2
$\begingroup$

I'm creating a number of models with a crossed random effects structure that allows for heteroscedasticity. In my analysis I have measurements of nest elevation (Z), each associated with a parent (MaleID) and a study area (Area). Males move between different study areas, so each level of MaleID can be associated with multiple levels of Area.

Additionally, the elevation measurements have been collected using a couple of different methods (Method) that will vary in their precision. Therefore, I wanted to build a heteroscedastic model that takes into account this variation in measurement error. As I understand it, this can only be done in nlme.

Using these resources (https://goo.gl/sK7nGf and http://goo.gl/EgEcje) I built this model with nlme:

lme(Z ~ 1, data = ELEV, 
    random = list(const = pdBlocked(list(pdIdent(~Area - 1), pdIdent(~MaleID - 1)))), 
    weights = varIdent(form = ~1|Method))

Now, as a next step, I want to include a fixed effect Year and add a term for random slopes of Year across levels of MaleID (in addition to random intercepts). I know in nlme this would normally be coded:

random = ~1 + Year|MaleID

But I can't work out how this can be done with my crossed random effects structure.

  1. Could anybody tell me how random slopes might be added in to my above example?
  2. Am I correct in assuming that this type of model can only be built using nlme or is there a possible work around for heteroscedastic models in lme4 that I've missed?

As my data often includes a crossed random effects structure using lme4 would make things heaps easier. Thank you!

I've included a dput() output of a subset of my data below. The whole dataset is a few thousand records long, but the basic structure of this subset is the same. Please note that MaleID is treated as a factor.

structure(list(Year = c(1995L, 1995L, 1995L, 1995L, 1995L, 1995L, 
1995L, 1996L, 1996L, 1996L, 1996L, 1996L, 1996L, 1996L, 1996L, 
1996L, 1996L, 2000L, 2000L, 2000L, 2000L, 2000L, 2000L, 2000L, 
2000L, 2000L, 2000L, 2000L, 2001L, 2001L, 2001L, 2001L, 2001L, 
2001L, 2001L, 2002L, 2002L, 2002L, 2002L, 2002L, 2002L, 2002L, 
2002L, 2002L, 2002L, 2002L, 2003L, 2003L, 2003L, 2004L, 2004L, 
2004L, 2004L, 2005L, 2005L, 2005L, 2005L, 2006L, 1996L, 1996L, 
1996L, 1996L, 2011L, 1995L, 1995L, 2001L, 2001L, 1996L, 1996L, 
1996L, 1996L, 2003L, 2004L, 2004L, 2004L, 2003L, 1996L, 1996L, 
2010L, 2010L, 2009L, 2009L, 1996L, 2001L, 2004L, 1995L, 1995L, 
1995L, 1996L, 2004L, 2012L, 2012L, 1995L, 2002L, 2002L, 2004L, 
2004L, 2011L, 2011L, 2011L, 2011L, 2011L, 2011L, 1995L, 2004L, 
1996L, 1996L, 2000L, 2003L, 2004L, 2004L, 2004L, 2004L, 2004L, 
1996L, 2005L, 2005L, 2005L, 1996L, 1996L, 1996L, 1996L, 1996L, 
1996L, 1996L, 2001L, 2011L, 2011L, 2011L, 2012L, 2012L, 2000L, 
2000L, 2000L, 2001L, 2009L, 2004L, 2004L, 2005L, 2005L, 2006L, 
2008L, 1996L, 2003L, 2003L, 2006L, 2006L, 2006L, 2009L, 2009L, 
2009L, 1995L, 1996L, 2000L, 2000L, 2005L, 2008L, 2010L, 1996L, 
2008L, 2008L, 2008L, 1996L, 1996L, 1996L, 2008L, 2009L, 2010L, 
2010L, 2011L, 1995L, 2012L, 2012L, 1995L, 2000L, 2004L, 2009L, 
2014L, 2014L, 2014L, 2006L, 2006L, 2006L, 2006L, 2009L, 2013L, 
2013L, 2013L, 1996L, 2003L, 2004L, 2011L, 2011L, 2011L, 2011L, 
1995L, 2009L, 2009L, 2009L, 2009L, 2010L, 1996L, 2003L, 2007L, 
2010L, 2010L, 2010L, 2010L, 2010L, 2005L, 2005L, 2012L, 2012L, 
2012L, 2013L, 2013L, 2013L, 1996L, 2000L, 2003L, 2003L, 2004L, 
2006L, 2006L, 2009L, 1995L, 2008L, 2011L, 2011L, 2011L, 1995L, 
1995L, 2000L, 2004L, 2006L, 2009L, 2010L, 2010L, 2010L, 2002L, 
2002L, 2004L, 2006L, 2007L, 2007L, 2007L, 2008L, 2008L, 1996L, 
2002L, 2006L, 2011L, 2011L, 1996L, 2001L, 1995L, 2001L, 2008L, 
2010L, 1995L, 1995L, 1995L, 1995L, 2001L, 2008L, 1996L, 2003L, 
2013L, 1995L, 1995L, 1995L, 2001L, 2001L, 2003L, 2003L, 2004L, 
2004L, 2004L, 2005L, 2006L, 2006L, 2009L, 2009L, 1995L, 1995L, 
1996L, 1996L, 1996L, 2003L, 2007L, 2007L, 2007L, 2009L, 2010L, 
2010L, 2005L, 2005L, 2005L, 2005L, 2006L, 2007L, 2007L, 2008L, 
2008L, 1995L, 1995L, 1995L, 1995L, 2008L, 2008L, 2008L, 2008L, 
2010L, 1996L, 1996L, 2001L, 2002L, 2004L, 2003L, 2004L, 1995L, 
2001L, 2007L, 2008L, 2009L, 2009L, 2009L, 2009L, 1996L, 1996L, 
1996L, 1996L, 2005L, 2005L, 1995L, 1995L, 1995L, 2001L, 2007L, 
2010L, 2010L, 1996L, 1996L, 2009L, 1995L, 2005L, 1995L, 1995L, 
1995L, 1995L, 1995L, 1996L, 1996L, 2007L, 2007L, 2006L, 2010L, 
1995L, 1995L, 1995L, 2013L, 2013L, 2013L, 2013L, 2001L, 2009L, 
2008L, 2011L, 2011L, 2011L, 1996L, 1996L, 1996L, 2005L, 2006L, 
2012L, 2014L, 1995L, 2012L, 2012L, 1995L, 1995L, 1996L, 1995L, 
1995L, 1995L, 2003L, 2007L, 1995L, 1995L, 1996L, 2003L, 2007L, 
2010L, 2010L, 1996L, 2009L, 2011L, 1996L, 2014L, 1995L, 1995L, 
2007L, 2013L, 2013L, 1996L, 1996L, 2005L, 2005L, 2007L, 2013L, 
2002L, 2002L, 2003L, 2008L, 1995L, 1995L, 1995L, 2008L, 2002L, 
2004L, 2005L, 2014L, 1996L, 2004L, 2004L, 2004L, 2005L, 2008L, 
2010L, 1995L, 1995L, 1995L, 2005L, 2004L, 2002L, 2006L, 1995L, 
2008L, 1996L, 2001L, 2014L, 2014L, 2009L, 2001L, 2001L, 2001L, 
1995L, 2013L, 1995L, 2006L, 2012L, 1995L, 1995L, 1995L, 1995L, 
2010L, 2007L, 2010L), Z = c(164, 136, 156, 147, 136, 141, 135, 
179, 167, 193, 153, 147, 152, 156, 140, 167, 143, 160, 175, 250, 
111, 163, 163, 171, 148, 150, 175, 197, 147, 146, 159, 147, 207, 
161, 168, 250, 250, 177, 168, 153, 118, 169, 162, 202, 168, 201, 
116, 180, 220, 196, 164, 184, 180, 174, 146, 198, 151, 148, 150, 
152, 156, 166, 168, 168, 155, 131, 143, 151, 161, 137, 156, 231, 
179, 172, 186, 236, 173, 144, 205, 188, 145, 154, 148, 145, 224, 
137, 157, 161, 142, 181, 154, 158, 148, 181, 181, 250, 250, 142, 
187, 142, 146, 146, 145, 145, 158, 141, 151, 165, 114, 160, 143, 
152, 206, 141, 170, 203, 130, 149, 150, 159, 162, 170, 178, 155, 
151, 243, 163, 197, 229, 185, 250, 144, 136, 158, 174, 178, 250, 
249, 189, 241, 218, 141, 160, 147, 202, 146, 148, 155, 183, 195, 
182, 161, 150, 250, 164, 172, 137, 143, 177, 154, 180, 138, 136, 
140, 145, 195, 233, 176, 166, 145, 160, 133, 137, 140, 164, 167, 
155, 143, 135, 250, 145, 145, 146, 141, 147, 201, 176, 179, 220, 
250, 149, 140, 147, 149, 155, 146, 131, 250, 154, 250, 160, 148, 
144, 175, 155, 143, 143, 155, 139, 153, 153, 140, 132, 143, 137, 
141, 143, 159, 143, 158, 143, 134, 146, 137, 177, 204, 144, 160, 
160, 161, 141, 131, 144, 204, 182, 142, 153, 157, 154, 169, 172, 
147, 147, 177, 208, 150, 142, 144, 137, 158, 154, 250, 189, 148, 
151, 160, 168, 149, 138, 149, 155, 161, 214, 250, 136, 146, 164, 
136, 154, 167, 144, 119, 147, 170, 136, 157, 131, 138, 180, 175, 
157, 177, 192, 152, 159, 136, 137, 142, 250, 195, 176, 145, 198, 
207, 145, 149, 166, 159, 193, 227, 166, 150, 155, 150, 162, 160, 
151, 142, 149, 140, 250, 180, 144, 161, 163, 136, 142, 148, 179, 
161, 170, 165, 221, 164, 129, 160, 159, 143, 163, 138, 155, 141, 
250, 243, 141, 146, 144, 166, 157, 157, 153, 142, 135, 162, 159, 
139, 146, 151, 149, 153, 147, 149, 128, 133, 192, 223, 156, 123, 
157, 164, 142, 157, 198, 203, 180, 165, 157, 196, 165, 210, 151, 
156, 155, 143, 162, 142, 148, 172, 140, 139, 146, 138, 155, 134, 
139, 167, 162, 176, 153, 158, 156, 138, 115, 164, 199, 156, 140, 
152, 151, 136, 148, 143, 138, 152, 152, 158, 142, 169, 124, 144, 
128, 156, 133, 145, 163, 165, 158, 155, 183, 190, 250, 170, 136, 
140, 144, 168, 173, 160, 162, 165, 151, 155, 153, 156, 165, 139, 
142, 165, 145, 204, 144, 177, 157, 173, 131, 149, 149, 158, 146, 
144, 150, 174, 159, 158, 155, 150, 150, 162, 225), Method = structure(c(1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
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, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 
2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 
1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 
2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 
2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 
2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 
2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 
1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 
1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L), .Label = c("DGPS", "LID"
), class = "factor"), Area = structure(c(7L, 1L, 7L, 1L, 1L, 
1L, 1L, 9L, 10L, 10L, 9L, 9L, 9L, 10L, 10L, 10L, 9L, 1L, 1L, 
19L, 1L, 7L, 1L, 1L, 1L, 7L, 19L, 19L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 19L, 19L, 1L, 13L, 1L, 7L, 20L, 1L, 17L, 20L, 15L, 13L, 20L, 
19L, 17L, 17L, 17L, 1L, 9L, 9L, 9L, 7L, 1L, 1L, 1L, 1L, 1L, 7L, 
1L, 1L, 1L, 1L, 7L, 7L, 1L, 1L, 19L, 8L, 8L, 8L, 19L, 7L, 8L, 
19L, 19L, 1L, 1L, 2L, 1L, 19L, 1L, 1L, 1L, 1L, 1L, 7L, 7L, 1L, 
19L, 19L, 19L, 19L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 8L, 8L, 1L, 
3L, 15L, 1L, 1L, 1L, 1L, 1L, 19L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 2L, 19L, 7L, 19L, 19L, 18L, 18L, 1L, 5L, 5L, 1L, 7L, 19L, 
19L, 1L, 19L, 9L, 7L, 1L, 1L, 1L, 1L, 1L, 3L, 9L, 9L, 9L, 7L, 
1L, 19L, 1L, 1L, 1L, 1L, 8L, 8L, 8L, 1L, 7L, 7L, 1L, 9L, 19L, 
9L, 7L, 1L, 7L, 5L, 5L, 1L, 1L, 7L, 1L, 6L, 5L, 6L, 1L, 1L, 1L, 
5L, 1L, 1L, 1L, 8L, 7L, 19L, 7L, 1L, 1L, 1L, 1L, 1L, 5L, 5L, 
5L, 5L, 7L, 8L, 7L, 17L, 1L, 1L, 1L, 1L, 1L, 7L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 7L, 1L, 1L, 1L, 7L, 7L, 1L, 7L, 7L, 5L, 7L, 7L, 
7L, 1L, 1L, 8L, 1L, 7L, 7L, 7L, 7L, 7L, 1L, 1L, 1L, 1L, 7L, 19L, 
1L, 1L, 1L, 1L, 5L, 1L, 5L, 5L, 7L, 3L, 1L, 19L, 1L, 5L, 7L, 
7L, 7L, 7L, 19L, 7L, 1L, 7L, 5L, 1L, 1L, 1L, 7L, 7L, 1L, 1L, 
3L, 3L, 3L, 8L, 7L, 1L, 19L, 19L, 1L, 1L, 1L, 1L, 1L, 19L, 9L, 
9L, 1L, 17L, 1L, 1L, 7L, 1L, 1L, 3L, 19L, 1L, 9L, 9L, 9L, 1L, 
7L, 7L, 7L, 1L, 7L, 19L, 19L, 1L, 7L, 7L, 7L, 1L, 1L, 1L, 1L, 
1L, 1L, 19L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 19L, 19L, 1L, 
1L, 1L, 1L, 7L, 1L, 1L, 8L, 8L, 1L, 1L, 1L, 1L, 7L, 7L, 7L, 7L, 
7L, 2L, 5L, 8L, 17L, 8L, 1L, 1L, 1L, 1L, 1L, 17L, 17L, 19L, 7L, 
19L, 3L, 3L, 17L, 1L, 7L, 7L, 1L, 8L, 1L, 1L, 7L, 1L, 1L, 1L, 
1L, 2L, 1L, 1L, 1L, 3L, 17L, 1L, 1L, 1L, 7L, 9L, 3L, 3L, 1L, 
3L, 1L, 1L, 1L, 1L, 7L, 1L, 1L, 1L, 8L, 1L, 7L, 3L, 3L, 7L, 1L, 
1L, 1L, 1L, 1L, 7L, 7L, 1L, 8L, 5L, 8L, 1L, 7L, 7L, 7L, 7L, 5L, 
8L, 8L, 1L, 1L, 1L, 3L, 7L, 3L, 7L, 1L, 3L, 2L, 1L, 17L, 19L, 
8L, 7L, 5L, 5L, 1L, 1L, 7L, 9L, 17L, 1L, 1L, 1L, 1L, 1L, 1L, 
17L), .Label = c("A", "B", "Be", "BE", "Bw", "BW", "C", "D", 
"E", "F", "Fe", "FE", "Fw", "FW", "HD", "Nbk", "NBK", "Obk", 
"OBK", "TBK"), class = "factor"), MaleID = c(67, 62, 88, 3, 3, 
3, 3, 2, 69, 60, 4, 35, 68, 53, 16, 61, 79, 9, 14, 55, 80, 77, 
47, 63, 74, 56, 19, 15, 47, 74, 85, 72, 72, 9, 25, 55, 15, 63, 
18, 34, 88, 1, 64, 42, 54, 6, 68, 54, 45, 92, 37, 37, 97, 79, 
94, 95, 86, 25, 12, 12, 12, 20, 77, 10, 12, 80, 80, 44, 44, 31, 
31, 19, 82, 82, 82, 33, 9, 73, 17, 17, 83, 83, 75, 83, 19, 20, 
20, 84, 30, 34, 67, 67, 24, 9, 9, 43, 43, 83, 83, 83, 83, 74, 
74, 36, 57, 81, 82, 28, 59, 33, 5, 5, 87, 80, 25, 15, 97, 97, 
8, 84, 84, 85, 85, 85, 57, 43, 67, 17, 17, 17, 17, 83, 78, 78, 
27, 77, 15, 45, 83, 55, 95, 77, 14, 74, 74, 5, 5, 57, 95, 95, 
95, 44, 97, 43, 85, 34, 83, 83, 52, 82, 82, 74, 40, 40, 27, 95, 
15, 95, 77, 85, 39, 78, 78, 29, 27, 77, 97, 78, 78, 78, 83, 83, 
83, 78, 32, 83, 83, 83, 46, 15, 39, 97, 97, 32, 32, 13, 78, 78, 
78, 78, 67, 98, 9, 93, 97, 97, 32, 32, 32, 77, 5, 97, 97, 97, 
97, 97, 97, 39, 64, 64, 80, 67, 86, 86, 67, 9, 78, 44, 44, 44, 
80, 80, 81, 85, 77, 44, 44, 44, 44, 47, 85, 32, 74, 77, 15, 32, 
32, 32, 3, 78, 33, 78, 78, 77, 57, 85, 94, 97, 78, 11, 11, 41, 
46, 55, 67, 80, 67, 78, 8, 59, 97, 88, 88, 85, 32, 59, 59, 59, 
82, 67, 97, 86, 86, 86, 86, 34, 34, 34, 43, 95, 95, 5, 93, 33, 
33, 67, 85, 32, 65, 43, 97, 94, 94, 94, 27, 71, 71, 66, 25, 44, 
15, 15, 74, 96, 96, 84, 80, 25, 87, 74, 14, 63, 43, 57, 74, 5, 
5, 5, 32, 47, 47, 76, 43, 43, 58, 58, 91, 97, 67, 5, 5, 56, 56, 
85, 22, 74, 50, 38, 38, 38, 38, 67, 59, 78, 82, 93, 15, 26, 26, 
48, 32, 32, 93, 93, 15, 56, 86, 59, 59, 93, 23, 23, 23, 80, 82, 
85, 32, 77, 83, 83, 47, 47, 89, 30, 30, 63, 57, 42, 21, 90, 28, 
49, 86, 59, 59, 86, 59, 5, 63, 83, 7, 70, 74, 5, 5, 99, 5, 44, 
59, 59, 77, 32, 32, 86, 85, 28, 87, 87, 33, 82, 78, 56, 97, 87, 
44, 44, 44, 78, 56, 81, 32, 32, 32, 57, 86, 59, 44, 25, 59, 51, 
34, 93, 93, 81, 44, 78, 78, 23, 85, 40, 94, 93, 31, 5, 5, 5, 
85, 85, 93), const = structure(c(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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 1L, 
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$\endgroup$

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