[R-sig-ME] Factors in nlme: singularity in backsolve error

Alexander Shenkin alexander.shenkin at ouce.ox.ac.uk
Fri Jul 15 17:16:11 CEST 2016


Hello all,

I am parameterizing exponential fits for some metabolic scaling models. 
I have done this in lmer already, without problem, using logged 
dependent and independent variables.  However, I would now like to 
incorporate other parameters that aren't necessarily exponentially 
related to the dependent variable.  Hence, I've turned to nlme, but I 
don't have much experience with it.  Apologies in advance for newbie 
mistakes.

With the code below, I am getting the following error.  I'm guessing 
that it has something to do with the 'site' factor being misspecified:

Error in nlme.formula(dep ~ scaling_fun(alpha, beta, ind, site), data = 
scale_df,  :
   Singularity in backsolve at level 0, block 1

When I fit a simpler function that does not involve 'site', the model 
seems to work correctly.

Any thoughts would be greatly appreciated!  I've added the dput object 
at the bottom of the email to avoid distraction...

Thanks,
Allie


 > head(scale_df)
           dep        ind spp site
2  0.28069471 -0.0322841 157    A
3 -0.69719050 -1.2568901 183    A
4  0.29252012  0.1592420 246    A
5  0.72030740 -0.3282789 154    A
6 -0.08601891  0.3623756 110    A
7  0.30793594  0.2230840 154    A


scaling_fun <- function(alpha, beta, ind, site) {
     return(beta + ind^alpha + site*(ind^alpha))
}

# results in singularity in backsolve error

nlme(dep ~ trait_scaling_fun(alpha, beta, ind, site),
      data = scale_df,
      fixed = list(alpha + beta + site ~ 1), random = alpha ~ 1|spp,
      start = list(fixed = c(0.7, 0, 1)))


##############################
# simpler function converges #
##############################

scaling_fun <- function(alpha, beta, ind) {
     return(beta + ind^alpha)
}

nlme(dep ~ scaling_fun(alpha, beta, ind),
      data = scale_df,
      fixed = list(alpha + beta ~ 1), random = alpha ~ 1|spp,
      start = list(fixed = c(0.7, 0)))


# dput for data

scale_df = structure(list(dep = structure(c(0.280694709349609, 
-0.697190504779316,
0.29252012378561, 0.720307403285465, -0.0860189064012942, 
0.307935942585907,
0.862281389721553, -0.265859454130292, -0.662753116661401, 
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1.17791119955669, 0.631729125553481, -0.556750637034717, 
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0.78495323332528, 0.355622302250686, -1.26351337875593, 0.343598303486811,
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2.87816317587089, -0.224750322639999, -0.497119013269447, 
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1.93466683745019, 1.0320275291612, 0.874248439252774, -0.327339718896358,
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     219L, 72L, 88L, 76L, 76L, 76L, 15L, 17L, 220L, 145L, 15L,
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     242L, 93L, 93L, 257L, 39L, 25L, 25L, 39L, 93L, 35L, 72L,
     214L, 83L, 211L, 102L, 102L, 93L, 145L, 211L, 219L, 72L,
     257L, 272L, 39L, 133L, 257L, 212L, 219L, 72L, 193L, 33L,
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     120L, 163L, 253L, 254L, 112L, 195L, 88L, 163L, 278L, 253L,
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     130L, 169L, 127L, 117L, 169L, 65L, 127L, 130L, 169L, 254L,
     228L, 172L, 148L, 187L, 204L, 19L, 204L, 117L, 228L, 187L,
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     228L, 230L, 158L, 158L, 172L, 191L, 38L, 172L, 224L, 228L,
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     40L, 95L, 125L, 50L, 171L, 178L, 82L, 178L, 74L, 204L, 194L,
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     85L, 267L, 66L, 38L, 255L, 139L, 85L, 161L, 215L, 268L, 204L,
     161L, 250L, 221L, 68L, 250L, 255L, 221L, 221L, 139L, 215L,
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     38L, 4L, 103L, 4L, 104L, 41L, 31L, 68L, 268L, 119L, 103L,
     187L, 119L, 187L, 53L, 215L, 267L, 235L, 119L, 204L, 113L,
     53L, 268L, 181L, 113L, 68L, 181L, 204L, 113L, 255L, 53L,
     139L, 38L, 68L, 103L, 68L, 187L, 31L, 36L, 206L, 177L, 128L,
     225L, 190L, 189L, 28L, 218L, 11L, 177L, 54L, 137L, 202L,
     121L, 202L, 129L, 206L, 121L, 177L, 91L, 190L, 189L, 169L,
     189L, 129L, 202L, 169L, 203L, 137L, 42L, 22L, 190L, 21L,
     106L, 138L, 194L, 251L, 138L, 36L, 21L, 194L, 137L, 54L,
     218L, 203L, 251L, 128L, 251L, 36L, 128L, 28L, 11L, 28L, 42L,
     138L, 206L, 169L, 22L, 218L, 91L, 203L, 106L, 106L, 91L,
     22L, 243L, 27L, 128L, 128L, 164L, 223L, 243L, 164L, 279L,
     16L, 194L, 164L, 207L, 27L, 223L, 244L, 188L, 45L, 143L,
     232L, 84L, 45L, 194L, 217L, 232L, 54L, 207L, 217L, 232L,
     176L, 45L, 217L, 143L, 243L, 144L, 143L, 49L, 176L, 176L,
     175L, 223L, 194L, 128L, 16L, 169L, 188L, 244L, 188L, 169L,
     84L, 54L, 244L, 49L, 166L, 108L, 52L, 166L, 166L, 56L, 273L,
     155L, 155L, 155L, 155L, 273L, 108L, 5L, 5L, 273L, 100L, 155L,
     100L, 97L, 59L, 59L, 100L, 198L, 165L, 171L, 171L, 171L,
     165L, 100L, 198L, 67L, 273L, 97L, 277L, 67L, 67L, 5L, 5L,
     97L, 165L, 108L, 198L, 182L, 182L, 182L, 59L, 277L, 108L,
     165L, 52L, 97L, 5L, 277L, 100L, 59L, 182L, 198L, 52L, 273L,
     56L, 56L, 198L, 165L, 67L, 166L, 277L, 59L, 56L, 52L, 171L,
     277L, 182L, 67L, 171L, 155L, 166L, 97L, 52L, 56L, 122L, 248L,
     12L, 47L, 142L, 142L, 32L, 7L, 248L, 87L, 122L, 122L, 7L,
     170L, 170L, 29L, 12L, 7L, 32L, 261L, 48L, 170L, 87L, 48L,
     29L, 142L, 12L, 261L, 47L, 87L, 261L, 29L, 248L, 48L, 122L,
     32L, 47L, 274L, 97L, 109L, 30L, 115L, 58L, 58L, 58L, 115L,
     56L, 274L, 56L, 55L, 273L, 273L, 274L, 56L, 274L, 274L, 274L,
     166L, 55L, 58L, 274L, 273L, 273L, 56L, 277L, 115L, 115L,
     58L, 55L, 18L, 18L, 166L, 166L, 277L, 109L, 56L, 274L, 115L,
     200L, 55L, 18L, 18L, 58L, 277L, 277L, 200L, 277L, 200L, 167L,
     273L, 200L, 274L, 274L), .Label = c("1", "2", "3", "4", "5",
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     "17", "18", "19", "20", "21", "22", "23", "24", "25", "26",
     "27", "28", "29", "30", "31", "32", "33", "34", "35", "36",
     "37", "38", "39", "40", "41", "42", "43", "44", "45", "46",
     "47", "48", "49", "50", "51", "52", "53", "54", "55", "56",
     "57", "58", "59", "60", "61", "62", "63", "64", "65", "66",
     "67", "68", "69", "70", "71", "72", "73", "74", "75", "76",
     "77", "78", "79", "80", "81", "82", "83", "84", "85", "86",
     "87", "88", "89", "90", "91", "92", "93", "94", "95", "96",
     "97", "98", "99", "100", "101", "102", "103", "104", "105",
     "106", "107", "108", "109", "110", "111", "112", "113", "114",
     "115", "116", "117", "118", "119", "120", "121", "122", "123",
     "124", "125", "126", "127", "128", "129", "130", "131", "132",
     "133", "134", "135", "136", "137", "138", "139", "140", "141",
     "142", "143", "144", "145", "146", "147", "148", "149", "150",
     "151", "152", "153", "154", "155", "156", "157", "158", "159",
     "160", "161", "162", "163", "164", "165", "166", "167", "168",
     "169", "170", "171", "172", "173", "174", "175", "176", "177",
     "178", "179", "180", "181", "182", "183", "184", "185", "186",
     "187", "188", "189", "190", "191", "192", "193", "194", "195",
     "196", "197", "198", "199", "200", "201", "202", "203", "204",
     "205", "206", "207", "208", "209", "210", "211", "212", "213",
     "214", "215", "216", "217", "218", "219", "220", "221", "222",
     "223", "224", "225", "226", "227", "228", "229", "230", "231",
     "232", "233", "234", "235", "236", "237", "238", "239", "240",
     "241", "242", "243", "244", "245", "246", "247", "248", "249",
     "250", "251", "252", "253", "254", "255", "256", "257", "258",
     "259", "260", "261", "262", "263", "264", "265", "266", "267",
     "268", "269", "270", "271", "272", "273", "274", "275", "276",
     "277", "278", "279"), class = "factor"), site = structure(c(1L,
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     1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
     1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
     19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L,
     19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L,
     19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L,
     19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L,
     19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L,
     19L, 19L, 19L, 19L, 19L, 19L, 20L, 20L, 20L, 20L, 20L, 20L,
     20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L,
     20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L,
     20L, 20L, 20L, 20L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L,
     18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L,
     18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L,
     18L, 18L, 18L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L,
     17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L,
     17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L,
     17L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L,
     11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L,
     11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L,
     11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L,
     11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L,
     11L, 11L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
     3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
     3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
     3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
     16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L,
     16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L,
     16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L,
     16L, 16L, 16L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L,
     15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 12L, 12L,
     12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L,
     12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L,
     12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L,
     12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L,
     12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L,
     12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L,
     12L, 12L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L,
     13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L,
     13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L,
     13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 8L, 8L,
     8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L,
     8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L,
     8L, 8L, 8L, 8L, 8L, 8L, 8L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
     7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
     7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 5L, 5L,
     5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
     5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
     5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
     5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
     5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L,
     6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
     6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
     6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
     6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
     6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
     6L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
     10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
     10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
     10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
     10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
     10L, 10L, 10L, 10L, 10L, 10L, 10L, 9L, 9L, 9L, 9L, 9L, 9L,
     9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L,
     9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L,
     9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L,
     9L, 9L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
     4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
     4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
     4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
     4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
     4L, 4L, 4L, 4L, 4L, 4L, 4L, 14L, 14L, 14L, 14L, 14L, 14L,
     14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L,
     14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L,
     14L, 14L, 14L, 14L, 14L, 14L, 14L, 2L, 2L, 2L, 2L, 2L, 2L,
     2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
     2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
     2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
     2L, 2L, 2L, 2L, 2L), .Label = c("A", "B", "C", "D", "E",
     "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "Q", "R",
     "S", "T", "U"), class = "factor")), .Names = c("dep", "ind",
"spp", "site"), row.names = c(2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L,
10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L, 22L,
23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L,
36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L,
49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L, 61L,
62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L, 71L, 72L, 73L, 74L,
75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L, 83L, 84L, 85L, 86L, 87L,
88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L, 97L, 98L, 99L, 100L,
101L, 102L, 103L, 104L, 105L, 106L, 107L, 108L, 109L, 110L, 111L,
112L, 113L, 114L, 115L, 116L, 117L, 118L, 119L, 120L, 121L, 122L,
123L, 124L, 125L, 126L, 127L, 128L, 129L, 130L, 131L, 132L, 133L,
134L, 135L, 136L, 137L, 138L, 139L, 140L, 141L, 142L, 143L, 144L,
145L, 146L, 147L, 148L, 149L, 150L, 151L, 152L, 153L, 154L, 155L,
156L, 157L, 158L, 159L, 160L, 162L, 163L, 164L, 165L, 166L, 167L,
168L, 169L, 170L, 171L, 172L, 173L, 174L, 175L, 176L, 177L, 178L,
179L, 180L, 181L, 182L, 184L, 185L, 186L, 187L, 188L, 189L, 190L,
191L, 192L, 193L, 194L, 195L, 196L, 197L, 198L, 199L, 200L, 201L,
202L, 203L, 204L, 205L, 206L, 207L, 208L, 209L, 210L, 211L, 212L,
213L, 214L, 215L, 216L, 217L, 218L, 219L, 220L, 221L, 222L, 223L,
224L, 225L, 226L, 227L, 228L, 229L, 230L, 231L, 232L, 233L, 234L,
235L, 236L, 237L, 238L, 239L, 240L, 241L, 242L, 243L, 244L, 245L,
246L, 247L, 248L, 249L, 250L, 251L, 252L, 253L, 254L, 255L, 256L,
257L, 258L, 259L, 260L, 261L, 262L, 263L, 264L, 265L, 266L, 267L,
268L, 269L, 270L, 271L, 272L, 273L, 274L, 275L, 276L, 277L, 279L,
280L, 290L, 291L, 292L, 293L, 294L, 295L, 296L, 297L, 298L, 299L,
300L, 301L, 302L, 303L, 304L, 305L, 306L, 307L, 308L, 309L, 310L,
311L, 312L, 313L, 314L, 315L, 316L, 317L, 318L, 319L, 320L, 321L,
322L, 323L, 324L, 325L, 326L, 327L, 328L, 329L, 330L, 331L, 332L,
333L, 334L, 335L, 336L, 337L, 338L, 339L, 340L, 341L, 342L, 343L,
344L, 345L, 346L, 347L, 348L, 349L, 350L, 352L, 353L, 354L, 355L,
356L, 357L, 358L, 359L, 360L, 361L, 362L, 363L, 364L, 365L, 366L,
367L, 368L, 369L, 370L, 371L, 372L, 373L, 374L, 375L, 376L, 377L,
378L, 379L, 380L, 382L, 383L, 384L, 385L, 386L, 387L, 389L, 390L,
391L, 392L, 393L, 394L, 395L, 396L, 397L, 398L, 399L, 400L, 401L,
402L, 403L, 404L, 405L, 406L, 407L, 408L, 409L, 410L, 411L, 412L,
413L, 414L, 415L, 416L, 418L, 419L, 420L, 422L, 423L, 424L, 425L,
427L, 428L, 429L, 430L, 431L, 432L, 433L, 434L, 435L, 436L, 437L,
438L, 439L, 440L, 442L, 443L, 444L, 445L, 446L, 447L, 448L, 449L,
450L, 451L, 452L, 453L, 454L, 455L, 456L, 458L, 459L, 460L, 462L,
463L, 464L, 465L, 466L, 467L, 468L, 469L, 470L, 472L, 473L, 474L,
475L, 476L, 477L, 479L, 480L, 481L, 482L, 483L, 484L, 485L, 486L,
487L, 489L, 490L, 491L, 492L, 493L, 494L, 495L, 496L, 497L, 498L,
499L, 501L, 502L, 503L, 504L, 505L, 506L, 507L, 508L, 509L, 510L,
511L, 512L, 513L, 514L, 515L, 516L, 517L, 518L, 519L, 520L, 521L,
522L, 523L, 524L, 525L, 526L, 527L, 528L, 529L, 530L, 531L, 532L,
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