      0.8854178  0.8508791  0.7571687
##   100      0.8785232  0.8566117  0.7512438
##   150      0.8728445  0.8489377  0.7542741
##   200      0.8708430  0.8451282  0.7542741
##   250      0.8672598  0.8374542  0.7453189
##    50      0.8865798  0.8527289  0.7722298
##   100      0.8781106  0.8546520  0.7722298
##   150      0.8726990  0.8489011  0.7632745
##   200      0.8715535  0.8489011  0.7543193
##   250      0.8688860  0.8489011  0.7483492
##    50      0.8770681  0.8471062  0.7603799
##   100      0.8753030  0.8584799  0.7544098
##   150      0.8682391  0.8547253  0.7394392
##   200      0.8637657  0.8412821  0.7424695
##   250      0.8603620  0.8469963  0.7215287
##    50      0.8710405  0.8412637  0.7483944
##   100      0.8672137  0.8317399  0.7424242
##   150      0.8702027  0.8336630  0.7663501
##   200      0.8696113  0.8393590  0.7573948
##   250      0.8680919  0.8317033  0.7484396
##    50      0.8695246  0.8450733  0.7364089
##   100      0.8640185  0.8469963  0.7273632
##   150      0.8679572  0.8508608  0.7274989
##   200      0.8642530  0.8508059  0.7244686
##   250      0.8655142  0.8393590  0.7364089
##    50      0.8751667  0.8394505  0.7601990
##   100      0.8713914  0.8490110  0.7424242
##   150      0.8691415  0.8374725  0.7393939
##   200      0.8673165  0.8470147  0.7273632
##   250      0.8686905  0.8431502  0.7244233
##    50      0.8738782  0.8451282  0.7571687
##   100      0.8701387  0.8451099  0.7603347
##   150      0.8712606  0.8527656  0.7572592
##   200      0.8680673  0.8412821  0.7453189
##   250      0.8669093  0.8432418  0.7483039
##    50      0.8770996  0.8393590  0.7573948
##   100      0.8724528  0.8489560  0.7393487
##   150      0.8719448  0.8450916  0.7453641
##   200      0.8686164  0.8508425  0.7364089
##   250      0.8705508  0.8432051  0.7483492
##    50      0.8794449  0.8623260  0.7483039
##   100      0.8728118  0.8623260  0.7482587
##   150      0.8699129  0.8508242  0.7512890
##   200      0.8702331  0.8546520  0.7513342
##   250      0.8689824  0.8642125  0.7542741
##    50      0.8770685  0.8527839  0.7632745
##   100      0.8716272  0.8432051  0.7632745
##   150      0.8690363  0.8489377  0.7483039
##   200      0.8692877  0.8412821  0.7393487
##   250      0.8683396  0.8374725  0.7513342
##    50      0.8802888  0.8432234  0.7601085
##   100      0.8750908  0.8432418  0.7541836
##   150      0.8710799  0.8432234  0.7452736
##   200      0.8694411  0.8432418  0.7423338
##   250      0.8683844  0.8374908  0.7453189
##    50      0.8804912  0.8393590  0.7661692
##   100      0.8737376  0.8470147  0.7482587
##   150      0.8692439  0.8432234  0.7542289
##   200      0.8702088  0.8432051  0.7602442
##   250      0.8698425  0.8432051  0.7572592
##    50      0.8775321  0.8451099  0.7482587
##   100      0.8731859  0.8430952  0.7543193
##   150      0.8676031  0.8355128  0.7513342
##   200      0.8588527  0.8296703  0.7483039
##   250      0.8612000  0.8354579  0.7364089
##    50      0.8737839  0.8431685  0.7424695
##   100      0.8645341  0.8451282  0.7304839
##   150      0.8648606  0.8412454  0.7394392
##   200      0.8614928  0.8393407  0.7364541
##   250      0.8604951  0.8374542  0.7214835
##    50      0.8768091  0.8412637  0.7572592
##   100      0.8664046  0.8354945  0.7453641
##   150      0.8646503  0.8336081  0.7512890
##   200      0.8644002  0.8202198  0.7513342
##   250      0.8644406  0.8259524  0.7454093
##    50      0.8877706  0.8680769  0.7663953
##   100      0.8760375  0.8565201  0.7573496
##   150      0.8697155  0.8526923  0.7513795
##   200      0.8680377  0.8450549  0.7574401
##   250      0.8661135  0.8489194  0.7484396
##    50      0.8773289  0.8374176  0.7512890
##   100      0.8754226  0.8373993  0.7692899
##   150      0.8705515  0.8335897  0.7603799
##   200      0.8688579  0.8393590  0.7543645
##   250      0.8646681  0.8317216  0.7364541
##    50      0.8737916  0.8412271  0.7632293
##   100      0.8678924  0.8412271  0.7602442
##   150      0.8664223  0.8336081  0.7482587
##   200      0.8625669  0.8297985  0.7512890
##   250      0.8629390  0.8355128  0.7422886
##    50      0.8782811  0.8546703  0.7573044
##   100      0.8727999  0.8469963  0.7573948
##   150      0.8680397  0.8393956  0.7454093
##   200      0.8650327  0.8393773  0.7513795
##   250      0.8620202  0.8413187  0.7423790
##    50      0.8823816  0.8489194  0.7572592
##   100      0.8763608  0.8451099  0.7513342
##   150      0.8705871  0.8393590  0.7453641
##   200      0.8691218  0.8413004  0.7423790
##   250      0.8667398  0.8413004  0.7423790
##    50      0.8764932  0.8546337  0.7571687
##   100      0.8700723  0.8412637  0.7662144
##   150      0.8680677  0.8508425  0.7662144
##   200      0.8644899  0.8546703  0.7602895
##   250      0.8628553  0.8508608  0.7632745
##    50      0.8817830  0.8450916  0.7661692
##   100      0.8721521  0.8450916  0.7511986
##   150      0.8669104  0.8412637  0.7543193
##   200      0.8651709  0.8450733  0.7452736
##   250      0.8625632  0.8431502  0.7482587
##    50      0.8952037  0.8719048  0.7601990
##   100      0.8932406  0.8661538  0.7572592
##   150      0.8955434  0.8661722  0.7662144
##   200      0.8931886  0.8547253  0.7573044
##   250      0.8914122  0.8471062  0.7633198
##    50      0.8961244  0.8719048  0.7572139
##   100      0.8976430  0.8604212  0.7662596
##   150      0.8964706  0.8585165  0.7781547
##   200      0.8950333  0.8680586  0.7691995
##   250      0.8947592  0.8547070  0.7663048
##    50      0.8972721  0.8757326  0.7422433
##   100      0.8962095  0.8699817  0.7452736
##   150      0.8973086  0.8603663  0.7632293
##   200      0.8932872  0.8642125  0.7662596
##   250      0.8915983  0.8546337  0.7631841
##    50      0.8998791  0.8680769  0.7483492
##   100      0.8993949  0.8489927  0.7781999
##   150      0.9006832  0.8547070  0.7933062
##   200      0.8997544  0.8566117  0.7842605
##   250      0.8958447  0.8623260  0.7752148
##    50      0.8928804  0.8565751  0.7544098
##   100      0.8947232  0.8699634  0.7603799
##   150      0.8944689  0.8623260  0.7544098
##   200      0.8949724  0.8623260  0.7572139
##   250      0.8920646  0.8642491  0.7573044
##    50      0.8998714  0.8700183  0.7691995
##   100      0.9010975  0.8700000  0.7692447
##   150      0.8977229  0.8623260  0.7662596
##   200      0.8996038  0.8623077  0.7602442
##   250      0.8940410  0.8508242  0.7661692
##    50      0.8943206  0.8546886  0.7332881
##   100      0.8958092  0.8546886  0.7513342
##   150      0.8928899  0.8508608  0.7453641
##   200      0.8923191  0.8527839  0.7603347
##   250      0.8927129  0.8470330  0.7692447
##    50      0.8991240  0.8585165  0.7661692
##   100      0.8978409  0.8470696  0.7661239
##   150      0.8977739  0.8642491  0.7751696
##   200      0.8986578  0.8584799  0.7661692
##   250      0.8966045  0.8642125  0.7781999
##    50      0.8891436  0.8680220  0.7362732
##   100      0.8916415  0.8565568  0.7661692
##   150      0.8966919  0.8603663  0.7572592
##   200      0.8969733  0.8623077  0.7661692
##   250      0.8954180  0.8604029  0.7661692
##    50      0.8967958  0.8623626  0.7812302
##   100      0.8961671  0.8604212  0.7751696
##   150      0.8951324  0.8585165  0.7662596
##   200      0.8935044  0.8604212  0.7632745
##   250      0.8939127  0.8623260  0.7752601
##    50      0.8782792  0.8565385  0.7482135
##   100      0.8669508  0.8489560  0.7303483
##   150      0.8623355  0.8432418  0.7274536
##   200      0.8601272  0.8527473  0.7154681
##   250      0.8628910  0.8412637  0.7213930
##    50      0.8764102  0.8451648  0.7511533
##   100      0.8702740  0.8508974  0.7273632
##   150      0.8609770  0.8374908  0.7363184
##   200      0.8642983  0.8355311  0.7393939
##   250      0.8606192  0.8279121  0.7274989
##    50      0.8785666  0.8336447  0.7512890
##   100      0.8711072  0.8394139  0.7663048
##   150      0.8652961  0.8355311  0.7423338
##   200      0.8644856  0.8336081  0.7512438
##   250      0.8630115  0.8393407  0.7393939
##    50      0.8849852  0.8432601  0.7663048
##   100      0.8725629  0.8394322  0.7482135
##   150      0.8682983  0.8355861  0.7452736
##   200      0.8625135  0.8336813  0.7422886
##   250      0.8603550  0.8317216  0.7393035
##    50      0.8798803  0.8451282  0.7451832
##   100      0.8721061  0.8489377  0.7572592
##   150      0.8675435  0.8393773  0.7572592
##   200      0.8645163  0.8469963  0.7482587
##   250      0.8630265  0.8431685  0.7512890
##    50      0.8759145  0.8565934  0.7393939
##   100      0.8703855  0.8374725  0.7393487
##   150      0.8655337  0.8335897  0.7363636
##   200      0.8616231  0.8259524  0.7303935
##   250      0.8607297  0.8412454  0.7333786
##    50      0.8804850  0.8469963  0.7452736
##   100      0.8713843  0.8469963  0.7483492
##   150      0.8655535  0.8241026  0.7423790
##   200      0.8640429  0.8374725  0.7453641
##   250      0.8623116  0.8412821  0.7453641
##    50      0.8843128  0.8547070  0.7722298
##   100      0.8751368  0.8450733  0.7542741
##   150      0.8726502  0.8469780  0.7512438
##   200      0.8718774  0.8470147  0.7452736
##   250      0.8713912  0.8527473  0.7393035
##    50      0.8773917  0.8451099  0.7573044
##   100      0.8694966  0.8451099  0.7542741
##   150      0.8660852  0.8489011  0.7423338
##   200      0.8637313  0.8412821  0.7483039
##   250      0.8623694  0.8432051  0.7453189
##    50      0.8854024  0.8546703  0.7752601
##   100      0.8819418  0.8528022  0.7722298
##   150      0.8760252  0.8393773  0.7752601
##   200      0.8734408  0.8450916  0.7692899
##   250      0.8703675  0.8489194  0.7692899
## 
## Tuning parameter 'gamma' was held constant at a value of 0
## 
## Tuning parameter 'min_child_weight' was held constant at a value of 1
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were nrounds = 100, max_depth = 3,
##  eta = 0.3, gamma = 0, subsample = 0.625, colsample_bytree =
##  0.8, rate_drop = 0.5, skip_drop = 0.05 and min_child_weight = 1.

Training SVM

set.seed(100)

# Train the model using MARS
model_svmRadial = train(Purchase ~ ., data=trainData, method='svmRadial', tuneLength=15, trControl = fitControl)
model_svmRadial

## Support Vector Machines with Radial Basis Function Kernel 
## 
## 857 samples
##  18 predictor
##   2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 685, 686, 685, 686, 686 
## Resampling results across tuning parameters:
## 
##   C        ROC        Sens       Spec     
##      0.25  0.8968213  0.8795055  0.7274084
##      0.50  0.8980530  0.8776007  0.7214835
##      1.00  0.8977832  0.8776190  0.7334238
##      2.00  0.8934719  0.8718681  0.7303483
##      4.00  0.8915500  0.8794689  0.7154229
##      8.00  0.8868855  0.8890293  0.6825418
##     16.00  0.8823947  0.8870696  0.6854817
##     32.00  0.8767745  0.8889744  0.6583899
##     64.00  0.8600145  0.8889744  0.6524197
##    128.00  0.8486717  0.8813370  0.6494346
##    256.00  0.8413847  0.8832784  0.6284487
##    512.00  0.8313846  0.8871062  0.6196744
##   1024.00  0.8198163  0.8909524  0.6136137
##   2048.00  0.8143498  0.8986081  0.5598372
##   4096.00  0.8113379  0.9024725  0.5388964
## 
## Tuning parameter 'sigma' was held constant at a value of 0.06525857
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were sigma = 0.06525857 and C = 0.5.

Run Ensemble to compare the models.

# Compare model performances using resample()
models_compare <- resamples(list(ADABOOST=model_adaboost, RF=model_rf, XGBDART=model_xgbDART, MARS=model_mars3, SVM=model_svmRadial))

# Summary of the models performances
summary(models_compare)

## 
## Call:
## summary.resamples(object = models_compare)
## 
## Models: ADABOOST, RF, XGBDART, MARS, SVM 
## Number of resamples: 5 
## 
## ROC 
##               Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## ADABOOST 0.8525253 0.8772245 0.8828932 0.8783495 0.8852878 0.8938166    0
## RF       0.8691198 0.8697618 0.8932262 0.8871323 0.8997868 0.9037669    0
## XGBDART  0.8878788 0.9026263 0.9111585 0.9105354 0.9199716 0.9310419    0
## MARS     0.8808081 0.8943743 0.9044776 0.9034469 0.9146411 0.9229334    0
## SVM      0.8712843 0.8823192 0.9022033 0.8980530 0.9166188 0.9178394    0
## 
## Sens 
##               Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## ADABOOST 0.7714286 0.8076923 0.8380952 0.8298535 0.8653846 0.8666667    0
## RF       0.8076923 0.8380952 0.8666667 0.8565751 0.8761905 0.8942308    0
## XGBDART  0.8190476 0.8461538 0.8761905 0.8680952 0.8952381 0.9038462    0
## MARS     0.8365385 0.8476190 0.8952381 0.8776007 0.9038462 0.9047619    0
## SVM      0.8173077 0.8666667 0.8857143 0.8776007 0.8952381 0.9230769    0
## 
## Spec 
##               Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## ADABOOST 0.6969697 0.7014925 0.7462687 0.7543193 0.8059701 0.8208955    0
## RF       0.6666667 0.6716418 0.7462687 0.7333333 0.7761194 0.8059701    0
## XGBDART  0.7575758 0.7910448 0.8059701 0.7962913 0.8059701 0.8208955    0
## MARS     0.7272727 0.7761194 0.7761194 0.7753053 0.7910448 0.8059701    0
## SVM      0.6716418 0.6969697 0.7164179 0.7214835 0.7313433 0.7910448    0

Lets Plot to resample Output to compare the models

# Draw box plots to compare models
scales <- list(x=list(relation="free"), y=list(relation="free"))
bwplot(models_compare, scales=scales)

The xgbDART model appears to be the be best performing model overall because of the high ROC. But if you need a model that predicts the positives better, you might want to consider MARS, given its high sensitivity

Ensembling the predictors

So we have predictions from multiple individual models. To do this we had to run the train() function once for each model, store the models and pass it to the res

The caretEnsemble package lets you do just that.

All you have to do is put the names of all the algorithms you want to run in a vector and pass it to caretEnsemble::caretList() instead of caret::train().

library(caretEnsemble)

# Stacking Algorithms - Run multiple algos in one call.
trainControl <- trainControl(method="repeatedcv", 
                             number=10, 
                             repeats=3,
                             savePredictions=TRUE, 
                             classProbs=TRUE)

algorithmList <- c('rf', 'adaboost', 'earth', 'xgbDART', 'svmRadial')

set.seed(100)
models <- caretList(Purchase ~ ., data=trainData, trControl=trainControl, methodList=algorithmList) 
results <- resamples(models)
summary(results)

## 
## Call:
## summary.resamples(object = results)
## 
## Models: rf, adaboost, earth, xgbDART, svmRadial 
## Number of resamples: 30 
## 
## Accuracy 
##                Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## rf        0.7011494 0.7813611 0.8245554 0.8148761 0.8488372 0.8823529    0
## adaboost  0.7126437 0.7764706 0.8117647 0.8079169 0.8367305 0.9058824    0
## earth     0.7529412 0.8117647 0.8304378 0.8311071 0.8501403 0.9069767    0
## xgbDART   0.7790698 0.8235294 0.8372093 0.8447774 0.8720930 0.9302326    0
## svmRadial 0.7647059 0.7930233 0.8245554 0.8261035 0.8567613 0.8953488    0
## 
## Kappa 
##                Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## rf        0.3656758 0.5412023 0.6239376 0.6106210 0.6816051 0.7523310    0
## adaboost  0.4059000 0.5332939 0.6054203 0.5973623 0.6539334 0.7973778    0
## earth     0.4883921 0.5879658 0.6400500 0.6410969 0.6839406 0.8073908    0
## xgbDART   0.5437483 0.6133688 0.6583877 0.6715447 0.7278216 0.8555431    0
## svmRadial 0.4959444 0.5598055 0.6190147 0.6280087 0.6897242 0.7774583    0

Plot the resamples output to compare the models.

# Box plots to compare models
scales <- list(x=list(relation="free"), y=list(relation="free"))
bwplot(results, scales=scales)

Combine the predictions of multiple Models

Turns out this can be done too, using the caretStack(). You just need to make sure you don’t use the same trainControl you used to build the models.

# Create the trainControl
set.seed(101)
stackControl <- trainControl(method="repeatedcv", 
                             number=10, 
                             repeats=3,
                             savePredictions=TRUE, 
                             classProbs=TRUE)

# Ensemble the predictions of `models` to form a new combined prediction based on glm
stack.glm <- caretStack(models, method="glm", metric="Accuracy", trControl=stackControl)
print(stack.glm)

## A glm ensemble of 5 base models: rf, adaboost, earth, xgbDART, svmRadial
## 
## Ensemble results:
## Generalized Linear Model 
## 
## 2571 samples
##    5 predictor
##    2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 3 times) 
## Summary of sample sizes: 2314, 2314, 2313, 2314, 2315, 2313, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.8445367  0.6708299

A point to consider: The ensembles tend to perform better if the predictions are less correlated with each other.

So you may want to try passing different types of models, both high and low performing rather than just stick to passing high accuracy models to the caretStack.

print(stack.glm)

## A glm ensemble of 5 base models: rf, adaboost, earth, xgbDART, svmRadial
## 
## Ensemble results:
## Generalized Linear Model 
## 
## 2571 samples
##    5 predictor
##    2 classes: 'CH', 'MM' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 3 times) 
## Summary of sample sizes: 2314, 2314, 2313, 2314, 2315, 2313, ... 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.8445367  0.6708299

# Predict on testData
stack_predicteds <- predict(stack.glm, newdata=testData4)
head(stack_predicteds)

## [1] CH CH CH CH MM CH
## Levels: CH MM

That’s it