# [R] Excel can do what R can't?????

Spencer Graves spencer.graves at pdf.com
Thu Jul 17 03:48:52 CEST 2003

```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

```