RICM4/PS 2014: Illustration de la loi des grands nombres et du théorème central limite

Soit X_1, X_2, … une suite de variables aléatoires réelles, indépendantes et identiquement distribuées suivant la même loi D. On considère la somme \(S_n = X_1 + X_2 + … + X_n\) et \(Y_n=\frac{S_n}{n}\)

Loi des grands nombres faible

∀ε>0, \(\lim_{n→+∞}ℙ(|\frac{X_1+X_2+⋯+X_n}{n}-E(X)|⩾ε)=0\)

Loi des grands nombres forte

\(ℙ(\lim_{n→+∞} Y_n=E(X))=1\)

Théorème central limite

On suppose que l’espérance μ et l’écart-type σ de D existent avec \(\sigma\neq 0\)

On montre facilement que \(S_n\) est d’espérance \(\mu\) et d’écart type \(\sigma\sqrt{n}\). Ce qui est moins évident, c’est que la loi normale \(N(n\mu,n\sigma^2)\) est une bonne approximation de \(S_n\).

Si on définit \(Z_n=\frac{Y_n-\mu}{\sigma/\sqrt{n}}\), \(Z_n\) converge en loi vers \(N(0,1)\).

Quelques illustration du théorème central limite

library(ggplot2)
library(plyr)
set.seed(42);

triangle <- function(n=10) {
  sqrt(runif(n)) 
}

broken <- function(n=10) {
  x=runif(n);
  x/(1-x);
}

broken_mid <- function(n=10) {
  x=(runif(n)+runif(n))/2;
  x/(1-x);
}


generate <- function(n=1000,N=c(1,2,5,10,15,20,30,100), law=c("unif","binom","triangle")) {
  df=data.frame();
  for(l in law) {
    for(p in N) {
      X=rep.int(0,n);
      for(i in 1:p) {
        X = X + switch(l, unif = runif(n),
                          binom = rbinom(n,1,.5), 
                          exp=rexp(n,rate = 2), 
                          norm=rnorm(n,mean = .5),
                          triangle=triangle(n)-1/6,
                          broken=broken(n),
                          broken_mid=broken_mid(n));
      }
      X = X/p;
      df=rbind(df,data.frame(N=p,SN=X,law=l));
    }
  } 
  df;
}
d=generate()

On converge donc bien vers un dirac. C’est la loi faible des grands nombres.

Renormalisons les choses (i.e., zoomons avec le bon facteur d’échelle qui est de (N)).

## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.
## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.

On obtient alors une belle gaussienne. La largeur varie d’une loi à l’autre car toutes les lois de départ n’ont pas la même variance…

À essayer avec d’autres lois…

En particulier, jetez un à oeil à:

broken(1000);

##    [1] 3.947e+00 1.079e+00 5.937e+00 7.097e+00 1.450e+01 4.044e+01
##    [7] 7.355e+00 6.550e-02 3.097e-01 1.856e-01 4.575e+00 5.910e+00
##   [13] 1.098e+00 1.591e-01 2.919e-01 2.275e-02 3.509e+01 3.026e-01
##   [19] 9.369e-01 7.346e-01 7.729e-01 1.268e-02 3.276e-01 6.292e-01
##   [25] 1.992e+01 4.178e+00 8.095e-02 2.185e+00 1.138e+00 6.141e+00
##   [31] 3.862e+01 4.901e+00 1.053e+00 1.098e+00 1.220e+00 1.885e-01
##   [37] 1.167e+01 3.251e+00 6.181e-01 5.268e-01 1.334e+00 4.087e+01
##   [43] 1.155e+00 2.933e-02 9.613e-01 9.334e-01 2.144e+00 2.663e+00
##   [49] 2.705e-01 1.591e-01 6.162e-02 3.116e-01 3.423e+00 8.484e-01
##   [55] 9.461e-01 2.697e+00 4.645e+00 1.322e+00 1.582e-01 1.940e-02
##   [61] 1.292e+00 1.063e+00 4.277e-01 3.718e+00 1.796e-01 7.145e-01
##   [67] 7.830e-01 4.229e-02 3.652e-01 5.174e-01 9.212e+00 2.552e-01
##   [73] 7.681e-01 2.937e-01 9.533e+00 1.373e+00 3.200e+00 2.176e-01
##   [79] 1.769e+00 2.285e+00 2.316e+00 3.621e+00 1.488e+01 7.703e-01
##   [85] 5.950e+01 4.255e-01 8.073e-01 6.207e-02 1.126e+00 4.504e-01
##   [91] 1.263e-01 6.580e-01 3.840e-01 4.140e+00 1.294e-01 1.209e+00
##   [97] 4.692e-01 2.872e-01 6.361e-01 8.861e+00 1.300e+00 1.148e+00
##  [103] 7.561e-01 1.868e+00 2.488e-01 9.198e+00 4.845e-01 2.402e-01
##  [109] 3.332e-01 1.022e-01 1.828e+00 5.558e-01 4.833e+00 2.309e-01
##  [115] 1.441e+00 9.285e-01 4.148e+00 3.752e+01 2.316e+00 8.516e-02
##  [121] 7.295e-01 1.207e+00 5.820e-01 1.072e+00 3.901e-01 8.678e+01
##  [127] 1.123e+01 3.204e+00 5.400e-02 6.063e+00 1.513e+00 2.847e-01
##  [133] 3.178e-01 5.201e+00 1.114e+00 6.278e+00 7.207e+00 7.196e-01
##  [139] 1.495e+00 6.338e-01 2.285e+00 1.979e-02 7.754e-01 2.644e+01
##  [145] 1.070e+02 8.893e-01 5.579e+00 8.732e-01 5.472e-01 1.129e-01
##  [151] 8.001e+01 1.778e+00 1.326e-01 1.089e+01 2.912e+00 3.663e+01
##  [157] 3.318e-01 4.807e-01 6.291e-02 8.809e-01 5.784e+00 4.152e-01
##  [163] 6.677e-01 4.268e-03 8.229e-01 8.296e+00 7.278e-02 8.756e-01
##  [169] 2.400e-03 6.094e+00 1.356e+00 1.424e-01 5.349e-01 2.535e+00
##  [175] 5.502e-01 1.282e+01 2.079e+00 5.844e+01 6.029e-02 3.934e+00
##  [181] 1.256e+00 9.906e+00 2.796e+00 7.797e+01 2.941e-01 2.825e-01
##  [187] 4.835e-01 5.404e-01 2.722e+02 3.029e+00 3.104e-01 9.541e+00
##  [193] 3.299e-01 4.308e-01 2.728e-01 3.338e+00 1.147e-03 1.189e-01
##  [199] 2.641e-01 6.640e+00 8.393e+01 4.222e+01 5.606e-02 3.990e-01
##  [205] 3.861e-01 7.973e+00 4.637e+00 5.450e+00 3.166e+00 1.712e-01
##  [211] 7.994e-01 1.898e+00 2.281e-01 3.344e-02 2.665e+00 2.168e-01
##  [217] 4.305e+00 7.370e-01 1.066e-01 5.538e+00 1.362e+00 3.324e-01
##  [223] 7.933e-01 2.846e-01 1.942e-01 1.870e+00 1.402e+00 7.928e-01
##  [229] 4.147e-01 5.047e-02 1.190e-01 7.175e-01 8.128e-01 5.180e-01
##  [235] 1.278e+01 1.636e-01 1.788e+00 4.048e+00 1.453e+01 2.128e+00
##  [241] 5.248e+00 1.081e-01 1.899e-01 1.605e-01 1.068e-01 9.297e-01
##  [247] 2.286e+00 1.117e+00 1.185e+00 1.964e+00 5.078e-01 3.446e+00
##  [253] 5.113e+00 1.802e+00 1.489e+00 4.579e-01 1.295e+00 2.984e-01
##  [259] 3.827e-01 3.214e-01 1.012e+01 2.727e+00 8.574e-01 8.089e-01
##  [265] 8.385e-01 2.361e+00 1.701e+01 1.269e+00 2.644e-01 1.235e+01
##  [271] 1.830e+00 1.933e+00 5.626e-01 7.736e-01 5.574e+00 1.014e+00
##  [277] 9.147e-04 1.592e-01 7.169e-01 8.524e-01 1.258e+01 6.384e+00
##  [283] 3.094e-01 2.359e-01 6.122e-01 1.085e+00 6.918e-01 1.078e+00
##  [289] 5.395e+00 2.345e+00 4.225e+00 3.421e-01 7.330e+00 4.577e-01
##  [295] 1.751e-01 4.395e+00 9.609e-01 2.046e-01 2.172e-01 1.117e-02
##  [301] 2.199e+00 2.588e+00 1.216e-01 2.979e-01 1.311e+00 6.850e-02
##  [307] 3.225e+00 6.078e+00 2.730e-01 2.269e+00 1.257e-01 3.615e-01
##  [313] 5.291e-01 2.054e+00 2.674e-01 6.498e+00 4.785e+00 6.949e-01
##  [319] 1.513e+00 2.120e-01 1.907e+00 1.125e+00 4.364e+01 1.631e+00
##  [325] 7.583e-01 2.645e+00 4.080e-01 2.928e-01 6.985e-02 9.840e-01
##  [331] 1.510e+01 2.906e-01 2.316e+00 4.450e-01 4.699e+00 3.667e+00
##  [337] 1.369e-01 2.121e+01 6.202e-02 6.391e-01 8.918e-03 7.142e-01
##  [343] 5.970e-01 2.358e-02 5.381e-02 1.640e+00 5.831e+00 5.177e-01
##  [349] 6.222e-01 2.670e+00 5.093e+00 1.047e+00 7.831e-01 3.187e-01
##  [355] 4.534e-01 2.414e+00 1.097e+01 5.789e+00 1.371e+00 3.217e-01
##  [361] 8.592e+00 3.824e-01 4.348e+00 7.152e-01 3.625e+00 2.843e+00
##  [367] 8.041e-02 6.590e-01 1.893e+01 1.033e+00 1.732e-01 1.426e+00
##  [373] 1.269e+01 2.883e+01 2.682e+00 8.264e-01 1.256e+00 2.328e+00
##  [379] 3.909e-01 8.555e+00 1.975e+00 1.344e+00 3.961e+00 2.384e+00
##  [385] 6.544e-02 2.529e+00 1.956e-01 5.751e-01 9.792e-02 5.964e-01
##  [391] 1.336e+00 3.544e-01 4.229e-02 2.030e-01 6.891e+00 3.283e+00
##  [397] 8.831e-01 7.155e-01 4.799e-02 1.794e+00 8.916e-02 1.586e-01
##  [403] 3.591e-01 2.741e-01 6.842e+01 1.988e+00 1.527e+00 3.133e-01
##  [409] 9.634e-01 3.598e-01 6.426e+00 3.969e-02 3.162e-01 1.092e+00
##  [415] 4.648e+00 1.126e+00 4.112e-02 1.304e+01 3.148e+00 2.342e+00
##  [421] 1.362e+00 1.175e+00 4.592e-01 2.191e+00 3.181e+00 1.177e+01
##  [427] 4.975e+00 1.085e-01 1.358e-01 2.531e+00 2.910e-02 3.463e+00
##  [433] 3.013e-01 4.041e-02 2.207e+00 7.797e-01 2.491e-01 6.675e-01
##  [439] 1.411e+00 2.849e+00 4.340e-01 1.542e+01 1.349e+00 3.301e+00
##  [445] 3.734e-01 1.309e+00 2.904e+00 5.572e+00 2.282e+00 4.508e-01
##  [451] 7.789e-01 7.162e-01 6.220e-01 9.654e-02 4.170e-01 2.397e+00
##  [457] 3.030e-01 4.757e-01 4.283e-01 6.430e-01 6.400e-01 3.123e+00
##  [463] 1.070e-01 2.556e+00 1.938e-02 2.566e-01 2.333e+00 1.516e-01
##  [469] 1.533e-01 1.443e+00 1.284e+01 1.331e+00 1.149e+00 1.143e+00
##  [475] 2.870e+01 4.198e-03 4.790e-01 3.666e+00 1.502e-01 1.935e-02
##  [481] 1.128e-01 7.888e-02 5.581e-01 1.344e+00 1.242e+00 3.373e+00
##  [487] 1.165e-01 8.683e-02 3.441e-01 2.914e+00 9.655e-03 2.476e+00
##  [493] 1.471e+00 8.199e-01 3.189e+00 1.750e-01 2.808e-01 1.548e-02
##  [499] 1.652e+01 3.073e+00 4.361e+00 1.113e-01 5.005e-01 2.877e-02
##  [505] 2.672e-01 1.874e+00 7.936e-01 5.425e-01 5.080e-02 4.538e-01
##  [511] 6.684e+00 2.933e+00 1.749e-01 6.603e-01 6.516e+01 2.955e-01
##  [517] 5.600e-01 4.320e-01 5.212e+00 3.133e-01 2.394e-01 1.108e+00
##  [523] 2.296e+00 1.540e-01 2.580e+01 3.615e+00 2.241e+01 2.528e+00
##  [529] 3.133e+00 5.338e-01 3.712e+00 3.470e+01 9.284e-01 9.113e+00
##  [535] 2.509e+00 9.205e-01 2.303e+00 3.880e+00 2.031e-01 4.648e+01
##  [541] 4.322e-01 8.357e-01 3.822e-01 2.830e-01 3.176e-01 2.700e-01
##  [547] 1.531e+03 5.893e+01 4.894e-01 8.044e+00 5.521e+00 3.185e+01
##  [553] 2.440e+00 1.055e+01 4.379e+00 4.293e+00 2.207e+00 3.362e-01
##  [559] 2.051e+00 4.994e+00 4.408e-01 2.772e+00 7.027e-01 7.593e+01
##  [565] 2.946e+00 3.757e+00 3.857e-01 6.285e+00 5.131e-03 4.825e-01
##  [571] 9.169e-02 1.142e+00 1.936e+00 4.743e-01 1.641e-01 1.376e+00
##  [577] 3.202e-01 6.075e-01 6.257e-02 3.002e-01 3.015e+01 3.472e-02
##  [583] 3.407e-02 3.494e-01 1.577e+00 9.720e-02 2.444e+00 2.534e-01
##  [589] 9.105e-01 2.859e+01 2.931e+00 6.375e-01 7.974e-01 1.109e+00
##  [595] 1.451e-01 5.223e-01 6.350e-01 1.543e+00 1.539e+00 1.233e+00
##  [601] 5.978e+00 1.715e+00 3.067e-01 9.900e-01 3.321e-01 4.390e-01
##  [607] 2.142e+00 6.080e-01 1.592e+00 1.324e+00 1.415e+00 1.261e+00
##  [613] 6.500e+00 5.993e+00 7.396e+00 5.244e+00 4.762e+01 2.535e+00
##  [619] 1.197e+01 5.475e+00 2.678e-01 1.600e+01 1.564e+01 2.507e-01
##  [625] 2.517e-01 8.958e-01 1.961e-01 3.155e+02 6.702e+00 8.080e-01
##  [631] 1.939e+00 8.433e+00 1.115e-01 1.009e+01 4.448e-01 9.509e-01
##  [637] 2.300e-01 1.790e+00 6.273e-01 2.632e+01 2.574e-02 2.390e-01
##  [643] 5.010e-01 2.525e+01 6.365e-01 9.428e-01 3.996e+00 3.666e-01
##  [649] 2.192e-02 8.549e-02 7.849e+00 1.616e-01 1.628e+00 1.368e+00
##  [655] 2.234e-01 3.186e+00 1.545e+00 3.581e+00 3.944e-01 1.703e+00
##  [661] 1.597e+00 4.946e-01 7.132e-01 7.081e-01 5.029e+00 3.396e+00
##  [667] 2.205e-01 1.046e-01 1.127e+00 2.217e-03 1.789e+00 1.254e+00
##  [673] 2.063e-01 2.204e+00 2.087e-01 4.571e-01 4.120e-01 5.143e+00
##  [679] 1.714e+00 1.981e+00 3.193e+01 7.050e-01 1.224e+00 2.412e+00
##  [685] 5.656e-01 2.385e+00 2.109e+00 1.614e+00 2.759e-01 9.537e-02
##  [691] 1.061e+01 2.822e+00 3.290e+00 3.210e+00 4.247e+00 1.298e+00
##  [697] 4.610e+00 1.684e+01 1.846e-01 5.373e+00 2.498e-01 1.028e+00
##  [703] 1.021e-01 8.149e-01 5.539e+00 3.921e+00 1.109e+01 1.458e-01
##  [709] 5.329e-01 2.041e-01 5.103e-01 1.426e+00 3.546e+00 4.954e-01
##  [715] 2.693e+00 2.978e+00 5.298e-01 1.542e-01 1.288e+00 4.691e+00
##  [721] 3.123e-01 1.062e-01 2.605e-03 7.461e-01 9.778e-01 3.002e+00
##  [727] 2.630e+01 1.204e-01 6.850e+00 1.098e+01 1.200e-01 1.566e-01
##  [733] 5.703e+00 1.304e+01 8.692e-01 3.305e-01 1.866e-01 2.904e-02
##  [739] 1.992e+00 2.898e-01 7.951e-03 1.312e-01 7.065e-02 7.549e-01
##  [745] 3.607e+01 4.581e-01 4.070e+00 1.025e+00 1.204e+01 2.058e+00
##  [751] 5.035e+00 6.030e+00 1.542e-01 1.655e+00 1.288e+00 1.235e+00
##  [757] 5.129e-01 2.172e-01 3.255e-01 6.641e-01 2.091e+00 5.091e-01
##  [763] 1.386e+00 9.604e+00 3.805e-02 1.522e-01 7.316e+00 2.073e+00
##  [769] 2.920e+00 2.707e+00 1.902e+01 2.667e-01 8.140e+00 1.811e+00
##  [775] 2.331e-01 1.342e+00 2.589e-01 1.333e+01 8.006e-01 7.844e-02
##  [781] 2.931e+00 2.280e+00 4.789e+00 2.873e-01 2.671e-01 1.790e+01
##  [787] 4.042e-01 1.021e+01 1.136e+00 1.128e+00 1.593e+00 3.117e-02
##  [793] 4.470e-02 1.255e+00 7.427e+00 6.383e-01 1.401e+00 8.418e+00
##  [799] 3.864e+01 3.533e-01 5.026e-01 6.922e+00 2.653e+01 2.002e+00
##  [805] 4.648e-01 4.030e+00 9.705e-01 2.945e+01 1.138e+00 4.578e-02
##  [811] 9.375e-01 5.450e+00 9.796e+01 2.871e-01 1.343e+00 4.597e+00
##  [817] 7.441e-01 3.105e-02 3.906e-01 3.722e-01 1.525e+00 1.628e-01
##  [823] 2.187e+00 1.502e+00 1.195e-01 8.218e-01 1.022e+00 5.013e-01
##  [829] 7.857e-02 5.235e+00 2.692e-01 2.551e-02 2.427e+00 4.254e-01
##  [835] 2.338e-02 2.315e+00 2.071e-02 5.264e+00 1.102e+00 3.390e+00
##  [841] 8.741e-01 3.189e-01 4.542e+01 9.978e-01 2.453e-01 9.620e-01
##  [847] 1.827e+00 2.918e+00 1.795e+00 4.819e-01 5.268e+00 7.805e-01
##  [853] 2.960e-01 3.161e-01 1.119e-01 2.236e+00 1.235e+00 6.961e+00
##  [859] 1.564e-01 2.882e+00 8.041e-01 7.884e-01 5.362e-01 4.582e-02
##  [865] 3.380e-01 2.405e-01 5.103e-03 2.213e-01 5.589e-01 2.354e+00
##  [871] 1.892e-01 4.695e-01 3.308e-01 2.927e+00 4.538e-01 2.890e+00
##  [877] 4.092e-02 1.511e+00 1.109e+00 2.105e+02 1.054e+00 2.160e-01
##  [883] 4.608e-02 2.323e-01 1.209e-01 9.016e-01 1.007e+00 6.552e-01
##  [889] 2.829e-01 3.741e-01 3.438e-01 1.196e+00 1.110e+00 7.634e-02
##  [895] 3.761e-01 5.093e-01 1.920e+00 2.102e+00 4.058e+00 1.886e+00
##  [901] 2.477e-01 5.299e-01 4.778e-01 1.591e+00 7.699e+00 2.530e-01
##  [907] 2.720e+00 3.178e-01 6.108e+00 7.427e-01 1.575e-01 4.051e+00
##  [913] 2.630e+02 2.558e-01 5.737e+01 7.344e-01 9.556e-01 1.566e+00
##  [919] 1.200e+00 1.441e+00 6.438e-01 3.537e+00 5.348e-01 5.051e-01
##  [925] 8.548e-01 5.195e-01 1.516e-01 3.199e+00 7.840e+00 2.542e+00
##  [931] 6.020e-01 3.161e-01 3.850e+01 6.860e-01 2.170e-01 1.999e+00
##  [937] 1.497e+00 6.648e+00 3.266e-01 4.354e-01 3.233e-01 3.073e-01
##  [943] 7.099e-01 1.414e+00 4.272e-02 2.186e+00 1.284e+00 4.361e-01
##  [949] 3.770e+00 5.356e+00 6.117e-01 5.763e-01 1.388e+00 1.773e-01
##  [955] 4.130e+00 1.222e+00 1.086e+00 1.604e-01 3.503e-01 2.079e+00
##  [961] 1.241e+00 2.962e-01 3.296e+00 4.169e-01 7.159e+00 1.656e+00
##  [967] 2.812e-01 1.325e+00 7.096e-01 1.647e-01 1.174e+00 3.086e-01
##  [973] 3.630e+00 5.973e+00 3.473e+00 8.886e-01 8.725e-01 7.008e-01
##  [979] 1.911e-01 5.000e+02 5.205e-01 2.339e-01 4.422e-01 5.812e+00
##  [985] 6.117e-02 2.462e+00 4.022e-01 3.620e+00 3.710e+00 1.329e+00
##  [991] 1.601e+00 7.426e-01 1.006e+00 3.287e-01 2.319e+00 1.563e+01
##  [997] 3.641e-02 9.828e-01 2.843e+01 6.460e-01

broken(1000);

##    [1] 4.635e-02 4.432e+00 1.071e-01 4.626e-01 1.083e-01 1.081e+00
##    [7] 7.129e-01 8.847e-01 1.840e+00 1.508e+00 2.833e-01 4.260e-01
##   [13] 1.144e+01 3.330e+00 3.646e-01 4.024e+00 7.040e-01 3.532e-01
##   [19] 1.246e+01 1.492e-01 1.180e+00 6.053e-01 1.866e-01 1.603e+01
##   [25] 1.432e+01 7.622e-01 2.106e+00 1.413e-01 7.981e-01 2.441e+00
##   [31] 2.766e-01 2.559e+00 5.035e-01 1.064e-01 4.071e-01 7.003e-01
##   [37] 7.337e-01 6.826e-02 5.719e-01 1.052e-01 8.795e+01 1.747e+00
##   [43] 4.628e-01 7.243e-02 1.006e+00 3.429e-01 2.709e-01 2.628e+00
##   [49] 1.669e+00 9.380e-01 7.985e-01 8.115e-01 3.466e-01 4.071e+00
##   [55] 3.102e+00 3.023e-01 1.578e+00 2.989e+00 1.612e+00 5.210e-01
##   [61] 2.640e+01 1.027e+01 2.154e+00 1.585e-01 5.289e-01 1.713e+00
##   [67] 3.505e-01 4.276e+00 2.779e-02 3.460e+00 9.354e-01 1.295e+00
##   [73] 1.313e+00 3.731e+00 3.338e+00 1.025e+00 1.396e+01 4.125e-01
##   [79] 5.551e-01 1.736e+00 8.068e-01 4.339e+00 2.653e-01 7.492e-01
##   [85] 8.122e-01 1.199e+00 4.422e-01 6.046e-01 5.003e-01 3.100e-01
##   [91] 2.053e+00 7.120e-01 4.427e+00 7.585e-01 4.219e+01 5.272e+00
##   [97] 1.960e-01 3.335e-01 4.689e-01 4.285e+00 1.040e+00 4.106e-01
##  [103] 6.568e-01 3.805e-01 1.073e+00 4.701e-01 2.011e+00 1.718e+01
##  [109] 2.921e+00 3.633e-01 1.113e+00 1.370e+00 2.075e+02 2.745e+00
##  [115] 4.626e-01 4.092e-02 1.083e+00 3.423e+00 1.500e-01 2.434e-01
##  [121] 1.849e+01 5.729e-01 2.711e-02 1.421e-01 3.871e-02 9.088e-01
##  [127] 6.869e-01 2.031e-01 3.885e-01 1.193e-01 3.629e-01 6.545e+01
##  [133] 8.087e-01 3.379e+01 2.263e-02 6.495e+00 4.204e-01 2.447e+00
##  [139] 1.699e+00 2.617e+00 9.749e-01 9.044e-01 1.950e-02 9.203e-01
##  [145] 1.097e+00 4.074e-02 4.023e-01 1.146e+00 5.324e+00 2.182e-01
##  [151] 1.324e+00 4.490e-02 6.926e+00 1.738e+00 7.379e-01 8.434e-02
##  [157] 6.227e-01 1.384e+02 6.444e+00 2.377e-01 2.023e-03 2.056e+00
##  [163] 7.580e+00 1.798e-01 9.806e-01 2.739e+00 1.963e+01 1.536e+01
##  [169] 4.602e+00 1.581e+00 4.199e+00 1.341e+00 2.690e-01 2.697e-01
##  [175] 6.861e-01 5.009e-02 2.334e+00 3.020e-01 1.205e+00 2.210e+00
##  [181] 4.240e+00 2.455e-01 2.487e-01 4.825e-01 7.791e+00 4.346e-01
##  [187] 5.919e-01 2.064e-01 1.008e+00 6.605e+00 1.175e-01 1.653e-01
##  [193] 1.678e+01 1.403e+00 5.015e-01 3.314e-01 4.258e-01 4.378e+00
##  [199] 4.556e-01 3.714e-01 1.479e-01 1.165e+01 2.259e+00 2.754e+01
##  [205] 1.719e+00 1.173e-01 8.346e+00 7.483e+00 9.605e-01 5.502e+00
##  [211] 1.576e-01 7.781e-01 5.991e-02 1.268e+00 1.521e+01 7.987e-01
##  [217] 8.957e-01 7.330e-02 1.872e+00 9.468e+01 1.157e+00 4.348e-01
##  [223] 9.285e+00 1.460e+00 2.167e+01 2.815e-01 1.582e+00 2.238e-01
##  [229] 1.093e+00 8.961e-01 3.231e+00 1.117e+00 1.918e+00 3.651e-01
##  [235] 2.766e-01 3.379e+01 1.959e+00 1.914e-01 6.624e+00 1.699e+00
##  [241] 1.011e+01 3.901e+00 4.189e+00 3.268e+00 5.893e-02 1.281e+00
##  [247] 5.464e-01 1.997e+00 5.521e-01 2.849e+00 1.679e-01 4.769e+01
##  [253] 1.885e+00 3.561e-01 8.762e-01 3.696e+00 3.120e-01 1.512e+00
##  [259] 8.350e-01 2.426e-01 9.006e-01 4.605e-01 5.982e-01 1.254e+00
##  [265] 9.857e+00 1.971e+00 1.052e+00 4.509e-01 6.881e-01 3.986e+00
##  [271] 5.353e-01 1.384e-01 1.571e-01 1.105e+02 1.204e+00 5.458e+01
##  [277] 7.023e-01 1.812e+00 2.108e+01 1.986e+01 3.272e-01 1.902e+00
##  [283] 3.666e-02 9.017e-01 3.625e-01 4.550e+00 8.857e-01 8.953e+00
##  [289] 3.926e-01 1.092e+00 5.607e-01 4.477e-01 3.596e-01 6.861e-01
##  [295] 2.524e+00 8.822e-02 2.159e+01 1.422e+00 2.474e-01 1.668e+00
##  [301] 2.877e-01 8.243e-01 1.771e-01 1.779e+00 1.510e+00 3.062e+00
##  [307] 1.385e+00 3.985e-01 5.754e-01 8.236e+00 1.152e+00 4.593e+01
##  [313] 4.936e+01 2.011e+00 2.779e+00 1.505e+00 5.948e+00 9.679e-01
##  [319] 2.129e+00 1.736e-01 4.099e+00 1.536e-01 1.153e+02 1.701e-01
##  [325] 7.521e-01 2.447e-02 1.668e+00 1.190e+00 3.236e+00 1.594e+00
##  [331] 1.334e-01 2.779e+00 1.788e+00 5.672e+00 9.347e-01 1.528e+00
##  [337] 5.549e+00 6.795e+00 4.612e-01 5.299e+01 8.402e-02 3.640e-01
##  [343] 1.068e+01 1.111e+01 1.862e-01 1.460e+00 1.513e+02 2.655e+00
##  [349] 1.393e+00 1.503e-01 3.102e+00 1.053e+00 2.818e+01 3.263e+00
##  [355] 1.226e+00 1.430e+01 3.393e+00 1.497e+00 8.651e-01 8.450e+00
##  [361] 1.541e+00 2.518e+01 7.983e-02 8.828e-01 4.351e-01 2.973e+00
##  [367] 5.950e-01 9.355e-01 2.838e-01 6.021e-01 6.229e-01 1.801e+00
##  [373] 2.108e-01 1.164e+00 9.630e-01 2.342e-01 5.923e-01 2.000e+00
##  [379] 1.360e+00 1.044e-01 1.824e-01 8.885e-01 7.687e-01 2.491e+00
##  [385] 1.714e+00 1.057e+01 1.403e-01 4.668e-01 3.582e-01 1.383e-01
##  [391] 1.032e+00 7.840e-01 1.891e+00 2.204e-01 1.258e+01 1.125e-01
##  [397] 4.757e-01 1.076e+00 1.402e-01 1.281e-01 3.203e+01 6.633e-01
##  [403] 7.406e-01 5.223e-01 4.655e+01 1.078e+02 1.894e+00 2.604e+00
##  [409] 4.147e-01 1.478e+01 1.234e+01 3.249e-01 8.490e-01 5.637e+00
##  [415] 1.846e-01 2.273e+00 1.306e-01 9.637e+00 8.317e-01 1.198e-01
##  [421] 1.761e+00 8.582e-01 7.623e-01 6.656e+00 5.786e+00 1.296e-01
##  [427] 7.131e-01 8.455e-01 1.614e-01 1.455e+00 2.360e+01 1.435e+00
##  [433] 3.105e+00 4.299e-01 6.875e-01 5.048e+00 1.947e+01 5.431e-01
##  [439] 2.989e+00 5.465e+00 1.528e+00 4.085e-01 1.519e+01 1.590e+00
##  [445] 4.674e-02 5.669e-02 2.441e-02 2.340e-02 5.175e+00 3.221e+00
##  [451] 1.371e-01 7.239e-01 3.780e+00 4.667e-01 6.469e+00 1.665e-01
##  [457] 2.534e-01 2.225e+00 1.557e+01 1.043e+00 2.960e+00 2.300e-01
##  [463] 8.246e-01 1.779e+00 2.242e-01 4.598e-01 1.083e-01 1.779e+00
##  [469] 5.285e-01 8.629e+00 8.342e-01 7.385e-01 4.769e-01 4.872e+01
##  [475] 1.121e+01 4.693e-01 1.782e-01 1.119e+00 4.894e-02 3.968e+00
##  [481] 7.272e-01 8.217e-02 8.337e-01 5.965e+01 6.936e-01 8.870e+00
##  [487] 5.321e-01 1.976e+00 7.597e-01 1.226e+01 8.673e-01 5.103e+00
##  [493] 4.677e+00 1.618e-01 7.713e-01 7.790e+00 4.496e-01 9.136e-01
##  [499] 1.191e-01 7.785e-01 8.875e-02 9.458e-01 1.212e+00 1.877e+00
##  [505] 1.225e+00 2.539e-01 9.170e+00 3.532e+00 3.624e-02 1.417e+01
##  [511] 6.928e-01 6.111e-01 1.256e+00 2.678e+00 8.427e+00 2.226e+00
##  [517] 3.355e-01 3.778e-01 3.053e+00 3.452e-02 5.891e-01 2.967e-01
##  [523] 3.435e+00 3.345e+01 1.752e+00 8.609e-01 6.779e-01 3.779e-03
##  [529] 2.838e-01 2.453e-01 2.279e+00 2.962e+00 1.040e+00 1.382e+00
##  [535] 1.121e+00 4.657e+00 2.623e+00 4.105e-01 9.186e-01 2.551e-01
##  [541] 2.134e+00 1.762e+00 2.057e+00 6.074e+00 7.843e-01 3.306e-01
##  [547] 7.205e-01 7.241e-02 1.906e-01 5.981e-01 4.188e-01 3.567e-01
##  [553] 6.486e-01 2.341e-02 6.354e+01 4.451e-01 5.069e-01 8.797e-01
##  [559] 5.916e-01 9.573e-01 2.978e+00 3.088e+00 6.055e-02 8.310e-02
##  [565] 1.603e+00 1.191e-01 2.727e-02 5.185e+01 4.270e-01 3.126e-01
##  [571] 2.005e-01 2.565e-01 1.973e-01 4.223e+00 8.860e-01 9.326e+01
##  [577] 8.127e+00 1.096e+00 7.733e+00 1.658e+01 3.396e+00 2.778e-01
##  [583] 1.740e-01 1.404e+01 2.436e-01 1.026e+00 1.342e+00 2.149e+00
##  [589] 1.596e+01 3.150e-01 6.564e-02 1.759e+00 4.705e-01 1.752e-01
##  [595] 9.528e-01 1.788e-01 3.251e-01 2.533e-01 2.662e-01 2.468e-01
##  [601] 1.086e+00 1.507e+01 2.511e+01 1.286e+00 4.775e-01 6.928e-02
##  [607] 5.169e-01 7.017e-02 8.122e+00 9.157e-02 6.944e-01 5.149e-01
##  [613] 4.684e-01 4.804e-01 2.243e-01 1.196e-01 4.384e+00 9.519e-01
##  [619] 9.625e-02 1.250e-01 2.730e+00 6.697e+00 1.039e+00 1.497e+00
##  [625] 3.831e+00 2.797e-02 9.108e-01 1.798e+00 7.040e-01 2.228e-01
##  [631] 1.090e-01 7.692e+00 1.385e+00 7.213e-02 1.131e+00 5.388e-01
##  [637] 2.725e-01 2.525e+01 2.765e+00 1.195e+01 3.383e-01 6.798e+01
##  [643] 1.265e-01 1.880e-01 2.717e+00 4.973e-04 1.722e+01 4.211e+00
##  [649] 3.880e+01 7.673e-01 3.616e+00 3.020e+00 1.540e-01 7.743e-01
##  [655] 2.264e+00 3.754e+00 2.881e+00 7.381e-01 4.451e+00 2.337e-01
##  [661] 2.382e+00 2.149e+01 5.261e-03 3.128e+01 7.745e+00 6.567e-01
##  [667] 2.420e+02 2.535e-04 2.845e+00 2.498e+00 1.005e+01 3.237e+01
##  [673] 8.613e+00 3.312e+00 2.111e-01 1.036e+00 1.425e+00 8.759e-02
##  [679] 1.109e+01 3.182e+01 2.618e-01 1.307e+01 2.669e+01 1.302e+00
##  [685] 3.925e-01 7.795e-03 1.535e+00 1.250e+00 3.809e-01 1.702e+00
##  [691] 5.824e+00 2.139e-01 1.955e+00 2.011e+00 1.143e+00 1.623e+00
##  [697] 1.161e+01 1.214e+01 2.199e-01 1.278e+00 7.579e-01 1.269e+00
##  [703] 1.032e+00 8.439e-01 1.101e+02 1.015e+00 1.762e-01 1.264e+00
##  [709] 1.795e-02 3.617e+00 5.495e+01 8.172e+00 6.200e-02 1.146e+01
##  [715] 4.971e-01 2.639e+00 2.811e-01 1.184e+00 3.540e+00 4.171e+00
##  [721] 5.211e-01 1.029e-01 3.238e-01 1.828e-01 1.743e+00 1.003e+00
##  [727] 1.271e+01 7.746e-01 2.614e-01 1.593e+00 7.476e-02 5.698e-01
##  [733] 9.954e-01 6.277e-01 1.069e+01 7.223e+01 7.605e+00 4.337e+00
##  [739] 2.048e+00 1.050e+02 7.929e-03 3.078e+00 1.011e+01 1.405e+02
##  [745] 1.695e+00 1.665e+01 1.275e+01 1.504e+00 1.922e+00 9.472e-02
##  [751] 5.368e-01 4.390e-01 4.926e-01 1.045e+00 1.301e-01 3.997e-01
##  [757] 6.096e-02 2.471e-01 5.690e-01 2.656e+00 8.568e-02 1.866e+01
##  [763] 1.660e+00 2.129e-01 2.104e-01 1.597e-01 2.968e-01 2.211e-01
##  [769] 1.358e-01 4.588e-01 4.803e-02 4.905e-01 2.476e-01 2.756e+01
##  [775] 1.596e+00 5.435e-01 1.742e-01 1.370e+00 2.315e+00 1.736e+00
##  [781] 1.150e+00 1.045e+01 3.900e+00 2.265e+00 2.610e+00 1.847e-01
##  [787] 2.269e+00 2.174e+00 4.266e+00 7.709e-03 1.203e-01 1.357e+00
##  [793] 1.034e+00 4.696e-01 2.516e+00 2.732e-01 2.398e+00 3.408e-01
##  [799] 6.353e+00 3.304e+00 1.703e+00 3.622e+01 2.565e+00 4.595e-01
##  [805] 1.578e+00 3.065e-01 5.469e+00 6.358e+00 1.422e+01 2.861e-01
##  [811] 2.952e-01 4.261e-01 4.281e+01 2.797e+01 2.951e+01 1.324e+00
##  [817] 4.744e+01 1.203e+00 5.529e+00 4.568e+00 4.230e+00 1.448e-01
##  [823] 8.613e-01 1.861e+00 1.299e+00 3.594e+01 2.896e+00 5.026e-01
##  [829] 3.489e+01 6.159e-03 1.056e-01 1.836e+00 5.160e+00 1.846e+00
##  [835] 1.082e+01 1.330e-01 3.673e+00 1.062e+00 1.171e+01 3.329e+00
##  [841] 3.936e+00 1.626e+02 2.392e-02 2.023e-01 6.419e-01 1.153e+00
##  [847] 2.234e+00 1.056e+00 1.038e+00 1.582e+00 7.062e+01 6.000e-02
##  [853] 1.694e+00 2.588e+00 6.028e-01 5.109e-01 7.708e-02 1.974e+00
##  [859] 1.275e+00 2.209e+00 2.476e+00 9.403e-01 6.109e+00 3.298e-01
##  [865] 7.488e-01 2.037e-02 9.303e-01 1.234e-01 6.637e-01 8.027e-01
##  [871] 5.447e+00 1.165e+00 5.935e-02 1.238e+00 5.800e-01 3.099e-01
##  [877] 6.173e+00 3.762e-01 2.702e-02 1.618e+00 1.271e-01 1.042e+00
##  [883] 7.469e-01 8.600e-02 3.511e+00 1.002e+00 1.901e+00 1.034e+00
##  [889] 2.052e+00 2.624e-01 3.321e+00 1.230e+01 2.840e+00 8.379e-01
##  [895] 1.322e+00 5.311e+00 7.513e+00 2.412e-01 4.604e-01 2.231e+01
##  [901] 6.708e-01 2.138e+00 4.235e+00 5.199e-01 8.188e+00 2.651e+00
##  [907] 3.458e-01 4.384e+01 7.832e+01 1.015e+00 6.102e-01 1.941e-01
##  [913] 5.947e+01 3.339e-03 1.048e+01 2.402e+01 3.675e+00 2.417e-01
##  [919] 6.909e-01 5.168e+00 2.195e-01 6.330e-01 2.179e-01 4.053e+00
##  [925] 1.292e+00 1.947e+00 2.414e+01 1.918e+01 2.906e-01 3.828e-01
##  [931] 1.401e+00 4.912e+00 8.104e-01 9.525e-02 1.183e-01 2.119e+00
##  [937] 1.760e+00 1.094e+00 1.352e+00 4.548e+00 3.524e+01 6.284e+00
##  [943] 6.018e-02 3.488e+00 2.286e+00 3.841e-01 1.236e+00 1.190e+00
##  [949] 3.269e-01 1.126e-01 1.673e+00 5.883e-01 4.583e-01 2.639e-01
##  [955] 7.784e-02 5.085e-01 6.398e-02 3.084e-01 1.967e+00 1.590e+00
##  [961] 2.520e+00 7.901e-01 3.585e-01 1.324e+00 9.472e-01 1.945e-01
##  [967] 1.402e-01 4.981e-01 3.715e-01 1.093e+01 6.456e-01 9.149e-01
##  [973] 9.085e-01 2.680e+00 2.735e+01 9.678e-01 1.459e+00 9.969e-01
##  [979] 1.172e+01 2.322e+00 2.717e-01 2.798e+00 5.221e-01 1.161e+01
##  [985] 2.323e+00 7.961e+01 3.298e+00 1.405e+00 2.668e-01 8.205e-02
##  [991] 3.507e+00 1.701e+00 1.739e-01 8.377e-02 2.731e-01 4.910e-01
##  [997] 6.517e-01 1.461e+00 2.086e+00 1.639e+00

broken(1000);

##    [1] 2.422e+00 2.198e+00 1.103e+01 2.709e+00 1.362e+00 3.694e-01
##    [7] 9.882e+00 2.171e-01 3.508e-01 1.106e-01 1.806e+01 3.445e-01
##   [13] 3.998e-02 1.763e+00 2.921e-01 2.493e-01 7.663e+00 2.382e-02
##   [19] 8.033e-01 6.262e-01 4.575e+00 8.338e-02 1.631e+01 3.989e+00
##   [25] 3.207e+00 2.298e-01 6.799e+00 3.365e+00 1.809e-01 5.370e-01
##   [31] 2.404e+00 9.759e-02 3.547e-01 1.197e+00 1.140e+00 6.236e+01
##   [37] 4.616e-01 6.560e-01 6.888e+01 1.328e+01 1.605e+00 5.799e-02
##   [43] 6.087e-02 3.135e+00 5.488e-01 3.986e+00 5.452e+00 2.702e+00
##   [49] 1.293e+01 4.504e+01 2.101e-01 1.426e+00 8.535e+00 1.391e-01
##   [55] 9.713e+00 1.574e+00 2.240e-01 1.258e+00 1.382e+00 1.079e+00
##   [61] 1.459e-01 1.318e+01 1.274e+00 4.176e+02 8.826e-01 5.303e+00
##   [67] 1.881e+00 5.727e-01 1.194e+01 6.255e-01 2.711e+00 2.260e-01
##   [73] 3.219e+00 7.303e-02 2.275e-01 3.655e-01 5.686e-01 1.025e-01
##   [79] 3.103e-01 2.288e-01 6.809e-01 3.164e-01 2.244e+01 8.251e-01
##   [85] 1.449e+00 4.579e-02 1.050e+00 2.529e-01 3.345e-01 1.119e+00
##   [91] 1.508e-01 3.473e+00 4.596e-01 1.139e+00 5.086e-01 1.576e+00
##   [97] 1.794e-01 1.413e+00 7.687e+00 8.117e-01 1.733e+00 5.343e-01
##  [103] 1.893e-01 2.251e+00 1.813e-01 2.670e-02 1.345e+00 1.313e-02
##  [109] 6.589e-01 1.479e-01 5.894e-01 4.257e-01 2.709e+00 3.861e-01
##  [115] 6.944e-01 7.640e-01 1.473e+00 1.597e-01 8.680e+00 2.251e+00
##  [121] 1.375e-01 2.812e+00 8.052e-01 7.221e+00 1.513e+01 4.503e+00
##  [127] 5.988e-01 1.134e+00 4.208e-01 3.234e+01 9.542e-01 2.232e+00
##  [133] 1.216e+00 7.083e+01 2.566e+00 6.457e+00 8.261e-02 2.309e+01
##  [139] 6.772e-01 8.937e+00 2.548e+00 3.042e+00 4.483e-01 2.042e+00
##  [145] 7.816e-01 7.559e+00 1.064e+00 4.310e-01 1.535e-01 2.908e-01
##  [151] 1.434e-01 2.103e-01 2.316e-01 3.887e-01 1.705e-01 1.227e-01
##  [157] 2.941e+00 1.614e+00 1.128e+00 2.573e-01 3.009e+00 1.402e+00
##  [163] 1.309e+00 2.297e-02 6.339e-01 6.092e+00 1.026e+01 1.301e-01
##  [169] 4.820e-01 3.724e-01 4.104e+00 3.884e-01 3.152e-01 3.034e-01
##  [175] 3.323e-02 1.523e-01 1.617e+00 1.255e+00 2.507e-01 1.432e+00
##  [181] 2.296e-01 2.327e-01 3.209e-01 5.754e-02 7.367e-02 1.311e+00
##  [187] 2.054e+00 1.045e-01 6.019e+00 5.924e+00 8.699e-01 3.012e-01
##  [193] 2.576e+00 5.794e+00 5.617e-02 1.473e-02 4.753e-01 4.291e-01
##  [199] 8.393e-02 9.759e-01 2.018e+00 4.253e-01 8.166e-01 7.882e+02
##  [205] 2.032e+00 1.490e+00 7.864e-01 1.305e+01 5.939e+00 2.654e+00
##  [211] 2.302e-01 3.272e+01 1.542e+00 2.842e+01 1.383e+00 1.364e-01
##  [217] 4.739e-01 1.860e+00 3.801e+00 2.384e-01 1.848e+00 1.226e+00
##  [223] 1.021e-01 7.540e-02 3.064e-01 5.985e-02 7.856e-02 4.304e-01
##  [229] 8.330e-01 4.187e+00 1.379e-01 1.298e+00 7.278e-01 5.151e-01
##  [235] 5.503e+00 5.136e-02 5.529e-02 7.902e-01 1.067e-01 2.572e-01
##  [241] 3.929e-01 1.523e+01 7.318e+00 2.820e-01 1.602e-01 4.217e-01
##  [247] 1.708e+00 2.153e+00 2.655e+01 6.561e-01 1.975e+00 2.971e-01
##  [253] 5.678e-01 3.517e-01 1.327e+00 1.116e+00 1.599e+00 1.924e-02
##  [259] 6.939e+00 2.012e-01 8.644e+00 1.761e+00 1.139e+01 2.487e+02
##  [265] 1.694e+00 1.138e+00 3.607e+00 1.509e+01 5.305e-01 4.557e-01
##  [271] 2.494e+00 1.622e+01 8.690e-01 1.131e+01 2.513e+00 4.199e+00
##  [277] 9.888e-02 1.429e+01 2.764e-01 9.803e-01 1.464e-02 1.240e+01
##  [283] 2.725e+01 1.533e-02 1.770e+01 2.417e-01 4.379e-01 2.690e-01
##  [289] 3.801e-02 1.675e-01 3.067e-01 1.888e-01 9.780e-03 1.671e-01
##  [295] 1.174e+00 8.475e-01 1.925e+00 4.326e+00 5.733e-02 2.915e+00
##  [301] 6.986e-01 3.315e-01 5.696e+01 1.629e-01 1.020e+01 5.060e+00
##  [307] 3.757e-01 1.671e+01 1.825e+00 3.830e-01 2.549e+00 7.807e+00
##  [313] 1.541e-01 3.248e-01 1.188e-01 5.396e-01 2.873e+00 1.552e+01
##  [319] 1.383e-01 2.483e+01 3.048e-01 9.542e-01 2.320e+01 2.671e+00
##  [325] 8.005e-01 3.132e-02 3.021e+00 1.329e+01 2.265e+00 9.898e+00
##  [331] 1.195e+00 6.263e+00 1.843e+01 8.594e-01 4.378e+00 5.371e-01
##  [337] 4.529e-01 1.042e+00 7.006e-01 1.045e+00 9.366e-01 1.847e+01
##  [343] 1.872e+01 1.144e-01 9.338e-01 2.271e-01 5.846e-01 3.642e+02
##  [349] 1.404e+00 1.369e-01 4.740e+00 7.421e-02 1.044e+01 1.966e+01
##  [355] 2.606e+00 3.796e-01 3.352e+01 1.748e-01 3.040e-01 3.273e-01
##  [361] 2.318e-01 3.215e-01 5.490e+00 2.365e+01 3.102e+00 1.842e-01
##  [367] 3.048e+00 1.517e-01 1.912e+00 2.270e-01 1.883e-01 4.548e+01
##  [373] 1.529e-01 1.328e+00 7.399e-01 7.991e-01 1.077e-01 8.007e-01
##  [379] 9.573e-01 5.381e-02 2.759e+00 1.235e-01 3.537e+00 1.238e+00
##  [385] 2.557e-02 4.330e-01 7.354e-02 5.659e-01 1.005e-02 8.491e-01
##  [391] 1.374e+01 3.100e-01 3.620e+00 7.248e+00 8.716e-01 2.359e-01
##  [397] 1.359e+00 2.082e+00 3.443e-01 1.657e+00 5.490e-01 7.084e-02
##  [403] 1.556e-01 3.072e-02 2.789e+00 6.349e-02 1.440e-01 5.162e-02
##  [409] 2.969e-01 6.288e-01 1.345e-01 1.077e-01 5.781e-01 4.661e+00
##  [415] 6.726e+02 8.412e-01 6.536e-01 3.419e+00 3.210e-01 7.172e+00
##  [421] 6.420e-01 6.725e-01 5.617e-01 9.996e-01 4.121e-01 1.542e+01
##  [427] 4.889e-01 1.104e+00 4.160e-01 1.970e-02 2.525e-01 2.702e-01
##  [433] 4.032e-01 1.109e-01 8.466e-02 8.591e-01 6.215e-01 4.638e+00
##  [439] 2.406e-01 7.586e+00 2.246e+00 7.097e-01 9.757e+00 1.696e-03
##  [445] 9.496e-02 2.095e+00 8.946e-01 2.362e+00 2.129e+00 4.185e+00
##  [451] 1.392e+00 6.844e-01 4.841e-01 1.207e+01 2.081e+00 3.093e-01
##  [457] 1.137e+00 8.866e-01 7.453e+00 3.434e-01 1.770e+00 2.146e-02
##  [463] 1.849e+00 8.915e-02 4.408e-01 5.929e-02 1.215e-01 3.283e-01
##  [469] 2.833e-01 1.658e+00 1.202e-01 1.721e+00 1.727e+00 1.906e-01
##  [475] 5.472e-01 1.459e+00 8.647e-01 8.131e+00 1.558e+00 2.170e+00
##  [481] 6.693e-01 2.466e+00 7.796e-01 2.728e-01 1.202e-01 3.744e-01
##  [487] 2.549e-02 6.975e-01 3.067e-01 1.180e+00 3.507e-01 1.801e+01
##  [493] 4.763e+01 6.599e+00 7.518e-01 1.451e+00 1.455e+00 5.543e+00
##  [499] 2.648e-01 1.539e+00 2.705e+00 2.986e-01 1.088e+00 1.450e+00
##  [505] 4.304e-01 2.584e+00 6.732e+00 1.171e+00 7.135e-02 2.242e+01
##  [511] 7.809e+00 5.719e-03 3.618e-01 3.443e-01 6.782e+00 3.632e+00
##  [517] 5.693e-01 1.074e+00 3.978e+00 3.001e+01 4.974e-01 3.711e+00
##  [523] 5.792e-01 3.291e-01 7.801e-01 7.725e+00 1.196e+00 1.612e+00
##  [529] 8.658e-01 1.785e+00 2.612e+00 6.271e-01 5.682e-01 8.093e-01
##  [535] 5.400e+00 4.058e+00 6.365e-03 1.788e-01 9.798e-02 8.934e-01
##  [541] 1.597e-01 6.368e-02 2.225e+01 2.821e-01 1.843e+00 4.201e+00
##  [547] 8.569e-01 6.069e-01 3.845e-03 1.551e-01 1.645e+00 3.322e-01
##  [553] 8.305e-01 8.172e-01 8.822e-01 2.278e-01 1.030e-01 3.113e+00
##  [559] 1.158e+00 8.015e+00 1.268e+00 2.788e+00 2.552e+00 8.146e+00
##  [565] 3.525e+01 9.703e+00 1.691e-01 2.448e+00 1.984e+00 3.339e-01
##  [571] 1.915e+00 2.834e+01 5.181e+00 3.414e+00 1.984e+00 1.164e-01
##  [577] 3.987e+00 6.128e-01 1.152e+01 2.120e+01 6.005e-01 1.259e+01
##  [583] 3.144e-01 1.920e+00 1.241e+00 2.063e-01 2.768e-01 3.164e-01
##  [589] 1.828e+00 7.923e+00 1.774e-01 7.345e+00 2.701e+00 5.547e-02
##  [595] 2.480e-01 3.422e+00 1.275e+00 2.913e+00 4.098e-01 3.103e-02
##  [601] 8.600e-01 3.187e+00 2.782e-01 7.902e-01 1.703e+01 1.577e+00
##  [607] 2.977e+00 8.625e-02 1.097e+00 1.034e+00 3.499e+00 8.246e-01
##  [613] 3.518e+00 4.981e+00 3.438e-01 9.984e-01 1.141e+00 2.575e-01
##  [619] 7.012e-02 7.863e-01 3.465e+00 6.030e-02 1.711e-01 5.324e+00
##  [625] 7.634e-01 7.520e-01 1.071e-01 3.289e+00 2.664e+00 3.090e+00
##  [631] 3.377e-01 1.081e+00 1.041e+01 8.228e-01 1.217e+01 1.711e+00
##  [637] 1.513e-01 1.779e-01 8.021e-02 5.256e-01 4.962e+00 9.579e-01
##  [643] 4.488e-01 1.322e-01 6.739e-01 1.181e+01 2.690e-01 2.359e-01
##  [649] 1.094e+00 9.109e-01 1.119e+00 1.947e+00 9.192e-01 1.776e-01
##  [655] 1.532e+00 2.727e+00 5.628e-01 5.266e+00 7.370e+00 1.778e+01
##  [661] 3.193e-01 1.415e+00 2.332e+00 6.120e-01 5.232e+01 1.978e+00
##  [667] 9.067e-01 1.884e+00 2.964e-01 2.410e+00 6.367e+00 5.076e-01
##  [673] 1.285e+00 4.112e+00 4.545e-02 9.887e-01 1.885e-01 4.255e+00
##  [679] 1.027e+01 7.440e-01 8.455e-02 2.957e+00 4.482e-01 4.729e-02
##  [685] 2.210e-01 1.329e+00 1.282e+00 1.750e+00 1.720e-01 2.127e+00
##  [691] 2.128e+00 7.996e+00 8.375e-03 8.139e+00 3.537e-01 1.174e+00
##  [697] 2.875e+00 2.918e+00 8.932e+00 6.931e-01 1.944e-01 4.382e-01
##  [703] 1.257e+00 3.203e+00 5.623e-01 8.284e-02 4.025e+00 1.894e+00
##  [709] 1.476e+00 1.601e-01 7.427e-02 5.299e-01 4.284e+00 1.707e+00
##  [715] 2.031e+00 3.973e-01 1.596e-01 1.354e+01 2.314e-01 4.322e-01
##  [721] 1.860e-02 3.310e-03 4.669e+00 2.748e+00 5.767e+01 6.710e-01
##  [727] 2.757e-01 2.289e+01 5.759e-01 2.870e+01 1.375e+00 9.451e+00
##  [733] 3.994e-01 7.056e-01 5.037e-01 4.251e-01 1.171e-01 9.109e-01
##  [739] 1.512e+00 4.041e-02 1.093e+00 1.921e-01 3.673e+00 5.726e+00
##  [745] 2.103e-01 8.404e+00 8.563e-01 1.870e-02 1.848e-01 4.866e-02
##  [751] 2.140e+00 2.702e+04 2.032e-01 3.553e+00 3.444e-02 1.335e+00
##  [757] 2.604e-02 3.720e-01 2.767e+01 4.930e+00 3.241e-01 2.679e-01
##  [763] 3.327e-01 2.694e+00 1.510e-01 2.261e-01 4.258e-01 9.817e-02
##  [769] 1.064e+00 4.892e-01 1.721e+00 2.557e+00 1.965e-01 7.837e+01
##  [775] 1.167e+00 7.426e+00 2.237e-01 2.617e+00 6.223e+00 4.324e-02
##  [781] 2.907e-01 4.680e+00 2.293e+00 1.033e-01 1.769e-01 5.474e-01
##  [787] 4.094e-01 7.293e-01 5.686e-01 7.005e-01 5.921e-01 6.642e-01
##  [793] 1.269e+00 9.545e-01 2.771e+00 8.023e-01 4.986e+01 9.511e-01
##  [799] 1.094e+01 9.749e+00 1.496e+00 4.024e+00 1.626e+00 1.679e+00
##  [805] 2.315e-01 8.294e-01 2.990e-01 3.250e-01 1.408e+00 2.333e+00
##  [811] 2.178e+00 2.641e+00 1.634e+01 2.733e+01 8.256e-01 8.652e-01
##  [817] 7.646e+00 4.568e+00 1.309e+01 1.680e+00 7.088e-01 3.423e+00
##  [823] 4.667e-01 5.763e-01 1.474e+00 8.509e+00 1.271e+00 2.973e-01
##  [829] 8.867e-02 1.713e+00 1.494e-02 2.536e+00 3.557e-01 5.928e-01
##  [835] 4.040e+00 8.550e-02 6.598e+00 5.379e+00 5.822e-01 8.696e-01
##  [841] 1.952e+00 4.680e+00 3.157e-01 4.396e-01 3.756e-01 7.309e+00
##  [847] 5.560e-01 7.977e-02 2.842e+00 1.588e+01 1.373e+00 4.869e-01
##  [853] 3.865e+01 1.085e-01 9.290e+00 3.387e+00 1.720e+00 1.595e+01
##  [859] 2.480e+01 1.400e+00 3.127e-02 9.169e-01 2.369e+00 1.056e+00
##  [865] 1.757e+00 7.998e-02 1.050e-02 1.969e-01 5.727e-01 3.182e-01
##  [871] 9.175e-01 3.798e+00 1.050e+00 2.048e+00 6.883e-03 1.720e+00
##  [877] 1.019e-01 6.024e-01 6.478e-01 3.254e+01 4.030e-03 4.461e-01
##  [883] 1.095e-01 1.666e+01 3.446e+00 4.442e-01 2.301e+01 3.015e-01
##  [889] 7.154e+00 1.298e-01 1.292e+01 2.105e-01 5.941e-01 1.192e+00
##  [895] 7.050e+00 4.665e+00 1.080e+00 5.826e-01 2.320e+00 1.314e-01
##  [901] 2.277e-01 2.470e-01 6.282e-01 3.903e-02 3.190e-01 3.459e-01
##  [907] 2.027e+01 3.148e+00 1.726e+00 1.235e+00 2.106e-02 6.329e-02
##  [913] 3.664e+00 1.224e+00 3.261e+00 7.112e+00 1.172e+00 6.182e+00
##  [919] 6.673e-01 3.940e-01 9.040e-01 1.530e-01 8.979e-02 2.297e+00
##  [925] 4.934e-02 8.768e-01 5.079e-01 1.386e+00 9.831e+00 7.773e-01
##  [931] 4.818e+00 1.788e-01 4.537e-01 8.641e-01 1.857e+00 6.471e-02
##  [937] 1.442e+00 5.115e+00 1.113e+01 1.139e+00 5.102e-01 5.317e-01
##  [943] 1.914e-01 4.121e+00 3.863e+00 3.948e-01 1.836e+00 1.570e+00
##  [949] 2.872e-01 1.581e-01 7.844e+00 1.822e+01 3.869e-01 1.156e+00
##  [955] 7.354e+00 5.219e-01 7.761e+00 1.489e+00 1.835e+00 2.678e+00
##  [961] 6.528e-01 9.726e-01 2.492e-01 5.025e-01 2.481e-02 5.601e-01
##  [967] 2.871e+00 1.846e-01 1.384e+01 5.679e+00 6.035e+01 2.121e-01
##  [973] 1.173e+00 6.310e-01 9.176e+00 3.499e+00 2.274e-01 8.284e-01
##  [979] 1.098e+00 4.125e-01 3.976e-02 3.716e+00 1.154e+00 8.805e-01
##  [985] 6.043e-01 2.571e+00 1.380e-01 1.189e-01 1.260e+00 2.268e+00
##  [991] 3.175e+00 3.449e-01 7.528e-02 5.809e+00 2.796e-01 3.116e-01
##  [997] 1.448e+00 3.052e-01 2.685e+00 5.806e+01

broken(1000);

##    [1] 2.016e-01 1.580e-01 1.616e+01 3.937e+01 4.398e-01 3.310e+00
##    [7] 1.242e+00 2.070e+00 4.673e-03 1.411e-01 1.313e+01 2.641e+00
##   [13] 1.645e+00 4.755e+01 1.955e-01 5.078e-01 2.028e+02 2.810e+00
##   [19] 1.418e+00 1.935e-01 1.053e-02 7.313e-01 2.413e+00 1.722e+00
##   [25] 2.146e-01 2.017e+00 4.037e+00 1.971e-01 1.651e-01 1.092e+00
##   [31] 3.019e+00 5.563e-01 7.408e-01 1.428e-01 1.760e-01 3.714e-02
##   [37] 4.420e-01 1.017e-01 3.072e-01 9.440e-01 5.317e+00 5.108e-01
##   [43] 1.049e+01 1.412e+02 1.820e+00 3.401e+00 2.922e-01 1.426e+00
##   [49] 1.045e-02 4.080e-02 8.715e-02 6.293e-01 6.707e+00 1.526e+00
##   [55] 8.623e-01 1.527e+00 8.388e-01 7.975e+00 6.277e-01 3.299e-01
##   [61] 2.881e+00 6.514e-02 4.156e-01 8.345e-01 3.029e+00 1.715e+00
##   [67] 3.044e+00 9.722e-01 9.521e-01 3.940e-01 1.534e-01 7.451e+00
##   [73] 1.053e+00 5.437e-01 1.600e+00 2.276e+00 5.667e-01 2.741e-01
##   [79] 3.142e+00 1.418e+00 1.503e+00 1.340e+00 3.034e+01 1.706e+00
##   [85] 5.742e-01 2.672e+00 1.952e-01 3.614e-01 1.530e-02 6.931e+00
##   [91] 2.350e-01 4.220e-02 1.755e+01 4.479e-01 7.564e-01 8.273e+00
##   [97] 4.024e-01 7.671e-01 2.855e-01 3.405e-01 4.030e-01 4.323e+00
##  [103] 6.093e+00 2.053e-01 1.364e-01 1.864e-01 2.703e-01 2.160e-01
##  [109] 1.318e+00 3.259e+01 4.459e+00 1.678e+00 1.844e+00 1.034e+00
##  [115] 8.448e-02 5.122e-01 4.368e+00 3.095e+00 3.442e-01 2.576e-01
##  [121] 1.582e+00 2.769e+00 2.291e+00 1.285e+00 3.604e+00 3.347e-01
##  [127] 2.289e+00 5.753e+01 1.096e+00 5.159e-01 1.689e+02 3.624e+00
##  [133] 2.707e-01 8.081e+00 7.545e-01 8.109e-03 1.582e+01 1.666e-01
##  [139] 1.445e-01 1.506e+00 8.418e-01 3.554e+00 2.631e-01 1.154e+01
##  [145] 1.966e+01 2.986e+00 1.156e+00 1.235e+00 1.323e+00 3.126e+00
##  [151] 5.127e-01 2.444e-01 1.144e+01 5.050e+00 1.185e-01 1.673e-01
##  [157] 1.037e+00 5.934e-01 1.607e+01 3.123e-01 9.945e+00 2.043e-01
##  [163] 2.788e-01 1.818e+00 2.735e+02 7.039e-01 2.174e+00 1.035e+00
##  [169] 2.167e+02 1.174e+00 1.492e+00 1.282e-01 7.798e+00 2.249e+00
##  [175] 5.931e-01 6.086e-01 6.162e+00 9.729e-01 8.990e-01 2.297e-01
##  [181] 1.085e-01 1.524e-01 1.151e+00 3.050e-01 3.731e+00 9.311e-02
##  [187] 5.707e-01 2.556e-01 6.258e-01 3.361e+00 5.551e+00 5.400e+00
##  [193] 1.677e+00 1.167e+02 1.289e+00 2.413e+00 3.983e+00 9.186e-01
##  [199] 6.809e+00 1.789e+01 5.009e-01 6.873e-01 6.911e-01 1.624e+00
##  [205] 1.364e+00 8.405e-01 7.059e+01 5.669e+01 4.658e-01 4.808e-01
##  [211] 8.046e-01 2.273e-01 6.355e-01 5.613e+01 1.859e+00 1.190e+00
##  [217] 1.232e-01 2.196e+00 6.195e-01 6.121e-01 8.122e-02 4.050e+00
##  [223] 8.766e-01 1.317e+00 3.132e-01 3.286e-01 2.406e-01 2.840e+01
##  [229] 7.891e-01 2.346e-01 2.829e-01 1.708e-01 3.308e-01 2.211e-01
##  [235] 9.263e-01 1.862e+00 1.049e+01 6.358e+00 3.019e+00 7.795e-01
##  [241] 8.168e+00 2.807e-01 6.855e-01 2.310e-01 2.906e-01 4.271e-01
##  [247] 2.606e+00 1.408e-01 2.589e+01 2.573e-01 2.508e+01 4.126e-01
##  [253] 7.617e-01 3.537e-01 1.080e+01 8.139e-01 8.887e-01 1.017e+00
##  [259] 2.926e-01 5.546e+01 1.120e+00 4.191e-01 8.775e-01 8.989e+00
##  [265] 9.126e-01 4.492e+00 2.146e+00 9.786e-02 7.782e+00 3.629e+00
##  [271] 5.117e-01 4.157e-01 7.234e-01 2.404e-01 1.010e+00 2.079e-01
##  [277] 9.276e-01 5.887e+00 7.031e-01 4.162e+00 1.303e+00 4.479e+00
##  [283] 5.993e+00 5.816e-01 9.420e-01 8.924e-01 5.705e-01 4.665e-01
##  [289] 5.917e+02 2.376e-01 7.581e-01 1.383e+00 7.501e-01 4.685e-01
##  [295] 7.504e-01 3.625e+00 8.890e-01 2.493e+00 2.932e-01 1.680e+00
##  [301] 1.825e+00 3.421e+01 1.379e+00 7.560e-02 1.116e+00 2.617e+01
##  [307] 1.803e+00 1.440e+02 9.211e-02 8.781e-01 6.244e+00 1.043e+00
##  [313] 4.192e+00 6.405e-01 1.113e+00 1.504e+00 3.234e-01 3.751e-01
##  [319] 2.242e+00 7.276e-02 1.514e+00 4.824e+00 6.959e+00 1.040e+00
##  [325] 1.800e+00 1.934e+00 1.736e+00 4.946e-02 1.422e+01 4.911e-01
##  [331] 5.400e-02 5.942e-01 8.020e-02 8.314e-01 2.483e+00 8.978e-01
##  [337] 1.890e-01 3.712e-01 1.081e-01 3.970e-01 5.462e+00 6.070e-01
##  [343] 2.452e-01 1.816e-01 2.464e+00 5.987e-03 5.522e+00 1.333e-01
##  [349] 5.748e-01 2.129e-02 1.915e+00 9.844e-01 1.628e+00 1.805e+01
##  [355] 5.625e-01 4.709e+00 1.169e+01 1.913e+00 6.231e-01 1.659e-01
##  [361] 2.353e-01 5.866e-01 1.346e+00 4.759e-01 1.514e-02 6.552e+01
##  [367] 1.849e+00 2.876e+01 1.804e+00 9.100e+01 5.475e+00 8.794e-01
##  [373] 9.892e-01 1.010e+01 1.271e+00 2.326e-01 5.049e-01 1.625e+00
##  [379] 3.489e+00 8.078e-02 1.363e+01 3.516e-01 1.187e+00 1.398e+00
##  [385] 1.315e+00 2.368e+00 2.292e+01 1.344e-01 6.231e-01 4.472e-01
##  [391] 7.671e+00 4.783e-01 3.152e+00 2.526e+00 4.507e+00 1.474e+00
##  [397] 4.162e+01 1.050e-01 7.300e-01 2.074e-01 9.898e-02 2.995e-01
##  [403] 9.790e+01 4.555e-01 2.107e+01 2.101e+00 2.196e-01 2.872e+00
##  [409] 3.788e-01 2.592e+00 2.297e+00 1.892e+00 4.535e-02 1.594e+00
##  [415] 4.148e-01 5.888e-01 1.027e+00 1.897e+00 1.557e+01 5.861e-01
##  [421] 1.330e+00 2.547e+00 1.016e-02 1.136e+00 2.889e-01 8.294e+00
##  [427] 1.638e+00 3.333e+01 1.470e-01 1.166e+00 2.700e+00 2.333e+00
##  [433] 3.864e+00 8.525e+00 2.693e+00 9.303e-02 2.499e-01 2.267e+01
##  [439] 1.643e-01 1.429e+00 3.301e+00 6.641e+00 4.091e-01 3.871e+00
##  [445] 2.764e+00 1.462e+00 1.969e+00 5.965e-02 4.473e-02 3.226e-02
##  [451] 7.514e-01 9.149e+01 3.298e-01 1.076e+00 4.005e-01 6.394e-01
##  [457] 3.637e-02 1.846e+00 5.005e-02 1.793e-01 4.113e-01 6.017e-01
##  [463] 9.624e-02 9.878e+00 4.405e-01 3.227e-01 2.553e+00 3.428e+00
##  [469] 8.037e+00 1.184e-02 4.613e-01 7.301e+00 3.809e-01 1.473e-01
##  [475] 4.594e-01 7.912e-01 1.919e+00 1.369e+00 7.329e-01 3.198e-01
##  [481] 1.984e-01 1.364e+01 2.201e+00 3.960e-01 2.778e-01 7.355e-01
##  [487] 4.570e-03 6.635e-01 9.236e+00 5.252e+00 5.169e-01 4.544e-01
##  [493] 8.525e-01 1.004e+00 3.983e+01 5.093e+00 2.325e+00 7.506e-02
##  [499] 2.177e+00 9.023e-01 2.243e-01 2.049e+00 8.489e-02 1.774e+00
##  [505] 4.339e+00 1.675e+00 1.025e-01 2.722e-01 1.735e-01 1.458e-01
##  [511] 4.345e-01 3.382e-01 3.726e-01 1.887e+00 3.308e+00 9.756e-01
##  [517] 8.403e+00 6.965e+00 9.151e-01 1.612e+00 7.399e-01 2.611e+00
##  [523] 4.110e-02 6.349e+01 5.168e+00 8.452e-01 1.520e+01 1.699e+00
##  [529] 5.302e-01 1.701e+02 3.116e+01 6.399e-01 8.341e-01 7.178e-03
##  [535] 5.258e-01 6.030e-01 5.675e-02 2.742e-02 4.240e+00 1.671e-01
##  [541] 4.050e+00 3.806e+00 1.142e-01 1.090e-02 2.670e+00 5.951e+01
##  [547] 7.123e-01 5.508e-01 1.621e-02 2.270e+00 4.902e-01 9.906e-01
##  [553] 2.138e+01 3.269e+01 3.100e-01 1.389e+00 5.339e-02 3.482e-01
##  [559] 6.590e-01 3.367e+00 1.222e-02 1.078e+00 4.319e-01 5.009e+00
##  [565] 2.868e-01 7.739e-01 8.841e-02 7.195e-01 4.257e-01 1.534e+00
##  [571] 2.291e+00 8.446e-01 4.822e+00 9.779e-02 1.306e+00 2.989e-01
##  [577] 1.417e-01 1.253e-01 7.102e+03 8.328e+00 1.391e+00 5.236e-01
##  [583] 6.043e-02 4.637e-01 9.788e-01 4.883e-01 1.354e+00 3.644e-01
##  [589] 2.428e+00 5.052e-01 5.069e+00 7.934e+00 5.572e-02 1.816e-01
##  [595] 7.180e-02 1.288e-01 8.897e-01 2.763e+00 8.793e-01 7.206e-01
##  [601] 1.304e+00 3.445e+00 5.491e+00 3.434e-01 2.485e-01 1.220e+00
##  [607] 2.597e+00 1.698e+00 8.434e-01 2.504e-02 2.026e+00 3.963e+00
##  [613] 4.697e-02 1.878e+01 2.713e+00 2.255e-01 8.106e-01 7.347e-01
##  [619] 1.400e+00 8.830e-01 4.201e+01 3.279e+00 8.733e-02 8.355e-01
##  [625] 1.571e+00 4.716e-01 2.797e-01 2.146e+01 5.914e-01 7.124e-01
##  [631] 8.185e-01 7.533e-02 9.891e-02 5.604e-01 3.910e-01 2.707e+01
##  [637] 3.522e+01 1.749e-01 4.276e-01 5.001e+00 8.924e-01 4.428e-01
##  [643] 5.371e-01 5.782e+00 1.892e+00 1.574e+02 4.976e+00 1.531e+00
##  [649] 1.079e+00 7.260e-03 5.818e+00 3.245e-01 7.854e+00 9.456e-01
##  [655] 6.040e-01 8.034e-01 1.916e+00 1.194e+00 3.354e+00 1.714e+00
##  [661] 2.797e+00 1.374e+00 1.283e+00 4.314e-01 2.280e+00 2.980e-02
##  [667] 1.714e+00 3.331e+00 4.564e+01 1.354e+00 4.084e-01 9.764e-01
##  [673] 6.682e-01 7.738e-01 9.915e+00 1.648e+01 1.306e-01 3.617e+00
##  [679] 5.645e+01 1.413e+00 2.033e+00 2.378e+00 9.238e-01 7.692e-02
##  [685] 1.083e+00 1.117e+00 1.245e-01 2.788e-03 3.357e+00 7.952e+00
##  [691] 1.355e+00 4.882e+00 2.689e-02 1.718e+00 4.886e+00 1.734e+01
##  [697] 9.245e+00 3.377e-01 8.953e-01 1.317e-01 2.128e-01 1.126e+00
##  [703] 2.478e-01 1.323e+01 1.902e+01 3.434e+01 3.340e-01 1.150e+00
##  [709] 2.260e-01 2.141e-02 5.883e-02 3.510e-02 6.988e+00 2.696e-01
##  [715] 2.142e+00 7.011e+00 5.770e+00 1.689e+00 3.151e-01 8.843e+00
##  [721] 2.660e+00 1.167e+01 1.352e+00 2.152e+00 1.195e+01 8.949e+00
##  [727] 2.176e+00 1.282e-01 1.507e+00 3.179e+00 6.468e-01 9.412e-01
##  [733] 1.370e+00 4.759e-01 1.486e+01 1.289e+00 7.346e-01 4.377e+00
##  [739] 2.840e-01 9.138e-01 6.928e-01 2.908e-01 1.505e+00 7.604e-01
##  [745] 1.971e+00 1.535e-01 6.525e-02 9.750e+00 4.823e-01 2.941e+00
##  [751] 9.470e-02 5.329e-01 7.463e-01 3.455e-01 2.565e+00 5.792e-01
##  [757] 2.796e+00 2.356e-01 7.580e-01 4.342e+00 1.235e+01 3.066e-01
##  [763] 2.757e-01 8.041e-01 5.012e-01 4.628e-01 3.574e-01 9.618e-02
##  [769] 7.931e-01 3.048e+00 7.066e-01 6.056e+00 4.491e-01 7.417e-01
##  [775] 8.160e-01 4.782e+00 7.319e-01 1.206e+00 4.134e-01 1.140e+00
##  [781] 1.382e+00 1.449e-01 1.940e+01 1.213e+00 8.806e+00 1.371e+01
##  [787] 1.554e+00 1.259e+01 1.094e+00 8.988e+00 2.225e+01 2.629e-01
##  [793] 5.952e-01 1.824e-01 7.580e-04 3.975e-01 4.017e+00 1.248e+00
##  [799] 1.164e-01 6.041e+00 1.860e+00 9.626e-01 2.376e-01 3.463e-01
##  [805] 3.827e-01 8.003e-02 1.604e-01 2.321e+03 1.500e+00 1.421e+01
##  [811] 1.236e+00 1.550e-01 4.027e-02 1.377e+01 8.987e-01 1.385e+01
##  [817] 2.436e-01 9.582e-01 4.717e+01 2.887e+00 4.595e-01 4.978e+00
##  [823] 4.106e-01 6.175e-01 2.719e+00 2.272e-01 3.608e+01 5.744e+00
##  [829] 3.602e+00 1.589e-01 1.271e+01 9.185e-01 3.182e+01 1.461e+00
##  [835] 4.287e-01 3.352e-01 2.913e-01 1.950e+00 1.505e-01 2.467e-01
##  [841] 7.502e-02 1.892e-01 4.018e+00 1.398e+00 4.369e+00 1.887e-01
##  [847] 1.920e+00 2.483e-01 4.369e+00 3.427e-02 2.655e-01 4.663e-01
##  [853] 1.421e+00 8.391e-01 1.395e+00 8.830e-01 2.101e+01 3.181e+00
##  [859] 8.158e+00 3.366e+00 5.293e-02 1.114e+00 2.874e+00 1.081e+00
##  [865] 1.124e+00 2.822e-02 1.332e-01 1.520e+01 4.055e+00 2.144e+00
##  [871] 3.253e+00 7.894e-01 6.333e+00 3.717e+00 3.382e+00 5.379e-01
##  [877] 1.849e-01 7.600e+00 4.482e-02 1.457e+00 1.154e+00 1.912e+00
##  [883] 4.533e+00 4.611e-01 1.491e-01 1.174e-01 4.381e-01 2.202e+01
##  [889] 2.554e+00 4.723e+00 4.596e-01 3.438e-01 1.772e-01 2.199e+00
##  [895] 7.026e+00 1.676e-01 4.357e-02 3.720e+00 1.350e+00 5.825e-01
##  [901] 6.275e+00 6.753e+00 3.618e+00 1.645e+01 9.251e-01 1.843e+01
##  [907] 4.802e+01 3.297e+00 1.101e+01 9.856e-01 2.792e-03 2.802e+00
##  [913] 1.064e+00 1.133e+00 8.767e-01 4.079e-01 5.493e-01 3.773e-01
##  [919] 1.293e+00 1.290e+01 3.165e-01 6.516e-01 1.094e+01 7.976e-01
##  [925] 8.192e-01 9.393e-02 1.695e+01 3.285e+00 4.339e-02 2.910e+00
##  [931] 1.662e+00 7.124e+00 1.123e-02 1.265e+00 1.552e+00 2.046e+00
##  [937] 8.410e-01 1.576e-02 1.960e-01 3.651e-01 1.188e+01 9.623e-01
##  [943] 1.197e-01 6.287e-01 1.718e-01 7.614e-01 1.207e+00 3.485e-01
##  [949] 2.315e-01 4.896e+00 8.444e-01 2.288e-01 1.609e-01 2.237e+00
##  [955] 9.669e+01 2.175e-01 1.515e+00 7.145e-01 5.654e-01 4.883e-01
##  [961] 6.766e-02 4.130e-01 8.976e-01 1.071e+00 1.788e+00 1.588e-01
##  [967] 5.254e-01 9.673e-02 1.960e+00 7.936e-01 1.233e+01 4.283e-01
##  [973] 6.402e+00 5.926e-01 4.400e-01 2.866e+00 2.193e+00 1.998e+00
##  [979] 2.803e-01 9.304e-01 5.853e-01 1.794e+00 6.865e+00 2.149e+00
##  [985] 1.329e+00 2.665e-01 2.178e+01 1.330e+00 4.504e-01 3.942e+00
##  [991] 3.593e+00 1.344e+00 6.143e-01 1.283e+00 3.536e-01 7.011e+00
##  [997] 7.099e-01 6.489e-01 2.861e+00 4.047e-01

broken(1000);

##    [1] 1.063e+00 1.573e+01 2.833e-01 2.759e+00 2.603e+00 1.341e-01
##    [7] 8.247e+00 2.031e-01 8.854e-02 5.460e+00 2.219e+00 6.696e+00
##   [13] 2.251e-01 4.761e-03 4.382e-01 5.835e-01 2.001e+01 2.457e-01
##   [19] 2.825e-02 4.790e+00 7.207e+00 7.254e+00 9.723e+00 6.354e-01
##   [25] 5.556e-01 3.020e+00 7.612e-01 9.177e-02 1.487e+00 1.186e+00
##   [31] 3.619e-01 4.368e-01 4.482e-01 2.205e-01 5.026e-01 2.700e+00
##   [37] 2.723e-01 9.062e-01 2.390e+01 5.031e-01 6.336e-01 4.252e-02
##   [43] 4.537e+00 1.107e+01 7.483e-01 5.269e-01 3.810e-02 8.549e-01
##   [49] 6.634e+00 1.711e+00 3.667e-01 6.036e-01 3.230e+00 1.562e-01
##   [55] 2.201e+00 8.213e-01 2.397e-01 1.432e+00 1.762e+00 3.886e+01
##   [61] 2.357e+00 2.597e-01 8.924e-02 4.985e-01 6.687e-02 1.428e+01
##   [67] 6.882e-03 2.668e-01 7.054e+00 9.880e-01 1.009e-01 4.972e-01
##   [73] 2.718e+00 2.836e-01 2.410e-01 1.756e+00 9.590e-01 5.695e+00
##   [79] 1.087e+01 4.575e-03 3.800e-01 3.154e-01 3.945e-01 1.120e+00
##   [85] 5.298e+00 4.058e+00 1.541e+00 8.095e-02 1.665e+00 2.722e+00
##   [91] 3.145e+00 5.328e-01 6.145e-01 3.778e-03 1.029e+00 1.555e+00
##   [97] 2.444e+00 1.452e-01 2.125e+00 2.626e+00 6.188e+00 2.988e-02
##  [103] 1.556e-02 2.058e-02 7.112e-02 6.403e-01 1.661e-01 2.486e+00
##  [109] 5.261e-01 7.868e+00 6.697e-02 9.765e-01 5.815e+00 1.466e-02
##  [115] 4.299e-01 6.200e-01 1.531e-01 7.893e+00 5.682e-02 4.568e-02
##  [121] 8.030e-01 7.002e+02 3.797e+00 5.811e-01 4.993e-01 1.180e-01
##  [127] 2.492e+00 2.366e-01 7.241e-01 1.225e-01 5.779e+00 7.222e-02
##  [133] 6.601e-01 1.577e-02 2.972e+00 1.991e+00 1.765e+01 1.032e+01
##  [139] 3.381e-03 1.611e+01 2.412e-01 7.704e+00 1.221e+00 6.418e-02
##  [145] 8.866e-02 4.851e-01 2.093e+00 2.513e+00 2.551e+01 1.998e+00
##  [151] 4.360e+01 1.507e+00 9.078e-01 2.265e+00 4.745e-01 5.472e+01
##  [157] 1.987e+00 1.190e+01 1.028e-01 9.696e-01 1.648e-01 4.933e+00
##  [163] 5.820e+00 3.161e+00 2.112e-01 8.883e-01 5.525e-02 6.680e-01
##  [169] 6.072e-01 9.886e-01 1.272e+00 2.499e+00 2.187e-01 6.460e-01
##  [175] 1.164e+00 2.724e+01 5.746e+01 5.127e-01 2.483e-01 1.334e+00
##  [181] 6.323e-01 1.206e+00 8.172e+00 1.009e-01 1.735e-01 1.691e-01
##  [187] 3.438e+00 3.894e-02 2.054e-01 1.327e+00 1.348e+00 3.219e-01
##  [193] 2.132e+00 2.431e+00 2.032e+00 1.190e+00 1.107e+01 8.558e+00
##  [199] 4.481e+00 2.005e+00 7.350e-02 3.689e-01 4.968e+00 2.836e-01
##  [205] 1.577e+01 9.145e-02 4.684e-01 1.177e+01 1.227e+01 2.480e+01
##  [211] 3.947e-01 1.937e-02 3.396e+00 8.553e-02 3.666e+00 1.141e+00
##  [217] 3.041e+00 3.585e-02 3.586e-01 1.833e-01 8.382e-01 3.355e-01
##  [223] 5.961e+00 3.300e-01 1.707e+00 6.804e-01 1.363e+00 1.900e-01
##  [229] 7.533e-01 4.965e-01 7.128e+00 2.564e+00 2.280e+02 2.086e+00
##  [235] 2.354e-01 8.911e-01 6.770e-01 2.641e+01 7.444e-01 1.642e+00
##  [241] 5.196e-01 3.127e-02 9.756e-01 8.972e-01 2.562e-02 1.559e+01
##  [247] 4.648e+00 8.620e-01 2.336e+00 3.230e-01 3.530e-01 5.814e-01
##  [253] 3.167e-01 8.092e-01 2.464e+00 8.164e+00 9.055e-01 9.297e-02
##  [259] 1.230e-01 8.449e+00 3.946e-01 8.446e-01 1.986e+00 1.240e-02
##  [265] 5.439e-01 7.799e-02 4.902e-01 2.015e+01 3.805e+00 1.743e+00
##  [271] 6.514e+00 5.153e+00 4.949e-01 3.928e-01 8.275e-01 3.727e+00
##  [277] 7.447e-01 1.290e+00 1.394e+00 1.633e+00 9.217e-01 2.214e-01
##  [283] 3.599e+00 3.549e+00 3.949e+00 1.321e-01 3.175e-01 3.632e+01
##  [289] 9.945e-02 6.569e-01 1.625e-01 5.044e+00 1.114e+00 4.675e-01
##  [295] 3.076e+00 2.533e+00 2.261e-01 2.003e-01 2.425e-01 6.676e+00
##  [301] 1.478e-01 3.361e-01 1.494e+00 1.340e+00 1.177e-01 5.292e+00
##  [307] 4.709e-02 4.554e+00 1.788e+00 1.030e-01 4.782e-01 2.447e-01
##  [313] 2.106e+00 4.281e-01 6.708e+00 1.238e+02 9.080e-01 1.399e+00
##  [319] 4.059e-01 8.002e-01 8.163e-01 3.538e-01 1.527e+00 3.272e+00
##  [325] 8.524e-01 1.005e+00 7.001e+00 1.222e+00 1.706e+00 1.153e+01
##  [331] 8.628e-02 3.450e-01 3.788e+01 4.181e+00 4.366e-01 4.220e-01
##  [337] 8.772e-01 1.039e+00 9.778e-01 3.173e+01 1.015e+00 2.447e+00
##  [343] 5.000e+00 1.373e-01 3.812e-01 7.374e-01 1.460e+00 8.329e-02
##  [349] 4.190e-02 7.065e+00 2.684e-01 9.649e-01 8.242e-01 6.173e-01
##  [355] 1.384e+00 1.036e-02 3.271e-02 2.815e-01 6.311e+00 1.193e+00
##  [361] 5.470e-01 4.152e-02 1.233e+01 1.870e-01 1.587e+00 1.018e+00
##  [367] 1.627e+00 3.084e-01 3.043e-01 4.946e-01 7.499e+01 3.016e+00
##  [373] 1.787e-01 8.830e+00 9.269e-04 1.021e+01 1.134e+00 4.189e+00
##  [379] 5.318e-01 1.897e-01 5.467e-01 3.430e-01 1.765e+01 2.431e+00
##  [385] 5.392e+00 3.149e-01 1.463e+00 2.056e+00 3.449e+00 1.767e+00
##  [391] 1.030e-01 1.339e+00 1.924e+00 2.163e-01 7.518e-02 1.193e-01
##  [397] 1.519e+00 9.223e-01 4.036e+00 4.765e-01 1.533e+00 2.894e+00
##  [403] 6.181e-01 6.974e-01 2.367e-01 5.194e-01 6.807e-01 1.229e+00
##  [409] 7.051e-01 1.265e-01 1.628e-02 4.491e-01 1.669e-01 1.191e+00
##  [415] 1.245e-01 5.892e+00 1.234e-01 4.919e-01 2.471e-01 9.320e-01
##  [421] 5.755e+01 2.966e+00 1.509e+01 4.213e-01 4.074e-01 1.479e+00
##  [427] 2.076e+00 1.153e+00 6.851e+01 9.826e-01 1.806e-01 5.182e-01
##  [433] 1.712e+01 2.856e-01 4.212e-01 2.286e+01 2.532e+00 6.053e+00
##  [439] 1.871e-01 1.234e+00 2.019e+00 6.404e-01 2.109e-01 8.417e-01
##  [445] 5.042e-01 2.907e+01 1.343e-01 1.045e+00 1.970e-01 7.119e-01
##  [451] 1.472e-01 8.472e-01 6.877e-02 4.737e-01 3.290e-01 4.507e-01
##  [457] 2.655e+00 3.671e+00 3.134e+00 1.419e+00 2.392e-01 4.811e-01
##  [463] 1.200e+01 3.311e-01 3.436e+00 3.028e+00 2.564e+00 2.553e+01
##  [469] 1.105e-01 1.826e-01 2.479e+00 6.846e+00 6.240e-01 2.389e+00
##  [475] 2.789e-01 1.842e+00 1.599e+00 3.019e+00 5.812e-01 3.465e-01
##  [481] 7.547e-01 2.850e-02 3.335e+00 2.000e-01 1.597e-01 4.108e-01
##  [487] 1.510e-01 2.842e+01 3.072e-01 3.267e-01 3.916e-01 8.487e-01
##  [493] 7.240e-02 2.614e-01 4.871e-01 3.297e-02 7.692e-03 1.423e+00
##  [499] 2.244e+00 9.105e+00 1.280e+00 1.938e+00 1.001e+01 2.651e-02
##  [505] 2.471e+00 2.890e+00 3.614e-01 2.556e+00 2.449e+01 9.041e+00
##  [511] 1.055e+00 2.464e-01 2.659e+01 2.382e+00 1.390e+00 2.443e+00
##  [517] 2.733e+00 2.015e+01 1.385e-01 1.550e+00 1.492e+00 1.730e+00
##  [523] 2.737e+00 6.215e+01 2.380e+00 9.728e-01 7.848e+00 3.236e-01
##  [529] 9.373e+00 3.310e+00 9.180e+00 3.357e-02 5.680e+01 1.257e+00
##  [535] 6.415e+00 7.731e-01 3.362e+00 1.079e+01 6.179e-01 5.444e+00
##  [541] 1.339e+00 1.052e+00 1.693e+00 9.645e+00 3.830e+00 4.354e-01
##  [547] 1.578e+00 4.388e-01 6.743e+01 6.462e-02 9.350e+00 3.966e+00
##  [553] 1.163e-01 1.487e+00 1.311e+00 8.861e-01 1.383e+01 8.674e-02
##  [559] 3.953e-01 1.177e+00 2.650e-02 6.281e+00 4.481e+00 2.362e-01
##  [565] 4.349e+00 2.804e+00 7.314e-03 9.171e+00 4.779e-01 9.037e-01
##  [571] 1.436e+00 2.233e+01 4.045e-01 1.381e+00 9.433e-02 3.300e-02
##  [577] 2.463e-01 1.053e+00 3.932e-02 8.079e-02 6.243e-02 8.105e+00
##  [583] 2.399e+00 5.045e+00 2.081e-01 8.695e-02 2.029e+00 7.164e+00
##  [589] 5.691e-01 1.861e+00 1.940e+00 1.344e+01 6.674e-01 2.292e-01
##  [595] 4.793e-01 1.096e+02 4.716e-01 6.937e-02 5.320e-01 2.428e-01
##  [601] 4.260e+00 4.304e+00 2.106e+00 7.462e+00 6.560e-01 2.153e+00
##  [607] 1.600e-01 2.288e-03 8.034e-02 4.949e+00 9.828e-01 2.502e+00
##  [613] 4.102e-01 1.654e+01 4.800e-01 3.344e-01 4.922e+00 1.087e-01
##  [619] 7.076e-01 1.092e+00 2.043e-01 1.192e-01 3.030e+00 2.025e+00
##  [625] 6.942e+01 2.249e+00 1.868e+00 9.056e-01 1.231e+00 4.895e-01
##  [631] 1.165e-01 4.232e-01 1.711e+00 1.853e-01 8.252e-01 3.547e-01
##  [637] 1.509e+00 1.535e+00 3.048e-01 4.045e+00 3.779e-01 3.176e-01
##  [643] 3.841e-02 5.618e-01 1.702e+00 4.245e-02 2.367e+00 3.404e+00
##  [649] 4.323e-01 1.371e+00 2.856e+00 8.308e-01 1.014e-01 1.856e+00
##  [655] 2.068e-01 4.852e+00 1.782e+01 6.662e+00 3.652e-01 2.218e+00
##  [661] 3.168e-01 2.090e+01 2.327e+00 4.534e-01 8.599e+01 2.412e+00
##  [667] 2.861e-01 4.836e-01 2.898e-01 1.622e+00 3.181e-01 6.839e-01
##  [673] 2.267e-01 1.013e+00 1.376e-01 8.039e-01 3.702e-02 1.746e+00
##  [679] 2.370e-01 6.784e-01 1.963e-01 1.687e+00 3.915e-01 2.003e+01
##  [685] 4.651e+00 2.522e+00 2.119e-01 1.129e+00 5.490e-01 3.392e+00
##  [691] 2.976e+00 2.170e+00 5.039e+00 1.771e+00 1.814e+00 8.822e-02
##  [697] 3.784e-01 2.008e-01 1.735e-01 1.296e+00 1.666e+00 2.686e+00
##  [703] 9.246e-02 2.597e+00 1.082e+00 9.603e+00 6.418e-02 8.583e-01
##  [709] 2.150e-01 6.475e+01 1.073e-01 1.405e+00 3.660e+01 2.967e+00
##  [715] 3.782e-01 6.454e-02 9.081e+00 1.452e+00 9.058e-01 2.079e+01
##  [721] 1.269e+00 6.381e-01 1.938e-01 3.254e-01 8.015e-01 1.072e-01
##  [727] 3.278e+00 1.100e+00 1.418e+00 9.189e-01 6.795e-02 6.380e-02
##  [733] 7.064e-02 1.819e+01 3.296e-01 5.878e-01 1.312e+00 4.202e+00
##  [739] 7.532e-01 9.652e-01 7.435e-01 3.336e+00 2.476e+00 4.256e-01
##  [745] 4.636e-01 1.391e-01 3.965e+00 1.643e-01 1.199e-01 2.781e-01
##  [751] 1.951e+00 6.357e-01 6.366e-01 1.140e+01 8.788e-02 1.199e+01
##  [757] 2.472e+00 1.824e-01 2.263e+00 2.506e-01 3.915e+00 1.183e+01
##  [763] 2.807e+00 1.682e+01 9.936e+00 5.516e-01 2.649e-02 1.701e+00
##  [769] 3.060e+00 1.780e-01 4.678e+00 6.677e+00 5.422e-01 2.738e+00
##  [775] 3.809e+01 8.005e+00 3.055e-01 2.347e-01 9.070e-01 8.937e-01
##  [781] 1.940e-01 1.782e+00 4.910e-01 1.264e-01 5.200e-01 7.345e-01
##  [787] 8.702e-01 3.889e-01 8.848e-01 4.624e-02 8.786e-01 8.981e-01
##  [793] 8.731e-01 2.259e-01 7.414e+00 1.131e+00 3.168e+00 3.005e+01
##  [799] 1.304e-01 8.268e+00 8.084e-01 2.621e-01 7.462e+00 6.167e-01
##  [805] 7.150e-03 3.905e-01 4.392e+00 1.688e-01 4.028e-01 1.672e+00
##  [811] 1.551e+00 3.156e-01 1.947e+00 6.222e-02 7.359e-01 2.450e+00
##  [817] 9.784e-01 6.313e-01 4.935e-01 5.420e-01 1.184e+01 2.351e+00
##  [823] 2.910e-01 4.999e+00 1.822e+01 2.186e+00 1.000e-01 1.919e+02
##  [829] 1.399e-01 5.123e-01 8.412e-01 6.630e-01 1.687e-02 3.637e-01
##  [835] 1.306e+00 1.149e+01 4.041e+00 2.086e+00 2.962e-02 2.154e-01
##  [841] 2.509e+00 1.433e+00 1.621e+00 2.618e-02 8.985e-01 1.673e+00
##  [847] 2.468e-01 5.484e+00 2.236e+01 4.477e-01 3.568e-01 3.906e-01
##  [853] 1.320e+00 2.653e-01 4.973e-01 2.196e+00 4.532e+00 6.915e+00
##  [859] 2.863e-01 1.467e+01 2.373e-03 5.909e-01 2.285e-02 2.180e+00
##  [865] 5.189e-01 8.219e-01 1.084e+00 2.104e+00 1.625e+00 7.216e-01
##  [871] 6.039e-01 9.248e-02 4.065e-01 1.241e-01 2.138e+00 9.885e-01
##  [877] 1.638e+00 2.626e+00 1.873e+00 5.284e+00 6.700e-01 2.932e+00
##  [883] 8.715e-01 1.311e-01 2.783e+00 3.117e-01 1.728e+00 2.154e+00
##  [889] 9.146e+01 3.137e-01 4.929e-02 9.103e-02 1.373e+01 9.384e+00
##  [895] 1.559e+00 8.162e-03 3.969e+00 4.852e-01 3.849e-01 6.160e+00
##  [901] 6.930e-01 7.194e-02 2.636e+00 1.178e+01 9.371e+00 3.162e-02
##  [907] 2.590e+00 2.117e-01 5.358e-01 2.141e-01 1.334e+00 2.115e+00
##  [913] 4.888e+01 1.185e+00 9.753e-01 1.163e+01 2.057e-01 4.246e+01
##  [919] 1.136e+01 1.515e-01 1.363e+01 1.518e+01 7.793e-01 9.617e+00
##  [925] 8.467e-02 3.153e-01 3.850e-01 1.700e-02 6.039e-01 3.416e+00
##  [931] 5.583e-01 1.537e+00 1.402e-01 1.717e+00 1.638e+00 1.249e+02
##  [937] 2.083e-02 1.133e-01 1.160e-01 1.652e+00 4.912e-01 2.982e+01
##  [943] 2.399e-01 4.594e-01 3.058e-01 8.723e-01 3.336e+00 1.082e+01
##  [949] 1.289e+00 2.959e-01 2.258e-02 1.732e-01 2.522e-01 2.753e+01
##  [955] 2.653e+00 6.981e-01 2.409e-03 6.241e-02 1.593e+00 6.741e+00
##  [961] 1.123e-01 1.295e-01 1.493e-01 1.217e-01 6.837e-02 1.714e+00
##  [967] 1.092e+00 5.607e+01 4.541e+00 3.796e-01 2.707e-01 5.844e-02
##  [973] 2.814e-01 1.035e+00 1.243e+00 5.879e-01 5.719e-01 1.471e+00
##  [979] 5.841e+00 3.439e-01 9.398e+00 2.023e+00 1.532e-01 3.030e-01
##  [985] 3.406e+00 1.256e+00 7.257e-02 4.734e-01 6.017e-01 3.131e-01
##  [991] 2.595e+00 2.778e-01 6.092e-01 2.984e+00 6.546e-01 2.775e-01
##  [997] 2.413e+01 5.527e-01 4.636e-01 1.387e-01

broken(1000);

##    [1] 4.764e+00 1.946e+00 3.958e+02 1.303e-02 1.992e-01 1.904e-01
##    [7] 2.698e-01 6.458e-01 4.248e-01 6.749e+00 5.192e+00 2.308e-01
##   [13] 1.466e-01 3.924e-01 1.555e+01 4.388e-01 2.684e-02 1.293e+01
##   [19] 1.573e+00 4.036e+00 1.960e-01 6.399e+00 1.231e+00 2.685e+00
##   [25] 4.543e-01 4.450e-01 1.461e-01 1.063e+01 1.302e-01 2.556e-01
##   [31] 1.221e+00 1.792e+00 5.528e+00 2.894e+00 3.302e+00 2.665e-01
##   [37] 1.480e+00 8.056e-01 2.255e-01 5.419e-01 3.001e-01 1.219e+00
##   [43] 3.306e+00 4.547e-01 7.962e-01 9.165e-01 8.741e-01 1.297e+01
##   [49] 6.784e+00 8.167e-01 2.832e-01 1.059e+00 3.845e-02 8.182e-01
##   [55] 2.053e-01 8.173e+01 4.632e-02 1.226e+01 2.559e+00 3.274e+00
##   [61] 1.519e-01 2.637e+00 2.192e+00 5.198e-01 8.018e-01 6.025e-01
##   [67] 2.545e-01 1.540e-01 3.979e-01 9.580e-01 4.700e-01 1.079e+01
##   [73] 1.862e+00 2.755e-01 1.445e-01 3.415e-01 1.686e-01 3.250e+00
##   [79] 1.565e-02 2.278e-01 1.831e+01 3.229e+00 5.578e-01 1.054e+00
##   [85] 4.279e+00 9.709e+00 1.640e+00 1.031e+01 3.290e+00 2.598e+00
##   [91] 1.713e+00 6.075e+00 4.641e-01 3.032e+00 1.523e+00 9.894e-01
##   [97] 5.090e-01 2.669e+01 2.814e-01 5.933e-01 4.426e-01 1.769e+00
##  [103] 4.640e-02 4.615e+00 9.887e-01 1.118e+01 1.364e+00 4.611e+00
##  [109] 4.353e-02 1.315e+00 3.494e-01 6.259e-01 2.265e+00 1.532e-01
##  [115] 2.421e+00 8.381e+00 5.092e-01 3.725e-01 1.923e-01 4.127e-01
##  [121] 1.416e+00 7.924e+01 6.932e+00 1.175e+00 4.665e+00 6.137e+00
##  [127] 2.583e-02 4.557e-01 1.304e+00 3.364e+00 5.361e+00 4.224e+01
##  [133] 1.245e+01 2.284e-01 2.166e-01 1.005e-01 1.143e+01 2.672e-01
##  [139] 3.067e+00 4.352e+00 7.503e+00 1.959e+00 4.891e+00 3.113e-01
##  [145] 5.417e-01 1.422e+00 3.449e+00 3.611e-01 3.543e+00 5.404e-01
##  [151] 2.290e+00 3.113e+00 1.825e-01 4.254e+00 3.883e-01 4.739e+00
##  [157] 1.457e+00 1.276e+00 2.456e+00 8.400e-01 4.041e-01 1.620e+00
##  [163] 3.239e-01 8.428e+01 2.364e-01 3.289e+00 1.200e-01 4.763e+00
##  [169] 1.347e-01 2.538e+00 8.845e-02 3.980e-01 3.535e+00 2.040e-01
##  [175] 8.636e-02 9.724e-01 5.563e-01 1.435e+00 7.941e-01 6.811e-02
##  [181] 1.942e+00 1.972e+00 2.621e-01 1.706e+00 8.222e+00 1.759e-01
##  [187] 7.298e-01 5.978e-01 6.881e-01 9.099e-01 8.513e-02 2.139e+00
##  [193] 1.685e-01 1.150e+00 3.947e-02 2.907e-01 3.502e+00 1.354e+00
##  [199] 3.737e+01 7.511e-02 2.233e+00 1.638e-01 2.077e+00 1.310e+01
##  [205] 7.454e-01 7.096e-01 6.840e-01 2.414e+00 9.518e-02 1.444e+00
##  [211] 2.401e+00 2.001e+00 3.495e+00 1.552e-01 4.160e-01 1.190e-01
##  [217] 8.193e-01 3.245e-01 4.278e+00 9.204e-02 4.594e-01 6.002e+00
##  [223] 3.697e+00 2.348e-01 6.122e+01 4.541e+00 8.420e-02 4.792e-01
##  [229] 2.566e+00 7.080e-01 4.952e+00 1.198e+00 1.049e+00 1.950e+00
##  [235] 1.846e-02 1.700e+00 1.618e-01 2.015e+00 7.013e+00 2.330e+00
##  [241] 3.535e-01 9.731e-01 1.009e+00 7.558e-02 2.323e+01 1.130e+01
##  [247] 4.825e-01 2.413e-02 1.181e+00 3.047e-01 9.791e+02 1.410e-02
##  [253] 2.733e-02 6.873e-01 2.282e+00 7.906e-01 2.285e-01 2.399e-01
##  [259] 8.245e+00 2.380e+01 1.055e+01 3.048e-02 2.907e+00 4.591e-01
##  [265] 1.279e-01 3.552e-01 1.790e-01 3.437e-01 1.893e+00 7.564e+00
##  [271] 1.873e+00 3.317e+00 2.159e+00 1.466e+00 2.718e+00 2.128e-01
##  [277] 1.596e-02 2.244e-01 1.051e-01 1.735e+00 2.317e-01 3.619e-01
##  [283] 3.813e-01 8.097e-01 1.448e+00 5.125e+00 1.898e+00 1.597e+01
##  [289] 2.836e+00 3.106e+01 1.789e+00 4.943e-02 1.198e+00 5.300e-02
##  [295] 1.765e-01 6.856e-01 1.941e+00 3.651e-01 1.269e+00 1.645e+00
##  [301] 1.133e+00 4.986e-01 1.969e+00 9.329e-01 2.521e+02 5.139e-02
##  [307] 8.261e-01 2.364e-01 7.066e-01 4.991e-01 5.593e+00 1.485e+00
##  [313] 1.221e-01 6.615e-01 5.617e-01 1.037e+00 2.152e+00 1.939e-01
##  [319] 1.705e-01 1.211e+00 6.527e+01 2.227e+01 1.215e+00 2.942e+00
##  [325] 4.830e+00 7.134e+00 1.415e+00 7.008e+00 2.071e-01 9.757e+01
##  [331] 1.426e-01 2.339e+00 5.535e+00 1.144e+00 1.266e+00 4.305e+01
##  [337] 7.068e-01 3.569e+00 8.269e-01 4.728e-01 3.539e-01 3.786e-01
##  [343] 3.927e-01 7.900e+00 1.059e+00 4.208e+00 1.548e-01 1.329e-01
##  [349] 1.842e+00 4.935e+00 2.777e-01 2.712e-01 6.237e-03 3.723e-01
##  [355] 3.099e+01 7.628e-01 7.011e-02 3.986e+00 4.125e+00 4.904e-01
##  [361] 2.097e+00 1.256e+00 2.356e+00 2.347e+00 5.920e+00 1.399e+00
##  [367] 4.715e+00 6.156e+01 1.166e+01 2.151e-01 5.828e-01 2.051e+00
##  [373] 1.213e+00 8.445e-01 6.740e-01 4.014e+00 1.260e+00 5.667e-01
##  [379] 1.399e+00 3.009e-01 8.331e-01 9.796e+00 1.432e+01 1.786e+00
##  [385] 9.756e+00 1.324e-02 9.387e+00 9.367e+01 4.746e-01 9.687e-01
##  [391] 6.111e-01 3.142e+00 3.506e+01 1.349e+00 1.963e+00 1.678e+00
##  [397] 4.366e-01 1.686e+00 1.080e+02 1.179e+00 1.348e-01 8.413e-01
##  [403] 1.587e+00 2.128e+00 9.978e-01 1.004e+00 1.602e+00 3.824e+01
##  [409] 1.466e-01 9.299e+00 5.419e-01 7.594e-01 2.991e-01 5.578e+01
##  [415] 3.236e+00 1.205e+02 8.267e-03 2.115e+00 9.472e-01 3.121e-01
##  [421] 2.886e+01 8.523e-01 4.348e-02 2.796e+00 9.289e-01 3.242e-01
##  [427] 6.176e-01 1.564e+00 4.118e-02 7.143e-01 1.791e+00 1.307e+00
##  [433] 1.427e+00 3.389e+00 1.066e+00 6.160e+00 1.030e+00 3.727e-01
##  [439] 1.495e+00 1.962e+00 2.468e+00 3.948e+00 1.155e-01 5.220e-01
##  [445] 5.977e-01 4.586e-01 1.899e-01 2.451e-01 2.241e-01 2.591e-01
##  [451] 5.969e-01 8.261e-01 1.339e+00 8.096e-02 9.763e-01 7.274e-01
##  [457] 3.762e+00 3.531e-01 3.053e+00 3.863e+00 2.683e+00 7.074e-01
##  [463] 4.447e+00 3.199e+00 2.504e-01 4.322e-01 4.130e+00 9.389e-02
##  [469] 4.496e+00 9.919e+00 3.448e-01 3.161e+00 3.049e+00 2.432e+00
##  [475] 1.317e+01 8.866e-01 1.166e+00 4.252e-01 4.775e-01 4.595e+01
##  [481] 1.383e+00 4.012e-01 1.943e+00 2.150e+00 2.700e+00 1.855e+00
##  [487] 1.064e+00 9.595e+00 3.387e+00 1.352e-01 4.428e+00 4.648e-02
##  [493] 6.442e-01 2.818e+01 1.623e-01 6.326e-01 8.319e-01 3.610e-01
##  [499] 5.103e-01 7.869e+00 2.124e+00 6.993e-01 4.075e+00 5.094e+00
##  [505] 1.107e+00 1.098e-02 1.912e-01 6.652e-01 2.849e-01 3.121e-02
##  [511] 3.441e-01 2.093e+00 1.315e+00 3.192e+00 3.623e+00 8.201e-01
##  [517] 5.035e+01 2.877e+00 2.207e+00 8.286e-02 5.216e+00 2.551e+00
##  [523] 4.687e-01 1.816e+00 2.994e+00 7.258e-02 1.595e+00 6.623e-01
##  [529] 4.214e-01 1.357e-01 3.996e-02 1.098e-02 7.965e-02 3.774e-01
##  [535] 8.250e-01 1.116e+01 2.348e+00 1.131e-01 3.882e+00 3.970e+00
##  [541] 2.939e+00 4.041e-01 1.110e-01 6.995e-02 2.048e-01 2.799e+00
##  [547] 9.431e-02 3.251e+00 3.996e+00 7.535e-02 4.264e-01 8.992e-01
##  [553] 8.438e-02 3.577e+00 8.574e+00 5.441e-01 7.663e-01 2.017e+00
##  [559] 2.806e-01 6.030e-01 2.162e-01 8.151e-01 7.732e+00 3.813e-01
##  [565] 1.428e+01 8.497e-01 1.233e+00 1.014e+00 1.729e+00 2.501e-01
##  [571] 6.633e-01 2.577e-01 5.996e-01 1.060e-01 1.992e+00 2.332e-01
##  [577] 8.538e+00 2.772e-01 1.801e-02 5.035e+00 8.901e-01 2.251e+00
##  [583] 3.579e-01 1.613e+00 3.666e+00 3.420e-01 1.963e+00 3.126e+00
##  [589] 1.846e-01 1.683e+00 2.073e+00 1.131e+00 1.697e-01 2.409e+00
##  [595] 1.396e-01 2.481e+00 9.094e-01 7.149e-01 9.790e-01 9.748e-02
##  [601] 3.154e+00 8.492e-02 7.366e+00 9.920e-01 1.060e+00 5.194e-01
##  [607] 1.740e-01 8.218e-02 5.439e-02 2.164e+01 6.259e-01 2.632e-02
##  [613] 3.293e+02 2.222e+00 2.174e-01 1.193e+00 1.803e+00 2.319e-01
##  [619] 1.768e+00 3.114e-02 1.264e+00 3.150e-01 7.646e-01 1.900e-02
##  [625] 1.328e+00 1.036e+00 1.933e-01 6.264e+00 5.214e+00 6.010e-01
##  [631] 5.974e-02 3.703e+00 6.864e+00 1.409e-01 9.462e-01 2.670e+03
##  [637] 1.769e+01 3.136e-01 1.135e+00 9.664e-01 4.688e-01 3.266e-01
##  [643] 1.892e-02 1.382e-03 1.832e+00 2.321e+01 7.132e-01 2.406e+00
##  [649] 4.433e-01 1.992e-02 1.060e+01 2.875e+00 5.089e+00 5.072e-02
##  [655] 1.707e-01 9.431e-01 1.937e-01 9.372e-03 5.494e-01 1.420e+00
##  [661] 2.426e-01 9.899e+01 6.620e-02 6.971e+00 3.123e+00 4.395e-01
##  [667] 7.832e-01 4.037e-02 1.832e+00 3.003e+00 4.353e+00 2.709e+00
##  [673] 2.559e+00 2.148e-01 3.928e-01 1.403e+00 6.525e-01 4.450e-01
##  [679] 3.123e+00 1.249e+01 3.092e+00 7.057e-01 6.047e-01 2.421e+00
##  [685] 1.164e+01 6.367e-01 1.489e+00 3.290e+00 2.401e-01 2.261e+00
##  [691] 4.833e-01 1.240e+01 8.756e-01 1.225e-01 2.755e+00 7.247e-02
##  [697] 2.821e+00 5.128e-01 4.865e-01 7.391e-02 1.428e+00 6.803e+00
##  [703] 4.754e-01 4.547e-02 1.065e+00 1.351e-01 1.217e+00 1.303e-01
##  [709] 3.425e-01 1.634e-01 4.706e+00 1.578e-01 6.099e-01 2.531e-01
##  [715] 2.079e+01 1.076e-01 9.919e-02 1.772e+00 6.090e-02 2.749e+00
##  [721] 2.370e-01 1.086e+00 6.387e-01 2.915e-01 3.321e-01 3.923e-01
##  [727] 1.740e-01 9.092e+00 3.577e-01 1.671e+01 2.554e+00 3.943e-01
##  [733] 2.817e-01 1.104e+00 4.916e+00 4.699e-01 4.601e-01 1.267e+00
##  [739] 4.066e+00 2.659e-01 6.597e-02 2.160e+00 4.957e-01 1.387e-01
##  [745] 6.723e-01 1.443e-01 1.675e-02 1.957e+01 9.477e+00 5.037e+01
##  [751] 9.795e+00 1.825e+00 8.768e-01 3.893e-01 8.435e-01 1.386e+00
##  [757] 2.223e-01 1.928e+00 1.089e-01 5.441e-02 5.334e+00 1.897e-01
##  [763] 8.820e-01 5.258e-01 3.782e-01 2.927e-01 2.999e-01 2.548e-01
##  [769] 1.446e+00 9.207e-01 1.568e+00 5.756e-01 5.900e-02 6.400e+00
##  [775] 3.083e+00 8.537e-02 8.737e-01 5.141e-02 3.447e+00 1.442e-02
##  [781] 3.350e+00 7.617e-01 6.191e+00 9.122e-01 3.412e+00 1.441e-01
##  [787] 3.156e+00 4.311e-01 4.553e+00 1.368e-01 1.085e-01 7.851e-01
##  [793] 1.820e+00 3.439e-01 2.156e-01 9.173e-02 1.032e+00 1.493e+00
##  [799] 7.701e-01 3.997e-01 3.582e-01 3.435e+00 8.180e-02 5.364e-01
##  [805] 1.203e+00 1.151e+00 1.156e-01 9.442e+00 1.725e-02 1.042e+00
##  [811] 6.360e-01 4.013e-01 7.687e-01 9.400e+00 5.923e-01 1.154e+01
##  [817] 4.815e+00 2.449e-02 9.966e-01 1.270e+00 9.377e-02 1.080e-02
##  [823] 1.096e-02 1.486e-01 6.146e-01 3.297e-01 1.469e+00 2.195e-01
##  [829] 1.854e+00 3.533e+00 3.936e+01 2.293e-01 1.096e+00 1.215e+00
##  [835] 2.656e-01 1.374e+00 1.546e+00 2.072e-01 1.462e+00 9.635e+01
##  [841] 2.619e+02 9.444e-01 1.920e-01 9.877e-03 2.367e+01 6.027e-01
##  [847] 4.255e-01 1.246e+00 5.973e+00 1.220e+00 1.556e+00 9.943e+00
##  [853] 1.141e-01 9.622e-01 1.039e+00 7.183e-01 2.825e+00 4.683e-01
##  [859] 3.389e-01 1.088e+00 4.133e-01 7.385e-01 3.854e+00 1.793e-01
##  [865] 6.313e+01 4.317e+00 1.041e+00 2.763e+00 1.641e-01 4.831e-01
##  [871] 1.263e-01 6.083e-01 3.377e-01 5.361e-01 1.537e+00 1.135e+00
##  [877] 9.489e-01 1.673e+00 4.078e+00 8.587e-01 4.955e+00 2.067e+00
##  [883] 8.500e+00 4.022e-01 5.251e-01 3.525e+00 1.202e-01 1.432e+00
##  [889] 4.047e+00 4.748e-01 1.013e+00 7.921e-01 7.639e-02 4.064e+00
##  [895] 2.092e+00 5.047e-02 1.054e+01 1.863e+00 7.705e-01 6.373e-02
##  [901] 3.328e-01 3.424e-02 9.399e-01 1.379e+00 1.265e+00 5.329e-01
##  [907] 4.094e-01 1.434e+00 7.086e+00 6.433e-01 2.205e+00 3.646e+00
##  [913] 2.999e-01 2.828e+01 1.763e+00 1.272e+00 1.428e+00 1.944e+01
##  [919] 2.240e+00 1.463e+00 4.737e-01 5.814e-01 6.410e+00 3.167e-01
##  [925] 1.469e+00 1.289e+00 1.043e+00 9.583e-01 9.020e-01 8.912e+00
##  [931] 5.120e-01 2.220e-01 1.672e+01 4.058e-01 8.384e+00 3.064e-02
##  [937] 7.414e-02 8.246e-01 3.402e+00 3.966e+00 9.862e-01 2.126e-01
##  [943] 3.333e-01 1.211e-01 1.272e+00 9.958e-01 6.995e-01 2.862e+00
##  [949] 5.104e+00 1.174e+00 3.683e-02 1.009e+01 9.764e-01 3.713e-01
##  [955] 4.582e+00 1.973e+00 1.295e+00 9.720e-01 3.355e+00 2.076e+01
##  [961] 6.934e-01 3.425e-01 7.269e+00 2.933e-01 3.429e-01 1.400e+00
##  [967] 8.127e-01 1.683e+00 3.856e+00 6.202e+00 4.132e-01 5.336e-01
##  [973] 8.157e-01 5.243e-01 1.015e+01 3.532e-01 5.132e-01 1.513e+00
##  [979] 8.747e-01 2.922e+00 1.824e+00 1.472e+00 3.020e-01 5.956e+00
##  [985] 3.355e+00 6.729e-01 3.462e+00 8.688e-01 9.765e-01 7.472e+00
##  [991] 1.255e+00 1.095e-01 3.146e+00 7.275e-01 1.571e+00 5.546e-02
##  [997] 2.393e+02 1.090e+00 1.468e-01 1.136e+00

broken(1000);

##    [1] 7.401e-01 9.141e-01 5.306e-01 3.170e+00 3.555e+00 1.136e+02
##    [7] 9.997e-01 1.613e+00 7.298e-01 6.550e-01 1.977e-01 3.104e+01
##   [13] 3.001e-01 4.688e+00 9.268e-01 3.106e+00 1.934e-01 1.245e+00
##   [19] 2.398e+00 2.003e+00 6.378e-01 4.510e-02 2.844e-02 2.571e+00
##   [25] 1.197e+00 4.145e+00 1.914e-01 3.403e-01 1.419e+00 1.655e+00
##   [31] 8.147e-01 3.531e-02 8.801e-02 5.203e-01 1.164e+00 1.731e+00
##   [37] 6.654e-01 6.748e-01 1.056e+01 1.291e+00 2.014e-01 2.648e-01
##   [43] 1.668e+00 3.679e-02 2.649e-01 6.590e+00 9.235e-01 7.026e+00
##   [49] 5.721e-01 5.582e-01 7.331e-01 1.074e-01 3.099e+01 1.380e+00
##   [55] 5.866e-03 7.490e-01 9.086e-01 3.809e+00 1.376e+00 2.938e+00
##   [61] 1.298e+00 5.018e-02 5.751e-02 2.993e-01 1.180e+00 2.718e-01
##   [67] 3.438e+01 2.876e-03 1.887e+00 7.049e+00 2.631e+00 2.089e+00
##   [73] 1.643e-01 5.211e+00 5.198e+00 4.734e-02 1.795e-02 7.267e-02
##   [79] 1.043e+00 7.952e-01 4.241e-01 4.931e-01 1.652e+01 8.114e+00
##   [85] 4.413e-01 3.714e-01 4.814e-01 4.907e+00 1.238e-01 3.681e+00
##   [91] 2.510e-01 5.737e-03 1.443e+00 2.939e+01 4.725e-01 1.023e-01
##   [97] 2.778e+00 3.366e-01 8.530e-02 2.097e+01 2.611e+00 7.007e-01
##  [103] 2.978e+00 3.814e+00 9.843e-01 3.029e+00 2.181e-02 4.039e+00
##  [109] 4.084e-02 2.072e+00 7.361e-01 9.133e+00 1.002e+00 5.641e-01
##  [115] 2.266e-01 5.411e-02 1.941e+00 1.198e+01 1.114e+00 6.249e-02
##  [121] 4.103e-01 1.921e+00 1.927e+00 1.839e+00 4.622e-02 4.984e-04
##  [127] 3.340e+00 6.064e-01 2.402e-01 4.078e-01 5.836e-01 3.541e-01
##  [133] 2.366e+00 7.176e-01 5.266e-01 2.785e+00 5.380e-01 9.700e-02
##  [139] 4.108e-01 1.061e+00 6.292e+00 2.086e-01 1.774e-01 6.557e-01
##  [145] 3.795e-01 3.487e+00 5.311e+01 2.931e-01 2.049e+00 1.423e+00
##  [151] 7.163e-01 3.756e-01 3.393e+00 5.662e-02 6.651e-01 5.504e-01
##  [157] 1.230e-01 6.134e+00 1.429e+00 6.851e-01 1.826e+00 2.708e+00
##  [163] 3.661e-01 3.579e+00 2.470e+00 1.919e+00 1.494e-01 5.406e-01
##  [169] 1.010e-01 2.168e+00 2.227e-01 5.711e-01 4.251e+01 2.561e-01
##  [175] 7.344e+00 7.460e-02 2.261e-01 2.671e+00 2.683e+01 3.425e+00
##  [181] 6.581e-01 1.127e+00 1.973e-01 3.298e+00 1.409e+00 8.543e-01
##  [187] 7.370e-02 3.769e+00 2.298e-01 7.557e-02 2.725e-01 5.119e-01
##  [193] 2.145e-01 1.051e+00 3.002e+00 4.077e-01 5.381e-01 7.177e-01
##  [199] 5.275e-01 1.105e+00 3.906e-01 3.280e+01 3.241e-02 2.582e+00
##  [205] 7.452e-01 8.990e-01 1.208e+02 1.978e+00 7.389e-01 3.281e-02
##  [211] 1.786e+00 2.440e+00 1.485e-02 5.445e+00 1.179e+00 4.481e-01
##  [217] 2.606e-01 6.819e-01 1.792e-01 1.407e+00 1.332e-01 9.524e-01
##  [223] 8.300e-01 4.756e-01 3.175e+00 9.186e-03 1.558e+01 2.508e+00
##  [229] 6.671e-01 1.496e+02 1.180e+00 2.956e+00 8.613e-02 3.850e-01
##  [235] 2.123e+00 7.564e-01 1.682e+00 1.316e+00 1.092e+00 7.208e-01
##  [241] 1.313e+00 2.070e-01 2.034e-01 2.200e-01 7.300e-01 4.560e+00
##  [247] 3.931e-02 4.624e-01 8.534e-02 5.788e-01 1.868e+00 2.005e-02
##  [253] 1.530e-01 4.637e-01 7.193e+00 6.076e-01 3.611e-02 3.247e-01
##  [259] 2.343e-01 3.092e+01 3.592e-01 6.855e+00 5.818e+02 1.255e-01
##  [265] 6.835e-02 4.182e+00 1.030e-01 2.945e-01 1.239e-01 2.324e+00
##  [271] 1.803e-01 4.058e-01 1.597e+00 1.044e+00 1.131e-02 2.552e-01
##  [277] 1.610e-01 6.709e-02 1.221e+00 1.435e-02 1.941e-01 7.615e-01
##  [283] 1.148e+01 6.390e-02 5.256e-01 1.573e+00 1.031e-01 7.375e-01
##  [289] 5.184e+00 4.904e+00 1.922e+00 1.149e-01 3.306e+01 1.311e+03
##  [295] 4.108e-01 9.419e-01 9.966e-01 6.521e-01 1.011e+00 1.521e+01
##  [301] 4.610e-01 3.065e+00 2.213e+00 1.651e+01 1.438e+00 9.257e+00
##  [307] 4.771e-01 1.202e+01 1.572e+00 6.331e-01 1.104e+00 7.386e+00
##  [313] 3.872e-01 7.127e-01 4.853e+00 2.633e-01 8.264e-01 6.342e-01
##  [319] 5.047e+00 2.903e+00 4.299e+00 8.366e-02 3.639e-01 5.954e+00
##  [325] 1.813e-01 4.477e+00 6.661e-01 8.078e-01 6.059e+00 3.620e-01
##  [331] 3.004e+00 2.737e-01 3.202e-01 1.423e-01 6.443e+00 1.366e+00
##  [337] 7.454e+00 3.815e-01 1.673e+00 1.299e+00 4.949e-02 1.991e-01
##  [343] 3.567e+00 1.034e+00 1.127e+00 2.311e-02 2.199e+00 5.004e+00
##  [349] 9.144e+00 7.931e+00 8.569e+00 3.457e-01 6.827e-01 1.771e-01
##  [355] 2.126e-01 3.190e+00 2.488e+00 1.863e+00 7.273e-01 1.929e-01
##  [361] 4.484e+00 2.637e+01 3.599e-02 4.423e-01 7.078e+00 6.705e+00
##  [367] 4.480e+00 9.657e+00 2.703e-01 1.276e+02 5.009e-01 5.737e+00
##  [373] 4.423e-01 1.375e+00 4.523e-01 9.295e-01 6.207e+00 9.713e-01
##  [379] 2.840e-01 1.736e-01 1.853e+00 1.098e+00 1.484e+01 1.489e+00
##  [385] 5.006e-01 1.711e+00 2.391e+00 9.574e+00 4.577e+00 1.402e-01
##  [391] 2.695e+00 2.557e+01 5.076e+00 4.206e-02 9.242e-01 8.211e+00
##  [397] 9.717e-01 1.134e+00 5.099e-01 1.413e-01 4.802e+00 5.799e-01
##  [403] 1.107e+00 6.501e+01 3.974e-01 1.577e-01 1.212e+01 3.348e-01
##  [409] 2.752e+00 1.339e-01 9.294e-01 2.896e+00 3.787e+00 4.059e+00
##  [415] 1.051e+00 1.156e-01 1.869e+00 3.311e-01 6.661e-01 2.432e+01
##  [421] 1.125e+00 4.248e+00 6.264e+00 2.243e+00 5.578e-01 5.244e+00
##  [427] 1.170e+00 1.017e+01 2.173e-01 1.304e+00 6.286e+00 3.407e+00
##  [433] 4.990e+00 7.411e-01 1.933e+00 2.355e+00 2.949e-01 5.303e-02
##  [439] 3.539e-01 4.296e-01 5.374e+00 2.238e-01 2.588e-01 5.937e-01
##  [445] 4.108e+01 3.265e-01 9.153e-01 1.265e+01 1.294e-01 2.987e-01
##  [451] 1.197e-01 1.773e+00 2.092e-01 4.873e+00 7.523e-01 9.206e-02
##  [457] 2.433e-01 6.039e-01 1.538e+03 1.238e+01 6.500e-02 2.218e+01
##  [463] 3.633e+00 2.242e+00 2.105e-01 2.767e-01 1.605e-01 3.662e-01
##  [469] 2.351e+00 4.624e-01 4.255e-01 1.119e+01 5.453e-01 1.371e+00
##  [475] 8.315e+00 1.705e-01 1.454e+00 7.876e-01 8.630e+00 8.209e+00
##  [481] 1.345e+00 2.726e-01 1.087e-01 1.316e+00 1.144e+01 4.126e-01
##  [487] 3.432e+00 9.242e+00 8.272e+00 4.703e-02 6.075e-01 4.937e-02
##  [493] 9.464e+00 5.363e+00 3.657e+00 1.506e+00 1.241e+00 9.191e+00
##  [499] 2.178e-01 1.413e+01 3.919e-01 5.768e-02 1.600e-01 5.673e+00
##  [505] 2.953e-01 1.886e-02 2.101e+00 9.746e-01 1.678e+00 1.266e-01
##  [511] 7.624e-01 9.019e+00 6.420e-01 4.310e-01 6.855e-02 7.959e-01
##  [517] 3.676e-01 7.499e-01 5.262e+00 1.694e-01 1.870e+00 5.972e-01
##  [523] 7.126e-01 5.478e-01 2.512e+00 3.563e+00 1.200e-01 3.197e+00
##  [529] 1.269e+01 2.699e+00 4.502e-01 2.169e-01 4.533e+00 9.810e-01
##  [535] 2.998e-01 6.340e-01 1.607e+00 5.643e-01 1.605e+01 2.182e+00
##  [541] 2.031e-01 1.647e-01 1.586e-02 1.587e+00 2.228e+00 1.072e-01
##  [547] 9.201e-01 9.218e-01 5.976e+00 7.040e+00 8.831e+00 7.331e-01
##  [553] 2.361e-01 1.699e-01 7.393e+00 5.503e-01 4.814e-01 4.616e+00
##  [559] 1.190e+00 4.091e+00 1.729e+00 5.369e+00 3.496e+00 3.629e+00
##  [565] 3.783e-01 6.326e+00 7.914e+00 2.548e+01 1.046e+01 3.998e-01
##  [571] 1.889e+00 8.820e+00 2.841e+00 1.769e+00 4.412e-04 4.038e-01
##  [577] 4.344e-01 1.483e-01 2.500e+00 4.062e-01 3.619e-01 2.077e+00
##  [583] 5.664e-01 2.541e+00 2.690e+00 1.721e+01 1.988e+01 3.751e+00
##  [589] 2.631e-01 9.380e-01 1.720e+00 1.140e-01 5.153e-01 3.443e+00
##  [595] 1.238e-01 2.882e+00 3.738e+00 3.280e+00 1.007e+00 6.718e-01
##  [601] 1.038e-01 2.785e-01 1.213e+01 1.405e-01 3.051e-01 2.675e-01
##  [607] 3.594e-01 1.584e+01 3.401e+00 1.678e-01 5.162e+00 7.876e-01
##  [613] 8.853e-02 3.479e-01 8.796e+00 1.410e+01 3.439e+00 3.544e-01
##  [619] 2.955e+00 1.107e+02 1.471e+00 7.038e+00 9.070e+00 1.582e-01
##  [625] 1.444e+00 1.728e+00 1.230e-01 1.736e+00 5.909e-01 1.087e+00
##  [631] 1.573e+00 4.265e-01 5.574e+00 2.655e-01 1.190e+00 1.223e+00
##  [637] 7.310e-01 7.998e+00 3.610e-01 2.671e+00 3.147e+00 1.268e-01
##  [643] 2.353e-01 5.289e+00 5.025e-02 7.267e+00 6.873e+00 3.116e+00
##  [649] 6.501e+00 5.248e-01 4.775e+00 6.425e-01 1.440e+00 5.823e-02
##  [655] 1.147e+00 6.718e+00 1.188e+00 3.482e+00 2.195e-01 4.126e-01
##  [661] 1.085e+00 3.867e-01 1.653e+00 3.563e+00 3.057e+00 1.129e-01
##  [667] 2.831e-01 5.665e-01 2.213e+00 2.782e+00 4.595e-01 2.143e+00
##  [673] 9.055e-01 2.612e+01 1.016e+00 2.936e-01 2.161e+01 9.756e+00
##  [679] 1.037e+01 7.250e+00 7.399e-01 4.169e+00 1.037e+00 7.098e-01
##  [685] 1.518e+00 2.363e-02 1.895e+00 4.016e+00 1.276e+00 3.133e-01
##  [691] 1.147e+00 4.078e-01 6.095e-01 5.952e-01 2.202e+00 3.628e-01
##  [697] 4.400e+00 7.657e+00 6.191e+00 5.397e+00 9.203e+00 4.619e+01
##  [703] 1.704e-01 8.777e-01 2.318e+00 1.750e+00 3.849e-01 3.146e-02
##  [709] 1.338e-01 6.314e-02 1.407e-01 2.803e+00 7.994e-01 9.955e+00
##  [715] 2.353e+00 1.897e-02 2.230e+00 1.017e+00 8.049e-01 8.606e+00
##  [721] 6.825e+00 2.049e+01 2.050e+00 7.554e-01 1.578e+01 1.549e+00
##  [727] 7.925e-01 1.446e-01 5.104e+00 5.507e-01 1.304e+00 4.351e-01
##  [733] 1.527e+00 5.160e-01 3.111e-01 1.191e+01 4.735e-01 3.231e-01
##  [739] 1.753e+00 2.082e+02 1.364e+01 3.761e+00 2.110e-01 6.942e+01
##  [745] 2.034e+00 2.065e+01 3.365e-01 5.411e+00 1.109e-01 1.712e+00
##  [751] 8.231e-01 7.309e-02 8.809e-01 4.928e-01 7.911e-01 9.210e+00
##  [757] 8.476e-01 3.488e-01 1.755e+00 2.684e-01 6.686e-01 9.796e-01
##  [763] 2.171e+00 3.522e-01 1.264e-01 1.196e+00 7.290e+00 1.086e-01
##  [769] 2.586e+00 7.906e-02 1.712e-01 5.244e+00 2.908e+00 7.942e+01
##  [775] 3.246e+00 8.848e-02 7.089e-01 3.811e-01 3.198e+01 6.933e+00
##  [781] 2.172e-01 3.153e+00 1.033e+00 9.539e-01 4.060e-01 1.540e-01
##  [787] 7.244e-01 2.710e-01 4.876e+00 1.147e-01 2.257e+00 3.947e-01
##  [793] 2.503e-01 4.062e-03 2.075e-01 1.463e-01 9.682e-02 5.603e+00
##  [799] 1.026e+00 1.393e+00 4.830e-01 5.730e-01 4.244e-01 2.166e-01
##  [805] 1.105e+00 3.769e-01 8.092e-01 3.788e-01 6.089e-01 8.790e-01
##  [811] 1.488e+00 7.731e-01 6.228e-01 1.491e-01 7.684e-01 1.711e+01
##  [817] 6.005e-01 1.159e-01 2.586e+00 5.762e+00 2.012e+00 1.197e-01
##  [823] 6.464e+00 2.529e-01 9.538e+00 8.496e-01 4.459e-01 1.344e+00
##  [829] 2.031e-01 9.232e-02 1.582e+00 4.669e-01 7.853e+00 7.960e-02
##  [835] 4.596e-01 4.631e-01 2.345e+00 4.511e+02 4.417e-01 2.223e+00
##  [841] 3.551e+00 3.161e+00 4.462e-01 5.925e+00 1.793e+00 6.674e-01
##  [847] 1.771e+00 1.089e+00 7.407e-01 5.094e-01 6.223e-01 1.930e-01
##  [853] 1.103e+00 4.661e-01 9.225e-01 5.673e-01 1.959e-01 2.757e+00
##  [859] 7.263e+00 5.756e-02 3.047e-01 1.175e+00 6.715e+00 4.596e+01
##  [865] 2.536e-02 3.650e-01 5.043e-01 4.113e-01 2.711e-01 9.636e-01
##  [871] 3.727e+00 1.159e+00 4.949e-01 6.282e-01 2.081e+01 1.786e+00
##  [877] 8.646e-01 4.247e+00 1.521e+01 1.818e+00 3.397e+00 2.251e-01
##  [883] 6.345e-02 5.791e-01 5.509e-01 5.074e+00 1.832e-01 1.983e-02
##  [889] 2.432e+00 1.047e+00 1.196e-01 6.498e+00 1.139e+00 6.132e+00
##  [895] 1.790e+00 4.264e-01 3.179e-01 6.984e-01 1.608e-01 1.217e+00
##  [901] 3.847e-01 1.234e+00 4.387e-01 7.565e-01 7.544e-01 6.824e+00
##  [907] 3.178e+01 2.488e+01 1.376e-02 7.313e-01 7.241e-01 1.068e-01
##  [913] 1.332e+00 1.035e+01 4.683e-03 1.887e+00 1.344e+00 5.423e-01
##  [919] 1.805e-01 5.465e-01 4.640e-01 1.068e+00 1.458e+01 6.060e-01
##  [925] 7.168e-01 1.182e-01 1.168e+00 2.827e-01 6.272e+00 8.843e-03
##  [931] 1.957e+01 1.327e+01 3.981e+00 4.649e-01 1.213e+00 8.387e-02
##  [937] 5.974e-01 3.286e+00 5.611e-02 8.966e+01 2.419e+00 6.033e+00
##  [943] 2.244e+00 7.610e+00 8.699e-01 4.116e+02 2.436e-01 7.295e+00
##  [949] 4.022e-02 7.614e+00 8.512e-01 2.052e-02 2.919e+00 4.389e-01
##  [955] 1.174e+00 5.695e+00 2.552e+00 1.724e-01 1.053e+01 7.442e-01
##  [961] 8.471e+00 3.204e-01 8.152e-02 1.818e+00 6.679e-01 2.353e-02
##  [967] 1.275e+00 8.339e-01 3.248e+00 1.802e+00 4.501e+00 8.943e-01
##  [973] 1.183e+00 1.701e+01 2.081e-01 3.460e-01 4.694e-01 3.324e+00
##  [979] 4.305e+00 1.517e+01 2.656e-01 2.831e-01 6.356e-01 3.753e-01
##  [985] 1.020e-04 6.284e+00 1.128e+00 4.975e-01 5.187e-03 6.263e-01
##  [991] 9.170e-01 2.221e-01 4.403e-01 1.070e+01 3.723e+00 7.591e-02
##  [997] 1.286e+00 4.831e-01 5.873e-01 1.650e+00

Que se passe-t-il ? Et que pensez vous des suivantes ?

broken_mid(1000);

##    [1]  0.48440  2.04793  1.02924  2.02927  2.78108  8.36067  0.40943
##    [8]  2.19235  0.71190  0.53082  0.07086  2.67997  2.56825  7.84970
##   [15]  1.64995 15.07917  1.04514  0.70939  0.27402  1.40944  0.73637
##   [22]  0.93059  0.96485  0.77482  2.57198  1.81376  0.55347  1.62774
##   [29]  1.19745  1.58430  3.87643  1.09151  1.30636  1.44425  0.58992
##   [36]  0.04957  0.83590  2.19763  7.04100  1.88156  1.34064  1.81569
##   [43]  1.04682  0.55563  1.79401  0.74902  0.96423  0.70583  0.74817
##   [50]  0.34890  1.79717  4.24954  2.29141  0.47705  0.24827  1.09328
##   [57]  0.51698  0.53908  2.09170 73.37763  0.51025  0.56507  1.10530
##   [64]  1.86910  0.82194  1.13253  2.29253  2.47969 11.15009  6.64383
##   [71]  0.59416  2.07110  1.06697  2.13090  4.70871  1.62912  0.11015
##   [78]  1.65287  0.71150  0.63158  3.92257  2.81849  0.53542  0.99396
##   [85]  1.29265 44.85766  1.18429  1.59264  0.49987  1.22725  1.57598
##   [92]  5.73294  1.16811  8.89433  1.33643  0.76891  3.52991  1.08968
##   [99]  2.75251  1.08868  4.06202  0.68115  2.31119  0.85357  0.41879
##  [106]  0.29960  3.36740  0.67979  0.90274  0.55444  2.12515  1.41774
##  [113]  0.97553  1.40841  0.74798  0.76683  1.89309  0.61559  0.69139
##  [120]  0.28531  0.28899  0.38254  4.35004  1.17129  5.26229  0.69293
##  [127]  1.92439  0.83560  2.96995  0.69401  0.76308  1.97186  1.81555
##  [134]  0.58465  1.53410  0.27531  1.88248  0.02375 72.84202  0.75075
##  [141]  0.98914  1.77853  1.47082  1.34215  1.65417  1.30222  1.21072
##  [148]  4.20673  0.08719  0.32423  0.55925  0.78989  2.04899  0.61660
##  [155]  0.23672  0.61780  0.95685  0.53000  0.99230  1.45299  0.82631
##  [162]  0.38544  5.85364  0.41549  4.71312  4.36096  0.28740  0.27393
##  [169]  0.51848  0.34586  0.49119  0.90328  0.12073  1.00872  0.41446
##  [176]  1.58257  0.64904  5.76778  0.95560  0.24515  1.21250  1.26728
##  [183]  0.98714  0.40342  0.73577  0.88480  0.87460  1.54430  5.31884
##  [190]  9.35365  0.48029  0.33014  0.11964  1.43618  1.94440  0.60666
##  [197]  0.24184  2.10604  1.29325  0.69625  0.69856  0.60381  2.75599
##  [204]  1.06927  2.77828  1.06226 16.91860  3.38679  1.30769 20.43531
##  [211]  0.68784  1.31004  4.24499  0.65744  1.13034  4.99286  1.36785
##  [218]  0.91502  2.09799  0.24936  0.81428  0.25668  0.41348  0.30686
##  [225]  0.57910  2.36640  1.40766  0.63161  0.06494  0.92383  1.81328
##  [232]  0.94207  0.67423  1.13964  0.88503  0.97499  0.38732  0.12477
##  [239]  2.10118  0.43313  0.67826  0.86292  0.56262  1.21488  1.28194
##  [246]  0.22865  0.96134  2.40476  0.86653  1.11319  0.43028  4.16492
##  [253]  0.95693  0.41774  1.50273  0.78388  0.47508  8.47656  0.57594
##  [260]  2.13624  4.84552  0.77733  1.33349  5.55847  0.56407  1.12874
##  [267]  0.51519  1.79577  0.83586  1.39015  0.79246  1.14674  1.32633
##  [274]  0.93311  3.91990  2.26458  1.45475  0.78226  0.28473  0.67970
##  [281]  4.50272  0.50779  5.02726  1.18971  1.23721  0.54775  2.59422
##  [288]  1.55121 10.78423  0.38756  0.53215  0.31035  0.81901  1.49007
##  [295]  1.74691  0.88567  0.14765  3.38074  0.61910  0.16830  1.14044
##  [302]  0.62193  0.50588  1.16297  2.95926  1.00643  1.13926  0.99177
##  [309]  0.33654  2.70157  0.84933  0.53331  0.55977  0.78919  0.28914
##  [316]  1.39879  0.84837  0.89279  0.94827  1.54997  2.51000  0.39271
##  [323]  1.28863  0.78760  3.94675  0.63611  0.73817  1.30297  0.83499
##  [330]  1.97757  1.66304  2.95353  0.54176  0.76118  1.44315  0.30535
##  [337]  0.52968  0.55088  1.27481  0.30713  0.82293  0.81324  3.82530
##  [344]  1.45106  1.70000  1.73205  1.42263  1.31734  1.17335  0.97494
##  [351]  1.34496  0.63171  0.04271  0.26941  1.71345  0.26591  1.02947
##  [358]  0.42542  0.34701  0.37860  1.29830  2.19666 14.57102  1.04001
##  [365]  2.20105  1.79780  0.72827  0.84328  1.10733  0.81106  0.18169
##  [372]  1.55396  0.65073  8.56198  0.62268  2.47256  2.42332  0.50124
##  [379]  0.54957  0.28197  0.38172  1.07771  0.96352  1.07337  0.33011
##  [386]  0.74628  0.89096  0.52295  5.42823  0.20447  0.56029  0.36778
##  [393]  2.08306  1.30787  1.96806  1.52389  2.59241  1.39394  1.90264
##  [400]  2.86137  1.51923  0.18113  2.09122  0.79059  0.91385  1.77884
##  [407]  2.17736  0.14908  0.88040  2.19823  0.42839  0.24249  1.39052
##  [414]  0.28228  0.59608  0.80730  3.14714  3.95923  0.68540  3.47903
##  [421]  0.94347  2.23486  0.62101  1.49973  0.12084  0.95791  0.49981
##  [428]  1.22327  1.05162  1.06025  3.67564  1.25093  0.95827  0.91490
##  [435]  2.55809  5.07153  0.61035  0.54670  0.30997  1.01609  2.48149
##  [442]  1.09582  3.03277  1.45907  0.93372  1.27113  0.93934  0.73463
##  [449]  0.33331  1.78283  0.81473  8.75099  0.31146  1.07010  2.48410
##  [456]  0.35208  1.01645  3.07986  0.31622  0.21534  0.46396  2.63020
##  [463]  0.42798  0.45049  1.32488  1.13114  0.43304  0.38114  1.00617
##  [470]  1.72662  0.72964  0.68453  0.44122  0.54811  1.68479  0.26390
##  [477]  1.27583  0.49399  0.66015 12.92382  0.61218  1.27042  1.81307
##  [484]  3.09689  0.26154  0.92076  0.29241  0.14988  0.42244  0.92438
##  [491]  0.14389  0.58951  2.10919  0.45137  1.33496  0.84256  1.45766
##  [498]  0.78631  0.21248  0.25152  0.68581  0.40754  1.32658  0.69025
##  [505]  0.10449  1.43270  0.23875  0.76868  1.12635  1.35418  2.74749
##  [512]  0.18730  7.29542  1.09584 14.81027  1.67509  0.65790  3.45168
##  [519]  2.42701  1.10459  1.05923  0.89589  1.01888  0.22680  0.17120
##  [526]  0.69337  0.14535  0.89186  0.99992  0.53841  1.44425  0.30191
##  [533]  0.57027  1.24231  3.14075  2.33232  0.57494  3.09623  1.47045
##  [540]  1.83756  0.24230  0.61120  1.12314  1.30995  1.26776  1.13554
##  [547]  1.34457  1.14543  4.12013  2.40195  0.35704  2.79265  0.99741
##  [554]  1.83551  1.41488  1.86163  4.07625  1.24729  0.78756  0.51430
##  [561]  1.09666  0.89792  1.88007  0.52565  0.77212  4.24837  1.03900
##  [568]  0.86446  1.09983  0.54510  1.46412  1.41071  0.51995  0.31561
##  [575]  0.20929  0.66325  0.75136  0.23072  1.09245  0.38869  2.62651
##  [582]  0.54813  4.33773  3.70962  2.51575  0.89076  1.16833  4.48988
##  [589]  0.38197  0.18258  2.63894  0.51246  0.74024  0.69494  0.95235
##  [596]  2.55207  0.65687  4.37860  0.58994  0.58430  1.06163  0.58012
##  [603]  2.03593  0.20712  0.20418  1.15561  1.16331  0.72183  0.95166
##  [610]  0.46128 21.37529  1.33249  0.65567  1.76523  0.73305  1.07778
##  [617]  1.49509  0.38462  1.68522  0.44209  9.36626  1.27000  1.95315
##  [624]  0.52731  0.52321  0.55216  1.25508  0.45037  1.26101  1.51988
##  [631]  6.92317  0.39624  0.44711  0.48999  0.72636  1.97445  0.40082
##  [638]  2.13244 13.07972  0.39682  0.93477  0.42956  8.68786  0.36457
##  [645]  7.63780  0.96478  7.05689  0.78317  0.37884  0.58678  1.02789
##  [652]  0.78158  1.11916  1.87413  9.16876  3.40945  9.07578  4.92931
##  [659]  0.98816  2.74180  0.36858  7.30929  1.10293  0.74488  0.27981
##  [666]  1.74108  1.16940  0.55722  0.38824  0.52542  0.34235  3.77587
##  [673]  1.09629  0.61898  1.63553  1.12572  1.40411  2.39615  0.32347
##  [680]  0.84007  0.53147  0.67529  0.20182  1.76828  1.00267  1.80003
##  [687]  2.55248  0.20776  0.63407  1.20966  1.14115  4.68269  1.67998
##  [694]  1.08173  4.20851  1.92559  0.28790  1.52019  1.90769  0.69663
##  [701]  4.54293  1.05618  0.31658  0.56017  0.90047  1.65674  4.37469
##  [708]  1.98064  2.96049  0.37895  0.60150  2.70468  2.47506  0.60954
##  [715]  2.38334  0.75952  1.74090  1.70336  1.76779  0.77557  0.08739
##  [722]  1.26139  0.98697  0.34540  3.47736  1.03912  0.27601  2.32023
##  [729]  0.15500  1.37144 10.37655  2.02339  5.58697  0.99929  1.58832
##  [736]  1.85026  0.70120  2.29493  2.72365  0.81192  1.77236  1.04153
##  [743]  0.18644  0.74347  3.29501  8.62285  0.42415  0.62957  3.57963
##  [750]  0.83636  1.16085  0.60995  1.29545  0.67162  0.85639  1.19929
##  [757]  0.23862  0.97821 15.62690  0.45719  0.38014  1.17664  0.08340
##  [764]  0.89196  0.11157  0.26765  1.02790  1.83582  3.68026  9.46259
##  [771]  1.12904  0.94085  1.60819  0.85457  1.47863  1.12994  3.30821
##  [778]  1.10018  0.84605  0.32865  0.57440  0.14254  1.68188  0.52929
##  [785]  1.09553  0.99823  0.45552  1.47832  0.46741  2.18784  0.88051
##  [792]  0.65952  0.88516  0.17477  1.58772  0.74637  4.36240  1.13509
##  [799]  0.80586  1.52839  0.70846  0.14179  1.44799  1.08096  0.39090
##  [806]  0.14541  0.18815  1.72459  2.50366  1.41622  1.23129  0.13045
##  [813]  0.20873  6.15347  0.75418  0.73832  0.62545  1.26575  1.26199
##  [820]  1.27287  0.87589  2.18128  1.58199  0.51513  0.32177  1.36915
##  [827]  0.51573  0.81041  1.05888  1.65200  0.92732  1.56913  3.36127
##  [834]  2.06869  1.57416  7.28028  0.39169  1.82913  2.32361  0.54003
##  [841]  0.75156  0.88855  1.62894 11.05467  3.04737  0.44384  0.93516
##  [848]  2.35570  0.82904  0.48625  1.89009  0.56425  0.96465  0.37820
##  [855]  0.68475  0.98963  2.23667  0.37064  0.98696  0.66099  5.49263
##  [862]  2.66418  0.95266  4.66703  6.34369  0.37877  0.22730  0.97831
##  [869]  0.28393  2.51867  2.00307  1.57323  1.41083  1.33781  1.66518
##  [876]  0.93902  0.21066  0.06148  1.55583  0.88887  1.69250  0.40309
##  [883]  2.32604  3.34506  1.35890  1.08224  6.58758  2.36039  1.24835
##  [890]  0.25580  0.57561  1.81757  0.81201  3.30591  1.32555  7.64907
##  [897]  1.19080  1.93728  0.27364  2.19556  1.15376  0.57613  2.44933
##  [904]  0.81421  0.43021  0.56349  0.40043  0.76362  0.86130  0.58582
##  [911]  0.13720  0.39087  0.36283  0.84737  4.30943  3.48390  1.94985
##  [918]  1.36115  0.46677  0.72676  0.76595  1.23899  0.66213  0.90421
##  [925]  0.33197  3.20035  0.47943  1.44678  1.21876  0.85857  1.01987
##  [932]  1.84640  0.50963  1.27559  1.41295  1.45233  0.33034  1.10731
##  [939]  2.04228  1.84885  1.77152  0.52821  2.50382  4.19011  0.82255
##  [946]  2.54179  0.27602  0.25844  1.32933  0.18719  0.46302  0.96384
##  [953]  2.38536  0.25847  1.11053  0.97454  0.20654  2.38873  0.49115
##  [960]  0.38322  0.53771  0.17589  1.08661  0.62545  0.37292  0.89805
##  [967]  0.74382  1.01110  0.68330  0.55126  6.69966  0.32642  3.21216
##  [974]  0.98786  0.64950  0.82567  0.32082  1.24302  1.00893  0.23915
##  [981]  1.17870  0.39704  0.89433  0.64157  4.96594  3.60002  0.25902
##  [988]  0.16948  0.21712  0.26890 11.08404  0.12966  2.73711  1.96676
##  [995]  0.60714  0.67784  2.02974  1.05553  0.80607  1.75338

broken_mid(1000);

##    [1]  0.322255  0.141200  1.085977  0.623804  0.811443  0.529770
##    [7]  0.965905  1.189384  0.820636  0.796745  6.629258  0.227231
##   [13]  0.462055  2.264747  0.902481  1.046469  1.573648  0.298871
##   [19]  2.077916  0.632149  1.618123  1.111231  1.041049  2.050227
##   [25]  2.108520  0.449163  3.744006  0.110098  1.327519  0.314467
##   [31]  5.676190  4.838532  0.104966  0.267829  1.586494  1.151588
##   [37]  0.891463  1.069838  0.994441  0.424081  1.913348 23.207982
##   [43]  1.386155  5.350298  0.306479  1.104657  1.240487  1.190018
##   [49]  1.212384  0.654241  2.047802  0.375935  0.259204  0.440370
##   [55]  1.031265  0.222678  0.885377  1.352002  2.975644  1.182164
##   [61]  0.990939  0.606972  0.379292  9.551476  0.791756  6.363555
##   [67]  3.187234  1.210553  4.747519  0.936241  2.412588  1.041524
##   [73]  0.349090  0.812399  0.275306  0.933797  1.904788  1.051024
##   [79]  0.719252  0.864938  0.729287  0.526929  4.437570  0.402536
##   [85]  1.747625  0.401577  0.676794  1.059806  3.602739  0.570962
##   [91]  0.091692  1.519808  0.899945  4.279659  0.328487  0.080031
##   [97]  0.209267  1.228122  1.080289  1.229104  1.980052  4.874549
##  [103]  0.471097  0.578931  1.012199  2.032869  2.366232  1.422110
##  [109]  0.591357  0.662853  1.584586  0.574927  1.397472  0.444980
##  [115]  2.762696  1.571287  7.724632  0.147767  6.430756  1.750806
##  [121]  4.346726  0.550084  0.966217  0.739311  3.636323  0.339568
##  [127]  1.179930  0.886295  0.889011  0.709408  1.230033  1.228179
##  [133]  1.868178  4.420346  0.035829  0.432341  0.288990  1.017961
##  [139]  2.212504  1.023775  1.657401  1.282991  2.900762  0.835184
##  [145]  7.274901  0.886616  1.984836  3.579716  4.302805  3.480448
##  [151]  0.593828  2.913033  0.293322  0.920961  1.550210  1.306320
##  [157]  0.475861  1.993096  0.211390  2.663560  0.089896  1.080537
##  [163]  1.573126  0.401371  2.416856  0.252405  2.765592  0.161719
##  [169]  0.436918  0.903816  1.251253  0.808504  0.656969  0.974620
##  [175]  0.734419  2.835345  0.562441  1.772804  0.295671  0.291225
##  [181]  3.625152  1.619629  0.629854  1.203694  0.736750  1.312668
##  [187]  0.735381  3.932228  0.591734  7.146354  2.108900  9.887110
##  [193]  0.926371  0.614001  0.309974  7.011100  0.316956  2.093694
##  [199]  0.330528  1.051197  0.785034  4.469091  0.385531  0.985950
##  [205]  0.690376  1.497433  0.591673  0.204466 25.082331  0.515451
##  [211]  2.761092  0.953457  0.890351  0.924046  1.938005  1.435206
##  [217]  0.062337  4.472942  1.167162  1.652112  0.544284  0.165284
##  [223]  1.144979  0.354727  0.436849  1.406551  2.048680  0.744982
##  [229]  0.698943  0.004326  4.729857  0.640422  2.065270  2.031757
##  [235]  0.923193  1.864237  4.358654  0.209194  1.486704  0.831425
##  [241]  2.367072  1.016282  1.585206  2.405133  0.504569  0.787704
##  [247]  1.308600  1.031980  0.672245  1.107138  0.516702  2.070934
##  [253]  0.058504  1.528081  0.433642  0.769405  1.601610  0.275986
##  [259]  0.537074  1.113431  1.235571  0.640431  2.655827  0.603014
##  [265]  1.532991  0.460045  0.405745  0.302518  1.663375  1.066332
##  [271]  2.968217  0.246018  0.833340  0.706960  0.501554  0.159228
##  [277]  0.373620  0.948054  2.481779  2.132777  1.073604  0.683826
##  [283]  1.761104  0.419961  2.336197  2.286809  0.241736  1.113967
##  [289]  1.242026  0.766113  0.324337  2.131794  0.684840  1.169331
##  [295]  0.868979  1.661715  0.373945  2.085954  0.826555  0.437046
##  [301]  0.412207  0.329371  0.521230  1.161300  0.794156  1.251875
##  [307]  0.605576  1.832616  1.638627  0.482892  2.399181  1.777116
##  [313]  0.825365  3.239784  5.761181  0.762282  1.285606  0.626491
##  [319]  0.856215  0.493111  0.377289  1.555606  1.676406  8.854415
##  [325]  0.460957  1.140601  0.785659  1.383426  0.235470  0.602355
##  [331] 18.464199  1.648292  1.131854  0.621628  0.841498  0.389113
##  [337]  0.937467  0.722307  2.312080  0.068426  1.044213  5.731464
##  [343]  3.125405  1.930472  0.227399  1.979205  0.286241  1.659933
##  [349]  0.680164  1.858545  0.834309  5.675118  3.745129  1.939868
##  [355]  1.107453  1.371037  0.294892  0.845039  0.868105  6.816163
##  [361]  1.366351  0.431964  2.505118  1.650220  0.748393  2.352678
##  [367]  3.430987  2.087975  0.458076  1.595662  0.530192  1.614902
##  [373]  2.779906  3.562829  0.398103  0.548651  0.781328  0.114131
##  [379]  0.816761  1.806140  2.285767  0.362438  2.892457  1.170797
##  [385]  0.045944  0.702213  1.946455  0.830842  0.823689  0.289481
##  [391]  0.926960  0.471896  7.114598  0.877381  0.525449  3.311556
##  [397]  0.124780  3.773773  1.016668  1.632321  2.349857  1.873965
##  [403]  0.408917  0.481814  0.262371  3.944025  0.807530  4.707066
##  [409]  0.279146  1.078604  0.725712  3.016339  1.664037  0.432073
##  [415]  4.943902  1.339553  1.046350  1.417814  0.650121  1.310716
##  [421]  0.888362  2.812863  0.124965  0.500838  1.747511  0.805025
##  [427]  0.551558  1.015164  1.101000  0.520461  0.589439  2.422964
##  [433]  1.377965  4.271120  0.929212  1.383673  0.919500  0.489480
##  [439] 36.021949  0.835140  1.925033  1.039387  0.250648  0.883063
##  [445]  9.983064  2.523968  2.322200  0.201048  0.556576  1.717040
##  [451]  0.699621  2.256913  0.416451  1.807168  2.711026  0.768018
##  [457]  2.253304  0.449618  0.297204  0.176013  0.636115  0.874608
##  [463]  3.664810  1.534225  1.367329  2.250048  0.559999  2.932623
##  [469]  1.144402  0.436346  0.741202  3.119168  1.388214  1.051399
##  [475]  0.950081  0.738871  0.353931  2.674564  0.428423  0.521151
##  [481]  1.395067  1.029351  1.190517  0.105767  0.686773  2.722206
##  [487]  0.603100  1.070296 16.242483  0.473048  3.227868  0.768302
##  [493]  0.254146  1.730526  1.459178  1.392311  0.430502  0.439603
##  [499]  1.768549  4.132381  0.845313  2.089220  1.634614  2.835087
##  [505]  0.289078  0.620939  0.096126  0.381024  0.875698  0.202351
##  [511]  1.383486  1.260466  0.449180  0.583346  1.475288  1.182306
##  [517]  0.391413  6.351017  0.346069  2.056405  0.596298  0.887126
##  [523]  0.914196  0.442802  0.694383  1.747834  0.890308  1.265133
##  [529]  1.109120  1.237077  0.234706  0.334535  0.962643  1.360064
##  [535]  3.564651  2.446970  0.981289  0.978872  0.385140  3.094409
##  [541]  2.228605  1.397517  0.229400  2.185587  0.302310  1.713923
##  [547]  0.944014  0.493187  0.157574  3.551497  7.520227  0.504368
##  [553]  0.545667  0.698955  3.036759  0.434246  0.351675  2.060007
##  [559]  1.627778  0.732011  1.241630  0.081202  0.034229  0.832733
##  [565]  1.060684  2.577991  1.019642  2.313550  3.074110  0.541661
##  [571]  3.719216  8.400286  1.099105  1.363868  0.452514  4.060773
##  [577]  0.471067  0.351393  2.037525  0.460950  0.524103  6.089805
##  [583]  1.716375  1.293826  0.566312  0.831224  0.571063  0.825678
##  [589]  2.521514  0.673349  0.682756  0.341153  0.640481  1.542293
##  [595]  4.409034  0.896777  0.353300  1.542322  0.848902  2.943087
##  [601]  1.110910  1.456982  1.318206  0.388550  0.588729  1.396556
##  [607]  1.745838  0.490516  0.277954  1.310975  0.954921  3.075255
##  [613]  1.509294  0.814645  4.048622  4.435393  0.124529  0.156273
##  [619]  0.925700  0.602103  1.531178  2.137678  1.059943  0.330479
##  [625]  0.392140  2.618472  0.492030  0.589049  2.876720  1.957197
##  [631]  0.288594  7.262101  0.709335  0.888095  1.556054  1.214367
##  [637]  0.374393  0.300389  0.847071  1.209039  0.655392  0.403242
##  [643]  0.301217  1.982645  0.732260  0.873141  0.425834  0.996035
##  [649]  0.661964  1.822217  0.486309  4.749489  2.241829  1.492815
##  [655]  1.178356  0.965261  1.515787  0.707812  1.650693  4.988287
##  [661]  1.152652  0.745291  1.888872  2.529972  0.762541  0.356672
##  [667]  1.824608  0.431586 11.447695  1.197377  0.932835  1.240183
##  [673]  1.572180  0.668166  0.735708  0.329775  0.700391  1.348242
##  [679]  1.182893  0.421162  0.711681  1.043857  2.310097  1.561242
##  [685]  0.485300  0.741315  1.102733  0.340504  1.298313  1.278744
##  [691]  1.359661  0.364500  0.538305  0.929216  1.702502  0.427099
##  [697]  0.930890  2.585130  2.121923  0.470123  0.120563  5.947563
##  [703]  0.464736  0.939699  0.919968  1.419901  1.862997  0.324954
##  [709]  0.950932  0.762564  1.133895  1.290964  0.385401  3.342993
##  [715]  0.162141  1.371051  1.603061  0.580077  0.570989  1.419970
##  [721]  0.968028  1.810185  0.769096  0.714906  0.505572  1.901214
##  [727]  3.187947  0.337138  1.714359  0.999176  1.563375  0.990722
##  [733]  1.664752  2.244855  0.331068  1.122917 10.078441  3.967642
##  [739]  5.263914  1.314226  0.423959  1.846185  0.552163  1.521742
##  [745]  1.622104  0.997010  0.633155  1.459303  0.464927  0.481344
##  [751]  0.367492  0.620397  0.626149  0.364005  0.722510  3.151093
##  [757]  0.410955  0.883355  1.014739  4.541330  0.444774  4.217241
##  [763]  0.221378  1.142902  0.420141  0.933012  3.129248  2.058777
##  [769]  0.303674  4.223894  1.138205  2.270164  6.818503  0.236944
##  [775]  0.183962  0.584493  0.969821  0.215926  0.808793  0.322639
##  [781]  1.344308  1.632163  2.392584  2.089386  1.423052  2.109622
##  [787]  3.287534  0.518229  3.136040  2.651453  5.124139  1.300825
##  [793]  0.764381  2.839392  0.893934  2.308302  0.933679  1.616558
##  [799]  0.744645  0.775481  4.773761  3.390300  0.400538  0.421310
##  [805]  0.468478  0.289904  0.876374  1.313035  1.328864  3.491348
##  [811]  0.531277  3.675009  1.242246  3.921391  1.722319  0.702994
##  [817]  1.831339  1.502943  1.501407  1.628567  0.663233  1.131096
##  [823]  2.155138  0.344328  0.209155  3.392043  0.717599  0.936573
##  [829]  3.183270  0.365580  1.761162  0.100145  1.405642  0.311486
##  [835]  2.897896  0.905293  3.866765  4.021231  0.705375  1.150356
##  [841]  3.805803  3.343853  0.780531  3.454470  1.377770  0.499206
##  [847]  0.427706  1.951166  0.748759  1.563521  1.146926  0.767081
##  [853]  0.541885  2.455612  1.234953  0.814780  4.830002  0.823416
##  [859]  0.418330  0.620619  1.416602  0.815311  0.506989  0.464918
##  [865]  0.786873  0.030270  5.577949  0.426657  0.160056  1.249242
##  [871]  1.487963  0.974126  1.478412  0.626236  1.927698  0.028895
##  [877]  0.542652  1.070310  2.206559  0.815230  1.582999  0.813125
##  [883]  1.834778  0.679119  2.275749  0.302593  0.561522  1.405524
##  [889]  0.400384  0.590525  0.739128  1.295277  0.894924  0.381470
##  [895]  0.138286  0.281254  1.108995  0.043909  1.233829  3.116487
##  [901]  1.511267  1.616468  1.719041  1.437458  1.675134  0.794893
##  [907]  0.728422  0.099569  0.638537  1.662047  1.578257  0.188937
##  [913]  0.875140  0.657091  1.093628  0.367114  1.721603  2.845343
##  [919]  0.872231  2.600872  1.238827  1.126284  0.403929  0.593360
##  [925]  1.555599  8.781913  1.306227  0.712453  0.522610  1.264927
##  [931]  2.426783  1.000260  0.326225  1.873706  0.400433  1.628831
##  [937]  0.862989  0.457386 29.099617  4.002056  0.881678  1.969697
##  [943]  1.007822  0.195572  1.351621  3.228273  1.437599  0.096129
##  [949]  0.723548  1.486701  0.706207  1.091343  0.597818  0.311314
##  [955]  0.760747  0.891793  1.388315  0.563810  1.922315  0.136843
##  [961]  1.668285  1.308169  1.126011  1.858404  0.864386  0.591228
##  [967]  2.996130  0.277134  0.932022  0.735883  1.138625  1.159589
##  [973]  0.916379  1.606633  0.502539  1.640646  7.653596  8.365650
##  [979]  0.925586  0.880721  7.916050  0.769760  3.112431  1.078061
##  [985]  0.132232  0.641999  1.321520  0.966735  0.556068  5.316833
##  [991]  0.401340  0.840099 38.758427  2.223859  0.483473  0.034987
##  [997]  1.965830  0.336686  0.853613  1.195234

broken_mid(1000);

##    [1]  2.09395  0.46791  1.37257  0.95084  0.35749  3.21035  0.24139
##    [8]  0.27210  0.30704  0.66292  1.00504  0.23580  0.91666  0.80029
##   [15]  0.73804  0.75311  2.43594  0.51651  1.36845  1.72845  0.12464
##   [22]  0.58067  0.88104  0.50655  0.93598  0.88669  1.39375  0.34256
##   [29]  1.82897  0.68006  1.02998  2.05652  0.40933  3.62885  5.32540
##   [36]  1.04395  3.01619  0.76242  1.31666  0.65728  0.29402  0.76009
##   [43]  0.37693  2.10047  0.89911  1.13429 15.78956  0.68088  2.82249
##   [50]  0.28041  1.01755  1.76040  0.26832  0.40558  3.83369  1.27545
##   [57]  0.92947  2.78837  0.87354  0.72177  1.38420  3.78163  1.20580
##   [64]  0.06685  0.79070  0.99420  0.92477  0.44235  1.41549  0.51523
##   [71]  0.51539  1.16982  0.27975  1.02724  0.78101  0.51919  2.01649
##   [78]  0.38514  6.75912  1.07027  0.32042  1.20665  0.15379  0.27310
##   [85]  0.25167  1.85904  0.60704  2.15731  0.45597  1.12329  0.39942
##   [92]  0.37575  0.06150  0.44312  0.21510  3.88466  1.11128  0.25816
##   [99]  1.37893  0.42186  0.94973  1.87522  1.50019  1.23844 21.44434
##  [106]  5.78112  1.76268  0.42059  0.41691  0.81777  2.38931  1.30421
##  [113]  1.42854  2.19588  0.46644  2.48605  0.17476  1.94966 46.62406
##  [120]  1.62207  1.41207  0.28393  1.29390  1.15372  1.29525  0.53478
##  [127]  1.62909  0.80024  0.31769  1.17951  1.74800  0.19874  3.95257
##  [134]  0.91105  0.03578  0.72448  0.56312  0.32480  0.52201  0.94820
##  [141]  2.53910  0.62630  0.90436  0.22357  0.69401  0.70603  1.14912
##  [148]  0.31708  0.13440  2.25890  0.81392  0.53222  1.63500  0.68724
##  [155]  1.38803  0.33786  2.43970  1.03343  0.62469  1.75926  2.94429
##  [162]  1.63403  0.79877  0.71239  0.15062  0.11891  1.91342  2.37849
##  [169]  4.00171  3.40728  1.77390  0.96985  0.57830  5.43320  2.86000
##  [176]  3.30267  1.44170  3.66101  0.52742  0.31688  5.53661  9.23967
##  [183]  1.09648  1.14752  0.07930  0.49554  0.87227  0.76848  2.29712
##  [190]  2.63477  0.85509  1.09826  0.30826  0.55063  0.87871  0.57244
##  [197]  1.09624  1.98740  2.47945  0.17539  1.35957  1.61902  2.58577
##  [204]  0.60359  0.21123  0.02744  1.88280  0.75176  1.27397  0.45348
##  [211]  0.90095  1.15694  0.80005  0.25473  0.69096  0.82321  0.91453
##  [218]  1.01671  0.65720  0.50573  0.18446  1.89423  0.39997  0.61546
##  [225]  1.76393  2.11234  1.93453  0.53539  0.51249  1.21347  0.74856
##  [232]  0.37724  1.30857  1.11159  0.52913  4.17654  0.07457  0.74766
##  [239]  1.48626  0.11699  0.76242  3.13381  1.84757  2.19582  1.02230
##  [246]  0.39826  0.95689  6.28176  0.64185  2.87033  0.22994  2.56407
##  [253]  0.37478  1.23147  1.18305  0.60936  0.60532  0.28020  0.60951
##  [260]  0.25630 62.60741  2.54066  0.11471  1.55306  0.28769  1.11117
##  [267]  0.27576  0.60265  0.33383  0.81664  4.11465  4.76119  1.02349
##  [274]  0.58123  0.52868  1.05536  0.26249  2.08244  3.27502  1.90145
##  [281]  1.57856  0.74604  1.45837  0.74970  0.72012  1.30610  0.91650
##  [288]  1.64444  1.80369  8.69627  1.11551  1.17343  0.12857  0.15902
##  [295]  0.63904  4.33709  1.22538  0.63147  1.36026  0.33435  0.80822
##  [302]  1.21058  0.99684  2.03989  1.15964  3.80062  3.62221  0.02347
##  [309]  0.97958  0.66643  1.32151  1.44173  0.39328  0.94809  0.88221
##  [316]  0.27096  0.25350  0.94248  4.20829  1.41300  1.66100  2.84017
##  [323]  0.60806  0.33805  5.48311  1.15244  1.11442  0.24697  1.94199
##  [330]  2.31407  0.35770  1.18104  1.45231  0.67831  2.18550  0.50676
##  [337]  1.98524  1.66610  0.76644  0.44427  3.66910  0.91391  1.01791
##  [344]  0.76821  1.04845  1.54886  3.60850  0.64368  0.96544  0.68312
##  [351]  0.71036  1.34024  5.13290  5.82197  0.15199  0.75189  1.14790
##  [358]  1.50768  2.13340  0.31188  0.52789  0.86872  0.60568  0.49249
##  [365]  3.09831  1.34315  2.03754  0.54428  1.84004  0.12134  4.09238
##  [372]  0.92691  0.64030  0.24219  2.40498  0.53902  0.77544  0.41815
##  [379]  0.15371  1.45412  0.74723  2.46001  1.54640  1.23835  1.79026
##  [386]  1.79871  3.39918  0.96378  2.91389  2.14770  0.01209  1.14113
##  [393]  3.46921  0.52366  0.04256  0.11611  0.94006  3.28648  1.57413
##  [400]  0.93255  1.72386  5.22393  0.93955  2.18901  4.07241  0.47828
##  [407]  1.67210  0.76952  0.06012  0.25054  1.72564  2.88604  1.24953
##  [414]  0.43818  1.18625  0.43641  0.55463  1.75915  0.15489  0.71387
##  [421]  0.89146  0.92773  1.30130  1.90001  0.62047  1.54638  0.27506
##  [428]  0.76260  1.04704  1.16807  0.20534  0.28060  1.05264  2.50282
##  [435]  1.92871  1.15125  1.28614  0.72356  2.46390  1.71107  2.60731
##  [442]  0.58926  1.19157  1.64283  2.00418  0.66267  0.68269  1.93487
##  [449]  1.81865  0.11315  1.76534  0.71750  1.85949  0.36877  1.12809
##  [456]  0.55475  0.80558  0.88447  0.78193  0.35702  2.03589  1.81808
##  [463]  1.01446  0.31368  1.19485  1.02937  2.84433  0.36641  1.26742
##  [470]  0.71907  0.77136  1.93256  0.85238  0.33435  0.60007  1.30012
##  [477]  1.70538  0.14687  2.12654  1.75442  2.42669  1.83436  0.29412
##  [484]  2.00691  0.46768  1.04671  1.62887  0.56709  0.80072  0.67781
##  [491]  1.14821  1.12060  0.99515  3.56958  2.30908  0.20603  1.11075
##  [498]  1.28745  0.18176  0.70624  2.69148  0.29768  0.99330  0.81144
##  [505]  4.85146  2.89934  0.18136  3.57629  1.14540  2.30972  1.01112
##  [512]  0.44750  0.25466  1.08301  1.12737  1.12652  1.10923  1.70495
##  [519]  1.10913  0.74481  0.94155  0.47998  0.28047  2.93701  0.35230
##  [526]  0.77824  1.06538  0.97743  0.23844  0.61658  0.59562  0.61650
##  [533]  1.39070  0.21574  0.49443  0.89429  0.61668  1.68117  3.11721
##  [540]  0.34364  0.48220  1.47217  1.15047  1.87291  1.08342  1.44080
##  [547]  1.45931  1.03107  0.58047  3.36567  0.62726  0.40128  1.57874
##  [554]  1.31783  0.26240  5.07449  1.96130  0.32339  1.13010  0.43839
##  [561]  0.25122  6.79059  0.72849  3.56632  0.82862  3.21029  2.53532
##  [568]  0.61993  0.62995  1.07484  0.99803  0.21208  3.42441  0.84103
##  [575]  3.88810  1.34212  0.24311  3.55162  0.40076  0.39379  1.71063
##  [582]  1.37256  4.41462  1.00333  0.08707  1.25684  2.61154  0.80520
##  [589]  0.67708  2.40390  8.52196  0.50943  0.52954  2.54320  0.65260
##  [596]  1.05923  0.20026  1.39251  0.83609  1.11270  0.83912  0.29845
##  [603]  0.49591  0.77926  1.20358  0.96433  0.96495  1.69140  1.43439
##  [610]  0.44213  0.97281  6.89977  1.15171  0.84611  0.88393  1.33187
##  [617]  2.84707  0.07007  0.80732  2.76550  0.68970  0.83772  0.19314
##  [624]  0.52033  0.26097  2.19391  0.29059  1.97598  4.10999  0.54713
##  [631]  1.30902  0.99348  0.98320  1.46056  0.41569  1.00893  1.76149
##  [638]  5.33590  0.22182  0.83248  0.58451  0.61686  0.55703  7.31416
##  [645]  4.72105  0.34240  1.91029  0.67484  0.78874  0.18327  5.53875
##  [652]  2.16061  1.10567  0.28637  1.20888  0.64012  0.91615  0.21368
##  [659]  0.59869  1.32738  1.98239  5.50773  0.51155  1.73803  0.34134
##  [666]  0.86068  2.68116  0.63090  0.94183  0.52281  0.75467  2.56360
##  [673]  0.57242  0.93558  0.69169  0.27022  0.94719  1.88753  5.83303
##  [680]  0.05846  0.26748  1.19450  1.85456  0.89286  2.34711  2.94896
##  [687]  0.10748  1.98356  0.81546  1.32951  0.92335  1.00875  0.98779
##  [694]  0.39527  1.06626  0.21826  0.42567  0.62201  0.83825  1.16707
##  [701]  0.29260  2.60459  0.60180  0.84430  1.00988  2.37485  0.84654
##  [708]  3.35104  0.10240  2.58064  1.51143  0.73062  0.91538  0.61844
##  [715]  0.99516  0.47932  4.75974  2.30043  1.14306  1.09651  0.89219
##  [722]  1.05885  0.74624  0.95762  1.09724  0.34640  5.38561  0.64157
##  [729]  0.06084  2.40564 12.68249  1.29549  0.63053  0.68867  0.91586
##  [736]  0.27845  0.57180  0.71854  3.17081  0.74532  0.28258  1.20470
##  [743]  0.45074  2.82210  0.95667  3.00341  1.17988  1.31944  0.30668
##  [750]  4.19533  1.94439  2.00715  1.65668  3.66476  1.87337  1.33190
##  [757]  1.07786  0.30176  0.35980  0.51928  0.35981  1.43301  1.56105
##  [764]  0.92085  0.29479  1.72933  2.68613  1.86580  1.32023  0.66567
##  [771]  1.40884  0.99401  3.57074  1.32255  1.00804  3.44250  2.27610
##  [778]  0.37122  2.17384  1.57894  3.05799  0.59796  0.09209  0.67641
##  [785]  0.89624  1.92361  1.67233  4.88795  1.74061  0.93621  0.74854
##  [792]  0.41404  0.79493  0.06837  0.68418  6.76335  0.16905  0.18823
##  [799]  2.41168  0.85309  0.27997  1.00508  0.40687 10.11609  2.36164
##  [806]  3.14014  0.63016  0.15987  3.85570  0.19058  0.72745  0.81321
##  [813]  0.23388  2.47797  1.34006  0.25913  0.81517  0.61303  2.94723
##  [820]  2.27293  1.47098  0.30738  0.27216  0.78340  0.93149  0.21687
##  [827]  0.85136  3.35750  0.71897  3.11281  0.53165  0.19041  0.70782
##  [834]  3.14217  0.56826  0.44243  1.22796  1.20196  6.20479  0.42652
##  [841]  0.71115  3.37527  1.14670  1.24891  2.96308  0.88256  2.55438
##  [848]  0.98446  0.85626  1.30948  0.37259  0.37712  0.42286  0.03722
##  [855]  0.96464  0.32212  2.99290  0.53132  1.61541  2.01544  0.69070
##  [862]  0.38610  1.49191  0.68612  0.35490  0.63950  1.23350  0.75522
##  [869]  0.10718  1.70780  0.28196  1.17061  1.04498  3.07881  0.51253
##  [876]  1.30762  0.86384  0.84200  0.68671  0.54984  0.91134  0.24165
##  [883]  0.30266  0.70440  1.17048  2.53993  3.02071  1.71405  2.15541
##  [890]  0.81212  1.30397  0.32877  0.97663  1.14735  3.96020  0.46747
##  [897]  1.63076  7.16179  1.18867  2.31076  0.64724  1.14166  4.87282
##  [904]  0.84302  1.38450  0.64272  0.37491 11.53646  1.20184  2.04879
##  [911]  0.60062  0.94897  1.15871  0.14390  1.20521  0.16598  1.05227
##  [918]  0.80673  0.18291  2.07128  0.47338  1.27434  0.62174  1.57638
##  [925]  1.69518  0.74998  0.37397  0.70657  1.26948  3.52495  2.67061
##  [932]  0.97779  1.03785  1.24234  1.10888  1.66645  1.32121 14.08890
##  [939]  2.00505  1.99366  0.10314  0.44677  0.09748  0.43070  1.24331
##  [946]  1.16322  0.89326  3.15840  0.27919  0.47913  0.69726  6.51187
##  [953]  0.95549  1.05694  0.36388 17.60939  1.34069  2.07382  1.06710
##  [960]  1.99757  0.82350  0.91748  1.03720  1.53865  0.32519  1.91616
##  [967]  1.25008  0.31134  2.26148  1.41369  0.42045  5.38261  3.84967
##  [974]  0.66254  0.94484  0.35236  0.63184  0.77600  6.26446  0.73931
##  [981]  0.93795  1.01246  3.86334  0.72922  0.64143  0.79051  0.56313
##  [988]  1.65269  8.93568  6.38491  4.61399  1.08082  0.41518  0.15404
##  [995]  0.44338  1.88462  1.96700  1.60587  1.51045  1.06153

broken_mid(1000);

##    [1]  0.24083  0.21847  0.23066  0.43715 14.26654 35.33225  4.10909
##    [8]  0.87074  0.86087  1.76985  1.18930  1.30046  0.33460  2.62628
##   [15]  3.38563  4.69665  0.14958  0.40443  1.13376  0.15151  3.35488
##   [22]  0.50183  0.35356  0.38857  1.14816  0.44938  0.16879  1.65393
##   [29]  0.85168  0.89074  0.45260  0.87088  0.36420  0.59979  3.52807
##   [36]  2.41778  1.18267  0.56756  0.71279  0.48855  0.35111  0.37401
##   [43]  4.92788  4.66129  0.79863  2.93350  1.41344  6.97763  1.53969
##   [50]  0.72520  0.33913  0.60525  0.58969  0.84383  2.22269  1.70184
##   [57]  0.06794  5.79198 13.50333  1.85772  6.20411  0.47932  0.48919
##   [64]  1.08914  2.86862  0.17968  1.02980  2.11966  0.17414  0.57316
##   [71]  0.67771  1.94647  1.03985  0.04639  1.21333  0.72438  1.32518
##   [78]  0.57699 11.19618  0.53522  0.44409 27.46538  2.56324  0.96999
##   [85]  0.60892  2.14467  2.80380  4.15997  0.32039  0.94819  2.35350
##   [92]  2.30177  0.52124  5.71456  0.83157  0.21827  0.41171  1.96738
##   [99]  0.56096  5.33994  1.40182  0.40522  1.59194  1.06668  1.31041
##  [106]  0.60261  0.50930  1.72500  0.85299  3.94373  0.53012  2.81306
##  [113]  3.05703  0.79606  1.11681  1.89439  7.51068  1.13430  0.55908
##  [120]  0.60222  2.22645  4.84161  1.05438  3.11463 12.14334  1.93037
##  [127]  1.39874  1.10008  0.55679  2.65369  1.54320  0.92066  5.94454
##  [134]  1.32774  8.54458  0.24867  4.06333  7.08292  2.06819  0.46912
##  [141]  0.72561  2.69031  1.03251  2.43916  0.33999  0.76764  0.53148
##  [148]  1.41603  2.34804  1.51400  6.81052  4.09574  1.88668  0.53769
##  [155]  0.35410  1.64784  2.09352  0.38389  2.07507  0.77417  0.33969
##  [162]  0.90967  0.29008  4.87769  2.42879  1.25444  5.17920  3.63088
##  [169]  0.37666 16.24537  0.32833  1.02435  1.17895  0.73885  0.70222
##  [176]  0.93270  4.15060  0.44300  0.68481  0.70396  0.80938  1.12276
##  [183]  0.96609  0.19766  0.88675  1.59284  0.90538  2.64576  0.17805
##  [190]  4.36874  1.48923  0.33166  0.67659  1.32710  0.88412  2.50777
##  [197]  1.09608  0.35208  0.60472  1.04250  0.75540  0.71803  1.98314
##  [204]  0.49541  1.17122  7.26282  1.81489  0.47646  0.06256  0.81489
##  [211]  0.82343  0.66361  2.91579  0.94351  2.15631  0.99083  2.01047
##  [218]  0.50520  1.07809  0.48729  2.18033  0.78335  1.17282  0.90891
##  [225]  0.98806  0.39164  0.79464  1.64795  1.70756  0.31155  0.57869
##  [232]  2.94648  1.08144  4.66010  0.41786  2.56809  0.21883  2.03365
##  [239]  2.00895  1.39313  0.81707  1.00536  0.97557  1.12174  0.29497
##  [246]  1.59117  1.07204  1.13240  0.29659  0.35829  0.17921  2.93194
##  [253]  0.89895  3.43246  0.20482  0.68932  0.79366  1.32419  0.09668
##  [260]  5.64532  7.24012  4.26869  0.93171  1.82850  0.45671  2.05653
##  [267]  0.24094  1.81507  1.31091  1.69061  0.56974  1.22721  4.40185
##  [274]  0.52122  0.52309  0.96303  0.53533  0.46223  1.07986  0.67222
##  [281]  0.47297  2.04338  0.93264  0.86386  3.43106  1.67673  3.70566
##  [288]  2.71583  0.74238  0.24918  5.70477  1.36070  0.42711  1.06728
##  [295]  0.71514  2.21491  0.20807  0.80769  1.23594  0.31857  1.76105
##  [302]  0.92877  2.44893  1.61415  0.96575  4.48043  3.29076  2.50782
##  [309]  0.48881  0.22163  0.51617  0.36719  2.54691  1.59475  1.32906
##  [316]  0.95765  1.14914  0.55631  0.86893  0.62373  0.90984  0.58422
##  [323]  0.83643  0.31618  0.50047  1.38884  1.39767  3.84049  3.24314
##  [330]  3.30720  1.34772  1.70813  0.63188  0.13884  1.30026  4.35559
##  [337]  0.61645  0.97314  0.39840  0.71259  1.83127  0.53187  2.37416
##  [344]  0.58739  0.89770  2.83436  0.61096  3.08732  3.16697  3.93897
##  [351]  1.85704  0.59252  0.77513  0.56975 16.69405  1.91530  1.37144
##  [358]  0.44375  5.99206  1.26590  1.45298  1.02575  1.89271  1.20617
##  [365]  1.48080  0.50508  0.05683  1.68283  1.40271  0.68933  0.49543
##  [372]  1.14879  0.75421  0.06236  7.36480  0.96311  0.63340  6.58510
##  [379]  1.07484  1.49564  0.35609  0.54068  4.40666  0.27748  5.40248
##  [386]  0.52198  0.41463  1.42493  2.03902  0.88897  0.89316  1.13535
##  [393] 36.57811  1.22273  1.08689  2.20262  0.71671  0.61896  2.13329
##  [400]  0.49829  1.42628  0.21439  2.64818  0.41204  2.25770  4.01364
##  [407]  0.66926  4.48124  0.95957  0.78117  1.36566  1.11847  7.95619
##  [414]  1.90888  0.65919  3.72579  2.54422  1.12264  0.33011  0.60313
##  [421]  0.77099 18.79557  0.54390  1.26124  1.00709  1.26058  0.88272
##  [428]  0.90938  0.20681  0.81640  0.95718  0.35623  1.15454  2.54732
##  [435]  0.78584  0.37206  0.90653  1.30667  0.81556  2.08483  1.64168
##  [442]  0.23522  4.45788  1.86134  0.50106  2.22442  0.83286  3.22538
##  [449]  1.27477  1.29195  4.55446  3.17381  6.37997  0.63558  0.71371
##  [456]  0.56522  0.35729  0.73505  0.55489  0.32581  0.36168  1.32829
##  [463]  0.43532  1.13762  0.53549  0.83784  0.53154  1.54868  6.60181
##  [470]  2.88533  5.60767  0.41399  1.48720  1.41532  1.21824  1.02108
##  [477]  1.62892  0.38324  4.77250  0.22650  0.89258  1.09431  0.43875
##  [484]  0.57054  0.42643  0.50076  1.09733  2.05628  5.88538  0.48890
##  [491]  4.47435  0.19404  2.25586  1.01657  0.41864  1.77677  0.40847
##  [498]  0.70916  2.06734  1.52864  1.02024  0.95449  1.65142  0.66636
##  [505]  1.24368  0.38222  1.14353  0.68335  0.28871  0.13285  1.05652
##  [512]  2.97978  2.38245  0.88897  0.26037  0.54066  1.15458  0.59729
##  [519]  1.98472  0.21957  0.54692  0.63379  0.63258  2.26138  0.98002
##  [526]  0.54842  0.47929  3.78823  0.73671  2.47790  1.21821  2.31244
##  [533]  0.18200  4.40489  3.43253  3.56614  0.45378  7.34336  1.45520
##  [540]  0.33090  1.62065  0.90234  1.21911  0.19448  0.80703  0.30033
##  [547]  1.72275  0.86771  5.44010  1.72952  4.57607  0.25609  1.25526
##  [554]  0.70907  1.18588  0.42370  4.14016  0.61946  1.29606  0.89562
##  [561]  0.72492  0.18286  2.01088  0.41914  6.45022  1.27483  1.94132
##  [568]  1.13795  0.62990  0.50833  0.42250  0.12340  0.82715  0.39623
##  [575]  0.93102  1.23173  1.47992  0.80817  0.16211  2.07306  1.19668
##  [582]  0.52968  0.76936  0.53970  0.95071  0.42452  0.36339  0.68471
##  [589]  0.38443  2.21881  0.81864  0.62899  0.76004  0.85773  0.85854
##  [596]  0.62383  1.27606  2.73295  0.92085  1.02746  0.66181  1.01946
##  [603]  1.89933  0.21921  1.95163  2.25440  1.40443  1.22575  0.77742
##  [610]  0.76444  0.70331  2.56870  0.40456  1.75409  0.56964  0.85174
##  [617]  1.02256  1.10301  0.27154  0.85477  0.33246  1.14955  1.28701
##  [624]  1.75816  1.02346  3.31396  0.83788  0.35629  0.72250  0.49443
##  [631]  1.26926  3.53834  1.20397  1.57654  1.24340  1.02913  0.20390
##  [638]  1.00120  0.30639  1.21295  8.50478  1.48906  1.04565  0.77461
##  [645]  0.23418  2.04621  2.51005  2.63361  1.43317  1.59660  2.25904
##  [652]  0.77950  1.44438 53.28792  2.10217  1.71419  0.45468  1.06497
##  [659]  1.12479  0.57103  0.97180  2.23109  0.44003  0.66882  0.59240
##  [666]  0.07902  3.52029  1.55257  0.72062 13.25686  0.64330  0.51386
##  [673]  0.18952  0.26396  0.87021  0.84126  0.41067  0.14443  0.46342
##  [680]  0.28931  3.12522  0.89463  0.85706  1.05077  0.51476  1.06855
##  [687]  2.38756  2.01298  1.02867  1.93059  1.31517  0.99179  1.65639
##  [694]  2.84407  0.66315  4.99907  4.30605  4.41301  0.82821  5.85154
##  [701]  0.25912  1.15338  1.38782  1.25153  1.85581  0.21116  0.58949
##  [708]  1.29491  1.65640  2.53344  0.51825  0.92718  0.68826  1.13491
##  [715]  2.24729  2.13651  0.78242  1.36348  1.40238  0.64386  1.97794
##  [722]  1.69337 16.22117  0.20394  1.04949  1.95815  0.54469  1.20736
##  [729]  4.34991  0.60438  0.75786  0.48066  0.01188  1.67402  0.39221
##  [736]  1.07840  1.98748  1.03439  2.30867  0.28495  2.25578  0.75263
##  [743]  1.55900  2.27888  5.52533  0.22403  1.19719  2.03768  1.33360
##  [750]  0.52842  2.88967  2.75198  0.53177  0.14176  4.41973  2.03072
##  [757]  0.83542  0.76985  1.80549  0.28713  1.26574  0.24677  1.65811
##  [764]  1.43190  1.03827  0.96363  1.55439  0.55147  1.93387  0.63068
##  [771]  1.21492  1.50865  0.58365  0.05026  0.33390  0.14994  1.03197
##  [778]  1.19624  1.01949  0.56526  1.97243  1.29734  0.42812  0.44547
##  [785]  0.34672  0.05326  1.35416  1.67430  0.25795  0.22684  0.58051
##  [792]  2.07708  2.81256  0.40341  0.78153  0.84096  0.46412  1.50668
##  [799]  1.45122  5.43878  1.61198  1.28470  2.58476  0.57200  1.43862
##  [806]  0.77813  0.10825  1.40817  0.32651  0.31262  2.82452  0.21582
##  [813]  1.25353  0.71369  0.80221  0.26297  3.83356  1.13028  1.04047
##  [820]  1.53938  2.23894  1.47684  0.83566  1.21910  0.65554  1.17507
##  [827]  2.02938  0.56653  0.06529  0.46829  3.46334  4.47950  3.35597
##  [834]  0.33196  2.29160  1.06220  1.61718  0.53872  2.09176  3.44339
##  [841]  1.95771  0.76819  0.78540  0.25916  4.20874  1.36438  3.35792
##  [848]  6.36317  1.47870 35.44219  2.86385  1.61757  1.09952  0.51630
##  [855]  2.12875  0.71885  0.50948  3.87270  1.15402  2.93477  0.04090
##  [862]  2.77330  3.01754  1.11099  1.29326  2.06031  0.44443  1.32078
##  [869]  1.82287  0.63403  0.48050  1.29579  0.36786  1.98055  1.09522
##  [876]  1.87982  2.41355  1.12183  0.08768  0.21180  1.22690  0.69969
##  [883]  3.79200  1.00077  1.64123  1.31185  0.13353  0.44852  0.11919
##  [890]  3.26896  0.58001  0.84648  1.50805  4.33475  0.32857  0.49832
##  [897]  2.85210  0.88680  3.76282  0.67367  1.03722  5.52342  1.00831
##  [904]  4.98026  0.20445  0.35688  0.95112  3.35157  1.46785  2.43282
##  [911]  0.61074  0.43582  0.71885 27.51134  0.46859  0.86354  1.61536
##  [918]  0.17923  1.26523  1.42468  0.38708  0.48393  0.58676  1.10408
##  [925]  0.17960  0.73910  3.30057  1.52123  0.58944  0.96754  0.96002
##  [932]  0.73447  0.25192  1.43276  0.37690  3.64882  0.83493  5.04822
##  [939]  9.25529  1.21895  0.37178  0.78389  8.05159  0.20915  2.77683
##  [946]  0.75899  1.15505  0.52683  0.23042  0.63574  0.66902  4.21676
##  [953]  0.19653  0.62048  0.61749  0.83920  0.99321  0.55243  0.69898
##  [960]  0.14727  1.36195  0.77938  0.19716  2.72785  5.65413  0.38724
##  [967]  0.75386  0.62558  0.85164  2.90770  0.39012  0.81253  1.70763
##  [974]  1.84626  2.79252  1.96905  0.53541  3.37714  1.12229  1.36244
##  [981]  0.55558  0.81127  1.06122  1.05517  0.43997  0.31804  2.91863
##  [988]  0.38392  1.17178  0.51270  0.98800  3.43913  0.85500  2.04175
##  [995]  2.74106  2.05836  0.35341  0.93583  0.14771  0.43136

broken_mid(1000);

##    [1]  8.13160  0.27082  1.60244  0.72781  1.45061  0.61788  0.88592
##    [8]  0.87140  0.08346  0.87327  3.16763  1.48660  1.00835  0.82371
##   [15]  0.50788  2.48431  1.52966  0.56336  0.43543  1.86948  0.97948
##   [22]  0.56614  0.36198  1.34140  0.33055  0.53044  0.90900  0.31041
##   [29]  0.39500  2.92998  0.76888  2.39158  1.34615  3.31763  1.37714
##   [36]  0.17123  1.10046  0.73623  0.68493  0.60257  0.40641  0.39859
##   [43]  0.20672  2.98720  0.64256  0.21473  5.42292  0.51664  0.92662
##   [50]  0.67137  0.73113  0.15043  1.76889  0.55677  0.52438  0.45581
##   [57]  1.92976  0.85515  0.48098  0.53178  0.03971  0.21074  3.77257
##   [64]  0.68413  4.50402  4.40059  0.79353  0.67395  0.66225  0.86607
##   [71]  4.61926  1.51003  1.52984  1.42307  0.88742  1.07747  1.83167
##   [78]  1.35441  2.66719  0.81416  2.93868  3.78494  3.03535  0.65286
##   [85]  0.80059  6.11187  0.80115  0.75846  2.89196  0.54036  1.10940
##   [92]  0.63826  4.72538  4.52588  0.21526  9.67840  1.28540  1.89297
##   [99]  0.17653  1.45534  1.14873  0.55169  0.47145  8.06271  1.15449
##  [106]  0.58650  0.28519  0.74813  6.90404  4.35668  1.67944 10.02633
##  [113]  0.57386  0.38453  0.44401  0.05953  7.44277  1.81291  5.18283
##  [120]  0.28344  0.56445  0.97041  0.33881  0.63044  5.37467  0.99035
##  [127]  1.73632  0.03084  0.11284  0.65792  3.13377  0.82290  0.27967
##  [134]  3.22032  1.02944  0.48066  1.42182  0.63277  0.40820 12.70629
##  [141]  1.27068  4.03271  2.15813  0.63908  0.53218  4.11434  0.79608
##  [148]  1.23648  0.62539  0.53550  1.94597  1.35110  2.25328  1.69692
##  [155]  0.79553  4.27390  2.96998  0.32258  1.28312  2.59216  0.90623
##  [162]  2.05726  2.17856  0.20723  0.21600  0.17336  0.23739  1.63143
##  [169]  0.37212  2.61118  1.11215  1.30198  4.23328  6.61200  1.30888
##  [176]  1.91351  1.17223  1.74792  1.07498  1.07381  3.01805  0.44882
##  [183]  0.81330  2.53515  0.07379  0.91621  0.50453  0.90676  1.39551
##  [190]  0.59013  2.65466  1.23683  0.90050  0.49153  0.37830  1.67727
##  [197]  0.13810  0.67789  4.56392  0.35544  1.75448  1.65344  0.29280
##  [204]  5.13358  0.96677  0.61990  1.76530  1.47422  0.85961  1.02757
##  [211]  0.11314  1.16816  2.91284  1.38094  0.97149  2.73688  2.80810
##  [218]  5.44306  1.46459  0.59013  0.16284  1.14803  0.41980  0.77594
##  [225]  2.46083  1.92695  0.82645  0.18062  0.77597  8.95702  1.15547
##  [232]  1.58183  0.59026  1.39109  4.51730  1.19963  0.60130  3.76372
##  [239]  0.80841  1.23509  1.05899  1.70216  0.95754  0.73713  1.23375
##  [246]  0.41229  0.95526  0.44247  0.81333  1.41130  1.51538  0.70618
##  [253]  1.16559  0.59295  3.80265  3.36014  0.58236  0.81956  1.91341
##  [260]  5.88665  1.65825  0.99997  1.23158  5.61367  0.82625  0.80317
##  [267]  0.28499  0.43576  1.59532  3.93269  0.12265  5.53353  1.87571
##  [274]  0.37694  0.42441  0.59752  0.24629  2.13936  0.71662  0.99775
##  [281]  0.44595  1.27652  0.67988  0.30026  1.00977  1.01867  1.28834
##  [288]  0.70710  0.04962  1.23585  1.30765  1.29644  1.91317  0.17565
##  [295]  3.10646  1.34152  1.51087  5.16716  2.45885  3.71546  0.29795
##  [302]  1.83657  4.97761  2.56090  0.61689  0.16850  0.75401 10.20139
##  [309]  0.22760  1.70925  1.07115  1.20161  0.36106  0.59191  2.82541
##  [316]  0.42598  7.01470  0.15821  6.57353  1.55597  4.24863  8.17947
##  [323]  1.25615  2.48938  0.37523  3.14546  1.99977  0.47950  3.64709
##  [330]  1.02072  0.43685  1.18351  1.35887  0.94238  3.97020  0.17864
##  [337]  1.04793  1.45096  0.67734  4.36294  3.33848  0.96918  1.01850
##  [344]  0.85086  1.53291 15.63891  2.65917  2.04238  0.35472  1.25404
##  [351]  1.09230  0.81734  0.69740  1.51853  3.26818  0.78516  0.40071
##  [358]  2.69746  0.87291  0.22756  0.76794  0.69771  2.00318  4.83098
##  [365]  0.73814  1.19770  0.59717  0.66413  2.62630  0.41277  1.35942
##  [372]  1.40858  0.67940  0.70490  0.99674  0.87326  1.10787  0.94802
##  [379]  8.94149  3.97118  3.38065  1.09590  2.17650  0.88115  0.09452
##  [386]  1.31732  0.31460  0.57184  0.74873  0.66281  0.56288  0.52568
##  [393]  0.27588  2.01621  0.38859  1.29920  0.21464 15.82824  1.68484
##  [400]  2.35043  0.70236  1.89172  0.32536  1.69944  1.65379  3.70425
##  [407]  1.11986  0.21578  0.52478  2.64962  0.24717  0.80375  0.14216
##  [414]  0.30887  0.43247  0.92559  0.38516  0.33311  0.87935  0.88871
##  [421]  0.82999  0.83042  1.10700  0.97878  0.18588  0.31178  0.96661
##  [428]  1.31536  0.38657  0.57803  0.39502  1.82528  0.07459  0.46552
##  [435]  2.55902 12.82438  1.22825  0.71589  0.24992  6.97400  1.82799
##  [442]  1.28028  0.38932  1.43548  1.87223  0.26695  2.53223  0.67656
##  [449]  0.99736  2.31186  0.70957  2.36861  1.56784  0.17957  1.08654
##  [456]  0.06987  0.61030  0.72133  1.72308  0.38257  0.34798 23.81799
##  [463]  1.42739  1.74917  1.50166  0.93972  0.82414  0.24602  3.43455
##  [470]  2.22912  1.62638  1.70550  0.06452  2.11717  0.33661  0.43738
##  [477]  0.98532  1.37978  0.17915  0.85068  0.76171  0.85174  0.89913
##  [484]  1.57029  2.69319  2.31776  5.31021  1.06902 19.36657  2.03840
##  [491]  1.24333  0.88507  0.56243  1.27493  1.73230  1.71909  3.48857
##  [498]  1.18370  0.91958  0.88518  0.30516  2.53170  1.21183  1.53381
##  [505]  0.17707  0.72938  0.74645  3.10125  0.81747  0.90392  0.52727
##  [512]  1.02017  2.64272  5.09164 13.72549  1.87950  1.67281  0.80642
##  [519]  2.27538  0.23695  1.96503  1.76014  0.40434  0.23580  3.37369
##  [526]  0.29984  0.69056  1.09444  0.77341  0.51921  0.50640  0.50867
##  [533]  1.52584  1.49990  1.78899  2.04013  0.59405  1.21902  0.93509
##  [540]  0.53840  2.59251  6.25668  1.44029  0.20482  5.73954  0.26299
##  [547]  0.28886  1.03614  0.75244  0.80196  0.45552  1.34503  0.73949
##  [554]  0.28573  0.76002  0.78474  0.67822  2.31914  0.45556 13.40782
##  [561]  0.99489  5.94934  2.45871  0.31107  2.39578  0.70495  1.50350
##  [568]  2.50741  1.25056  6.86481  8.85915  0.05626  3.84202  0.45415
##  [575]  1.27354  0.67057  0.35067  0.46531  0.11110  2.88416  1.66689
##  [582]  1.04664  0.22943  2.21732  0.73300  0.35094  3.89190  0.79149
##  [589]  1.02680  0.47741  2.29802  2.28357  0.19353  0.44705  1.18395
##  [596]  0.44291  1.20918  0.37146  1.28035  0.64715  0.56718  2.28522
##  [603]  1.08497  0.33267 11.74237  2.50008  4.08477  4.75107  1.04897
##  [610]  0.91036  3.96532  0.42854  0.32831  0.23360  3.69977  1.37280
##  [617]  0.15369  0.51104  1.60149  0.42359  1.36671  0.55499  4.01645
##  [624]  2.83497  1.66766  5.49328  0.76567  1.03160  1.64714  4.15313
##  [631]  1.42034  1.06826  0.10398  1.06280  0.91346  1.55707  1.29169
##  [638]  1.43411  0.77939  0.92076  1.50839  0.09440  0.96597  0.43684
##  [645]  0.10328  0.62001  0.17984  0.79968  1.85450  0.73292  0.42279
##  [652]  1.40827  0.65748  0.42926  2.29909  1.05340  1.09930  0.04760
##  [659]  1.82589  1.58966  0.33509  0.44747  0.87570  0.52070  0.11522
##  [666]  1.37233  1.54351  0.76489  0.97022  1.33586  0.39680  2.46661
##  [673]  0.90742  0.76130  1.36709  1.82534  1.11157  1.43026  2.39003
##  [680]  1.56707  1.22432  0.13472  4.22830  5.79693  0.38518  5.12036
##  [687]  1.18936  1.98123  5.30233  1.25663  1.56927  0.73890  1.30332
##  [694]  0.21176  5.79118  1.59325  0.67194  1.01622  0.85325  1.16576
##  [701]  0.66511  0.50825  1.09021  2.81477  0.77640  0.06686  1.36006
##  [708]  0.86066  0.07599  0.78219  0.54325  1.55180  0.60478  2.33217
##  [715]  0.52387  0.65109  0.30905  6.95599  5.32525  1.34818  0.70511
##  [722]  1.95220  2.36934  1.69605  2.94124  1.73794  1.06918  0.38086
##  [729]  1.69282  0.22235  0.35873  1.18635  0.08559  1.19172  0.13694
##  [736]  0.93223  3.72391  0.66021  0.59920  3.34889  0.82833  0.80088
##  [743]  0.50633  0.77807  0.92566  1.75444  1.88936  1.74439  0.53456
##  [750]  2.71863  2.79621  0.54357  0.69681  0.66160  0.38233  0.81244
##  [757]  4.90884  0.53303  2.77757 18.57964  1.02817  0.76888  1.37141
##  [764]  0.54253  2.17197  1.63995  0.68397  5.54053  0.68784  1.49392
##  [771]  0.87001  1.94579  1.25345  1.14354  0.75302  3.18702  2.98445
##  [778]  0.94783  0.53465  1.09905  0.81947  0.98914  0.80003  2.10646
##  [785]  0.31036  1.31620  0.66929  0.25390 38.19273  1.78415  1.31196
##  [792]  0.55695  2.80631  0.29827  3.02265  0.17990  0.46763  1.47541
##  [799]  0.10548  2.70793  0.38921  0.27152  4.63784  1.53797  0.29204
##  [806]  0.79028  0.55807  1.04274  0.87039  0.85713  0.47079  1.75485
##  [813]  0.67191  1.54317  0.23169  7.11140 68.78723  1.05971  3.88386
##  [820]  9.50166  2.20640  4.56853  0.85974  7.65029  1.25422  2.53016
##  [827]  1.33656  0.24790  3.03557  0.48826  0.58859  1.16907  1.05981
##  [834]  3.42881  1.63783  0.35913  0.27735  0.81424  1.77770  0.77874
##  [841]  0.87448  1.05544  0.16817  0.42116  0.98317  1.53635  0.29695
##  [848]  3.80042  0.72624  0.28132  0.28727  0.70365  0.92374  0.65225
##  [855]  3.91257  0.57658  2.05328  5.63398  0.17774  0.21042  2.10412
##  [862]  0.39264  1.08645  3.71307  1.22670 10.44967  1.09840  0.46294
##  [869]  1.19567  0.55456  1.78812  2.65057  0.53276  1.62057  0.81217
##  [876]  0.56013  1.53001  1.81370  0.91255  0.90128  0.48784  0.31650
##  [883]  0.27641  1.04136  0.44030  1.24391  0.21233  0.46468  1.48652
##  [890]  2.17685  1.19096  1.19055  0.23545  1.28393  2.49991  1.17278
##  [897]  0.71443  0.69850  1.42314  1.98125  0.75566  2.29637  0.23076
##  [904]  0.49800  0.82055  3.91028  0.27626  0.51821  1.20728  0.72984
##  [911]  1.35843  0.81908  0.87466  1.02303  0.72269  2.56132  0.44504
##  [918]  0.92841  0.54141  0.39077 17.87590  1.77488  1.39943  2.59850
##  [925]  2.46564  2.30054  3.17907  0.63620  0.80803  0.37296  2.83297
##  [932]  1.57306  0.65783  0.92342  5.60032  1.45374  0.93311  1.75953
##  [939]  1.74833  0.77408  0.55834  2.93778  2.20845  0.17077  4.24563
##  [946]  0.21595  0.48763  0.99748  0.69940  0.64691  6.60300  0.55914
##  [953]  1.80491  1.18890  0.29121  0.72737  1.06661  0.63952  1.12523
##  [960]  0.89566  0.85236  0.75869  7.68724  1.14498  1.41128  9.18425
##  [967]  0.29040  2.94384  2.77506  0.80195  0.84501  0.41850  2.10868
##  [974]  4.25703  2.11004  0.48806  1.16376  0.60351 16.35650  3.05469
##  [981]  0.08580  0.36413  3.08468  0.63975  1.21717  0.62531  1.24468
##  [988]  0.98664  0.16335  2.35807  7.85132  2.07941  1.26354  0.52493
##  [995]  1.03842  1.00412  0.30331  0.97754  2.01976  2.62715

broken_mid(1000);

##    [1]  2.25222  0.89171  1.03482  1.48528  1.63599  0.58943  1.19140
##    [8]  2.24065  0.50876  1.35907  1.20760  4.12045  2.17143  0.88004
##   [15]  0.71057  0.21436  0.85244  0.92506  1.04368  0.57101 18.15349
##   [22]  1.31292  4.08000  2.23127  3.79875  1.14623  1.12008  0.15129
##   [29]  0.23144  0.59049  0.89183  1.17071  0.18871  5.09382  0.61098
##   [36]  1.54777  0.81929  0.20363  0.10810  0.26094  1.30450  0.54985
##   [43]  0.53256  2.79883  2.63372  0.52080  3.48110  0.94557  8.90784
##   [50]  2.00902  1.62954  0.13948  0.88043  1.03001  3.71013  3.40392
##   [57]  1.36095  1.10619  1.13134  0.33927  2.05541  3.79214  1.30535
##   [64]  1.01359  0.53508  5.48178  0.33098  0.67619  0.67688  2.11284
##   [71]  0.76291  0.65845  0.24584  3.42843  2.48667  1.29863  3.56770
##   [78]  1.12931  1.13822  0.07609  1.24122  2.69054  8.94922  1.12193
##   [85]  3.29561  0.84326  1.35657  0.31036  0.53382  1.61632  3.45314
##   [92]  1.04562  0.50013  0.43635  1.69118  0.99951  8.17202  1.36473
##   [99]  0.52450  3.08723  1.21266  1.91920  1.26404  0.56471  0.81002
##  [106]  3.47892  0.62513  0.93487  1.97798  0.46026  2.53787  1.99100
##  [113]  6.09117  0.49686  2.68236  2.87573  0.72400  0.87868  0.78606
##  [120]  1.10964  0.78527  0.36449  1.37115  0.37487  3.11352  1.63956
##  [127]  2.29534  0.69873  0.76458  0.05153  2.26259  3.60248  1.17805
##  [134]  2.22052  2.17166  0.80749  4.56801  1.57255  0.33612  1.93844
##  [141]  0.27472  1.11373  3.51247  0.27214  1.42266  3.30779  0.33552
##  [148]  1.17468  0.87837  0.86711  0.69360  1.25631  0.68751  1.29043
##  [155]  1.47496  1.10142  1.16997  3.78824  0.72855  0.94595  3.25074
##  [162]  0.75045  3.28385  1.07863  0.50711  0.86276  0.55128  0.58943
##  [169]  7.00621  2.00121  0.43261  0.91769  0.64893  0.23739  1.34415
##  [176]  0.59946  0.05756  1.08725  0.52343  2.53072  0.84333  2.30286
##  [183]  2.09436  0.16965  1.44092  1.59499  1.77524  4.40364  2.26688
##  [190]  0.48677  1.21490  2.98343  0.82086  0.07800  0.43345  0.68144
##  [197]  0.64965  0.51174  0.78163  2.09094  0.91212  7.14750  1.44935
##  [204]  0.33487  0.50940  2.28390  3.68159  4.18322  1.57593  0.47759
##  [211]  1.67436  0.67310  4.20942  0.19570  4.43695  0.44856  1.30220
##  [218]  0.39583  0.66806  0.55837  1.91041  0.31136  0.85669  0.51456
##  [225]  1.35021  0.33652  0.37549  0.73514  0.71513  0.40928  0.32976
##  [232]  1.64765  4.36811  1.58879  1.41994  0.46858  0.56241  1.04628
##  [239]  2.91311  3.67609  0.77498  0.88680  2.49105  0.66328  0.13956
##  [246]  0.76676  2.18102  3.18334  2.79831  0.26764  1.63247  0.63791
##  [253]  3.45835  1.88267  7.12115  0.44745  0.97051  0.46358  5.44786
##  [260]  4.52163  0.77341  5.54552  0.75090  2.11564  0.46211  0.55666
##  [267]  0.54651  0.39998  0.27186  0.93598  0.42220  0.16149  2.48712
##  [274]  0.88347  1.03333  2.66968  0.57171  1.80523  0.27386  0.67577
##  [281] 15.82730  0.10218  3.94443  1.13965  1.03763  0.95848  1.77169
##  [288]  2.13093  0.39358  0.30658  1.64196  0.83049  1.27423  2.45079
##  [295]  3.24198  0.88876  0.50831  0.65913  1.29020  0.22717  1.48745
##  [302]  0.80286  0.12746  0.31150  0.98895  2.52801  0.74138  0.41564
##  [309]  0.45615  0.73949  0.19924  0.33436  0.18686  1.01206  2.92748
##  [316]  1.22983  0.85814  1.03128  0.25554  1.34009  2.76631  1.09038
##  [323]  0.98159  2.09005  0.46110  0.83649  1.49491  1.39188  5.42685
##  [330]  0.23404  3.58678  0.47687  1.90801  0.76798  0.24873  0.18003
##  [337]  2.20901  0.56946  6.41248  1.40553  0.86479  1.76523  0.74861
##  [344]  0.62961  0.82973  1.82298  0.75844  0.77897  0.72805  0.06473
##  [351]  0.43762  6.41751  1.56413  1.47267  0.44872  0.54205  2.18461
##  [358]  2.51051  2.31889  1.75659  4.61851  0.47031  0.66587  0.98658
##  [365]  1.45325  0.74396  0.21041  0.92901  7.74423  2.32724  0.73276
##  [372]  1.42712  1.08734  1.05595  0.73434  2.46715  5.14698  0.69979
##  [379]  0.61086  7.74252  0.65009  2.04916  0.56555  0.71739  1.88839
##  [386]  0.69416 27.26164  0.72730  0.96763  0.18870  2.41419  1.29937
##  [393]  0.75587  0.56682  9.41780  0.30055  2.85750  0.76714  6.59324
##  [400]  4.96564  0.86562  0.45178  0.85997  0.47052  1.30424  0.65394
##  [407]  2.17662  1.14362  1.65483  5.09448  0.89679  0.80735  0.34138
##  [414]  3.74744  1.49619  1.00838  0.07517  0.77657  1.77005  0.33345
##  [421]  0.82527  0.39862  1.09003  1.38255  1.85720  1.31989  1.18461
##  [428]  0.82941  1.36903  1.54586  0.50421  0.83972  0.67398  0.86226
##  [435]  1.25984  1.49677  0.25635  0.24352  0.62900  0.20302  3.09385
##  [442]  1.70370  0.76892  0.29393  4.26425  0.81656  0.86740  1.37362
##  [449]  8.90372  0.86885  0.52035  0.94096  1.82712  0.28107  1.39576
##  [456]  1.29952  4.21264  1.11057  0.47504  0.31816  0.34334  1.32818
##  [463]  1.07061  0.64356  0.19498  2.19825 13.88001  1.28599  0.38559
##  [470]  1.14958  1.20903  0.09455  2.26784  4.02104  2.07425  2.20422
##  [477]  1.35410  0.76770  2.25290  0.15373  1.78747  3.06470  0.43972
##  [484]  0.27954  1.11932  0.64397  1.17521  0.01561  0.90427  0.44879
##  [491]  0.69619  0.73936  0.51069  2.46050  2.79189  0.55254  1.68627
##  [498]  1.09456  0.83978  0.43771  0.70354  0.63634  0.69564  0.66981
##  [505]  1.78818  0.45224  0.07671  0.66836  0.40423  0.37517  0.35526
##  [512]  0.94553  2.18461  1.98814  0.21914  1.21692  1.54461  0.43346
##  [519]  2.30584  0.69287  2.22705  0.23615  0.59876  3.73919  0.37006
##  [526]  1.94167  0.87145  0.20910  1.05150  0.77840  0.15279  0.84528
##  [533]  0.53532  2.22364  0.55421  1.02875 12.10690  0.39076  0.78028
##  [540]  2.01527  0.87298  2.70303  0.05829  0.36394  1.22883  1.16302
##  [547]  1.65485  1.14957  0.27049  0.70383  2.53651  2.07476  2.27408
##  [554]  1.00774  0.24743  0.76756  2.72733  1.01097  2.24279  0.68001
##  [561]  0.77648  2.16329  1.99478  1.07593  0.11200  2.56778  0.24257
##  [568]  1.63483  2.43110  1.41510  1.60645  0.28737  0.16586  7.10434
##  [575]  2.46453  1.35936  0.15099  1.05521  6.20843  0.88962  0.37510
##  [582]  3.06923  0.49593  0.82405  3.06325  1.96544  0.61078  1.76979
##  [589]  1.36868  2.76047  1.57420  0.40880  0.10214  0.52124  0.19481
##  [596]  0.80741  1.44194  1.70463  7.52895  0.50456  8.27937  1.29300
##  [603]  0.17577  0.76627  0.62555  0.42591  1.02331  0.49005  5.86675
##  [610]  0.63930  1.59048  0.04138  1.26372  0.61350  0.90630  0.47075
##  [617]  0.29979  0.53167  0.82908  0.75902  0.24178  0.71017  0.34425
##  [624]  1.39310  0.46721  1.01045  1.30516  7.15397  0.35995  1.20958
##  [631]  0.63999  1.61066  0.52121  0.51003  2.59854  0.13849  2.69203
##  [638]  0.53313  3.47092  0.72908  1.21589  0.45561  0.49360  0.78201
##  [645]  0.49089  0.44828  2.06179  9.02459  0.39602  0.21079  0.73750
##  [652]  0.80789  0.91046  4.99935 10.62599  1.10600  0.69693  0.88885
##  [659]  2.39935  0.35249  1.11989  0.65471  7.89512  0.57192  0.32445
##  [666]  0.31586  1.47503  0.42308  1.21087  1.42860  0.94952  0.66913
##  [673]  0.57552  2.20973  0.53433  1.25088  2.62177  0.64148  1.04102
##  [680]  0.59612  0.37139  2.40857  3.41063  3.50474  1.01625  1.62005
##  [687]  0.09417  0.38597  0.48433  0.44241  1.30644  0.34529  1.11253
##  [694]  0.82622  1.65363  0.85073  0.46029  1.53408  0.67620  2.70652
##  [701]  0.60357  0.53605  2.93777 14.00626  0.53091  0.99078  0.95716
##  [708]  0.62669  1.18102  0.57701  0.45264  2.20422  1.24474  1.75323
##  [715]  2.27714  2.23228  0.70666  1.68046  0.98601  0.86060  1.59309
##  [722]  1.58687  0.13203  1.06092  0.23265  0.94022  0.84903  0.86796
##  [729]  0.49458  6.11061  3.36496  1.14902  1.68885  1.69836  0.83012
##  [736]  0.94800  0.21321  0.63065  0.31773  1.03548  0.45157  1.18845
##  [743]  0.57393  2.12075  1.02777  2.38532  2.22227  0.68158  1.19718
##  [750]  0.41613  1.40431  0.10559  0.59712  0.53060  0.60068  1.94720
##  [757]  0.18067  2.84363  1.04503  1.03638  0.48950  0.39919  2.00775
##  [764]  0.93322  3.12649  0.60017  1.47984  2.01698  0.22598  1.00355
##  [771]  0.95954  1.71370  0.89782  2.55651  0.49121  0.44482  0.18113
##  [778]  0.87004  5.86375  4.54457  4.04719  1.06437  1.89791  1.89858
##  [785]  1.41480  0.50551  3.05493  3.01665  5.86798  1.17333  0.31665
##  [792]  0.96801  1.86772  0.20366  5.49056  0.74918  2.24644  0.63037
##  [799]  0.05234  2.06721  0.58995  0.57126  3.64363  3.89882  0.74337
##  [806]  2.39092  8.15322  1.90887  0.66289  1.61736  2.02764  0.68708
##  [813]  0.41624  2.03317 16.57436  0.42401  0.68024  0.56240  0.55636
##  [820]  1.62508  1.13890  0.76817  0.50208  2.16088  1.64426  4.98024
##  [827]  2.33213  0.51877  2.11411  1.08199  0.57327  1.40175  0.30701
##  [834]  0.07530  0.19351  0.36985  1.09337  0.79000  1.71544  0.43280
##  [841]  0.13539  0.53515  0.27285  0.89984  2.68088  2.41280 14.86525
##  [848]  5.93110  1.22433  1.41198  1.53443  0.66870  1.45061  0.91285
##  [855]  1.21196 56.15911  1.63262  0.87469  0.93447  3.42390  1.21260
##  [862]  7.17907  0.23413  1.29075  0.92300  0.54321  1.60115  2.45308
##  [869]  1.38829  5.67988  0.47647  0.16642  0.13342  5.83418  0.39612
##  [876]  2.00656  0.19783  2.00302 23.21451  0.23084  1.17293  1.17085
##  [883]  0.17397  0.42459  0.97087  1.53303  0.16758  0.33856  1.34190
##  [890]  1.77135  1.47117  1.49433  0.99883  0.70044  2.50178  0.91711
##  [897]  0.51707  0.75890  2.93512  5.26177  0.73283  0.50188  1.43816
##  [904]  0.55483  1.74463  1.34464  0.04200  0.61215  0.93962  0.16288
##  [911]  2.86121  1.08014  4.06788  0.66752  1.21882  0.72580  0.77430
##  [918]  0.60933  0.90326  0.19652  0.88725  1.96321  1.11505  0.60818
##  [925]  0.19169  0.96179  1.87509  1.26113  0.19442  0.19719  3.83393
##  [932]  0.34491  0.50622  0.69365  1.53948  1.79988  2.31968  0.16866
##  [939]  0.75898  0.27278  0.37509  0.54405  0.25990  4.87461  0.40648
##  [946]  0.81539  1.03969  2.09792  0.26640  0.87028  0.80930  1.02587
##  [953] 11.20600  0.45527  0.06216  0.45722  0.74506  0.82173  1.04397
##  [960]  0.22251  6.44076  0.90728  0.05849  0.97333  0.96413  0.41839
##  [967]  0.25043  0.37558  0.42613  2.52882  0.14670  0.92449  1.10228
##  [974]  1.05896  0.96626  0.36017  1.94962  0.95149  3.95480  2.34852
##  [981]  0.54615  0.76613  1.77726  0.49659  1.72229  1.01182  3.65010
##  [988]  0.51694  2.56151  0.82795  3.75908  0.21851  0.40243  1.74747
##  [995] 13.21933  4.02009  0.69781  0.77374  1.51912  2.42516

broken_mid(1000);

##    [1]  1.57830  0.17054  0.74501  0.58378  0.36663  4.02498  0.53859
##    [8]  0.62691  0.93841  0.28954  1.12931  0.60570  0.45919  0.28623
##   [15]  1.29159  1.44380  0.46406  1.56617  1.62097  3.12085  0.89747
##   [22]  0.10345  0.74898  1.18222  2.13678  1.01927  1.79565  1.41146
##   [29]  1.08331  0.29492  1.67502  0.55649  2.20120  0.40393  0.94118
##   [36]  0.47786  0.89771  0.24532  0.41496  0.78863  0.58128  0.67131
##   [43]  3.40199  0.66152  1.23146  2.36046  0.23728  0.78609  0.34711
##   [50]  2.00225  4.27916  1.16320  1.14321  0.19052  0.96495  1.88313
##   [57]  3.23895  1.78441  0.01147  4.59369  1.52918  0.57392  0.81939
##   [64]  0.28845 11.75079  1.60728  0.23107  1.83799  1.45777  0.55108
##   [71]  1.95236  0.10768  1.91865  0.53147  1.50797  0.72183  0.95301
##   [78]  0.89471  0.89379  0.42078  2.47415  1.36628  1.03126  1.04227
##   [85]  1.04638  0.11502  1.04900  4.44689  1.29324  0.60616  1.30007
##   [92]  1.00599  4.81258  0.77391  0.12925  0.18139  0.81100  0.62785
##   [99]  1.31693  2.54429  2.09787  4.40935  2.41316  0.46338  1.58163
##  [106]  2.19972  0.32083  1.09446  2.74942 40.03151  0.62079  0.36062
##  [113]  1.01686  4.96375  2.06088  1.25434  2.41240  0.78583  0.11275
##  [120]  0.58154  1.71673  0.57930  0.14460  0.80643  1.24918  1.11692
##  [127]  0.49900  2.14972  0.86050  0.19109  2.09800  1.35609  4.23870
##  [134]  0.17490  0.91594  0.21557  0.61039  1.06975  0.47551  1.36185
##  [141]  0.98815  0.47917  1.14757  0.43000  0.78954  2.93978  0.26660
##  [148]  0.41072  1.13376  0.32132  1.57659  0.52393  0.49154  0.11487
##  [155]  2.01374  0.15329  0.97004  0.53301  0.13719  1.81765  1.10308
##  [162]  0.46012  0.97643  1.40042  1.53597  1.38516  1.00849  1.57704
##  [169]  0.68029  1.23096  1.30127  0.22722  0.92843  0.51462  0.42893
##  [176]  0.20596  9.43167  2.24575  0.84555  1.40057  0.46913  1.57790
##  [183]  1.02922  0.77751  0.72429  2.97942  0.71424  0.24231  0.75015
##  [190]  0.64434  4.80971  1.19960  0.09964  1.31593  2.00995  0.74818
##  [197]  4.14428  0.89074  2.20632  1.28281  0.80785  0.73791  0.92259
##  [204]  0.91604  0.56490  1.46895  0.60729  0.76610  0.67037  0.34505
##  [211]  0.49591  0.33358  2.91692  0.04553  0.10245  0.84971  3.00907
##  [218]  0.82046  0.14253  0.69871  0.13859  0.16734  0.72020  0.77175
##  [225]  1.19974  1.24542  2.12647  0.71099  0.68842  0.12587  6.14241
##  [232]  1.28203  1.69790  0.14232  3.22798  0.22790  0.19017  1.04545
##  [239]  4.86702  0.76723  0.65456  2.17934  2.56675  1.34299  1.88423
##  [246]  0.56622  0.59108  1.04243  2.16484  1.40525  0.39817  1.24799
##  [253]  3.65338  0.26124  1.91538  1.11450  1.21941  1.00056  1.10644
##  [260]  0.86805  0.69630  2.06407  0.38130  1.38121  1.89154  1.18650
##  [267]  2.11119  1.56805  1.34312  0.36260  0.47627  0.71649  0.33915
##  [274]  1.07311 16.46833  1.79781  0.54270  2.66747  0.89810  0.64201
##  [281]  9.81392  0.86904  0.14095  1.28204  2.13016  0.83633  1.38918
##  [288]  2.20102  1.68298  0.73885  1.10984  4.64513  0.87652  1.68651
##  [295]  0.59144  0.58565  1.10356  0.85901  3.05749  0.47855  0.56620
##  [302]  0.66264  0.57817  3.87300  0.89124  1.78554  0.46631  0.07147
##  [309]  0.90235  1.25290  1.55968  0.25094  0.41426  0.27055  1.22648
##  [316]  2.09067  1.55186  1.72654  1.44425  1.13339  0.91427  0.51566
##  [323]  2.36761  1.03608  0.28793  0.41376  0.57925  0.06947  2.26772
##  [330]  0.78605  1.63780  3.69471  1.65485  2.65545  0.52999  0.74072
##  [337]  1.73173  0.44858  0.78832  0.90392  1.93431  1.95776  0.44600
##  [344]  0.64583  0.84979  0.27419  0.34446  1.17067  0.76400  0.90615
##  [351]  0.89628  0.87891 16.72288  2.61392  0.88225  1.13297  0.23374
##  [358]  1.64275  2.95036  1.89038  0.34495  3.68886  1.72587  1.02583
##  [365]  0.75236  0.81905  0.65930  0.41860  0.32519  3.15989  0.31897
##  [372]  2.09854  0.53425  3.82061  0.58464  0.35850  2.58588  1.16914
##  [379]  3.45521  0.01745  1.82503  0.18212  5.88938  1.03414  1.37140
##  [386]  1.74940  2.06451  2.62908  1.78382  0.94384  0.80300  1.29024
##  [393]  1.44178  0.21543  0.94075  0.13880  1.26647  0.62835  1.89163
##  [400]  0.70495  0.19858  0.55227  0.77494  0.82285  0.96856  1.38367
##  [407]  0.50797  1.54508  3.12558  9.72564  1.21260  1.67927  0.43755
##  [414]  1.00537  6.60363  8.34263  1.44424  2.10440  2.31031  1.81092
##  [421]  2.73499  1.34554  3.82053  7.67457  0.27685  2.58316  6.13646
##  [428]  0.65745  0.93713  0.44045  1.14118  1.24664  0.45369  0.99683
##  [435]  0.49062  0.88928  1.01436  1.00401  0.13870  1.88260  0.83296
##  [442]  0.39004  1.90847  0.47813  0.68459  6.21874  0.69696  1.34182
##  [449]  0.47542  0.21604  2.41845  4.28062  0.68527  2.30942  1.44371
##  [456]  0.69472  0.76826  0.93978  1.09841  3.59876  1.48807  0.28952
##  [463]  0.86721  0.59688  3.73769  0.70229  1.00322  6.91527  1.89174
##  [470]  0.73606  0.57396  0.30915  0.78867  7.29295  1.62985  0.60998
##  [477]  1.04626  2.42286  0.89509  0.45565  0.52834  0.86892  2.54921
##  [484]  4.73945  2.34767  4.17607  3.00160  1.05453  0.46516  0.50185
##  [491]  1.29543  3.46176  0.69954  0.31673  3.45083  1.88787  0.88343
##  [498]  0.69049  1.25101  0.73234  1.25579  0.47154  0.35839  2.27791
##  [505]  0.91889  5.61825  0.96553  1.95508  0.42551  2.21408  0.61773
##  [512]  0.48135  0.97943  0.41533  1.57139  6.06937  0.20571  0.12845
##  [519]  1.27365  0.82212  0.07908  0.66424  2.76484  0.69886  0.72711
##  [526]  0.93896  1.57807  0.72341  0.79718  0.98496  1.24040  2.65963
##  [533]  0.17773  1.98268  3.16865  0.71380  0.55592  4.69660  0.09495
##  [540]  0.92279  1.01893  2.22125  1.43302  0.64419  2.51295  2.46890
##  [547]  0.61317  3.51001  2.92623  0.25400  2.59850  1.20037  0.92012
##  [554]  1.13443  1.45019  0.42376  1.41781  1.75847  0.32750  1.21854
##  [561]  5.48043  0.95193  2.96076  1.15295  2.76598  1.34938  0.18652
##  [568]  0.71294  0.26076  1.15401  0.24196  1.95637  0.51683  0.60886
##  [575]  0.66615  0.44112  0.63569  2.86038  0.21054  4.27332  0.61546
##  [582]  2.89983  1.04074  2.60518  0.45349  2.60116  1.13753  1.50162
##  [589]  0.54738  1.20494  0.32877  2.14906  1.48054  1.62565  2.70861
##  [596]  0.10086  1.42905  1.23827  0.54985  4.40552  2.34773  1.33645
##  [603]  0.26091  0.55479  0.87978  1.48873  1.11216  2.31625  1.31319
##  [610]  6.22668  1.58712  0.71177  1.69640  1.39671  1.14091  1.34079
##  [617]  0.70578  1.39052  0.72539  0.62072  0.97448  0.84792  2.51371
##  [624]  0.42702  0.58114  0.10836  0.75526  2.02549  1.17313  0.79348
##  [631]  1.46179  0.62788  1.44632  3.17836  0.85487  4.12280  0.80600
##  [638]  1.16293  2.32220  1.00948  1.22341  0.62724  1.15634 11.61305
##  [645]  0.68280  1.01433  0.58104  1.16180  6.24245  1.53916  2.04201
##  [652]  2.01975  3.29439  0.69310  1.14483  3.53599  1.55263  0.29887
##  [659]  1.57618  2.27420  1.10430  0.53586  0.14169  4.04907  0.91976
##  [666]  0.54151  0.41914  1.98883  0.05048  1.23938  1.21944  0.62715
##  [673]  0.83659  0.56522  1.74221  0.38459  1.66969  2.17498  1.77015
##  [680]  0.49506  2.07704  1.13451  2.21595  0.58863  3.48010  3.02096
##  [687]  1.59079  0.97308  2.06418  3.45061  1.19276  0.68751  0.51116
##  [694]  0.57759  1.75102  2.29042  1.50708  0.46319  0.27127  0.34340
##  [701]  0.21558  0.80666  0.69384  1.11829  0.61510  0.55249  1.30295
##  [708]  1.55390  4.62205  0.84977  0.47380 10.14866  0.92830  0.73547
##  [715]  2.08667  0.20038  0.70397  2.28495  0.49148  0.85956  3.02510
##  [722]  1.35579  1.10544  1.25757  1.25374  0.47214  2.54069  1.02785
##  [729]  0.30084  0.96631  0.96686  3.23742  1.12296  0.66255  0.16697
##  [736]  1.04866  0.93547  1.54983  0.24184  1.43858  1.10397  1.28237
##  [743]  0.61986  1.75645  1.46968  0.95173  1.40125  2.93831  1.59731
##  [750]  0.55479  0.55204  5.01950  0.37009  0.83856  0.93215  1.07281
##  [757]  1.73093  0.15200  0.44804  0.67840  0.38619  3.12130  0.56333
##  [764]  0.67573  2.55560  0.40922  1.28198  4.94347  1.17468  1.11630
##  [771]  0.89714  1.28978  2.10206  1.23997  2.30696  1.00967  0.23797
##  [778]  0.10893  0.66651  0.46208  1.87670  0.55216  2.35251  1.09099
##  [785]  0.12358  0.78851  0.81028  0.07812  0.68087  4.97126  0.81514
##  [792]  0.44539  1.38112  0.30430  3.75346  0.63543  1.60721  1.19864
##  [799]  1.15251  1.65527  1.16912  2.70333  1.01943  1.26655  3.50608
##  [806]  0.85528  0.77638  0.24389  0.81464  1.40842  0.88293  1.66385
##  [813]  0.94880  0.73772  2.56043  0.90086  0.10335  1.08995  3.01313
##  [820]  0.16079  3.09012  1.09987  0.29197  2.69582  1.85482  2.53662
##  [827]  2.13832  1.15237  3.52574  1.57717  1.85478  0.47489  0.53341
##  [834]  1.58760  0.68329  0.78903  1.52863  0.45736  6.01165  1.77774
##  [841]  1.24318  0.72155  0.06378  0.35799  1.04525  0.40982  1.02467
##  [848]  0.36943  1.83496  2.46133  3.63621  0.70281  3.55274  1.64146
##  [855]  4.99931  0.10216  2.04986  0.66049  0.33739  0.73425  0.65037
##  [862]  1.21763  0.33416  2.05272  1.96342  1.38541  1.53201  1.41621
##  [869]  0.30928  0.42607  0.34220  1.36050  3.02836  1.71546  1.70641
##  [876]  0.12944  8.26135  0.79487  0.78851  0.89591  5.76274  1.09316
##  [883]  1.52975  0.80506  0.76087  1.94685  0.77083  0.97740  1.96508
##  [890]  3.07517  8.26206  0.19610  1.05683  0.28490  5.34754  1.44062
##  [897]  2.55731  3.01042  0.18255  1.07603  0.24029  4.18035  1.16840
##  [904]  3.31540  0.99263  1.64172  1.24526  0.40281  2.03958  0.92645
##  [911]  1.61918  0.41738  0.27812  0.39241  0.64926  3.75586  0.82421
##  [918]  0.93643  6.72475  1.29417  1.84811  1.29641  1.06966  0.42377
##  [925]  0.56609 10.13696  0.74773  0.90384  1.22054  2.01755  0.65404
##  [932]  1.87916  0.50867  1.29812  3.47600  0.83322  2.71430  0.37551
##  [939]  0.85284  0.13801  1.45094  3.83071  0.16645  0.80641  1.83790
##  [946]  1.37369  0.47942  0.43910  1.25520  0.69894  4.11392  0.88130
##  [953]  2.63778  0.92099  0.41391  0.82845  1.14750  0.50510  1.04685
##  [960]  2.56680  0.15935  3.65526  1.38363  0.19852  1.31084  0.53084
##  [967]  0.60452  1.79283  1.31004  1.55397  0.66765  0.42367  0.67696
##  [974]  0.58615  0.43563  0.52236  1.00959  1.73996  8.06906  1.51475
##  [981]  0.57548  3.41204  0.71264  0.80307  0.65538  1.94691  0.45160
##  [988]  0.20734  0.94564  1.08388  0.96206  1.22753  2.42446  2.49351
##  [995]  0.60201  0.72445  0.18869  0.31019  0.22586  0.92584

Est-ce que les théorèmes d’avant s’appliquent ?..

Combiner plusieurs graphiques avec les fonctions de base de R

Pour nos histogrammes, on aurait aussi pu faire quelque chose dans le genre:

par(mfrow=c(2,2))
hist(runif(1000))
hist(runif(1000)+runif(1000))
hist(runif(1000))
hist(runif(1000)+runif(1000)+runif(1000)+runif(1000))

Le problème, c’est que les graphes sont difficilement comparables les uns avec les autres et qu’il vaut mieux utiliser ggplot2…

Quelques illustrations des fonctionnalités de ggplot2

Mais comme j’espère vous l’avoir montré, ggplot est bien plus riche et souple…

ggplot(data=mtcars,aes(x=mpg,y=qsec,shape=factor(carb), color=factor(gear))) +
    geom_point(size=3) + theme_bw() + facet_wrap(~cyl)