The goal of the project is to predict the manner in which people did the exercise. This is the “classe” variable in the training set. Any of the other variables may be used to predict with. Describe how the model was built, and cross validation used. Calculate the expected out of sample error is. Use the prediction model to predict 20 different test cases.

Loading data

trainUrl <- "http://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv"
testUrl <- "http://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv"
download.file(trainUrl, destfile="./training.csv", method="curl")
download.file(testUrl, destfile="./testing.csv", method="curl")
training<-read.csv("training.csv")
testing<-read.csv("testing.csv")

Partitioning the training set into 2 data sets

The below code loads the required packagesand partitions the training data set into 2 parts, test and train such that 75% of the data set is in train and 25% in test.

library(caret)
library(kernlab)
library(e1071)
## Warning: package 'e1071' was built under R version 3.1.1
inTrain<-createDataPartition(y=training$classe,p=0.75,list=FALSE)
train<-training[inTrain,]
test<-training[-inTrain,]
dim(train)
## [1] 14718   160
dim(test)
## [1] 4904  160

Preprocessing Data

Removing additional variables like username, timestamp and the outcome variable classe:

remove<-c(1:7)
train<-train[,-remove]

Removing near zero variance variables to reduce the number of predictors:

dataNZV<-nearZeroVar(train, saveMetrics=TRUE)
train<-train[,!dataNZV$nzv]

Removing variables with NA values:

cols<-vector()
index<-0
for (i in 1:ncol(train))
{
  if (sum(is.na(train[,i]))/nrow(train) >=0.6)
  {
    index<-index+1
    cols[index]<-i
  }
}
train<-train[,-cols]
dim(train)
## [1] 14718    53

Performing the same on the test and testing data sets:

col1<-colnames(train)
col2<-colnames(train[,-53])
test<-test[col1]
testing<-testing[col2]
dim(test)
## [1] 4904   53
dim(testing)
## [1] 20 52

Building Prediction Model

Decision Tree
library(rpart)
library(rpart.plot)
library(RColorBrewer)
library(rattle)
## Warning: package 'rattle' was built under R version 3.1.1
## Rattle: A free graphical interface for data mining with R.
## Version 3.3.0 Copyright (c) 2006-2014 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.
library(randomForest)
## Warning: package 'randomForest' was built under R version 3.1.1
## randomForest 4.6-10
## Type rfNews() to see new features/changes/bug fixes.
modelFit <- rpart(classe ~ ., data=train, method="class")
fancyRpartPlot(modelFit)
## Warning: labs do not fit even at cex 0.15, there may be some overplotting

plot of chunk model

prediction1 <- predict(modelFit, test, type="class")

Result:

confusionMatrix(prediction1, test$classe)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    A    B    C    D    E
##          A 1255  202   37   65   23
##          B   34  501   24   24   18
##          C   14   57  691  112   65
##          D   78  127   50  520   90
##          E   14   62   53   83  705
## 
## Overall Statistics
##                                         
##                Accuracy : 0.749         
##                  95% CI : (0.736, 0.761)
##     No Information Rate : 0.284         
##     P-Value [Acc > NIR] : <2e-16        
##                                         
##                   Kappa : 0.681         
##  Mcnemar's Test P-Value : <2e-16        
## 
## Statistics by Class:
## 
##                      Class: A Class: B Class: C Class: D Class: E
## Sensitivity             0.900    0.528    0.808    0.647    0.782
## Specificity             0.907    0.975    0.939    0.916    0.947
## Pos Pred Value          0.793    0.834    0.736    0.601    0.769
## Neg Pred Value          0.958    0.896    0.959    0.930    0.951
## Prevalence              0.284    0.194    0.174    0.164    0.184
## Detection Rate          0.256    0.102    0.141    0.106    0.144
## Detection Prevalence    0.323    0.123    0.191    0.176    0.187
## Balanced Accuracy       0.903    0.751    0.873    0.781    0.865

This model is 74.9% accurate. Using random forests as the prediction model:

Random Forests

Building the model:

modelFit2 <- randomForest(classe ~. , data=train)
prediction2 <- predict(modelFit2, test, type = "class")

Result:

confusionMatrix(prediction2, test$classe)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    A    B    C    D    E
##          A 1395    0    0    0    0
##          B    0  949    2    0    0
##          C    0    0  853    7    0
##          D    0    0    0  797    0
##          E    0    0    0    0  901
## 
## Overall Statistics
##                                         
##                Accuracy : 0.998         
##                  95% CI : (0.997, 0.999)
##     No Information Rate : 0.284         
##     P-Value [Acc > NIR] : <2e-16        
##                                         
##                   Kappa : 0.998         
##  Mcnemar's Test P-Value : NA            
## 
## Statistics by Class:
## 
##                      Class: A Class: B Class: C Class: D Class: E
## Sensitivity             1.000    1.000    0.998    0.991    1.000
## Specificity             1.000    0.999    0.998    1.000    1.000
## Pos Pred Value          1.000    0.998    0.992    1.000    1.000
## Neg Pred Value          1.000    1.000    1.000    0.998    1.000
## Prevalence              0.284    0.194    0.174    0.164    0.184
## Detection Rate          0.284    0.194    0.174    0.163    0.184
## Detection Prevalence    0.284    0.194    0.175    0.163    0.184
## Balanced Accuracy       1.000    1.000    0.998    0.996    1.000

We now get an accuracy of 99.3%.

Final Result:

Using random forests gave an accuracy of 99.3%, hence this model is more effective than decision trees. The expected out-of-sample error is 0.7% (100-99.3).

Prediction on the test sample

finalPrediction<-predict(modelFit2,test, type= "class")
finalPrediction
##     2     3     7    14    15    20    24    29    30    31    32    36 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##    37    41    44    47    52    60    64    65    67    70    75    79 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##    82    86    87    94   106   112   113   115   116   120   125   133 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   136   137   139   140   142   145   153   158   159   160   164   165 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   167   183   185   193   198   199   202   209   215   221   226   230 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   234   238   239   242   244   249   251   252   254   255   266   267 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   269   274   277   280   285   286   289   296   298   301   309   310 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   311   314   316   317   318   319   334   336   337   347   352   356 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   357   363   368   375   376   380   381   382   384   385   392   394 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   399   401   402   406   410   411   412   415   417   419   422   423 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   428   432   433   448   451   452   453   454   455   457   459   478 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   482   484   485   486   487   492   493   494   501   504   507   508 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   512   515   521   522   523   534   536   543   544   545   546   548 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   549   550   557   562   565   566   567   575   576   579   581   584 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   592   596   602   603   604   610   611   615   617   618   620   637 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   638   641   644   645   647   650   652   656   660   676   681   682 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   683   684   687   696   702   704   705   708   709   710   711   726 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   727   729   734   749   751   754   756   757   758   759   761   766 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   776   781   782   784   785   788   794   798   799   800   802   805 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   806   807   809   811   813   814   815   818   822   823   833   835 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   836   843   844   855   857   858   865   866   869   871   878   886 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   892   894   896   905   906   907   908   910   918   922   928   931 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   932   935   941   949   956   959   968   971   976   977   978   981 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##   984   985   990   991   993  1003  1004  1008  1009  1010  1019  1021 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1024  1031  1032  1037  1040  1043  1047  1050  1052  1058  1059  1061 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1064  1065  1072  1075  1092  1093  1098  1099  1100  1101  1102  1104 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1108  1111  1114  1118  1121  1126  1127  1134  1135  1140  1144  1145 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1148  1149  1153  1154  1161  1164  1165  1168  1170  1172  1173  1177 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1179  1180  1182  1183  1185  1186  1191  1199  1202  1205  1210  1213 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1222  1223  1229  1230  1232  1239  1243  1249  1254  1261  1263  1265 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1271  1272  1277  1281  1284  1295  1297  1298  1302  1310  1316  1325 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1326  1328  1336  1339  1340  1341  1342  1343  1344  1346  1354  1365 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1366  1373  1383  1384  1386  1387  1393  1394  1395  1402  1412  1422 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1427  1434  1435  1436  1438  1443  1450  1460  1461  1462  1467  1469 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1470  1481  1488  1489  1490  1491  1494  1500  1512  1515  1517  1531 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1539  1542  1550  1551  1556  1563  1564  1567  1571  1574  1575  1578 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1580  1583  1586  1588  1594  1596  1605  1610  1617  1618  1619  1622 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1624  1629  1633  1634  1639  1646  1648  1660  1661  1663  1664  1667 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1669  1673  1684  1686  1690  1691  1694  1701  1706  1717  1721  1722 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1724  1730  1737  1744  1745  1748  1749  1753  1755  1758  1761  1763 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1766  1767  1768  1783  1787  1790  1793  1799  1811  1813  1819  1830 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1841  1845  1853  1860  1866  1870  1871  1873  1875  1879  1885  1892 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1893  1894  1897  1905  1907  1911  1917  1923  1924  1928  1938  1947 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  1964  1975  1984  1985  1986  2011  2019  2022  2034  2037  2040  2045 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2046  2049  2050  2065  2068  2071  2073  2075  2085  2099  2111  2119 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2126  2134  2136  2137  2138  2140  2141  2142  2143  2149  2152  2155 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2158  2162  2163  2167  2170  2177  2178  2180  2183  2185  2191  2196 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2197  2205  2208  2209  2210  2212  2215  2218  2220  2225  2236  2239 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2248  2249  2261  2264  2272  2281  2287  2290  2298  2301  2304  2306 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2314  2315  2327  2328  2331  2344  2347  2348  2357  2358  2360  2364 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2370  2374  2375  2379  2382  2385  2386  2387  2390  2392  2397  2398 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2400  2402  2403  2407  2411  2418  2422  2423  2424  2426  2428  2431 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2435  2447  2450  2451  2456  2457  2462  2463  2471  2475  2480  2485 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2487  2489  2493  2495  2497  2502  2510  2515  2519  2525  2532  2536 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2539  2543  2547  2553  2559  2565  2566  2571  2579  2582  2584  2592 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2593  2594  2596  2597  2602  2606  2612  2621  2625  2628  2631  2637 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2639  2641  2661  2663  2664  2668  2669  2670  2673  2681  2683  2686 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2687  2699  2701  2706  2708  2710  2714  2730  2731  2733  2736  2743 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2757  2763  2764  2766  2769  2781  2796  2800  2801  2807  2809  2811 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2812  2815  2819  2822  2823  2824  2828  2830  2836  2839  2842  2844 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2846  2851  2857  2858  2865  2872  2875  2892  2898  2914  2917  2918 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2921  2923  2924  2925  2927  2930  2932  2933  2940  2952  2954  2961 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  2965  2967  2974  2983  2984  2985  2987  2990  2992  2994  2996  3002 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3007  3013  3015  3022  3023  3024  3026  3027  3032  3040  3048  3066 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3070  3071  3073  3075  3080  3082  3083  3086  3089  3090  3092  3095 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3096  3101  3105  3108  3110  3116  3118  3121  3124  3125  3128  3129 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3131  3132  3138  3148  3154  3156  3158  3161  3163  3167  3172  3178 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3182  3183  3193  3195  3199  3200  3211  3214  3216  3221  3226  3228 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3234  3245  3254  3255  3257  3260  3262  3263  3264  3281  3283  3284 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3287  3293  3294  3298  3306  3312  3316  3317  3323  3325  3328  3334 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3343  3344  3346  3350  3355  3356  3363  3365  3366  3369  3377  3378 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3385  3388  3389  3392  3400  3401  3406  3413  3416  3418  3421  3422 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3423  3433  3436  3443  3447  3456  3464  3468  3470  3475  3484  3492 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3494  3499  3500  3503  3504  3510  3517  3523  3527  3528  3532  3534 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3542  3545  3552  3553  3554  3555  3557  3560  3561  3563  3564  3566 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3569  3583  3584  3585  3588  3592  3593  3597  3607  3610  3611  3617 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3618  3621  3623  3629  3630  3631  3632  3635  3645  3648  3651  3657 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3666  3672  3673  3675  3677  3682  3683  3692  3702  3705  3708  3717 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3719  3724  3728  3734  3736  3748  3750  3751  3752  3753  3762  3764 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3768  3779  3782  3787  3794  3800  3804  3805  3815  3819  3820  3822 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3825  3827  3834  3839  3842  3845  3846  3851  3852  3853  3869  3873 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3884  3887  3896  3901  3903  3905  3915  3917  3919  3926  3927  3929 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3931  3934  3935  3937  3943  3948  3962  3963  3964  3965  3969  3972 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  3974  3980  4000  4001  4008  4010  4013  4017  4020  4024  4025  4032 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4041  4043  4053  4054  4055  4065  4069  4070  4071  4073  4078  4080 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4097  4099  4101  4106  4111  4114  4115  4117  4119  4123  4124  4127 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4132  4136  4161  4167  4168  4169  4171  4177  4178  4182  4183  4184 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4186  4189  4190  4192  4193  4196  4204  4219  4222  4223  4229  4230 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4231  4233  4235  4241  4249  4250  4251  4252  4254  4255  4256  4262 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4264  4265  4271  4272  4277  4282  4287  4294  4301  4305  4308  4309 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4319  4320  4326  4329  4330  4332  4334  4336  4339  4349  4350  4351 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4353  4359  4363  4375  4380  4385  4393  4403  4404  4408  4412  4414 
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##  4418  4419  4431  4432  4442  4443  4449  4450  4456  4462  4463  4466 
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##  4470  4471  4479  4482  4484  4488  4491  4495  4499  4502  4508  4522 
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##  4528  4529  4543  4544  4548  4552  4553  4557  4573  4581  4582  4586 
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##  4591  4599  4600  4601  4604  4607  4609  4612  4620  4622  4625  4626 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4627  4635  4637  4639  4649  4651  4656  4657  4660  4661  4671  4676 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4681  4685  4687  4690  4693  4706  4709  4710  4724  4727  4737  4739 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4746  4757  4761  4764  4767  4771  4778  4785  4787  4788  4789  4794 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4798  4806  4810  4815  4824  4836  4842  4849  4850  4861  4863  4865 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4870  4871  4878  4880  4888  4889  4890  4896  4898  4900  4903  4908 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4911  4914  4917  4919  4921  4924  4926  4927  4930  4937  4956  4958 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  4959  4966  4967  4970  4976  4977  4982  4983  4989  4991  5002  5004 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5006  5010  5012  5015  5019  5025  5030  5032  5033  5034  5035  5036 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5039  5042  5044  5048  5055  5056  5061  5068  5069  5072  5073  5076 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5077  5078  5083  5087  5090  5095  5101  5102  5103  5106  5108  5109 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5117  5118  5119  5120  5126  5133  5135  5136  5142  5148  5149  5153 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5155  5157  5166  5170  5171  5184  5185  5186  5188  5191  5194  5196 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5204  5207  5218  5227  5228  5230  5231  5232  5237  5238  5251  5257 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5259  5265  5268  5272  5273  5274  5275  5276  5278  5286  5295  5301 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5303  5307  5309  5312  5316  5320  5323  5331  5341  5342  5347  5349 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5359  5362  5363  5365  5374  5376  5379  5382  5386  5390  5392  5393 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5395  5398  5399  5400  5406  5413  5417  5419  5421  5425  5426  5427 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5429  5434  5435  5436  5443  5444  5447  5451  5452  5463  5465  5472 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5473  5476  5478  5488  5505  5506  5507  5508  5511  5517  5527  5530 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5535  5538  5540  5541  5552  5555  5557  5560  5561  5563  5567  5573 
##     A     A     A     A     A     A     A     A     A     A     A     A 
##  5575  5577  5579  5583  5584  5590  5592  5597  5601  5603  5608  5612 
##     A     A     A     B     B     B     B     B     B     B     B     B 
##  5615  5619  5620  5622  5624  5625  5627  5629  5633  5642  5643  5644 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5645  5646  5656  5673  5675  5680  5682  5683  5687  5691  5696  5700 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5714  5716  5735  5737  5740  5743  5744  5751  5754  5758  5759  5760 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5765  5766  5770  5772  5778  5783  5796  5798  5800  5811  5813  5816 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5825  5828  5834  5835  5838  5842  5843  5848  5850  5855  5862  5873 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5875  5877  5880  5882  5885  5888  5890  5893  5895  5901  5906  5915 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5916  5919  5920  5921  5922  5924  5925  5928  5929  5933  5934  5935 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5936  5937  5939  5944  5947  5948  5960  5965  5974  5976  5978  5988 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  5990  6002  6004  6005  6026  6028  6032  6038  6041  6046  6057  6058 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6059  6060  6062  6070  6074  6081  6084  6085  6091  6092  6094  6097 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6099  6107  6108  6110  6114  6118  6124  6126  6129  6131  6134  6142 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6154  6157  6159  6160  6161  6167  6170  6177  6181  6183  6191  6197 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6198  6199  6202  6204  6214  6216  6219  6221  6226  6229  6230  6232 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6233  6237  6246  6252  6261  6263  6267  6272  6279  6281  6283  6289 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6295  6300  6302  6305  6307  6309  6313  6317  6326  6332  6335  6338 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6347  6348  6349  6350  6352  6355  6366  6370  6372  6378  6384  6385 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6394  6397  6400  6410  6412  6415  6416  6424  6426  6432  6435  6440 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6452  6453  6459  6466  6476  6481  6483  6490  6491  6502  6504  6507 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6510  6511  6514  6515  6525  6527  6528  6533  6536  6538  6540  6542 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6543  6550  6557  6563  6564  6568  6571  6572  6574  6581  6585  6588 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6592  6595  6598  6605  6607  6609  6613  6623  6624  6625  6627  6628 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6632  6633  6635  6637  6641  6642  6650  6651  6660  6663  6664  6665 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6678  6682  6683  6687  6688  6691  6695  6716  6717  6732  6734  6737 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6740  6743  6747  6748  6751  6754  6758  6760  6765  6767  6770  6773 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6775  6777  6782  6783  6785  6791  6792  6793  6794  6801  6802  6808 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6818  6819  6822  6825  6828  6829  6834  6836  6838  6841  6843  6847 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6848  6849  6850  6854  6855  6861  6863  6865  6867  6872  6882  6885 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6886  6891  6893  6896  6897  6901  6903  6915  6916  6918  6919  6921 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6925  6931  6932  6935  6941  6947  6949  6951  6955  6961  6963  6966 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  6971  6974  6976  6980  6984  6993  6994  6995  7004  7012  7013  7014 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7020  7021  7028  7032  7034  7035  7037  7039  7044  7050  7053  7054 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7058  7067  7072  7074  7085  7094  7096  7097  7098  7099  7101  7102 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7106  7115  7116  7117  7119  7124  7126  7128  7129  7150  7151  7153 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7155  7156  7164  7167  7169  7170  7172  7175  7186  7200  7211  7212 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7213  7216  7221  7222  7226  7248  7251  7260  7264  7269  7275  7279 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7283  7287  7289  7294  7295  7296  7298  7311  7322  7327  7329  7337 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7339  7341  7342  7345  7348  7354  7361  7362  7365  7366  7368  7369 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7372  7375  7376  7377  7380  7391  7395  7396  7411  7413  7415  7425 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7429  7431  7432  7433  7436  7437  7438  7444  7446  7447  7448  7452 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7455  7459  7460  7466  7470  7471  7472  7474  7479  7486  7488  7489 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7492  7497  7498  7500  7501  7505  7506  7507  7508  7509  7514  7520 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7530  7531  7535  7538  7542  7552  7553  7564  7566  7567  7583  7584 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7590  7592  7593  7599  7602  7604  7612  7613  7623  7635  7642  7646 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7647  7650  7667  7670  7673  7676  7677  7678  7679  7686  7691  7693 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7714  7722  7723  7729  7732  7734  7735  7740  7741  7743  7744  7747 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7754  7779  7781  7784  7785  7787  7800  7803  7813  7818  7820  7823 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7824  7829  7830  7831  7835  7840  7841  7848  7849  7864  7865  7867 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7868  7869  7870  7873  7874  7880  7882  7885  7890  7898  7899  7907 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7921  7923  7938  7939  7942  7948  7951  7964  7968  7971  7973  7980 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  7983  7987  7997  7999  8001  8002  8003  8005  8007  8011  8026  8027 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8032  8037  8050  8056  8057  8059  8060  8063  8070  8071  8076  8077 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8088  8091  8097  8099  8101  8104  8106  8108  8117  8121  8122  8124 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8128  8130  8132  8136  8147  8149  8150  8151  8159  8161  8162  8167 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8176  8178  8179  8189  8197  8203  8205  8208  8213  8215  8216  8217 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8220  8222  8226  8240  8242  8244  8249  8252  8257  8259  8260  8262 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8263  8276  8284  8290  8293  8296  8308  8311  8313  8330  8333  8334 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8339  8344  8345  8346  8347  8349  8351  8356  8358  8365  8372  8375 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8379  8380  8385  8391  8393  8394  8395  8397  8400  8405  8406  8411 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8415  8418  8420  8421  8423  8431  8446  8447  8449  8452  8455  8456 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8458  8468  8471  8474  8481  8486  8496  8498  8502  8503  8510  8517 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8521  8528  8531  8534  8542  8549  8552  8554  8562  8570  8573  8574 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8575  8578  8579  8581  8584  8587  8590  8595  8598  8601  8602  8606 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8611  8612  8614  8623  8625  8627  8631  8632  8635  8647  8649  8650 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8654  8663  8668  8670  8672  8678  8680  8681  8684  8688  8698  8700 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8705  8710  8716  8717  8718  8723  8729  8741  8742  8748  8751  8753 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8754  8757  8761  8766  8769  8775  8776  8782  8793  8794  8795  8797 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8799  8801  8806  8808  8810  8811  8822  8823  8829  8833  8834  8839 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8844  8856  8861  8862  8869  8882  8884  8886  8891  8892  8898  8901 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8902  8904  8915  8916  8917  8918  8919  8923  8925  8926  8928  8930 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8937  8940  8941  8944  8953  8957  8963  8966  8977  8980  8981  8985 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  8986  8991  8992  8994  9009  9011  9020  9022  9025  9031  9032  9041 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9046  9049  9057  9060  9061  9067  9068  9085  9088  9096  9102  9104 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9106  9111  9113  9119  9120  9129  9131  9132  9143  9144  9148  9150 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9160  9161  9166  9170  9172  9175  9180  9181  9184  9188  9190  9191 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9193  9197  9202  9204  9207  9209  9215  9220  9222  9223  9226  9239 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9241  9242  9245  9249  9252  9253  9261  9266  9274  9276  9296  9305 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9306  9309  9313  9314  9316  9317  9318  9328  9329  9331  9334  9335 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9336  9337  9342  9343  9344  9347  9350  9351  9352  9353  9359  9361 
##     B     B     B     B     B     B     B     B     B     B     B     B 
##  9363  9364  9368  9373  9381  9391  9392  9394  9409  9411  9412  9414 
##     B     B     B     B     C     C     C     C     C     C     C     C 
##  9415  9421  9422  9426  9427  9429  9430  9431  9443  9448  9451  9453 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9457  9460  9463  9464  9467  9473  9480  9481  9484  9495  9496  9499 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9500  9503  9504  9505  9514  9518  9525  9528  9532  9537  9544  9554 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9555  9558  9560  9563  9564  9566  9569  9571  9575  9584  9590  9594 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9595  9597  9599  9601  9611  9613  9614  9616  9626  9638  9640  9644 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9652  9660  9667  9672  9673  9675  9676  9679  9683  9684  9694  9697 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9700  9702  9704  9705  9710  9721  9722  9724  9725  9727  9733  9734 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9735  9738  9742  9749  9752  9755  9758  9759  9765  9775  9779  9781 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9782  9786  9795  9805  9809  9811  9815  9823  9826  9831  9839  9841 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9844  9845  9846  9848  9849  9851  9871  9872  9873  9875  9880  9882 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9895  9905  9906  9912  9913  9917  9918  9919  9920  9922  9932  9936 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9937  9938  9940  9946  9947  9950  9951  9955  9958  9963  9964  9969 
##     C     C     C     C     C     C     C     C     C     C     C     C 
##  9980  9982  9983  9987  9995  9997 10000 10001 10007 10008 10010 10011 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10014 10022 10028 10038 10043 10047 10049 10050 10052 10054 10059 10062 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10069 10074 10075 10078 10081 10084 10091 10093 10095 10109 10110 10116 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10119 10121 10131 10134 10138 10142 10154 10156 10159 10172 10173 10175 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10178 10181 10182 10183 10190 10191 10198 10206 10217 10220 10226 10231 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10237 10243 10245 10250 10258 10259 10265 10271 10277 10281 10282 10284 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10292 10294 10299 10301 10302 10304 10310 10311 10316 10317 10320 10321 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10323 10324 10335 10339 10340 10343 10349 10354 10364 10367 10369 10370 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10376 10378 10382 10390 10391 10392 10400 10401 10403 10407 10411 10412 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10414 10415 10423 10424 10430 10434 10441 10443 10445 10446 10461 10463 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10467 10472 10473 10474 10479 10483 10489 10494 10495 10496 10502 10508 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10514 10516 10520 10521 10525 10527 10528 10529 10530 10534 10538 10540 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10542 10551 10556 10557 10562 10569 10578 10584 10586 10587 10590 10596 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10606 10614 10616 10620 10621 10627 10630 10632 10645 10651 10652 10653 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10654 10661 10663 10668 10673 10678 10682 10684 10686 10687 10693 10696 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10702 10709 10718 10724 10732 10735 10740 10742 10748 10762 10763 10766 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10772 10778 10779 10781 10793 10794 10799 10800 10806 10812 10814 10816 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10818 10822 10824 10834 10843 10845 10850 10853 10855 10858 10877 10878 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10887 10888 10890 10892 10893 10905 10906 10910 10920 10922 10923 10926 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10930 10932 10933 10935 10936 10938 10942 10945 10949 10950 10951 10956 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 10972 10974 10975 10984 10989 10997 10998 11000 11004 11009 11013 11016 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11022 11024 11026 11027 11029 11030 11036 11037 11042 11046 11051 11053 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11059 11064 11067 11070 11077 11078 11087 11091 11092 11093 11097 11098 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11100 11102 11110 11111 11121 11123 11124 11125 11131 11144 11152 11155 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11157 11158 11159 11165 11166 11169 11172 11175 11179 11194 11210 11215 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11221 11226 11233 11235 11236 11240 11244 11246 11249 11253 11262 11264 
##     C     C     C     B     C     C     C     C     C     C     C     C 
## 11267 11269 11270 11276 11279 11282 11283 11286 11298 11304 11306 11315 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11316 11320 11323 11325 11327 11328 11329 11331 11341 11345 11350 11354 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11355 11357 11365 11370 11371 11381 11382 11384 11389 11392 11393 11394 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11396 11399 11406 11407 11415 11416 11420 11425 11426 11427 11429 11436 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11441 11442 11443 11454 11456 11459 11461 11462 11475 11482 11487 11490 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11497 11502 11507 11510 11512 11519 11522 11523 11531 11533 11537 11538 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11546 11552 11556 11567 11570 11571 11573 11576 11578 11582 11588 11591 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11592 11597 11601 11612 11617 11618 11620 11623 11630 11633 11642 11648 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11654 11659 11661 11672 11674 11675 11680 11681 11690 11693 11695 11696 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11701 11706 11707 11711 11713 11715 11718 11721 11722 11724 11726 11740 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11749 11753 11754 11755 11761 11764 11765 11766 11772 11774 11780 11786 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11794 11799 11801 11810 11811 11813 11814 11816 11817 11821 11825 11827 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11828 11832 11833 11838 11840 11848 11851 11854 11856 11867 11871 11878 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11881 11883 11885 11889 11891 11893 11899 11901 11910 11912 11916 11920 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 11922 11931 11936 11952 11953 11955 11957 11958 11962 11963 11964 11965 
##     C     C     C     C     C     C     C     B     C     C     C     C 
## 11968 11970 11973 11980 11984 11990 11991 11992 11999 12000 12001 12002 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12009 12013 12015 12017 12027 12028 12037 12038 12043 12045 12047 12052 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12059 12061 12062 12066 12075 12078 12080 12088 12089 12097 12098 12099 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12101 12102 12105 12111 12114 12119 12121 12138 12139 12143 12146 12147 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12152 12162 12166 12167 12176 12197 12198 12202 12212 12218 12221 12224 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12225 12231 12232 12233 12235 12236 12239 12241 12243 12244 12245 12249 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12251 12253 12254 12268 12279 12284 12286 12288 12292 12295 12298 12303 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12310 12320 12321 12325 12336 12337 12341 12344 12346 12347 12353 12354 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12362 12363 12366 12369 12373 12377 12383 12385 12397 12398 12401 12406 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12407 12409 12410 12411 12419 12428 12431 12434 12440 12444 12446 12455 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12458 12463 12464 12470 12471 12473 12474 12475 12480 12481 12497 12499 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12503 12504 12508 12512 12515 12518 12519 12523 12524 12525 12528 12534 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12535 12538 12542 12543 12546 12549 12551 12560 12561 12568 12572 12575 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12576 12578 12581 12582 12586 12588 12594 12596 12607 12610 12612 12614 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12617 12624 12625 12636 12637 12641 12648 12656 12662 12665 12667 12674 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12676 12690 12691 12693 12694 12696 12700 12706 12708 12713 12717 12720 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12723 12727 12729 12732 12733 12737 12742 12743 12744 12748 12759 12771 
##     C     C     C     C     C     C     C     C     C     C     C     C 
## 12775 12780 12783 12785 12787 12793 12799 12801 12802 12805 12809 12819 
##     C     C     C     C     C     C     C     D     D     D     D     D 
## 12823 12830 12836 12838 12844 12845 12847 12858 12863 12866 12869 12878 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 12881 12882 12901 12902 12908 12909 12912 12917 12918 12924 12931 12933 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 12942 12948 12959 12966 12971 12976 12982 12994 12997 13011 13017 13025 
##     D     D     D     C     D     D     D     D     D     D     D     D 
## 13027 13032 13037 13042 13050 13051 13055 13057 13058 13068 13075 13076 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13080 13084 13095 13097 13100 13101 13102 13105 13107 13108 13109 13113 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13114 13118 13119 13121 13124 13129 13131 13134 13146 13150 13154 13160 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13166 13167 13170 13172 13173 13177 13182 13185 13187 13190 13193 13194 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13196 13200 13206 13207 13208 13209 13219 13223 13226 13232 13234 13235 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13241 13243 13249 13253 13257 13260 13273 13275 13291 13292 13298 13299 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13304 13307 13308 13309 13316 13319 13320 13326 13329 13333 13334 13339 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13341 13345 13359 13360 13362 13364 13376 13378 13380 13383 13385 13386 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13390 13391 13392 13395 13403 13407 13413 13415 13416 13422 13427 13437 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13438 13441 13442 13445 13446 13450 13460 13463 13464 13467 13468 13469 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13471 13472 13475 13476 13490 13494 13498 13500 13506 13509 13514 13520 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13523 13524 13525 13528 13529 13531 13535 13540 13546 13548 13550 13552 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13556 13557 13559 13567 13568 13571 13573 13577 13588 13591 13595 13603 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13606 13609 13616 13617 13621 13627 13635 13637 13640 13642 13648 13649 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13652 13653 13658 13659 13663 13674 13675 13678 13684 13686 13689 13690 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13696 13697 13704 13705 13710 13712 13713 13717 13718 13721 13727 13728 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13740 13746 13751 13756 13757 13760 13770 13776 13780 13781 13783 13784 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13789 13791 13795 13801 13809 13818 13823 13824 13827 13828 13835 13846 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13851 13854 13855 13859 13869 13876 13877 13878 13879 13882 13883 13888 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13898 13905 13906 13910 13912 13913 13917 13922 13927 13930 13935 13937 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 13947 13957 13961 13963 13965 13975 13977 13987 13988 13993 13998 14007 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14009 14010 14018 14019 14021 14025 14026 14028 14029 14031 14033 14039 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14048 14050 14052 14054 14056 14060 14062 14063 14064 14066 14069 14070 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14072 14073 14084 14085 14089 14090 14095 14096 14097 14101 14107 14112 
##     D     D     C     C     D     D     C     C     C     D     D     D 
## 14114 14118 14121 14122 14127 14129 14131 14138 14140 14142 14157 14159 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14162 14163 14164 14171 14178 14185 14186 14189 14191 14196 14197 14214 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14215 14224 14228 14231 14233 14234 14236 14240 14241 14245 14248 14251 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14255 14271 14272 14281 14283 14284 14285 14286 14288 14289 14294 14295 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14298 14310 14317 14329 14332 14340 14346 14349 14355 14356 14361 14372 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14380 14382 14385 14387 14389 14390 14396 14405 14408 14409 14410 14412 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14413 14415 14416 14419 14422 14430 14433 14448 14460 14463 14464 14467 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14475 14481 14486 14489 14498 14511 14519 14525 14526 14530 14532 14537 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14540 14541 14543 14549 14550 14551 14562 14564 14567 14568 14569 14589 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14591 14592 14595 14596 14598 14599 14602 14606 14607 14608 14613 14614 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14620 14622 14624 14625 14629 14630 14633 14637 14638 14639 14642 14648 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14654 14657 14659 14670 14672 14675 14678 14686 14688 14691 14699 14702 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14707 14709 14711 14712 14724 14727 14728 14729 14730 14734 14739 14745 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14750 14755 14756 14758 14759 14761 14766 14767 14768 14773 14774 14779 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14785 14787 14791 14794 14806 14814 14815 14816 14817 14819 14832 14833 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14839 14840 14841 14843 14853 14863 14874 14879 14882 14886 14888 14890 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14894 14895 14896 14901 14909 14911 14912 14914 14915 14922 14924 14928 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14936 14939 14941 14945 14946 14952 14955 14958 14959 14967 14968 14970 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 14974 14983 14986 14991 14995 14998 15000 15005 15009 15010 15013 15017 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15018 15019 15024 15028 15029 15031 15045 15047 15048 15063 15065 15070 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15072 15073 15075 15081 15083 15084 15088 15090 15095 15096 15101 15104 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15106 15107 15108 15109 15118 15120 15121 15123 15124 15137 15144 15150 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15161 15162 15164 15185 15186 15188 15190 15194 15195 15204 15206 15213 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15218 15222 15225 15227 15230 15234 15235 15242 15244 15246 15247 15248 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15251 15253 15255 15257 15258 15263 15271 15278 15280 15281 15283 15284 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15288 15299 15302 15303 15308 15309 15310 15312 15315 15318 15324 15325 
##     D     D     D     D     D     D     D     D     D     D     C     D 
## 15350 15351 15353 15359 15363 15364 15365 15368 15371 15374 15378 15380 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15385 15388 15389 15393 15395 15403 15405 15410 15417 15418 15426 15428 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15429 15430 15433 15435 15436 15440 15442 15446 15455 15457 15461 15462 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15467 15471 15482 15489 15491 15494 15495 15499 15503 15512 15518 15532 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15534 15536 15537 15539 15542 15546 15549 15550 15554 15569 15573 15574 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15577 15579 15608 15609 15610 15611 15616 15617 15622 15625 15630 15633 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15635 15636 15637 15639 15641 15659 15660 15661 15664 15665 15666 15673 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15679 15686 15690 15700 15708 15710 15718 15719 15724 15726 15727 15732 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15737 15741 15746 15747 15749 15754 15756 15758 15769 15775 15777 15783 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15786 15790 15793 15797 15798 15804 15812 15813 15815 15816 15818 15826 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15827 15832 15833 15841 15842 15852 15853 15854 15855 15857 15865 15870 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15877 15879 15880 15884 15892 15895 15906 15919 15922 15923 15930 15934 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15936 15940 15944 15957 15964 15965 15971 15974 15977 15979 15983 15992 
##     D     D     D     D     D     D     D     D     D     D     D     D 
## 15993 15995 15997 16001 16003 16005 16007 16016 16019 16030 16031 16034 
##     D     D     D     D     D     D     D     E     E     E     E     E 
## 16038 16051 16053 16055 16057 16058 16061 16063 16065 16069 16072 16076 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16077 16080 16084 16086 16087 16089 16090 16092 16093 16094 16105 16107 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16110 16111 16117 16122 16123 16124 16125 16127 16129 16131 16133 16135 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16138 16143 16146 16151 16155 16161 16164 16165 16166 16169 16174 16178 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16183 16185 16186 16187 16189 16190 16192 16193 16197 16199 16202 16208 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16209 16212 16219 16223 16224 16228 16230 16231 16232 16235 16242 16250 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16266 16267 16275 16280 16290 16293 16294 16311 16314 16333 16340 16344 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16353 16356 16361 16364 16365 16371 16376 16377 16379 16381 16390 16396 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16411 16414 16415 16416 16425 16432 16435 16441 16445 16448 16449 16450 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16454 16459 16461 16462 16463 16466 16471 16473 16477 16479 16481 16485 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16495 16499 16500 16510 16515 16519 16521 16523 16526 16531 16532 16537 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16544 16546 16547 16548 16552 16554 16555 16556 16562 16563 16570 16573 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16575 16578 16580 16581 16586 16587 16588 16589 16591 16598 16602 16604 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16607 16608 16613 16616 16624 16631 16636 16645 16657 16658 16659 16664 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16682 16691 16693 16694 16695 16714 16727 16733 16734 16738 16739 16744 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16747 16750 16753 16755 16769 16772 16774 16779 16781 16784 16785 16787 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16788 16791 16795 16803 16811 16813 16817 16822 16824 16826 16830 16831 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16837 16841 16847 16862 16869 16872 16874 16880 16883 16884 16889 16902 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16907 16918 16921 16925 16926 16934 16936 16939 16943 16946 16959 16966 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 16968 16969 16970 16984 16994 16995 16996 16999 17002 17005 17009 17016 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17017 17024 17025 17039 17040 17042 17045 17050 17056 17063 17068 17070 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17071 17078 17082 17085 17086 17092 17093 17109 17118 17121 17122 17123 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17126 17129 17133 17141 17147 17151 17157 17159 17165 17168 17171 17172 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17181 17193 17195 17202 17204 17211 17216 17221 17228 17230 17232 17233 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17235 17236 17237 17239 17240 17243 17245 17252 17256 17258 17268 17275 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17277 17279 17280 17282 17283 17293 17295 17297 17299 17300 17304 17310 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17311 17312 17314 17319 17331 17335 17339 17343 17345 17349 17350 17353 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17356 17359 17361 17369 17374 17375 17376 17378 17379 17381 17383 17389 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17390 17393 17396 17398 17406 17407 17412 17413 17415 17416 17422 17425 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17428 17436 17437 17438 17440 17443 17447 17450 17456 17462 17465 17468 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17472 17473 17476 17480 17482 17488 17492 17499 17502 17504 17510 17516 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17517 17522 17524 17528 17530 17533 17536 17537 17539 17540 17545 17548 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17549 17557 17558 17560 17565 17566 17573 17574 17579 17581 17582 17588 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17589 17590 17591 17592 17599 17606 17609 17618 17628 17635 17653 17655 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17657 17665 17669 17670 17671 17673 17675 17677 17680 17682 17683 17686 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17687 17688 17689 17695 17704 17705 17729 17735 17740 17741 17744 17745 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17755 17760 17765 17769 17777 17781 17784 17789 17790 17804 17805 17807 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17808 17810 17812 17813 17816 17819 17821 17830 17838 17839 17846 17848 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17852 17853 17868 17869 17872 17876 17877 17884 17896 17899 17902 17911 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17912 17913 17917 17936 17939 17947 17949 17954 17956 17962 17965 17975 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 17980 17981 17982 17983 17989 17994 18002 18010 18021 18023 18024 18034 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18035 18038 18041 18046 18047 18050 18056 18058 18064 18065 18081 18085 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18094 18095 18100 18101 18106 18109 18113 18115 18119 18120 18123 18124 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18125 18128 18129 18132 18144 18148 18152 18159 18162 18165 18169 18171 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18174 18178 18182 18184 18185 18193 18194 18201 18204 18206 18208 18209 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18215 18217 18222 18224 18226 18232 18234 18239 18245 18246 18265 18270 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18271 18274 18280 18289 18292 18298 18299 18301 18304 18307 18313 18315 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18319 18320 18325 18327 18340 18343 18362 18366 18367 18374 18380 18382 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18386 18392 18394 18398 18399 18403 18404 18406 18413 18416 18419 18420 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18422 18423 18425 18433 18434 18439 18443 18444 18447 18448 18450 18456 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18457 18458 18461 18463 18468 18480 18485 18487 18489 18492 18494 18496 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18500 18501 18503 18505 18513 18523 18525 18526 18527 18531 18533 18535 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18536 18538 18550 18551 18552 18556 18565 18567 18572 18574 18575 18587 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18592 18594 18595 18600 18602 18603 18606 18610 18614 18623 18624 18630 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18631 18634 18636 18637 18640 18641 18644 18646 18655 18656 18657 18659 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18663 18670 18673 18676 18682 18683 18684 18696 18699 18706 18712 18713 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18715 18716 18724 18728 18729 18735 18744 18745 18747 18761 18764 18765 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18775 18778 18779 18780 18781 18784 18789 18797 18806 18809 18810 18815 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18817 18818 18822 18828 18832 18835 18836 18839 18841 18843 18844 18847 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18854 18856 18859 18866 18867 18869 18873 18888 18890 18891 18897 18898 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18901 18902 18903 18905 18913 18922 18927 18933 18935 18937 18939 18945 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18950 18952 18953 18957 18958 18965 18967 18970 18975 18978 18979 18984 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 18988 18990 18995 19001 19006 19011 19013 19020 19022 19028 19029 19040 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19047 19051 19055 19057 19065 19067 19072 19078 19082 19084 19085 19099 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19103 19105 19106 19108 19113 19119 19126 19129 19131 19140 19141 19155 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19156 19157 19167 19173 19184 19186 19190 19195 19199 19200 19206 19213 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19216 19219 19222 19224 19230 19234 19237 19241 19243 19251 19254 19255 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19256 19261 19265 19271 19272 19273 19274 19275 19276 19278 19281 19283 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19299 19300 19301 19304 19314 19319 19320 19323 19335 19339 19343 19347 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19351 19352 19356 19360 19364 19365 19369 19373 19375 19376 19379 19389 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19391 19395 19399 19406 19410 19416 19423 19425 19429 19432 19436 19438 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19440 19444 19445 19448 19450 19453 19468 19476 19485 19487 19490 19492 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19498 19500 19503 19504 19516 19522 19523 19525 19528 19533 19535 19538 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19541 19542 19544 19553 19561 19571 19574 19575 19581 19583 19591 19596 
##     E     E     E     E     E     E     E     E     E     E     E     E 
## 19599 19600 19604 19606 19607 19609 19615 19621 
##     E     E     E     E     E     E     E     E 
## Levels: A B C D E