[R-sig-ME] lme vs. lmer

Raldo Kruger raldo.kruger at gmail.com
Wed Sep 30 21:40:38 CEST 2009


Chris,
Thanks for that - I should probably have mentioned that I'm using
family=quasipoisson  in glmer since my data has Poisson distribution
as well as being overdispersed. I'm unsure how one decides which term
to drop without being informed by p-values, and so don't quite
understand how the "Likelihood ratio test using anova()" , or the AIC
or BIC model comparison will work in this case (I thought one's
supposed to remove the term with the highest p-value from the model,
and compare it with the model with the term included to see if there's
a difference, not so?).

Douglas,
Yes I have data (see attached). The response variable ('Counts'
column) is the number of seedlings per plot. There are four sites that
are not the same (since these are previously mined sites and it's
impossible to get even two sites that are exactly the same, in terms
of age, soil properties etc). Each site has 20 reps of each treatment
- Control, G, N and NG, and the data was collected over three
consecutive years. Each set of treatments were grouped together in a
'Patch' (sort of a split plot design, although I've ignored this thus
far).

So the model using glmer looks like this (I'm not sure if the 'random'
factors are correct, or if it should just be '(1|Site)', and i've
ignore the split plot design...):

> ex4o_r2<-glmer(Counts~N+G+Year+N:Year+G:Year+N:G:Year+(Year|Site), data=ex4o, family=quasipoisson)
> ex4o_r2
Generalized linear mixed model fit by the Laplace approximation
Formula: Counts~ N + G + Year + N:Year + G:Year + N:G:Year + (Year |      Site)
   Data: ex4o
  AIC  BIC logLik deviance
 5731 5823  -2846     5693
Random effects:
 Groups   Name        Variance Std.Dev. Corr
 Site     (Intercept) 1.35594  1.1644
          Yearthree   3.53069  1.8790   0.752
          Yeartwo     0.88908  0.9429   0.169 0.777
 Residual             6.76955  2.6018
Number of obs: 936, groups: Site, 4

Fixed effects:
              Estimate Std. Error t value
(Intercept)    2.93093    0.58598   5.002
N              0.03767    0.09071   0.415
G              0.14927    0.08833   1.690
Yearthree     -3.22170    0.98325  -3.277
Yeartwo       -1.96111    0.50636  -3.873
N:Yearthree    0.15713    0.37544   0.419
N:Yeartwo      0.14736    0.24210   0.609
G:Yearthree   -0.25103    0.40152  -0.625
G:Yeartwo      0.07549    0.23937   0.315
N:G:Yearone   -0.31633    0.12888  -2.455
N:G:Yearthree  0.04722    0.52594   0.090
N:G:Yeartwo   -0.32787    0.31260  -1.049

Correlation of Fixed Effects:
            (Intr) N      G      Yerthr Yeartw N:Yrth N:Yrtw G:Yrth
G:Yrtw N:G:Yrn N:G:Yrth
N           -0.079
G           -0.081  0.523
Yearthree    0.706  0.047  0.048
Yeartwo      0.141  0.091  0.094  0.707
N:Yearthree  0.019 -0.242 -0.126 -0.209 -0.022
N:Yeartwo    0.030 -0.375 -0.196 -0.018 -0.259  0.091
G:Yearthree  0.018 -0.115 -0.220 -0.195 -0.021  0.511  0.043
G:Yeartwo    0.030 -0.193 -0.369 -0.018 -0.262  0.047  0.547  0.081
N:G:Yearone  0.056 -0.704 -0.685 -0.033 -0.064  0.170  0.264  0.151
0.253
N:G:Yearthr  0.000  0.000  0.000  0.141  0.000 -0.672  0.000 -0.726
0.000  0.000
N:G:Yeartwo  0.000  0.000  0.000  0.000  0.174  0.000 -0.666  0.000
-0.661  0.000   0.000

Hope you can work with that?
Thanks,
Raldo

On Wed, Sep 30, 2009 at 6:20 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
> On Wed, Sep 30, 2009 at 4:45 AM, Raldo Kruger <raldo.kruger at gmail.com> wrote:
>> Hi all, I've been following this thread since it's of interest to the
>> analyses i'm currenty doing.
>> My question is, how does one do model simplification with lmer (or
>> glmer in my case) if there are no p-values (since p-values are used to
>> determine which terms to drop, and the drop1 function does not work
>> for glmer)?
>
>> And Douglas, could you provide a working example of getting the
>> p-values as you described, preferably with glmer (glmer does not have
>> the REML=FALSE option)? I understand the 1st part of fitting two
>> models, one with and one without the term of interest... So does it
>> mean one has to do this for every term in order to get all the
>> p-values?
>
> Got data? (I live in "the dairy state" in the United States and the
> milk producers have an advertising campaign with the slogan "Got
> milk?")
>
> It would be easier, and probably more useful, if you could propose a
> data set and model for illustration.
>
> For a binary response the summary of a glmer fitted model actually
> provides p-values for the coefficients.  Refitting the model without a
> particular term and using a likelihood ratio test may be more
> reasonable than using those p-values, simply because both models are
> being fit to the data.  The "Wald test" statistics are based on an
> inferred model fit for the simpler model, which may or may not be
> reasonable.
>
>> On 9/29/09, Douglas Bates <bates at stat.wisc.edu> wrote:
>>> On Tue, Sep 29, 2009 at 3:58 PM, Peter Dalgaard
>>> <p.dalgaard at biostat.ku.dk> wrote:
>>>> Ben Bolker wrote:
>>>>>
>>>>> Douglas Bates wrote:
>>>>>>
>>>>>> On Tue, Sep 29, 2009 at 1:02 PM, Ben Bolker <bolker at ufl.edu> wrote:
>>>>>>
>>>>>>> Christopher David Desjardins wrote:
>>>>>>>>
>>>>>>>> I've started working through Pinheiro & Bates, 2000 and noticed the
>>>>>>>> use
>>>>>>>> of lme from the nlme package. I am curious if lmer from lme4 has
>>>>>>>> superseded lme or if lme still holds its own? The reason I ask is that
>>>>>>>> I
>>>>>>>> have taken a few classes where we've solely used lmer and just read
>>>>>>>> about lme today. If both functions are on equal footing, can the
>>>>>>>> p-values from lme be trusted?
>>>>>>>> Thanks!
>>>>>>>> Chris
>>>>>>>
>>>>>>>  You should read the extended discussion of p-values, degrees of
>>>>>>> freedom, etc. that is on the R wiki (I think) and referenced from the R
>>>>>>> FAQ.  At least in my opinion, (n)lme is still fine (and indeed
>>>>>>> necessary
>>>>>>> at this stage for fitting heteroscedastic and correlated models).  The
>>>>>>> df/p-value estimates, however, are "use at your own risk" -- you'll
>>>>>>> have
>>>>>>> to read the literature and decide for yourself.
>>>>>>>  I still think there's room for someone to implement (at least)
>>>>>>> Satterthwaite and (possibly) Kenward-Roger corrections, at least for
>>>>>>> the
>>>>>>> sake of comparison, but I'm not volunteering.
>>>>>>
>>>>>> You may need to define them first.  Many of the formulas in the mixed
>>>>>> models literature assume a hierarchical structure in the random
>>>>>> effects - certainly we used such a formula for calculating the
>>>>>> denominator degrees of freedom in the nlme package. But lme4 allows
>>>>>> for fully or partially crossed random effects so you can't think in
>>>>>> terms of "levels" of random effects.
>>>>>>
>>>>>> Referring to the "Satterthwaite and Kenward-Roger corrections" gives
>>>>>> the impression that these are well-known formulas and implementing
>>>>>> them would be a simple matter of writing a few lines of code.  I don't
>>>>>> think it is.  I would be very pleased to incorporate such code if it
>>>>>> could be written but, as I said, I don't even know if such things are
>>>>>> defined in the general case, let alone easy to calculate.
>>>>>>
>>>>>> I am not trying to be argumentative (although of late I seem to have
>>>>>> succeeded in being that).  I'm just saying that I don't think this is
>>>>>> trivial. (It I wanted to be argumentative I would say that it is
>>>>>> difficult and, for the most part, irrelevant. :-)
>>>>>
>>>>>  Fair enough. Actually, I'm not sure I meant implementing them in lmer
>>>>> -- even implementing them in nlme would be useful (and perhaps more
>>>>> straightforward, if not trivial). I also wouldn't impose the requirement
>>>>> that they have to be feasible for huge data sets -- I'm just curious if
>>>>> they can be implemented within lme in a relatively straightforward/
>>>>> boneheaded way.
>>>>>   But again, this is very far down my to-do list (and at the edge
>>>>> of my abilities) and completely off yours, so unless someone else bites
>>>>> it won't happen.
>>>>
>>>> I don't think (n)lme is all that easy either; you still need to sort out
>>>> the
>>>> connection between its multilevel formulation and the projection matrices
>>>> in
>>>> the K-R paper. In both nlme and lme4, an implementation is almost
>>>> certainly
>>>> possible, although probably complicated and perhaps at the expense of all
>>>> computational efficiency.
>>>>
>>>> One main problem is that even when they can be calculated, the corrections
>>>> rely on a normal distribution assumption which is more than likely wrong
>>>> in
>>>> practice. This isn't any different from ordinary t-tests: once you get
>>>> into
>>>> the single-digit df regime, you really don't know what you are doing, and
>>>> if
>>>> there are more than 30 df, the normal approximation works well enough
>>>> without the correction.
>>>>
>>>> Accordingly, I tend to see low df more as a warning flag than as something
>>>> that gives accurate p values, and I sometimes wonder whether there is a
>>>> way
>>>> to raise such a flag more expediently.
>>>
>>> I agree, wholeheartedly.
>>>
>>> My general advice to those who are required to produce a p-value for a
>>> particular fixed-effects term in a mixed-effects model is to use a
>>> likelihood ratio test.  Fit the model including that term using
>>> maximum likelihood (i.e. REML = FALSE), fit it again without the term
>>> and compare the results using anova.
>>>
>>> The likelihood ratio statistic will be compared to a chi-squared
>>> distribution to get a p-value and this process is somewhat suspect
>>> when the degrees of freedom would be small.  However, so many other
>>> things could be going wrong when you are fitting complex models to few
>>> observations that this may be the least of your worries.
>>>
>>> I appreciate that for Ben and others in fields like ecology the need
>>> to incorporate many different possible terms in models for
>>> comparatively small data sets may be inevitable.  But it is also
>>> inevitable that the precision of the information one can extract from
>>> such small data sets is low.  Reducing such analysis to a set of
>>> p-values for various terms and treating these p-values as if they were
>>> precisely determined is an oversimplification, even when journal
>>> editors insist on such an oversimplification.
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>> --
>> Sent from my mobile device
>>
>> Raldo
>>
>



-- 
Raldo
-------------- next part --------------
Site	Soil	Patch 	Treat	Plant	Year	Counts	N	G
N	N	1	C	O	one	31	0	0
N	N	1	C	O	three	10	0	0
N	N	1	C	O	two	6	0	0
N	N	2	C	O	one	25	0	0
N	N	2	C	O	three	1	0	0
N	N	2	C	O	two	2	0	0
N	N	3	C	O	one	22	0	0
N	N	3	C	O	three	1	0	0
N	N	3	C	O	two	2	0	0
N	N	4	C	O	one	38	0	0
N	N	4	C	O	three	2	0	0
N	N	4	C	O	two	8	0	0
N	N	5	C	O	one	7	0	0
N	N	5	C	O	three	0	0	0
N	N	5	C	O	two	5	0	0
N	N	6	C	O	one	19	0	0
N	N	6	C	O	three	1	0	0
N	N	6	C	O	two	1	0	0
N	N	7	C	O	one	10	0	0
N	N	7	C	O	three	0	0	0
N	N	7	C	O	two	6	0	0
N	N	8	C	O	one	13	0	0
N	N	8	C	O	three	1	0	0
N	N	8	C	O	two	2	0	0
N	N	9	C	O	one	25	0	0
N	N	9	C	O	three	4	0	0
N	N	9	C	O	two	1	0	0
N	N	10	C	O	one	51	0	0
N	N	10	C	O	three	0	0	0
N	N	10	C	O	two	3	0	0
N	N	11	C	O	one	21	0	0
N	N	11	C	O	three	0	0	0
N	N	11	C	O	two	0	0	0
N	N	12	C	O	one	19	0	0
N	N	12	C	O	three	2	0	0
N	N	12	C	O	two	4	0	0
N	N	13	C	O	one	18	0	0
N	N	13	C	O	three	0	0	0
N	N	13	C	O	two	2	0	0
N	N	14	C	O	one	34	0	0
N	N	14	C	O	three	0	0	0
N	N	14	C	O	two	0	0	0
N	N	15	C	O	one	28	0	0
N	N	15	C	O	three	2	0	0
N	N	15	C	O	two	0	0	0
N	N	16	C	O	one	38	0	0
N	N	16	C	O	three	8	0	0
N	N	16	C	O	two	8	0	0
N	N	17	C	O	one	39	0	0
N	N	17	C	O	three	1	0	0
N	N	17	C	O	two	7	0	0
N	N	18	C	O	one	39	0	0
N	N	18	C	O	three	1	0	0
N	N	18	C	O	two	5	0	0
N	N	19	C	O	one	8	0	0
N	N	19	C	O	three	3	0	0
N	N	19	C	O	two	2	0	0
N	N	20	C	O	one	38	0	0
N	N	20	C	O	three	1	0	0
N	N	20	C	O	two	4	0	0
B	O	1	C	O	one	52	0	0
B	O	1	C	O	three	0	0	0
B	O	1	C	O	two	4	0	0
B	O	2	C	O	one	8	0	0
B	O	2	C	O	three	0	0	0
B	O	2	C	O	two	0	0	0
B	O	3	C	O	one	6	0	0
B	O	3	C	O	three	5	0	0
B	O	3	C	O	two	7	0	0
B	O	4	C	O	one	41	0	0
B	O	4	C	O	three	0	0	0
B	O	4	C	O	two	1	0	0
B	O	5	C	O	one	21	0	0
B	O	5	C	O	three	2	0	0
B	O	5	C	O	two	9	0	0
B	O	6	C	O	one	25	0	0
B	O	6	C	O	three	1	0	0
B	O	6	C	O	two	10	0	0
B	O	7	C	O	one	5	0	0
B	O	7	C	O	three	0	0	0
B	O	7	C	O	two	0	0	0
B	O	8	C	O	one	5	0	0
B	O	8	C	O	three	9	0	0
B	O	8	C	O	two	10	0	0
B	O	9	C	O	one	26	0	0
B	O	9	C	O	three	0	0	0
B	O	9	C	O	two	1	0	0
B	O	10	C	O	one	3	0	0
B	O	10	C	O	three	0	0	0
B	O	10	C	O	two	7	0	0
B	O	11	C	O	one	5	0	0
B	O	11	C	O	three	2	0	0
B	O	11	C	O	two	7	0	0
B	O	12	C	O	one	2	0	0
B	O	12	C	O	three	3	0	0
B	O	12	C	O	two	12	0	0
B	O	13	C	O	one	19	0	0
B	O	13	C	O	three	0	0	0
B	O	13	C	O	two	5	0	0
B	O	14	C	O	one	28	0	0
B	O	14	C	O	three	7	0	0
B	O	14	C	O	two	13	0	0
B	O	15	C	O	one	3	0	0
B	O	15	C	O	three	0	0	0
B	O	15	C	O	two	0	0	0
B	O	16	C	O	one	30	0	0
B	O	16	C	O	three	1	0	0
B	O	16	C	O	two	10	0	0
B	O	17	C	O	one	28	0	0
B	O	17	C	O	three	1	0	0
B	O	17	C	O	two	5	0	0
B	O	18	C	O	one	21	0	0
B	O	18	C	O	three	4	0	0
B	O	18	C	O	two	6	0	0
B	O	19	C	O	one	21	0	0
B	O	19	C	O	three	1	0	0
B	O	19	C	O	two	7	0	0
B	O	20	C	O	one	0	0	0
B	O	20	C	O	three	0	0	0
B	O	20	C	O	two	0	0	0
F	O	2	C	O	one	51	0	0
F	O	2	C	O	three	2	0	0
F	O	2	C	O	two	4	0	0
F	O	3	C	O	one	84	0	0
F	O	3	C	O	three	0	0	0
F	O	3	C	O	two	0	0	0
F	O	4	C	O	one	35	0	0
F	O	4	C	O	three	0	0	0
F	O	4	C	O	two	0	0	0
F	O	5	C	O	one	74	0	0
F	O	5	C	O	three	3	0	0
F	O	5	C	O	two	1	0	0
F	O	6	C	O	one	43	0	0
F	O	6	C	O	three	0	0	0
F	O	6	C	O	two	1	0	0
F	O	7	C	O	one	40	0	0
F	O	7	C	O	three	0	0	0
F	O	7	C	O	two	2	0	0
F	O	8	C	O	one	2	0	0
F	O	8	C	O	three	0	0	0
F	O	8	C	O	two	0	0	0
F	O	9	C	O	one	13	0	0
F	O	9	C	O	three	0	0	0
F	O	9	C	O	two	0	0	0
F	O	10	C	O	one	7	0	0
F	O	10	C	O	three	0	0	0
F	O	10	C	O	two	0	0	0
F	O	11	C	O	one	37	0	0
F	O	11	C	O	three	3	0	0
F	O	11	C	O	two	3	0	0
F	O	12	C	O	one	8	0	0
F	O	12	C	O	three	0	0	0
F	O	12	C	O	two	1	0	0
F	O	13	C	O	one	29	0	0
F	O	13	C	O	three	0	0	0
F	O	13	C	O	two	2	0	0
F	O	14	C	O	one	19	0	0
F	O	14	C	O	three	0	0	0
F	O	14	C	O	two	0	0	0
F	O	15	C	O	one	16	0	0
F	O	15	C	O	three	2	0	0
F	O	15	C	O	two	0	0	0
F	O	16	C	O	one	23	0	0
F	O	16	C	O	three	0	0	0
F	O	16	C	O	two	0	0	0
F	O	17	C	O	one	23	0	0
F	O	17	C	O	three	0	0	0
F	O	17	C	O	two	0	0	0
F	O	18	C	O	one	39	0	0
F	O	18	C	O	three	7	0	0
F	O	18	C	O	two	10	0	0
F	O	19	C	O	one	20	0	0
F	O	19	C	O	three	1	0	0
F	O	19	C	O	two	11	0	0
F	O	20	C	O	one	3	0	0
F	O	20	C	O	three	0	0	0
F	O	20	C	O	two	1	0	0
P	O	1	C	O	one	20	0	0
P	O	1	C	O	three	0	0	0
P	O	1	C	O	two	2	0	0
P	O	2	C	O	one	13	0	0
P	O	2	C	O	three	0	0	0
P	O	2	C	O	two	0	0	0
P	O	4	C	O	one	12	0	0
P	O	4	C	O	three	0	0	0
P	O	4	C	O	two	2	0	0
P	O	5	C	O	one	20	0	0
P	O	5	C	O	three	1	0	0
P	O	5	C	O	two	4	0	0
P	O	6	C	O	one	15	0	0
P	O	6	C	O	three	0	0	0
P	O	6	C	O	two	0	0	0
P	O	7	C	O	one	11	0	0
P	O	7	C	O	three	0	0	0
P	O	7	C	O	two	0	0	0
P	O	8	C	O	one	14	0	0
P	O	8	C	O	three	0	0	0
P	O	8	C	O	two	3	0	0
P	O	9	C	O	one	14	0	0
P	O	9	C	O	three	0	0	0
P	O	9	C	O	two	2	0	0
P	O	10	C	O	one	2	0	0
P	O	10	C	O	three	0	0	0
P	O	10	C	O	two	1	0	0
P	O	11	C	O	one	0	0	0
P	O	11	C	O	three	0	0	0
P	O	11	C	O	two	0	0	0
P	O	12	C	O	one	2	0	0
P	O	12	C	O	three	0	0	0
P	O	12	C	O	two	2	0	0
P	O	13	C	O	one	0	0	0
P	O	13	C	O	three	0	0	0
P	O	13	C	O	two	0	0	0
P	O	14	C	O	one	0	0	0
P	O	14	C	O	three	0	0	0
P	O	14	C	O	two	2	0	0
P	O	15	C	O	one	0	0	0
P	O	15	C	O	three	0	0	0
P	O	15	C	O	two	0	0	0
P	O	16	C	O	one	1	0	0
P	O	16	C	O	three	0	0	0
P	O	16	C	O	two	0	0	0
P	O	17	C	O	one	24	0	0
P	O	17	C	O	three	0	0	0
P	O	17	C	O	two	10	0	0
P	O	18	C	O	one	10	0	0
P	O	18	C	O	three	0	0	0
P	O	18	C	O	two	0	0	0
P	O	19	C	O	one	19	0	0
P	O	19	C	O	three	0	0	0
P	O	19	C	O	two	0	0	0
P	O	20	C	O	one	0	0	0
P	O	20	C	O	three	0	0	0
P	O	20	C	O	two	0	0	0
N	N	1	G	O	one	13	0	1
N	N	1	G	O	three	1	0	1
N	N	1	G	O	two	3	0	1
N	N	2	G	O	one	50	0	1
N	N	2	G	O	three	1	0	1
N	N	2	G	O	two	4	0	1
N	N	3	G	O	one	14	0	1
N	N	3	G	O	three	2	0	1
N	N	3	G	O	two	5	0	1
N	N	4	G	O	one	15	0	1
N	N	4	G	O	three	0	0	1
N	N	4	G	O	two	0	0	1
N	N	5	G	O	one	36	0	1
N	N	5	G	O	three	1	0	1
N	N	5	G	O	two	22	0	1
N	N	6	G	O	one	56	0	1
N	N	6	G	O	three	1	0	1
N	N	6	G	O	two	2	0	1
N	N	7	G	O	one	15	0	1
N	N	7	G	O	three	0	0	1
N	N	7	G	O	two	10	0	1
N	N	8	G	O	one	47	0	1
N	N	8	G	O	three	1	0	1
N	N	8	G	O	two	1	0	1
N	N	9	G	O	one	26	0	1
N	N	9	G	O	three	2	0	1
N	N	9	G	O	two	2	0	1
N	N	10	G	O	one	61	0	1
N	N	10	G	O	three	2	0	1
N	N	10	G	O	two	3	0	1
N	N	11	G	O	one	46	0	1
N	N	11	G	O	three	3	0	1
N	N	11	G	O	two	9	0	1
N	N	12	G	O	one	32	0	1
N	N	12	G	O	three	2	0	1
N	N	12	G	O	two	2	0	1
N	N	13	G	O	one	10	0	1
N	N	13	G	O	three	0	0	1
N	N	13	G	O	two	6	0	1
N	N	14	G	O	one	37	0	1
N	N	14	G	O	three	1	0	1
N	N	14	G	O	two	3	0	1
N	N	15	G	O	one	36	0	1
N	N	15	G	O	three	3	0	1
N	N	15	G	O	two	6	0	1
N	N	16	G	O	one	79	0	1
N	N	16	G	O	three	10	0	1
N	N	16	G	O	two	29	0	1
N	N	17	G	O	one	53	0	1
N	N	17	G	O	three	4	0	1
N	N	17	G	O	two	9	0	1
N	N	18	G	O	one	45	0	1
N	N	18	G	O	three	1	0	1
N	N	18	G	O	two	5	0	1
N	N	19	G	O	one	13	0	1
N	N	19	G	O	three	4	0	1
N	N	19	G	O	two	13	0	1
N	N	20	G	O	one	54	0	1
N	N	20	G	O	three	4	0	1
N	N	20	G	O	two	4	0	1
B	O	1	G	O	one	31	0	1
B	O	1	G	O	three	4	0	1
B	O	1	G	O	two	7	0	1
B	O	2	G	O	one	31	0	1
B	O	2	G	O	three	0	0	1
B	O	2	G	O	two	3	0	1
B	O	3	G	O	one	12	0	1
B	O	3	G	O	three	4	0	1
B	O	3	G	O	two	1	0	1
B	O	4	G	O	one	13	0	1
B	O	4	G	O	three	1	0	1
B	O	4	G	O	two	0	0	1
B	O	5	G	O	one	39	0	1
B	O	5	G	O	three	2	0	1
B	O	5	G	O	two	26	0	1
B	O	6	G	O	one	0	0	1
B	O	6	G	O	three	0	0	1
B	O	6	G	O	two	0	0	1
B	O	7	G	O	one	12	0	1
B	O	7	G	O	three	9	0	1
B	O	7	G	O	two	3	0	1
B	O	8	G	O	one	17	0	1
B	O	8	G	O	three	1	0	1
B	O	8	G	O	two	13	0	1
B	O	9	G	O	one	19	0	1
B	O	9	G	O	three	0	0	1
B	O	9	G	O	two	2	0	1
B	O	10	G	O	one	7	0	1
B	O	10	G	O	three	1	0	1
B	O	10	G	O	two	14	0	1
B	O	11	G	O	one	4	0	1
B	O	11	G	O	three	0	0	1
B	O	11	G	O	two	3	0	1
B	O	12	G	O	one	2	0	1
B	O	12	G	O	three	1	0	1
B	O	12	G	O	two	6	0	1
B	O	13	G	O	one	6	0	1
B	O	13	G	O	three	0	0	1
B	O	13	G	O	two	4	0	1
B	O	14	G	O	one	47	0	1
B	O	14	G	O	three	0	0	1
B	O	14	G	O	two	2	0	1
B	O	15	G	O	one	5	0	1
B	O	15	G	O	three	0	0	1
B	O	15	G	O	two	0	0	1
B	O	16	G	O	one	14	0	1
B	O	16	G	O	three	0	0	1
B	O	16	G	O	two	3	0	1
B	O	17	G	O	one	22	0	1
B	O	17	G	O	three	3	0	1
B	O	17	G	O	two	7	0	1
B	O	18	G	O	one	22	0	1
B	O	18	G	O	three	1	0	1
B	O	18	G	O	two	4	0	1
B	O	19	G	O	one	7	0	1
B	O	19	G	O	three	0	0	1
B	O	19	G	O	two	0	0	1
B	O	20	G	O	one	28	0	1
B	O	20	G	O	three	0	0	1
B	O	20	G	O	two	1	0	1
F	O	2	G	O	one	65	0	1
F	O	2	G	O	three	0	0	1
F	O	2	G	O	two	1	0	1
F	O	3	G	O	one	61	0	1
F	O	3	G	O	three	1	0	1
F	O	3	G	O	two	0	0	1
F	O	4	G	O	one	54	0	1
F	O	4	G	O	three	0	0	1
F	O	4	G	O	two	0	0	1
F	O	5	G	O	one	48	0	1
F	O	5	G	O	three	0	0	1
F	O	5	G	O	two	2	0	1
F	O	6	G	O	one	37	0	1
F	O	6	G	O	three	0	0	1
F	O	6	G	O	two	0	0	1
F	O	7	G	O	one	1	0	1
F	O	7	G	O	three	0	0	1
F	O	7	G	O	two	0	0	1
F	O	8	G	O	one	12	0	1
F	O	8	G	O	three	0	0	1
F	O	8	G	O	two	0	0	1
F	O	9	G	O	one	22	0	1
F	O	9	G	O	three	0	0	1
F	O	9	G	O	two	0	0	1
F	O	10	G	O	one	15	0	1
F	O	10	G	O	three	0	0	1
F	O	10	G	O	two	0	0	1
F	O	11	G	O	one	6	0	1
F	O	11	G	O	three	0	0	1
F	O	11	G	O	two	0	0	1
F	O	12	G	O	one	29	0	1
F	O	12	G	O	three	0	0	1
F	O	12	G	O	two	0	0	1
F	O	13	G	O	one	32	0	1
F	O	13	G	O	three	10	0	1
F	O	13	G	O	two	22	0	1
F	O	14	G	O	one	8	0	1
F	O	14	G	O	three	1	0	1
F	O	14	G	O	two	0	0	1
F	O	15	G	O	one	11	0	1
F	O	15	G	O	three	0	0	1
F	O	15	G	O	two	0	0	1
F	O	16	G	O	one	14	0	1
F	O	16	G	O	three	0	0	1
F	O	16	G	O	two	0	0	1
F	O	17	G	O	one	45	0	1
F	O	17	G	O	three	0	0	1
F	O	17	G	O	two	6	0	1
F	O	18	G	O	one	32	0	1
F	O	18	G	O	three	1	0	1
F	O	18	G	O	two	3	0	1
F	O	19	G	O	one	24	0	1
F	O	19	G	O	three	0	0	1
F	O	19	G	O	two	2	0	1
F	O	20	G	O	one	14	0	1
F	O	20	G	O	three	0	0	1
F	O	20	G	O	two	5	0	1
P	O	1	G	O	one	11	0	1
P	O	1	G	O	three	0	0	1
P	O	1	G	O	two	1	0	1
P	O	2	G	O	one	21	0	1
P	O	2	G	O	three	0	0	1
P	O	2	G	O	two	0	0	1
P	O	4	G	O	one	14	0	1
P	O	4	G	O	three	0	0	1
P	O	4	G	O	two	0	0	1
P	O	5	G	O	one	14	0	1
P	O	5	G	O	three	0	0	1
P	O	5	G	O	two	0	0	1
P	O	6	G	O	one	30	0	1
P	O	6	G	O	three	0	0	1
P	O	6	G	O	two	0	0	1
P	O	7	G	O	one	15	0	1
P	O	7	G	O	three	0	0	1
P	O	7	G	O	two	0	0	1
P	O	8	G	O	one	25	0	1
P	O	8	G	O	three	0	0	1
P	O	8	G	O	two	3	0	1
P	O	9	G	O	one	3	0	1
P	O	9	G	O	three	0	0	1
P	O	9	G	O	two	0	0	1
P	O	10	G	O	one	1	0	1
P	O	10	G	O	three	0	0	1
P	O	10	G	O	two	12	0	1
P	O	11	G	O	one	5	0	1
P	O	11	G	O	three	0	0	1
P	O	11	G	O	two	3	0	1
P	O	12	G	O	one	4	0	1
P	O	12	G	O	three	0	0	1
P	O	12	G	O	two	1	0	1
P	O	13	G	O	one	0	0	1
P	O	13	G	O	three	0	0	1
P	O	13	G	O	two	0	0	1
P	O	14	G	O	one	7	0	1
P	O	14	G	O	three	0	0	1
P	O	14	G	O	two	3	0	1
P	O	15	G	O	one	0	0	1
P	O	15	G	O	three	0	0	1
P	O	15	G	O	two	0	0	1
P	O	16	G	O	one	46	0	1
P	O	16	G	O	three	0	0	1
P	O	16	G	O	two	0	0	1
P	O	17	G	O	one	0	0	1
P	O	17	G	O	three	0	0	1
P	O	17	G	O	two	1	0	1
P	O	18	G	O	one	33	0	1
P	O	18	G	O	three	0	0	1
P	O	18	G	O	two	1	0	1
P	O	19	G	O	one	30	0	1
P	O	19	G	O	three	1	0	1
P	O	19	G	O	two	4	0	1
P	O	20	G	O	one	10	0	1
P	O	20	G	O	three	0	0	1
P	O	20	G	O	two	1	0	1
N	N	1	N	O	one	0	1	0
N	N	1	N	O	three	12	1	0
N	N	1	N	O	two	9	1	0
N	N	2	N	O	one	34	1	0
N	N	2	N	O	three	4	1	0
N	N	2	N	O	two	7	1	0
N	N	3	N	O	one	48	1	0
N	N	3	N	O	three	4	1	0
N	N	3	N	O	two	14	1	0
N	N	4	N	O	one	31	1	0
N	N	4	N	O	three	0	1	0
N	N	4	N	O	two	1	1	0
N	N	5	N	O	one	47	1	0
N	N	5	N	O	three	3	1	0
N	N	5	N	O	two	15	1	0
N	N	6	N	O	one	37	1	0
N	N	6	N	O	three	6	1	0
N	N	6	N	O	two	13	1	0
N	N	7	N	O	one	77	1	0
N	N	7	N	O	three	3	1	0
N	N	7	N	O	two	8	1	0
N	N	8	N	O	one	52	1	0
N	N	8	N	O	three	5	1	0
N	N	8	N	O	two	4	1	0
N	N	9	N	O	one	17	1	0
N	N	9	N	O	three	0	1	0
N	N	9	N	O	two	0	1	0
N	N	10	N	O	one	68	1	0
N	N	10	N	O	three	1	1	0
N	N	10	N	O	two	2	1	0
N	N	11	N	O	one	47	1	0
N	N	11	N	O	three	3	1	0
N	N	11	N	O	two	4	1	0
N	N	12	N	O	one	40	1	0
N	N	12	N	O	three	4	1	0
N	N	12	N	O	two	5	1	0
N	N	13	N	O	one	37	1	0
N	N	13	N	O	three	0	1	0
N	N	13	N	O	two	0	1	0
N	N	14	N	O	one	34	1	0
N	N	14	N	O	three	6	1	0
N	N	14	N	O	two	7	1	0
N	N	15	N	O	one	31	1	0
N	N	15	N	O	three	0	1	0
N	N	15	N	O	two	4	1	0
N	N	16	N	O	one	44	1	0
N	N	16	N	O	three	5	1	0
N	N	16	N	O	two	9	1	0
N	N	17	N	O	one	46	1	0
N	N	17	N	O	three	1	1	0
N	N	17	N	O	two	1	1	0
N	N	18	N	O	one	56	1	0
N	N	18	N	O	three	4	1	0
N	N	18	N	O	two	4	1	0
N	N	19	N	O	one	39	1	0
N	N	19	N	O	three	5	1	0
N	N	19	N	O	two	6	1	0
N	N	20	N	O	one	45	1	0
N	N	20	N	O	three	4	1	0
N	N	20	N	O	two	9	1	0
B	O	1	N	O	one	26	1	0
B	O	1	N	O	three	0	1	0
B	O	1	N	O	two	14	1	0
B	O	2	N	O	one	40	1	0
B	O	2	N	O	three	5	1	0
B	O	2	N	O	two	5	1	0
B	O	3	N	O	one	12	1	0
B	O	3	N	O	three	4	1	0
B	O	3	N	O	two	2	1	0
B	O	4	N	O	one	18	1	0
B	O	4	N	O	three	2	1	0
B	O	4	N	O	two	0	1	0
B	O	5	N	O	one	3	1	0
B	O	5	N	O	three	0	1	0
B	O	5	N	O	two	1	1	0
B	O	6	N	O	one	14	1	0
B	O	6	N	O	three	0	1	0
B	O	6	N	O	two	9	1	0
B	O	7	N	O	one	15	1	0
B	O	7	N	O	three	0	1	0
B	O	7	N	O	two	8	1	0
B	O	8	N	O	one	2	1	0
B	O	8	N	O	three	4	1	0
B	O	8	N	O	two	5	1	0
B	O	9	N	O	one	30	1	0
B	O	9	N	O	three	7	1	0
B	O	9	N	O	two	17	1	0
B	O	10	N	O	one	17	1	0
B	O	10	N	O	three	1	1	0
B	O	10	N	O	two	7	1	0
B	O	11	N	O	one	13	1	0
B	O	11	N	O	three	1	1	0
B	O	11	N	O	two	5	1	0
B	O	12	N	O	one	5	1	0
B	O	12	N	O	three	1	1	0
B	O	12	N	O	two	6	1	0
B	O	13	N	O	one	20	1	0
B	O	13	N	O	three	0	1	0
B	O	13	N	O	two	2	1	0
B	O	14	N	O	one	24	1	0
B	O	14	N	O	three	1	1	0
B	O	14	N	O	two	0	1	0
B	O	15	N	O	one	7	1	0
B	O	15	N	O	three	0	1	0
B	O	15	N	O	two	0	1	0
B	O	16	N	O	one	0	1	0
B	O	16	N	O	three	0	1	0
B	O	16	N	O	two	0	1	0
B	O	17	N	O	one	42	1	0
B	O	17	N	O	three	0	1	0
B	O	17	N	O	two	4	1	0
B	O	18	N	O	one	20	1	0
B	O	18	N	O	three	0	1	0
B	O	18	N	O	two	9	1	0
B	O	19	N	O	one	16	1	0
B	O	19	N	O	three	0	1	0
B	O	19	N	O	two	3	1	0
B	O	20	N	O	one	23	1	0
B	O	20	N	O	three	2	1	0
B	O	20	N	O	two	3	1	0
F	O	2	N	O	one	45	1	0
F	O	2	N	O	three	1	1	0
F	O	2	N	O	two	3	1	0
F	O	3	N	O	one	0	1	0
F	O	3	N	O	three	0	1	0
F	O	3	N	O	two	2	1	0
F	O	4	N	O	one	16	1	0
F	O	4	N	O	three	0	1	0
F	O	4	N	O	two	0	1	0
F	O	5	N	O	one	34	1	0
F	O	5	N	O	three	1	1	0
F	O	5	N	O	two	2	1	0
F	O	6	N	O	one	18	1	0
F	O	6	N	O	three	0	1	0
F	O	6	N	O	two	5	1	0
F	O	7	N	O	one	17	1	0
F	O	7	N	O	three	1	1	0
F	O	7	N	O	two	7	1	0
F	O	8	N	O	one	35	1	0
F	O	8	N	O	three	1	1	0
F	O	8	N	O	two	2	1	0
F	O	9	N	O	one	16	1	0
F	O	9	N	O	three	0	1	0
F	O	9	N	O	two	1	1	0
F	O	10	N	O	one	1	1	0
F	O	10	N	O	three	0	1	0
F	O	10	N	O	two	0	1	0
F	O	11	N	O	one	1	1	0
F	O	11	N	O	three	1	1	0
F	O	11	N	O	two	2	1	0
F	O	12	N	O	one	34	1	0
F	O	12	N	O	three	3	1	0
F	O	12	N	O	two	0	1	0
F	O	13	N	O	one	39	1	0
F	O	13	N	O	three	2	1	0
F	O	13	N	O	two	8	1	0
F	O	14	N	O	one	3	1	0
F	O	14	N	O	three	0	1	0
F	O	14	N	O	two	1	1	0
F	O	15	N	O	one	5	1	0
F	O	15	N	O	three	0	1	0
F	O	15	N	O	two	0	1	0
F	O	16	N	O	one	23	1	0
F	O	16	N	O	three	0	1	0
F	O	16	N	O	two	1	1	0
F	O	17	N	O	one	15	1	0
F	O	17	N	O	three	0	1	0
F	O	17	N	O	two	10	1	0
F	O	18	N	O	one	13	1	0
F	O	18	N	O	three	3	1	0
F	O	18	N	O	two	12	1	0
F	O	19	N	O	one	5	1	0
F	O	19	N	O	three	0	1	0
F	O	19	N	O	two	0	1	0
F	O	20	N	O	one	0	1	0
F	O	20	N	O	three	0	1	0
F	O	20	N	O	two	0	1	0
P	O	1	N	O	one	21	1	0
P	O	1	N	O	three	0	1	0
P	O	1	N	O	two	1	1	0
P	O	2	N	O	one	2	1	0
P	O	2	N	O	three	0	1	0
P	O	2	N	O	two	0	1	0
P	O	4	N	O	one	1	1	0
P	O	4	N	O	three	0	1	0
P	O	4	N	O	two	1	1	0
P	O	5	N	O	one	19	1	0
P	O	5	N	O	three	0	1	0
P	O	5	N	O	two	3	1	0
P	O	6	N	O	one	9	1	0
P	O	6	N	O	three	0	1	0
P	O	6	N	O	two	0	1	0
P	O	7	N	O	one	7	1	0
P	O	7	N	O	three	0	1	0
P	O	7	N	O	two	0	1	0
P	O	8	N	O	one	7	1	0
P	O	8	N	O	three	0	1	0
P	O	8	N	O	two	0	1	0
P	O	9	N	O	one	21	1	0
P	O	9	N	O	three	1	1	0
P	O	9	N	O	two	6	1	0
P	O	10	N	O	one	9	1	0
P	O	10	N	O	three	0	1	0
P	O	10	N	O	two	1	1	0
P	O	11	N	O	one	3	1	0
P	O	11	N	O	three	0	1	0
P	O	11	N	O	two	0	1	0
P	O	12	N	O	one	1	1	0
P	O	12	N	O	three	0	1	0
P	O	12	N	O	two	0	1	0
P	O	13	N	O	one	0	1	0
P	O	13	N	O	three	0	1	0
P	O	13	N	O	two	0	1	0
P	O	14	N	O	one	0	1	0
P	O	14	N	O	three	1	1	0
P	O	14	N	O	two	1	1	0
P	O	15	N	O	one	2	1	0
P	O	15	N	O	three	0	1	0
P	O	15	N	O	two	0	1	0
P	O	16	N	O	one	0	1	0
P	O	16	N	O	three	0	1	0
P	O	16	N	O	two	0	1	0
P	O	17	N	O	one	19	1	0
P	O	17	N	O	three	0	1	0
P	O	17	N	O	two	2	1	0
P	O	18	N	O	one	9	1	0
P	O	18	N	O	three	0	1	0
P	O	18	N	O	two	0	1	0
P	O	19	N	O	one	41	1	0
P	O	19	N	O	three	0	1	0
P	O	19	N	O	two	3	1	0
P	O	20	N	O	one	9	1	0
P	O	20	N	O	three	0	1	0
P	O	20	N	O	two	0	1	0
N	N	1	NG 	O	one	17	1	1
N	N	1	NG 	O	three	7	1	1
N	N	1	NG 	O	two	0	1	1
N	N	2	NG 	O	one	16	1	1
N	N	2	NG 	O	three	3	1	1
N	N	2	NG 	O	two	4	1	1
N	N	3	NG 	O	one	7	1	1
N	N	3	NG 	O	three	0	1	1
N	N	3	NG 	O	two	4	1	1
N	N	4	NG 	O	one	26	1	1
N	N	4	NG 	O	three	0	1	1
N	N	4	NG 	O	two	5	1	1
N	N	5	NG 	O	one	0	1	1
N	N	5	NG 	O	three	0	1	1
N	N	5	NG 	O	two	13	1	1
N	N	6	NG 	O	one	59	1	1
N	N	6	NG 	O	three	4	1	1
N	N	6	NG 	O	two	12	1	1
N	N	7	NG 	O	one	68	1	1
N	N	7	NG 	O	three	7	1	1
N	N	7	NG 	O	two	6	1	1
N	N	8	NG 	O	one	42	1	1
N	N	8	NG 	O	three	6	1	1
N	N	8	NG 	O	two	0	1	1
N	N	9	NG 	O	one	22	1	1
N	N	9	NG 	O	three	1	1	1
N	N	9	NG 	O	two	8	1	1
N	N	10	NG 	O	one	15	1	1
N	N	10	NG 	O	three	1	1	1
N	N	10	NG 	O	two	12	1	1
N	N	11	NG 	O	one	56	1	1
N	N	11	NG 	O	three	5	1	1
N	N	11	NG 	O	two	5	1	1
N	N	12	NG 	O	one	21	1	1
N	N	12	NG 	O	three	3	1	1
N	N	12	NG 	O	two	7	1	1
N	N	13	NG 	O	one	45	1	1
N	N	13	NG 	O	three	0	1	1
N	N	13	NG 	O	two	1	1	1
N	N	14	NG 	O	one	30	1	1
N	N	14	NG 	O	three	8	1	1
N	N	14	NG 	O	two	7	1	1
N	N	15	NG 	O	one	21	1	1
N	N	15	NG 	O	three	1	1	1
N	N	15	NG 	O	two	2	1	1
N	N	16	NG 	O	one	49	1	1
N	N	16	NG 	O	three	5	1	1
N	N	16	NG 	O	two	13	1	1
N	N	17	NG 	O	one	41	1	1
N	N	17	NG 	O	three	0	1	1
N	N	17	NG 	O	two	10	1	1
N	N	18	NG 	O	one	5	1	1
N	N	18	NG 	O	three	0	1	1
N	N	18	NG 	O	two	4	1	1
N	N	19	NG 	O	one	42	1	1
N	N	19	NG 	O	three	3	1	1
N	N	19	NG 	O	two	4	1	1
N	N	20	NG 	O	one	17	1	1
N	N	20	NG 	O	three	0	1	1
N	N	20	NG 	O	two	0	1	1
B	O	1	NG 	O	one	44	1	1
B	O	1	NG 	O	three	1	1	1
B	O	1	NG 	O	two	4	1	1
B	O	2	NG 	O	one	36	1	1
B	O	2	NG 	O	three	6	1	1
B	O	2	NG 	O	two	6	1	1
B	O	3	NG 	O	one	14	1	1
B	O	3	NG 	O	three	5	1	1
B	O	3	NG 	O	two	4	1	1
B	O	4	NG 	O	one	0	1	1
B	O	4	NG 	O	three	2	1	1
B	O	4	NG 	O	two	5	1	1
B	O	5	NG 	O	one	72	1	1
B	O	5	NG 	O	three	2	1	1
B	O	5	NG 	O	two	3	1	1
B	O	6	NG 	O	one	39	1	1
B	O	6	NG 	O	three	0	1	1
B	O	6	NG 	O	two	18	1	1
B	O	7	NG 	O	one	14	1	1
B	O	7	NG 	O	three	0	1	1
B	O	7	NG 	O	two	9	1	1
B	O	8	NG 	O	one	7	1	1
B	O	8	NG 	O	three	1	1	1
B	O	8	NG 	O	two	1	1	1
B	O	9	NG 	O	one	17	1	1
B	O	9	NG 	O	three	3	1	1
B	O	9	NG 	O	two	4	1	1
B	O	10	NG 	O	one	43	1	1
B	O	10	NG 	O	three	0	1	1
B	O	10	NG 	O	two	0	1	1
B	O	11	NG 	O	one	1	1	1
B	O	11	NG 	O	three	0	1	1
B	O	11	NG 	O	two	0	1	1
B	O	12	NG 	O	one	1	1	1
B	O	12	NG 	O	three	1	1	1
B	O	12	NG 	O	two	2	1	1
B	O	13	NG 	O	one	14	1	1
B	O	13	NG 	O	three	0	1	1
B	O	13	NG 	O	two	0	1	1
B	O	14	NG 	O	one	3	1	1
B	O	14	NG 	O	three	0	1	1
B	O	14	NG 	O	two	0	1	1
B	O	15	NG 	O	one	10	1	1
B	O	15	NG 	O	three	4	1	1
B	O	15	NG 	O	two	9	1	1
B	O	16	NG 	O	one	2	1	1
B	O	16	NG 	O	three	0	1	1
B	O	16	NG 	O	two	0	1	1
B	O	17	NG 	O	one	26	1	1
B	O	17	NG 	O	three	0	1	1
B	O	17	NG 	O	two	3	1	1
B	O	18	NG 	O	one	18	1	1
B	O	18	NG 	O	three	1	1	1
B	O	18	NG 	O	two	3	1	1
B	O	19	NG 	O	one	22	1	1
B	O	19	NG 	O	three	1	1	1
B	O	19	NG 	O	two	2	1	1
B	O	20	NG 	O	one	15	1	1
B	O	20	NG 	O	three	6	1	1
B	O	20	NG 	O	two	11	1	1
F	O	2	NG 	O	one	64	1	1
F	O	2	NG 	O	three	4	1	1
F	O	2	NG 	O	two	11	1	1
F	O	3	NG 	O	one	26	1	1
F	O	3	NG 	O	three	0	1	1
F	O	3	NG 	O	two	1	1	1
F	O	4	NG 	O	one	34	1	1
F	O	4	NG 	O	three	4	1	1
F	O	4	NG 	O	two	6	1	1
F	O	5	NG 	O	one	16	1	1
F	O	5	NG 	O	three	0	1	1
F	O	5	NG 	O	two	3	1	1
F	O	6	NG 	O	one	7	1	1
F	O	6	NG 	O	three	0	1	1
F	O	6	NG 	O	two	0	1	1
F	O	7	NG 	O	one	20	1	1
F	O	7	NG 	O	three	0	1	1
F	O	7	NG 	O	two	0	1	1
F	O	8	NG 	O	one	20	1	1
F	O	8	NG 	O	three	0	1	1
F	O	8	NG 	O	two	1	1	1
F	O	9	NG 	O	one	29	1	1
F	O	9	NG 	O	three	0	1	1
F	O	9	NG 	O	two	0	1	1
F	O	10	NG 	O	one	0	1	1
F	O	10	NG 	O	three	0	1	1
F	O	10	NG 	O	two	0	1	1
F	O	11	NG 	O	one	4	1	1
F	O	11	NG 	O	three	1	1	1
F	O	11	NG 	O	two	3	1	1
F	O	12	NG 	O	one	7	1	1
F	O	12	NG 	O	three	0	1	1
F	O	12	NG 	O	two	0	1	1
F	O	13	NG 	O	one	3	1	1
F	O	13	NG 	O	three	0	1	1
F	O	13	NG 	O	two	1	1	1
F	O	14	NG 	O	one	4	1	1
F	O	14	NG 	O	three	1	1	1
F	O	14	NG 	O	two	0	1	1
F	O	15	NG 	O	one	7	1	1
F	O	15	NG 	O	three	0	1	1
F	O	15	NG 	O	two	0	1	1
F	O	16	NG 	O	one	4	1	1
F	O	16	NG 	O	three	0	1	1
F	O	16	NG 	O	two	0	1	1
F	O	17	NG 	O	one	34	1	1
F	O	17	NG 	O	three	3	1	1
F	O	17	NG 	O	two	6	1	1
F	O	18	NG 	O	one	11	1	1
F	O	18	NG 	O	three	2	1	1
F	O	18	NG 	O	two	10	1	1
F	O	19	NG 	O	one	14	1	1
F	O	19	NG 	O	three	2	1	1
F	O	19	NG 	O	two	7	1	1
F	O	20	NG 	O	one	0	1	1
F	O	20	NG 	O	three	0	1	1
F	O	20	NG 	O	two	0	1	1
P	O	1	NG 	O	one	0	1	1
P	O	1	NG 	O	three	0	1	1
P	O	1	NG 	O	two	0	1	1
P	O	2	NG 	O	one	9	1	1
P	O	2	NG 	O	three	0	1	1
P	O	2	NG 	O	two	1	1	1
P	O	4	NG 	O	one	12	1	1
P	O	4	NG 	O	three	1	1	1
P	O	4	NG 	O	two	2	1	1
P	O	5	NG 	O	one	12	1	1
P	O	5	NG 	O	three	1	1	1
P	O	5	NG 	O	two	1	1	1
P	O	6	NG 	O	one	20	1	1
P	O	6	NG 	O	three	0	1	1
P	O	6	NG 	O	two	0	1	1
P	O	7	NG 	O	one	10	1	1
P	O	7	NG 	O	three	0	1	1
P	O	7	NG 	O	two	0	1	1
P	O	8	NG 	O	one	7	1	1
P	O	8	NG 	O	three	0	1	1
P	O	8	NG 	O	two	1	1	1
P	O	9	NG 	O	one	5	1	1
P	O	9	NG 	O	three	0	1	1
P	O	9	NG 	O	two	2	1	1
P	O	10	NG 	O	one	8	1	1
P	O	10	NG 	O	three	0	1	1
P	O	10	NG 	O	two	6	1	1
P	O	11	NG 	O	one	0	1	1
P	O	11	NG 	O	three	0	1	1
P	O	11	NG 	O	two	0	1	1
P	O	12	NG 	O	one	0	1	1
P	O	12	NG 	O	three	0	1	1
P	O	12	NG 	O	two	1	1	1
P	O	13	NG 	O	one	0	1	1
P	O	13	NG 	O	three	0	1	1
P	O	13	NG 	O	two	0	1	1
P	O	14	NG 	O	one	2	1	1
P	O	14	NG 	O	three	0	1	1
P	O	14	NG 	O	two	0	1	1
P	O	15	NG 	O	one	0	1	1
P	O	15	NG 	O	three	0	1	1
P	O	15	NG 	O	two	0	1	1
P	O	16	NG 	O	one	0	1	1
P	O	16	NG 	O	three	0	1	1
P	O	16	NG 	O	two	0	1	1
P	O	17	NG 	O	one	18	1	1
P	O	17	NG 	O	three	0	1	1
P	O	17	NG 	O	two	0	1	1
P	O	18	NG 	O	one	1	1	1
P	O	18	NG 	O	three	0	1	1
P	O	18	NG 	O	two	0	1	1
P	O	19	NG 	O	one	9	1	1
P	O	19	NG 	O	three	1	1	1
P	O	19	NG 	O	two	3	1	1
P	O	20	NG 	O	one	5	1	1
P	O	20	NG 	O	three	0	1	1
P	O	20	NG 	O	two	0	1	1


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