[R] Excel can do what R can't?????
Spencer Graves
spencer.graves at pdf.com
Thu Jul 17 05:38:48 CEST 2003
Are you familiar with "How to Solve It" by George Polya? Among other
things, Polya discusses the value of solving hypersimplified versions of
a problem, because the solutions to the simple problems may help you see
how you can solve the real problem. Am I correct that prior to the
completion of the transcontinental railroad, the quickest path from
Toronto to Vancouver was by way of Tierra del Fuego?
spencer graves
Spencer Graves wrote:
> I don't expect you to have a complete solution from the simplifications.
> I expect you to learn something from the toy problems that can help you
> solve the real problems.
>
> Michael Rennie wrote:
>
>> Hmmm.
>>
>> I tried entering 'Hgtmod = Hgt' at the end of my 'optim' function, but
>> that didn't help me any- still getting poor optimizations. Perhaps
>> this isn't working to set a condition, as I was hoping it to. I think
>> that if I can set the condition Hgmod = Hgt, then it should be able to
>> find reasonable solutions to this problem set, since that seems to be
>> the trick in my Excel 'solver' function.
>>
>> Also, I'm a little hesitant to simplify this too much in terms of
>> reducing the model, becuase I need this thing to work over 365
>> iterations, as it does in excel. I've at least cleaned up some of the
>> commenting so it should be a bit more straightforward. I tried making
>> the arrays more clear with tabs, but lost them upon pasting them into
>> this file.
>>
>> I've included below the code I am currently using with my temp.dat
>> file attached (it's also below so someone can copy and paste it into a
>> text file named 'temp.dat')- that's all anyone should need to play
>> around with this if they are feeling so inclined by cutting and
>> pasting into R.
>>
>> Thanks again,
>>
>> Mike
>>
>>
>> #Weight at time 0
>> Wo<- 9.2
>>
>> #Hg concentration at time 0 (ugHg/g wet weight)
>> Hgo<- 0.08
>> #Weight at time t
>> Wt<- 32.2
>>
>> #Hg concentration at time t (ugHg/g wet weight) Hgt<- 0.110
>>
>> #Prey methylmercury concentration (as constant)
>> Hgp<- 0.033
>>
>> #Prey caloric value (as constant)
>> Pc<- 800
>>
>> #Energy density of fish (as constant, calories)
>> Ef <- 1000
>>
>> #Maturity status, 0=immature, 1=mature
>> Mat<- 0
>>
>> #Sex, 1=male, 2=female
>> Sex<- 1
>>
>> #USER INPUT ABOVE
>>
>> #Bioenergetics parameters for perch
>> CA <- 0.25
>> CB <- 0.73 #same as 1+(-0.27)- convert g/g/d to g/d * Pc to get cal/d
>> CQ <- 2.3
>> CTO <- 23
>> CTM <- 28
>> Zc<- (log(CQ))*(CTM-CTO)
>> Yc<- (log(CQ))*(CTM-CTO+2)
>> Xc<- ((Zc^2)*(1+(1+40/Yc)^0.5)^2)/400
>>
>> RA <- 34.992 #0.0108*3240 cal/g 02, converting weight of 02 to cal
>> RB <- 0.8 #same as 1+(-0.2) see above...
>> RQ <- 2.1
>> RTO <- 28
>> RTM <- 33
>> Za <- (log(RQ))*(RTM-RTO)
>> Ya<- (log(RQ))*(RTM-RTO+2)
>> Xa<- ((Za^2)*(1+(1+40/Ya)^0.5)^2)/400
>>
>> S <- 0.172
>>
>> FA <- 0.158
>> FB <- -0.222
>> FG <- 0.631
>>
>> UA<- 0.0253
>> UB<- 0.58
>> UG<- -0.299
>>
>> #Mass balance model parameters
>> EA <- 0.002938
>> EB <- -0.2
>> EQ <- 0.066
>> a <- 0.8
>>
>> #Specifying sex-specific parameters
>>
>> GSI<- NULL
>>
>> if (Sex==1) GSI<-0.05 else if (Sex==2) GSI<-0.17
>> #Bring in temp file
>>
>> temper <- scan("temp.dat", na.strings = ".", list(Day=0, jday=0, Temp=0))
>>
>> Day<-temper$Day ; jday<-temper$jday ; Temp<-temper$Temp ;
>> temp<- cbind (Day, jday, Temp)
>> #Day = number of days modelled, jday=julian day, Temp = daily avg. temp.
>> #temp [,2]
>>
>> Vc<-(CTM-(temp[,3]))/(CTM-CTO)
>> Vr<-(RTM-(temp[,3]))/(RTM-RTO)
>>
>> comp<- cbind (Day, jday, Temp, Vc, Vr)
>>
>> #comp
>>
>> bio<-matrix(NA, ncol=13, nrow=length(Day))
>> W<-NULL
>> C<-NULL
>> ASMR<-NULL
>> SMR<-NULL
>> A<-NULL
>> F<-NULL
>> U<-NULL
>> SDA<-NULL
>> Gr<-NULL
>> Hg<-NULL
>> Ed<-NULL
>> GHg<-NULL
>> K<-NULL
>> Expegk<-NULL
>> EGK<-NULL
>> p<-NULL
>> ACT<-NULL
>>
>>
>> p <- 1 # 0.558626306252032 ACT <- 2 # 1.66764519286918
>>
>> q<-c(p,ACT)
>>
>> #introduce function to solve
>> f <- function (q, Hgtmod)
>> {
>>
>> M<- length(Day) #number of days iterated
>>
>> for (i in 1:M)
>> {
>>
>> #Bioenergetics model
>> if (Day[i]==1) W[i] <- Wo else
>> if (jday[i]==121 && Mat==1) W[i] <- (W[i-1]-(W[i-1]*GSI*1.2)) else
>> W[i] <- (W[i-1]+(Gr[i-1]/Ef))
>>
>> C[i]<- q[1]*CA*(W[i]^CB)*((comp[i,4])^Xc)*(exp(Xc*(1-(comp[i,4]))))*Pc
>>
>> ASMR[i]<- q[2]*RA*(W[i]^RB)*((comp[i,5])^Xa)*(exp(Xa*(1-(comp[i,5]))))
>>
>> SMR[i]<- (ASMR[i]/q[2])
>>
>> A[i]<- (ASMR[i]-SMR[i])
>>
>> F[i]<- (FA*((comp[i,3])^FB)*(exp(FG*p))*C[i])
>>
>> U[i]<- (UA*((comp[i,3])^UB)*(exp(UG*p))*(C[i]-F[i]))
>>
>> SDA[i]<- (S*(C[i]-F[i]))
>>
>> Gr[i]<- (C[i]-(ASMR[i]+F[i]+U[i]+SDA[i]))
>>
>> #Trudel MMBM
>>
>> if (Day[i]==1) Hg[i] <- Hgo else Hg[i] <-
>> a*Hgp*(C[i-1]/Pc/W[i-1])/EGK[i-1]*(1-
>> Expegk[i-1])+(Hg[i-1]*Expegk[i-1])
>>
>> Ed[i]<- EA*(W[i]^EB)*(exp(EQ*(comp[i,3])))
>>
>> GHg[i] <- Gr[i]/Ef/W[i]
>>
>> if (Sex==1)
>> K[i]<-(((0.1681*(10^(1.3324+(0.000453*Hg[i])))/1000)/Hg[i])*GSI)/M else
>> if (Sex==2)
>> K[i]<-(((0.1500*(10^(0.8840+(0.000903*Hg[i])))/1000)/Hg[i])*GSI)/M
>> # = dw/ww conversion * gonad ~ body conc'n function(ng/g) / convert to
>> ug/g # then express as Q times GSI gives K / M gives daily K
>>
>> EGK[i] <- (Ed[i] + GHg[i] + (K[i]*Mat))
>>
>> Expegk[i] <- exp(-1*EGK[i])
>>
>> bio<- cbind(W, C, ASMR, SMR, A, F, U, SDA, Gr, Ed, GHg, EGK, Hg)
>>
>> }
>>
>> dimnames (bio) <-list(NULL, c
>> ("W", "C", "ASMR", "SMR", "A", "F", "U", "SDA", "Gr", "Ed", "GHg",
>> "EGK", "Hg"))
>>
>> bioday<-cbind(jday, W, C, ASMR, SMR, A, F, U, SDA, Gr, Ed, GHg, EGK, Hg)
>>
>> dimnames (bioday) <-list(NULL, c
>> ("jday", "W", "C", "ASMR", "SMR", "A", "F", "U", "SDA", "Gr", "Ed",
>> "GHg", "EGK"
>> , "Hg"))
>>
>>
>> Wtmod<- bioday [length(W),2]
>> Wtmod
>>
>> Hgtmod<- bioday [length(Hg),14]
>> Hgtmod
>>
>> q
>>
>> f <- 1000000000*((((Wt-Wtmod)^2)/Wt) + (((Hgt-Hgtmod)^2)/Hgt)) ; f
>> }
>>
>> optim(q, f, method = "L-BFGS-B",
>> lower = c(0.2, 2), upper=c(2, 3),
>> Hgtmod = Hgt)
>>
>> #-----------------------------
>>
>> Temp.dat:
>>
>> 1 153 9.4
>> 2 154 9.6
>> 3 155 9.8
>> 4 156 10
>> 5 157 10.2
>> 6 158 10.4
>> 7 159 10.6
>> 8 160 10.8
>> 9 161 11
>> 10 162 11.2
>> 11 163 11.4
>> 12 164 11.6
>> 13 165 11.8
>> 14 166 12
>> 15 167 12.3
>> 16 168 12.5
>> 17 169 12.7
>> 18 170 12.9
>> 19 171 13.1
>> 20 172 13.4
>> 21 173 13.6
>> 22 174 13.8
>> 23 175 14
>> 24 176 14.2
>> 25 177 14.5
>> 26 178 14.7
>> 27 179 14.9
>> 28 180 15.1
>> 29 181 15.4
>> 30 182 15.6
>> 31 183 15.8
>> 32 184 16
>> 33 185 16.2
>> 34 186 16.5
>> 35 187 16.7
>> 36 188 16.9
>> 37 189 17.1
>> 38 190 17.3
>> 39 191 17.5
>> 40 192 17.7
>> 41 193 17.9
>> 42 194 18.1
>> 43 195 18.3
>> 44 196 18.5
>> 45 197 18.7
>> 46 198 18.9
>> 47 199 19
>> 48 200 19.2
>> 49 201 19.4
>> 50 202 19.5
>> 51 203 19.7
>> 52 204 19.9
>> 53 205 20
>> 54 206 20.2
>> 55 207 20.3
>> 56 208 20.4
>> 57 209 20.5
>> 58 210 20.7
>> 59 211 20.8
>> 60 212 20.9
>> 61 213 21
>> 62 214 21.1
>> 63 215 21.2
>> 64 216 21.3
>> 65 217 21.3
>> 66 218 21.4
>> 67 219 21.5
>> 68 220 21.5
>> 69 221 21.6
>> 70 222 21.6
>> 71 223 21.6
>> 72 224 21.7
>> 73 225 21.7
>> 74 226 21.7
>> 75 227 21.7
>> 76 228 21.7
>> 77 229 21.7
>> 78 230 21.7
>> 79 231 21.6
>> 80 232 21.6
>> 81 233 21.6
>> 82 234 21.5
>> 83 235 21.5
>> 84 236 21.4
>> 85 237 21.3
>> 86 238 21.3
>> 87 239 21.2
>> 88 240 21.1
>> 89 241 21
>> 90 242 20.9
>> 91 243 20.8
>> 92 244 20.7
>> 93 245 20.5
>> 94 246 20.4
>> 95 247 20.3
>> 96 248 20.2
>> 97 249 20
>> 98 250 19.9
>> 99 251 19.7
>> 100 252 19.5
>> 101 253 19.4
>> 102 254 19.2
>> 103 255 19
>> 104 256 18.9
>> 105 257 18.7
>> 106 258 18.5
>> 107 259 18.3
>> 108 260 18.1
>> 109 261 17.9
>> 110 262 17.7
>> 111 263 17.5
>> 112 264 17.3
>> 113 265 17.1
>> 114 266 16.9
>> 115 267 16.7
>> 116 268 16.5
>> 117 269 16.2
>> 118 270 16
>> 119 271 15.8
>> 120 272 15.6
>> 121 273 15.4
>> 122 274 15.1
>> 123 275 14.9
>> 124 276 14.7
>> 125 277 14.5
>> 126 278 14.2
>> 127 279 14
>> 128 280 13.8
>> 129 281 13.6
>> 130 282 13.4
>> 131 283 13.1
>> 132 284 12.9
>> 133 285 12.7
>> 134 286 12.5
>> 135 287 12.3
>> 136 288 12
>> 137 289 11.8
>> 138 290 11.6
>> 139 291 11.4
>> 140 292 11.2
>> 141 293 11
>> 142 294 10.8
>> 143 295 10.6
>> 144 296 10.4
>> 145 297 10.2
>> 146 298 10
>> 147 299 9.8
>> 148 300 9.6
>> 149 301 9.4
>> 150 302 9.3
>> 151 303 9.1
>> 152 304 8.9
>> 153 305 8.7
>> 154 306 8.6
>> 155 307 8.4
>> 156 308 8.2
>> 157 309 8.1
>> 158 310 7.9
>> 159 311 7.8
>> 160 312 7.6
>> 161 313 7.5
>> 162 314 7.3
>> 163 315 7.2
>> 164 316 7
>> 165 317 6.9
>> 166 318 6.8
>> 167 319 6.7
>> 168 320 6.5
>> 169 321 6.4
>> 170 322 6.3
>> 171 323 6.2
>> 172 324 6.1
>> 173 325 6
>> 174 326 5.8
>> 175 327 5.7
>> 176 328 5.6
>> 177 329 5.5
>> 178 330 5.5
>> 179 331 5.4
>> 180 332 5.3
>> 181 333 5.2
>> 182 334 5.1
>> 183 335 5
>> 184 336 5
>> 185 337 4.9
>> 186 338 4.8
>> 187 339 4.7
>> 188 340 4.7
>> 189 341 4.6
>> 190 342 4.5
>> 191 343 4.5
>> 192 344 4.4
>> 193 345 4.4
>> 194 346 4.3
>> 195 347 4.3
>> 196 348 4.2
>> 197 349 4.2
>> 198 350 4.1
>> 199 351 4.1
>> 200 352 4
>> 201 353 4
>> 202 354 4
>> 203 355 3.9
>> 204 356 3.9
>> 205 357 3.8
>> 206 358 3.8
>> 207 359 3.8
>> 208 360 3.8
>> 209 361 3.7
>> 210 362 3.7
>> 211 363 3.7
>> 212 364 3.6
>> 213 365 3.6
>> 214 366 3.6
>> 215 1 3.2
>> 216 2 3.2
>> 217 3 3.2
>> 218 4 3.2
>> 219 5 3.2
>> 220 6 3.2
>> 221 7 3.2
>> 222 8 3.2
>> 223 9 3.2
>> 224 10 3.2
>> 225 11 3.2
>> 226 12 3.2
>> 227 13 3.2
>> 228 14 3.2
>> 229 15 3.2
>> 230 16 3.2
>> 231 17 3.2
>> 232 18 3.2
>> 233 19 3.2
>> 234 20 3.2
>> 235 21 3.2
>> 236 22 3.2
>> 237 23 3.2
>> 238 24 3.2
>> 239 25 3.2
>> 240 26 3.2
>> 241 27 3.2
>> 242 28 3.2
>> 243 29 3.2
>> 244 30 3.2
>> 245 31 3.2
>> 246 32 3.2
>> 247 33 3.2
>> 248 34 3.2
>> 249 35 3.2
>> 250 36 3.2
>> 251 37 3.2
>> 252 38 3.2
>> 253 39 3.2
>> 254 40 3.2
>> 255 41 3.2
>> 256 42 3.2
>> 257 43 3.2
>> 258 44 3.2
>> 259 45 3.2
>> 260 46 3.2
>> 261 47 3.2
>> 262 48 3.2
>> 263 49 3.2
>> 264 50 3.2
>> 265 51 3.2
>> 266 52 3.2
>> 267 53 3.2
>> 268 54 3.3
>> 269 55 3.3
>> 270 56 3.3
>> 271 57 3.3
>> 272 58 3.3
>> 273 59 3.3
>> 274 60 3.3
>> 275 61 3.3
>> 276 62 3.3
>> 277 63 3.3
>> 278 64 3.3
>> 279 65 3.3
>> 280 66 3.3
>> 281 67 3.3
>> 282 68 3.3
>> 283 69 3.3
>> 284 70 3.3
>> 285 71 3.4
>> 286 72 3.4
>> 287 73 3.4
>> 288 74 3.4
>> 289 75 3.4
>> 290 76 3.4
>> 291 77 3.4
>> 292 78 3.4
>> 293 79 3.5
>> 294 80 3.5
>> 295 81 3.5
>> 296 82 3.5
>> 297 83 3.5
>> 298 84 3.5
>> 299 85 3.6
>> 300 86 3.6
>> 301 87 3.6
>> 302 88 3.6
>> 303 89 3.6
>> 304 90 3.7
>> 305 91 3.7
>> 306 92 3.7
>> 307 93 3.8
>> 308 94 3.8
>> 309 95 3.8
>> 310 96 3.8
>> 311 97 3.9
>> 312 98 3.9
>> 313 99 4
>> 314 100 4
>> 315 101 4
>> 316 102 4.1
>> 317 103 4.1
>> 318 104 4.2
>> 319 105 4.2
>> 320 106 4.3
>> 321 107 4.3
>> 322 108 4.4
>> 323 109 4.4
>> 324 110 4.5
>> 325 111 4.5
>> 326 112 4.6
>> 327 113 4.7
>> 328 114 4.7
>> 329 115 4.8
>> 330 116 4.9
>> 331 117 5
>> 332 118 5
>> 333 119 5.1
>> 334 120 5.2
>> 335 121 5.3
>> 336 122 5.4
>> 337 123 5.5
>> 338 124 5.5
>> 339 125 5.6
>> 340 126 5.7
>> 341 127 5.8
>> 342 128 6
>> 343 129 6.1
>> 344 130 6.2
>> 345 131 6.3
>> 346 132 6.4
>> 347 133 6.5
>> 348 134 6.7
>> 349 135 6.8
>> 350 136 6.9
>> 351 137 7
>> 352 138 7.2
>> 353 139 7.3
>> 354 140 7.5
>> 355 141 7.6
>> 356 142 7.8
>> 357 143 7.9
>> 358 144 8.1
>> 359 145 8.2
>> 360 146 8.4
>> 361 147 8.6
>> 362 148 8.7
>> 363 149 8.9
>> 364 150 9.1
>> 365 151 9.3
>> 366 152 9.3
>>
>>
>>
>> ------------------------------------------------------------------------
>>
>> 1 153 9.4
>> 2 154 9.6
>> 3 155 9.8
>> 4 156 10
>> 5 157 10.2
>> 6 158 10.4
>> 7 159 10.6
>> 8 160 10.8
>> 9 161 11
>> 10 162 11.2
>> 11 163 11.4
>> 12 164 11.6
>> 13 165 11.8
>> 14 166 12
>> 15 167 12.3
>> 16 168 12.5
>> 17 169 12.7
>> 18 170 12.9
>> 19 171 13.1
>> 20 172 13.4
>> 21 173 13.6
>> 22 174 13.8
>> 23 175 14
>> 24 176 14.2
>> 25 177 14.5
>> 26 178 14.7
>> 27 179 14.9
>> 28 180 15.1
>> 29 181 15.4
>> 30 182 15.6
>> 31 183 15.8
>> 32 184 16
>> 33 185 16.2
>> 34 186 16.5
>> 35 187 16.7
>> 36 188 16.9
>> 37 189 17.1
>> 38 190 17.3
>> 39 191 17.5
>> 40 192 17.7
>> 41 193 17.9
>> 42 194 18.1
>> 43 195 18.3
>> 44 196 18.5
>> 45 197 18.7
>> 46 198 18.9
>> 47 199 19
>> 48 200 19.2
>> 49 201 19.4
>> 50 202 19.5
>> 51 203 19.7
>> 52 204 19.9
>> 53 205 20
>> 54 206 20.2
>> 55 207 20.3
>> 56 208 20.4
>> 57 209 20.5
>> 58 210 20.7
>> 59 211 20.8
>> 60 212 20.9
>> 61 213 21
>> 62 214 21.1
>> 63 215 21.2
>> 64 216 21.3
>> 65 217 21.3
>> 66 218 21.4
>> 67 219 21.5
>> 68 220 21.5
>> 69 221 21.6
>> 70 222 21.6
>> 71 223 21.6
>> 72 224 21.7
>> 73 225 21.7
>> 74 226 21.7
>> 75 227 21.7
>> 76 228 21.7
>> 77 229 21.7
>> 78 230 21.7
>> 79 231 21.6
>> 80 232 21.6
>> 81 233 21.6
>> 82 234 21.5
>> 83 235 21.5
>> 84 236 21.4
>> 85 237 21.3
>> 86 238 21.3
>> 87 239 21.2
>> 88 240 21.1
>> 89 241 21
>> 90 242 20.9
>> 91 243 20.8
>> 92 244 20.7
>> 93 245 20.5
>> 94 246 20.4
>> 95 247 20.3
>> 96 248 20.2
>> 97 249 20
>> 98 250 19.9
>> 99 251 19.7
>> 100 252 19.5
>> 101 253 19.4
>> 102 254 19.2
>> 103 255 19
>> 104 256 18.9
>> 105 257 18.7
>> 106 258 18.5
>> 107 259 18.3
>> 108 260 18.1
>> 109 261 17.9
>> 110 262 17.7
>> 111 263 17.5
>> 112 264 17.3
>> 113 265 17.1
>> 114 266 16.9
>> 115 267 16.7
>> 116 268 16.5
>> 117 269 16.2
>> 118 270 16
>> 119 271 15.8
>> 120 272 15.6
>> 121 273 15.4
>> 122 274 15.1
>> 123 275 14.9
>> 124 276 14.7
>> 125 277 14.5
>> 126 278 14.2
>> 127 279 14
>> 128 280 13.8
>> 129 281 13.6
>> 130 282 13.4
>> 131 283 13.1
>> 132 284 12.9
>> 133 285 12.7
>> 134 286 12.5
>> 135 287 12.3
>> 136 288 12
>> 137 289 11.8
>> 138 290 11.6
>> 139 291 11.4
>> 140 292 11.2
>> 141 293 11
>> 142 294 10.8
>> 143 295 10.6
>> 144 296 10.4
>> 145 297 10.2
>> 146 298 10
>> 147 299 9.8
>> 148 300 9.6
>> 149 301 9.4
>> 150 302 9.3
>> 151 303 9.1
>> 152 304 8.9
>> 153 305 8.7
>> 154 306 8.6
>> 155 307 8.4
>> 156 308 8.2
>> 157 309 8.1
>> 158 310 7.9
>> 159 311 7.8
>> 160 312 7.6
>> 161 313 7.5
>> 162 314 7.3
>> 163 315 7.2
>> 164 316 7
>> 165 317 6.9
>> 166 318 6.8
>> 167 319 6.7
>> 168 320 6.5
>> 169 321 6.4
>> 170 322 6.3
>> 171 323 6.2
>> 172 324 6.1
>> 173 325 6
>> 174 326 5.8
>> 175 327 5.7
>> 176 328 5.6
>> 177 329 5.5
>> 178 330 5.5
>> 179 331 5.4
>> 180 332 5.3
>> 181 333 5.2
>> 182 334 5.1
>> 183 335 5
>> 184 336 5
>> 185 337 4.9
>> 186 338 4.8
>> 187 339 4.7
>> 188 340 4.7
>> 189 341 4.6
>> 190 342 4.5
>> 191 343 4.5
>> 192 344 4.4
>> 193 345 4.4
>> 194 346 4.3
>> 195 347 4.3
>> 196 348 4.2
>> 197 349 4.2
>> 198 350 4.1
>> 199 351 4.1
>> 200 352 4
>> 201 353 4
>> 202 354 4
>> 203 355 3.9
>> 204 356 3.9
>> 205 357 3.8
>> 206 358 3.8
>> 207 359 3.8
>> 208 360 3.8
>> 209 361 3.7
>> 210 362 3.7
>> 211 363 3.7
>> 212 364 3.6
>> 213 365 3.6
>> 214 366 3.6
>> 215 1 3.2
>> 216 2 3.2
>> 217 3 3.2
>> 218 4 3.2
>> 219 5 3.2
>> 220 6 3.2
>> 221 7 3.2
>> 222 8 3.2
>> 223 9 3.2
>> 224 10 3.2
>> 225 11 3.2
>> 226 12 3.2
>> 227 13 3.2
>> 228 14 3.2
>> 229 15 3.2
>> 230 16 3.2
>> 231 17 3.2
>> 232 18 3.2
>> 233 19 3.2
>> 234 20 3.2
>> 235 21 3.2
>> 236 22 3.2
>> 237 23 3.2
>> 238 24 3.2
>> 239 25 3.2
>> 240 26 3.2
>> 241 27 3.2
>> 242 28 3.2
>> 243 29 3.2
>> 244 30 3.2
>> 245 31 3.2
>> 246 32 3.2
>> 247 33 3.2
>> 248 34 3.2
>> 249 35 3.2
>> 250 36 3.2
>> 251 37 3.2
>> 252 38 3.2
>> 253 39 3.2
>> 254 40 3.2
>> 255 41 3.2
>> 256 42 3.2
>> 257 43 3.2
>> 258 44 3.2
>> 259 45 3.2
>> 260 46 3.2
>> 261 47 3.2
>> 262 48 3.2
>> 263 49 3.2
>> 264 50 3.2
>> 265 51 3.2
>> 266 52 3.2
>> 267 53 3.2
>> 268 54 3.3
>> 269 55 3.3
>> 270 56 3.3
>> 271 57 3.3
>> 272 58 3.3
>> 273 59 3.3
>> 274 60 3.3
>> 275 61 3.3
>> 276 62 3.3
>> 277 63 3.3
>> 278 64 3.3
>> 279 65 3.3
>> 280 66 3.3
>> 281 67 3.3
>> 282 68 3.3
>> 283 69 3.3
>> 284 70 3.3
>> 285 71 3.4
>> 286 72 3.4
>> 287 73 3.4
>> 288 74 3.4
>> 289 75 3.4
>> 290 76 3.4
>> 291 77 3.4
>> 292 78 3.4
>> 293 79 3.5
>> 294 80 3.5
>> 295 81 3.5
>> 296 82 3.5
>> 297 83 3.5
>> 298 84 3.5
>> 299 85 3.6
>> 300 86 3.6
>> 301 87 3.6
>> 302 88 3.6
>> 303 89 3.6
>> 304 90 3.7
>> 305 91 3.7
>> 306 92 3.7
>> 307 93 3.8
>> 308 94 3.8
>> 309 95 3.8
>> 310 96 3.8
>> 311 97 3.9
>> 312 98 3.9
>> 313 99 4
>> 314 100 4
>> 315 101 4
>> 316 102 4.1
>> 317 103 4.1
>> 318 104 4.2
>> 319 105 4.2
>> 320 106 4.3
>> 321 107 4.3
>> 322 108 4.4
>> 323 109 4.4
>> 324 110 4.5
>> 325 111 4.5
>> 326 112 4.6
>> 327 113 4.7
>> 328 114 4.7
>> 329 115 4.8
>> 330 116 4.9
>> 331 117 5
>> 332 118 5
>> 333 119 5.1
>> 334 120 5.2
>> 335 121 5.3
>> 336 122 5.4
>> 337 123 5.5
>> 338 124 5.5
>> 339 125 5.6
>> 340 126 5.7
>> 341 127 5.8
>> 342 128 6
>> 343 129 6.1
>> 344 130 6.2
>> 345 131 6.3
>> 346 132 6.4
>> 347 133 6.5
>> 348 134 6.7
>> 349 135 6.8
>> 350 136 6.9
>> 351 137 7
>> 352 138 7.2
>> 353 139 7.3
>> 354 140 7.5
>> 355 141 7.6
>> 356 142 7.8
>> 357 143 7.9
>> 358 144 8.1
>> 359 145 8.2
>> 360 146 8.4
>> 361 147 8.6
>> 362 148 8.7
>> 363 149 8.9
>> 364 150 9.1
>> 365 151 9.3
>> 366 152 9.3
>
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