de_mean() computes group- and de-meaned versions of a
variable that can be used in regression analysis to model the between-
and within-subject effect.
de_mean(x, ..., grp, append = TRUE, suffix.dm = "_dm", suffix.gm = "_gm")A data frame.
Names of variables that should be group- and de-meaned.
Quoted or unquoted name of the variable that indicates the group- or cluster-ID.
Logical, if TRUE (the default) and x is a data frame,
x including the new variables as additional columns is returned;
if FALSE, only the new variables are returned.
String value, will be appended to the names of the
group-meaned and de-meaned variables of x. By default, de-meaned
variables will be suffixed with "_dm" and grouped-meaned variables
with "_gm".
For append = TRUE, x including the group-/de-meaned
variables as new columns is returned; if append = FALSE, only the
group-/de-meaned variables will be returned.
de_mean() is intended to create group- and de-meaned variables
for complex random-effect-within-between models (see Bell et al. 2018),
where group-effects (random effects) and fixed effects correlate (see
Bafumi and Gelman 2006)). This violation of one of the
Gauss-Markov-assumptions can happen, for instance, when analysing panel
data. To control for correlating predictors and group effects, it is
recommended to include the group-meaned and de-meaned version of
time-varying covariates in the model. By this, one can fit
complex multilevel models for panel data, including time-varying,
time-invariant predictors and random effects. This approach is superior to
simple fixed-effects models, which lack information of variation in the
group-effects or between-subject effects.
A description of how to translate the
formulas described in Bell et al. 2018 into R using lmer()
from lme4 or glmmTMB() from glmmTMB can be found here:
for lmer()
and for glmmTMB().
Bafumi J, Gelman A. 2006. Fitting Multilevel Models When Predictors and Group Effects Correlate. In. Philadelphia, PA: Annual meeting of the American Political Science Association.
Bell A, Fairbrother M, Jones K. 2018. Fixed and Random Effects Models: Making an Informed Choice. Quality & Quantity. doi:10.1007/s11135-018-0802-x
data(efc)
efc$ID <- sample(1:4, nrow(efc), replace = TRUE) # fake-ID
de_mean(efc, c12hour, barthtot, grp = ID, append = FALSE)
#> c12hour barthtot c12hour_dm barthtot_dm c12hour_gm barthtot_gm
#> 1 16 75 -23.7834101 4.1784038 39.78341 70.82160
#> 2 148 75 103.8272727 10.4166667 44.17273 64.58333
#> 3 70 35 30.2165899 -35.8215962 39.78341 70.82160
#> 4 168 0 124.1409692 -59.8642534 43.85903 59.86425
#> 5 168 25 126.2478992 -38.2188841 41.75210 63.21888
#> 6 16 60 -25.7521008 -3.2188841 41.75210 63.21888
#> 7 161 5 121.2165899 -65.8215962 39.78341 70.82160
#> 8 110 35 70.2165899 -35.8215962 39.78341 70.82160
#> 9 28 15 -13.7521008 -48.2188841 41.75210 63.21888
#> 10 40 0 0.2165899 -70.8215962 39.78341 70.82160
#> 11 100 25 56.1409692 -34.8642534 43.85903 59.86425
#> 12 25 85 -18.8590308 25.1357466 43.85903 59.86425
#> 13 25 15 -19.1727273 -49.5833333 44.17273 64.58333
#> 14 24 70 -19.8590308 10.1357466 43.85903 59.86425
#> 15 56 NA 14.2478992 NA 41.75210 63.21888
#> 16 20 0 -21.7521008 -63.2188841 41.75210 63.21888
#> 17 25 95 -14.7834101 24.1784038 39.78341 70.82160
#> 18 126 55 86.2165899 -15.8215962 39.78341 70.82160
#> 19 168 55 123.8272727 -9.5833333 44.17273 64.58333
#> 20 118 45 73.8272727 -19.5833333 44.17273 64.58333
#> 21 150 0 108.2478992 -63.2188841 41.75210 63.21888
#> 22 50 70 10.2165899 -0.8215962 39.78341 70.82160
#> 23 18 20 -25.8590308 -39.8642534 43.85903 59.86425
#> 24 168 0 126.2478992 -63.2188841 41.75210 63.21888
#> 25 15 95 -24.7834101 24.1784038 39.78341 70.82160
#> 26 168 10 128.2165899 -60.8215962 39.78341 70.82160
#> 27 12 75 -32.1727273 10.4166667 44.17273 64.58333
#> 28 7 90 -36.8590308 30.1357466 43.85903 59.86425
#> 29 35 60 -6.7521008 -3.2188841 41.75210 63.21888
#> 30 168 20 124.1409692 -39.8642534 43.85903 59.86425
#> 31 150 NA 108.2478992 NA 41.75210 63.21888
#> 32 168 50 128.2165899 -20.8215962 39.78341 70.82160
#> 33 168 75 126.2478992 11.7811159 41.75210 63.21888
#> 34 119 50 74.8272727 -14.5833333 44.17273 64.58333
#> 35 168 30 124.1409692 -29.8642534 43.85903 59.86425
#> 36 168 0 126.2478992 -63.2188841 41.75210 63.21888
#> 37 168 30 124.1409692 -29.8642534 43.85903 59.86425
#> 38 28 90 -16.1727273 25.4166667 44.17273 64.58333
#> 39 168 15 123.8272727 -49.5833333 44.17273 64.58333
#> 40 30 70 -11.7521008 6.7811159 41.75210 63.21888
#> 41 14 85 -25.7834101 14.1784038 39.78341 70.82160
#> 42 168 NA 124.1409692 NA 43.85903 59.86425
#> 43 168 0 126.2478992 -63.2188841 41.75210 63.21888
#> 44 50 30 8.2478992 -33.2188841 41.75210 63.21888
#> 45 168 60 128.2165899 -10.8215962 39.78341 70.82160
#> 46 24 25 -17.7521008 -38.2188841 41.75210 63.21888
#> 47 168 NA 124.1409692 NA 43.85903 59.86425
#> 48 42 30 -1.8590308 -29.8642534 43.85903 59.86425
#> 49 154 85 114.2165899 14.1784038 39.78341 70.82160
#> 50 60 0 18.2478992 -63.2188841 41.75210 63.21888
#> 51 168 0 124.1409692 -59.8642534 43.85903 59.86425
#> 52 168 0 123.8272727 -64.5833333 44.17273 64.58333
#> 53 24 10 -19.8590308 -49.8642534 43.85903 59.86425
#> 54 168 10 123.8272727 -54.5833333 44.17273 64.58333
#> 55 150 20 105.8272727 -44.5833333 44.17273 64.58333
#> 56 168 0 128.2165899 -70.8215962 39.78341 70.82160
#> 57 168 0 123.8272727 -64.5833333 44.17273 64.58333
#> 58 168 50 123.8272727 -14.5833333 44.17273 64.58333
#> 59 168 85 123.8272727 20.4166667 44.17273 64.58333
#> 60 168 5 128.2165899 -65.8215962 39.78341 70.82160
#> 61 128 0 86.2478992 -63.2188841 41.75210 63.21888
#> 62 168 40 128.2165899 -30.8215962 39.78341 70.82160
#> 63 11 50 -30.7521008 -13.2188841 41.75210 63.21888
#> 64 50 80 10.2165899 9.1784038 39.78341 70.82160
#> 65 80 70 38.2478992 6.7811159 41.75210 63.21888
#> 66 15 70 -24.7834101 -0.8215962 39.78341 70.82160
#> 67 7 65 -34.7521008 1.7811159 41.75210 63.21888
#> 68 21 90 -23.1727273 25.4166667 44.17273 64.58333
#> 69 168 0 126.2478992 -63.2188841 41.75210 63.21888
#> 70 24 50 -19.8590308 -9.8642534 43.85903 59.86425
#> 71 6 70 -33.7834101 -0.8215962 39.78341 70.82160
#> 72 30 70 -11.7521008 6.7811159 41.75210 63.21888
#> 73 168 45 126.2478992 -18.2188841 41.75210 63.21888
#> 74 42 40 2.2165899 -30.8215962 39.78341 70.82160
#> 75 30 20 -13.8590308 -39.8642534 43.85903 59.86425
#> 76 85 85 43.2478992 21.7811159 41.75210 63.21888
#> 77 35 15 -9.1727273 -49.5833333 44.17273 64.58333
#> 78 70 85 25.8272727 20.4166667 44.17273 64.58333
#> 79 9 80 -34.8590308 20.1357466 43.85903 59.86425
#> 80 168 20 123.8272727 -44.5833333 44.17273 64.58333
#> 81 77 NA 33.1409692 NA 43.85903 59.86425
#> 82 24 85 -15.7834101 14.1784038 39.78341 70.82160
#> 83 91 45 46.8272727 -19.5833333 44.17273 64.58333
#> 84 6 NA -35.7521008 NA 41.75210 63.21888
#> 85 22 50 -21.8590308 -9.8642534 43.85903 59.86425
#> 86 168 0 126.2478992 -63.2188841 41.75210 63.21888
#> 87 168 10 126.2478992 -53.2188841 41.75210 63.21888
#> 88 168 50 126.2478992 -13.2188841 41.75210 63.21888
#> 89 168 35 128.2165899 -35.8215962 39.78341 70.82160
#> 90 50 50 5.8272727 -14.5833333 44.17273 64.58333
#> 91 40 75 -1.7521008 11.7811159 41.75210 63.21888
#> 92 9 95 -35.1727273 30.4166667 44.17273 64.58333
#> 93 25 95 -16.7521008 31.7811159 41.75210 63.21888
#> 94 14 100 -27.7521008 36.7811159 41.75210 63.21888
#> 95 49 80 5.1409692 20.1357466 43.85903 59.86425
#> 96 5 90 -34.7834101 19.1784038 39.78341 70.82160
#> 97 7 75 -32.7834101 4.1784038 39.78341 70.82160
#> 98 21 60 -23.1727273 -4.5833333 44.17273 64.58333
#> 99 24 NA -19.8590308 NA 43.85903 59.86425
#> 100 7 60 -36.8590308 0.1357466 43.85903 59.86425
#> 101 168 65 124.1409692 5.1357466 43.85903 59.86425
#> 102 168 75 124.1409692 15.1357466 43.85903 59.86425
#> 103 4 80 -37.7521008 16.7811159 41.75210 63.21888
#> 104 168 0 124.1409692 -59.8642534 43.85903 59.86425
#> 105 168 30 124.1409692 -29.8642534 43.85903 59.86425
#> 106 15 65 -28.8590308 5.1357466 43.85903 59.86425
#> 107 168 80 126.2478992 16.7811159 41.75210 63.21888
#> 108 168 90 123.8272727 25.4166667 44.17273 64.58333
#> 109 20 65 -23.8590308 5.1357466 43.85903 59.86425
#> 110 59 55 19.2165899 -15.8215962 39.78341 70.82160
#> 111 24 50 -15.7834101 -20.8215962 39.78341 70.82160
#> 112 7 75 -36.8590308 15.1357466 43.85903 59.86425
#> 113 100 35 55.8272727 -29.5833333 44.17273 64.58333
#> 114 168 15 128.2165899 -55.8215962 39.78341 70.82160
#> 115 168 25 128.2165899 -45.8215962 39.78341 70.82160
#> 116 28 80 -16.1727273 15.4166667 44.17273 64.58333
#> 117 20 80 -21.7521008 16.7811159 41.75210 63.21888
#> 118 50 80 5.8272727 15.4166667 44.17273 64.58333
#> 119 89 30 45.1409692 -29.8642534 43.85903 59.86425
#> 120 168 70 128.2165899 -0.8215962 39.78341 70.82160
#> 121 12 55 -31.8590308 -4.8642534 43.85903 59.86425
#> 122 24 55 -15.7834101 -15.8215962 39.78341 70.82160
#> 123 91 5 47.1409692 -54.8642534 43.85903 59.86425
#> 124 168 35 126.2478992 -28.2188841 41.75210 63.21888
#> 125 168 100 124.1409692 40.1357466 43.85903 59.86425
#> 126 168 5 124.1409692 -54.8642534 43.85903 59.86425
#> 127 11 100 -32.8590308 40.1357466 43.85903 59.86425
#> 128 35 0 -8.8590308 -59.8642534 43.85903 59.86425
#> 129 10 80 -29.7834101 9.1784038 39.78341 70.82160
#> 130 125 45 81.1409692 -14.8642534 43.85903 59.86425
#> 131 140 80 98.2478992 16.7811159 41.75210 63.21888
#> 132 28 70 -11.7834101 -0.8215962 39.78341 70.82160
#> 133 84 0 39.8272727 -64.5833333 44.17273 64.58333
#> 134 15 75 -24.7834101 4.1784038 39.78341 70.82160
#> 135 15 60 -29.1727273 -4.5833333 44.17273 64.58333
#> 136 14 65 -27.7521008 1.7811159 41.75210 63.21888
#> 137 24 10 -19.8590308 -49.8642534 43.85903 59.86425
#> 138 4 75 -37.7521008 11.7811159 41.75210 63.21888
#> 139 140 0 98.2478992 -63.2188841 41.75210 63.21888
#> 140 168 80 128.2165899 9.1784038 39.78341 70.82160
#> 141 6 55 -38.1727273 -9.5833333 44.17273 64.58333
#> 142 10 45 -29.7834101 -25.8215962 39.78341 70.82160
#> 143 20 60 -24.1727273 -4.5833333 44.17273 64.58333
#> 144 15 60 -28.8590308 0.1357466 43.85903 59.86425
#> 145 65 35 23.2478992 -28.2188841 41.75210 63.21888
#> 146 35 40 -9.1727273 -24.5833333 44.17273 64.58333
#> 147 105 10 61.1409692 -49.8642534 43.85903 59.86425
#> 148 50 30 5.8272727 -34.5833333 44.17273 64.58333
#> 149 168 45 128.2165899 -25.8215962 39.78341 70.82160
#> 150 77 50 33.1409692 -9.8642534 43.85903 59.86425
#> 151 168 15 123.8272727 -49.5833333 44.17273 64.58333
#> 152 42 10 -1.8590308 -49.8642534 43.85903 59.86425
#> 153 4 75 -35.7834101 4.1784038 39.78341 70.82160
#> 154 168 5 128.2165899 -65.8215962 39.78341 70.82160
#> 155 168 0 124.1409692 -59.8642534 43.85903 59.86425
#> 156 42 75 0.2478992 11.7811159 41.75210 63.21888
#> 157 6 60 -33.7834101 -10.8215962 39.78341 70.82160
#> 158 168 5 123.8272727 -59.5833333 44.17273 64.58333
#> 159 70 60 30.2165899 -10.8215962 39.78341 70.82160
#> 160 15 45 -24.7834101 -25.8215962 39.78341 70.82160
#> 161 30 65 -11.7521008 1.7811159 41.75210 63.21888
#> 162 9 50 -35.1727273 -14.5833333 44.17273 64.58333
#> 163 16 30 -25.7521008 -33.2188841 41.75210 63.21888
#> 164 35 0 -8.8590308 -59.8642534 43.85903 59.86425
#> 165 28 75 -16.1727273 10.4166667 44.17273 64.58333
#> 166 168 0 123.8272727 -64.5833333 44.17273 64.58333
#> 167 9 70 -30.7834101 -0.8215962 39.78341 70.82160
#> 168 168 5 126.2478992 -58.2188841 41.75210 63.21888
#> 169 15 75 -29.1727273 10.4166667 44.17273 64.58333
#> 170 6 30 -35.7521008 -33.2188841 41.75210 63.21888
#> 171 14 90 -29.8590308 30.1357466 43.85903 59.86425
#> 172 35 70 -6.7521008 6.7811159 41.75210 63.21888
#> 173 7 75 -36.8590308 15.1357466 43.85903 59.86425
#> 174 12 75 -29.7521008 11.7811159 41.75210 63.21888
#> 175 50 35 10.2165899 -35.8215962 39.78341 70.82160
#> 176 6 50 -38.1727273 -14.5833333 44.17273 64.58333
#> 177 22 65 -21.8590308 5.1357466 43.85903 59.86425
#> 178 35 45 -6.7521008 -18.2188841 41.75210 63.21888
#> 179 6 55 -35.7521008 -8.2188841 41.75210 63.21888
#> 180 168 15 126.2478992 -48.2188841 41.75210 63.21888
#> 181 28 5 -15.8590308 -54.8642534 43.85903 59.86425
#> 182 10 85 -33.8590308 25.1357466 43.85903 59.86425
#> 183 91 70 51.2165899 -0.8215962 39.78341 70.82160
#> 184 8 60 -33.7521008 -3.2188841 41.75210 63.21888
#> 185 168 15 124.1409692 -44.8642534 43.85903 59.86425
#> 186 24 15 -17.7521008 -48.2188841 41.75210 63.21888
#> 187 168 5 123.8272727 -59.5833333 44.17273 64.58333
#> 188 168 45 123.8272727 -19.5833333 44.17273 64.58333
#> 189 14 85 -25.7834101 14.1784038 39.78341 70.82160
#> 190 28 45 -16.1727273 -19.5833333 44.17273 64.58333
#> 191 16 50 -28.1727273 -14.5833333 44.17273 64.58333
#> 192 168 30 124.1409692 -29.8642534 43.85903 59.86425
#> 193 6 95 -37.8590308 35.1357466 43.85903 59.86425
#> 194 168 0 128.2165899 -70.8215962 39.78341 70.82160
#> 195 28 75 -11.7834101 4.1784038 39.78341 70.82160
#> 196 160 95 116.1409692 35.1357466 43.85903 59.86425
#> 197 39 55 -5.1727273 -9.5833333 44.17273 64.58333
#> 198 15 NA -29.1727273 NA 44.17273 64.58333
#> 199 10 NA -31.7521008 NA 41.75210 63.21888
#> 200 10 85 -34.1727273 20.4166667 44.17273 64.58333
#> 201 17 90 -22.7834101 19.1784038 39.78341 70.82160
#> 202 168 10 124.1409692 -49.8642534 43.85903 59.86425
#> 203 70 65 25.8272727 0.4166667 44.17273 64.58333
#> 204 50 NA 6.1409692 NA 43.85903 59.86425
#> 205 12 75 -29.7521008 11.7811159 41.75210 63.21888
#> 206 10 90 -33.8590308 30.1357466 43.85903 59.86425
#> 207 168 0 128.2165899 -70.8215962 39.78341 70.82160
#> 208 168 25 124.1409692 -34.8642534 43.85903 59.86425
#> 209 168 75 128.2165899 4.1784038 39.78341 70.82160
#> 210 28 55 -11.7834101 -15.8215962 39.78341 70.82160
#> 211 12 65 -31.8590308 5.1357466 43.85903 59.86425
#> 212 8 55 -35.8590308 -4.8642534 43.85903 59.86425
#> 213 21 70 -18.7834101 -0.8215962 39.78341 70.82160
#> 214 24 30 -15.7834101 -40.8215962 39.78341 70.82160
#> 215 15 85 -24.7834101 14.1784038 39.78341 70.82160
#> 216 8 75 -35.8590308 15.1357466 43.85903 59.86425
#> 217 16 40 -27.8590308 -19.8642534 43.85903 59.86425
#> 218 56 40 11.8272727 -24.5833333 44.17273 64.58333
#> 219 42 75 2.2165899 4.1784038 39.78341 70.82160
#> 220 4 100 -35.7834101 29.1784038 39.78341 70.82160
#> 221 25 60 -14.7834101 -10.8215962 39.78341 70.82160
#> 222 35 40 -4.7834101 -30.8215962 39.78341 70.82160
#> 223 30 70 -11.7521008 6.7811159 41.75210 63.21888
#> 224 6 65 -38.1727273 0.4166667 44.17273 64.58333
#> 225 110 15 65.8272727 -49.5833333 44.17273 64.58333
#> 226 30 60 -9.7834101 -10.8215962 39.78341 70.82160
#> 227 24 45 -15.7834101 -25.8215962 39.78341 70.82160
#> 228 14 65 -30.1727273 0.4166667 44.17273 64.58333
#> 229 4 95 -40.1727273 30.4166667 44.17273 64.58333
#> 230 20 100 -24.1727273 35.4166667 44.17273 64.58333
#> 231 10 60 -29.7834101 -10.8215962 39.78341 70.82160
#> 232 7 75 -37.1727273 10.4166667 44.17273 64.58333
#> 233 161 15 116.8272727 -49.5833333 44.17273 64.58333
#> 234 28 80 -16.1727273 15.4166667 44.17273 64.58333
#> 235 14 45 -30.1727273 -19.5833333 44.17273 64.58333
#> 236 4 60 -37.7521008 -3.2188841 41.75210 63.21888
#> 237 50 95 10.2165899 24.1784038 39.78341 70.82160
#> 238 10 90 -31.7521008 26.7811159 41.75210 63.21888
#> 239 18 95 -23.7521008 31.7811159 41.75210 63.21888
#> 240 15 85 -29.1727273 20.4166667 44.17273 64.58333
#> 241 6 95 -38.1727273 30.4166667 44.17273 64.58333
#> 242 17 70 -26.8590308 10.1357466 43.85903 59.86425
#> 243 14 70 -29.8590308 10.1357466 43.85903 59.86425
#> 244 5 85 -36.7521008 21.7811159 41.75210 63.21888
#> 245 10 65 -31.7521008 1.7811159 41.75210 63.21888
#> 246 30 75 -13.8590308 15.1357466 43.85903 59.86425
#> 247 10 95 -33.8590308 35.1357466 43.85903 59.86425
#> 248 10 100 -29.7834101 29.1784038 39.78341 70.82160
#> 249 84 80 40.1409692 20.1357466 43.85903 59.86425
#> 250 10 60 -34.1727273 -4.5833333 44.17273 64.58333
#> 251 6 100 -33.7834101 29.1784038 39.78341 70.82160
#> 252 15 75 -29.1727273 10.4166667 44.17273 64.58333
#> 253 40 100 0.2165899 29.1784038 39.78341 70.82160
#> 254 21 10 -18.7834101 -60.8215962 39.78341 70.82160
#> 255 11 100 -33.1727273 35.4166667 44.17273 64.58333
#> 256 8 75 -36.1727273 10.4166667 44.17273 64.58333
#> 257 5 95 -34.7834101 24.1784038 39.78341 70.82160
#> 258 12 15 -31.8590308 -44.8642534 43.85903 59.86425
#> 259 10 90 -34.1727273 25.4166667 44.17273 64.58333
#> 260 20 90 -23.8590308 30.1357466 43.85903 59.86425
#> 261 12 60 -31.8590308 0.1357466 43.85903 59.86425
#> 262 24 30 -19.8590308 -29.8642534 43.85903 59.86425
#> 263 27 40 -14.7521008 -23.2188841 41.75210 63.21888
#> 264 14 80 -25.7834101 9.1784038 39.78341 70.82160
#> 265 18 75 -21.7834101 4.1784038 39.78341 70.82160
#> 266 168 75 123.8272727 10.4166667 44.17273 64.58333
#> 267 14 90 -27.7521008 26.7811159 41.75210 63.21888
#> 268 10 NA -29.7834101 NA 39.78341 70.82160
#> 269 6 100 -38.1727273 35.4166667 44.17273 64.58333
#> 270 21 65 -20.7521008 1.7811159 41.75210 63.21888
#> 271 16 85 -23.7834101 14.1784038 39.78341 70.82160
#> 272 15 70 -26.7521008 6.7811159 41.75210 63.21888
#> 273 20 85 -19.7834101 14.1784038 39.78341 70.82160
#> 274 10 90 -31.7521008 26.7811159 41.75210 63.21888
#> 275 22 60 -19.7521008 -3.2188841 41.75210 63.21888
#> 276 35 60 -6.7521008 -3.2188841 41.75210 63.21888
#> 277 30 70 -11.7521008 6.7811159 41.75210 63.21888
#> 278 16 70 -25.7521008 6.7811159 41.75210 63.21888
#> 279 24 95 -19.8590308 35.1357466 43.85903 59.86425
#> 280 168 75 128.2165899 4.1784038 39.78341 70.82160
#> 281 168 90 123.8272727 25.4166667 44.17273 64.58333
#> 282 40 95 -1.7521008 31.7811159 41.75210 63.21888
#> 283 40 100 -1.7521008 36.7811159 41.75210 63.21888
#> 284 50 100 8.2478992 36.7811159 41.75210 63.21888
#> 285 20 100 -23.8590308 40.1357466 43.85903 59.86425
#> 286 20 100 -23.8590308 40.1357466 43.85903 59.86425
#> 287 6 NA -35.7521008 NA 41.75210 63.21888
#> 288 5 80 -34.7834101 9.1784038 39.78341 70.82160
#> 289 48 65 4.1409692 5.1357466 43.85903 59.86425
#> 290 168 25 123.8272727 -39.5833333 44.17273 64.58333
#> 291 6 90 -38.1727273 25.4166667 44.17273 64.58333
#> 292 8 65 -33.7521008 1.7811159 41.75210 63.21888
#> 293 43 90 1.2478992 26.7811159 41.75210 63.21888
#> 294 90 55 45.8272727 -9.5833333 44.17273 64.58333
#> 295 100 60 58.2478992 -3.2188841 41.75210 63.21888
#> 296 8 95 -36.1727273 30.4166667 44.17273 64.58333
#> 297 15 70 -24.7834101 -0.8215962 39.78341 70.82160
#> 298 5 80 -36.7521008 16.7811159 41.75210 63.21888
#> 299 8 80 -31.7834101 9.1784038 39.78341 70.82160
#> 300 10 95 -29.7834101 24.1784038 39.78341 70.82160
#> 301 30 50 -14.1727273 -14.5833333 44.17273 64.58333
#> 302 168 40 123.8272727 -24.5833333 44.17273 64.58333
#> 303 20 70 -24.1727273 5.4166667 44.17273 64.58333
#> 304 30 60 -9.7834101 -10.8215962 39.78341 70.82160
#> 305 30 100 -14.1727273 35.4166667 44.17273 64.58333
#> 306 12 75 -27.7834101 4.1784038 39.78341 70.82160
#> 307 30 55 -11.7521008 -8.2188841 41.75210 63.21888
#> 308 30 95 -13.8590308 35.1357466 43.85903 59.86425
#> 309 14 85 -30.1727273 20.4166667 44.17273 64.58333
#> 310 15 90 -26.7521008 26.7811159 41.75210 63.21888
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#> 312 20 50 -23.8590308 -9.8642534 43.85903 59.86425
#> 313 25 55 -19.1727273 -9.5833333 44.17273 64.58333
#> 314 40 10 0.2165899 -60.8215962 39.78341 70.82160
#> 315 9 80 -35.1727273 15.4166667 44.17273 64.58333
#> 316 18 60 -25.8590308 0.1357466 43.85903 59.86425
#> 317 25 50 -18.8590308 -9.8642534 43.85903 59.86425
#> 318 100 45 56.1409692 -14.8642534 43.85903 59.86425
#> 319 6 95 -37.8590308 35.1357466 43.85903 59.86425
#> 320 25 95 -16.7521008 31.7811159 41.75210 63.21888
#> 321 15 75 -24.7834101 4.1784038 39.78341 70.82160
#> 322 20 100 -23.8590308 40.1357466 43.85903 59.86425
#> 323 10 100 -29.7834101 29.1784038 39.78341 70.82160
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#> 325 10 85 -31.7521008 21.7811159 41.75210 63.21888
#> 326 30 60 -14.1727273 -4.5833333 44.17273 64.58333
#> 327 6 70 -33.7834101 -0.8215962 39.78341 70.82160
#> 328 40 55 -3.8590308 -4.8642534 43.85903 59.86425
#> 329 7 100 -32.7834101 29.1784038 39.78341 70.82160
#> 330 8 100 -35.8590308 40.1357466 43.85903 59.86425
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#> 333 4 50 -37.7521008 -13.2188841 41.75210 63.21888
#> 334 168 0 126.2478992 -63.2188841 41.75210 63.21888
#> 335 7 85 -32.7834101 14.1784038 39.78341 70.82160
#> 336 22 75 -21.8590308 15.1357466 43.85903 59.86425
#> 337 30 50 -11.7521008 -13.2188841 41.75210 63.21888
#> 338 15 65 -26.7521008 1.7811159 41.75210 63.21888
#> 339 30 75 -9.7834101 4.1784038 39.78341 70.82160
#> 340 20 100 -24.1727273 35.4166667 44.17273 64.58333
#> 341 25 100 -16.7521008 36.7811159 41.75210 63.21888
#> 342 20 90 -24.1727273 25.4166667 44.17273 64.58333
#> 343 20 100 -23.8590308 40.1357466 43.85903 59.86425
#> 344 25 95 -16.7521008 31.7811159 41.75210 63.21888
#> 345 14 55 -30.1727273 -9.5833333 44.17273 64.58333
#> 346 30 80 -14.1727273 15.4166667 44.17273 64.58333
#> 347 20 80 -19.7834101 9.1784038 39.78341 70.82160
#> 348 15 50 -28.8590308 -9.8642534 43.85903 59.86425
#> 349 6 100 -38.1727273 35.4166667 44.17273 64.58333
#> 350 5 90 -39.1727273 25.4166667 44.17273 64.58333
#> 351 50 10 5.8272727 -54.5833333 44.17273 64.58333
#> 352 8 100 -31.7834101 29.1784038 39.78341 70.82160
#> 353 20 75 -21.7521008 11.7811159 41.75210 63.21888
#> 354 14 95 -25.7834101 24.1784038 39.78341 70.82160
#> 355 18 70 -25.8590308 10.1357466 43.85903 59.86425
#> 356 16 60 -25.7521008 -3.2188841 41.75210 63.21888
#> 357 20 35 -23.8590308 -24.8642534 43.85903 59.86425
#> 358 15 NA -29.1727273 NA 44.17273 64.58333
#> 359 25 65 -14.7834101 -5.8215962 39.78341 70.82160
#> 360 18 100 -26.1727273 35.4166667 44.17273 64.58333
#> 361 22 55 -19.7521008 -8.2188841 41.75210 63.21888
#> 362 18 75 -23.7521008 11.7811159 41.75210 63.21888
#> 363 48 95 3.8272727 30.4166667 44.17273 64.58333
#> 364 60 70 15.8272727 5.4166667 44.17273 64.58333
#> 365 10 85 -33.8590308 25.1357466 43.85903 59.86425
#> 366 7 100 -34.7521008 36.7811159 41.75210 63.21888
#> 367 5 100 -38.8590308 40.1357466 43.85903 59.86425
#> 368 35 70 -6.7521008 6.7811159 41.75210 63.21888
#> 369 28 90 -11.7834101 19.1784038 39.78341 70.82160
#> 370 5 90 -34.7834101 19.1784038 39.78341 70.82160
#> 371 25 90 -14.7834101 19.1784038 39.78341 70.82160
#> 372 40 50 -1.7521008 -13.2188841 41.75210 63.21888
#> 373 49 25 7.2478992 -38.2188841 41.75210 63.21888
#> 374 4 95 -39.8590308 35.1357466 43.85903 59.86425
#> 375 70 90 25.8272727 25.4166667 44.17273 64.58333
#> 376 6 65 -38.1727273 0.4166667 44.17273 64.58333
#> 377 7 65 -32.7834101 -5.8215962 39.78341 70.82160
#> 378 40 85 -4.1727273 20.4166667 44.17273 64.58333
#> 379 50 35 5.8272727 -29.5833333 44.17273 64.58333
#> 380 30 5 -9.7834101 -65.8215962 39.78341 70.82160
#> 381 70 35 28.2478992 -28.2188841 41.75210 63.21888
#> 382 14 85 -27.7521008 21.7811159 41.75210 63.21888
#> 383 70 50 30.2165899 -20.8215962 39.78341 70.82160
#> 384 7 40 -37.1727273 -24.5833333 44.17273 64.58333
#> 385 6 70 -35.7521008 6.7811159 41.75210 63.21888
#> 386 14 100 -27.7521008 36.7811159 41.75210 63.21888
#> 387 10 95 -31.7521008 31.7811159 41.75210 63.21888
#> 388 25 20 -18.8590308 -39.8642534 43.85903 59.86425
#> 389 5 85 -38.8590308 25.1357466 43.85903 59.86425
#> 390 11 75 -28.7834101 4.1784038 39.78341 70.82160
#> 391 120 10 76.1409692 -49.8642534 43.85903 59.86425
#> 392 18 80 -26.1727273 15.4166667 44.17273 64.58333
#> 393 6 100 -38.1727273 35.4166667 44.17273 64.58333
#> 394 20 65 -21.7521008 1.7811159 41.75210 63.21888
#> 395 15 60 -28.8590308 0.1357466 43.85903 59.86425
#> 396 35 10 -8.8590308 -49.8642534 43.85903 59.86425
#> 397 15 55 -24.7834101 -15.8215962 39.78341 70.82160
#> 398 15 55 -29.1727273 -9.5833333 44.17273 64.58333
#> 399 120 25 76.1409692 -34.8642534 43.85903 59.86425
#> 400 28 65 -15.8590308 5.1357466 43.85903 59.86425
#> 401 10 10 -33.8590308 -49.8642534 43.85903 59.86425
#> 402 120 55 75.8272727 -9.5833333 44.17273 64.58333
#> 403 100 40 55.8272727 -24.5833333 44.17273 64.58333
#> 404 18 80 -23.7521008 16.7811159 41.75210 63.21888
#> 405 8 100 -36.1727273 35.4166667 44.17273 64.58333
#> 406 40 100 -4.1727273 35.4166667 44.17273 64.58333
#> 407 140 75 100.2165899 4.1784038 39.78341 70.82160
#> 408 6 85 -35.7521008 21.7811159 41.75210 63.21888
#> 409 11 35 -33.1727273 -29.5833333 44.17273 64.58333
#> 410 15 65 -24.7834101 -5.8215962 39.78341 70.82160
#> 411 80 10 35.8272727 -54.5833333 44.17273 64.58333
#> 412 5 95 -34.7834101 24.1784038 39.78341 70.82160
#> 413 6 95 -35.7521008 31.7811159 41.75210 63.21888
#> 414 40 80 0.2165899 9.1784038 39.78341 70.82160
#> 415 5 90 -36.7521008 26.7811159 41.75210 63.21888
#> 416 7 85 -36.8590308 25.1357466 43.85903 59.86425
#> 417 4 95 -37.7521008 31.7811159 41.75210 63.21888
#> 418 24 45 -19.8590308 -14.8642534 43.85903 59.86425
#> 419 28 15 -13.7521008 -48.2188841 41.75210 63.21888
#> 420 25 55 -16.7521008 -8.2188841 41.75210 63.21888
#> 421 140 50 96.1409692 -9.8642534 43.85903 59.86425
#> 422 14 70 -30.1727273 5.4166667 44.17273 64.58333
#> 423 40 15 -1.7521008 -48.2188841 41.75210 63.21888
#> 424 5 70 -34.7834101 -0.8215962 39.78341 70.82160
#> 425 20 40 -19.7834101 -30.8215962 39.78341 70.82160
#> 426 168 5 123.8272727 -59.5833333 44.17273 64.58333
#> 427 40 70 -1.7521008 6.7811159 41.75210 63.21888
#> 428 80 35 35.8272727 -29.5833333 44.17273 64.58333
#> 429 120 10 78.2478992 -53.2188841 41.75210 63.21888
#> 430 160 75 115.8272727 10.4166667 44.17273 64.58333
#> 431 7 95 -32.7834101 24.1784038 39.78341 70.82160
#> 432 7 70 -34.7521008 6.7811159 41.75210 63.21888
#> 433 4 80 -37.7521008 16.7811159 41.75210 63.21888
#> 434 6 95 -33.7834101 24.1784038 39.78341 70.82160
#> 435 14 85 -25.7834101 14.1784038 39.78341 70.82160
#> 436 7 100 -37.1727273 35.4166667 44.17273 64.58333
#> 437 28 75 -16.1727273 10.4166667 44.17273 64.58333
#> 438 25 30 -18.8590308 -29.8642534 43.85903 59.86425
#> 439 28 80 -16.1727273 15.4166667 44.17273 64.58333
#> 440 7 80 -37.1727273 15.4166667 44.17273 64.58333
#> 441 21 NA -18.7834101 NA 39.78341 70.82160
#> 442 30 50 -11.7521008 -13.2188841 41.75210 63.21888
#> 443 25 40 -16.7521008 -23.2188841 41.75210 63.21888
#> 444 65 85 21.1409692 25.1357466 43.85903 59.86425
#> 445 18 75 -23.7521008 11.7811159 41.75210 63.21888
#> 446 40 15 -4.1727273 -49.5833333 44.17273 64.58333
#> 447 20 65 -21.7521008 1.7811159 41.75210 63.21888
#> 448 80 40 36.1409692 -19.8642534 43.85903 59.86425
#> 449 7 60 -34.7521008 -3.2188841 41.75210 63.21888
#> 450 50 60 8.2478992 -3.2188841 41.75210 63.21888
#> 451 30 85 -11.7521008 21.7811159 41.75210 63.21888
#> 452 10 100 -33.8590308 40.1357466 43.85903 59.86425
#> 453 8 100 -35.8590308 40.1357466 43.85903 59.86425
#> 454 6 95 -37.8590308 35.1357466 43.85903 59.86425
#> 455 6 80 -37.8590308 20.1357466 43.85903 59.86425
#> 456 42 35 -2.1727273 -29.5833333 44.17273 64.58333
#> 457 10 95 -33.8590308 35.1357466 43.85903 59.86425
#> 458 30 25 -13.8590308 -34.8642534 43.85903 59.86425
#> 459 15 95 -26.7521008 31.7811159 41.75210 63.21888
#> 460 10 95 -29.7834101 24.1784038 39.78341 70.82160
#> 461 10 80 -34.1727273 15.4166667 44.17273 64.58333
#> 462 130 75 90.2165899 4.1784038 39.78341 70.82160
#> 463 160 0 116.1409692 -59.8642534 43.85903 59.86425
#> 464 168 45 123.8272727 -19.5833333 44.17273 64.58333
#> 465 24 15 -19.8590308 -44.8642534 43.85903 59.86425
#> 466 24 15 -19.8590308 -44.8642534 43.85903 59.86425
#> 467 30 15 -11.7521008 -48.2188841 41.75210 63.21888
#> 468 20 90 -24.1727273 25.4166667 44.17273 64.58333
#> 469 10 90 -34.1727273 25.4166667 44.17273 64.58333
#> 470 7 95 -36.8590308 35.1357466 43.85903 59.86425
#> 471 120 15 75.8272727 -49.5833333 44.17273 64.58333
#> 472 6 95 -35.7521008 31.7811159 41.75210 63.21888
#> 473 6 85 -33.7834101 14.1784038 39.78341 70.82160
#> 474 10 100 -33.8590308 40.1357466 43.85903 59.86425
#> 475 20 100 -23.8590308 40.1357466 43.85903 59.86425
#> 476 5 NA -39.1727273 NA 44.17273 64.58333
#> 477 60 35 18.2478992 -28.2188841 41.75210 63.21888
#> 478 20 90 -19.7834101 19.1784038 39.78341 70.82160
#> 479 6 100 -35.7521008 36.7811159 41.75210 63.21888
#> 480 10 75 -29.7834101 4.1784038 39.78341 70.82160
#> 481 84 10 42.2478992 -53.2188841 41.75210 63.21888
#> 482 8 85 -33.7521008 21.7811159 41.75210 63.21888
#> 483 168 65 126.2478992 1.7811159 41.75210 63.21888
#> 484 40 55 0.2165899 -15.8215962 39.78341 70.82160
#> 485 40 55 -1.7521008 -8.2188841 41.75210 63.21888
#> 486 20 55 -23.8590308 -4.8642534 43.85903 59.86425
#> 487 56 60 14.2478992 -3.2188841 41.75210 63.21888
#> 488 6 100 -33.7834101 29.1784038 39.78341 70.82160
#> 489 7 100 -34.7521008 36.7811159 41.75210 63.21888
#> 490 12 80 -31.8590308 20.1357466 43.85903 59.86425
#> 491 10 75 -29.7834101 4.1784038 39.78341 70.82160
#> 492 14 75 -27.7521008 11.7811159 41.75210 63.21888
#> 493 28 45 -11.7834101 -25.8215962 39.78341 70.82160
#> 494 12 75 -32.1727273 10.4166667 44.17273 64.58333
#> 495 28 65 -11.7834101 -5.8215962 39.78341 70.82160
#> 496 11 75 -30.7521008 11.7811159 41.75210 63.21888
#> 497 16 85 -28.1727273 20.4166667 44.17273 64.58333
#> 498 12 65 -29.7521008 1.7811159 41.75210 63.21888
#> 499 22 65 -22.1727273 0.4166667 44.17273 64.58333
#> 500 17 95 -22.7834101 24.1784038 39.78341 70.82160
#> 501 16 85 -23.7834101 14.1784038 39.78341 70.82160
#> 502 50 0 5.8272727 -64.5833333 44.17273 64.58333
#> 503 6 85 -37.8590308 25.1357466 43.85903 59.86425
#> 504 5 75 -38.8590308 15.1357466 43.85903 59.86425
#> 505 45 10 1.1409692 -49.8642534 43.85903 59.86425
#> 506 16 40 -27.8590308 -19.8642534 43.85903 59.86425
#> 507 15 65 -24.7834101 -5.8215962 39.78341 70.82160
#> 508 20 45 -24.1727273 -19.5833333 44.17273 64.58333
#> 509 20 55 -21.7521008 -8.2188841 41.75210 63.21888
#> 510 8 45 -33.7521008 -18.2188841 41.75210 63.21888
#> 511 8 90 -31.7834101 19.1784038 39.78341 70.82160
#> 512 15 60 -26.7521008 -3.2188841 41.75210 63.21888
#> 513 10 50 -33.8590308 -9.8642534 43.85903 59.86425
#> 514 15 90 -28.8590308 30.1357466 43.85903 59.86425
#> 515 27 80 -16.8590308 20.1357466 43.85903 59.86425
#> 516 14 70 -27.7521008 6.7811159 41.75210 63.21888
#> 517 28 50 -15.8590308 -9.8642534 43.85903 59.86425
#> 518 168 20 128.2165899 -50.8215962 39.78341 70.82160
#> 519 168 0 126.2478992 -63.2188841 41.75210 63.21888
#> 520 21 95 -22.8590308 35.1357466 43.85903 59.86425
#> 521 12 95 -32.1727273 30.4166667 44.17273 64.58333
#> 522 62 55 18.1409692 -4.8642534 43.85903 59.86425
#> 523 20 85 -19.7834101 14.1784038 39.78341 70.82160
#> 524 7 80 -37.1727273 15.4166667 44.17273 64.58333
#> 525 10 80 -29.7834101 9.1784038 39.78341 70.82160
#> 526 20 80 -19.7834101 9.1784038 39.78341 70.82160
#> 527 8 90 -36.1727273 25.4166667 44.17273 64.58333
#> 528 9 90 -35.1727273 25.4166667 44.17273 64.58333
#> 529 12 90 -31.8590308 30.1357466 43.85903 59.86425
#> 530 10 90 -29.7834101 19.1784038 39.78341 70.82160
#> 531 35 45 -6.7521008 -18.2188841 41.75210 63.21888
#> 532 5 100 -36.7521008 36.7811159 41.75210 63.21888
#> 533 18 45 -23.7521008 -18.2188841 41.75210 63.21888
#> 534 15 90 -29.1727273 25.4166667 44.17273 64.58333
#> 535 6 95 -33.7834101 24.1784038 39.78341 70.82160
#> 536 8 100 -36.1727273 35.4166667 44.17273 64.58333
#> 537 12 100 -31.8590308 40.1357466 43.85903 59.86425
#> 538 25 0 -18.8590308 -59.8642534 43.85903 59.86425
#> 539 10 60 -33.8590308 0.1357466 43.85903 59.86425
#> 540 40 NA -3.8590308 NA 43.85903 59.86425
#> 541 20 45 -23.8590308 -14.8642534 43.85903 59.86425
#> 542 6 75 -38.1727273 10.4166667 44.17273 64.58333
#> 543 168 80 124.1409692 20.1357466 43.85903 59.86425
#> 544 4 100 -37.7521008 36.7811159 41.75210 63.21888
#> 545 168 95 123.8272727 30.4166667 44.17273 64.58333
#> 546 24 80 -15.7834101 9.1784038 39.78341 70.82160
#> 547 25 65 -19.1727273 0.4166667 44.17273 64.58333
#> 548 40 25 -1.7521008 -38.2188841 41.75210 63.21888
#> 549 18 75 -23.7521008 11.7811159 41.75210 63.21888
#> 550 20 75 -21.7521008 11.7811159 41.75210 63.21888
#> 551 40 55 0.2165899 -15.8215962 39.78341 70.82160
#> 552 6 100 -33.7834101 29.1784038 39.78341 70.82160
#> 553 5 100 -39.1727273 35.4166667 44.17273 64.58333
#> 554 30 100 -9.7834101 29.1784038 39.78341 70.82160
#> 555 14 90 -29.8590308 30.1357466 43.85903 59.86425
#> 556 8 100 -36.1727273 35.4166667 44.17273 64.58333
#> 557 28 15 -16.1727273 -49.5833333 44.17273 64.58333
#> 558 45 0 1.1409692 -59.8642534 43.85903 59.86425
#> 559 40 15 -3.8590308 -44.8642534 43.85903 59.86425
#> 560 30 55 -14.1727273 -9.5833333 44.17273 64.58333
#> 561 28 35 -11.7834101 -35.8215962 39.78341 70.82160
#> 562 50 60 6.1409692 0.1357466 43.85903 59.86425
#> 563 84 35 42.2478992 -28.2188841 41.75210 63.21888
#> 564 12 75 -31.8590308 15.1357466 43.85903 59.86425
#> 565 40 50 -3.8590308 -9.8642534 43.85903 59.86425
#> 566 10 90 -34.1727273 25.4166667 44.17273 64.58333
#> 567 15 100 -29.1727273 35.4166667 44.17273 64.58333
#> 568 40 65 -1.7521008 1.7811159 41.75210 63.21888
#> 569 24 50 -17.7521008 -13.2188841 41.75210 63.21888
#> 570 168 5 126.2478992 -58.2188841 41.75210 63.21888
#> 571 160 50 115.8272727 -14.5833333 44.17273 64.58333
#> 572 162 5 122.2165899 -65.8215962 39.78341 70.82160
#> 573 100 0 56.1409692 -59.8642534 43.85903 59.86425
#> 574 110 45 65.8272727 -19.5833333 44.17273 64.58333
#> 575 140 10 96.1409692 -49.8642534 43.85903 59.86425
#> 576 25 65 -16.7521008 1.7811159 41.75210 63.21888
#> 577 15 45 -28.8590308 -14.8642534 43.85903 59.86425
#> 578 35 95 -6.7521008 31.7811159 41.75210 63.21888
#> 579 30 45 -13.8590308 -14.8642534 43.85903 59.86425
#> 580 40 65 -1.7521008 1.7811159 41.75210 63.21888
#> 581 10 0 -33.8590308 -59.8642534 43.85903 59.86425
#> 582 25 95 -19.1727273 30.4166667 44.17273 64.58333
#> 583 12 80 -29.7521008 16.7811159 41.75210 63.21888
#> 584 35 65 -6.7521008 1.7811159 41.75210 63.21888
#> 585 10 100 -33.8590308 40.1357466 43.85903 59.86425
#> 586 30 100 -9.7834101 29.1784038 39.78341 70.82160
#> 587 10 95 -29.7834101 24.1784038 39.78341 70.82160
#> 588 100 0 60.2165899 -70.8215962 39.78341 70.82160
#> 589 12 50 -31.8590308 -9.8642534 43.85903 59.86425
#> 590 56 40 12.1409692 -19.8642534 43.85903 59.86425
#> 591 40 80 0.2165899 9.1784038 39.78341 70.82160
#> 592 30 0 -13.8590308 -59.8642534 43.85903 59.86425
#> 593 60 30 18.2478992 -33.2188841 41.75210 63.21888
#> 594 100 45 58.2478992 -18.2188841 41.75210 63.21888
#> 595 20 35 -21.7521008 -28.2188841 41.75210 63.21888
#> 596 35 5 -8.8590308 -54.8642534 43.85903 59.86425
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#> 598 22 90 -22.1727273 25.4166667 44.17273 64.58333
#> 599 60 0 18.2478992 -63.2188841 41.75210 63.21888
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#> 601 20 50 -24.1727273 -14.5833333 44.17273 64.58333
#> 602 70 10 26.1409692 -49.8642534 43.85903 59.86425
#> 603 25 65 -19.1727273 0.4166667 44.17273 64.58333
#> 604 6 100 -37.8590308 40.1357466 43.85903 59.86425
#> 605 18 95 -21.7834101 24.1784038 39.78341 70.82160
#> 606 10 95 -34.1727273 30.4166667 44.17273 64.58333
#> 607 15 100 -28.8590308 40.1357466 43.85903 59.86425
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#> 609 20 90 -23.8590308 30.1357466 43.85903 59.86425
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#> 613 48 45 4.1409692 -14.8642534 43.85903 59.86425
#> 614 80 30 35.8272727 -34.5833333 44.17273 64.58333
#> 615 77 85 33.1409692 25.1357466 43.85903 59.86425
#> 616 6 85 -37.8590308 25.1357466 43.85903 59.86425
#> 617 6 65 -35.7521008 1.7811159 41.75210 63.21888
#> 618 8 85 -31.7834101 14.1784038 39.78341 70.82160
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#> 625 10 60 -34.1727273 -4.5833333 44.17273 64.58333
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#> 633 28 90 -13.7521008 26.7811159 41.75210 63.21888
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#> 647 14 NA -30.1727273 NA 44.17273 64.58333
#> 648 40 40 -3.8590308 -19.8642534 43.85903 59.86425
#> 649 10 80 -33.8590308 20.1357466 43.85903 59.86425
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#> 653 42 45 -2.1727273 -19.5833333 44.17273 64.58333
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#> 655 5 100 -39.1727273 35.4166667 44.17273 64.58333
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#> 666 5 95 -34.7834101 24.1784038 39.78341 70.82160
#> 667 4 95 -39.8590308 35.1357466 43.85903 59.86425
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#> 670 10 80 -34.1727273 15.4166667 44.17273 64.58333
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#> 672 16 75 -28.1727273 10.4166667 44.17273 64.58333
#> 673 22 70 -22.1727273 5.4166667 44.17273 64.58333
#> 674 100 NA 60.2165899 NA 39.78341 70.82160
#> 675 100 30 58.2478992 -33.2188841 41.75210 63.21888
#> 676 30 95 -13.8590308 35.1357466 43.85903 59.86425
#> 677 120 30 75.8272727 -34.5833333 44.17273 64.58333
#> 678 100 55 60.2165899 -15.8215962 39.78341 70.82160
#> 679 10 95 -33.8590308 35.1357466 43.85903 59.86425
#> 680 120 75 80.2165899 4.1784038 39.78341 70.82160
#> 681 6 100 -35.7521008 36.7811159 41.75210 63.21888
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#> 684 10 65 -33.8590308 5.1357466 43.85903 59.86425
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#> 686 9 95 -35.1727273 30.4166667 44.17273 64.58333
#> 687 12 95 -31.8590308 35.1357466 43.85903 59.86425
#> 688 20 90 -19.7834101 19.1784038 39.78341 70.82160
#> 689 10 95 -34.1727273 30.4166667 44.17273 64.58333
#> 690 160 70 118.2478992 6.7811159 41.75210 63.21888
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#> 692 20 45 -24.1727273 -19.5833333 44.17273 64.58333
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#> 694 7 95 -32.7834101 24.1784038 39.78341 70.82160
#> 695 35 10 -8.8590308 -49.8642534 43.85903 59.86425
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#> 704 4 100 -35.7834101 29.1784038 39.78341 70.82160
#> 705 8 90 -35.8590308 30.1357466 43.85903 59.86425
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#> 708 10 90 -33.8590308 30.1357466 43.85903 59.86425
#> 709 30 55 -13.8590308 -4.8642534 43.85903 59.86425
#> 710 10 95 -31.7521008 31.7811159 41.75210 63.21888
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#> 713 15 60 -29.1727273 -4.5833333 44.17273 64.58333
#> 714 35 NA -4.7834101 NA 39.78341 70.82160
#> 715 21 65 -18.7834101 -5.8215962 39.78341 70.82160
#> 716 168 45 126.2478992 -18.2188841 41.75210 63.21888
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#> 718 10 85 -34.1727273 20.4166667 44.17273 64.58333
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#> 721 6 95 -37.8590308 35.1357466 43.85903 59.86425
#> 722 8 100 -35.8590308 40.1357466 43.85903 59.86425
#> 723 15 90 -28.8590308 30.1357466 43.85903 59.86425
#> 724 84 5 40.1409692 -54.8642534 43.85903 59.86425
#> 725 45 75 5.2165899 4.1784038 39.78341 70.82160
#> 726 40 70 -4.1727273 5.4166667 44.17273 64.58333
#> 727 90 0 50.2165899 -70.8215962 39.78341 70.82160
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#> 729 70 65 28.2478992 1.7811159 41.75210 63.21888
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#> 733 8 90 -35.8590308 30.1357466 43.85903 59.86425
#> 734 30 5 -14.1727273 -59.5833333 44.17273 64.58333
#> 735 4 90 -35.7834101 19.1784038 39.78341 70.82160
#> 736 84 75 42.2478992 11.7811159 41.75210 63.21888
#> 737 10 90 -29.7834101 19.1784038 39.78341 70.82160
#> 738 25 75 -19.1727273 10.4166667 44.17273 64.58333
#> 739 60 95 16.1409692 35.1357466 43.85903 59.86425
#> 740 6 100 -33.7834101 29.1784038 39.78341 70.82160
#> 741 26 0 -17.8590308 -59.8642534 43.85903 59.86425
#> 742 12 90 -31.8590308 30.1357466 43.85903 59.86425
#> 743 25 70 -14.7834101 -0.8215962 39.78341 70.82160
#> 744 15 100 -24.7834101 29.1784038 39.78341 70.82160
#> 745 50 25 6.1409692 -34.8642534 43.85903 59.86425
#> 746 18 85 -26.1727273 20.4166667 44.17273 64.58333
#> 747 12 75 -27.7834101 4.1784038 39.78341 70.82160
#> 748 22 75 -21.8590308 15.1357466 43.85903 59.86425
#> 749 21 55 -22.8590308 -4.8642534 43.85903 59.86425
#> 750 70 70 25.8272727 5.4166667 44.17273 64.58333
#> 751 168 30 123.8272727 -34.5833333 44.17273 64.58333
#> 752 5 15 -36.7521008 -48.2188841 41.75210 63.21888
#> 753 30 65 -13.8590308 5.1357466 43.85903 59.86425
#> 754 70 40 28.2478992 -23.2188841 41.75210 63.21888
#> 755 168 90 126.2478992 26.7811159 41.75210 63.21888
#> 756 9 95 -32.7521008 31.7811159 41.75210 63.21888
#> 757 6 90 -37.8590308 30.1357466 43.85903 59.86425
#> 758 4 35 -40.1727273 -29.5833333 44.17273 64.58333
#> 759 20 45 -19.7834101 -25.8215962 39.78341 70.82160
#> 760 8 85 -36.1727273 20.4166667 44.17273 64.58333
#> 761 14 80 -30.1727273 15.4166667 44.17273 64.58333
#> 762 9 50 -30.7834101 -20.8215962 39.78341 70.82160
#> 763 6 90 -38.1727273 25.4166667 44.17273 64.58333
#> 764 14 95 -25.7834101 24.1784038 39.78341 70.82160
#> 765 7 90 -36.8590308 30.1357466 43.85903 59.86425
#> 766 6 100 -33.7834101 29.1784038 39.78341 70.82160
#> 767 20 70 -19.7834101 -0.8215962 39.78341 70.82160
#> 768 20 70 -24.1727273 5.4166667 44.17273 64.58333
#> 769 48 85 6.2478992 21.7811159 41.75210 63.21888
#> 770 10 90 -29.7834101 19.1784038 39.78341 70.82160
#> 771 5 100 -34.7834101 29.1784038 39.78341 70.82160
#> 772 6 85 -33.7834101 14.1784038 39.78341 70.82160
#> 773 8 75 -31.7834101 4.1784038 39.78341 70.82160
#> 774 8 100 -33.7521008 36.7811159 41.75210 63.21888
#> 775 8 65 -31.7834101 -5.8215962 39.78341 70.82160
#> 776 8 80 -31.7834101 9.1784038 39.78341 70.82160
#> 777 4 90 -37.7521008 26.7811159 41.75210 63.21888
#> 778 4 80 -37.7521008 16.7811159 41.75210 63.21888
#> 779 8 85 -35.8590308 25.1357466 43.85903 59.86425
#> 780 25 60 -19.1727273 -4.5833333 44.17273 64.58333
#> 781 20 90 -24.1727273 25.4166667 44.17273 64.58333
#> 782 6 85 -33.7834101 14.1784038 39.78341 70.82160
#> 783 21 65 -23.1727273 0.4166667 44.17273 64.58333
#> 784 28 75 -13.7521008 11.7811159 41.75210 63.21888
#> 785 70 45 30.2165899 -25.8215962 39.78341 70.82160
#> 786 8 70 -33.7521008 6.7811159 41.75210 63.21888
#> 787 21 20 -23.1727273 -44.5833333 44.17273 64.58333
#> 788 28 70 -11.7834101 -0.8215962 39.78341 70.82160
#> 789 14 20 -29.8590308 -39.8642534 43.85903 59.86425
#> 790 4 100 -37.7521008 36.7811159 41.75210 63.21888
#> 791 5 100 -34.7834101 29.1784038 39.78341 70.82160
#> 792 6 95 -33.7834101 24.1784038 39.78341 70.82160
#> 793 7 90 -34.7521008 26.7811159 41.75210 63.21888
#> 794 140 40 98.2478992 -23.2188841 41.75210 63.21888
#> 795 4 90 -40.1727273 25.4166667 44.17273 64.58333
#> 796 8 90 -31.7834101 19.1784038 39.78341 70.82160
#> 797 7 90 -36.8590308 30.1357466 43.85903 59.86425
#> 798 8 95 -33.7521008 31.7811159 41.75210 63.21888
#> 799 7 100 -36.8590308 40.1357466 43.85903 59.86425
#> 800 30 60 -13.8590308 0.1357466 43.85903 59.86425
#> 801 40 60 -3.8590308 0.1357466 43.85903 59.86425
#> 802 50 45 5.8272727 -19.5833333 44.17273 64.58333
#> 803 35 55 -4.7834101 -15.8215962 39.78341 70.82160
#> 804 42 15 -1.8590308 -44.8642534 43.85903 59.86425
#> 805 40 85 0.2165899 14.1784038 39.78341 70.82160
#> 806 168 85 128.2165899 14.1784038 39.78341 70.82160
#> 807 150 80 105.8272727 15.4166667 44.17273 64.58333
#> 808 168 60 126.2478992 -3.2188841 41.75210 63.21888
#> 809 168 40 124.1409692 -19.8642534 43.85903 59.86425
#> 810 168 45 124.1409692 -14.8642534 43.85903 59.86425
#> 811 14 60 -30.1727273 -4.5833333 44.17273 64.58333
#> 812 6 85 -33.7834101 14.1784038 39.78341 70.82160
#> 813 8 70 -35.8590308 10.1357466 43.85903 59.86425
#> 814 22 55 -19.7521008 -8.2188841 41.75210 63.21888
#> 815 10 95 -34.1727273 30.4166667 44.17273 64.58333
#> 816 6 90 -38.1727273 25.4166667 44.17273 64.58333
#> 817 30 90 -13.8590308 30.1357466 43.85903 59.86425
#> 818 8 90 -31.7834101 19.1784038 39.78341 70.82160
#> 819 10 100 -31.7521008 36.7811159 41.75210 63.21888
#> 820 10 65 -31.7521008 1.7811159 41.75210 63.21888
#> 821 12 95 -29.7521008 31.7811159 41.75210 63.21888
#> 822 20 95 -23.8590308 35.1357466 43.85903 59.86425
#> 823 15 85 -26.7521008 21.7811159 41.75210 63.21888
#> 824 20 75 -24.1727273 10.4166667 44.17273 64.58333
#> 825 15 80 -29.1727273 15.4166667 44.17273 64.58333
#> 826 20 90 -24.1727273 25.4166667 44.17273 64.58333
#> 827 25 95 -16.7521008 31.7811159 41.75210 63.21888
#> 828 7 65 -34.7521008 1.7811159 41.75210 63.21888
#> 829 4 95 -40.1727273 30.4166667 44.17273 64.58333
#> 830 20 40 -24.1727273 -24.5833333 44.17273 64.58333
#> 831 10 90 -33.8590308 30.1357466 43.85903 59.86425
#> 832 50 40 10.2165899 -30.8215962 39.78341 70.82160
#> 833 20 85 -19.7834101 14.1784038 39.78341 70.82160
#> 834 25 90 -19.1727273 25.4166667 44.17273 64.58333
#> 835 5 95 -39.1727273 30.4166667 44.17273 64.58333
#> 836 7 90 -37.1727273 25.4166667 44.17273 64.58333
#> 837 5 95 -36.7521008 31.7811159 41.75210 63.21888
#> 838 12 95 -27.7834101 24.1784038 39.78341 70.82160
#> 839 35 80 -4.7834101 9.1784038 39.78341 70.82160
#> 840 35 65 -6.7521008 1.7811159 41.75210 63.21888
#> 841 30 10 -14.1727273 -54.5833333 44.17273 64.58333
#> 842 40 70 -1.7521008 6.7811159 41.75210 63.21888
#> 843 15 90 -28.8590308 30.1357466 43.85903 59.86425
#> 844 10 90 -31.7521008 26.7811159 41.75210 63.21888
#> 845 8 95 -31.7834101 24.1784038 39.78341 70.82160
#> 846 5 80 -36.7521008 16.7811159 41.75210 63.21888
#> 847 14 95 -25.7834101 24.1784038 39.78341 70.82160
#> 848 14 95 -25.7834101 24.1784038 39.78341 70.82160
#> 849 6 95 -37.8590308 35.1357466 43.85903 59.86425
#> 850 14 90 -27.7521008 26.7811159 41.75210 63.21888
#> 851 7 90 -34.7521008 26.7811159 41.75210 63.21888
#> 852 20 55 -24.1727273 -9.5833333 44.17273 64.58333
#> 853 6 95 -35.7521008 31.7811159 41.75210 63.21888
#> 854 10 100 -33.8590308 40.1357466 43.85903 59.86425
#> 855 30 55 -9.7834101 -15.8215962 39.78341 70.82160
#> 856 14 70 -30.1727273 5.4166667 44.17273 64.58333
#> 857 10 85 -33.8590308 25.1357466 43.85903 59.86425
#> 858 10 80 -31.7521008 16.7811159 41.75210 63.21888
#> 859 28 85 -11.7834101 14.1784038 39.78341 70.82160
#> 860 8 100 -35.8590308 40.1357466 43.85903 59.86425
#> 861 6 100 -38.1727273 35.4166667 44.17273 64.58333
#> 862 20 100 -21.7521008 36.7811159 41.75210 63.21888
#> 863 5 95 -36.7521008 31.7811159 41.75210 63.21888
#> 864 7 95 -37.1727273 30.4166667 44.17273 64.58333
#> 865 20 90 -23.8590308 30.1357466 43.85903 59.86425
#> 866 18 100 -26.1727273 35.4166667 44.17273 64.58333
#> 867 12 90 -29.7521008 26.7811159 41.75210 63.21888
#> 868 17 90 -26.8590308 30.1357466 43.85903 59.86425
#> 869 14 85 -27.7521008 21.7811159 41.75210 63.21888
#> 870 5 100 -39.1727273 35.4166667 44.17273 64.58333
#> 871 6 100 -33.7834101 29.1784038 39.78341 70.82160
#> 872 4 100 -40.1727273 35.4166667 44.17273 64.58333
#> 873 4 100 -40.1727273 35.4166667 44.17273 64.58333
#> 874 6 100 -35.7521008 36.7811159 41.75210 63.21888
#> 875 10 100 -33.8590308 40.1357466 43.85903 59.86425
#> 876 6 100 -33.7834101 29.1784038 39.78341 70.82160
#> 877 14 10 -30.1727273 -54.5833333 44.17273 64.58333
#> 878 30 65 -11.7521008 1.7811159 41.75210 63.21888
#> 879 35 50 -8.8590308 -9.8642534 43.85903 59.86425
#> 880 10 100 -31.7521008 36.7811159 41.75210 63.21888
#> 881 100 100 56.1409692 40.1357466 43.85903 59.86425
#> 882 8 100 -35.8590308 40.1357466 43.85903 59.86425
#> 883 10 100 -33.8590308 40.1357466 43.85903 59.86425
#> 884 20 35 -21.7521008 -28.2188841 41.75210 63.21888
#> 885 40 55 -4.1727273 -9.5833333 44.17273 64.58333
#> 886 40 65 -1.7521008 1.7811159 41.75210 63.21888
#> 887 40 10 -3.8590308 -49.8642534 43.85903 59.86425
#> 888 6 60 -33.7834101 -10.8215962 39.78341 70.82160
#> 889 30 85 -9.7834101 14.1784038 39.78341 70.82160
#> 890 28 85 -16.1727273 20.4166667 44.17273 64.58333
#> 891 20 85 -24.1727273 20.4166667 44.17273 64.58333
#> 892 25 70 -14.7834101 -0.8215962 39.78341 70.82160
#> 893 30 55 -9.7834101 -15.8215962 39.78341 70.82160
#> 894 50 50 10.2165899 -20.8215962 39.78341 70.82160
#> 895 20 70 -23.8590308 10.1357466 43.85903 59.86425
#> 896 15 100 -26.7521008 36.7811159 41.75210 63.21888
#> 897 110 35 70.2165899 -35.8215962 39.78341 70.82160
#> 898 28 80 -13.7521008 16.7811159 41.75210 63.21888
#> 899 85 70 43.2478992 6.7811159 41.75210 63.21888
#> 900 160 25 118.2478992 -38.2188841 41.75210 63.21888
#> 901 10 100 -29.7834101 29.1784038 39.78341 70.82160
#> 902 8 85 -33.7521008 21.7811159 41.75210 63.21888
#> 903 NA NA NA NA 39.78341 70.82160
#> 904 NA NA NA NA 39.78341 70.82160
#> 905 NA NA NA NA 44.17273 64.58333
#> 906 NA NA NA NA 44.17273 64.58333
#> 907 NA NA NA NA 43.85903 59.86425
#> 908 NA NA NA NA 39.78341 70.82160