CS112 Assignment 2, Fall 2020

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QUESTION 1

STEP 1

Create a set of 1000 outcome observations using a data-generating process (DGP) that incorporates a systematic component and a stochastic component (of your choice)

# YOUR CODE HERE

#systematic element
age = sample(7:90, 1000, replace = TRUE)
income = sample(30000:500000, 1000)

#stochastic element
noise = rnorm(1000)

#equation
climate_awareness =floor(age * -0.1 + income*0.00003 + noise*0.03)

#clean up the data so that it has a range between 0 and 10
climate_awareness = lapply(climate_awareness,function(x) ifelse(x > 10, 10, x))
climate_awareness = lapply(climate_awareness,function(x) ifelse(x < 0, 0, x))
climate_awareness = as.numeric(climate_awareness)
hist(climate_awareness)

STEP 2

Tell a 2-3 sentence story about the data generating process you coded up above. What is it about and what each component mean?

This is a fake survey data on how aware people are about climate change based on their age and income. So the older the person, the less likely they are to know about climate change. The higher their income, the more likely they are to know about climate change. The noise reflect other variables we did not measure, for instance, level of education, countries, etc.

STEP 3

Using an incorrect model of the systematic component (of your choice), and using the simulation-based approach covered in class (the arm library, etc.), generate 1 prediction for every observation and calculate and report RMSE. Make sure you write out your model and report your RMSE.

Each prediction should be conditional on the predictor values of the corresponding observation. E.g., when predicting for observation #1, use the predictor values of observation #1.

# YOUR CODE HERE
library(arm)

## Loading required package: Matrix

## Loading required package: lme4

## 
## arm (Version 1.11-2, built: 2020-7-27)

## Working directory is /Users/sherlockieee/Minerva/Second year/CS112

## 
## Attaching package: 'arm'

## The following object is masked from 'package:boot':
## 
##     logit

wrong_model <- lm(climate_awareness ~ income)
wrong_model_sim <- sim(wrong_model, n.sims = 1000)
avg_intercept <- mean(coef(wrong_model_sim)[,1])
avg_coef_income <- mean(coef(wrong_model_sim)[,2])

y_pred <- avg_intercept + income * avg_coef_income 
rmse <- function(real, prediction){sqrt(mean((real-prediction)^2))}
rmse(climate_awareness, y_pred)

## [1] 1.908881

STEP 4

Using the correct model (correct systematic and stochastic components), and using the simulation-based approach covered in class (the arm library, etc.), generate 1 prediction for every observation and calculate & report your RMSE. Once again, write out your model and report your RMSE.

Each prediction should be conditional on the predictor values of the corresponding observation. E.g., when predicting for observation #1, use the predictor values of observation #1.

# YOUR CODE HERE
right_model <- lm(climate_awareness ~ income + age + noise)
right_model_sim <- sim(right_model, n.sims = 1000)

avg_intercept <- mean(coef(right_model_sim)[,1])
avg_coef_income <- mean(coef(right_model_sim)[,2])
avg_coef_age <- mean(coef(right_model_sim)[,3])
avg_coef_noise <- mean(coef(right_model_sim)[,4])

y_pred <- avg_intercept + income * avg_coef_income + age * avg_coef_age + noise * avg_coef_noise
rmse <- function(real, prediction){sqrt(mean((real-prediction)^2))}
rmse(climate_awareness, y_pred)

## [1] 1.103187

STEP 5

Which RMSE is larger: The one from the correct model or the one from the incorrect model? Why?

RMSE from the correct model is lower.

QUESTION 2

Imagine that you want to create a data viz that illustrates the sensitivity of regression to outlier data points. So, you want to create two figures:

One figure that shows a regression line fit to a 2-dimensional (x and y) scatterplot, such that the regression line clearly has a positive slope.

# YOUR CODE HERE
set.seed(1)
library(ggplot2)

## 
## Attaching package: 'ggplot2'

## The following object is masked from 'package:randomForest':
## 
##     margin

X = rnorm(100)
Y = X * 0.5 + 1 + rnorm(100)
df = data.frame(x=X, y=Y)
mod <- lm(Y~X, data=df)
intercept1 <- coef(mod)[1]
slope1 <- coef(mod)[2]

ggplot(df, aes(X, Y)) + geom_point() +
  geom_abline(aes(intercept=intercept1, slope=slope1), col = 'blue', lwd=1)

And, another figure that shows a regression line with a negative slope fit to a scatter plot of the same data plus one additional outlier data point. This one data point is what changes the sign of the regression line’s slope from positive to negative.

# YOUR CODE HERE
X.out = c(X, 10)
Y.out = c(Y, -10)


data.out = data.frame(x=X.out, y=Y.out)

mod2 <- lm(Y.out ~ X.out, data=data.out)
intercept2 <- coef(mod2)[1]
slope2 <- coef(mod2)[2]

ggplot(data.out, aes(X.out, Y.out)) + geom_point() + 
  labs(x = "X", y ="Y") + ggtitle("Effect of outlier") +
   geom_abline(aes(intercept=intercept2, slope=slope2, color='With outlier'), lwd=1)+
  geom_abline(aes(intercept=intercept1, slope=slope1, color='Without outlier'), lwd=1) +
  geom_point(aes(10, -10), col = 'red') + 
  annotate("text", x=9.5, y = -9.5, label="outlier")

  scale_color_manual('Regression Line', values = c("Without outlier" = 'blue', "With outlier" = 'red') )

## <ggproto object: Class ScaleDiscrete, Scale, gg>
##     aesthetics: colour
##     axis_order: function
##     break_info: function
##     break_positions: function
##     breaks: waiver
##     call: call
##     clone: function
##     dimension: function
##     drop: TRUE
##     expand: waiver
##     get_breaks: function
##     get_breaks_minor: function
##     get_labels: function
##     get_limits: function
##     guide: legend
##     is_discrete: function
##     is_empty: function
##     labels: waiver
##     limits: NULL
##     make_sec_title: function
##     make_title: function
##     map: function
##     map_df: function
##     n.breaks.cache: NULL
##     na.translate: TRUE
##     na.value: NA
##     name: Regression Line
##     palette: function
##     palette.cache: NULL
##     position: left
##     range: <ggproto object: Class RangeDiscrete, Range, gg>
##         range: NULL
##         reset: function
##         train: function
##         super:  <ggproto object: Class RangeDiscrete, Range, gg>
##     rescale: function
##     reset: function
##     scale_name: manual
##     train: function
##     train_df: function
##     transform: function
##     transform_df: function
##     super:  <ggproto object: Class ScaleDiscrete, Scale, gg>

Be sure to label the axes and the title the figures appropriately. Include a brief paragraph that explains the number of observations and how you created the data set and the outlier.

QUESTION 3

STEP 1

Using the laLonde data set, run a linear regression that models re78 as a function of age, education, re74, re75, hisp, and black. Note that the lalonde data set comes with the package Matching.

# YOUR CODE HERE
library(Matching)
data(lalonde)
head(lalonde)

lm01 <- lm(re78~age+educ + re74 + re75 + hisp + black, data = lalonde)

STEP 2

Report coefficients and R-squared.

summary(lm01)

## 
## Call:
## lm(formula = re78 ~ age + educ + re74 + re75 + hisp + black, 
##     data = lalonde)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##  -9065  -4577  -1775   3186  55037 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1.126e+03  2.434e+03   0.463   0.6437  
## age          5.928e+01  4.409e+01   1.345   0.1794  
## educ         4.293e+02  1.758e+02   2.442   0.0150 *
## re74         7.462e-02  7.699e-02   0.969   0.3330  
## re75         6.676e-02  1.314e-01   0.508   0.6116  
## hisp        -2.125e+02  1.546e+03  -0.137   0.8907  
## black       -2.323e+03  1.162e+03  -1.999   0.0462 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6544 on 438 degrees of freedom
## Multiple R-squared:  0.03942,    Adjusted R-squared:  0.02627 
## F-statistic: 2.996 on 6 and 438 DF,  p-value: 0.007035

Then calculate R-squared by hand and confirm / report that you get the same or nearly the same answer as the summary (lm) command.

Write out hand calculations here.

STEP 3

Then, setting all the predictors at their means EXCEPT education, create a data visualization that shows the 95% confidence interval of the expected values of re78 as education varies from 3 to 16. Be sure to include axes labels and figure titles.

# YOUR CODE HERE
#create a temporary storage for all people in each simulation
temp.storage <- matrix(NA, nrow = 1000, ncol = 100)

#create a storage for all simulations in each level of education
sim.storage <- matrix(NA, nrow = 1000, ncol = 14)


for (education in 3:16){
  for (simulation in 1:1000){
    #simulate 100 people
    lm_object <- sim(lm01, n.sims = 100)
    lm_coefs <- coef(lm_object)

    for (person in 1:100){
      #find the prediction for the average mean
      avg_person <- c(mean(lalonde$age), education, mean(lalonde$re74), mean(lalonde$re75), mean(lalonde$hisp), mean(lalonde$black))
      temp.storage[simulation, person] <- sum(lm_coefs[person,] * c(1, avg_person))
    }
    
  sim.storage[simulation, education - 2] <- mean(temp.storage[simulation,])
  }
}

exp.conf.intervals <- apply(sim.storage, 2, quantile, probs = c(0.025, 0.5, 0.975))

exp.conf.intervals <- rbind(exp.conf.intervals, c(3:16)) %>% t %>% as.data.frame

colnames(exp.conf.intervals) = c("lower_bound", "average", "upper_bound", "educ")


ggplot(data = exp.conf.intervals) + geom_point(mapping = aes(x=educ, y=average), size = 0.7) + 
  geom_errorbar(mapping = aes(x=educ, ymin = lower_bound, ymax = upper_bound), color="dark gray", width = 0.5) + 
  labs(x = "Years of education", y ="Expected income in 1978") + ggtitle("Effect of education on expected income in 1978") 

STEP 4

Then, do the same thing, but this time for the predicted values of re78. Be sure to include axes labels and figure titles.

# YOUR CODE HERE
storage.matrix <- matrix(NA, nrow = 1000, ncol = 14)
lm_object <- sim(lm01, n.sims = 1000)
lm_coefs <- coef(lm_object)
lm_coefs[1,]

##   (Intercept)           age          educ          re74          re75 
##  1.879414e+03  3.935348e+01  5.426023e+02 -6.850469e-03  9.738652e-02 
##          hisp         black 
## -1.214841e+03 -3.019228e+03

for (education in 3:16){
  for (simulation in 1:1000){
      avg_person <- c(mean(lalonde$age), education, mean(lalonde$re74), mean(lalonde$re75), mean(lalonde$hisp), mean(lalonde$black))
      storage.matrix[simulation, education - 2] <- sum(lm_coefs[simulation,] * c(1, avg_person))
    }
}

pred.conf.intervals <- apply(storage.matrix, 2, quantile, probs = c(0.025, 0.5, 0.975)) %>% rbind(c(3:16)) %>% t %>% as.data.frame

colnames(pred.conf.intervals) = c("lower_bound", "average", "upper_bound", "educ")


ggplot(data = pred.conf.intervals) + geom_point(mapping = aes(x=educ, y=average), size = 0.7) + 
  geom_errorbar(mapping = aes(x=educ, ymin = lower_bound, ymax = upper_bound), color="dark gray", width = 0.5) + 
  labs(x = "Years of education", y ="Predicted income in 1978") + ggtitle("Effect of education on predicted income in 1978") 

STEP 5

Lastly, write a short paragraph with your reflections on this exercise (specifically, the length of intervals for given expected vs. predicted values) and the results you obtained.

QUESTION 4

STEP 1

Using the lalonde data set, run a logistic regression, modeling treatment status as a function of age, education, hisp, re74 and re75. Report and interpret the regression coefficient and 95% confidence intervals for age and education.

# YOUR CODE HERE

lr01 <- glm(treat~age + educ + hisp + re74 + re75, data=lalonde, family=binomial)


age_ci_lower= confint(lr01)['age',1]

## Waiting for profiling to be done...

age_ci_upper= confint(lr01)['age',2]

## Waiting for profiling to be done...

age_average = (age_ci_lower + age_ci_upper)/2

educ_ci_lower= confint(lr01)['educ',1]

## Waiting for profiling to be done...

educ_ci_upper= confint(lr01)['educ',2]

## Waiting for profiling to be done...

educ_average = (educ_ci_lower + educ_ci_upper)/2

sprintf("The age regression coefficient is: %.4f. Its 95th confidence interval is (%.4f, %.4f)", age_average, age_ci_lower, age_ci_upper)

## [1] "The age regression coefficient is: 0.0116. Its 95th confidence interval is (-0.0154, 0.0385)"

sprintf("The education regression coefficient is: %.4f. Its 95th confidence interval is (%.4f, %.4f)", educ_average, educ_ci_lower, educ_ci_upper)

## [1] "The education regression coefficient is: 0.0705. Its 95th confidence interval is (-0.0385, 0.1796)"

Report and interpret regression coefficient and 95% confidence intervals for age and education here.

STEP 2

Use a simple bootstrap to estimate (and report) bootstrapped confidence intervals for age and education given the logistic regression above. Code the bootstrap algorithm yourself.

# YOUR CODE HERE
confint_bootstrap = function(variable){
  confint.matrix = matrix(NA, nrow = 1000)
  for (i in 1:1000){
    samples = sample(nrow(lalonde), 1000, replace = TRUE)
    lalonde.train = lalonde[samples,]
    lr01 = glm(treat~age + educ + hisp + re74 + re75, data=lalonde.train, family=binomial)
    confint.matrix[i,1] = coefficients(lr01)[variable]
  }
  ci = quantile(confint.matrix[,1], c(0.025, 0.5, 0.975))
  return (ci)
}

print(confint_bootstrap("age"))

##        2.5%         50%       97.5% 
## -0.00667227  0.01139394  0.02970603

print(confint_bootstrap("educ"))

##         2.5%          50%        97.5% 
## -0.005926616  0.068969389  0.147690362

Report bootstrapped confidence intervals for age and education here.

STEP 3

Then, using the simulation-based approach and the arm library, set all the predictors at their means EXCEPT education, create a data visualization that shows the 95% confidence interval of the expected values of the probability of receiving treatment as education varies from 3 to 16. Be sure to include axes labels and figure titles.

# YOUR CODE HERE

lr01 <- glm(treat~age + educ + hisp + re74 + re75, data=lalonde, family=binomial)

temp.storage <- matrix(NA, nrow = 1000, ncol = 100)

#create a storage for all simulations in each level of education
lr.storage <- matrix(NA, nrow = 1000, ncol = 14)


for (education in 3:16){
  #simulate 1000 times
  for (simulation in 1:1000){
    #simulate 100 people
    lr_object <- sim(lr01, n.sims = 100)
    lr_coefs <- coef(lr_object)

    for (person in 1:100){
      #find the prediction for the average mean
      avg_person <- c(1, mean(lalonde$age), education, mean(lalonde$hisp), mean(lalonde$re74), mean(lalonde$re75))
      temp.storage[simulation, person] <- exp(sum(lr_coefs[person,]*avg_person))/(1 + exp(sum(lr_coefs[person,]*avg_person)))
    }
    
  lr.storage[simulation, education - 2] <- mean(temp.storage[simulation,])
  }
}

lr.storage

##              [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
##    [1,] 0.2963613 0.3280378 0.3332479 0.3541290 0.3550942 0.3778512 0.3905288
##    [2,] 0.3073947 0.3220396 0.3330854 0.3384048 0.3625767 0.3741660 0.3938944
##    [3,] 0.2959032 0.3254757 0.3451852 0.3543682 0.3667927 0.3818980 0.3990186
##    [4,] 0.3179127 0.3398865 0.3459174 0.3507608 0.3606708 0.3756735 0.3922193
##    [5,] 0.3130910 0.3205387 0.3272070 0.3510602 0.3650893 0.3733219 0.3966398
##    [6,] 0.2960003 0.3236790 0.3283941 0.3439124 0.3728118 0.3800435 0.3883685
##    [7,] 0.3038485 0.3348237 0.3399741 0.3445397 0.3611635 0.3787289 0.3975079
##    [8,] 0.3024719 0.3170378 0.3389827 0.3561863 0.3616727 0.3757452 0.3957116
##    [9,] 0.3118523 0.3252209 0.3350651 0.3438741 0.3643859 0.3751546 0.3916623
##   [10,] 0.2999204 0.3231287 0.3430395 0.3547637 0.3629544 0.3799451 0.3911700
##   [11,] 0.2991944 0.3228391 0.3267901 0.3503239 0.3565314 0.3805807 0.3964310
##   [12,] 0.3175824 0.3183980 0.3310653 0.3591690 0.3673638 0.3712807 0.3955089
##   [13,] 0.3002927 0.3115909 0.3240418 0.3438164 0.3630828 0.3747790 0.3966707
##   [14,] 0.3123371 0.3083109 0.3281244 0.3506081 0.3632830 0.3683996 0.3923376
##   [15,] 0.2835158 0.3006626 0.3322709 0.3469988 0.3470125 0.3749913 0.3948633
##   [16,] 0.3117239 0.3175175 0.3167593 0.3494841 0.3572922 0.3753844 0.3988931
##   [17,] 0.3110556 0.3234053 0.3286881 0.3451728 0.3617381 0.3785337 0.3924193
##   [18,] 0.3017873 0.3337034 0.3360125 0.3516770 0.3651105 0.3790671 0.3931813
##   [19,] 0.2948207 0.3207522 0.3384336 0.3447899 0.3590339 0.3756170 0.3950802
##   [20,] 0.3055994 0.3094971 0.3265962 0.3567767 0.3618340 0.3719390 0.3919831
##   [21,] 0.3095017 0.3069724 0.3250744 0.3459326 0.3625892 0.3724504 0.3929789
##   [22,] 0.3222412 0.3240863 0.3300603 0.3437404 0.3777793 0.3793722 0.3958153
##   [23,] 0.3108520 0.3370239 0.3313468 0.3450983 0.3651071 0.3781452 0.3974001
##   [24,] 0.3187207 0.3222832 0.3331794 0.3454916 0.3628834 0.3827738 0.3990031
##   [25,] 0.3132778 0.3171905 0.3515186 0.3472052 0.3588877 0.3692456 0.3921778
##   [26,] 0.3106399 0.3117166 0.3367670 0.3494788 0.3542861 0.3750391 0.3998288
##   [27,] 0.2986317 0.3277721 0.3332197 0.3445457 0.3652733 0.3757850 0.3924930
##   [28,] 0.3063250 0.3107616 0.3190693 0.3545451 0.3581396 0.3868559 0.3966956
##   [29,] 0.3161942 0.3274692 0.3318156 0.3421944 0.3673880 0.3751395 0.3961937
##   [30,] 0.3072311 0.3135331 0.3321131 0.3420553 0.3629750 0.3799456 0.3977366
##   [31,] 0.3025307 0.3202681 0.3219777 0.3554825 0.3595753 0.3764578 0.3918610
##   [32,] 0.3065030 0.3208254 0.3295415 0.3509431 0.3562886 0.3843861 0.3970129
##   [33,] 0.2902087 0.3178415 0.3324196 0.3450866 0.3630212 0.3848762 0.3985310
##   [34,] 0.3065674 0.3187682 0.3328600 0.3484831 0.3653360 0.3798581 0.3941242
##   [35,] 0.3135576 0.3247191 0.3364568 0.3510461 0.3753945 0.3770689 0.3946371
##   [36,] 0.3063087 0.3153717 0.3344842 0.3517566 0.3616554 0.3760107 0.3939725
##   [37,] 0.3124017 0.3237932 0.3496949 0.3347420 0.3648139 0.3743348 0.3966640
##   [38,] 0.3128225 0.3067852 0.3420825 0.3346072 0.3600394 0.3755217 0.3905216
##   [39,] 0.3137365 0.3243551 0.3256531 0.3403628 0.3634431 0.3774178 0.3939062
##   [40,] 0.3018570 0.3085910 0.3304790 0.3574411 0.3628816 0.3787564 0.3958392
##   [41,] 0.3163058 0.3245458 0.3261403 0.3540074 0.3622847 0.3817995 0.3928043
##   [42,] 0.3023926 0.3132451 0.3301918 0.3462814 0.3612607 0.3778115 0.3968769
##   [43,] 0.3066155 0.3251233 0.3271895 0.3465531 0.3648333 0.3768769 0.3915585
##   [44,] 0.3093880 0.3190040 0.3406365 0.3587152 0.3691677 0.3727029 0.3953124
##   [45,] 0.3059691 0.3343994 0.3371413 0.3452012 0.3621975 0.3751963 0.3938623
##   [46,] 0.3008733 0.3206885 0.3288227 0.3572853 0.3581055 0.3797693 0.3955716
##   [47,] 0.3176293 0.3074815 0.3375298 0.3540477 0.3687314 0.3794657 0.3909951
##   [48,] 0.3105940 0.3321552 0.3269209 0.3377874 0.3665638 0.3803739 0.3931824
##   [49,] 0.2940216 0.3295530 0.3296673 0.3511330 0.3606092 0.3806257 0.4012138
##   [50,] 0.2987687 0.3124889 0.3248326 0.3509712 0.3596957 0.3816435 0.3927631
##   [51,] 0.3042359 0.3081181 0.3371188 0.3542300 0.3604829 0.3794077 0.3952585
##   [52,] 0.3112907 0.3174212 0.3297989 0.3497667 0.3658459 0.3830203 0.3902553
##   [53,] 0.3157479 0.3234027 0.3302032 0.3522115 0.3614649 0.3764698 0.3900261
##   [54,] 0.2954942 0.3073752 0.3300414 0.3411333 0.3584654 0.3788132 0.3973577
##   [55,] 0.2998982 0.3326356 0.3291403 0.3600537 0.3644167 0.3867233 0.3954795
##   [56,] 0.3011632 0.3203126 0.3319314 0.3542650 0.3544648 0.3757758 0.3952697
##   [57,] 0.3016289 0.3244610 0.3356401 0.3538681 0.3684707 0.3834976 0.3923774
##   [58,] 0.3104054 0.3134136 0.3362156 0.3466160 0.3607995 0.3813852 0.3937619
##   [59,] 0.3036794 0.3197604 0.3483286 0.3563600 0.3627073 0.3785136 0.3896930
##   [60,] 0.2918978 0.3220852 0.3315898 0.3438119 0.3649791 0.3741925 0.3960479
##   [61,] 0.3062444 0.3197923 0.3307773 0.3464258 0.3751163 0.3803820 0.3953437
##   [62,] 0.3095021 0.3267438 0.3401885 0.3574502 0.3670722 0.3742817 0.3931363
##   [63,] 0.3076508 0.3150108 0.3287161 0.3505401 0.3647418 0.3787676 0.3898246
##   [64,] 0.3036901 0.3119569 0.3271550 0.3460894 0.3671880 0.3769172 0.3916703
##   [65,] 0.3084861 0.3213083 0.3372350 0.3474115 0.3662725 0.3772792 0.3922115
##   [66,] 0.3117684 0.3124271 0.3340471 0.3508484 0.3642331 0.3791827 0.3934737
##   [67,] 0.3031308 0.3129997 0.3373795 0.3440548 0.3701907 0.3769467 0.3946127
##   [68,] 0.2985835 0.3183886 0.3402924 0.3377743 0.3619718 0.3836807 0.3955331
##   [69,] 0.3115148 0.3134643 0.3331749 0.3499900 0.3605761 0.3691800 0.3964810
##   [70,] 0.3132366 0.3290078 0.3396392 0.3451426 0.3633365 0.3772553 0.3967941
##   [71,] 0.2991192 0.3217856 0.3303901 0.3453323 0.3634431 0.3791429 0.3918854
##   [72,] 0.3090087 0.3187331 0.3288561 0.3452256 0.3709835 0.3775764 0.3936783
##   [73,] 0.3161373 0.3184340 0.3410193 0.3468800 0.3630450 0.3786167 0.3935129
##   [74,] 0.3122298 0.3091358 0.3286769 0.3531534 0.3493175 0.3775624 0.3946505
##   [75,] 0.3111117 0.3335433 0.3301852 0.3477890 0.3650085 0.3740310 0.3939908
##   [76,] 0.2936891 0.3356742 0.3349428 0.3439021 0.3548956 0.3841374 0.3971773
##   [77,] 0.3104374 0.3246381 0.3320850 0.3497041 0.3587060 0.3788325 0.3924190
##   [78,] 0.3054005 0.3187611 0.3353818 0.3543268 0.3609026 0.3758593 0.3939426
##   [79,] 0.3027602 0.3117293 0.3418556 0.3519223 0.3598236 0.3796467 0.3933803
##   [80,] 0.3193723 0.3227717 0.3339880 0.3554773 0.3700048 0.3724793 0.3954046
##   [81,] 0.3152415 0.3231931 0.3272408 0.3526920 0.3736617 0.3768885 0.3989334
##   [82,] 0.3134125 0.3131075 0.3347433 0.3497419 0.3608235 0.3794655 0.3939207
##   [83,] 0.3008669 0.3155831 0.3449250 0.3518641 0.3514580 0.3757912 0.3938488
##   [84,] 0.3198703 0.3109138 0.3225799 0.3475155 0.3687527 0.3749267 0.3962712
##   [85,] 0.3100502 0.3119138 0.3345698 0.3589815 0.3642153 0.3716246 0.3937804
##   [86,] 0.3106093 0.3146954 0.3303266 0.3501485 0.3647828 0.3824964 0.3962711
##   [87,] 0.3077614 0.3142355 0.3311446 0.3512859 0.3730559 0.3730222 0.3934778
##   [88,] 0.3045926 0.3335601 0.3362033 0.3430992 0.3676703 0.3732402 0.3954167
##   [89,] 0.3343213 0.3162729 0.3337216 0.3510379 0.3549883 0.3747059 0.3982235
##   [90,] 0.2965633 0.3182164 0.3328818 0.3503250 0.3645542 0.3769047 0.3996687
##   [91,] 0.3049865 0.3320364 0.3298789 0.3325446 0.3661954 0.3814246 0.3923345
##   [92,] 0.2921329 0.3259431 0.3380086 0.3597597 0.3579162 0.3735888 0.3969567
##   [93,] 0.3010210 0.3216042 0.3303505 0.3518705 0.3619871 0.3816420 0.3975519
##   [94,] 0.3086376 0.3244558 0.3318661 0.3465151 0.3619742 0.3735782 0.3902916
##   [95,] 0.2944338 0.3241097 0.3257888 0.3454401 0.3612107 0.3813672 0.3959027
##   [96,] 0.3010372 0.3125115 0.3412911 0.3463247 0.3630181 0.3753387 0.3899522
##   [97,] 0.2975700 0.3131049 0.3316414 0.3416021 0.3636460 0.3773963 0.3951645
##   [98,] 0.3097558 0.3281169 0.3325532 0.3585865 0.3621493 0.3780188 0.3888778
##   [99,] 0.3143167 0.3011650 0.3306201 0.3495655 0.3646570 0.3784906 0.3914989
##  [100,] 0.3125234 0.3138957 0.3268974 0.3520436 0.3601998 0.3840053 0.3979567
##  [101,] 0.3122079 0.3141553 0.3305456 0.3485039 0.3598885 0.3789923 0.3950866
##  [102,] 0.3148760 0.3276157 0.3387189 0.3479119 0.3613870 0.3766594 0.3961187
##  [103,] 0.3022968 0.3262345 0.3310758 0.3516529 0.3569781 0.3786458 0.3953104
##  [104,] 0.3157258 0.3208416 0.3380654 0.3557363 0.3592305 0.3757161 0.3942704
##  [105,] 0.2995753 0.3375810 0.3362352 0.3476303 0.3637417 0.3760473 0.3951948
##  [106,] 0.3041752 0.3114095 0.3259923 0.3512726 0.3675195 0.3736889 0.3950209
##  [107,] 0.3013587 0.3211456 0.3373933 0.3503246 0.3629156 0.3808576 0.3904062
##  [108,] 0.2947794 0.3218991 0.3314576 0.3476852 0.3631107 0.3761071 0.3965011
##  [109,] 0.3081512 0.3195536 0.3350650 0.3494579 0.3663808 0.3839831 0.3939217
##  [110,] 0.2938051 0.3231258 0.3272755 0.3378663 0.3651764 0.3809786 0.3921840
##  [111,] 0.2973785 0.3244678 0.3345248 0.3446054 0.3614445 0.3742876 0.3966260
##  [112,] 0.2949584 0.3207031 0.3366348 0.3421099 0.3636712 0.3764075 0.3932748
##  [113,] 0.3050921 0.3244375 0.3510865 0.3444096 0.3622231 0.3812442 0.3923037
##  [114,] 0.3204292 0.3210603 0.3259136 0.3500322 0.3647718 0.3777976 0.3942113
##  [115,] 0.3131140 0.3236720 0.3306178 0.3473242 0.3682542 0.3783811 0.3898548
##  [116,] 0.3138340 0.3230956 0.3228726 0.3502034 0.3622004 0.3724152 0.3927523
##  [117,] 0.2980530 0.3299574 0.3270839 0.3509987 0.3654916 0.3840521 0.3927895
##  [118,] 0.3075224 0.3094528 0.3175277 0.3541258 0.3600180 0.3830801 0.3927044
##  [119,] 0.3026034 0.3142091 0.3309628 0.3572408 0.3670027 0.3725192 0.3921456
##  [120,] 0.3036880 0.3322693 0.3278042 0.3452126 0.3603676 0.3788584 0.3920236
##  [121,] 0.3054673 0.3261808 0.3370375 0.3494612 0.3634020 0.3772825 0.3922444
##  [122,] 0.3050285 0.3191265 0.3425901 0.3487933 0.3636869 0.3799798 0.3935356
##  [123,] 0.3099954 0.3203263 0.3292669 0.3486559 0.3666231 0.3790370 0.3918894
##  [124,] 0.3110000 0.3303377 0.3369535 0.3482703 0.3666524 0.3784101 0.3921522
##  [125,] 0.2980719 0.3172952 0.3436037 0.3500240 0.3779189 0.3834072 0.3957452
##  [126,] 0.3115262 0.3197188 0.3318734 0.3490140 0.3639665 0.3799334 0.3922235
##  [127,] 0.3014279 0.3084322 0.3271190 0.3503219 0.3608486 0.3810900 0.3916701
##  [128,] 0.3075754 0.3214255 0.3404535 0.3517200 0.3678488 0.3815538 0.3945355
##  [129,] 0.2941194 0.3259009 0.3363882 0.3472730 0.3553962 0.3752569 0.3951539
##  [130,] 0.3101052 0.3375005 0.3359850 0.3487078 0.3649211 0.3799460 0.3957952
##  [131,] 0.3059483 0.3162434 0.3452556 0.3560467 0.3685148 0.3787201 0.3961713
##  [132,] 0.2980592 0.3284811 0.3395938 0.3420079 0.3596469 0.3777759 0.3953748
##  [133,] 0.2942492 0.3371437 0.3201261 0.3442237 0.3659894 0.3766992 0.3905750
##  [134,] 0.2898967 0.3216755 0.3331667 0.3419559 0.3611339 0.3762471 0.4023402
##  [135,] 0.3008376 0.3064995 0.3333523 0.3521057 0.3609645 0.3763602 0.3918685
##  [136,] 0.2978639 0.3158260 0.3356623 0.3444516 0.3665023 0.3773766 0.3962381
##  [137,] 0.3107507 0.3370842 0.3401616 0.3510883 0.3660286 0.3859483 0.3924833
##  [138,] 0.3213539 0.3190270 0.3344831 0.3439785 0.3604881 0.3758338 0.3938825
##  [139,] 0.3053716 0.3122176 0.3316494 0.3509152 0.3683426 0.3789681 0.3968962
##  [140,] 0.3005510 0.3236227 0.3396132 0.3471036 0.3566420 0.3756437 0.3948347
##  [141,] 0.3013199 0.3242029 0.3234696 0.3512696 0.3640025 0.3713225 0.3959394
##  [142,] 0.3089939 0.3263978 0.3321515 0.3481203 0.3516754 0.3743326 0.3954642
##  [143,] 0.2960926 0.3315600 0.3381570 0.3505355 0.3659777 0.3766145 0.3941856
##  [144,] 0.3119717 0.3281291 0.3481008 0.3434806 0.3642602 0.3822453 0.3917365
##  [145,] 0.2931230 0.3384747 0.3277930 0.3551977 0.3611510 0.3752933 0.3954820
##  [146,] 0.3237636 0.3332521 0.3231676 0.3514322 0.3680032 0.3758949 0.3985248
##  [147,] 0.3000125 0.3181403 0.3335852 0.3472699 0.3639605 0.3762196 0.3963916
##  [148,] 0.3105642 0.3205871 0.3401914 0.3417542 0.3665325 0.3788409 0.3976835
##  [149,] 0.3083147 0.3254038 0.3280692 0.3473354 0.3648449 0.3769927 0.3966822
##  [150,] 0.2975178 0.3311454 0.3340258 0.3557735 0.3636047 0.3786589 0.3928981
##  [151,] 0.3262132 0.3147613 0.3430512 0.3487597 0.3600469 0.3762910 0.3910265
##  [152,] 0.3132388 0.3288850 0.3410318 0.3339687 0.3675543 0.3792598 0.3916489
##  [153,] 0.3284307 0.3170554 0.3353957 0.3458878 0.3553424 0.3783413 0.3932968
##  [154,] 0.2937195 0.3125056 0.3348871 0.3460063 0.3613018 0.3716757 0.3941628
##  [155,] 0.3088600 0.3298895 0.3334728 0.3511036 0.3670670 0.3851190 0.3979019
##  [156,] 0.3116769 0.3238514 0.3242797 0.3357956 0.3585154 0.3814486 0.3917055
##  [157,] 0.3125817 0.3216232 0.3401763 0.3499915 0.3675151 0.3771394 0.3961203
##  [158,] 0.3200646 0.3176083 0.3406084 0.3461382 0.3632818 0.3807447 0.3958655
##  [159,] 0.3135643 0.3165748 0.3318624 0.3564162 0.3665015 0.3785555 0.3991448
##  [160,] 0.3026325 0.3259702 0.3297312 0.3462811 0.3557830 0.3727311 0.3932245
##  [161,] 0.3031914 0.3272035 0.3363128 0.3609036 0.3741114 0.3787728 0.3985909
##  [162,] 0.2968725 0.3226528 0.3230318 0.3512334 0.3545623 0.3771648 0.3928168
##  [163,] 0.3182607 0.3200505 0.3330454 0.3443442 0.3554767 0.3765120 0.3918907
##  [164,] 0.3295732 0.3184573 0.3302135 0.3441018 0.3523425 0.3816878 0.3938321
##  [165,] 0.3077584 0.3319226 0.3259918 0.3503977 0.3607117 0.3816994 0.3973984
##  [166,] 0.3185917 0.3091341 0.3324645 0.3442100 0.3557403 0.3773851 0.3976939
##  [167,] 0.3005756 0.3282303 0.3410601 0.3453250 0.3590926 0.3792043 0.3951459
##  [168,] 0.3000971 0.3192017 0.3340661 0.3543497 0.3589963 0.3819818 0.3888700
##  [169,] 0.2950129 0.3182095 0.3345249 0.3442915 0.3660635 0.3844205 0.3966550
##  [170,] 0.3192318 0.3321338 0.3264610 0.3415149 0.3624691 0.3763179 0.3943803
##  [171,] 0.2953639 0.3194170 0.3297438 0.3372803 0.3655348 0.3787131 0.3937856
##  [172,] 0.3015861 0.3251476 0.3294812 0.3450139 0.3627928 0.3732873 0.3894443
##  [173,] 0.2974709 0.3277635 0.3262289 0.3519107 0.3634649 0.3826850 0.3940804
##  [174,] 0.3005815 0.3234434 0.3348238 0.3456007 0.3521617 0.3732005 0.3900565
##  [175,] 0.3061211 0.3234523 0.3295141 0.3520244 0.3504846 0.3757507 0.3968719
##  [176,] 0.3040329 0.3107621 0.3310308 0.3467741 0.3594961 0.3816883 0.3963145
##  [177,] 0.3043287 0.3263359 0.3300678 0.3443578 0.3659178 0.3732961 0.3973178
##  [178,] 0.3122553 0.3076984 0.3247877 0.3486360 0.3564867 0.3735068 0.3971967
##  [179,] 0.3193283 0.3132169 0.3322365 0.3462667 0.3500128 0.3821997 0.3991082
##  [180,] 0.3050361 0.3213393 0.3288795 0.3493281 0.3619096 0.3821931 0.3954975
##  [181,] 0.3036923 0.3271756 0.3325007 0.3448998 0.3615939 0.3757721 0.3960993
##  [182,] 0.2931289 0.3135606 0.3243510 0.3572414 0.3593717 0.3761255 0.3947979
##  [183,] 0.3199657 0.3278567 0.3271409 0.3432064 0.3606328 0.3814601 0.3895905
##  [184,] 0.3082810 0.3106008 0.3357193 0.3540929 0.3663452 0.3831879 0.3920340
##  [185,] 0.3053834 0.3282725 0.3338300 0.3558349 0.3634419 0.3719214 0.3863800
##  [186,] 0.3104221 0.3288601 0.3325818 0.3441443 0.3574252 0.3716427 0.3968629
##  [187,] 0.3238198 0.3067636 0.3344849 0.3410485 0.3640916 0.3749889 0.3920113
##  [188,] 0.2942857 0.3465449 0.3495116 0.3440202 0.3650947 0.3767321 0.3958799
##  [189,] 0.3111499 0.3194943 0.3404134 0.3478969 0.3647656 0.3805164 0.3971002
##  [190,] 0.3088798 0.3305675 0.3306361 0.3442559 0.3547581 0.3798603 0.3992449
##  [191,] 0.3000722 0.3235662 0.3387649 0.3475540 0.3692229 0.3798585 0.3874742
##  [192,] 0.3037911 0.3168597 0.3319614 0.3436566 0.3534707 0.3782459 0.3934981
##  [193,] 0.3000367 0.3261382 0.3334393 0.3500119 0.3644521 0.3790166 0.3968112
##  [194,] 0.3022373 0.3207167 0.3302675 0.3473985 0.3645503 0.3755230 0.3930856
##  [195,] 0.3074451 0.3253220 0.3338245 0.3456142 0.3627105 0.3788963 0.3946611
##  [196,] 0.3063863 0.3269793 0.3272161 0.3453043 0.3601984 0.3772433 0.3916246
##  [197,] 0.3020120 0.3137424 0.3289837 0.3467741 0.3673971 0.3750369 0.3945803
##  [198,] 0.3105900 0.3250668 0.3340863 0.3569229 0.3661575 0.3753100 0.3968310
##  [199,] 0.3065341 0.3256723 0.3354377 0.3502234 0.3590774 0.3832299 0.3937663
##  [200,] 0.2988863 0.3151289 0.3279891 0.3405840 0.3635528 0.3772651 0.3938646
##  [201,] 0.3159643 0.3243679 0.3442779 0.3431496 0.3585469 0.3729995 0.3929877
##  [202,] 0.3110711 0.3251488 0.3455432 0.3464217 0.3668846 0.3751087 0.3981366
##  [203,] 0.3110910 0.3295333 0.3380451 0.3549888 0.3630016 0.3763298 0.3925551
##  [204,] 0.3120571 0.3137665 0.3360992 0.3488857 0.3600965 0.3802663 0.3965763
##  [205,] 0.3000639 0.3060516 0.3274702 0.3503690 0.3637763 0.3864805 0.3961638
##  [206,] 0.3150168 0.3319363 0.3364799 0.3467668 0.3635968 0.3793509 0.3937974
##  [207,] 0.3062666 0.3259593 0.3322360 0.3431963 0.3585495 0.3865765 0.3977238
##  [208,] 0.2978868 0.3277073 0.3302171 0.3468267 0.3596228 0.3781559 0.3971324
##  [209,] 0.3108843 0.3286649 0.3351326 0.3446028 0.3642953 0.3764844 0.3939118
##  [210,] 0.3052108 0.3101837 0.3249547 0.3509669 0.3618821 0.3783455 0.3942568
##  [211,] 0.3148721 0.3136672 0.3440273 0.3480774 0.3623991 0.3743865 0.3917465
##  [212,] 0.3168483 0.3144947 0.3222601 0.3528782 0.3637838 0.3844393 0.3990703
##  [213,] 0.3068218 0.3023129 0.3219035 0.3498500 0.3559118 0.3768544 0.3942852
##  [214,] 0.3040392 0.3110826 0.3444918 0.3480509 0.3624787 0.3721300 0.3965534
##  [215,] 0.3151445 0.3144325 0.3365509 0.3495123 0.3605294 0.3775069 0.3945042
##  [216,] 0.3066043 0.3216523 0.3243452 0.3472088 0.3628226 0.3698172 0.3909376
##  [217,] 0.2999086 0.3336081 0.3392675 0.3526686 0.3674309 0.3830385 0.3979914
##  [218,] 0.2934358 0.3433040 0.3409469 0.3509730 0.3599449 0.3759743 0.3974860
##  [219,] 0.3001760 0.3090836 0.3280326 0.3449119 0.3659029 0.3807179 0.3989358
##  [220,] 0.2993051 0.3147022 0.3286237 0.3490872 0.3649550 0.3850696 0.3900214
##  [221,] 0.3136526 0.3144206 0.3324714 0.3439651 0.3619150 0.3797173 0.3937284
##  [222,] 0.3128611 0.3164082 0.3285545 0.3383844 0.3607597 0.3795814 0.3972793
##  [223,] 0.3100106 0.3213244 0.3250852 0.3540674 0.3644005 0.3842976 0.3975716
##  [224,] 0.3151825 0.3287638 0.3322481 0.3430028 0.3598009 0.3741456 0.3952781
##  [225,] 0.3046766 0.3131932 0.3418901 0.3520743 0.3610411 0.3808784 0.3901739
##  [226,] 0.3208121 0.3213566 0.3280769 0.3485634 0.3641215 0.3708809 0.3944927
##  [227,] 0.3087845 0.3057756 0.3319787 0.3484248 0.3637690 0.3834180 0.3925874
##  [228,] 0.3110814 0.3240783 0.3432515 0.3527696 0.3603838 0.3733273 0.3931816
##  [229,] 0.3143026 0.3116869 0.3324493 0.3579489 0.3641835 0.3723794 0.3958647
##  [230,] 0.3131480 0.3397498 0.3402658 0.3571087 0.3622219 0.3818545 0.3946697
##  [231,] 0.2924758 0.3123719 0.3221016 0.3391159 0.3561173 0.3806732 0.3902072
##  [232,] 0.3131235 0.3152475 0.3295605 0.3317908 0.3632999 0.3805949 0.3975862
##  [233,] 0.3144649 0.3310072 0.3286447 0.3425121 0.3539809 0.3805727 0.3933388
##  [234,] 0.2992128 0.3250058 0.3252863 0.3535079 0.3645691 0.3811773 0.3933412
##  [235,] 0.3133515 0.3168465 0.3286861 0.3446806 0.3624322 0.3782440 0.3939305
##  [236,] 0.3167994 0.3139881 0.3430812 0.3511399 0.3689119 0.3822485 0.3976181
##  [237,] 0.3053717 0.3176946 0.3321273 0.3571877 0.3704314 0.3801033 0.3921721
##  [238,] 0.3085644 0.3164786 0.3327910 0.3541559 0.3623264 0.3716303 0.3957200
##  [239,] 0.3025254 0.3203990 0.3338615 0.3475902 0.3579262 0.3759623 0.3957805
##  [240,] 0.3184709 0.3090917 0.3276699 0.3491522 0.3681634 0.3761919 0.3939933
##  [241,] 0.3066495 0.3135080 0.3201783 0.3539612 0.3602782 0.3732070 0.3921097
##  [242,] 0.3071479 0.3185432 0.3367939 0.3386594 0.3545812 0.3787478 0.3964054
##  [243,] 0.3098224 0.3243966 0.3355996 0.3508149 0.3541668 0.3788573 0.3976044
##  [244,] 0.2994216 0.3205828 0.3169747 0.3476554 0.3713209 0.3791138 0.3907567
##  [245,] 0.3092303 0.3233334 0.3361427 0.3367608 0.3570309 0.3764356 0.3935187
##  [246,] 0.3188434 0.3198441 0.3355271 0.3539565 0.3692374 0.3764387 0.3996272
##  [247,] 0.3045607 0.3211303 0.3306084 0.3498919 0.3569517 0.3775593 0.3922233
##  [248,] 0.2965064 0.3198003 0.3304701 0.3516071 0.3719604 0.3799907 0.3943904
##  [249,] 0.3077423 0.3156169 0.3268919 0.3460906 0.3647864 0.3781056 0.3886232
##  [250,] 0.2936190 0.3198628 0.3346564 0.3472017 0.3566354 0.3738443 0.3962278
##  [251,] 0.3085391 0.3113626 0.3350819 0.3586230 0.3737979 0.3747732 0.3913330
##  [252,] 0.2958378 0.3281472 0.3423444 0.3458899 0.3631648 0.3759882 0.3925047
##  [253,] 0.3122856 0.3166789 0.3326015 0.3507276 0.3647535 0.3781761 0.4007841
##  [254,] 0.3141108 0.3310963 0.3273466 0.3426196 0.3626469 0.3793413 0.3913808
##  [255,] 0.3065335 0.3219746 0.3308325 0.3504816 0.3655056 0.3830276 0.3982170
##  [256,] 0.2998118 0.3092979 0.3314934 0.3424723 0.3636162 0.3788119 0.3933474
##  [257,] 0.3093966 0.3135124 0.3175414 0.3522893 0.3680109 0.3803757 0.4007765
##  [258,] 0.2974231 0.3181813 0.3294961 0.3437485 0.3579038 0.3769961 0.3910308
##  [259,] 0.3110175 0.3153384 0.3393695 0.3631520 0.3610095 0.3793323 0.3918843
##  [260,] 0.3146703 0.3076560 0.3379883 0.3579806 0.3721940 0.3774134 0.3900104
##  [261,] 0.3077058 0.3110418 0.3332939 0.3465967 0.3662034 0.3796259 0.3938906
##  [262,] 0.3207960 0.3244701 0.3191924 0.3595323 0.3650069 0.3798826 0.3929026
##  [263,] 0.3142870 0.3219697 0.3337743 0.3422277 0.3621341 0.3794865 0.3951914
##  [264,] 0.2991512 0.3208103 0.3373850 0.3484180 0.3596219 0.3745293 0.3942805
##  [265,] 0.3088301 0.3153658 0.3240509 0.3439935 0.3621963 0.3721442 0.3934645
##  [266,] 0.3011339 0.3292013 0.3202850 0.3456540 0.3627542 0.3819852 0.3928653
##  [267,] 0.2975418 0.3277534 0.3276435 0.3473416 0.3696890 0.3780108 0.3934057
##  [268,] 0.2955882 0.3125525 0.3326229 0.3649062 0.3662583 0.3721372 0.3944552
##  [269,] 0.3035874 0.3306090 0.3331730 0.3521958 0.3583935 0.3739859 0.3974276
##  [270,] 0.3067504 0.3260854 0.3311400 0.3511980 0.3635714 0.3801940 0.3949549
##  [271,] 0.3113638 0.3217982 0.3183271 0.3470142 0.3658759 0.3780376 0.3928845
##  [272,] 0.2911114 0.3307735 0.3364455 0.3415370 0.3638196 0.3851921 0.3924503
##  [273,] 0.3173981 0.3192344 0.3419131 0.3506668 0.3605534 0.3806735 0.3930841
##  [274,] 0.3069154 0.3188664 0.3337002 0.3532587 0.3629173 0.3781886 0.3967914
##  [275,] 0.3067115 0.3260953 0.3307843 0.3416505 0.3607513 0.3781005 0.3915308
##  [276,] 0.3267888 0.3141012 0.3294759 0.3394892 0.3638688 0.3751230 0.3927681
##  [277,] 0.2935971 0.3217559 0.3422671 0.3413108 0.3584089 0.3772298 0.3933292
##  [278,] 0.3081742 0.3131769 0.3364290 0.3540406 0.3589089 0.3772860 0.3963463
##  [279,] 0.3013670 0.3189508 0.3384745 0.3450234 0.3559132 0.3821263 0.3921995
##  [280,] 0.3065706 0.3207327 0.3303429 0.3549077 0.3680355 0.3778955 0.3933067
##  [281,] 0.2937578 0.3141490 0.3278380 0.3491878 0.3593355 0.3773366 0.3969689
##  [282,] 0.3110750 0.3161044 0.3477023 0.3537871 0.3624732 0.3818073 0.3920904
##  [283,] 0.2892607 0.3183208 0.3267105 0.3437824 0.3604690 0.3733094 0.3950158
##  [284,] 0.3090021 0.3226574 0.3297662 0.3415170 0.3590301 0.3758104 0.3934755
##  [285,] 0.3011686 0.3145757 0.3361794 0.3511395 0.3665736 0.3762700 0.3963965
##  [286,] 0.3071267 0.3211168 0.3240855 0.3537408 0.3686562 0.3786715 0.3947791
##  [287,] 0.3000935 0.3202457 0.3291014 0.3405007 0.3565988 0.3739280 0.3970541
##  [288,] 0.3068089 0.3229851 0.3383827 0.3536190 0.3641636 0.3781099 0.3936871
##  [289,] 0.2964792 0.3335028 0.3390782 0.3527306 0.3631249 0.3791640 0.3998403
##  [290,] 0.2950808 0.3094140 0.3273809 0.3499230 0.3614186 0.3745724 0.3968520
##  [291,] 0.3108475 0.3019293 0.3238313 0.3538254 0.3554416 0.3803226 0.3952398
##  [292,] 0.3060215 0.3165551 0.3369124 0.3479122 0.3734437 0.3725484 0.3939386
##  [293,] 0.3009601 0.3243278 0.3379261 0.3458213 0.3623711 0.3831013 0.3964713
##  [294,] 0.2892812 0.3178933 0.3286992 0.3433685 0.3654393 0.3755898 0.3955253
##  [295,] 0.3099016 0.3286467 0.3380463 0.3513844 0.3646911 0.3751905 0.3957595
##  [296,] 0.2998497 0.3108257 0.3284989 0.3565042 0.3617207 0.3743853 0.3979033
##  [297,] 0.3039383 0.3243163 0.3380191 0.3504285 0.3576153 0.3803660 0.3920474
##  [298,] 0.2894166 0.3241192 0.3271575 0.3420595 0.3646823 0.3839897 0.3946714
##  [299,] 0.3083118 0.3237682 0.3317052 0.3440986 0.3651079 0.3811321 0.3913488
##  [300,] 0.3012701 0.3301827 0.3447383 0.3521822 0.3527927 0.3852491 0.3931893
##  [301,] 0.3017103 0.3379896 0.3385035 0.3524784 0.3669854 0.3791769 0.3972472
##  [302,] 0.2925643 0.3125981 0.3331288 0.3482553 0.3640458 0.3741127 0.3987864
##  [303,] 0.3240794 0.3173335 0.3342702 0.3573032 0.3679433 0.3795387 0.3957682
##  [304,] 0.3030543 0.3184813 0.3332568 0.3463710 0.3583164 0.3805725 0.3989299
##  [305,] 0.3013572 0.3211041 0.3242385 0.3448338 0.3661225 0.3738537 0.3985558
##  [306,] 0.2964586 0.3158346 0.3315391 0.3475707 0.3573203 0.3786688 0.3949297
##  [307,] 0.3039741 0.3144188 0.3332437 0.3513648 0.3582362 0.3780045 0.3904631
##  [308,] 0.3047839 0.3305620 0.3418549 0.3491594 0.3604382 0.3775372 0.3937176
##  [309,] 0.3181562 0.3251274 0.3267378 0.3535967 0.3553790 0.3822564 0.3983620
##  [310,] 0.3081111 0.3149965 0.3378706 0.3567619 0.3577003 0.3726048 0.3974949
##  [311,] 0.3242934 0.3220554 0.3244851 0.3471726 0.3654263 0.3785442 0.3941011
##  [312,] 0.2884576 0.3061303 0.3345020 0.3434019 0.3646691 0.3812989 0.3954445
##  [313,] 0.3106119 0.3203303 0.3255328 0.3435617 0.3610437 0.3804134 0.3953514
##  [314,] 0.3149965 0.3180717 0.3453514 0.3532766 0.3627000 0.3786652 0.3941653
##  [315,] 0.3093434 0.3300175 0.3335065 0.3490790 0.3633480 0.3779609 0.3991389
##  [316,] 0.3119996 0.3225700 0.3328821 0.3459331 0.3599500 0.3833479 0.3974358
##  [317,] 0.3094668 0.3147552 0.3298046 0.3420009 0.3684639 0.3853740 0.3966513
##  [318,] 0.3150552 0.3217428 0.3487601 0.3531980 0.3631782 0.3779881 0.3967370
##  [319,] 0.3055781 0.3230168 0.3344972 0.3515469 0.3604883 0.3776278 0.3926725
##  [320,] 0.3252694 0.3171782 0.3360727 0.3425534 0.3659085 0.3805657 0.3963053
##  [321,] 0.3093201 0.3149540 0.3238814 0.3424894 0.3699428 0.3822882 0.3967052
##  [322,] 0.2987647 0.3326065 0.3333843 0.3498179 0.3638462 0.3763315 0.3899402
##  [323,] 0.3080572 0.3171925 0.3472178 0.3586347 0.3596858 0.3796615 0.3942654
##  [324,] 0.2988368 0.3233087 0.3256274 0.3583558 0.3659181 0.3845603 0.3894242
##  [325,] 0.3039984 0.3108305 0.3314677 0.3411584 0.3665192 0.3742066 0.3950678
##  [326,] 0.3105596 0.3198101 0.3319838 0.3464701 0.3681301 0.3812288 0.3979306
##  [327,] 0.2947264 0.3120884 0.3308849 0.3471482 0.3682987 0.3732664 0.3955792
##  [328,] 0.2959127 0.3192336 0.3231408 0.3512825 0.3563642 0.3788870 0.3904415
##  [329,] 0.2940096 0.3106337 0.3262738 0.3451365 0.3613901 0.3777978 0.3910674
##  [330,] 0.3013513 0.3230370 0.3272208 0.3398385 0.3618258 0.3732911 0.3926026
##  [331,] 0.3142637 0.3309694 0.3418969 0.3337999 0.3675544 0.3791255 0.3903241
##  [332,] 0.3015849 0.3206937 0.3418002 0.3432135 0.3676857 0.3782534 0.3980994
##  [333,] 0.3132228 0.3155429 0.3438387 0.3500758 0.3684158 0.3719463 0.3931483
##  [334,] 0.3059191 0.3196481 0.3318606 0.3582658 0.3702161 0.3812795 0.3947265
##  [335,] 0.3087895 0.3277644 0.3322460 0.3533903 0.3590840 0.3751566 0.3951740
##  [336,] 0.3007211 0.3113857 0.3261161 0.3470102 0.3626818 0.3791033 0.3929468
##  [337,] 0.3094108 0.3258806 0.3346878 0.3518505 0.3585789 0.3820428 0.3877743
##  [338,] 0.3024916 0.3218138 0.3318569 0.3497428 0.3627260 0.3749240 0.3908887
##  [339,] 0.3026485 0.3283418 0.3417740 0.3499088 0.3638488 0.3827280 0.3928698
##  [340,] 0.3082330 0.3265627 0.3413157 0.3394910 0.3582931 0.3816195 0.3957941
##  [341,] 0.3066999 0.3367430 0.3380044 0.3480637 0.3643383 0.3813355 0.3901112
##  [342,] 0.3192517 0.3208141 0.3421786 0.3419878 0.3564861 0.3920059 0.3902375
##  [343,] 0.3169207 0.3225947 0.3334311 0.3487096 0.3667704 0.3772190 0.3931788
##  [344,] 0.3074579 0.3178084 0.3442556 0.3443267 0.3634401 0.3801076 0.3963087
##  [345,] 0.3113410 0.3176701 0.3403917 0.3449897 0.3634815 0.3783234 0.3906340
##  [346,] 0.3149553 0.3224983 0.3313227 0.3355635 0.3628867 0.3809213 0.3925039
##  [347,] 0.3201029 0.3132398 0.3375092 0.3487682 0.3656598 0.3746802 0.3946504
##  [348,] 0.3111837 0.3211900 0.3391746 0.3387072 0.3638636 0.3753680 0.3960821
##  [349,] 0.3000814 0.3205356 0.3422544 0.3341096 0.3658015 0.3731913 0.3904454
##  [350,] 0.3110413 0.3140921 0.3346736 0.3461453 0.3594004 0.3795161 0.3959955
##  [351,] 0.3192624 0.3267531 0.3330859 0.3452877 0.3651183 0.3769192 0.3944256
##  [352,] 0.2969053 0.3204973 0.3507050 0.3483290 0.3646942 0.3808710 0.3966321
##  [353,] 0.3145243 0.3109647 0.3294935 0.3382255 0.3691561 0.3833732 0.3932581
##  [354,] 0.3018844 0.3253382 0.3370412 0.3545465 0.3658206 0.3841342 0.3957505
##  [355,] 0.3257647 0.3020324 0.3399889 0.3520594 0.3586777 0.3785622 0.4025342
##  [356,] 0.3121689 0.3067827 0.3408174 0.3369649 0.3529458 0.3750860 0.3963262
##  [357,] 0.3021719 0.3203215 0.3294863 0.3463548 0.3595718 0.3859275 0.3961566
##  [358,] 0.2844233 0.3166315 0.3382533 0.3415490 0.3615677 0.3900584 0.3882366
##  [359,] 0.3077021 0.3201087 0.3274826 0.3420097 0.3685395 0.3800139 0.3995078
##  [360,] 0.3051615 0.3261099 0.3327727 0.3377364 0.3606208 0.3768926 0.3913178
##  [361,] 0.3111276 0.3231070 0.3283886 0.3445220 0.3597659 0.3820251 0.3952333
##  [362,] 0.2960033 0.3227023 0.3297868 0.3444356 0.3624833 0.3701549 0.3970502
##  [363,] 0.3052729 0.3296999 0.3252061 0.3537234 0.3613794 0.3818559 0.3955841
##  [364,] 0.3038206 0.3183278 0.3389345 0.3574533 0.3650046 0.3870584 0.3917364
##  [365,] 0.3028031 0.3174426 0.3405590 0.3574017 0.3632103 0.3799046 0.3925989
##  [366,] 0.3140004 0.3222119 0.3312754 0.3372049 0.3630679 0.3840429 0.3958190
##  [367,] 0.3010779 0.3256069 0.3277366 0.3500547 0.3678243 0.3747574 0.3910191
##  [368,] 0.3171378 0.3262317 0.3309890 0.3447920 0.3618984 0.3793310 0.3930892
##  [369,] 0.3000760 0.3370656 0.3284689 0.3439473 0.3651289 0.3763399 0.3923666
##  [370,] 0.3034725 0.3204687 0.3364097 0.3465329 0.3652150 0.3708557 0.3869300
##  [371,] 0.3054722 0.3095172 0.3426997 0.3533097 0.3670846 0.3808751 0.3923797
##  [372,] 0.3209950 0.3165616 0.3430140 0.3517041 0.3634165 0.3758175 0.3928896
##  [373,] 0.3231477 0.3282877 0.3371048 0.3503424 0.3676157 0.3825616 0.3991707
##  [374,] 0.3011975 0.3167328 0.3394138 0.3468722 0.3587173 0.3781873 0.3952566
##  [375,] 0.3043491 0.3175213 0.3326869 0.3525961 0.3600083 0.3807030 0.3945895
##  [376,] 0.3061427 0.3203724 0.3458458 0.3555807 0.3591808 0.3752034 0.3971839
##  [377,] 0.3058588 0.3187676 0.3340253 0.3520655 0.3663657 0.3805618 0.3937231
##  [378,] 0.3018798 0.3165310 0.3284518 0.3475390 0.3671092 0.3740435 0.3934223
##  [379,] 0.2989941 0.3175193 0.3363042 0.3644846 0.3664946 0.3750055 0.3899206
##  [380,] 0.2981661 0.3146588 0.3404695 0.3573261 0.3703746 0.3828802 0.3947744
##  [381,] 0.3154005 0.3146367 0.3277605 0.3478103 0.3621175 0.3796061 0.3927319
##  [382,] 0.3174168 0.3263087 0.3297080 0.3546244 0.3622940 0.3783831 0.3952763
##  [383,] 0.2967046 0.3131559 0.3322241 0.3466448 0.3565699 0.3840447 0.3945936
##  [384,] 0.3075781 0.3365594 0.3399451 0.3544949 0.3640705 0.3753948 0.4028263
##  [385,] 0.3144893 0.3082130 0.3205875 0.3391059 0.3567432 0.3835777 0.3949318
##  [386,] 0.2976295 0.3150163 0.3428196 0.3470437 0.3541331 0.3824280 0.3934180
##  [387,] 0.2974779 0.3231068 0.3295980 0.3518900 0.3600105 0.3741482 0.4006479
##  [388,] 0.3093845 0.3126518 0.3236550 0.3555895 0.3571699 0.3831928 0.3917821
##  [389,] 0.3034299 0.3126229 0.3349905 0.3470853 0.3629823 0.3816974 0.3963756
##  [390,] 0.3133574 0.3136070 0.3309732 0.3392541 0.3663616 0.3697730 0.3925556
##  [391,] 0.3147679 0.3143323 0.3289705 0.3471391 0.3640570 0.3796751 0.3939115
##  [392,] 0.3157263 0.3291666 0.3338787 0.3511649 0.3590529 0.3755475 0.3937156
##  [393,] 0.3128450 0.3259818 0.3402872 0.3469735 0.3747044 0.3750852 0.3962037
##  [394,] 0.3128067 0.3172444 0.3331812 0.3521079 0.3620709 0.3815712 0.3895786
##  [395,] 0.3004414 0.3239664 0.3385627 0.3541586 0.3628773 0.3733507 0.3917030
##  [396,] 0.3060842 0.3132826 0.3374749 0.3391552 0.3665839 0.3761318 0.3941031
##  [397,] 0.3066220 0.3309947 0.3269669 0.3419541 0.3685122 0.3733526 0.3953167
##  [398,] 0.2950816 0.3144441 0.3347421 0.3436894 0.3630327 0.3770192 0.3952602
##  [399,] 0.3178259 0.3112796 0.3391605 0.3493672 0.3586900 0.3730252 0.3956863
##  [400,] 0.2923830 0.3204544 0.3292340 0.3362927 0.3628638 0.3834518 0.3950042
##  [401,] 0.3077884 0.3031480 0.3304305 0.3355958 0.3637141 0.3746114 0.3967166
##  [402,] 0.3171707 0.3074547 0.3383895 0.3443552 0.3606788 0.3828033 0.3953006
##  [403,] 0.3098831 0.3114974 0.3381047 0.3513509 0.3626011 0.3730968 0.3966709
##  [404,] 0.3155657 0.3129220 0.3269753 0.3436874 0.3510260 0.3790483 0.3901556
##  [405,] 0.3121370 0.3198304 0.3337479 0.3480768 0.3785649 0.3799192 0.3958512
##  [406,] 0.3098964 0.3178491 0.3422562 0.3432175 0.3649990 0.3797670 0.3946976
##  [407,] 0.3064606 0.3163603 0.3368780 0.3637140 0.3599561 0.3803576 0.3933022
##  [408,] 0.3096840 0.3088977 0.3323429 0.3385915 0.3592934 0.3804100 0.4018112
##  [409,] 0.3168755 0.3136723 0.3330272 0.3437069 0.3627784 0.3789591 0.3974177
##  [410,] 0.3131512 0.3228841 0.3360977 0.3476544 0.3685302 0.3751826 0.3943729
##  [411,] 0.3085331 0.3181901 0.3278065 0.3468848 0.3593563 0.3808067 0.3911575
##  [412,] 0.3124416 0.3126983 0.3227256 0.3369461 0.3716465 0.3788150 0.3919569
##  [413,] 0.3029650 0.3064462 0.3291873 0.3510644 0.3606101 0.3818245 0.3941267
##  [414,] 0.3083537 0.3189877 0.3203146 0.3430146 0.3672260 0.3837217 0.3897417
##  [415,] 0.3165119 0.3243579 0.3320074 0.3494589 0.3672210 0.3792376 0.3947446
##  [416,] 0.3102811 0.3096492 0.3333307 0.3571340 0.3584239 0.3840541 0.3892548
##  [417,] 0.3079846 0.3295755 0.3305891 0.3446910 0.3570806 0.3766140 0.3938557
##  [418,] 0.3224219 0.3301557 0.3352498 0.3466176 0.3582530 0.3840838 0.3873577
##  [419,] 0.3056579 0.3314542 0.3250343 0.3481930 0.3618043 0.3810398 0.3913958
##  [420,] 0.2996703 0.3235414 0.3327016 0.3550257 0.3626332 0.3810855 0.3915628
##  [421,] 0.3041383 0.3252813 0.3377742 0.3515806 0.3681091 0.3773725 0.3890214
##  [422,] 0.3128020 0.3096323 0.3308974 0.3352353 0.3571064 0.3741118 0.3954854
##  [423,] 0.3116232 0.3185639 0.3272483 0.3468872 0.3652602 0.3766553 0.3956086
##  [424,] 0.3084386 0.3179012 0.3380438 0.3385708 0.3588899 0.3825958 0.3965853
##  [425,] 0.2909013 0.3196526 0.3327498 0.3538285 0.3721222 0.3725074 0.3953446
##  [426,] 0.2977430 0.3184318 0.3354839 0.3459920 0.3722682 0.3810945 0.3927557
##  [427,] 0.2988225 0.3284991 0.3401679 0.3479854 0.3674111 0.3780509 0.3967883
##  [428,] 0.3038996 0.3181152 0.3286147 0.3603226 0.3643544 0.3803188 0.3940899
##  [429,] 0.3088634 0.3063576 0.3185434 0.3520173 0.3683613 0.3788033 0.3977342
##  [430,] 0.3041089 0.3292528 0.3461086 0.3428391 0.3577796 0.3724574 0.3984651
##  [431,] 0.3107564 0.3206143 0.3329561 0.3415230 0.3748962 0.3815342 0.3959976
##  [432,] 0.3109570 0.3337247 0.3346006 0.3460609 0.3610602 0.3736563 0.3937795
##  [433,] 0.2971576 0.3307157 0.3276368 0.3364893 0.3603593 0.3839126 0.3954945
##  [434,] 0.3123644 0.3279883 0.3297171 0.3428285 0.3563245 0.3771098 0.3937994
##  [435,] 0.3074592 0.3280632 0.3433653 0.3431634 0.3583378 0.3751087 0.3938767
##  [436,] 0.2909867 0.3184628 0.3386546 0.3459336 0.3593763 0.3778311 0.3953958
##  [437,] 0.3005322 0.3354573 0.3345344 0.3419770 0.3616120 0.3843801 0.3946563
##  [438,] 0.3118774 0.3149882 0.3352914 0.3489573 0.3648257 0.3730011 0.3892643
##  [439,] 0.3049457 0.3254229 0.3353670 0.3351969 0.3603593 0.3805547 0.3948899
##  [440,] 0.3159238 0.3314016 0.3239699 0.3489611 0.3622461 0.3824460 0.3979537
##  [441,] 0.3100908 0.3112187 0.3310284 0.3494714 0.3622578 0.3785508 0.3946818
##  [442,] 0.2978607 0.3190225 0.3399833 0.3434662 0.3696656 0.3832395 0.3928623
##  [443,] 0.3056627 0.3150365 0.3372421 0.3380999 0.3642782 0.3759258 0.3921936
##  [444,] 0.3118273 0.3335034 0.3357707 0.3436365 0.3687099 0.3833945 0.3906355
##  [445,] 0.3057292 0.3157025 0.3326883 0.3525903 0.3593045 0.3738627 0.3972420
##  [446,] 0.3050414 0.3141665 0.3237806 0.3457319 0.3704776 0.3828066 0.3999520
##  [447,] 0.3103713 0.3166115 0.3344975 0.3534044 0.3619313 0.3766843 0.3932248
##  [448,] 0.3002257 0.3090647 0.3349974 0.3423271 0.3707858 0.3785257 0.3922859
##  [449,] 0.3202844 0.3265588 0.3462903 0.3409674 0.3600292 0.3789377 0.3939140
##  [450,] 0.3231567 0.3226188 0.3425336 0.3524817 0.3628493 0.3721763 0.3937619
##  [451,] 0.3065207 0.3212664 0.3438524 0.3485833 0.3553373 0.3736360 0.3909736
##  [452,] 0.3085831 0.3127837 0.3336007 0.3367191 0.3733810 0.3765807 0.3959823
##  [453,] 0.3109405 0.3288287 0.3360099 0.3561959 0.3635708 0.3793582 0.3958834
##  [454,] 0.2958819 0.3209367 0.3353888 0.3469639 0.3625960 0.3792439 0.3976318
##  [455,] 0.3122667 0.3173823 0.3327768 0.3383548 0.3638461 0.3749877 0.3922162
##  [456,] 0.3007465 0.3247777 0.3475819 0.3465608 0.3589739 0.3725559 0.3926262
##  [457,] 0.3019368 0.3210009 0.3412919 0.3400828 0.3596966 0.3724262 0.3981484
##  [458,] 0.3084805 0.3247459 0.3414154 0.3449439 0.3678824 0.3725097 0.3968060
##  [459,] 0.3126945 0.3168108 0.3418473 0.3507648 0.3606581 0.3735620 0.3944198
##  [460,] 0.3020993 0.3210245 0.3327532 0.3488102 0.3580457 0.3778431 0.3994313
##  [461,] 0.3165054 0.3115925 0.3417430 0.3466942 0.3576762 0.3814240 0.3905666
##  [462,] 0.3006878 0.3273665 0.3365830 0.3441368 0.3641444 0.3758661 0.3932702
##  [463,] 0.3041530 0.3273035 0.3255845 0.3459564 0.3579536 0.3761208 0.3919005
##  [464,] 0.3110996 0.3227242 0.3310838 0.3529261 0.3626766 0.3781406 0.3981035
##  [465,] 0.3106168 0.3186560 0.3370628 0.3431315 0.3605466 0.3764043 0.3966589
##  [466,] 0.3202472 0.3258399 0.3408815 0.3445109 0.3658632 0.3762006 0.3973704
##  [467,] 0.2920465 0.3124189 0.3395219 0.3515311 0.3669978 0.3733309 0.3925474
##  [468,] 0.3035980 0.3228271 0.3441647 0.3507352 0.3552651 0.3846307 0.3943744
##  [469,] 0.3180071 0.3281040 0.3233176 0.3483520 0.3551575 0.3764608 0.3882288
##  [470,] 0.3146945 0.3219224 0.3356689 0.3488091 0.3655383 0.3732690 0.3938056
##  [471,] 0.3139208 0.3272055 0.3365435 0.3479359 0.3719390 0.3776822 0.3938886
##  [472,] 0.3086073 0.3164699 0.3297218 0.3520760 0.3572006 0.3802966 0.3989735
##  [473,] 0.3191054 0.3426597 0.3378311 0.3504634 0.3734451 0.3801404 0.3941667
##  [474,] 0.2967749 0.3211308 0.3421263 0.3419453 0.3677409 0.3713467 0.3931172
##  [475,] 0.3112201 0.3141295 0.3382100 0.3564815 0.3667229 0.3778273 0.3990304
##  [476,] 0.2958438 0.3252237 0.3451294 0.3642443 0.3628714 0.3764828 0.3951202
##  [477,] 0.3070829 0.3184944 0.3388147 0.3540644 0.3681817 0.3739675 0.3889410
##  [478,] 0.3245269 0.3140501 0.3489777 0.3401742 0.3585187 0.3810324 0.3930574
##  [479,] 0.3105572 0.3091537 0.3304717 0.3486576 0.3595343 0.3757353 0.3928105
##  [480,] 0.2970372 0.3194721 0.3273287 0.3506082 0.3600283 0.3745549 0.3973861
##  [481,] 0.3017868 0.3201698 0.3226104 0.3521668 0.3653075 0.3771815 0.3932774
##  [482,] 0.2968213 0.3229530 0.3326950 0.3422481 0.3654292 0.3798591 0.3933071
##  [483,] 0.3165296 0.3185262 0.3356474 0.3471940 0.3581425 0.3793783 0.3949923
##  [484,] 0.3074398 0.3127468 0.3352664 0.3454508 0.3610220 0.3797783 0.3979280
##  [485,] 0.3002932 0.3301752 0.3337485 0.3427570 0.3706609 0.3761491 0.3931462
##  [486,] 0.3023481 0.3104474 0.3303729 0.3446446 0.3549713 0.3785423 0.3962353
##  [487,] 0.3077938 0.3074129 0.3376434 0.3457101 0.3620499 0.3851420 0.3954915
##  [488,] 0.2885832 0.3262742 0.3456394 0.3485394 0.3554476 0.3770906 0.3974831
##  [489,] 0.3087787 0.3230210 0.3294261 0.3493427 0.3620951 0.3815778 0.3916219
##  [490,] 0.3234157 0.3082386 0.3392390 0.3368368 0.3576711 0.3758878 0.3888993
##  [491,] 0.3088684 0.3189652 0.3370189 0.3546618 0.3597865 0.3749303 0.3952593
##  [492,] 0.2952041 0.3162311 0.3358180 0.3480848 0.3591384 0.3808281 0.3930231
##  [493,] 0.3027726 0.3243730 0.3379156 0.3522670 0.3668656 0.3813274 0.3928088
##  [494,] 0.2957890 0.3120795 0.3197903 0.3531979 0.3654061 0.3786292 0.3925955
##  [495,] 0.2939453 0.3076660 0.3376991 0.3545179 0.3642771 0.3816781 0.3994145
##  [496,] 0.2988635 0.3127251 0.3262117 0.3547657 0.3627272 0.3823794 0.3963009
##  [497,] 0.2934020 0.3154336 0.3268623 0.3532281 0.3597734 0.3875279 0.3907414
##  [498,] 0.3067135 0.3122749 0.3285037 0.3415528 0.3576320 0.3839388 0.3925896
##  [499,] 0.3232845 0.3332339 0.3289444 0.3480615 0.3595893 0.3869569 0.3938241
##  [500,] 0.3132389 0.3140538 0.3306356 0.3446344 0.3629634 0.3817554 0.3949810
##  [501,] 0.3106160 0.3328248 0.3377117 0.3485838 0.3602573 0.3853633 0.3983612
##  [502,] 0.2912256 0.3160156 0.3355384 0.3511807 0.3609073 0.3754236 0.3942234
##  [503,] 0.3113720 0.3212585 0.3225157 0.3475140 0.3614829 0.3763246 0.3945568
##  [504,] 0.2974013 0.3162434 0.3411341 0.3451877 0.3619101 0.3743390 0.3929830
##  [505,] 0.2977252 0.3180308 0.3410124 0.3475684 0.3677962 0.3780813 0.3912123
##  [506,] 0.3184766 0.3155192 0.3258709 0.3417370 0.3623065 0.3754019 0.3912999
##  [507,] 0.3036105 0.3183604 0.3226987 0.3451746 0.3672061 0.3775565 0.3941307
##  [508,] 0.3194300 0.3227452 0.3371820 0.3512089 0.3634961 0.3738637 0.4003907
##  [509,] 0.3258015 0.3162518 0.3324561 0.3404872 0.3629925 0.3885047 0.3892778
##  [510,] 0.3205356 0.3244383 0.3331471 0.3433529 0.3667157 0.3742480 0.3947654
##  [511,] 0.2944167 0.3349244 0.3360393 0.3449496 0.3583247 0.3711213 0.3946446
##  [512,] 0.3057698 0.3168108 0.3282712 0.3550975 0.3629018 0.3868290 0.3973393
##  [513,] 0.3117406 0.3214154 0.3329316 0.3523193 0.3636031 0.3820158 0.3936031
##  [514,] 0.3000332 0.3276903 0.3247334 0.3525969 0.3623086 0.3789496 0.3922053
##  [515,] 0.3015120 0.3302137 0.3309573 0.3422146 0.3657517 0.3774607 0.3958378
##  [516,] 0.3040520 0.3240536 0.3289563 0.3414964 0.3643402 0.3806367 0.3906170
##  [517,] 0.2878959 0.3228402 0.3251208 0.3530293 0.3717813 0.3782985 0.3927573
##  [518,] 0.3056110 0.3125005 0.3353989 0.3509356 0.3551655 0.3825214 0.3966683
##  [519,] 0.3103651 0.3102524 0.3260954 0.3543939 0.3661890 0.3780814 0.3923528
##  [520,] 0.3007626 0.3156582 0.3468402 0.3506185 0.3652490 0.3812621 0.3954821
##  [521,] 0.3038408 0.3247298 0.3470344 0.3491482 0.3630470 0.3776706 0.3927720
##  [522,] 0.3206107 0.3302886 0.3294928 0.3554661 0.3638087 0.3814457 0.3915480
##  [523,] 0.3209452 0.3266360 0.3357304 0.3539247 0.3678916 0.3728812 0.3962463
##  [524,] 0.2998316 0.3176371 0.3277705 0.3603956 0.3612207 0.3795209 0.3993352
##  [525,] 0.3011976 0.3144791 0.3371550 0.3558598 0.3687574 0.3745127 0.3947730
##  [526,] 0.3049988 0.3144506 0.3150777 0.3457505 0.3682448 0.3803272 0.3933329
##  [527,] 0.3046690 0.3151612 0.3315415 0.3531344 0.3697761 0.3811967 0.3992654
##  [528,] 0.3096840 0.3269692 0.3373745 0.3403542 0.3591260 0.3800011 0.3950453
##  [529,] 0.3054273 0.3217256 0.3275165 0.3394964 0.3552646 0.3785804 0.3952656
##  [530,] 0.3099865 0.3168809 0.3320754 0.3455805 0.3618107 0.3874378 0.3958087
##  [531,] 0.2941428 0.3194909 0.3432580 0.3532170 0.3704194 0.3812428 0.3996632
##  [532,] 0.3040153 0.3254417 0.3401444 0.3441752 0.3647062 0.3763058 0.3972507
##  [533,] 0.2960035 0.3125306 0.3320162 0.3419426 0.3666912 0.3860149 0.3972625
##  [534,] 0.3011595 0.3227775 0.3324694 0.3420462 0.3575276 0.3790126 0.3968828
##  [535,] 0.3071785 0.3173359 0.3281945 0.3479972 0.3659777 0.3801832 0.3939785
##  [536,] 0.3159042 0.3169227 0.3382788 0.3620916 0.3605919 0.3705366 0.3930469
##  [537,] 0.3019412 0.3106731 0.3308440 0.3433343 0.3592250 0.3786800 0.3879436
##  [538,] 0.2992616 0.3332900 0.3338811 0.3484360 0.3624612 0.3805660 0.3954252
##  [539,] 0.3146072 0.3194572 0.3268754 0.3530711 0.3686598 0.3741114 0.3935231
##  [540,] 0.3186541 0.3172573 0.3462987 0.3633767 0.3664010 0.3788937 0.3984870
##  [541,] 0.2943831 0.3201295 0.3360678 0.3528553 0.3578848 0.3799963 0.3991131
##  [542,] 0.3108398 0.3212351 0.3343083 0.3424119 0.3578669 0.3760595 0.3971435
##  [543,] 0.2923438 0.3206968 0.3295983 0.3507346 0.3635393 0.3771257 0.3950210
##  [544,] 0.2987346 0.3377242 0.3465994 0.3501217 0.3615245 0.3772862 0.3990316
##  [545,] 0.2989790 0.3064151 0.3290887 0.3479302 0.3629194 0.3846426 0.3922135
##  [546,] 0.3026605 0.3372658 0.3376355 0.3528946 0.3664110 0.3758180 0.3942118
##  [547,] 0.3034184 0.3235566 0.3302845 0.3586672 0.3554566 0.3777567 0.3912884
##  [548,] 0.3064813 0.3237350 0.3363666 0.3440379 0.3625355 0.3766938 0.3995505
##  [549,] 0.2973832 0.3212334 0.3335345 0.3454822 0.3645385 0.3780740 0.3947806
##  [550,] 0.3102994 0.3194751 0.3432438 0.3423216 0.3675598 0.3772036 0.3914197
##  [551,] 0.3075081 0.3265680 0.3321408 0.3582259 0.3685403 0.3828760 0.3970988
##  [552,] 0.3144670 0.3154683 0.3369640 0.3473303 0.3600112 0.3775535 0.3896570
##  [553,] 0.3046029 0.3141359 0.3405345 0.3352993 0.3549179 0.3798675 0.3941144
##  [554,] 0.3104605 0.3236175 0.3353088 0.3444740 0.3580305 0.3827763 0.3926927
##  [555,] 0.3125741 0.3245100 0.3280721 0.3486219 0.3620025 0.3813228 0.3953707
##  [556,] 0.3047161 0.3160327 0.3302460 0.3447588 0.3535452 0.3769527 0.3935985
##  [557,] 0.2929563 0.3214558 0.3242022 0.3436989 0.3577365 0.3767732 0.3944882
##  [558,] 0.3025138 0.3022372 0.3303057 0.3551857 0.3579761 0.3764587 0.3925653
##  [559,] 0.3079559 0.3208748 0.3265541 0.3434281 0.3674375 0.3776259 0.3961027
##  [560,] 0.2995272 0.3105271 0.3479956 0.3483316 0.3607244 0.3718022 0.3916095
##  [561,] 0.3042557 0.3275518 0.3362549 0.3462455 0.3626897 0.3797278 0.4006832
##  [562,] 0.3084246 0.3121836 0.3366958 0.3528993 0.3717773 0.3751789 0.3926294
##  [563,] 0.3068455 0.3227378 0.3355205 0.3465245 0.3649716 0.3796369 0.4010437
##  [564,] 0.3142986 0.3261651 0.3370461 0.3442553 0.3641131 0.3847780 0.3967930
##  [565,] 0.3101025 0.3203981 0.3364284 0.3508000 0.3666330 0.3745798 0.3951478
##  [566,] 0.3066303 0.3244977 0.3339343 0.3473192 0.3615393 0.3824215 0.3884495
##  [567,] 0.2992451 0.3197592 0.3258187 0.3484944 0.3549925 0.3770100 0.3934904
##  [568,] 0.3101521 0.3347058 0.3238695 0.3435342 0.3712804 0.3785219 0.3932951
##  [569,] 0.3101076 0.3224655 0.3336650 0.3569780 0.3664110 0.3742099 0.3934255
##  [570,] 0.2879684 0.3266132 0.3372245 0.3429437 0.3728235 0.3759115 0.3939584
##  [571,] 0.3112614 0.3176095 0.3342462 0.3514102 0.3601975 0.3753122 0.3935722
##  [572,] 0.3041929 0.3177629 0.3337469 0.3442385 0.3630878 0.3701247 0.3944768
##  [573,] 0.3056146 0.3189240 0.3331170 0.3442656 0.3682410 0.3856097 0.3963858
##  [574,] 0.3180815 0.3224867 0.3388977 0.3446713 0.3638677 0.3843936 0.3948857
##  [575,] 0.2965136 0.3186484 0.3266882 0.3448785 0.3597887 0.3776511 0.3915908
##  [576,] 0.3016100 0.3180341 0.3315367 0.3400455 0.3590947 0.3871062 0.3925645
##  [577,] 0.3186748 0.3179054 0.3375456 0.3519501 0.3628596 0.3755732 0.3950881
##  [578,] 0.2986647 0.3189246 0.3470854 0.3540738 0.3745873 0.3801382 0.3918250
##  [579,] 0.3107318 0.3196511 0.3322200 0.3524180 0.3670894 0.3803252 0.3960647
##  [580,] 0.3047415 0.3150677 0.3169356 0.3485306 0.3654844 0.3754210 0.3956121
##  [581,] 0.2979634 0.3148625 0.3374098 0.3502560 0.3628499 0.3744855 0.3922960
##  [582,] 0.3150017 0.3246545 0.3218808 0.3539398 0.3646461 0.3791239 0.3891265
##  [583,] 0.3130441 0.3135765 0.3218833 0.3506038 0.3597546 0.3819882 0.4008524
##  [584,] 0.3009290 0.3229214 0.3258215 0.3430503 0.3678296 0.3820240 0.3986771
##  [585,] 0.2937880 0.3035783 0.3414692 0.3489602 0.3641726 0.3776165 0.3999017
##  [586,] 0.3084933 0.3106687 0.3200882 0.3478921 0.3564730 0.3775366 0.3929792
##  [587,] 0.2886697 0.3240278 0.3417380 0.3546893 0.3540930 0.3712530 0.3937995
##  [588,] 0.2983171 0.3167188 0.3296927 0.3466738 0.3578249 0.3769890 0.3935391
##  [589,] 0.2912799 0.3151367 0.3370663 0.3512397 0.3587333 0.3815476 0.3932464
##  [590,] 0.3071084 0.3227150 0.3417640 0.3400787 0.3551436 0.3758415 0.3940204
##  [591,] 0.3001681 0.3218229 0.3340309 0.3524880 0.3642523 0.3791279 0.3979567
##  [592,] 0.3182457 0.3199705 0.3276911 0.3471559 0.3689340 0.3770027 0.3929976
##  [593,] 0.3067705 0.3300349 0.3432252 0.3489837 0.3666876 0.3813389 0.4007559
##  [594,] 0.3008097 0.3245480 0.3327481 0.3461642 0.3652983 0.3773260 0.3961713
##  [595,] 0.2952877 0.3232253 0.3356659 0.3609939 0.3579101 0.3791120 0.3943241
##  [596,] 0.3001023 0.3256775 0.3342097 0.3523796 0.3639443 0.3811615 0.3946741
##  [597,] 0.3003918 0.3184970 0.3373152 0.3477193 0.3631248 0.3759424 0.3960746
##  [598,] 0.3021293 0.3268712 0.3403059 0.3483058 0.3619637 0.3788933 0.3953571
##  [599,] 0.3030969 0.3038162 0.3333694 0.3484839 0.3605081 0.3788250 0.3966373
##  [600,] 0.3118126 0.3166351 0.3346755 0.3509550 0.3638901 0.3771788 0.3953988
##  [601,] 0.3044009 0.3179669 0.3278851 0.3495397 0.3671933 0.3775271 0.3954931
##  [602,] 0.3036469 0.3158299 0.3278612 0.3480891 0.3653101 0.3809038 0.3980651
##  [603,] 0.2996571 0.3190311 0.3248050 0.3575635 0.3649687 0.3793083 0.3943819
##  [604,] 0.3109426 0.3293109 0.3482561 0.3485855 0.3620648 0.3775732 0.3917259
##  [605,] 0.3003475 0.3270479 0.3352022 0.3500237 0.3586234 0.3808044 0.3935028
##  [606,] 0.2953985 0.3177389 0.3279360 0.3438986 0.3579319 0.3729819 0.3930815
##  [607,] 0.3098012 0.3172533 0.3261849 0.3458897 0.3627324 0.3779910 0.3913156
##  [608,] 0.3094267 0.3237818 0.3424680 0.3402292 0.3650685 0.3758267 0.3933493
##  [609,] 0.3090427 0.3106056 0.3299162 0.3429778 0.3624690 0.3717421 0.3923964
##  [610,] 0.2958915 0.3141819 0.3361890 0.3557293 0.3657149 0.3749309 0.3901468
##  [611,] 0.3144615 0.3228565 0.3342271 0.3470279 0.3587927 0.3830483 0.3958233
##  [612,] 0.3025173 0.3273182 0.3348749 0.3485730 0.3627398 0.3784270 0.3972308
##  [613,] 0.3078188 0.3209380 0.3322612 0.3454807 0.3623432 0.3751682 0.3996213
##  [614,] 0.3174758 0.3248666 0.3342911 0.3438343 0.3686131 0.3760119 0.3871446
##  [615,] 0.3115642 0.3103702 0.3405137 0.3380200 0.3599632 0.3772668 0.3953820
##  [616,] 0.3121803 0.3090120 0.3396770 0.3579536 0.3549803 0.3812556 0.3926065
##  [617,] 0.2970376 0.3261527 0.3355642 0.3474691 0.3508760 0.3759791 0.3935533
##  [618,] 0.3089954 0.3133758 0.3359715 0.3415532 0.3627622 0.3783728 0.3881978
##  [619,] 0.3030557 0.3265556 0.3351726 0.3522156 0.3530322 0.3811737 0.3943379
##  [620,] 0.3222829 0.3195899 0.3360930 0.3451540 0.3639432 0.3742519 0.3954342
##  [621,] 0.3027103 0.3124915 0.3355142 0.3471615 0.3659094 0.3786363 0.3968517
##  [622,] 0.3143500 0.3054060 0.3233630 0.3540299 0.3640823 0.3747745 0.3989522
##  [623,] 0.2897049 0.3285059 0.3343221 0.3529951 0.3638365 0.3772229 0.3992478
##  [624,] 0.2969962 0.3314557 0.3382743 0.3422721 0.3687625 0.3794278 0.3963245
##  [625,] 0.2935372 0.3110940 0.3339196 0.3422888 0.3668258 0.3722032 0.3926602
##  [626,] 0.3075407 0.3023265 0.3380895 0.3408687 0.3546782 0.3816769 0.3920976
##  [627,] 0.2899496 0.3090761 0.3291811 0.3370174 0.3661233 0.3826483 0.3963830
##  [628,] 0.2937914 0.3246518 0.3410010 0.3424705 0.3627819 0.3788383 0.3965214
##  [629,] 0.3083855 0.3158755 0.3393423 0.3463076 0.3690598 0.3724285 0.3954065
##  [630,] 0.2967740 0.3065553 0.3267419 0.3513105 0.3643764 0.3805534 0.3929301
##  [631,] 0.2921596 0.3223424 0.3429805 0.3432598 0.3573402 0.3758664 0.3926967
##  [632,] 0.3074118 0.3226422 0.3316237 0.3475260 0.3654350 0.3764900 0.3917285
##  [633,] 0.3226455 0.3114990 0.3307989 0.3524082 0.3614670 0.3824571 0.3942943
##  [634,] 0.3090629 0.3173814 0.3459045 0.3468910 0.3583635 0.3775757 0.3900976
##  [635,] 0.3207861 0.3120268 0.3365353 0.3545958 0.3612834 0.3779286 0.3992642
##  [636,] 0.3140282 0.3238456 0.3418836 0.3449864 0.3614725 0.3765289 0.3903920
##  [637,] 0.3161338 0.3251690 0.3282381 0.3558011 0.3678196 0.3768044 0.3975347
##  [638,] 0.3213759 0.3032026 0.3419896 0.3410121 0.3644004 0.3759954 0.3905833
##  [639,] 0.3186630 0.3356350 0.3293215 0.3463764 0.3606536 0.3795704 0.3975905
##  [640,] 0.3133953 0.3165561 0.3294588 0.3503714 0.3519230 0.3731234 0.3909879
##  [641,] 0.3017859 0.3137867 0.3412659 0.3434449 0.3666388 0.3786642 0.3952629
##  [642,] 0.3139742 0.3156937 0.3423431 0.3480175 0.3583202 0.3810495 0.3934475
##  [643,] 0.2942844 0.3212258 0.3359955 0.3471556 0.3617243 0.3756212 0.3929680
##  [644,] 0.3035704 0.3034207 0.3297938 0.3508521 0.3665406 0.3787115 0.3961563
##  [645,] 0.3003755 0.3129275 0.3291691 0.3334215 0.3623275 0.3759189 0.3941499
##  [646,] 0.3021164 0.3178114 0.3355712 0.3437116 0.3675636 0.3775479 0.4016090
##  [647,] 0.2973542 0.3249637 0.3316617 0.3497478 0.3612037 0.3758575 0.3919796
##  [648,] 0.3124392 0.3217988 0.3344382 0.3562673 0.3589108 0.3748131 0.3934355
##  [649,] 0.2972559 0.3165428 0.3312356 0.3478920 0.3620510 0.3745462 0.3961593
##  [650,] 0.3019911 0.3266028 0.3295755 0.3613581 0.3659168 0.3809841 0.3971509
##  [651,] 0.3167307 0.3281179 0.3374899 0.3475224 0.3630154 0.3840862 0.3923836
##  [652,] 0.2964253 0.3205814 0.3272463 0.3555240 0.3744404 0.3812729 0.3974639
##  [653,] 0.3198151 0.3229565 0.3390228 0.3482619 0.3655330 0.3758353 0.3905622
##  [654,] 0.2952490 0.3253629 0.3356010 0.3525672 0.3590768 0.3771506 0.3934288
##  [655,] 0.2815530 0.3364771 0.3385692 0.3385769 0.3717811 0.3712170 0.3943934
##  [656,] 0.2942483 0.3144721 0.3318078 0.3416572 0.3692458 0.3753517 0.3956338
##  [657,] 0.3010827 0.3125556 0.3408996 0.3525494 0.3649883 0.3738837 0.3913896
##  [658,] 0.3048637 0.3110947 0.3303045 0.3436040 0.3613828 0.3770334 0.3870554
##  [659,] 0.3085696 0.3278049 0.3267606 0.3458863 0.3608295 0.3764919 0.3922620
##  [660,] 0.3028471 0.3198373 0.3375347 0.3543961 0.3597488 0.3803025 0.3927072
##  [661,] 0.2971268 0.3271382 0.3353262 0.3436152 0.3575704 0.3752078 0.3944117
##  [662,] 0.2972762 0.3209192 0.3332165 0.3406101 0.3619454 0.3767230 0.4031188
##  [663,] 0.3108622 0.3292562 0.3471516 0.3551806 0.3631514 0.3781144 0.3962471
##  [664,] 0.3084530 0.3106582 0.3260461 0.3520762 0.3621781 0.3817447 0.3898095
##  [665,] 0.2980576 0.3183181 0.3440141 0.3503673 0.3629610 0.3753445 0.3916698
##  [666,] 0.3117211 0.3164081 0.3328571 0.3436084 0.3568003 0.3784690 0.3911269
##  [667,] 0.3099754 0.3017728 0.3294492 0.3369010 0.3661239 0.3810129 0.3957217
##  [668,] 0.3140366 0.3200553 0.3370679 0.3490262 0.3622924 0.3769024 0.3920823
##  [669,] 0.3009630 0.3238088 0.3453436 0.3558542 0.3588877 0.3779066 0.3954925
##  [670,] 0.3046746 0.3297134 0.3409809 0.3445965 0.3636992 0.3767624 0.3953885
##  [671,] 0.2897611 0.3250388 0.3347277 0.3393001 0.3553714 0.3774036 0.3970578
##  [672,] 0.2754567 0.3199775 0.3283188 0.3419353 0.3676703 0.3784939 0.3916917
##  [673,] 0.3102272 0.3010440 0.3342247 0.3484029 0.3582778 0.3814517 0.3946945
##  [674,] 0.3085629 0.3279813 0.3250272 0.3449485 0.3581366 0.3837737 0.3897780
##  [675,] 0.3008931 0.3068460 0.3316729 0.3458358 0.3635692 0.3769237 0.3950448
##  [676,] 0.3099330 0.3096126 0.3371705 0.3524761 0.3640894 0.3763007 0.3957113
##  [677,] 0.2963128 0.3174378 0.3267765 0.3502009 0.3672384 0.3789321 0.3986498
##  [678,] 0.2993877 0.3126973 0.3350939 0.3412815 0.3531341 0.3790359 0.3947870
##  [679,] 0.3143642 0.3270969 0.3301442 0.3489243 0.3518790 0.3783842 0.3946600
##  [680,] 0.2962820 0.3240320 0.3357403 0.3351158 0.3631441 0.3815402 0.3925787
##  [681,] 0.3152981 0.3303909 0.3385955 0.3403935 0.3654992 0.3741159 0.3953805
##  [682,] 0.3113582 0.3216076 0.3419591 0.3587422 0.3611878 0.3803518 0.3973385
##  [683,] 0.3160285 0.3325565 0.3354478 0.3394979 0.3571788 0.3831412 0.3935665
##  [684,] 0.3109485 0.3293507 0.3293179 0.3427626 0.3630924 0.3737605 0.3943956
##  [685,] 0.3055072 0.2973092 0.3275706 0.3580652 0.3666793 0.3796216 0.3957140
##  [686,] 0.3112511 0.3107771 0.3330747 0.3517482 0.3635062 0.3768943 0.3900370
##  [687,] 0.3056992 0.3187191 0.3340611 0.3461790 0.3656187 0.3744994 0.3898327
##  [688,] 0.3081194 0.3152108 0.3459558 0.3483516 0.3619713 0.3772211 0.3992106
##  [689,] 0.3061575 0.3040286 0.3213018 0.3456621 0.3622481 0.3831640 0.3941850
##  [690,] 0.2968712 0.3298451 0.3245965 0.3488610 0.3570511 0.3801403 0.3920791
##  [691,] 0.3170167 0.3184871 0.3395540 0.3482940 0.3675757 0.3761229 0.3934598
##  [692,] 0.3163138 0.3275753 0.3404706 0.3450610 0.3683619 0.3812031 0.3944874
##  [693,] 0.3178298 0.3153562 0.3082132 0.3530197 0.3693464 0.3737878 0.3919592
##  [694,] 0.2985654 0.3208844 0.3385223 0.3458235 0.3572865 0.3795780 0.3944720
##  [695,] 0.3257224 0.3168289 0.3283563 0.3486403 0.3724011 0.3770736 0.3940072
##  [696,] 0.3036935 0.3179560 0.3402038 0.3609257 0.3624931 0.3774648 0.3987162
##  [697,] 0.3219184 0.3336404 0.3288445 0.3514372 0.3541400 0.3718689 0.3962870
##  [698,] 0.3119423 0.3127045 0.3390655 0.3459616 0.3625723 0.3765571 0.3991387
##  [699,] 0.2991627 0.3129695 0.3354139 0.3327590 0.3636981 0.3814311 0.3966826
##  [700,] 0.2988058 0.3170850 0.3248015 0.3525263 0.3611376 0.3796598 0.3930914
##  [701,] 0.3101175 0.3221317 0.3420602 0.3290937 0.3627491 0.3748830 0.3936422
##  [702,] 0.2947967 0.3207402 0.3328648 0.3449456 0.3671675 0.3848231 0.3930424
##  [703,] 0.3000553 0.3233006 0.3346110 0.3459049 0.3607689 0.3777924 0.3938471
##  [704,] 0.2995695 0.3249314 0.3318242 0.3415675 0.3623737 0.3796477 0.3883473
##  [705,] 0.3166665 0.3139046 0.3411990 0.3478017 0.3568234 0.3777872 0.3891558
##  [706,] 0.3100810 0.3127135 0.3320173 0.3520554 0.3558888 0.3829259 0.3937356
##  [707,] 0.3196161 0.3327809 0.3269988 0.3408677 0.3665187 0.3769333 0.3963805
##  [708,] 0.3122451 0.3125154 0.3286760 0.3465894 0.3659679 0.3772749 0.3939117
##  [709,] 0.3147651 0.3213674 0.3298472 0.3388503 0.3590188 0.3803397 0.3931345
##  [710,] 0.2925128 0.3204436 0.3427949 0.3471000 0.3562266 0.3819827 0.3893034
##  [711,] 0.3086162 0.3009876 0.3420151 0.3505806 0.3633796 0.3883819 0.3895753
##  [712,] 0.3151748 0.3289167 0.3292426 0.3561890 0.3631107 0.3780121 0.3908177
##  [713,] 0.2988816 0.3160208 0.3282177 0.3523747 0.3588150 0.3816216 0.3936613
##  [714,] 0.3078923 0.3256305 0.3343628 0.3475820 0.3656912 0.3720605 0.3928322
##  [715,] 0.3120509 0.3188658 0.3291082 0.3529774 0.3601039 0.3676007 0.3943607
##  [716,] 0.2991938 0.3324849 0.3347903 0.3519652 0.3602299 0.3708683 0.3967995
##  [717,] 0.2991348 0.3174864 0.3298401 0.3594435 0.3602028 0.3836279 0.3977468
##  [718,] 0.3044742 0.3169220 0.3324143 0.3480297 0.3617394 0.3852392 0.3927786
##  [719,] 0.3059252 0.3266175 0.3327191 0.3452950 0.3673342 0.3820526 0.3914052
##  [720,] 0.2993402 0.3210776 0.3418441 0.3482095 0.3617725 0.3810719 0.3958822
##  [721,] 0.3118885 0.3107174 0.3386768 0.3509879 0.3633657 0.3729991 0.3961223
##  [722,] 0.3081749 0.3289333 0.3390735 0.3559726 0.3650949 0.3745422 0.3904560
##  [723,] 0.3097871 0.3165588 0.3304391 0.3526820 0.3614115 0.3818350 0.3978883
##  [724,] 0.3122060 0.3220812 0.3390024 0.3511688 0.3642442 0.3799466 0.3893670
##  [725,] 0.3110002 0.3234128 0.3291314 0.3506156 0.3550221 0.3784499 0.3946662
##  [726,] 0.3016156 0.3148959 0.3366432 0.3481867 0.3714118 0.3801223 0.3965666
##  [727,] 0.3116628 0.3238378 0.3411890 0.3435106 0.3552325 0.3812913 0.3934910
##  [728,] 0.3212804 0.3303108 0.3327214 0.3454610 0.3627652 0.3752715 0.3897864
##  [729,] 0.3146306 0.3102012 0.3421916 0.3467991 0.3623802 0.3773199 0.3918920
##  [730,] 0.3148023 0.3188529 0.3284197 0.3459793 0.3681867 0.3725555 0.3949113
##  [731,] 0.3056813 0.3287060 0.3281814 0.3548040 0.3570513 0.3738723 0.4019159
##  [732,] 0.3181049 0.3161888 0.3434836 0.3629931 0.3694866 0.3784949 0.3934777
##  [733,] 0.3306620 0.3340777 0.3381075 0.3393488 0.3635278 0.3795336 0.4002309
##  [734,] 0.3002188 0.3166432 0.3317767 0.3516192 0.3548905 0.3847593 0.3951742
##  [735,] 0.3029083 0.3173797 0.3392740 0.3492477 0.3598657 0.3805676 0.3965943
##  [736,] 0.3069297 0.3203893 0.3299615 0.3565445 0.3721391 0.3838830 0.3957151
##  [737,] 0.3068134 0.3314001 0.3292930 0.3544523 0.3611328 0.3793492 0.3901579
##  [738,] 0.2998170 0.3190985 0.3263519 0.3468028 0.3683410 0.3824700 0.3947328
##  [739,] 0.3179915 0.3279020 0.3411222 0.3453911 0.3571755 0.3795356 0.3926954
##  [740,] 0.3308363 0.3327604 0.3416870 0.3514856 0.3632439 0.3747696 0.3967840
##  [741,] 0.2931180 0.3214407 0.3399218 0.3502773 0.3674143 0.3745911 0.3940725
##  [742,] 0.2896646 0.3172763 0.3271692 0.3407306 0.3583447 0.3855548 0.3919520
##  [743,] 0.3155838 0.3154176 0.3237912 0.3403263 0.3587609 0.3792727 0.3952245
##  [744,] 0.3013299 0.3168744 0.3319915 0.3461997 0.3640217 0.3803531 0.3914532
##  [745,] 0.3161697 0.3177087 0.3375583 0.3424958 0.3564266 0.3714084 0.3919881
##  [746,] 0.3117599 0.3102379 0.3380223 0.3358538 0.3600861 0.3741390 0.3981459
##  [747,] 0.3215065 0.3087320 0.3262922 0.3430604 0.3645137 0.3739315 0.4024267
##  [748,] 0.2873639 0.3135621 0.3435964 0.3619328 0.3617775 0.3730781 0.3989511
##  [749,] 0.2985437 0.3186886 0.3302304 0.3481419 0.3597848 0.3820194 0.3934314
##  [750,] 0.3214337 0.3199109 0.3357467 0.3420465 0.3576003 0.3834774 0.3919691
##  [751,] 0.3115411 0.3150879 0.3323280 0.3455399 0.3600829 0.3787222 0.3946343
##  [752,] 0.3033464 0.3175347 0.3299457 0.3461399 0.3581366 0.3771770 0.3976332
##  [753,] 0.3130137 0.3134504 0.3382891 0.3558168 0.3625469 0.3760374 0.3984730
##  [754,] 0.3188689 0.3123144 0.3380987 0.3382430 0.3651003 0.3827621 0.3908851
##  [755,] 0.2993499 0.3284533 0.3344576 0.3465881 0.3662635 0.3809822 0.3961599
##  [756,] 0.2966054 0.3183016 0.3464678 0.3487690 0.3632679 0.3726739 0.3949819
##  [757,] 0.3124666 0.3075351 0.3361938 0.3556937 0.3612706 0.3751675 0.3919190
##  [758,] 0.3081135 0.3151007 0.3380980 0.3447699 0.3613736 0.3720694 0.3955105
##  [759,] 0.3062423 0.3159881 0.3363034 0.3497097 0.3655529 0.3731948 0.3956530
##  [760,] 0.2931088 0.3235935 0.3276158 0.3507150 0.3649335 0.3805507 0.3926845
##  [761,] 0.3037855 0.3228442 0.3354575 0.3345257 0.3560097 0.3821113 0.3895861
##  [762,] 0.3149023 0.3144700 0.3188934 0.3415152 0.3606391 0.3781203 0.3945453
##  [763,] 0.3126379 0.3235356 0.3302535 0.3536317 0.3678719 0.3823646 0.3913965
##  [764,] 0.3033629 0.3351213 0.3254764 0.3559410 0.3626834 0.3831091 0.3914879
##  [765,] 0.3082210 0.3160615 0.3252332 0.3393277 0.3657805 0.3785700 0.3929355
##  [766,] 0.3159799 0.3268374 0.3292749 0.3480772 0.3701421 0.3793755 0.3945230
##  [767,] 0.3035427 0.3140596 0.3406570 0.3500820 0.3617805 0.3742064 0.3914380
##  [768,] 0.3002768 0.3175402 0.3259489 0.3476387 0.3628537 0.3769873 0.3985184
##  [769,] 0.3126980 0.3180170 0.3424070 0.3514789 0.3684318 0.3746663 0.3947538
##  [770,] 0.3066205 0.3217009 0.3232402 0.3399733 0.3684626 0.3783285 0.3929421
##  [771,] 0.3051739 0.3212074 0.3468950 0.3503413 0.3687055 0.3835545 0.3881780
##  [772,] 0.3039545 0.3163488 0.3268881 0.3508088 0.3669048 0.3812256 0.3907002
##  [773,] 0.3167510 0.3229196 0.3363773 0.3491501 0.3679534 0.3804534 0.3944989
##  [774,] 0.3081932 0.3200578 0.3344888 0.3492092 0.3553112 0.3816797 0.3980180
##  [775,] 0.3181342 0.3184237 0.3326408 0.3415483 0.3668108 0.3715538 0.3911644
##  [776,] 0.3018835 0.3196553 0.3364301 0.3515555 0.3700550 0.3791955 0.3974353
##  [777,] 0.3260833 0.3049354 0.3370319 0.3537168 0.3653441 0.3736520 0.3911192
##  [778,] 0.2998366 0.3113759 0.3233642 0.3402435 0.3603089 0.3795652 0.3980930
##  [779,] 0.3047924 0.3277419 0.3333390 0.3504852 0.3611894 0.3778919 0.4032881
##  [780,] 0.3026255 0.3251531 0.3200221 0.3518623 0.3641777 0.3794493 0.3898930
##  [781,] 0.3089427 0.3171940 0.3336942 0.3485665 0.3604835 0.3768242 0.3930095
##  [782,] 0.3094730 0.3304948 0.3312335 0.3446252 0.3661098 0.3777594 0.3904312
##  [783,] 0.3074712 0.3165469 0.3266084 0.3479244 0.3638952 0.3792723 0.3960629
##  [784,] 0.3094451 0.3291908 0.3400908 0.3478634 0.3630048 0.3841551 0.3889001
##  [785,] 0.2915394 0.3239045 0.3378221 0.3574085 0.3627088 0.3814941 0.3971695
##  [786,] 0.3023302 0.3194926 0.3353412 0.3594381 0.3661974 0.3838750 0.3869270
##  [787,] 0.2969378 0.3149501 0.3484548 0.3527824 0.3592806 0.3798071 0.3927764
##  [788,] 0.3160090 0.3257066 0.3262515 0.3448100 0.3622223 0.3761332 0.3992362
##  [789,] 0.3147864 0.3217373 0.3308245 0.3492862 0.3633416 0.3741553 0.3953577
##  [790,] 0.3065461 0.3243694 0.3314697 0.3441703 0.3599981 0.3745250 0.3911103
##  [791,] 0.3029940 0.3191143 0.3366732 0.3508963 0.3637641 0.3801264 0.3893294
##  [792,] 0.3137834 0.3196381 0.3465705 0.3418117 0.3537373 0.3739067 0.3912956
##  [793,] 0.3074893 0.3128170 0.3293178 0.3416847 0.3643076 0.3841633 0.3930272
##  [794,] 0.3187319 0.3201356 0.3346530 0.3452529 0.3588726 0.3750633 0.3915137
##  [795,] 0.3067055 0.3237942 0.3311604 0.3435569 0.3547838 0.3752866 0.3990814
##  [796,] 0.3003460 0.3130820 0.3302338 0.3420093 0.3572512 0.3754313 0.3905635
##  [797,] 0.3135222 0.3125231 0.3397664 0.3558598 0.3572275 0.3822530 0.3999213
##  [798,] 0.3016040 0.3130296 0.3240309 0.3482170 0.3618451 0.3759499 0.3988184
##  [799,] 0.2986827 0.3236437 0.3389843 0.3517664 0.3725073 0.3704521 0.3925827
##  [800,] 0.2965577 0.3117605 0.3295349 0.3524305 0.3594488 0.3803787 0.3972813
##  [801,] 0.3120730 0.3133525 0.3317454 0.3503919 0.3603037 0.3714925 0.3965890
##  [802,] 0.3025549 0.3160300 0.3351859 0.3514387 0.3672747 0.3858401 0.3955633
##  [803,] 0.3213349 0.3093893 0.3282971 0.3521468 0.3577658 0.3825940 0.3928396
##  [804,] 0.3113951 0.3048096 0.3243395 0.3446607 0.3536132 0.3749935 0.3977787
##  [805,] 0.3009358 0.3094124 0.3406845 0.3518719 0.3614698 0.3757814 0.3933526
##  [806,] 0.3111171 0.3247321 0.3372560 0.3423485 0.3684790 0.3766791 0.3941530
##  [807,] 0.3036261 0.3184783 0.3341385 0.3485080 0.3693741 0.3797791 0.3939046
##  [808,] 0.3160926 0.3118776 0.3305447 0.3355361 0.3619385 0.3873403 0.3999843
##  [809,] 0.3200149 0.3246773 0.3309486 0.3523537 0.3629326 0.3726509 0.3956120
##  [810,] 0.3099725 0.3150233 0.3392294 0.3446306 0.3678165 0.3779827 0.3900546
##  [811,] 0.3219382 0.3195397 0.3346564 0.3486927 0.3598512 0.3783838 0.3952450
##  [812,] 0.3036981 0.3105445 0.3328489 0.3519254 0.3615536 0.3785287 0.3971488
##  [813,] 0.2916880 0.3237496 0.3468342 0.3508965 0.3634827 0.3776637 0.3970925
##  [814,] 0.3006942 0.3282407 0.3397621 0.3508375 0.3584326 0.3770003 0.3920129
##  [815,] 0.2914686 0.3208375 0.3295781 0.3413200 0.3685634 0.3791363 0.3961119
##  [816,] 0.3029337 0.3152121 0.3372750 0.3495235 0.3597140 0.3803240 0.3925173
##  [817,] 0.3023164 0.3166082 0.3291645 0.3407359 0.3689074 0.3796051 0.3957482
##  [818,] 0.2991291 0.3290107 0.3272307 0.3492157 0.3561591 0.3754836 0.3952648
##  [819,] 0.3133168 0.3111402 0.3455123 0.3494654 0.3615092 0.3767282 0.3962344
##  [820,] 0.3038330 0.3166893 0.3465469 0.3413848 0.3606048 0.3773443 0.3923710
##  [821,] 0.2981611 0.3165889 0.3380039 0.3407576 0.3594025 0.3809513 0.3922130
##  [822,] 0.3057957 0.3150952 0.3431277 0.3434415 0.3717182 0.3815345 0.3961218
##  [823,] 0.2953229 0.3166138 0.3438965 0.3488508 0.3534664 0.3844948 0.3947139
##  [824,] 0.2995294 0.3175269 0.3445361 0.3447684 0.3636201 0.3750203 0.3992974
##  [825,] 0.3144550 0.3089694 0.3186667 0.3535281 0.3603664 0.3810176 0.3913051
##  [826,] 0.3112011 0.3244962 0.3309704 0.3416894 0.3584421 0.3765788 0.3943717
##  [827,] 0.3144831 0.3210840 0.3296008 0.3397733 0.3613484 0.3733748 0.3894340
##  [828,] 0.3103280 0.3133493 0.3260331 0.3481377 0.3680032 0.3768159 0.3968622
##  [829,] 0.3169090 0.3177801 0.3368862 0.3495569 0.3538896 0.3787525 0.3949006
##  [830,] 0.3255077 0.3288782 0.3413487 0.3497146 0.3638434 0.3829651 0.3960846
##  [831,] 0.2991481 0.3125681 0.3446751 0.3463571 0.3535872 0.3753104 0.3966854
##  [832,] 0.3207037 0.3071939 0.3384234 0.3444861 0.3658808 0.3731407 0.3914813
##  [833,] 0.3231078 0.3192640 0.3272948 0.3439230 0.3672059 0.3744836 0.3952040
##  [834,] 0.2988048 0.3209116 0.3319963 0.3472771 0.3590112 0.3806373 0.3928113
##  [835,] 0.3112886 0.3298316 0.3297488 0.3445648 0.3654046 0.3788859 0.3897135
##  [836,] 0.3145142 0.3288475 0.3339717 0.3480124 0.3637643 0.3778653 0.3908777
##  [837,] 0.3009478 0.3309035 0.3404136 0.3386790 0.3596852 0.3742150 0.4023545
##  [838,] 0.3045265 0.3204286 0.3351470 0.3476258 0.3611898 0.3773776 0.3951518
##  [839,] 0.3173368 0.3170174 0.3334260 0.3407940 0.3595780 0.3820500 0.3977420
##  [840,] 0.2989776 0.3200776 0.3314735 0.3537306 0.3611258 0.3802605 0.3970582
##  [841,] 0.3153920 0.3145750 0.3326619 0.3486814 0.3588229 0.3800412 0.4004471
##  [842,] 0.3110840 0.3257977 0.3329206 0.3451405 0.3668148 0.3777108 0.3953114
##  [843,] 0.3169451 0.3068014 0.3322254 0.3511511 0.3636204 0.3776119 0.3958643
##  [844,] 0.3099575 0.3149017 0.3373718 0.3546475 0.3623544 0.3798965 0.3976003
##  [845,] 0.2972729 0.3220813 0.3219133 0.3427233 0.3611800 0.3782002 0.3983477
##  [846,] 0.3077231 0.3230270 0.3243788 0.3522933 0.3651038 0.3800185 0.3976435
##  [847,] 0.3082081 0.3251925 0.3220071 0.3386746 0.3611247 0.3767769 0.3925524
##  [848,] 0.3084046 0.3150540 0.3265464 0.3558189 0.3604878 0.3761175 0.3902920
##  [849,] 0.3081579 0.3134627 0.3311924 0.3498815 0.3593650 0.3816004 0.3977025
##  [850,] 0.2959653 0.3181115 0.3293206 0.3492414 0.3666032 0.3825111 0.3979271
##  [851,] 0.3125445 0.3153836 0.3271936 0.3486051 0.3693787 0.3754048 0.3932665
##  [852,] 0.2992026 0.3236561 0.3433107 0.3341575 0.3644110 0.3789122 0.3918747
##  [853,] 0.2986896 0.3255178 0.3222843 0.3486583 0.3665633 0.3799719 0.3929198
##  [854,] 0.2994158 0.3319431 0.3225059 0.3503415 0.3605103 0.3849478 0.3940952
##  [855,] 0.3004332 0.3176335 0.3315452 0.3528381 0.3630720 0.3794979 0.3948355
##  [856,] 0.2994121 0.3172996 0.3244439 0.3495021 0.3646276 0.3740243 0.3939762
##  [857,] 0.3051173 0.3219128 0.3341024 0.3500031 0.3647317 0.3774770 0.3907238
##  [858,] 0.2978243 0.3274907 0.3378937 0.3463902 0.3681206 0.3787002 0.3966840
##  [859,] 0.3022485 0.3398244 0.3307156 0.3462952 0.3634204 0.3851196 0.3938404
##  [860,] 0.3101543 0.3134109 0.3325139 0.3566744 0.3612045 0.3830064 0.3969690
##  [861,] 0.2981872 0.3204490 0.3234436 0.3550965 0.3572329 0.3774997 0.3963516
##  [862,] 0.3225085 0.3244902 0.3303627 0.3386890 0.3712581 0.3811809 0.3951573
##  [863,] 0.3006320 0.3321609 0.3413923 0.3424631 0.3624398 0.3717776 0.3927819
##  [864,] 0.3043066 0.3197762 0.3252200 0.3515113 0.3650263 0.3734839 0.3940417
##  [865,] 0.3071831 0.3127020 0.3381596 0.3425747 0.3637857 0.3756724 0.3902430
##  [866,] 0.2934200 0.3161617 0.3451996 0.3434237 0.3629985 0.3765783 0.3930388
##  [867,] 0.3042814 0.3084078 0.3415345 0.3452360 0.3622610 0.3757956 0.3919323
##  [868,] 0.3073496 0.3326872 0.3369470 0.3517368 0.3691204 0.3751992 0.3923790
##  [869,] 0.3144862 0.3274355 0.3463571 0.3477767 0.3641696 0.3760714 0.3968502
##  [870,] 0.2998447 0.3276579 0.3452041 0.3510490 0.3531261 0.3830292 0.3909934
##  [871,] 0.3044453 0.3240946 0.3392144 0.3633637 0.3622486 0.3777932 0.3928402
##  [872,] 0.3139713 0.3134968 0.3212093 0.3425983 0.3613368 0.3815229 0.3913993
##  [873,] 0.3091586 0.3037733 0.3429219 0.3506696 0.3625537 0.3787511 0.3930543
##  [874,] 0.3049586 0.3197713 0.3370352 0.3440655 0.3668099 0.3815126 0.3963087
##  [875,] 0.3175893 0.3253225 0.3374059 0.3499900 0.3561104 0.3789734 0.3944371
##  [876,] 0.3050965 0.3158936 0.3464884 0.3521594 0.3702819 0.3775622 0.3960392
##  [877,] 0.2935763 0.3176357 0.3296252 0.3477509 0.3589036 0.3769879 0.3905936
##  [878,] 0.3310040 0.3166712 0.3317349 0.3501954 0.3521809 0.3787839 0.3927955
##  [879,] 0.2993627 0.3242945 0.3343261 0.3447693 0.3576845 0.3720507 0.3992964
##  [880,] 0.3022732 0.3141156 0.3310549 0.3527101 0.3628007 0.3732754 0.3935014
##  [881,] 0.3052104 0.3250794 0.3175077 0.3512881 0.3629011 0.3797296 0.3966314
##  [882,] 0.3092573 0.3057016 0.3340614 0.3480066 0.3658742 0.3791301 0.3935569
##  [883,] 0.3072829 0.3074214 0.3344482 0.3453059 0.3637713 0.3748145 0.3918983
##  [884,] 0.3100292 0.3265229 0.3318600 0.3539276 0.3654174 0.3833112 0.4019588
##  [885,] 0.3160735 0.3250255 0.3244169 0.3398804 0.3698108 0.3782269 0.3910226
##  [886,] 0.3142000 0.3284383 0.3239702 0.3457338 0.3536921 0.3769308 0.3913575
##  [887,] 0.3025306 0.3199569 0.3367230 0.3393640 0.3595590 0.3758300 0.3930126
##  [888,] 0.2987672 0.3151513 0.3285302 0.3536338 0.3564379 0.3805444 0.3995115
##  [889,] 0.3132037 0.3136605 0.3358978 0.3495318 0.3641226 0.3766032 0.3993708
##  [890,] 0.3046005 0.3335722 0.3317637 0.3365123 0.3603037 0.3800392 0.3958680
##  [891,] 0.3093203 0.3028547 0.3374033 0.3483450 0.3590084 0.3707041 0.3932591
##  [892,] 0.3193434 0.3151880 0.3288471 0.3476013 0.3606720 0.3744404 0.3980696
##  [893,] 0.3226807 0.3137102 0.3329162 0.3426329 0.3649753 0.3754827 0.3988132
##  [894,] 0.3014447 0.3192945 0.3424033 0.3545101 0.3650057 0.3801280 0.3980197
##  [895,] 0.3057566 0.3329338 0.3278765 0.3587590 0.3588343 0.3827704 0.3973509
##  [896,] 0.3139022 0.3209357 0.3375477 0.3393247 0.3631510 0.3808039 0.3930806
##  [897,] 0.3179036 0.3105322 0.3272272 0.3535591 0.3637705 0.3699752 0.3924482
##  [898,] 0.3075352 0.3070715 0.3356554 0.3510210 0.3604784 0.3751199 0.3945127
##  [899,] 0.3157725 0.3127003 0.3220174 0.3458578 0.3679875 0.3811242 0.3917820
##  [900,] 0.3144919 0.3122619 0.3391827 0.3493829 0.3642611 0.3763129 0.3891942
##  [901,] 0.3031674 0.3265481 0.3393481 0.3492750 0.3603979 0.3817456 0.4003227
##  [902,] 0.3008403 0.3115556 0.3391521 0.3543504 0.3601115 0.3793091 0.3930669
##  [903,] 0.3090472 0.3146586 0.3424966 0.3494431 0.3645723 0.3746519 0.3923239
##  [904,] 0.2977731 0.3172446 0.3235524 0.3406539 0.3603947 0.3831477 0.3953747
##  [905,] 0.3164461 0.3273556 0.3222103 0.3456525 0.3657485 0.3809541 0.3963326
##  [906,] 0.3172565 0.3183320 0.3326183 0.3568322 0.3638435 0.3796068 0.3897315
##  [907,] 0.3118078 0.3133738 0.3431631 0.3611369 0.3630147 0.3781312 0.3955733
##  [908,] 0.2925996 0.3174173 0.3387882 0.3455025 0.3573383 0.3824149 0.3959435
##  [909,] 0.3090778 0.3293985 0.3449116 0.3569603 0.3614492 0.3842926 0.3959263
##  [910,] 0.3039832 0.3161994 0.3364469 0.3435719 0.3636445 0.3818690 0.3949401
##  [911,] 0.2998531 0.3311880 0.3262492 0.3458168 0.3596788 0.3837151 0.3930814
##  [912,] 0.3066205 0.3148990 0.3279934 0.3413615 0.3628844 0.3775802 0.3933586
##  [913,] 0.3222514 0.3300158 0.3290682 0.3473101 0.3625709 0.3818135 0.3948267
##  [914,] 0.3082726 0.3227919 0.3321578 0.3496178 0.3626856 0.3777134 0.3918986
##  [915,] 0.3270267 0.3346239 0.3314334 0.3535796 0.3710054 0.3788430 0.3928001
##  [916,] 0.2954923 0.3068480 0.3419820 0.3482970 0.3682762 0.3795944 0.3923558
##  [917,] 0.3196150 0.3170765 0.3333146 0.3433912 0.3622412 0.3712364 0.3930861
##  [918,] 0.3134199 0.3195072 0.3305553 0.3415102 0.3674231 0.3763987 0.3947751
##  [919,] 0.3002458 0.3139048 0.3178552 0.3402619 0.3654197 0.3805527 0.3961575
##  [920,] 0.3102489 0.3255772 0.3358663 0.3482123 0.3694031 0.3741226 0.4021050
##  [921,] 0.3130756 0.3124509 0.3285817 0.3514700 0.3560652 0.3771145 0.3966974
##  [922,] 0.3025233 0.3290019 0.3344163 0.3452777 0.3613492 0.3741427 0.3917345
##  [923,] 0.3128324 0.3461394 0.3248348 0.3493019 0.3622280 0.3782472 0.3948550
##  [924,] 0.3016553 0.3169676 0.3340458 0.3458249 0.3601288 0.3801145 0.3914949
##  [925,] 0.3015756 0.3251850 0.3399993 0.3499022 0.3638980 0.3770551 0.3930312
##  [926,] 0.2986122 0.3259298 0.3379032 0.3447411 0.3579565 0.3794773 0.3950194
##  [927,] 0.2927886 0.3236504 0.3275998 0.3505480 0.3677528 0.3739146 0.3945672
##  [928,] 0.3055286 0.3255865 0.3396313 0.3465247 0.3645229 0.3736882 0.3914563
##  [929,] 0.3026664 0.3204961 0.3290483 0.3493388 0.3673866 0.3757621 0.3901956
##  [930,] 0.3123143 0.3196047 0.3478682 0.3464331 0.3588967 0.3801007 0.3930730
##  [931,] 0.3055888 0.3191922 0.3272093 0.3508106 0.3609840 0.3780025 0.3924786
##  [932,] 0.3023035 0.3205845 0.3207910 0.3477615 0.3627466 0.3832478 0.3919717
##  [933,] 0.3040338 0.3002171 0.3307062 0.3475340 0.3607620 0.3804091 0.3974088
##  [934,] 0.2857185 0.3141195 0.3304911 0.3412133 0.3709338 0.3784323 0.3948476
##  [935,] 0.3072610 0.3180051 0.3339235 0.3386098 0.3647889 0.3677135 0.3954792
##  [936,] 0.3030217 0.3148512 0.3316822 0.3507871 0.3601200 0.3803646 0.3979611
##  [937,] 0.3188846 0.3188751 0.3430523 0.3450458 0.3595797 0.3756686 0.4009561
##  [938,] 0.2942525 0.3211031 0.3313258 0.3515552 0.3646573 0.3818778 0.3928272
##  [939,] 0.3035952 0.3288477 0.3257429 0.3489889 0.3514577 0.3803108 0.3921447
##  [940,] 0.3114938 0.3216429 0.3377330 0.3589085 0.3664658 0.3794744 0.3963600
##  [941,] 0.3001721 0.3320783 0.3285141 0.3526034 0.3596474 0.3747822 0.3958527
##  [942,] 0.3006472 0.3252735 0.3300754 0.3452135 0.3536588 0.3757234 0.3940853
##  [943,] 0.3092798 0.3126493 0.3209484 0.3453536 0.3655522 0.3889503 0.3942581
##  [944,] 0.3046659 0.3189460 0.3373524 0.3442632 0.3565682 0.3781824 0.3917624
##  [945,] 0.3127116 0.3194395 0.3251366 0.3542834 0.3718827 0.3770610 0.3933325
##  [946,] 0.3161668 0.3204095 0.3386424 0.3525491 0.3713789 0.3797840 0.3963634
##  [947,] 0.2915780 0.3127871 0.3330758 0.3483940 0.3651585 0.3812865 0.3916254
##  [948,] 0.3125462 0.3259523 0.3357009 0.3512645 0.3624019 0.3786145 0.3928501
##  [949,] 0.3024064 0.3087304 0.3326821 0.3432556 0.3628938 0.3812264 0.3951735
##  [950,] 0.3071964 0.3341164 0.3345543 0.3435370 0.3649888 0.3749810 0.3963803
##  [951,] 0.3207886 0.3245359 0.3372099 0.3576489 0.3569330 0.3787119 0.3934477
##  [952,] 0.3200849 0.3125886 0.3245329 0.3511367 0.3547140 0.3754677 0.3951315
##  [953,] 0.2975786 0.3150278 0.3399987 0.3459831 0.3636694 0.3811408 0.3936547
##  [954,] 0.3003913 0.3301993 0.3313834 0.3504619 0.3594126 0.3751864 0.3942939
##  [955,] 0.3071087 0.3174018 0.3378645 0.3388062 0.3608746 0.3705811 0.3895952
##  [956,] 0.3091719 0.3162398 0.3420205 0.3549619 0.3638789 0.3790291 0.3874068
##  [957,] 0.2911515 0.3309847 0.3451301 0.3463031 0.3627334 0.3780088 0.3894126
##  [958,] 0.3081674 0.3223934 0.3438145 0.3451627 0.3569541 0.3802201 0.3930293
##  [959,] 0.3021938 0.3211449 0.3295994 0.3530149 0.3596923 0.3789918 0.3966776
##  [960,] 0.3028784 0.3203469 0.3469008 0.3411888 0.3653513 0.3768109 0.3875320
##  [961,] 0.3078834 0.3187358 0.3313450 0.3489213 0.3591748 0.3823476 0.3960177
##  [962,] 0.3119414 0.3168834 0.3355868 0.3400834 0.3595269 0.3766405 0.3904775
##  [963,] 0.2953805 0.3147264 0.3501104 0.3556199 0.3678605 0.3737866 0.3994891
##  [964,] 0.3056500 0.3219629 0.3349096 0.3432964 0.3623614 0.3857750 0.4008423
##  [965,] 0.3009626 0.3162866 0.3355752 0.3504867 0.3656339 0.3695340 0.3926975
##  [966,] 0.3138261 0.3132361 0.3328571 0.3390211 0.3640434 0.3813868 0.3905558
##  [967,] 0.3085342 0.3126280 0.3166923 0.3450433 0.3601152 0.3799357 0.3983905
##  [968,] 0.2925546 0.3234913 0.3445472 0.3479837 0.3619035 0.3813680 0.3950277
##  [969,] 0.2927318 0.3130711 0.3174764 0.3495304 0.3688394 0.3806692 0.3977274
##  [970,] 0.3274935 0.3160238 0.3326783 0.3468353 0.3597875 0.3828498 0.3941502
##  [971,] 0.3113426 0.3192380 0.3307653 0.3481706 0.3529556 0.3813151 0.3951599
##  [972,] 0.3002752 0.3260482 0.3479461 0.3414504 0.3614272 0.3783318 0.3902077
##  [973,] 0.3076284 0.3229249 0.3193007 0.3473164 0.3646276 0.3732919 0.3902684
##  [974,] 0.3040955 0.3327648 0.3419127 0.3471688 0.3610590 0.3756018 0.4033829
##  [975,] 0.3035795 0.3213568 0.3423330 0.3487377 0.3589501 0.3753619 0.3912921
##  [976,] 0.3000150 0.3244746 0.3394619 0.3466682 0.3640930 0.3744982 0.3926360
##  [977,] 0.3078295 0.3163772 0.3268641 0.3437513 0.3703213 0.3740328 0.3950350
##  [978,] 0.3065782 0.3275111 0.3379471 0.3483726 0.3541778 0.3841701 0.3926140
##  [979,] 0.3089283 0.3150688 0.3264001 0.3480523 0.3611589 0.3864208 0.3931093
##  [980,] 0.3044640 0.3203098 0.3413415 0.3534487 0.3620410 0.3766792 0.4021931
##  [981,] 0.3240972 0.3198274 0.3385329 0.3405081 0.3596727 0.3787206 0.3943109
##  [982,] 0.3100009 0.3249683 0.3388172 0.3410820 0.3682354 0.3786925 0.3963431
##  [983,] 0.3050547 0.3202081 0.3332350 0.3589080 0.3653665 0.3829901 0.3979289
##  [984,] 0.3088215 0.3361089 0.3285448 0.3511757 0.3642684 0.3756639 0.3969155
##  [985,] 0.3061930 0.3140545 0.3358267 0.3480048 0.3662990 0.3783507 0.3934811
##  [986,] 0.3053008 0.3288108 0.3349606 0.3542971 0.3681826 0.3754035 0.3943598
##  [987,] 0.3037079 0.3244943 0.3383790 0.3451307 0.3519998 0.3773554 0.3901887
##  [988,] 0.2980016 0.3258472 0.3402973 0.3374215 0.3609904 0.3856580 0.3946901
##  [989,] 0.3068063 0.3303927 0.3408457 0.3513882 0.3639146 0.3822996 0.3946413
##  [990,] 0.3204315 0.3167179 0.3243343 0.3453955 0.3656555 0.3796088 0.3895148
##  [991,] 0.3157344 0.3354556 0.3339592 0.3492517 0.3630940 0.3805487 0.3949023
##  [992,] 0.3039707 0.3198089 0.3279042 0.3510583 0.3552011 0.3849280 0.3966286
##  [993,] 0.3241730 0.3242044 0.3345664 0.3492964 0.3669229 0.3842116 0.3933894
##  [994,] 0.3139443 0.3081887 0.3457111 0.3446399 0.3669621 0.3797265 0.3978407
##  [995,] 0.2991847 0.3179822 0.3228350 0.3491551 0.3674009 0.3771623 0.3909484
##  [996,] 0.2934675 0.3201853 0.3384492 0.3606973 0.3679912 0.3758387 0.3877588
##  [997,] 0.3133593 0.3225729 0.3203422 0.3444665 0.3600385 0.3741082 0.3972357
##  [998,] 0.3147253 0.3251720 0.3351126 0.3608694 0.3629069 0.3747719 0.3879266
##  [999,] 0.3096285 0.3182273 0.3265225 0.3489222 0.3584830 0.3735341 0.3973887
## [1000,] 0.3134016 0.3195443 0.3312235 0.3473228 0.3672984 0.3761019 0.3932504
##              [,8]      [,9]     [,10]     [,11]     [,12]     [,13]     [,14]
##    [1,] 0.4106171 0.4283901 0.4399775 0.4631253 0.4807041 0.5029539 0.5243446
##    [2,] 0.4088892 0.4243367 0.4378901 0.4657435 0.4668743 0.5103231 0.4985556
##    [3,] 0.4123905 0.4298728 0.4476833 0.4686845 0.4744312 0.5031182 0.5093408
##    [4,] 0.4069330 0.4299215 0.4473830 0.4599647 0.4741358 0.5008757 0.5225187
##    [5,] 0.4090170 0.4289321 0.4483412 0.4554967 0.4829933 0.4938266 0.5097422
##    [6,] 0.4112076 0.4309231 0.4461135 0.4631716 0.4748655 0.4992243 0.5256486
##    [7,] 0.4089091 0.4227328 0.4435722 0.4665855 0.4835855 0.4833805 0.5187899
##    [8,] 0.4107762 0.4267507 0.4514376 0.4676840 0.4743059 0.4943856 0.5182994
##    [9,] 0.4083213 0.4302398 0.4456928 0.4648675 0.4710183 0.4931820 0.5221961
##   [10,] 0.4166782 0.4275315 0.4430089 0.4583475 0.4710998 0.4869595 0.5046826
##   [11,] 0.4100257 0.4250494 0.4423088 0.4601064 0.4757721 0.5046382 0.5214226
##   [12,] 0.4064714 0.4264356 0.4393950 0.4590290 0.4756087 0.4935876 0.5044021
##   [13,] 0.4088627 0.4284476 0.4411456 0.4603982 0.4858937 0.4887115 0.5109052
##   [14,] 0.4091505 0.4295508 0.4444808 0.4663204 0.4763349 0.4903508 0.5062157
##   [15,] 0.4119568 0.4277996 0.4453994 0.4608176 0.4687798 0.5047323 0.5099938
##   [16,] 0.4075508 0.4329287 0.4405423 0.4670566 0.4741091 0.4946902 0.5108809
##   [17,] 0.4128283 0.4293480 0.4453225 0.4499766 0.4793087 0.5001794 0.5059597
##   [18,] 0.4113289 0.4285946 0.4410735 0.4675353 0.4792606 0.4978388 0.5124978
##   [19,] 0.4107349 0.4310308 0.4490947 0.4640065 0.4789273 0.4868659 0.5111018
##   [20,] 0.4061377 0.4308879 0.4438111 0.4640487 0.4826261 0.5053259 0.4965738
##   [21,] 0.4146569 0.4328393 0.4442806 0.4611531 0.4859387 0.4955788 0.5173670
##   [22,] 0.4104808 0.4299582 0.4510546 0.4571017 0.4762302 0.4870121 0.5145638
##   [23,] 0.4145814 0.4306018 0.4464141 0.4682822 0.4815058 0.5055138 0.5059997
##   [24,] 0.4089567 0.4283414 0.4404612 0.4620743 0.4692544 0.4902033 0.5141850
##   [25,] 0.4092595 0.4299443 0.4419965 0.4635306 0.4806122 0.4958155 0.5121534
##   [26,] 0.4101722 0.4264671 0.4459876 0.4599816 0.4862775 0.5024618 0.4999232
##   [27,] 0.4124426 0.4248985 0.4432475 0.4601268 0.4742987 0.4933821 0.5078762
##   [28,] 0.4101866 0.4299177 0.4447064 0.4571514 0.4759672 0.4940781 0.5141986
##   [29,] 0.4120293 0.4318003 0.4444338 0.4568858 0.4763100 0.5001352 0.5148522
##   [30,] 0.4121776 0.4292146 0.4419597 0.4598888 0.4822099 0.5015622 0.5164455
##   [31,] 0.4123360 0.4238502 0.4434714 0.4663022 0.4729032 0.5003197 0.5052217
##   [32,] 0.4076993 0.4324858 0.4456343 0.4621811 0.4729496 0.4996871 0.5078242
##   [33,] 0.4119488 0.4239119 0.4474871 0.4610849 0.4819567 0.4884037 0.4995873
##   [34,] 0.4120708 0.4224006 0.4365999 0.4597026 0.4881947 0.5076743 0.5079493
##   [35,] 0.4117659 0.4268376 0.4452847 0.4661536 0.4754534 0.5056247 0.5153981
##   [36,] 0.4146360 0.4297467 0.4376753 0.4623524 0.4755637 0.4941080 0.5114296
##   [37,] 0.4107099 0.4254148 0.4495623 0.4709815 0.4777327 0.4888588 0.5043688
##   [38,] 0.4098813 0.4295016 0.4418263 0.4700604 0.4752659 0.5109724 0.5262498
##   [39,] 0.4101867 0.4262665 0.4423756 0.4583684 0.4850220 0.5001250 0.5005270
##   [40,] 0.4096207 0.4304482 0.4453682 0.4584058 0.4743931 0.4963534 0.5069763
##   [41,] 0.4142385 0.4245847 0.4465752 0.4602965 0.4806081 0.4924366 0.5178320
##   [42,] 0.4097234 0.4256783 0.4463595 0.4670985 0.4849745 0.4915493 0.5083940
##   [43,] 0.4087597 0.4255989 0.4444705 0.4630167 0.4829214 0.4905610 0.5088577
##   [44,] 0.4041879 0.4250317 0.4478976 0.4625860 0.4790662 0.4828457 0.4939758
##   [45,] 0.4112349 0.4276866 0.4423881 0.4557386 0.4896702 0.5046041 0.5148839
##   [46,] 0.4164153 0.4248949 0.4387214 0.4565501 0.4771187 0.4977485 0.5011816
##   [47,] 0.4058452 0.4255365 0.4503806 0.4657225 0.4829493 0.5021835 0.5209603
##   [48,] 0.4119458 0.4267590 0.4403186 0.4545534 0.4886285 0.5040310 0.5179520
##   [49,] 0.4112621 0.4299858 0.4476330 0.4525616 0.4732868 0.4861716 0.5247135
##   [50,] 0.4154925 0.4275220 0.4426701 0.4563403 0.4784467 0.4947832 0.5059761
##   [51,] 0.4066969 0.4338610 0.4424601 0.4608604 0.4713507 0.4975425 0.5123813
##   [52,] 0.4144886 0.4328376 0.4461309 0.4643450 0.4868189 0.4912077 0.5063182
##   [53,] 0.4147621 0.4293519 0.4467328 0.4606701 0.4812026 0.4997382 0.5175081
##   [54,] 0.4102112 0.4294115 0.4415048 0.4638836 0.4782571 0.4959306 0.5153469
##   [55,] 0.4130748 0.4266052 0.4516698 0.4598620 0.4879655 0.5039147 0.5064015
##   [56,] 0.4130782 0.4253573 0.4476606 0.4670373 0.4764962 0.4901308 0.5021147
##   [57,] 0.4072646 0.4294193 0.4442236 0.4635124 0.4806100 0.5034648 0.4981697
##   [58,] 0.4075733 0.4296507 0.4448796 0.4530130 0.4819630 0.5010623 0.5251829
##   [59,] 0.4138265 0.4267227 0.4517316 0.4590752 0.4827766 0.4996791 0.5129966
##   [60,] 0.4081882 0.4246633 0.4480927 0.4567361 0.4823457 0.5024778 0.5006206
##   [61,] 0.4093811 0.4267670 0.4454981 0.4608414 0.4889352 0.4828365 0.4999837
##   [62,] 0.4107036 0.4259873 0.4414014 0.4649050 0.4790469 0.4855648 0.5094140
##   [63,] 0.4095756 0.4302838 0.4468818 0.4638436 0.4761570 0.4949083 0.5225375
##   [64,] 0.4105720 0.4228306 0.4475610 0.4610507 0.4806204 0.4796251 0.5192240
##   [65,] 0.4101553 0.4283409 0.4491093 0.4592230 0.4921984 0.4923015 0.5127948
##   [66,] 0.4107374 0.4309091 0.4448135 0.4642259 0.4859690 0.5096942 0.5114835
##   [67,] 0.4076409 0.4235866 0.4450882 0.4672571 0.4687682 0.4961441 0.5207236
##   [68,] 0.4104112 0.4265816 0.4489962 0.4557134 0.4808033 0.4892911 0.5200209
##   [69,] 0.4082667 0.4250553 0.4433066 0.4626450 0.4786066 0.4939897 0.5145144
##   [70,] 0.4081799 0.4261327 0.4433412 0.4512413 0.4776856 0.4940352 0.5107021
##   [71,] 0.4118346 0.4277671 0.4400915 0.4512005 0.4791498 0.4894284 0.5053942
##   [72,] 0.4065042 0.4336036 0.4470300 0.4661065 0.4750518 0.4991597 0.5181024
##   [73,] 0.4109755 0.4244393 0.4448617 0.4644789 0.4799368 0.5034580 0.5232901
##   [74,] 0.4099317 0.4269618 0.4436002 0.4614892 0.4713518 0.4966146 0.5018263
##   [75,] 0.4128499 0.4262760 0.4468445 0.4668156 0.4857079 0.4790996 0.5165177
##   [76,] 0.4135756 0.4288189 0.4407704 0.4624129 0.4774545 0.4907146 0.5148412
##   [77,] 0.4115139 0.4290264 0.4471264 0.4590705 0.4807420 0.4980818 0.5124731
##   [78,] 0.4110784 0.4225613 0.4468324 0.4592620 0.4765686 0.4874327 0.5028165
##   [79,] 0.4104528 0.4289014 0.4465025 0.4608141 0.4851140 0.5000716 0.5119472
##   [80,] 0.4065260 0.4280434 0.4449960 0.4567461 0.4691419 0.5083218 0.5134274
##   [81,] 0.4143653 0.4284597 0.4395057 0.4631438 0.4723091 0.4903190 0.4953678
##   [82,] 0.4139875 0.4272921 0.4474373 0.4606707 0.4807998 0.5089784 0.5196179
##   [83,] 0.4127969 0.4285805 0.4465879 0.4619007 0.4779417 0.4872123 0.5079657
##   [84,] 0.4100522 0.4330014 0.4479727 0.4640356 0.4783521 0.4973627 0.5095259
##   [85,] 0.4124548 0.4266800 0.4450499 0.4559306 0.4817031 0.4977890 0.4982151
##   [86,] 0.4076652 0.4254938 0.4499582 0.4560528 0.4757172 0.4954451 0.5290187
##   [87,] 0.4116109 0.4279856 0.4477998 0.4531549 0.4663338 0.4977901 0.5203506
##   [88,] 0.4107082 0.4254865 0.4468978 0.4636906 0.4816564 0.4866601 0.5127202
##   [89,] 0.4117145 0.4247009 0.4426705 0.4628336 0.4728420 0.4969022 0.5126496
##   [90,] 0.4105077 0.4276354 0.4419405 0.4599525 0.4770141 0.4955993 0.5102301
##   [91,] 0.4120048 0.4248496 0.4441417 0.4553460 0.4737837 0.4814406 0.4993306
##   [92,] 0.4084494 0.4281135 0.4442090 0.4654679 0.4821548 0.5024448 0.5062075
##   [93,] 0.4133205 0.4278853 0.4432736 0.4607139 0.4776538 0.4936757 0.5285481
##   [94,] 0.4096891 0.4260916 0.4446735 0.4626806 0.4859641 0.4970508 0.5132446
##   [95,] 0.4110032 0.4303648 0.4434843 0.4655969 0.4818046 0.5005235 0.5117349
##   [96,] 0.4118203 0.4262122 0.4450880 0.4505201 0.4802381 0.4959957 0.5006721
##   [97,] 0.4106437 0.4286140 0.4489775 0.4650014 0.4774292 0.4907723 0.5175196
##   [98,] 0.4128553 0.4277508 0.4478864 0.4722653 0.4838660 0.5091907 0.4964259
##   [99,] 0.4167877 0.4237910 0.4486808 0.4662050 0.4843968 0.5022325 0.4920768
##  [100,] 0.4127722 0.4295219 0.4498672 0.4701658 0.4686955 0.5024406 0.4960755
##  [101,] 0.4107746 0.4310141 0.4501622 0.4596810 0.4805076 0.4931804 0.5282836
##  [102,] 0.4123591 0.4267956 0.4521506 0.4656397 0.4848670 0.4923555 0.5115200
##  [103,] 0.4130090 0.4287317 0.4424334 0.4613542 0.4730609 0.4898618 0.5158648
##  [104,] 0.4126221 0.4269867 0.4451849 0.4670731 0.4766795 0.4887269 0.5167093
##  [105,] 0.4136818 0.4260364 0.4485759 0.4591548 0.4815418 0.4987251 0.5215624
##  [106,] 0.4120335 0.4270653 0.4444861 0.4520840 0.4643599 0.4985899 0.5133912
##  [107,] 0.4119502 0.4284935 0.4426299 0.4596267 0.4899621 0.4810595 0.5164493
##  [108,] 0.4132599 0.4239146 0.4389778 0.4582287 0.4829219 0.4974344 0.5233483
##  [109,] 0.4099829 0.4271670 0.4441087 0.4614980 0.4771602 0.4884871 0.5250042
##  [110,] 0.4126727 0.4257888 0.4468636 0.4515620 0.4832112 0.4994178 0.5094059
##  [111,] 0.4116524 0.4289627 0.4460769 0.4549388 0.4732735 0.4927005 0.5024119
##  [112,] 0.4135049 0.4306706 0.4453985 0.4564687 0.4871288 0.4997077 0.5194250
##  [113,] 0.4124355 0.4274207 0.4402036 0.4671862 0.4853344 0.4867471 0.5246075
##  [114,] 0.4104122 0.4284891 0.4442993 0.4591170 0.4808280 0.5014358 0.5088067
##  [115,] 0.4073509 0.4256229 0.4427772 0.4571528 0.4821360 0.5007660 0.5119494
##  [116,] 0.4092088 0.4262907 0.4456247 0.4620935 0.4616211 0.5009634 0.5092050
##  [117,] 0.4130134 0.4304224 0.4423231 0.4544501 0.4785642 0.4924495 0.5148636
##  [118,] 0.4081947 0.4232933 0.4387867 0.4716318 0.4788343 0.4913083 0.5294795
##  [119,] 0.4125625 0.4302887 0.4500264 0.4613262 0.4751743 0.4927908 0.5147498
##  [120,] 0.4092676 0.4284509 0.4452665 0.4605006 0.4701978 0.4932656 0.5140943
##  [121,] 0.4094208 0.4273567 0.4505296 0.4613832 0.4718883 0.4920570 0.5163800
##  [122,] 0.4136207 0.4247796 0.4454239 0.4664178 0.4771855 0.4994513 0.5136461
##  [123,] 0.4156549 0.4270677 0.4394613 0.4763117 0.4725054 0.4900235 0.5205759
##  [124,] 0.4139427 0.4268755 0.4392435 0.4686746 0.4880947 0.5005790 0.5035774
##  [125,] 0.4099500 0.4324166 0.4479970 0.4615550 0.4808620 0.5104353 0.5265593
##  [126,] 0.4073995 0.4258024 0.4451329 0.4660847 0.4840378 0.5000616 0.5122508
##  [127,] 0.4110109 0.4312194 0.4491063 0.4599695 0.4768450 0.4846776 0.5245941
##  [128,] 0.4147360 0.4307568 0.4478368 0.4688596 0.4679216 0.4896304 0.5125362
##  [129,] 0.4105953 0.4294335 0.4428208 0.4591453 0.4895452 0.4955013 0.5177182
##  [130,] 0.4127745 0.4322145 0.4410364 0.4636455 0.4865234 0.4829109 0.5153340
##  [131,] 0.4079767 0.4293415 0.4459642 0.4637771 0.4732835 0.4946168 0.5038950
##  [132,] 0.4125874 0.4251535 0.4437162 0.4636850 0.4851764 0.4979926 0.5135814
##  [133,] 0.4099237 0.4316149 0.4429286 0.4608056 0.4735110 0.4935883 0.5146048
##  [134,] 0.4140260 0.4315591 0.4412494 0.4686154 0.4881510 0.5067127 0.5109818
##  [135,] 0.4132937 0.4303392 0.4440847 0.4581422 0.4847519 0.4885759 0.5142482
##  [136,] 0.4127828 0.4251708 0.4465123 0.4628235 0.4844774 0.5002148 0.5161467
##  [137,] 0.4109026 0.4261877 0.4488124 0.4693384 0.4745838 0.4954770 0.5163028
##  [138,] 0.4121080 0.4294364 0.4484527 0.4714607 0.4847215 0.4954735 0.5257863
##  [139,] 0.4128239 0.4317333 0.4445735 0.4647134 0.4765983 0.4990052 0.5131448
##  [140,] 0.4093184 0.4277642 0.4506243 0.4671036 0.4898419 0.4901480 0.5163066
##  [141,] 0.4110662 0.4310021 0.4463994 0.4641815 0.4813915 0.4919570 0.5158047
##  [142,] 0.4168185 0.4313647 0.4522381 0.4656625 0.4835754 0.5137525 0.5177352
##  [143,] 0.4126280 0.4287707 0.4431258 0.4589455 0.4748339 0.4986810 0.5104819
##  [144,] 0.4096457 0.4247813 0.4437691 0.4611461 0.4770378 0.5109526 0.5234972
##  [145,] 0.4087933 0.4260985 0.4481694 0.4555190 0.4818904 0.4974454 0.5155040
##  [146,] 0.4113044 0.4307377 0.4430579 0.4693762 0.4852531 0.4881736 0.5150134
##  [147,] 0.4148011 0.4280105 0.4452729 0.4581501 0.4730356 0.5015238 0.5138322
##  [148,] 0.4129984 0.4282308 0.4473985 0.4620045 0.4826356 0.5006870 0.5177988
##  [149,] 0.4114132 0.4312005 0.4424482 0.4522798 0.4870378 0.4973255 0.5221858
##  [150,] 0.4119969 0.4281270 0.4422480 0.4599996 0.4805398 0.5036566 0.5054351
##  [151,] 0.4111620 0.4268797 0.4446535 0.4592290 0.4747251 0.4889812 0.5143386
##  [152,] 0.4135800 0.4295075 0.4462763 0.4722379 0.4790998 0.4988206 0.5143794
##  [153,] 0.4126841 0.4241939 0.4394389 0.4633661 0.4838424 0.4902471 0.5115906
##  [154,] 0.4100550 0.4315210 0.4407244 0.4633783 0.4719376 0.5130727 0.5277556
##  [155,] 0.4107039 0.4283974 0.4440373 0.4642534 0.4795751 0.4911680 0.5186987
##  [156,] 0.4062026 0.4257581 0.4441029 0.4648325 0.4784922 0.5052727 0.5085077
##  [157,] 0.4096471 0.4255705 0.4476136 0.4592636 0.4707761 0.4944481 0.5161813
##  [158,] 0.4090213 0.4299129 0.4435367 0.4553219 0.4698467 0.5070236 0.5204974
##  [159,] 0.4113280 0.4298805 0.4392125 0.4652519 0.4841498 0.4973988 0.5218997
##  [160,] 0.4136410 0.4288250 0.4410848 0.4629742 0.4726821 0.4910668 0.5273588
##  [161,] 0.4088040 0.4292894 0.4435388 0.4635532 0.4765558 0.4962843 0.5216697
##  [162,] 0.4099135 0.4295094 0.4379451 0.4660901 0.4790176 0.4991716 0.5159378
##  [163,] 0.4128731 0.4265375 0.4452128 0.4671322 0.4838356 0.4966981 0.5006137
##  [164,] 0.4102199 0.4282220 0.4486033 0.4643623 0.4710086 0.4915998 0.5036668
##  [165,] 0.4093703 0.4261163 0.4463804 0.4630031 0.4869126 0.4971388 0.5166991
##  [166,] 0.4130259 0.4268718 0.4499789 0.4609156 0.4783124 0.5028428 0.5038857
##  [167,] 0.4120598 0.4250407 0.4498327 0.4582715 0.4875861 0.4965239 0.5122480
##  [168,] 0.4068558 0.4309907 0.4432593 0.4620891 0.4736568 0.4926244 0.5175472
##  [169,] 0.4097184 0.4247561 0.4464351 0.4633361 0.4789541 0.5150925 0.5183190
##  [170,] 0.4131206 0.4252065 0.4427850 0.4571720 0.4734081 0.4948302 0.5181021
##  [171,] 0.4111055 0.4242278 0.4435485 0.4557016 0.4879868 0.5000238 0.5133850
##  [172,] 0.4090556 0.4269666 0.4380885 0.4661045 0.4832115 0.4973859 0.4994978
##  [173,] 0.4145162 0.4270207 0.4495663 0.4567107 0.4729566 0.4898918 0.5193936
##  [174,] 0.4099845 0.4310241 0.4429597 0.4602551 0.4713401 0.4946246 0.5103780
##  [175,] 0.4092896 0.4279967 0.4433290 0.4569887 0.4822620 0.4991046 0.5178740
##  [176,] 0.4090661 0.4261068 0.4509073 0.4681473 0.4685820 0.4871430 0.5125223
##  [177,] 0.4098302 0.4311709 0.4416237 0.4608818 0.4590372 0.5024243 0.5239851
##  [178,] 0.4119737 0.4311613 0.4360232 0.4565519 0.4875083 0.4889264 0.5105016
##  [179,] 0.4108075 0.4289062 0.4409640 0.4627449 0.4846927 0.4949160 0.5024686
##  [180,] 0.4083216 0.4331769 0.4420680 0.4684526 0.4731814 0.4847668 0.5156939
##  [181,] 0.4105888 0.4283253 0.4480263 0.4637255 0.4720469 0.4965569 0.5198240
##  [182,] 0.4138185 0.4291196 0.4458200 0.4589570 0.4748160 0.5075576 0.5163932
##  [183,] 0.4095506 0.4287728 0.4443083 0.4629942 0.4724984 0.4866513 0.5233292
##  [184,] 0.4146120 0.4271159 0.4448267 0.4586883 0.4832387 0.4957171 0.5048520
##  [185,] 0.4108325 0.4299700 0.4429338 0.4643516 0.4771841 0.5042097 0.5066421
##  [186,] 0.4095316 0.4333638 0.4420445 0.4639348 0.4775738 0.4922385 0.4980772
##  [187,] 0.4124928 0.4269750 0.4463585 0.4657457 0.4815192 0.4932449 0.5047797
##  [188,] 0.4121111 0.4247781 0.4418988 0.4565120 0.4784682 0.4938797 0.5159558
##  [189,] 0.4083732 0.4265120 0.4466575 0.4632257 0.4887440 0.5052729 0.5065016
##  [190,] 0.4125369 0.4287882 0.4388841 0.4620016 0.4887725 0.4840339 0.5098122
##  [191,] 0.4092344 0.4283973 0.4411131 0.4648277 0.4737199 0.4989668 0.5117263
##  [192,] 0.4108497 0.4304595 0.4467585 0.4580678 0.4756619 0.4929816 0.5082260
##  [193,] 0.4107790 0.4237727 0.4446919 0.4571462 0.4887312 0.5009822 0.5171903
##  [194,] 0.4131790 0.4249549 0.4467435 0.4674238 0.4750652 0.5067548 0.5093161
##  [195,] 0.4137219 0.4251215 0.4413251 0.4635116 0.4694301 0.4920362 0.5157048
##  [196,] 0.4105665 0.4264563 0.4500243 0.4553603 0.4820221 0.5024319 0.5147830
##  [197,] 0.4149805 0.4259588 0.4494286 0.4578153 0.4797220 0.4949638 0.5108868
##  [198,] 0.4089685 0.4268552 0.4487955 0.4664669 0.4781837 0.5083204 0.5127048
##  [199,] 0.4122460 0.4288573 0.4473799 0.4624249 0.4702899 0.4936654 0.5090562
##  [200,] 0.4134535 0.4263782 0.4416390 0.4591546 0.4825107 0.4954027 0.5115308
##  [201,] 0.4069782 0.4259418 0.4433423 0.4671169 0.4944041 0.5015894 0.5197161
##  [202,] 0.4130269 0.4258725 0.4458837 0.4667587 0.4704435 0.5083150 0.5230036
##  [203,] 0.4137215 0.4272024 0.4473428 0.4641975 0.4707473 0.5096257 0.5076238
##  [204,] 0.4072213 0.4292160 0.4476292 0.4629028 0.4847957 0.4909225 0.5113681
##  [205,] 0.4078252 0.4302922 0.4478228 0.4645034 0.4742620 0.4922017 0.5197357
##  [206,] 0.4126128 0.4272943 0.4537954 0.4649060 0.4704017 0.5021188 0.5197821
##  [207,] 0.4084176 0.4298392 0.4431864 0.4665988 0.4808492 0.5095519 0.5153975
##  [208,] 0.4086325 0.4276307 0.4375745 0.4618133 0.4826798 0.4973744 0.4918476
##  [209,] 0.4138039 0.4282262 0.4429498 0.4611062 0.4799017 0.4979901 0.5288995
##  [210,] 0.4100550 0.4264380 0.4403636 0.4553959 0.4722343 0.5068146 0.5083996
##  [211,] 0.4120319 0.4298630 0.4458941 0.4560799 0.4771097 0.4960144 0.5134522
##  [212,] 0.4102197 0.4240972 0.4357216 0.4588557 0.4897242 0.5066137 0.5148714
##  [213,] 0.4103248 0.4257394 0.4435648 0.4655597 0.4799271 0.5047038 0.5222152
##  [214,] 0.4142786 0.4305459 0.4441245 0.4592432 0.4660302 0.4832257 0.5132093
##  [215,] 0.4119126 0.4276771 0.4457405 0.4636836 0.4834987 0.4843449 0.5221147
##  [216,] 0.4103703 0.4251017 0.4432449 0.4626032 0.4826008 0.4855370 0.5154765
##  [217,] 0.4068544 0.4263431 0.4418656 0.4710169 0.4765480 0.4895472 0.5082989
##  [218,] 0.4132266 0.4251471 0.4460078 0.4628702 0.4778993 0.4917746 0.5207452
##  [219,] 0.4113868 0.4277940 0.4474211 0.4642268 0.4774989 0.4963910 0.5034285
##  [220,] 0.4101344 0.4256691 0.4478464 0.4634823 0.4776147 0.4963858 0.5243335
##  [221,] 0.4080114 0.4284169 0.4451764 0.4555638 0.4672040 0.4952716 0.5144780
##  [222,] 0.4102827 0.4265498 0.4415786 0.4600152 0.4841087 0.4995859 0.5222075
##  [223,] 0.4106162 0.4269117 0.4400283 0.4625964 0.4688248 0.4945045 0.5085547
##  [224,] 0.4122419 0.4300854 0.4459265 0.4569762 0.4773975 0.4969676 0.5000940
##  [225,] 0.4117530 0.4268859 0.4477712 0.4662360 0.4800937 0.4976040 0.5145534
##  [226,] 0.4114170 0.4299687 0.4469600 0.4562223 0.4754288 0.5030871 0.5207979
##  [227,] 0.4087260 0.4270701 0.4439523 0.4610587 0.4747591 0.4947682 0.5163582
##  [228,] 0.4098904 0.4309046 0.4490784 0.4606481 0.4749915 0.4981601 0.5103783
##  [229,] 0.4096193 0.4291359 0.4440054 0.4634298 0.4902626 0.5120789 0.5128056
##  [230,] 0.4099688 0.4261580 0.4462548 0.4630340 0.4814283 0.5049715 0.5158173
##  [231,] 0.4097020 0.4275257 0.4439049 0.4611934 0.4767218 0.4969879 0.5275024
##  [232,] 0.4114135 0.4279143 0.4481386 0.4646750 0.4844253 0.4926764 0.5087147
##  [233,] 0.4134138 0.4301329 0.4526171 0.4608546 0.4789871 0.4963747 0.5160453
##  [234,] 0.4104301 0.4278818 0.4504202 0.4570439 0.4678143 0.5030699 0.5112816
##  [235,] 0.4103674 0.4277834 0.4475376 0.4613562 0.4792859 0.4959478 0.5126067
##  [236,] 0.4129077 0.4272693 0.4464016 0.4692198 0.4797053 0.5100004 0.5204709
##  [237,] 0.4106605 0.4274414 0.4419822 0.4619672 0.4748119 0.4939073 0.5180417
##  [238,] 0.4030198 0.4279117 0.4412202 0.4604587 0.4840592 0.4975557 0.5220761
##  [239,] 0.4163650 0.4234036 0.4418566 0.4640422 0.4857148 0.4976090 0.5069287
##  [240,] 0.4095279 0.4320961 0.4465525 0.4585645 0.4749598 0.5016185 0.5215950
##  [241,] 0.4090463 0.4230917 0.4448867 0.4579013 0.4794620 0.4967331 0.5067773
##  [242,] 0.4076781 0.4267049 0.4435225 0.4556434 0.4771636 0.4909842 0.5049241
##  [243,] 0.4126912 0.4287591 0.4467444 0.4633902 0.4837956 0.5042683 0.5010740
##  [244,] 0.4105574 0.4279253 0.4515800 0.4637730 0.4896463 0.5013104 0.5119378
##  [245,] 0.4143706 0.4285248 0.4439914 0.4610474 0.4778867 0.4950663 0.5238415
##  [246,] 0.4115837 0.4283144 0.4500466 0.4710932 0.4703981 0.4957719 0.5109303
##  [247,] 0.4132772 0.4284367 0.4479421 0.4631349 0.4692916 0.4998312 0.5147190
##  [248,] 0.4123805 0.4266240 0.4440112 0.4583680 0.4780699 0.4963244 0.5174144
##  [249,] 0.4105012 0.4289652 0.4388080 0.4585496 0.4788352 0.4974292 0.5184783
##  [250,] 0.4126173 0.4286877 0.4435432 0.4707615 0.4761904 0.5029603 0.5154105
##  [251,] 0.4115575 0.4233347 0.4456787 0.4568577 0.4829061 0.4948767 0.5059258
##  [252,] 0.4112930 0.4289321 0.4389111 0.4587196 0.4791612 0.4939403 0.5116642
##  [253,] 0.4123290 0.4347314 0.4474195 0.4565908 0.4789182 0.5000417 0.5001580
##  [254,] 0.4070523 0.4306708 0.4438800 0.4619178 0.4809554 0.4896091 0.5222139
##  [255,] 0.4102267 0.4250015 0.4393569 0.4620245 0.4815699 0.4997314 0.5104969
##  [256,] 0.4068291 0.4277831 0.4470678 0.4600222 0.4783997 0.4977833 0.4982443
##  [257,] 0.4140854 0.4251479 0.4434770 0.4571471 0.4792842 0.4917608 0.5078384
##  [258,] 0.4092935 0.4272186 0.4464782 0.4618544 0.4807919 0.4930477 0.5073325
##  [259,] 0.4079695 0.4246532 0.4441780 0.4578735 0.4681012 0.5020328 0.5091674
##  [260,] 0.4103901 0.4233070 0.4500857 0.4707576 0.4672784 0.4942768 0.5010129
##  [261,] 0.4090397 0.4257454 0.4398189 0.4681541 0.4807463 0.4927625 0.5080497
##  [262,] 0.4097258 0.4288649 0.4389335 0.4643524 0.4794403 0.4873752 0.5115676
##  [263,] 0.4077896 0.4290707 0.4442689 0.4609173 0.4865464 0.5023530 0.5122757
##  [264,] 0.4100230 0.4283913 0.4467293 0.4670272 0.4804599 0.4983040 0.5188705
##  [265,] 0.4080356 0.4288247 0.4391093 0.4592714 0.4683991 0.4994910 0.5224736
##  [266,] 0.4123805 0.4283674 0.4443513 0.4592178 0.4796823 0.5095471 0.5143248
##  [267,] 0.4144061 0.4281610 0.4521538 0.4643911 0.4769261 0.5014184 0.5003249
##  [268,] 0.4144459 0.4303219 0.4396927 0.4596353 0.4814847 0.4950093 0.5095412
##  [269,] 0.4090588 0.4248385 0.4459497 0.4624049 0.4766072 0.4738574 0.5132143
##  [270,] 0.4106443 0.4289170 0.4475535 0.4670133 0.4707254 0.4905273 0.5057884
##  [271,] 0.4104408 0.4257204 0.4419293 0.4534937 0.4736984 0.4900063 0.5117671
##  [272,] 0.4113829 0.4229433 0.4396164 0.4648513 0.4796520 0.4933665 0.5036080
##  [273,] 0.4115275 0.4251055 0.4412980 0.4597453 0.4751629 0.5013499 0.5003525
##  [274,] 0.4105772 0.4287858 0.4430848 0.4621762 0.4574410 0.4920480 0.5186671
##  [275,] 0.4092137 0.4309733 0.4450064 0.4631863 0.4812845 0.4942401 0.5249895
##  [276,] 0.4122912 0.4266654 0.4411843 0.4599944 0.4814821 0.4975306 0.5035443
##  [277,] 0.4092608 0.4241348 0.4498835 0.4645540 0.4889934 0.4901906 0.4937112
##  [278,] 0.4104236 0.4290028 0.4434165 0.4610008 0.4802112 0.4961315 0.5114616
##  [279,] 0.4077446 0.4243951 0.4443686 0.4687488 0.4775202 0.4941916 0.5004102
##  [280,] 0.4152938 0.4250331 0.4473015 0.4658252 0.4909943 0.4923694 0.5083806
##  [281,] 0.4122344 0.4305168 0.4469609 0.4669180 0.4783568 0.4951517 0.5218086
##  [282,] 0.4124717 0.4258828 0.4454936 0.4625528 0.4801769 0.5018526 0.5113515
##  [283,] 0.4090096 0.4260954 0.4434406 0.4642651 0.4785458 0.4898621 0.5225642
##  [284,] 0.4125092 0.4315906 0.4470685 0.4649847 0.4822896 0.4779640 0.5166214
##  [285,] 0.4109198 0.4292310 0.4436189 0.4565716 0.4754547 0.4761728 0.5028925
##  [286,] 0.4098341 0.4265477 0.4454447 0.4612129 0.4786234 0.4981200 0.5270430
##  [287,] 0.4147250 0.4262291 0.4459513 0.4588557 0.4728693 0.5136476 0.5260324
##  [288,] 0.4057804 0.4297447 0.4444961 0.4543177 0.4758669 0.4894171 0.5099222
##  [289,] 0.4094814 0.4284925 0.4457419 0.4727769 0.4867892 0.4935250 0.5066564
##  [290,] 0.4131798 0.4277205 0.4505211 0.4666117 0.4770392 0.5069964 0.5072605
##  [291,] 0.4124066 0.4276502 0.4396454 0.4652771 0.4795740 0.5063626 0.5174490
##  [292,] 0.4091065 0.4290207 0.4492393 0.4676072 0.4783582 0.4982988 0.5183569
##  [293,] 0.4131412 0.4310931 0.4451190 0.4614876 0.4814757 0.4935832 0.5044468
##  [294,] 0.4092033 0.4319609 0.4409691 0.4659278 0.4782410 0.4901619 0.5212655
##  [295,] 0.4135557 0.4281285 0.4496611 0.4667258 0.4767157 0.4947489 0.4972250
##  [296,] 0.4140594 0.4277002 0.4437458 0.4596377 0.4790362 0.5038378 0.5205297
##  [297,] 0.4118493 0.4261675 0.4446988 0.4602604 0.4735317 0.5018358 0.5075892
##  [298,] 0.4081919 0.4227057 0.4461177 0.4593735 0.4773136 0.5014158 0.5157470
##  [299,] 0.4122340 0.4276671 0.4448146 0.4607302 0.4813673 0.4924409 0.5251153
##  [300,] 0.4101380 0.4295468 0.4481168 0.4663888 0.4816106 0.4997502 0.5135524
##  [301,] 0.4143005 0.4265890 0.4460016 0.4627007 0.4771095 0.4882995 0.5083553
##  [302,] 0.4134214 0.4341667 0.4474992 0.4656894 0.4712062 0.4974182 0.5126384
##  [303,] 0.4155988 0.4255838 0.4469222 0.4551877 0.4832516 0.4950693 0.5048076
##  [304,] 0.4108934 0.4330633 0.4428421 0.4572200 0.4802295 0.4947115 0.5115397
##  [305,] 0.4136143 0.4305735 0.4402733 0.4575953 0.4757762 0.4969210 0.5010679
##  [306,] 0.4044209 0.4292934 0.4423511 0.4665014 0.4801323 0.4939731 0.5029422
##  [307,] 0.4077901 0.4278936 0.4444239 0.4640941 0.4868416 0.5035805 0.5235253
##  [308,] 0.4080497 0.4252925 0.4494993 0.4592101 0.4795759 0.5004223 0.5153913
##  [309,] 0.4053015 0.4260204 0.4376919 0.4542696 0.4726240 0.4893604 0.5234922
##  [310,] 0.4137640 0.4263940 0.4460415 0.4618468 0.4747670 0.4905891 0.5057261
##  [311,] 0.4072492 0.4297851 0.4393884 0.4641478 0.4862275 0.4966571 0.5211268
##  [312,] 0.4143822 0.4305651 0.4415463 0.4659563 0.4719442 0.4881990 0.5164240
##  [313,] 0.4126132 0.4286056 0.4419965 0.4630679 0.4851384 0.5029388 0.5148681
##  [314,] 0.4073592 0.4233016 0.4449488 0.4657864 0.4797383 0.5130540 0.5020240
##  [315,] 0.4128791 0.4312812 0.4507193 0.4659436 0.4820061 0.4933930 0.4988374
##  [316,] 0.4105037 0.4266551 0.4477284 0.4602475 0.4783440 0.4865712 0.5252852
##  [317,] 0.4100524 0.4219309 0.4481515 0.4624706 0.4845208 0.4992694 0.5253914
##  [318,] 0.4104983 0.4274294 0.4470513 0.4646535 0.4771292 0.4975485 0.5146127
##  [319,] 0.4088754 0.4259915 0.4430401 0.4570123 0.4827490 0.4950541 0.5070650
##  [320,] 0.4115931 0.4238849 0.4425699 0.4636405 0.4861725 0.4897526 0.5035091
##  [321,] 0.4150035 0.4255389 0.4482899 0.4672184 0.4748464 0.4974876 0.5171903
##  [322,] 0.4102172 0.4338756 0.4533058 0.4634807 0.4798307 0.4918277 0.5114143
##  [323,] 0.4066385 0.4302686 0.4511456 0.4590879 0.4833429 0.4920208 0.5152371
##  [324,] 0.4136326 0.4231896 0.4478318 0.4590138 0.4764334 0.5046532 0.5028457
##  [325,] 0.4114880 0.4294326 0.4437267 0.4673093 0.4752976 0.4934981 0.5211893
##  [326,] 0.4094218 0.4305820 0.4447016 0.4646205 0.4879002 0.5003174 0.5186386
##  [327,] 0.4058824 0.4283819 0.4465150 0.4588389 0.4684603 0.5023149 0.5241844
##  [328,] 0.4125068 0.4296408 0.4479328 0.4614265 0.4808119 0.4874517 0.5139541
##  [329,] 0.4135192 0.4257058 0.4428929 0.4660850 0.4819601 0.4992647 0.5254548
##  [330,] 0.4082464 0.4264872 0.4472295 0.4517460 0.4783074 0.4953127 0.5216267
##  [331,] 0.4104434 0.4311345 0.4485028 0.4545031 0.4756712 0.5042227 0.5063478
##  [332,] 0.4082870 0.4284420 0.4460202 0.4579585 0.4721463 0.4938161 0.5138388
##  [333,] 0.4118224 0.4284377 0.4481964 0.4714554 0.4747362 0.4879104 0.5098667
##  [334,] 0.4174066 0.4297977 0.4391639 0.4647044 0.4881586 0.5034255 0.5004486
##  [335,] 0.4096881 0.4287154 0.4447960 0.4707520 0.4799517 0.4998668 0.5088403
##  [336,] 0.4123974 0.4279194 0.4438029 0.4599115 0.4789034 0.4917795 0.5126407
##  [337,] 0.4077598 0.4256189 0.4397946 0.4603709 0.4804167 0.5022122 0.5093668
##  [338,] 0.4102922 0.4235832 0.4448553 0.4658832 0.4819166 0.4980246 0.5128977
##  [339,] 0.4096578 0.4267465 0.4451024 0.4541718 0.4676447 0.5028224 0.4971377
##  [340,] 0.4119087 0.4218104 0.4387726 0.4529631 0.4741548 0.5020476 0.5130728
##  [341,] 0.4116506 0.4232336 0.4453830 0.4612039 0.4774984 0.4994442 0.5322633
##  [342,] 0.4143800 0.4268445 0.4475420 0.4578261 0.4776016 0.4930178 0.5224001
##  [343,] 0.4132146 0.4286908 0.4387641 0.4590919 0.4758904 0.4906343 0.5213752
##  [344,] 0.4092388 0.4278847 0.4471490 0.4656679 0.4803432 0.4939617 0.5130247
##  [345,] 0.4140193 0.4294186 0.4451503 0.4666992 0.4665082 0.4902526 0.5135026
##  [346,] 0.4080585 0.4305597 0.4406011 0.4585293 0.4803911 0.4953066 0.5133722
##  [347,] 0.4147054 0.4235863 0.4475702 0.4586443 0.4816295 0.4997755 0.5152850
##  [348,] 0.4108503 0.4293716 0.4492575 0.4674601 0.4719225 0.5009370 0.5269423
##  [349,] 0.4136302 0.4292922 0.4411605 0.4605273 0.4745053 0.4956640 0.5127899
##  [350,] 0.4106885 0.4288487 0.4494490 0.4628245 0.4789305 0.4959261 0.5326953
##  [351,] 0.4127343 0.4287737 0.4454747 0.4608238 0.4790381 0.4968650 0.5141978
##  [352,] 0.4147392 0.4240522 0.4510239 0.4615194 0.4806585 0.4928076 0.4996118
##  [353,] 0.4091330 0.4294713 0.4479985 0.4557200 0.4686950 0.4982167 0.5269323
##  [354,] 0.4104186 0.4246720 0.4422411 0.4638732 0.4738151 0.4895883 0.5181586
##  [355,] 0.4070571 0.4300259 0.4446144 0.4670872 0.4835877 0.4884671 0.5113512
##  [356,] 0.4088612 0.4289316 0.4406331 0.4651949 0.4675851 0.4933390 0.5110077
##  [357,] 0.4083118 0.4271458 0.4445229 0.4521948 0.4903312 0.4865383 0.5202182
##  [358,] 0.4139778 0.4282696 0.4461799 0.4680516 0.4815877 0.5034098 0.5238350
##  [359,] 0.4122791 0.4320452 0.4441442 0.4611284 0.4774487 0.5143575 0.5084502
##  [360,] 0.4098912 0.4261991 0.4466642 0.4559535 0.4774696 0.4908896 0.5170233
##  [361,] 0.4083661 0.4303064 0.4460466 0.4647243 0.4745058 0.4812645 0.5214414
##  [362,] 0.4051733 0.4297389 0.4485475 0.4589435 0.4773752 0.4914697 0.5070929
##  [363,] 0.4160157 0.4298971 0.4458337 0.4662807 0.4661350 0.4814679 0.5040475
##  [364,] 0.4122191 0.4305625 0.4436383 0.4569840 0.4846375 0.4977195 0.5036026
##  [365,] 0.4045944 0.4277789 0.4449810 0.4698806 0.4831971 0.4989953 0.5171593
##  [366,] 0.4113729 0.4279941 0.4455871 0.4632782 0.4797582 0.4961616 0.4948289
##  [367,] 0.4114606 0.4249411 0.4396365 0.4631170 0.4768629 0.5061882 0.5108494
##  [368,] 0.4061231 0.4196669 0.4460518 0.4555581 0.4795197 0.4961990 0.5074809
##  [369,] 0.4127713 0.4269093 0.4436151 0.4572342 0.4838370 0.4918676 0.5211858
##  [370,] 0.4084010 0.4269682 0.4501536 0.4585229 0.4805066 0.4953307 0.5105765
##  [371,] 0.4072569 0.4268385 0.4443116 0.4590966 0.4789017 0.4838202 0.5109425
##  [372,] 0.4091922 0.4292863 0.4464261 0.4665645 0.4827436 0.5052097 0.5086217
##  [373,] 0.4116449 0.4274668 0.4405709 0.4629007 0.4834027 0.4948997 0.5013095
##  [374,] 0.4103599 0.4249136 0.4433214 0.4532107 0.4746850 0.4998171 0.5118577
##  [375,] 0.4127063 0.4294201 0.4395199 0.4623201 0.4750371 0.4848545 0.5191372
##  [376,] 0.4120991 0.4277114 0.4476011 0.4637902 0.4921758 0.5041662 0.5206978
##  [377,] 0.4110574 0.4265634 0.4395935 0.4616371 0.4929902 0.4974912 0.5049363
##  [378,] 0.4106922 0.4243696 0.4484561 0.4674735 0.4824498 0.4927419 0.5136283
##  [379,] 0.4103667 0.4305666 0.4467491 0.4627959 0.4803298 0.4954080 0.4997410
##  [380,] 0.4103774 0.4296391 0.4460864 0.4506778 0.4709318 0.5094219 0.5151245
##  [381,] 0.4073794 0.4321599 0.4427993 0.4703395 0.4763978 0.4946082 0.5050790
##  [382,] 0.4061438 0.4256948 0.4420497 0.4608419 0.4772058 0.4941155 0.5120117
##  [383,] 0.4111492 0.4280559 0.4445246 0.4602013 0.4816316 0.4855604 0.5059062
##  [384,] 0.4069712 0.4241077 0.4459632 0.4564154 0.4734374 0.4961313 0.4960620
##  [385,] 0.4074308 0.4210374 0.4432284 0.4651350 0.4812196 0.5035587 0.5003209
##  [386,] 0.4115254 0.4280830 0.4407997 0.4535574 0.4867401 0.4945887 0.5238838
##  [387,] 0.4106055 0.4314669 0.4475035 0.4679760 0.4750951 0.4844873 0.5214905
##  [388,] 0.4137687 0.4319857 0.4400963 0.4644973 0.4771796 0.5056044 0.5129066
##  [389,] 0.4072870 0.4314112 0.4447675 0.4604468 0.4867038 0.4967199 0.5119339
##  [390,] 0.4148664 0.4330633 0.4416727 0.4615247 0.4768037 0.5070909 0.5189814
##  [391,] 0.4108115 0.4310879 0.4489633 0.4563990 0.4791140 0.4968725 0.5156487
##  [392,] 0.4108649 0.4291586 0.4417869 0.4654429 0.4837551 0.5072894 0.5194862
##  [393,] 0.4100212 0.4256393 0.4446961 0.4554969 0.4762290 0.4970558 0.5176910
##  [394,] 0.4114791 0.4270624 0.4479901 0.4521887 0.4784983 0.4860503 0.5180027
##  [395,] 0.4138912 0.4328011 0.4442700 0.4612964 0.4848014 0.5021630 0.5211489
##  [396,] 0.4134338 0.4261549 0.4475697 0.4703907 0.4818034 0.5089303 0.5059588
##  [397,] 0.4122506 0.4246851 0.4500147 0.4698107 0.4744459 0.5051083 0.5194607
##  [398,] 0.4125133 0.4275508 0.4405424 0.4571140 0.4846424 0.5062980 0.5268302
##  [399,] 0.4099212 0.4280699 0.4445569 0.4621657 0.4801730 0.5051787 0.5173490
##  [400,] 0.4113338 0.4250959 0.4456549 0.4590311 0.4822038 0.4907963 0.5211222
##  [401,] 0.4120257 0.4268740 0.4440284 0.4653506 0.4790777 0.4942618 0.5067383
##  [402,] 0.4130257 0.4263778 0.4450689 0.4590353 0.4717516 0.5021827 0.5043590
##  [403,] 0.4112503 0.4235871 0.4440089 0.4565759 0.4822275 0.4929146 0.5190252
##  [404,] 0.4103631 0.4230198 0.4428439 0.4629780 0.4818858 0.4840063 0.5072496
##  [405,] 0.4153244 0.4271679 0.4443549 0.4715071 0.4776192 0.5024202 0.5074069
##  [406,] 0.4124665 0.4283376 0.4480904 0.4578074 0.4818240 0.4961986 0.5041026
##  [407,] 0.4102299 0.4243226 0.4439613 0.4599684 0.4767518 0.5023032 0.5279203
##  [408,] 0.4088142 0.4271037 0.4431738 0.4563202 0.4868516 0.4996629 0.5052756
##  [409,] 0.4103048 0.4299937 0.4423515 0.4682386 0.4833495 0.5011654 0.5109408
##  [410,] 0.4144355 0.4290643 0.4427472 0.4593963 0.4719711 0.5052522 0.5066121
##  [411,] 0.4119555 0.4258048 0.4464857 0.4520011 0.4799486 0.4849015 0.5162308
##  [412,] 0.4074907 0.4256196 0.4433910 0.4637859 0.4781551 0.4896441 0.5192813
##  [413,] 0.4120282 0.4299851 0.4406054 0.4614846 0.4750345 0.5162551 0.5061752
##  [414,] 0.4121347 0.4296199 0.4481137 0.4622296 0.4708919 0.4961189 0.5011308
##  [415,] 0.4126994 0.4252222 0.4405103 0.4619344 0.4808784 0.4965351 0.5155800
##  [416,] 0.4083186 0.4282248 0.4458635 0.4650788 0.4677080 0.4847756 0.5161466
##  [417,] 0.4089402 0.4321417 0.4472323 0.4635782 0.4865613 0.4861338 0.5236898
##  [418,] 0.4104625 0.4291720 0.4419930 0.4680362 0.4836161 0.4943665 0.5327684
##  [419,] 0.4108123 0.4250605 0.4518378 0.4600157 0.4765796 0.5011810 0.5204970
##  [420,] 0.4124310 0.4241416 0.4461299 0.4506995 0.4847350 0.5067470 0.5212550
##  [421,] 0.4116139 0.4252623 0.4480104 0.4614798 0.4760051 0.4927989 0.5112307
##  [422,] 0.4131403 0.4335643 0.4369899 0.4624885 0.4727229 0.4957941 0.5024524
##  [423,] 0.4119307 0.4209785 0.4455586 0.4629234 0.4817258 0.5069827 0.5063280
##  [424,] 0.4084707 0.4267892 0.4426331 0.4635781 0.4802081 0.4968102 0.5134439
##  [425,] 0.4078150 0.4249953 0.4485431 0.4643701 0.4722450 0.4967342 0.5179481
##  [426,] 0.4107129 0.4289189 0.4468978 0.4601573 0.4853146 0.5087702 0.5119586
##  [427,] 0.4082533 0.4231230 0.4386947 0.4609354 0.4719010 0.4908864 0.5082841
##  [428,] 0.4077577 0.4290286 0.4494490 0.4675991 0.4755159 0.4918174 0.5023222
##  [429,] 0.4131222 0.4301626 0.4427217 0.4638560 0.4735194 0.5025280 0.4973188
##  [430,] 0.4121270 0.4247380 0.4496590 0.4631983 0.4824326 0.4992877 0.5108975
##  [431,] 0.4096242 0.4286356 0.4428219 0.4558633 0.4865969 0.4817234 0.5264141
##  [432,] 0.4144945 0.4309142 0.4448308 0.4670332 0.4804607 0.4946330 0.5191943
##  [433,] 0.4134259 0.4268477 0.4482425 0.4726917 0.4857951 0.4916437 0.5169032
##  [434,] 0.4119639 0.4265879 0.4484371 0.4581765 0.4806659 0.5002812 0.5099826
##  [435,] 0.4114848 0.4277094 0.4394482 0.4624236 0.4819556 0.4831212 0.5117047
##  [436,] 0.4096734 0.4275143 0.4493264 0.4614172 0.4848016 0.4942548 0.5107034
##  [437,] 0.4073724 0.4329435 0.4429073 0.4686596 0.4819124 0.4964226 0.5180540
##  [438,] 0.4106858 0.4247180 0.4441820 0.4746353 0.4810103 0.4910288 0.5113041
##  [439,] 0.4068496 0.4276226 0.4486168 0.4627841 0.4792012 0.4913504 0.5022365
##  [440,] 0.4117423 0.4299466 0.4388925 0.4603616 0.4782697 0.5005672 0.5059527
##  [441,] 0.4118053 0.4257486 0.4443940 0.4592612 0.4813831 0.5010800 0.5216896
##  [442,] 0.4115656 0.4261430 0.4450137 0.4583728 0.4903014 0.4886501 0.5037885
##  [443,] 0.4079209 0.4318814 0.4468426 0.4629472 0.4800790 0.4792933 0.5090694
##  [444,] 0.4113242 0.4271944 0.4471034 0.4615090 0.4859797 0.4914683 0.5044871
##  [445,] 0.4133626 0.4275167 0.4443575 0.4622294 0.4763273 0.4881307 0.5068705
##  [446,] 0.4100045 0.4269425 0.4400911 0.4669652 0.4793867 0.4919251 0.5322752
##  [447,] 0.4116280 0.4304929 0.4525482 0.4694214 0.4787453 0.4982498 0.5254026
##  [448,] 0.4114579 0.4232684 0.4474878 0.4590887 0.4910820 0.4982637 0.5194855
##  [449,] 0.4117932 0.4249458 0.4423774 0.4652243 0.4823789 0.5052445 0.5071243
##  [450,] 0.4122862 0.4216373 0.4453900 0.4603954 0.4771994 0.4953332 0.5141149
##  [451,] 0.4066736 0.4256705 0.4452412 0.4604716 0.4822267 0.4946205 0.5140465
##  [452,] 0.4144393 0.4289664 0.4506779 0.4685573 0.4855807 0.4916359 0.5290742
##  [453,] 0.4084118 0.4249357 0.4397754 0.4625342 0.4798908 0.4999629 0.5151926
##  [454,] 0.4114243 0.4268749 0.4451239 0.4549317 0.4700302 0.4845912 0.5180289
##  [455,] 0.4089866 0.4299911 0.4391484 0.4641252 0.4795054 0.4991009 0.5123520
##  [456,] 0.4158146 0.4279791 0.4431251 0.4610534 0.4780222 0.4988578 0.5165329
##  [457,] 0.4102747 0.4294615 0.4445423 0.4673883 0.4726652 0.4931651 0.5202032
##  [458,] 0.4128691 0.4276581 0.4483170 0.4582776 0.4771558 0.5062043 0.5020885
##  [459,] 0.4121747 0.4290745 0.4476751 0.4615041 0.4778063 0.4883212 0.5104254
##  [460,] 0.4091175 0.4249865 0.4442617 0.4590368 0.4760095 0.4973356 0.5069681
##  [461,] 0.4093512 0.4281388 0.4476169 0.4583111 0.4883804 0.4942262 0.5256556
##  [462,] 0.4159446 0.4292409 0.4463332 0.4661089 0.4814216 0.4930871 0.5166066
##  [463,] 0.4136166 0.4318836 0.4409156 0.4688325 0.4864439 0.5026739 0.5197669
##  [464,] 0.4098712 0.4259359 0.4444298 0.4547104 0.4684347 0.4945256 0.5172655
##  [465,] 0.4110709 0.4284430 0.4420322 0.4595429 0.4712403 0.4990484 0.4998299
##  [466,] 0.4140672 0.4259389 0.4484928 0.4656177 0.4845183 0.4898812 0.5115644
##  [467,] 0.4095202 0.4237400 0.4446032 0.4572928 0.4775863 0.5074533 0.5115483
##  [468,] 0.4107237 0.4253772 0.4503535 0.4667522 0.4798667 0.4995290 0.5187283
##  [469,] 0.4097890 0.4268084 0.4447412 0.4529565 0.4763927 0.4946344 0.5074828
##  [470,] 0.4074392 0.4295629 0.4421234 0.4634331 0.4673656 0.4894275 0.5159652
##  [471,] 0.4104679 0.4298964 0.4455236 0.4594905 0.4761533 0.5070474 0.5077583
##  [472,] 0.4140991 0.4294977 0.4461254 0.4657315 0.4850978 0.5075296 0.5226949
##  [473,] 0.4086869 0.4306630 0.4444574 0.4706074 0.4742370 0.4927391 0.5213616
##  [474,] 0.4178358 0.4316863 0.4431920 0.4605677 0.4713414 0.5100580 0.5146760
##  [475,] 0.4125812 0.4259142 0.4432615 0.4606365 0.4776207 0.4927054 0.5070461
##  [476,] 0.4131869 0.4257323 0.4431922 0.4680607 0.4833667 0.4906795 0.4994483
##  [477,] 0.4119227 0.4335281 0.4448566 0.4527797 0.4785702 0.4883673 0.5289377
##  [478,] 0.4077919 0.4261560 0.4447590 0.4591694 0.4754626 0.4909959 0.5016060
##  [479,] 0.4140261 0.4278904 0.4469083 0.4575530 0.4822717 0.5055695 0.5191509
##  [480,] 0.4137357 0.4293497 0.4446788 0.4677703 0.4652858 0.5015693 0.5045694
##  [481,] 0.4098150 0.4263496 0.4450852 0.4600235 0.4816140 0.4914137 0.5258727
##  [482,] 0.4116999 0.4266174 0.4440326 0.4638234 0.4772161 0.4936710 0.5113090
##  [483,] 0.4091112 0.4287893 0.4427472 0.4625433 0.4728610 0.5104966 0.5057939
##  [484,] 0.4066474 0.4267951 0.4473885 0.4653134 0.4753443 0.4921738 0.5112862
##  [485,] 0.4080428 0.4294365 0.4524078 0.4641974 0.4784958 0.4867121 0.5086996
##  [486,] 0.4131628 0.4279749 0.4436321 0.4645810 0.4744226 0.4950816 0.5117220
##  [487,] 0.4115988 0.4274463 0.4479167 0.4561596 0.4732512 0.4905047 0.5143799
##  [488,] 0.4097547 0.4227311 0.4451113 0.4570651 0.4721374 0.5002352 0.5246957
##  [489,] 0.4103562 0.4276165 0.4445487 0.4537586 0.4834790 0.4964306 0.5093388
##  [490,] 0.4090834 0.4311580 0.4369547 0.4601508 0.4827045 0.4895939 0.5176533
##  [491,] 0.4101028 0.4272965 0.4481410 0.4652452 0.4782842 0.4880830 0.5080365
##  [492,] 0.4082889 0.4296303 0.4465663 0.4605826 0.4830294 0.4924745 0.5102701
##  [493,] 0.4092703 0.4288504 0.4473764 0.4660593 0.4762704 0.4966940 0.5113098
##  [494,] 0.4057426 0.4270366 0.4440266 0.4604667 0.4779628 0.5043016 0.5158031
##  [495,] 0.4093034 0.4305367 0.4422914 0.4626287 0.4622278 0.4873377 0.5101780
##  [496,] 0.4129031 0.4274692 0.4433713 0.4633015 0.4827799 0.4806526 0.5256565
##  [497,] 0.4035097 0.4269277 0.4458783 0.4544592 0.4808462 0.4927523 0.5240639
##  [498,] 0.4115160 0.4278999 0.4408733 0.4667962 0.4702120 0.4979236 0.4977231
##  [499,] 0.4105495 0.4289389 0.4471490 0.4614476 0.4902298 0.4959449 0.5115618
##  [500,] 0.4118901 0.4311543 0.4362479 0.4619747 0.4774509 0.4947420 0.5072210
##  [501,] 0.4129685 0.4275709 0.4447926 0.4587026 0.4864157 0.4995775 0.5001133
##  [502,] 0.4149520 0.4274070 0.4473529 0.4583322 0.4702978 0.4977452 0.5256911
##  [503,] 0.4155210 0.4281373 0.4424184 0.4620479 0.4751105 0.4885446 0.5116532
##  [504,] 0.4127150 0.4296230 0.4411313 0.4609002 0.4726505 0.4866239 0.5258409
##  [505,] 0.4095678 0.4292485 0.4514652 0.4637069 0.4763788 0.4984172 0.5040671
##  [506,] 0.4124231 0.4257915 0.4444785 0.4590796 0.4921031 0.5073008 0.5104286
##  [507,] 0.4124831 0.4278960 0.4427935 0.4632150 0.4806345 0.4954662 0.5267970
##  [508,] 0.4137127 0.4252483 0.4454802 0.4600731 0.4754766 0.4775593 0.5248127
##  [509,] 0.4134071 0.4242302 0.4421128 0.4629445 0.4762467 0.5029468 0.5161628
##  [510,] 0.4139118 0.4261005 0.4482475 0.4610504 0.4763496 0.5019520 0.5113013
##  [511,] 0.4091293 0.4297776 0.4469153 0.4600559 0.4654538 0.5033921 0.5150004
##  [512,] 0.4095982 0.4288181 0.4435984 0.4600220 0.4748931 0.5067345 0.5132711
##  [513,] 0.4079854 0.4240394 0.4395856 0.4643378 0.4737151 0.4978614 0.5022728
##  [514,] 0.4067748 0.4278924 0.4467655 0.4666045 0.4877899 0.4985458 0.5218758
##  [515,] 0.4125987 0.4251528 0.4438561 0.4600858 0.4767227 0.5016382 0.5186636
##  [516,] 0.4127416 0.4272144 0.4463279 0.4597567 0.4702321 0.4924767 0.5129942
##  [517,] 0.4090582 0.4291931 0.4434744 0.4646333 0.4846503 0.4990141 0.5051340
##  [518,] 0.4149893 0.4259568 0.4400735 0.4617193 0.4869287 0.4902589 0.5190557
##  [519,] 0.4138341 0.4287474 0.4437673 0.4659712 0.4773884 0.5044232 0.5242908
##  [520,] 0.4118072 0.4292728 0.4413204 0.4607362 0.4804558 0.4916224 0.5268269
##  [521,] 0.4136039 0.4265025 0.4451430 0.4583681 0.4914247 0.5020598 0.5233311
##  [522,] 0.4103758 0.4221347 0.4440630 0.4760039 0.4783352 0.4995720 0.5091736
##  [523,] 0.4098988 0.4303905 0.4478119 0.4674623 0.4768884 0.5022413 0.5256976
##  [524,] 0.4118997 0.4274547 0.4415165 0.4647413 0.4880883 0.5028490 0.5044184
##  [525,] 0.4128703 0.4303830 0.4480536 0.4611893 0.4676957 0.5016052 0.5194385
##  [526,] 0.4084500 0.4298919 0.4426264 0.4597157 0.4803915 0.5009835 0.4974008
##  [527,] 0.4082475 0.4296522 0.4380308 0.4589544 0.4702270 0.5013442 0.5032286
##  [528,] 0.4159536 0.4304073 0.4466138 0.4593971 0.4805193 0.4996434 0.5079824
##  [529,] 0.4126647 0.4254703 0.4452619 0.4618458 0.4771282 0.4930011 0.5173611
##  [530,] 0.4131060 0.4254603 0.4366769 0.4601752 0.4814464 0.5043206 0.5128512
##  [531,] 0.4118701 0.4266547 0.4410351 0.4631141 0.4728775 0.4830758 0.5174771
##  [532,] 0.4114973 0.4236584 0.4435764 0.4642508 0.4798405 0.4931179 0.5138026
##  [533,] 0.4113048 0.4282834 0.4390033 0.4612088 0.4679146 0.4941989 0.5183445
##  [534,] 0.4134231 0.4282631 0.4459063 0.4644324 0.4808408 0.4891649 0.5267086
##  [535,] 0.4086388 0.4303319 0.4451033 0.4634735 0.4826899 0.4849170 0.5094412
##  [536,] 0.4120260 0.4320078 0.4502222 0.4569709 0.4848105 0.4920917 0.5089395
##  [537,] 0.4126367 0.4297906 0.4440005 0.4628832 0.4838779 0.4935318 0.4974526
##  [538,] 0.4095254 0.4277359 0.4474653 0.4719638 0.4713004 0.5062343 0.5135523
##  [539,] 0.4114089 0.4245782 0.4417856 0.4571790 0.4843129 0.4968953 0.5134880
##  [540,] 0.4080673 0.4305901 0.4394489 0.4686357 0.4719978 0.5082279 0.5190883
##  [541,] 0.4136179 0.4268135 0.4491866 0.4612331 0.4782826 0.4761220 0.5146183
##  [542,] 0.4136585 0.4295904 0.4478879 0.4664135 0.4810155 0.4848324 0.5157391
##  [543,] 0.4086119 0.4273090 0.4438680 0.4578036 0.4819998 0.4986608 0.5207573
##  [544,] 0.4101723 0.4257717 0.4468470 0.4631178 0.4857731 0.5022430 0.5254110
##  [545,] 0.4100581 0.4273512 0.4407081 0.4666847 0.4800191 0.4830166 0.5178135
##  [546,] 0.4096095 0.4263608 0.4390101 0.4671152 0.4664878 0.5051466 0.5248709
##  [547,] 0.4082366 0.4280752 0.4422266 0.4686723 0.4684758 0.4843753 0.5087748
##  [548,] 0.4116213 0.4269116 0.4487402 0.4665449 0.4749733 0.5017611 0.5071398
##  [549,] 0.4115561 0.4252173 0.4455304 0.4728344 0.4882732 0.4975971 0.5206859
##  [550,] 0.4135447 0.4289595 0.4414786 0.4668476 0.4826873 0.5021016 0.5069679
##  [551,] 0.4125905 0.4272326 0.4493075 0.4631741 0.4763896 0.4919783 0.5092186
##  [552,] 0.4078629 0.4282182 0.4458339 0.4504270 0.4716498 0.4976028 0.5097952
##  [553,] 0.4066808 0.4275989 0.4464510 0.4573203 0.4816005 0.5013920 0.5161179
##  [554,] 0.4111156 0.4236479 0.4428395 0.4594614 0.4901927 0.4812624 0.5086859
##  [555,] 0.4116221 0.4318269 0.4472201 0.4639367 0.4810984 0.4966795 0.5179775
##  [556,] 0.4083555 0.4289918 0.4434580 0.4647070 0.4729495 0.4914861 0.5003633
##  [557,] 0.4082834 0.4313281 0.4439292 0.4568713 0.4795554 0.4971645 0.5164349
##  [558,] 0.4116898 0.4250384 0.4483835 0.4664340 0.4775634 0.4947271 0.5133343
##  [559,] 0.4115802 0.4278717 0.4472903 0.4544393 0.4822862 0.4921513 0.5351877
##  [560,] 0.4075266 0.4281919 0.4404757 0.4602198 0.4797863 0.5000243 0.5297112
##  [561,] 0.4091276 0.4303547 0.4427120 0.4603492 0.4754836 0.4983538 0.5257508
##  [562,] 0.4049102 0.4273726 0.4419462 0.4576570 0.4780447 0.4964239 0.5158740
##  [563,] 0.4102033 0.4263661 0.4424093 0.4661718 0.4754941 0.4891841 0.5067329
##  [564,] 0.4094704 0.4260708 0.4416830 0.4651882 0.4714116 0.5107415 0.5004721
##  [565,] 0.4116058 0.4295168 0.4412983 0.4658692 0.4749640 0.5018739 0.5028700
##  [566,] 0.4094761 0.4309004 0.4475175 0.4546795 0.4722446 0.5036505 0.4993993
##  [567,] 0.4150341 0.4294922 0.4444464 0.4588123 0.4774032 0.4923186 0.5061871
##  [568,] 0.4078605 0.4282593 0.4390696 0.4649506 0.4769675 0.4965147 0.5137313
##  [569,] 0.4112241 0.4272597 0.4495748 0.4595170 0.4762553 0.4924722 0.5153733
##  [570,] 0.4125468 0.4279504 0.4412638 0.4681501 0.4845926 0.4940754 0.5149872
##  [571,] 0.4156015 0.4294967 0.4464648 0.4584717 0.4848692 0.4888447 0.5179724
##  [572,] 0.4080614 0.4282481 0.4463561 0.4606114 0.4814452 0.5093460 0.5168716
##  [573,] 0.4122815 0.4276638 0.4491343 0.4607950 0.4749287 0.5064679 0.5113955
##  [574,] 0.4126411 0.4297579 0.4468057 0.4606930 0.4784005 0.4933502 0.5137134
##  [575,] 0.4137285 0.4251047 0.4434509 0.4546109 0.4839732 0.5069810 0.5298708
##  [576,] 0.4113659 0.4292471 0.4452845 0.4626181 0.4788211 0.5021630 0.5149542
##  [577,] 0.4107621 0.4261663 0.4502765 0.4572973 0.4865828 0.5034964 0.5297906
##  [578,] 0.4162446 0.4246248 0.4463293 0.4634684 0.4758839 0.4989531 0.5149345
##  [579,] 0.4111800 0.4229093 0.4485706 0.4557983 0.4763172 0.4943720 0.5140135
##  [580,] 0.4099813 0.4316815 0.4419460 0.4604362 0.4785394 0.4971040 0.5156028
##  [581,] 0.4076234 0.4244242 0.4421483 0.4573729 0.4705184 0.5062610 0.5152405
##  [582,] 0.4109100 0.4254866 0.4420090 0.4547074 0.4794601 0.4933202 0.5101653
##  [583,] 0.4087431 0.4256174 0.4424320 0.4611748 0.4943937 0.4936751 0.5072016
##  [584,] 0.4139691 0.4290406 0.4391819 0.4658089 0.4844983 0.5007646 0.5127039
##  [585,] 0.4067676 0.4262783 0.4345232 0.4596459 0.4738409 0.4909495 0.5206221
##  [586,] 0.4119121 0.4248316 0.4435318 0.4590551 0.4790742 0.4919867 0.5134621
##  [587,] 0.4120976 0.4242576 0.4445188 0.4505351 0.4726852 0.5071702 0.5216285
##  [588,] 0.4089703 0.4335196 0.4384478 0.4618405 0.4870070 0.4956156 0.5017747
##  [589,] 0.4137878 0.4267732 0.4457521 0.4599919 0.4672729 0.4970293 0.5121364
##  [590,] 0.4116824 0.4304700 0.4391495 0.4630335 0.4787858 0.4899121 0.5096667
##  [591,] 0.4112055 0.4285037 0.4390618 0.4680071 0.4794371 0.4970614 0.5074416
##  [592,] 0.4091078 0.4251077 0.4410710 0.4594495 0.4775400 0.5031004 0.5070173
##  [593,] 0.4072677 0.4258083 0.4446570 0.4664247 0.4775760 0.4953088 0.5107895
##  [594,] 0.4177948 0.4308143 0.4376879 0.4567691 0.4883013 0.4969315 0.5171410
##  [595,] 0.4132249 0.4237938 0.4411268 0.4572066 0.4748569 0.4938310 0.5107653
##  [596,] 0.4073087 0.4312449 0.4456351 0.4655703 0.4873932 0.4892673 0.5128611
##  [597,] 0.4068524 0.4207192 0.4474867 0.4614249 0.4888975 0.5036615 0.5234851
##  [598,] 0.4118692 0.4257176 0.4406491 0.4626547 0.4748192 0.4924336 0.5191406
##  [599,] 0.4130993 0.4261407 0.4418584 0.4565584 0.4896028 0.4910066 0.5058735
##  [600,] 0.4111155 0.4298058 0.4438225 0.4619659 0.4792176 0.4965721 0.5156854
##  [601,] 0.4135950 0.4262484 0.4437753 0.4652869 0.4760207 0.4794792 0.5139955
##  [602,] 0.4113505 0.4253294 0.4460029 0.4564790 0.4717985 0.4958626 0.5195189
##  [603,] 0.4094290 0.4240234 0.4411292 0.4544194 0.4718050 0.4983100 0.5104854
##  [604,] 0.4081541 0.4222171 0.4404201 0.4596884 0.4764559 0.4852538 0.5168957
##  [605,] 0.4064493 0.4247790 0.4438020 0.4606922 0.4853136 0.4977871 0.5101098
##  [606,] 0.4090296 0.4286009 0.4459811 0.4612330 0.4796959 0.4936694 0.5084793
##  [607,] 0.4113651 0.4303777 0.4358032 0.4585984 0.4764534 0.4995378 0.5106649
##  [608,] 0.4116706 0.4289499 0.4424502 0.4700316 0.4808090 0.4908083 0.5217012
##  [609,] 0.4136980 0.4248842 0.4452769 0.4646548 0.4782791 0.4901156 0.5114902
##  [610,] 0.4136058 0.4252511 0.4402967 0.4591480 0.4717257 0.5058374 0.5042766
##  [611,] 0.4129555 0.4251662 0.4442296 0.4541971 0.4758960 0.4974921 0.5142038
##  [612,] 0.4114935 0.4278340 0.4479306 0.4589818 0.4857101 0.5045732 0.5147813
##  [613,] 0.4106894 0.4320205 0.4402276 0.4646884 0.4752210 0.4868835 0.5101564
##  [614,] 0.4136478 0.4334293 0.4553778 0.4588529 0.4730676 0.5119699 0.5149842
##  [615,] 0.4094698 0.4253618 0.4479192 0.4592528 0.4811444 0.4978775 0.5176276
##  [616,] 0.4107128 0.4213074 0.4488436 0.4727048 0.4850906 0.4933049 0.5087857
##  [617,] 0.4136895 0.4260096 0.4441209 0.4627987 0.4780604 0.4921038 0.5189782
##  [618,] 0.4114394 0.4226420 0.4426263 0.4583079 0.4899535 0.4895767 0.5014177
##  [619,] 0.4093963 0.4315727 0.4407125 0.4675725 0.4823064 0.4995007 0.5139329
##  [620,] 0.4117670 0.4281839 0.4500920 0.4518481 0.4785802 0.4891988 0.5130412
##  [621,] 0.4113314 0.4236370 0.4468809 0.4591762 0.4913769 0.5001123 0.5198295
##  [622,] 0.4115269 0.4326537 0.4473647 0.4648871 0.4873771 0.4983147 0.5278873
##  [623,] 0.4115745 0.4239011 0.4481110 0.4644747 0.4830751 0.4997107 0.5141832
##  [624,] 0.4071101 0.4270839 0.4471221 0.4611081 0.4865173 0.5026034 0.5092251
##  [625,] 0.4117936 0.4299287 0.4395458 0.4547005 0.4795759 0.4898618 0.5128521
##  [626,] 0.4096548 0.4247992 0.4391854 0.4604915 0.4772946 0.4962910 0.5184417
##  [627,] 0.4143268 0.4238920 0.4502426 0.4658966 0.4625958 0.4990417 0.5192248
##  [628,] 0.4102417 0.4311998 0.4477373 0.4612054 0.4770925 0.4898834 0.5122175
##  [629,] 0.4115607 0.4272117 0.4418218 0.4631499 0.4874635 0.5012176 0.5086175
##  [630,] 0.4110399 0.4279838 0.4453011 0.4698685 0.4804200 0.4825678 0.5110105
##  [631,] 0.4100613 0.4343821 0.4398012 0.4659679 0.4867781 0.4998276 0.5069128
##  [632,] 0.4117940 0.4277556 0.4463853 0.4636771 0.4728908 0.5062340 0.5117984
##  [633,] 0.4140233 0.4321172 0.4469562 0.4662677 0.4809952 0.4842588 0.5072233
##  [634,] 0.4087745 0.4254097 0.4422642 0.4601058 0.4710747 0.4928115 0.5032172
##  [635,] 0.4132962 0.4265223 0.4422472 0.4584584 0.4845521 0.5046736 0.5103256
##  [636,] 0.4088506 0.4254360 0.4398303 0.4635952 0.4803157 0.4998837 0.5114994
##  [637,] 0.4152549 0.4250517 0.4443122 0.4625447 0.4724219 0.4987279 0.5059132
##  [638,] 0.4113338 0.4256180 0.4426128 0.4565913 0.4900326 0.4920018 0.5045736
##  [639,] 0.4144546 0.4303419 0.4385275 0.4596147 0.4880330 0.4988111 0.5210257
##  [640,] 0.4114650 0.4257949 0.4436620 0.4571574 0.4694549 0.4953432 0.5081741
##  [641,] 0.4103448 0.4308420 0.4398035 0.4610931 0.4708399 0.5019194 0.5093021
##  [642,] 0.4091050 0.4240862 0.4399051 0.4577728 0.4750243 0.4983694 0.4998756
##  [643,] 0.4135405 0.4272136 0.4426002 0.4597255 0.4738526 0.5143776 0.5173093
##  [644,] 0.4122198 0.4286628 0.4495055 0.4659599 0.4737734 0.4974307 0.5022391
##  [645,] 0.4098977 0.4252945 0.4422617 0.4611750 0.4801406 0.5100611 0.5153584
##  [646,] 0.4149526 0.4249715 0.4479013 0.4527059 0.4777172 0.4864425 0.5058299
##  [647,] 0.4104349 0.4325593 0.4464202 0.4651909 0.4798366 0.4948317 0.5081158
##  [648,] 0.4107866 0.4274538 0.4411381 0.4636347 0.4716425 0.4996819 0.5114646
##  [649,] 0.4144029 0.4297152 0.4467683 0.4604706 0.4849805 0.4882025 0.5024438
##  [650,] 0.4090752 0.4249574 0.4424581 0.4566849 0.4874088 0.5101318 0.5088338
##  [651,] 0.4141971 0.4271474 0.4437975 0.4583283 0.4836041 0.4982304 0.5266885
##  [652,] 0.4111947 0.4307697 0.4413596 0.4579726 0.4864544 0.4955041 0.5194589
##  [653,] 0.4094565 0.4246748 0.4462550 0.4630174 0.4857653 0.4958233 0.5182773
##  [654,] 0.4074387 0.4241084 0.4446335 0.4575989 0.4811579 0.4994701 0.5191157
##  [655,] 0.4047161 0.4288462 0.4443137 0.4712650 0.4862051 0.4877185 0.5185010
##  [656,] 0.4096557 0.4281976 0.4438002 0.4602232 0.4879657 0.4964786 0.5108746
##  [657,] 0.4141328 0.4305582 0.4429990 0.4604955 0.4761804 0.4896427 0.5169332
##  [658,] 0.4125019 0.4255702 0.4419838 0.4578279 0.4819623 0.4970382 0.5298038
##  [659,] 0.4138438 0.4244354 0.4397444 0.4676849 0.4823338 0.4888836 0.5143979
##  [660,] 0.4089659 0.4289712 0.4494438 0.4594862 0.4768850 0.4942039 0.5093522
##  [661,] 0.4051678 0.4331282 0.4472343 0.4608090 0.4697300 0.4922608 0.5093839
##  [662,] 0.4090887 0.4249708 0.4474491 0.4594771 0.4885712 0.5080764 0.5166600
##  [663,] 0.4113390 0.4219629 0.4485692 0.4633072 0.4795464 0.5023146 0.5091179
##  [664,] 0.4111391 0.4294152 0.4435377 0.4615352 0.4829721 0.4921924 0.5152551
##  [665,] 0.4130022 0.4245079 0.4393386 0.4546544 0.4824169 0.4971241 0.5138991
##  [666,] 0.4112320 0.4297906 0.4486434 0.4638671 0.4734904 0.4988824 0.5081351
##  [667,] 0.4135908 0.4246302 0.4415849 0.4614078 0.4810499 0.4887917 0.5055095
##  [668,] 0.4097687 0.4286582 0.4429088 0.4597386 0.4782295 0.4934564 0.5080218
##  [669,] 0.4084201 0.4272004 0.4472857 0.4608934 0.4923202 0.4931449 0.5202222
##  [670,] 0.4119184 0.4258736 0.4491431 0.4663064 0.4777225 0.4974722 0.5074719
##  [671,] 0.4134575 0.4234669 0.4450207 0.4544527 0.4729434 0.4990049 0.5126541
##  [672,] 0.4131537 0.4282438 0.4406471 0.4611176 0.4770322 0.4961222 0.5152603
##  [673,] 0.4123456 0.4272556 0.4484766 0.4693903 0.4729007 0.4963596 0.5126792
##  [674,] 0.4116178 0.4288026 0.4477125 0.4564271 0.4830784 0.4874785 0.5095683
##  [675,] 0.4085458 0.4277096 0.4423454 0.4646205 0.4789858 0.5024358 0.5083378
##  [676,] 0.4112758 0.4245845 0.4470678 0.4606646 0.4827934 0.4861900 0.4997074
##  [677,] 0.4095728 0.4273795 0.4451879 0.4623212 0.4830573 0.4991797 0.5163484
##  [678,] 0.4103653 0.4232614 0.4458957 0.4626189 0.4717822 0.5029344 0.5137036
##  [679,] 0.4099366 0.4263732 0.4478506 0.4623922 0.4873468 0.4838570 0.4984324
##  [680,] 0.4107574 0.4206693 0.4407200 0.4620115 0.4838095 0.4904381 0.5142754
##  [681,] 0.4103641 0.4301730 0.4438486 0.4673797 0.4703694 0.4947552 0.5116999
##  [682,] 0.4085689 0.4251066 0.4436815 0.4662972 0.4738637 0.4981827 0.5321771
##  [683,] 0.4071321 0.4269117 0.4437457 0.4621592 0.4755995 0.4929023 0.5066485
##  [684,] 0.4092699 0.4277853 0.4465439 0.4649544 0.4789852 0.4959166 0.5041912
##  [685,] 0.4073352 0.4216897 0.4458376 0.4544271 0.4868196 0.4985954 0.5129766
##  [686,] 0.4103800 0.4270758 0.4459523 0.4701839 0.4895875 0.4982969 0.5026518
##  [687,] 0.4099647 0.4291747 0.4407748 0.4583759 0.4741338 0.4966872 0.4861670
##  [688,] 0.4123030 0.4304592 0.4439518 0.4660196 0.4773443 0.4896566 0.5197671
##  [689,] 0.4109914 0.4250805 0.4464851 0.4637460 0.4783817 0.4803129 0.5069981
##  [690,] 0.4114053 0.4305768 0.4428426 0.4589307 0.4786101 0.4964107 0.5213541
##  [691,] 0.4131853 0.4288911 0.4469170 0.4578676 0.4802874 0.5143303 0.5121162
##  [692,] 0.4123170 0.4316546 0.4424755 0.4520729 0.4761294 0.4931063 0.5054030
##  [693,] 0.4122804 0.4291654 0.4452912 0.4657763 0.4860296 0.4977366 0.5107818
##  [694,] 0.4127041 0.4263980 0.4451275 0.4577467 0.4873212 0.4969938 0.5069707
##  [695,] 0.4104700 0.4291663 0.4453369 0.4545723 0.4798159 0.4981160 0.5171154
##  [696,] 0.4125251 0.4286064 0.4454765 0.4693928 0.4823611 0.4935929 0.5150707
##  [697,] 0.4080656 0.4263791 0.4441004 0.4565264 0.4697207 0.4997645 0.5068224
##  [698,] 0.4104730 0.4268937 0.4468655 0.4607109 0.4851801 0.4948095 0.5202879
##  [699,] 0.4108968 0.4229912 0.4484842 0.4670374 0.4810534 0.5003583 0.5134249
##  [700,] 0.4082192 0.4268551 0.4464362 0.4598282 0.4707562 0.4998580 0.5040872
##  [701,] 0.4115141 0.4260983 0.4448425 0.4638298 0.4736856 0.4887067 0.5116070
##  [702,] 0.4135039 0.4309296 0.4424302 0.4604640 0.4663065 0.5126799 0.5036210
##  [703,] 0.4124581 0.4334210 0.4475416 0.4693454 0.4841395 0.4992858 0.4952847
##  [704,] 0.4078448 0.4312818 0.4409940 0.4715745 0.4808214 0.4885675 0.5200143
##  [705,] 0.4128182 0.4305658 0.4410448 0.4640772 0.4904701 0.4973655 0.5126533
##  [706,] 0.4134071 0.4260181 0.4460148 0.4656979 0.4849171 0.4953224 0.5286017
##  [707,] 0.4084760 0.4244083 0.4498655 0.4577665 0.4724789 0.4932345 0.5131524
##  [708,] 0.4117306 0.4266905 0.4400214 0.4638992 0.4784806 0.4964721 0.5109236
##  [709,] 0.4137170 0.4249462 0.4437402 0.4571236 0.4821690 0.4871012 0.5062968
##  [710,] 0.4088614 0.4312719 0.4430970 0.4615943 0.4694801 0.5013289 0.5176139
##  [711,] 0.4086425 0.4232629 0.4431082 0.4654693 0.4747898 0.4884459 0.5199490
##  [712,] 0.4115922 0.4266855 0.4434102 0.4569082 0.4804209 0.4941892 0.5155847
##  [713,] 0.4106055 0.4303844 0.4458811 0.4636840 0.4786107 0.5087659 0.5099194
##  [714,] 0.4112624 0.4241427 0.4494427 0.4614915 0.4722006 0.4877097 0.5180519
##  [715,] 0.4160489 0.4266359 0.4453371 0.4611379 0.4669318 0.4902395 0.5036620
##  [716,] 0.4129094 0.4307395 0.4488520 0.4650479 0.4780140 0.4979152 0.5133106
##  [717,] 0.4093411 0.4245300 0.4442335 0.4704326 0.4860765 0.4856997 0.5103552
##  [718,] 0.4108440 0.4205043 0.4453750 0.4548727 0.4721167 0.4930798 0.5233463
##  [719,] 0.4095260 0.4221084 0.4466431 0.4561623 0.4745285 0.4903862 0.5058586
##  [720,] 0.4089656 0.4293018 0.4440287 0.4622099 0.4802609 0.4975771 0.5206589
##  [721,] 0.4124772 0.4249853 0.4413606 0.4571789 0.4870062 0.4977439 0.5263272
##  [722,] 0.4160533 0.4226884 0.4428034 0.4639714 0.4836477 0.4930823 0.5192171
##  [723,] 0.4118298 0.4301771 0.4373452 0.4602305 0.4814326 0.4888919 0.5132527
##  [724,] 0.4105538 0.4285504 0.4429624 0.4642752 0.4729801 0.4962625 0.5144841
##  [725,] 0.4093859 0.4294972 0.4432495 0.4597647 0.4821997 0.5035192 0.5092215
##  [726,] 0.4089806 0.4309082 0.4466394 0.4566028 0.4806323 0.4965852 0.5180540
##  [727,] 0.4122922 0.4214238 0.4452303 0.4614607 0.4682191 0.5022298 0.5138009
##  [728,] 0.4083895 0.4247348 0.4414259 0.4597886 0.4827412 0.5017235 0.5113044
##  [729,] 0.4094861 0.4301743 0.4463325 0.4681536 0.4788589 0.4940038 0.5216205
##  [730,] 0.4125106 0.4329424 0.4445232 0.4634673 0.4734044 0.4947196 0.5054650
##  [731,] 0.4100606 0.4257214 0.4385745 0.4577968 0.4747397 0.4900585 0.5026548
##  [732,] 0.4089048 0.4289737 0.4445137 0.4676219 0.4699678 0.4886282 0.5037664
##  [733,] 0.4098547 0.4330250 0.4476164 0.4523975 0.4820510 0.4947756 0.5041856
##  [734,] 0.4147797 0.4288216 0.4460703 0.4563480 0.4878221 0.4927743 0.5248782
##  [735,] 0.4144144 0.4239397 0.4429061 0.4536436 0.4858790 0.5061414 0.5164698
##  [736,] 0.4103821 0.4309629 0.4415658 0.4688682 0.4799877 0.4987411 0.5051302
##  [737,] 0.4098681 0.4263316 0.4454287 0.4691542 0.4860759 0.4937844 0.5124336
##  [738,] 0.4152112 0.4275479 0.4483073 0.4590020 0.4812483 0.4986516 0.5187827
##  [739,] 0.4100784 0.4279396 0.4420003 0.4643736 0.4748023 0.4999429 0.5213420
##  [740,] 0.4090003 0.4266822 0.4453363 0.4661873 0.4748229 0.4834603 0.5101653
##  [741,] 0.4092360 0.4245748 0.4457219 0.4602087 0.4806632 0.5020197 0.4992611
##  [742,] 0.4147698 0.4295653 0.4436161 0.4545782 0.4899392 0.4977727 0.5094293
##  [743,] 0.4083184 0.4247921 0.4425344 0.4736357 0.4820024 0.4930075 0.5223655
##  [744,] 0.4067945 0.4238207 0.4450858 0.4612306 0.4790216 0.4886436 0.5173183
##  [745,] 0.4102605 0.4326116 0.4444458 0.4669159 0.4653083 0.4925673 0.5158410
##  [746,] 0.4099821 0.4261196 0.4440494 0.4639248 0.4910895 0.5058497 0.5232208
##  [747,] 0.4130102 0.4271902 0.4397039 0.4622447 0.4755310 0.4929472 0.5006890
##  [748,] 0.4145211 0.4266790 0.4464687 0.4697006 0.4684421 0.5083724 0.5163606
##  [749,] 0.4114618 0.4331203 0.4453245 0.4602947 0.4808602 0.4944813 0.5072433
##  [750,] 0.4079596 0.4283218 0.4421421 0.4558075 0.4801230 0.4986013 0.5125241
##  [751,] 0.4115149 0.4273892 0.4406337 0.4636118 0.4772185 0.4898714 0.5134770
##  [752,] 0.4158775 0.4297364 0.4460790 0.4613981 0.4931861 0.4894044 0.5176625
##  [753,] 0.4063937 0.4249194 0.4462857 0.4683696 0.4751311 0.5033814 0.5097318
##  [754,] 0.4132690 0.4287713 0.4469306 0.4600429 0.4750219 0.4920104 0.5281200
##  [755,] 0.4067641 0.4260526 0.4415243 0.4554370 0.4786133 0.4996351 0.5053764
##  [756,] 0.4041224 0.4280094 0.4443591 0.4596744 0.4793048 0.4857514 0.5178926
##  [757,] 0.4051349 0.4251258 0.4373209 0.4561806 0.4755162 0.5002495 0.5212546
##  [758,] 0.4104362 0.4277478 0.4416647 0.4644153 0.4849138 0.4977276 0.5301252
##  [759,] 0.4084609 0.4272523 0.4447626 0.4668782 0.4700831 0.5050008 0.5178068
##  [760,] 0.4103669 0.4302134 0.4429057 0.4666469 0.4777842 0.4909931 0.4992938
##  [761,] 0.4101969 0.4269449 0.4484198 0.4636878 0.4742172 0.4939438 0.5173939
##  [762,] 0.4123901 0.4311234 0.4437405 0.4631812 0.4799744 0.5028832 0.5148622
##  [763,] 0.4097950 0.4272465 0.4466910 0.4568248 0.4627869 0.5013980 0.5170269
##  [764,] 0.4057794 0.4231033 0.4503835 0.4667848 0.4872475 0.4994807 0.5187079
##  [765,] 0.4095946 0.4301764 0.4422354 0.4607224 0.4709745 0.5061618 0.5251731
##  [766,] 0.4122980 0.4276891 0.4491874 0.4635454 0.4786365 0.4918263 0.5132561
##  [767,] 0.4084289 0.4284222 0.4358012 0.4594744 0.4826664 0.4948481 0.5141525
##  [768,] 0.4092133 0.4306555 0.4448112 0.4624370 0.4760654 0.4918245 0.5099309
##  [769,] 0.4111015 0.4329354 0.4483553 0.4574622 0.4858071 0.4967616 0.5207527
##  [770,] 0.4096562 0.4309221 0.4490118 0.4563983 0.4764769 0.5036827 0.5106501
##  [771,] 0.4096667 0.4321884 0.4429429 0.4633217 0.4628857 0.4929593 0.5171032
##  [772,] 0.4141196 0.4269374 0.4456066 0.4537872 0.4835190 0.4916890 0.5126907
##  [773,] 0.4092303 0.4299442 0.4439432 0.4687077 0.4738937 0.5017585 0.5047975
##  [774,] 0.4098037 0.4299308 0.4439358 0.4593115 0.4766636 0.4803142 0.5344048
##  [775,] 0.4098947 0.4289337 0.4488033 0.4623389 0.4766442 0.4920392 0.5084371
##  [776,] 0.4125445 0.4278764 0.4414252 0.4630752 0.4841731 0.4974269 0.5101255
##  [777,] 0.4142787 0.4265939 0.4472785 0.4591382 0.4801677 0.4893885 0.5185045
##  [778,] 0.4126332 0.4258029 0.4453868 0.4670189 0.4778859 0.5034410 0.5111450
##  [779,] 0.4111466 0.4268608 0.4399512 0.4587285 0.4774498 0.4915781 0.5121388
##  [780,] 0.4127431 0.4312331 0.4448545 0.4513400 0.4806694 0.4916043 0.5354466
##  [781,] 0.4118250 0.4265897 0.4403458 0.4631112 0.4793613 0.4907927 0.5160935
##  [782,] 0.4115225 0.4297289 0.4462801 0.4538697 0.4726746 0.4969636 0.5174864
##  [783,] 0.4102525 0.4260209 0.4443893 0.4704218 0.4764803 0.4889051 0.5117212
##  [784,] 0.4082120 0.4243229 0.4450487 0.4620153 0.4815302 0.4918463 0.5025453
##  [785,] 0.4144828 0.4260233 0.4506866 0.4583697 0.4813786 0.4955028 0.5174599
##  [786,] 0.4088951 0.4265306 0.4438516 0.4611829 0.4802002 0.4915321 0.5201362
##  [787,] 0.4103089 0.4233596 0.4404550 0.4698267 0.4812439 0.4999317 0.5117625
##  [788,] 0.4061603 0.4290020 0.4452030 0.4682111 0.4822938 0.5018499 0.5276712
##  [789,] 0.4112595 0.4268931 0.4372309 0.4614316 0.4786680 0.4923672 0.5032509
##  [790,] 0.4107453 0.4278550 0.4491154 0.4635098 0.4737595 0.4971683 0.4984549
##  [791,] 0.4110529 0.4269471 0.4414300 0.4642693 0.4859300 0.5093279 0.5108349
##  [792,] 0.4092956 0.4278571 0.4451298 0.4726797 0.4748871 0.4914698 0.5132976
##  [793,] 0.4083801 0.4254245 0.4401209 0.4640260 0.4755137 0.5023240 0.5029850
##  [794,] 0.4089990 0.4273728 0.4439737 0.4592197 0.4881341 0.4878996 0.5151622
##  [795,] 0.4135321 0.4324541 0.4433108 0.4627991 0.4790025 0.4953215 0.5296012
##  [796,] 0.4130583 0.4243835 0.4409286 0.4578773 0.4868339 0.4956578 0.5198520
##  [797,] 0.4059067 0.4227198 0.4468918 0.4633722 0.4738943 0.5008918 0.5151755
##  [798,] 0.4122326 0.4301252 0.4407835 0.4692088 0.4817416 0.5128365 0.5070119
##  [799,] 0.4106426 0.4284133 0.4421932 0.4619704 0.4802780 0.4991639 0.5078985
##  [800,] 0.4078430 0.4322957 0.4390202 0.4530538 0.4797107 0.4906735 0.5054101
##  [801,] 0.4113009 0.4278204 0.4397676 0.4635996 0.4888955 0.4876993 0.5105760
##  [802,] 0.4163219 0.4273471 0.4428960 0.4594339 0.4880726 0.4902140 0.5017195
##  [803,] 0.4114547 0.4282369 0.4434905 0.4583489 0.4828185 0.4998260 0.5230511
##  [804,] 0.4121485 0.4277254 0.4457839 0.4618552 0.4815434 0.4987423 0.5212605
##  [805,] 0.4088988 0.4290706 0.4472149 0.4601439 0.4885305 0.4944094 0.5168998
##  [806,] 0.4091479 0.4277058 0.4432940 0.4594477 0.4715396 0.5017344 0.5165493
##  [807,] 0.4128923 0.4277869 0.4388162 0.4681804 0.4819827 0.5003627 0.5033226
##  [808,] 0.4113584 0.4247934 0.4454329 0.4536172 0.4732505 0.4968409 0.5123623
##  [809,] 0.4118147 0.4272423 0.4410493 0.4597742 0.4824010 0.4740105 0.5065228
##  [810,] 0.4080437 0.4310875 0.4466265 0.4639999 0.4782485 0.4993753 0.5000495
##  [811,] 0.4108601 0.4270135 0.4450990 0.4612345 0.4820579 0.4916064 0.5189318
##  [812,] 0.4083119 0.4281396 0.4450359 0.4659117 0.4726697 0.4954830 0.5165370
##  [813,] 0.4098629 0.4262882 0.4520638 0.4601084 0.4872276 0.4887777 0.5049488
##  [814,] 0.4098245 0.4258748 0.4428316 0.4627257 0.4764849 0.5007076 0.5295310
##  [815,] 0.4104615 0.4232757 0.4498568 0.4633997 0.4832616 0.4885171 0.5216002
##  [816,] 0.4072993 0.4280971 0.4477479 0.4565453 0.4784351 0.4881197 0.5048698
##  [817,] 0.4116273 0.4308886 0.4470530 0.4683676 0.4787951 0.5072982 0.5060239
##  [818,] 0.4122758 0.4325209 0.4392075 0.4680090 0.4736663 0.5036682 0.5139159
##  [819,] 0.4111631 0.4350081 0.4437956 0.4658811 0.4808456 0.5006652 0.5043687
##  [820,] 0.4081498 0.4260561 0.4454346 0.4720420 0.4833093 0.4900466 0.5268817
##  [821,] 0.4107616 0.4337214 0.4444129 0.4655255 0.4713084 0.4914355 0.5104331
##  [822,] 0.4101478 0.4302911 0.4440855 0.4596169 0.4846777 0.5016229 0.5199220
##  [823,] 0.4121340 0.4265981 0.4522593 0.4573992 0.4717552 0.4936454 0.4986166
##  [824,] 0.4047247 0.4254686 0.4466697 0.4549591 0.4794273 0.4971953 0.5158305
##  [825,] 0.4132359 0.4253786 0.4453468 0.4647966 0.4786470 0.4925585 0.5114168
##  [826,] 0.4095765 0.4253878 0.4421732 0.4614209 0.4719413 0.5042955 0.5223696
##  [827,] 0.4078941 0.4315131 0.4467532 0.4584234 0.4777599 0.5026962 0.5234865
##  [828,] 0.4100386 0.4289778 0.4416549 0.4571072 0.4834700 0.5060520 0.5144065
##  [829,] 0.4050294 0.4283943 0.4403403 0.4672891 0.4711780 0.4992755 0.5160980
##  [830,] 0.4092884 0.4284019 0.4514994 0.4613252 0.4792215 0.5045564 0.5120124
##  [831,] 0.4159133 0.4317448 0.4472145 0.4635095 0.4794069 0.4929853 0.5292645
##  [832,] 0.4118730 0.4255412 0.4485588 0.4649238 0.4818168 0.5011867 0.5225249
##  [833,] 0.4111125 0.4267056 0.4460027 0.4695579 0.4841966 0.4932502 0.5019261
##  [834,] 0.4112113 0.4221161 0.4485712 0.4661587 0.4753728 0.5027896 0.5147814
##  [835,] 0.4104769 0.4253494 0.4496866 0.4640329 0.4748799 0.4965189 0.5013302
##  [836,] 0.4099537 0.4310137 0.4399493 0.4594294 0.4788134 0.4994885 0.5089176
##  [837,] 0.4084518 0.4257868 0.4465480 0.4603314 0.4902819 0.4887163 0.5022707
##  [838,] 0.4103067 0.4262867 0.4458345 0.4666425 0.4905391 0.4910164 0.5153852
##  [839,] 0.4074400 0.4285889 0.4495757 0.4642268 0.4845619 0.4935211 0.5144720
##  [840,] 0.4108352 0.4282003 0.4489161 0.4595883 0.4911058 0.4988233 0.5141692
##  [841,] 0.4099446 0.4253600 0.4442585 0.4617365 0.4822908 0.4909668 0.5172509
##  [842,] 0.4079418 0.4278660 0.4447917 0.4589301 0.4840024 0.5052236 0.5112770
##  [843,] 0.4121019 0.4306171 0.4438092 0.4615495 0.4761850 0.4911374 0.4992766
##  [844,] 0.4120495 0.4276018 0.4450703 0.4590472 0.4796908 0.4946941 0.5092948
##  [845,] 0.4132506 0.4291007 0.4467399 0.4602729 0.4894858 0.4956315 0.5224897
##  [846,] 0.4069548 0.4274526 0.4453024 0.4618992 0.4771128 0.5024297 0.5086749
##  [847,] 0.4107139 0.4311565 0.4411813 0.4583000 0.4819358 0.4934298 0.5226209
##  [848,] 0.4125302 0.4231601 0.4463879 0.4611823 0.4791908 0.5015663 0.5239638
##  [849,] 0.4115369 0.4254149 0.4423133 0.4657014 0.4745137 0.5013893 0.5125520
##  [850,] 0.4120135 0.4275070 0.4426720 0.4624624 0.4796486 0.4945862 0.5023585
##  [851,] 0.4074602 0.4251566 0.4498670 0.4560088 0.4849146 0.4887541 0.5216890
##  [852,] 0.4129344 0.4296331 0.4487606 0.4576155 0.4838826 0.4931733 0.5228881
##  [853,] 0.4101884 0.4287254 0.4407768 0.4575120 0.4853554 0.4928387 0.5199986
##  [854,] 0.4143730 0.4247827 0.4456209 0.4626896 0.4814448 0.4949461 0.5332869
##  [855,] 0.4077518 0.4303317 0.4446636 0.4634323 0.4742309 0.4859459 0.5126689
##  [856,] 0.4099552 0.4277459 0.4435480 0.4651420 0.4837932 0.4991681 0.5108273
##  [857,] 0.4123296 0.4288008 0.4494528 0.4580893 0.4795956 0.5072086 0.5033270
##  [858,] 0.4121455 0.4292983 0.4418329 0.4579604 0.4846303 0.4924093 0.5158054
##  [859,] 0.4143715 0.4293408 0.4439020 0.4678660 0.4828259 0.5080249 0.5115936
##  [860,] 0.4089195 0.4320791 0.4477897 0.4592261 0.4791262 0.5009551 0.5055217
##  [861,] 0.4065585 0.4269800 0.4431463 0.4630158 0.4719077 0.4908602 0.5205769
##  [862,] 0.4077372 0.4283546 0.4473584 0.4645504 0.4772857 0.5013297 0.5148925
##  [863,] 0.4059884 0.4307469 0.4417467 0.4579002 0.4798798 0.5015546 0.5140451
##  [864,] 0.4092339 0.4342588 0.4425397 0.4684366 0.4784378 0.4978006 0.5214241
##  [865,] 0.4098568 0.4275571 0.4450469 0.4618108 0.4806349 0.5024485 0.5123964
##  [866,] 0.4090346 0.4223712 0.4406099 0.4607804 0.4802452 0.5009632 0.5173250
##  [867,] 0.4076716 0.4263947 0.4440917 0.4568528 0.4796586 0.5001712 0.5079290
##  [868,] 0.4134486 0.4254007 0.4444376 0.4553697 0.4782088 0.5023494 0.5091559
##  [869,] 0.4118522 0.4253684 0.4433918 0.4747311 0.4757825 0.5015045 0.5126848
##  [870,] 0.4094889 0.4237240 0.4384329 0.4607944 0.4779614 0.4866874 0.5040993
##  [871,] 0.4114022 0.4302405 0.4422670 0.4663077 0.4805506 0.4938753 0.5187131
##  [872,] 0.4116696 0.4263742 0.4433666 0.4568294 0.4842539 0.4876961 0.5061455
##  [873,] 0.4073586 0.4265720 0.4436029 0.4675780 0.4811799 0.4925420 0.5067192
##  [874,] 0.4101691 0.4326267 0.4452261 0.4632357 0.4761980 0.4912326 0.5193783
##  [875,] 0.4137243 0.4265015 0.4451524 0.4549914 0.4729177 0.4941398 0.5061731
##  [876,] 0.4149128 0.4277365 0.4455561 0.4661438 0.4846498 0.5036984 0.5172428
##  [877,] 0.4112921 0.4306414 0.4480284 0.4600272 0.4807610 0.4952906 0.5140278
##  [878,] 0.4112616 0.4252431 0.4489993 0.4613579 0.4819810 0.4863537 0.5096862
##  [879,] 0.4137279 0.4234328 0.4415054 0.4638327 0.4894062 0.4854312 0.5232330
##  [880,] 0.4090737 0.4274777 0.4422870 0.4569486 0.4839302 0.5021231 0.4982434
##  [881,] 0.4095533 0.4288472 0.4434624 0.4623682 0.4775689 0.4942872 0.5101753
##  [882,] 0.4131986 0.4288330 0.4465359 0.4591971 0.4849302 0.4928673 0.5364180
##  [883,] 0.4064097 0.4295931 0.4474208 0.4619768 0.4919772 0.4889330 0.5079547
##  [884,] 0.4105670 0.4308300 0.4490130 0.4676876 0.4744349 0.5012442 0.5178689
##  [885,] 0.4080952 0.4234814 0.4472818 0.4608858 0.4794020 0.5047462 0.5122517
##  [886,] 0.4078431 0.4258955 0.4529162 0.4664960 0.4787676 0.4864943 0.5181902
##  [887,] 0.4082730 0.4312263 0.4442513 0.4586539 0.4688614 0.5047934 0.5151593
##  [888,] 0.4114110 0.4306476 0.4462744 0.4671744 0.4667118 0.4995800 0.5179113
##  [889,] 0.4123351 0.4275545 0.4485888 0.4686194 0.4860595 0.4911305 0.5127060
##  [890,] 0.4044331 0.4273375 0.4445489 0.4606955 0.4784377 0.4938640 0.5152951
##  [891,] 0.4129075 0.4267797 0.4420483 0.4596212 0.4765412 0.4952079 0.5169099
##  [892,] 0.4106662 0.4237547 0.4462006 0.4622165 0.4790309 0.4885772 0.5066399
##  [893,] 0.4103439 0.4292305 0.4500863 0.4657511 0.4785071 0.4876164 0.4984370
##  [894,] 0.4089878 0.4273333 0.4494714 0.4570759 0.4791611 0.4905469 0.5082145
##  [895,] 0.4125704 0.4270352 0.4448837 0.4609172 0.4798091 0.5005040 0.5067135
##  [896,] 0.4079246 0.4288301 0.4449922 0.4609536 0.4822450 0.5004992 0.5262979
##  [897,] 0.4103199 0.4276714 0.4430609 0.4588954 0.4848342 0.4836077 0.5064562
##  [898,] 0.4094214 0.4279680 0.4435571 0.4737888 0.4723071 0.4954184 0.5254696
##  [899,] 0.4079035 0.4277413 0.4476270 0.4595902 0.4866790 0.4971235 0.5161945
##  [900,] 0.4114269 0.4271954 0.4480044 0.4560950 0.4732282 0.5011833 0.5158699
##  [901,] 0.4114399 0.4281953 0.4424660 0.4574633 0.4769148 0.5035170 0.5017866
##  [902,] 0.4077653 0.4269798 0.4457050 0.4643948 0.4780039 0.4927288 0.5034467
##  [903,] 0.4069353 0.4294157 0.4475027 0.4629583 0.4749972 0.5057492 0.5238593
##  [904,] 0.4107894 0.4235150 0.4467963 0.4590527 0.4809973 0.4994515 0.5124541
##  [905,] 0.4103257 0.4258284 0.4435950 0.4659210 0.4970269 0.4975067 0.5017852
##  [906,] 0.4148782 0.4257151 0.4433376 0.4596193 0.4814895 0.5118485 0.5200664
##  [907,] 0.4095549 0.4297407 0.4495348 0.4631485 0.4868398 0.4973834 0.5163277
##  [908,] 0.4113171 0.4284846 0.4463198 0.4602822 0.4895799 0.4962650 0.5161935
##  [909,] 0.4107861 0.4262146 0.4358152 0.4646723 0.4775385 0.5068746 0.5257269
##  [910,] 0.4055903 0.4320792 0.4417576 0.4620342 0.4806626 0.5039641 0.5236597
##  [911,] 0.4110336 0.4240496 0.4481088 0.4586645 0.4800315 0.4943339 0.5075779
##  [912,] 0.4085854 0.4267842 0.4482609 0.4649291 0.4723925 0.4951482 0.5226113
##  [913,] 0.4128662 0.4330404 0.4377433 0.4651201 0.4855108 0.4863632 0.4997571
##  [914,] 0.4082072 0.4290288 0.4425826 0.4645636 0.4819159 0.4933528 0.5056833
##  [915,] 0.4142913 0.4270754 0.4441455 0.4610853 0.4770838 0.4986106 0.5073722
##  [916,] 0.4106903 0.4274701 0.4405518 0.4575248 0.4803967 0.4964298 0.5123847
##  [917,] 0.4095810 0.4317114 0.4426225 0.4614196 0.4870544 0.4830411 0.5200028
##  [918,] 0.4094087 0.4279510 0.4481471 0.4592512 0.4819367 0.4928906 0.5147254
##  [919,] 0.4101959 0.4254477 0.4421555 0.4570837 0.4708660 0.5042118 0.5178447
##  [920,] 0.4116117 0.4281806 0.4463467 0.4583443 0.4809859 0.5093568 0.5130339
##  [921,] 0.4085985 0.4242050 0.4435160 0.4670922 0.4707360 0.4982468 0.5309646
##  [922,] 0.4102429 0.4253974 0.4394291 0.4563307 0.4877525 0.4871694 0.5222222
##  [923,] 0.4143734 0.4277053 0.4507633 0.4739099 0.4691225 0.5014480 0.5046691
##  [924,] 0.4127643 0.4240538 0.4453146 0.4614351 0.4750893 0.4947139 0.5209633
##  [925,] 0.4098651 0.4276254 0.4366903 0.4615290 0.4877604 0.4983160 0.5174451
##  [926,] 0.4094374 0.4266337 0.4418544 0.4605957 0.4801591 0.4910586 0.5121898
##  [927,] 0.4132641 0.4253117 0.4426707 0.4536864 0.4787145 0.4948104 0.5025504
##  [928,] 0.4110214 0.4301845 0.4435920 0.4502661 0.4861393 0.4985978 0.5038251
##  [929,] 0.4098518 0.4295840 0.4482374 0.4631897 0.4824221 0.4884539 0.5082338
##  [930,] 0.4136296 0.4330747 0.4446514 0.4648361 0.4939681 0.5022300 0.5185876
##  [931,] 0.4129799 0.4326409 0.4462190 0.4558202 0.4827677 0.4836848 0.5122674
##  [932,] 0.4147997 0.4279693 0.4478474 0.4588921 0.4812155 0.4953796 0.5060023
##  [933,] 0.4109818 0.4263068 0.4462783 0.4626971 0.4885679 0.5013280 0.5226943
##  [934,] 0.4078432 0.4278880 0.4442889 0.4599172 0.4793754 0.4937724 0.5157037
##  [935,] 0.4149727 0.4238927 0.4496411 0.4728989 0.4850762 0.4788575 0.5252368
##  [936,] 0.4121246 0.4297881 0.4395174 0.4605950 0.4733933 0.4930442 0.5221089
##  [937,] 0.4078412 0.4279064 0.4423797 0.4562905 0.4796768 0.4907483 0.5085858
##  [938,] 0.4122200 0.4233756 0.4449898 0.4633894 0.4832427 0.4952124 0.4897122
##  [939,] 0.4120285 0.4288689 0.4376083 0.4579454 0.4815370 0.4973537 0.5209916
##  [940,] 0.4100387 0.4329875 0.4462850 0.4588531 0.4762146 0.4986183 0.4958663
##  [941,] 0.4078991 0.4280780 0.4475175 0.4655802 0.4769223 0.5072642 0.5115775
##  [942,] 0.4134723 0.4278509 0.4473178 0.4592966 0.4850352 0.4974941 0.5194715
##  [943,] 0.4136316 0.4264587 0.4439354 0.4570702 0.4766386 0.4909472 0.5019215
##  [944,] 0.4117127 0.4283756 0.4437896 0.4626779 0.4804548 0.5081320 0.5192044
##  [945,] 0.4135529 0.4290088 0.4432886 0.4617213 0.4797586 0.4914834 0.5136397
##  [946,] 0.4103680 0.4272711 0.4477198 0.4674103 0.4740730 0.4954431 0.5207830
##  [947,] 0.4051818 0.4296860 0.4401660 0.4668077 0.4869661 0.4971224 0.5155116
##  [948,] 0.4111607 0.4306965 0.4544044 0.4607807 0.4762295 0.5033903 0.5137767
##  [949,] 0.4128298 0.4278588 0.4457763 0.4616921 0.4843775 0.5003531 0.5042460
##  [950,] 0.4089724 0.4278683 0.4403340 0.4647186 0.4785738 0.4914011 0.5065482
##  [951,] 0.4115270 0.4227643 0.4505445 0.4681851 0.4747298 0.4893669 0.5183398
##  [952,] 0.4117438 0.4275607 0.4461548 0.4692766 0.4806541 0.4937303 0.5237251
##  [953,] 0.4103300 0.4285878 0.4437502 0.4611389 0.4741118 0.4983554 0.5188649
##  [954,] 0.4093751 0.4266774 0.4465934 0.4585283 0.4742922 0.4958354 0.5166669
##  [955,] 0.4099158 0.4340270 0.4514438 0.4596002 0.4850000 0.5058074 0.5181894
##  [956,] 0.4072780 0.4285171 0.4412418 0.4606025 0.4865538 0.5011267 0.5017541
##  [957,] 0.4109345 0.4314324 0.4461614 0.4614460 0.4761773 0.5036643 0.5098724
##  [958,] 0.4082537 0.4283293 0.4450845 0.4590539 0.4803230 0.5017723 0.5123530
##  [959,] 0.4082500 0.4255173 0.4442194 0.4687429 0.4701427 0.5030129 0.4973081
##  [960,] 0.4087938 0.4285486 0.4442084 0.4595056 0.4800762 0.4903266 0.5071669
##  [961,] 0.4119937 0.4320417 0.4448510 0.4700469 0.4778438 0.5006339 0.5015936
##  [962,] 0.4120356 0.4264210 0.4451168 0.4662196 0.4753824 0.4939124 0.5242682
##  [963,] 0.4109622 0.4257577 0.4541206 0.4695164 0.4897147 0.4948600 0.5185236
##  [964,] 0.4122458 0.4296376 0.4463103 0.4608950 0.4776918 0.4916037 0.5188421
##  [965,] 0.4123451 0.4330413 0.4482923 0.4670295 0.4793400 0.4963355 0.5051406
##  [966,] 0.4124521 0.4252034 0.4461560 0.4601381 0.4752947 0.4930046 0.5236027
##  [967,] 0.4113944 0.4266980 0.4438161 0.4623072 0.4881704 0.5034811 0.5141575
##  [968,] 0.4077220 0.4281152 0.4464492 0.4626612 0.4873051 0.4939226 0.5114011
##  [969,] 0.4081913 0.4306571 0.4401322 0.4641430 0.4782500 0.4901285 0.4976371
##  [970,] 0.4116792 0.4244619 0.4470599 0.4531416 0.4736962 0.4958524 0.5109104
##  [971,] 0.4116435 0.4311973 0.4530937 0.4636516 0.4791319 0.4955603 0.5195255
##  [972,] 0.4127246 0.4252370 0.4450028 0.4625030 0.4861147 0.4921296 0.5136915
##  [973,] 0.4110431 0.4290583 0.4484866 0.4684887 0.4781063 0.4847527 0.5011540
##  [974,] 0.4096293 0.4325920 0.4432864 0.4545675 0.4847427 0.4901897 0.5155784
##  [975,] 0.4101239 0.4257620 0.4466618 0.4647686 0.4754047 0.4987008 0.5037940
##  [976,] 0.4109841 0.4302868 0.4430201 0.4635311 0.4796680 0.5006276 0.5159201
##  [977,] 0.4137877 0.4226961 0.4450052 0.4654538 0.4758426 0.4938512 0.5153709
##  [978,] 0.4124853 0.4279148 0.4418572 0.4647394 0.4899229 0.5095665 0.5100064
##  [979,] 0.4130311 0.4253064 0.4480521 0.4670875 0.4873698 0.4998055 0.5079721
##  [980,] 0.4145579 0.4308720 0.4435890 0.4585323 0.4705463 0.5089716 0.5177195
##  [981,] 0.4102888 0.4255564 0.4442993 0.4527704 0.4849675 0.4924146 0.5068886
##  [982,] 0.4148799 0.4259847 0.4432924 0.4644327 0.4799269 0.5061242 0.5121592
##  [983,] 0.4088496 0.4299562 0.4479196 0.4688551 0.4668818 0.4947029 0.5233528
##  [984,] 0.4120047 0.4293526 0.4435828 0.4660620 0.4795180 0.5027417 0.5295599
##  [985,] 0.4107922 0.4301996 0.4444934 0.4658160 0.4774682 0.4978216 0.5169944
##  [986,] 0.4158611 0.4309833 0.4469599 0.4531207 0.4772771 0.4875190 0.5227713
##  [987,] 0.4108936 0.4263526 0.4448144 0.4629353 0.4706812 0.4910760 0.5166631
##  [988,] 0.4098458 0.4267531 0.4402344 0.4707551 0.4846232 0.4998562 0.5219312
##  [989,] 0.4093409 0.4238782 0.4447749 0.4638416 0.4761456 0.5047128 0.5155209
##  [990,] 0.4112036 0.4269708 0.4444455 0.4662585 0.4810956 0.4958212 0.5173623
##  [991,] 0.4113326 0.4322198 0.4498456 0.4637672 0.4833416 0.4992057 0.5074405
##  [992,] 0.4075071 0.4320249 0.4445704 0.4659707 0.4901141 0.4849180 0.5170234
##  [993,] 0.4087634 0.4266662 0.4446142 0.4625172 0.4790351 0.5145073 0.5177015
##  [994,] 0.4041552 0.4337101 0.4457213 0.4614756 0.4865176 0.4834693 0.5107510
##  [995,] 0.4074445 0.4320425 0.4397528 0.4688495 0.4827922 0.4934213 0.4990473
##  [996,] 0.4093011 0.4296153 0.4408415 0.4625039 0.4778784 0.4830433 0.5203711
##  [997,] 0.4084353 0.4331801 0.4452885 0.4636749 0.4761189 0.5053793 0.5104424
##  [998,] 0.4128289 0.4221402 0.4353626 0.4537876 0.4868415 0.4880409 0.4996605
##  [999,] 0.4097301 0.4296348 0.4471661 0.4664240 0.4838295 0.4886998 0.5093255
## [1000,] 0.4117724 0.4278614 0.4423597 0.4622552 0.4761630 0.5014238 0.5242684

lr.exp.confint <- apply(lr.storage, 2, quantile, probs = c(0.025, 0.5, 0.975)) %>% rbind(c(3:16)) %>% t %>% as.data.frame
colnames(lr.exp.confint) = c("lower_bound", "average", "upper_bound", "educ")
lr.exp.confint

ggplot(data = lr.exp.confint) + geom_point(mapping = aes(x=educ, y=average), size = 0.7) + 
  geom_errorbar(mapping = aes(x=educ, ymin = lower_bound, ymax = upper_bound), color="dark gray", width = 0.5) + 
  labs(x = "Years of education", y ="Probability of treatment") + ggtitle("Expected probability of treatment based on years of education") 

#### STEP 4

Then, do the same thing, but this time for the predicted values of the probability of receiving treatment as education varies from 3 to 16. Be sure to include axes labels and figure titles.

# YOUR CODE HERE
storage.matrix2 <- matrix(NA, nrow = 1000, ncol = 14)
lr_object <- sim(lr01, n.sims = 1000)
lr_coefs <- coef(lr_object)

for (education in 3:16){
  for (simulation in 1:1000){
      avg_person <- c(1, mean(lalonde$age), education, mean(lalonde$hisp), mean(lalonde$re74), mean(lalonde$re75))
      storage.matrix2[simulation, education-2] <- exp(sum(lr_coefs[simulation,]*avg_person))/(1 + exp(sum(lr_coefs[simulation,]*avg_person)))
    }
}

lr.pred.confint <- apply(storage.matrix2, 2, quantile, probs = c(0.025, 0.5, 0.975)) %>% rbind(c(3:16)) %>% t %>% as.data.frame

colnames(lr.pred.confint) = c("lower_bound", "average", "upper_bound", "educ")


ggplot(data = lr.pred.confint) + geom_point(mapping = aes(x=educ, y=average), size = 0.7) + 
  geom_errorbar(mapping = aes(x=educ, ymin = lower_bound, ymax = upper_bound), color="dark gray", width = 0.5) + 
  labs(x = "Years of education", y ="Predicted income in 1978") + ggtitle("Effect of education on predicted income in 1978") 

STEP 5

Lastly, write a short paragraph with your reflections on this exercise and the results you obtained.

QUESTION 5

Write the executive summary for a decision brief about the impact of a stress therapy program, targeted at individuals age 18-42, intended to reduce average monthly stress. The program was tested via RCT, and the results are summarized by the figure that you get if you run this code chunk:

# Note that if you knit this document, this part of the code won't 
# show up in the final pdf which is OK. We don't need to see the code
# we wrote.

# How effective is a therapy method against stress

# Participants in the study record their stress level for a month.
# Every day, participants assign a value from 1 to 10 for their stress level. 
# At the end of the month, we average the results for each participant.

#adds the confidence interval (first row of the matrix is lower 
# bound, second row is the upper bound)
trt1 = matrix(NA,nrow=2,ncol=7)
ctrl = matrix(NA,nrow=2,ncol=7) 

trt1[,1]=c(3.7, 6.5) #18  
ctrl[,1]=c(5, 8)

trt1[,2]=c(5, 8.5) #22
ctrl[,2]=c(7.5, 9)

trt1[,3]=c(6, 9) #26
ctrl[,3]=c(8.5, 10)

trt1[,4]=c(5, 7) #30
ctrl[,4]=c(6, 8)

trt1[,5]=c(3.5, 5) #34
ctrl[,5]=c(4.5, 7)

trt1[,6]=c(2, 3.5) #38
ctrl[,6]=c(3.5, 6)

trt1[,7]=c(0.5, 2) #42
ctrl[,7]=c(2.5, 5)

# colors to each group
c1 = rgb(red = 0.3, green = 0, blue = 1, alpha = 0.7) #trt1
c2 = rgb(red = 1, green = 0.6, blue = 0, alpha = 1) #trt2
c3 = rgb(red = 0, green = 0.5, blue = 0, alpha = 0.7) #ctrl

# creates the background of the graph
plot(x = c(1:100), y = c(1:100), 
     type = "n", 
     xlim = c(17,43), 
     ylim = c(0,11), 
     cex.lab=1,
     main = "Stress Level - 95% Prediction Intervals", 
     xlab = "Age", 
     ylab = "Average Stress Level per Month", 
     xaxt = "n")

axis(1, at=seq(18,42,by=4), seq(18, 42, by=4))

grid(nx = NA, ny = NULL, col = "lightgray", lty = "dotted",
     lwd=par("lwd"), equilogs = TRUE)

# adds the legend
legend('topright',legend=c('Treatment','Control'),fill=c(c1,c2))

# iterates to add stuff to plot
for (age in seq(from=18,to=42,by=4)) { 
  #treatment
  segments(x0=age-0.2, y0=trt1[1, (age-18)/4+1],
           x1=age-0.2, y1=trt1[2, (age-18)/4+1], lwd=4, col=c1)
  
  #control
  segments(x0=age+0.2, y0=ctrl[1, (age-18)/4+1],
           x1=age+0.2, y1=ctrl[2, (age-18)/4+1], lwd=4, col=c2)
}

(Not that it matters, really, but you can imagine that these results were obtained via simulation, just like the results you have hopefully obtained for question 2 above).

Your executive summary should be between about 4 and 10 sentences long, it should briefly describe the the purpose of the study, the methodology, and the policy implications/prescription. (Feel free to imaginatively but realistically embellish/fill-in-the-blanks with respect to any of the above, since I am not giving you backstory here).

Write your executive summary here.

QUESTION 6

Can we predict what projects end up being successful on Kickstarter?

We have data from the Kickstarter company.

From Wikipedia: Kickstarter is an American public-benefit corporation based in Brooklyn, New York, that maintains a global crowdfunding platform focused on creativity and merchandising. The company’s stated mission is to “help bring creative projects to life”. As of May 2019, Kickstarter has received more than $4 billion in pledges from 16.3 million backers to fund 445,000 projects, such as films, music, stage shows, comics, journalism, video games, technology, publishing, and food-related projects.

The data is collected by Mickaël Mouillé and is last updated in 2018. Columns are self explanatory. Note that usd_pledged is the column pledged in US dollars (conversion done by kickstarter) and usd_pledge_real is the pledged column in real US dollars of the pledged column. Finally, usd_goal_real is the column goal in real US dollars. You should use the real columns.

So what makes a project successful? Undoubtedly, there are many factors, but perhaps we could set up a prediction problem here, similar to the one from the bonus part of the last assignment where we used GDP to predict personnel contributions.

We have columns representing the the number of backers, project length, the main category, and the real project goal in USD for each project.

Let’s explore the relationship between those predictors and the dependent variable of interest — the success of a project.

Instead of running a simple linear regression and calling it a day, let’s use cross-validation to make our prediction a little more sophisticated.

Our general plan is the following:

1. Build the model on a training data set
2. Apply the model on a new test data set to make predictions based on the inferred model parameters.
3. Compute and track the prediction errors to check performance using the mean squared difference between the observed and the predicted outcome values in the test set.

Let’s get to it, step, by step. Make sure you have loaded the necessary packages for this project.

STEP 1: Import & Clean the Data

Import the dataset from this link: https://tinyurl.com/KaggleDataCS112

Remove any rows that include missing values.

# YOUR CODE HERE

df = read.csv("https://tinyurl.com/KaggleDataCS112")
head(df)

STEP 2: Codify outcome variable

Create a new variable that is either successful or NOT successful and call it success and save it in your dataframe. It should take values of 1 (successful) or 0 (unsuccessful).

# YOUR CODE HERE

STEP 3: Getting the project length variable

Projects on Kickstarter can last anywhere from 1 - 60 days. Kickstarter claims that projects lasting any longer are rarely successful and campaigns with shorter durations have higher success rates, and create a helpful sense of urgency around your project. Using the package lubridate or any other package in R you come across by Googling, create a new column that shows the length of the project by taking the difference between the variable deadline and the variable launched. Call the new column length and save it in your dataframe.

Remove any project length that is higher than 60.

# YOUR CODE HERE

STEP 4: Splitting the data into a training and a testing set

While there are several variations of the k-fold cross-validation method, let’s stick with the simplest one where we just split randomly the dataset into two (k = 2) and split our available data from the link above into a training and a testing (aka validation) set.

Randomly select 80% of the data to be put in a training set and leave the rest for a test set.

# YOUR CODE HERE

STEP 5: Fitting a model

Use a logistic regression to find what factors determine the chances a project is successful. Use the variable indicating whether a project is successful or not as the dependent variables (Y) and number of backers, project length, main category of the project, and the real project goal as independent variables. Make sure to use the main category as factor.

# YOUR CODE HERE

STEP 6: Predictions

Use the model you’ve inferred from the previous step to predict the success outcomes in the test set.

# YOUR CODE HERE

STEP 7: How well did it do?

Report the Root Mean Squared Error (RMSE) of the predictions for the training and the test sets.

# YOUR CODE HERE

Step 8: LOOCV method

Apply the leave-one-out cross validation (LOOCV) method to the training set. What is the RMSE of the training and test sets. How similar are the RMSEs?

# YOUR CODE HERE

Step 9: Explanations

Compare the RMSE from the simple method to the LOOCV method?

How do data scientists really use cross-validation? How is the approach in this project differ from real-world cases? Give an example to make your point!

Extra Credit: Least Absolute Deviation Estimator

STEP 1

Figure out how to use rgenoud to run a regression that maximizes the least absolute deviation instead of the traditional sum of the squared residuals. Show that this works by running that regression on the lalonde data set with outcome being re78 and independent variables being age, education, hisp, re74, re75, and treat.

# YOUR CODE HERE

STEP 2

How different is this coef on treat from the coef on treat that you get from the corresponding traditional least squares regression?

STEP 3

Now figure out how to do the same by using rgenoud to run the logistic regression (modeling treatment status as a function of age, education, hisp, re74 and re75).

# YOUR CODE HERE

END OF Assignment!!!

Final Steps

Add Markdown Text to .Rmd

Before finalizing your project you’ll want be sure there are comments in your code chunks and text outside of your code chunks to explain what you’re doing in each code chunk. These explanations are incredibly helpful for someone who doesn’t code or someone unfamiliar to your project. You have two options for submission:

1. You can complete this .rmd file, knit it to pdf and submit both the .rmd file and the .pdf file on Forum as one .zip file.
2. You can submit your assignment as a separate pdf using your favorite text editor and submit the pdf file along with a lint to your github code. Note that links to Google Docs are not accepted.

Knitting your R Markdown Document

Last but not least, you’ll want to Knit your .Rmd document into an HTML document. If you get an error, take a look at what the error says and edit your .Rmd document. Then, try to Knit again! Troubleshooting these error messages will teach you a lot about coding in R. If you get any error that doesn’t make sense to you, post it on Perusall.

A Few Final Checks

If you are submitting an .rmd file, a complete project should have:

• Completed code chunks throughout the .Rmd document (your RMarkdown document should Knit without any error)
• Comments in your code chunks
• Answered all questions throughout this exercise.

If you are NOT submitting an .rmd file, a complete project should have:

• A pdf that includes all the answers and their questions.
• A link to Github (gist or repository) that contais all the code used to answer the questions. Each part of you code should say which question it’s referring to.