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mike-lawrence/gp_regression.stan

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gp_regression_example
Raw
gp_regression.stan
functions{
# GP: computes noiseless Gaussian Process given pre-computed unique distances
vector GP(real volatility, real amplitude, vector normal01, int n_x, int n_dx, vector dx_unique, int [,] dx_index) {
# covars: unique entries in covariance matrix
vector[n_dx] covars ;
# covMat: covariance matrix
matrix[n_x,n_x] covMat ;
# compute unique entries in covariance matrix
covars = exp(dx_unique*(volatility^2))*(amplitude^2) ;
covars[1] = (amplitude^2) + .001 ; #jitter diagonal for positive definiteness
# loop throug the covariance matrix, copying in entries
for(i in 1:(n_x-1)){
covMat[i,i] = covars[1] ;
for(j in (i+1):n_x){
covMat[i,j] = covars[dx_index[i,j]] ;
covMat[j,i] = covMat[i,j] ;
}
}
covMat[n_x,n_x] = covars[1] ; #final diagonal entry
# combine with normal01 & return
return(cholesky_decompose(covMat) * normal01 ) ;
}
}
data {
# n_dx: number of unique x-distances
int<lower=1> n_dx ;
# dx_unique: vector of unique x-distances
vector[n_dx] dx_unique ;
# n_x: number of unique x values
int<lower=1> n_x ;
# dx_index: matrix of indices into the x-distance matrix of each value in dx_unique
int dx_index[n_x,n_x] ;
# n_y: number of observations in y
int<lower=1> n_y ;
# y: vector of observations for y
vector[n_y] y ;
# x_index: vector indicating which x is associated with each y
int x_index[n_y] ;
# n_w: number of columns in predictor matrix w
int n_w ;
# w: predictor matrix (each column gets its own GP)
matrix[n_y,n_w] w ;
# n_subj: number of subjects
int<lower=1> n_subj ;
# n_subj: vector indicating which subject is associated with each y
int<lower=1,upper=n_subj> subj[n_y] ;
}
transformed data{
# y_scaled: z-transform of y (for easy prior specification)
vector[n_y] y_scaled ;
y_scaled = (y-mean(y))/sd(y) ;
}
parameters {
# subj_noise: noise per subject
vector[n_subj] subj_noise ;
# subj_noise_sd: sd of subj_noise values
real<lower=0> subj_noise_sd ;
# volatility_helper: helper for cauchy-distributed volatility (see transformed parameters)
vector<lower=0,upper=pi()/2>[n_w] volatility_helper ;
# subj_volatility_helper: helper for cauchy-distributed volitilities per subject (see transformed parameters)
vector<lower=0,upper=pi()/2>[n_subj] subj_volatility_helper[n_w] ;
# subj_volatility_sd: sd of subject volitilities
vector<lower=0>[n_w] subj_volatility_sd ;
# amplitude: amplitude of population GPs
vector<lower=0>[n_w] amplitude ;
# subj_amplitude: amplitude of per-subject GPs
vector<lower=0>[n_subj] subj_amplitude[n_w] ;
# subj_amplitude_sd: sd of subj_amplitude
vector<lower=0>[n_w] subj_amplitude_sd ;
# f_normal01: helper variable for population GPs (see transformed parameters)
vector[n_x] f_normal01[n_w] ;
# f_normal01: helper variable for per-subject GPs (see transformed parameters)
vector[n_x] subj_f_normal01[n_w,n_subj] ;
}
transformed parameters{
# volatility: volatility of population GPs
vector[n_w] volatility ;
# volatility: volatility of per-subject GPs
vector[n_subj] subj_volatility[n_w] ;
# f: population GPs
vector[n_x] f[n_w] ;
# subj_f: per-subject GPs
vector[n_x] subj_f[n_w,n_subj] ;
#next line implies volatility ~ cauchy(0,10)
volatility = 10*tan(volatility_helper) ;
# loop over predictors, computing population GP and per-subject GPs
for(wi in 1:n_w){
# next line implies subj_volatility ~ cauchy(0,subj_volatility_sd)
subj_volatility[wi] = subj_volatility_sd[wi] * tan(subj_volatility_helper[wi]) ;
# population GP
f[wi] = GP(
volatility[wi]
, amplitude[wi]
, f_normal01[wi]
, n_x , n_dx , dx_unique , dx_index
) ;
# loop over subjects, computing per-subject GPs
for(si in 1:n_subj){
# per-subject GP
subj_f[wi,si] = f[wi] +
GP(
subj_volatility[wi][si]
, subj_amplitude[wi][si]
, subj_f_normal01[wi,si]
, n_x , n_dx , dx_unique , dx_index
) ;
}
}
}
model {
# noise priors
subj_noise_sd ~ weibull(2,1) ; #peaked at .8ish
subj_noise ~ normal(0,subj_noise_sd) ; #peaked at 0
# volatility priors:
# - population GPs have volatility ~ cauchy(0,10)
# - per-subject GPs have subj_volatility ~ cauchy(0,subj_volatility_sd)
# - subj_volatility pooled via subj_volatility_sd
subj_volatility_sd ~ weibull(2,10) ;#peaked around 8
# amplitude priors
# - population GPs have amplitude as weibull peaked at .8
# - per-subject GPs have amplitude as normal peaked at zero with pooled sd
amplitude ~ weibull(2,1) ; #peaked at .8ish
subj_amplitude_sd ~ weibull(2,1) ;#peaked at .8ish
for(wi in 1:n_w){
subj_amplitude[wi] ~ normal(0,subj_amplitude_sd[wi]) ; #peaked at 0
}
# normal(0,1) priors on GP helpers
for(wi in 1:n_w){
f_normal01[wi] ~ normal(0,1);
for(si in 1:n_subj){
subj_f_normal01[wi,si] ~ normal(0,1) ;
}
}
# set local environment to so subj_noise_exp isn't saved
{
# subj_noise_exp: exponentiated subj_noise
vector[n_subj] subj_noise_exp ;
subj_noise_exp = exp(subj_noise) ;
# loop over observations
for(yi in 1:n_y){
real temp ;
temp = 0 ;
# loop over predictors to gather sum for this observation's mean
for(wi in 1:n_w){
temp = temp + w[yi,wi] * subj_f[wi,subj[yi]][x_index[yi]] ;
}
# y_scaled as temp with gaussian noise
y_scaled[yi] ~ normal( temp , subj_noise_exp[subj[yi]] ) ;
# below commented-out is equivalent but a smidge slower than the above loop
// y_scaled[yi] ~ normal(
// dot_product(w[yi],to_vector(subj_f[,subj[yi],x_index[yi]]))
// , subj_noise_exp[subj[yi]]
// ) ;
}
}
}
Raw
gp_regression_example.R
# set MAKEFLAGS in case a package needs to be installed/compiled
Sys.setenv(MAKEFLAGS = paste0("-j",parallel::detectCores()))
# load useful packages
library(tidyverse)
library(rstan)
library(devtools)
# load ezStan (installing if necessary)
devtools::install_github('mike-lawrence/ezStan')
library(ezStan)
# tweak of the rounding function
round0 = function(x,z){
round(x/z,0)*z
}
# load a function to do some pre-computation on x
source('prep_x.R')
# load the data
source('z.R')
head(z)
# round soa to 10ms bins and prep as x
x_list = prep_x(round0(z$soa,10))
# how many unique x values?
print(x_list$n_x)
# this will be the size of the covariance matrices of the GP, so big values will mean slow models
# get the predictor matrix W
W = ezStan::get_contrast_matrix(
data = z
, formula = ~ cue*simon
)
# collect data for stan
stan_data = list(
n_dx = x_list$n_dx
, dx_unique = x_list$dx_unique
, n_x = x_list$n_x
, dx_index = x_list$dx_index
, n_y = nrow(z)
, y = log(z$rt) #y is log-rt
, x_index = x_list$x_index
, n_w = ncol(W)
, w = W
, n_subj = length(unique(z$id))
, subj = as.numeric(factor(z$id))
)
# compile the model
mod = rstan::stan_model("gp_regression.stan")
# set the model running on each core
startBigStan(
stanMod = mod
, stanData = stan_data
, iter = 2e2 #2e2 takes about a day per chain
, stanArgs = "
init = 0
, include = F
, pars = c(
'f_normal01'
, 'subj_f_normal01'
, 'volatility_helper'
, 'subj_volatility_helper'
)
"
)
# watch progress (if lots of chains, try setting "one_line_per_chain=F").
# It's safe to stop this function, cores will keep sampling and you can
# check in on them again by simply calling watchBigStan() again.
watchBigStan()
# collect results
post_rt = collectBigStan()
# kill just in case
killBigStan()
# delete temp folder
cleanBigStan()
#save result for later
save(
post_rt
, file = 'post_rt.rdata'
)
Raw
gp_regression_example.Rproj
Version: 1.0
RestoreWorkspace: No
SaveWorkspace: No
AlwaysSaveHistory: No
EnableCodeIndexing: Yes
UseSpacesForTab: No
NumSpacesForTab: 4
Encoding: UTF-8
RnwWeave: Sweave
LaTeX: pdfLaTeX
AutoAppendNewline: Yes
StripTrailingWhitespace: Yes
Raw
prep_x.R
prep_x = function(x){
x_orig = x
x = (x-min(x))/max(x-min(x)) - .5 # -.5 to +.5
#compute unique pairwise x differences & indices thereof for the pairwise matrix
x_unique = sort(unique(x))
nX = length(x_unique)
dx = matrix(NA,nX,nX)
for(i in 1:nX){
for(j in 1:nX){
dx[i,j] = round(-((x_unique[i]-x_unique[j])^2),10)
}
}
dx_unique = rev(sort(unique(as.vector(dx))))
dx_index = matrix(NA,nX,nX)
for(i in 1:nX){
for(j in 1:nX){
dx_index[i,j] = which(dx_unique==dx[i,j])
}
}
# #check that we computed the above correctly
# temp = matrix(NA,nX,nX)
# for(i in 1:nX){
# for(j in 1:nX){
# temp[i,j] = dx[i,j]==dx_unique[dx_index[i,j]]
# }
# }
# all(temp)
to_return = list(
dx_index = dx_index
, dx_unique = dx_unique
, n_dx = length(dx_unique)
, n_x = length(x_unique)
, x_index = match(x,sort(unique(x)))
, x_scaled = x
, x_scaled_unique = sort(unique(x))
, x_unique = sort(unique(x_orig))
)
return(to_return)
}
Raw
z.R
z <-
structure(list(id = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
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2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L,
1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L,
1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L,
1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L,
2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L,
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1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L,
1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
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2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L,
1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L,
1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L,
2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L,
2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L,
1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L,
2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L), .Label = c("invalid",
"valid"), class = "factor"), simon = structure(c(1L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L,
1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L,
2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L,
1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L,
1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L,
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2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L,
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2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L,
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1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L,
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1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
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1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
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1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
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1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
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2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
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2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
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2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
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2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L,
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2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L,
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1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
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1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
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1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L,
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2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
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2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
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2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
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2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L,
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L,
2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L,
1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L,
1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L,
2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L,
2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L,
2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L,
1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L,
1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
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2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
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1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L,
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2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L,
2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
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1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L,
1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L,
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1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
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2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
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1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L), .Label = c("congruent",
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1802L, 1806L, 1810L, 1812L, 1815L, 1816L, 1819L, 1821L, 1822L,
1823L, 1826L, 1827L, 1828L, 1829L, 1835L, 1836L, 1839L, 1843L,
1845L, 1848L, 1849L, 1850L, 1851L, 1852L, 1853L, 1859L, 1863L,
1868L, 1871L, 1873L, 1875L, 1879L, 1883L, 1885L, 1886L, 1887L,
1889L, 1890L, 1891L, 1892L, 1893L, 1899L, 1902L, 1903L, 1909L,
1913L, 1914L, 1918L, 1919L, 1920L, 1922L, 1925L, 1926L, 1928L,
1930L, 1932L, 1934L, 1935L, 1937L, 1938L, 1939L, 1941L, 1944L,
1945L, 1946L, 1948L, 1950L, 1951L, 1952L, 1953L, 1954L, 1955L,
1962L, 1967L, 1971L, 1975L, 1979L, 1981L, 1983L, 1987L, 1993L,
1994L, 1995L, 1996L, 2026L, 2028L, 2032L, 2033L, 2040L, 2041L,
2042L, 2043L, 2049L, 2050L, 2055L, 2056L, 2065L, 2069L, 2070L,
2071L, 2072L, 2073L, 2076L, 2077L, 2079L, 2080L, 2085L, 2086L,
2088L, 2089L, 2092L, 2098L, 2099L, 2101L, 2107L, 2109L, 2110L,
2112L, 2113L, 2114L, 2115L, 2118L, 2120L, 2121L, 2124L, 2128L,
2129L, 2136L, 2137L, 2141L, 2143L, 2145L, 2150L, 2151L, 2153L,
2157L, 2162L, 2163L, 2171L, 2174L, 2176L, 2178L, 2185L, 2188L,
2191L, 2194L, 2196L, 2198L, 2199L, 2200L, 2208L, 2210L, 2211L,
2212L, 2213L, 2214L, 2221L, 2222L, 2225L, 2226L, 2227L, 2230L,
2231L, 2232L, 2233L, 2234L, 2235L, 2236L, 2237L, 2239L, 2241L,
2244L, 2245L, 2246L, 2249L, 2253L, 2254L, 2256L, 2257L, 2258L,
2278L, 2279L, 2323L, 2325L, 2326L, 2328L, 2329L, 2335L, 2336L,
2340L, 2349L, 2352L, 2354L, 2355L, 2356L, 2358L, 2364L, 2365L,
2366L, 2367L, 2370L, 2371L, 2379L, 2385L, 2386L, 2389L, 2390L,
2391L, 2393L, 2398L, 2399L, 2400L, 2402L, 2405L, 2411L, 2412L,
2413L, 2414L, 2423L, 2424L, 2425L, 2427L, 2428L, 2429L, 2431L,
2432L, 2434L, 2435L, 2436L, 2437L, 2441L, 2446L, 2449L, 2451L,
2452L, 2456L, 2457L, 2458L, 2460L, 2462L, 2464L, 2465L, 2466L,
2470L, 2473L, 2476L, 2477L, 2487L, 2488L, 2489L, 2493L, 2496L,
2498L, 2501L, 2502L, 2503L, 2506L, 2508L, 2509L, 2510L, 2511L,
2512L, 2513L, 2514L, 2515L, 2516L, 2517L, 2519L, 2521L, 2523L,
2524L, 2525L, 2529L, 2530L, 2531L, 2537L, 2538L, 2539L, 2540L,
2541L, 2542L, 2543L, 2546L, 2547L, 2550L, 2551L, 2552L, 2553L,
2554L, 2557L, 2559L, 2560L, 2598L, 2599L, 2605L, 2608L, 2610L,
2613L, 2615L, 2616L, 2617L, 2618L, 2619L, 2620L, 2629L, 2630L,
2637L, 2638L, 2639L, 2643L, 2646L, 2647L, 2655L, 2657L, 2660L,
2661L, 2664L, 2665L, 2668L, 2672L, 2673L, 2682L, 2685L, 2691L,
2692L, 2694L, 2695L, 2698L, 2699L, 2702L, 2703L, 2704L, 2705L,
2711L, 2716L, 2717L, 2725L, 2727L, 2728L, 2729L, 2730L, 2731L,
2732L, 2734L, 2735L, 2736L, 2737L, 2738L, 2741L, 2749L, 2750L,
2752L, 2753L, 2758L, 2759L, 2760L, 2768L, 2781L, 2784L, 2786L,
2787L, 2788L, 2791L, 2798L, 2799L, 2801L, 2811L, 2813L, 2814L,
2815L, 2816L, 2817L, 2818L, 2821L, 2829L, 2831L, 2839L, 2840L,
2884L, 2888L, 2889L, 2891L, 2896L, 2900L, 2902L, 2903L, 2908L,
2914L, 2915L, 2916L, 2917L, 2918L, 2919L, 2922L, 2923L, 2928L,
2933L, 2939L, 2941L, 2945L, 2949L, 2952L, 2955L, 2959L, 2960L,
2961L, 2968L, 2977L, 2979L, 2983L, 2986L, 2988L, 2989L, 2995L,
2996L, 2998L, 3005L, 3006L, 3010L, 3013L, 3017L, 3018L, 3027L,
3031L, 3032L, 3033L, 3035L, 3036L, 3042L, 3046L, 3051L, 3057L,
3058L, 3072L, 3073L, 3075L, 3076L, 3077L, 3078L, 3079L, 3081L,
3093L, 3099L, 3104L, 3105L, 3107L, 3127L, 3128L, 3129L, 3130L,
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3230L, 3231L, 3235L, 3238L, 3241L, 3242L, 3243L, 3246L, 3250L,
3256L, 3260L, 3266L, 3267L, 3274L, 3275L, 3288L, 3290L, 3291L,
3294L, 3297L, 3301L, 3302L, 3303L, 3304L, 3305L, 3306L, 3307L,
3308L, 3309L, 3310L, 3311L, 3312L, 3313L, 3315L, 3316L, 3324L,
3329L, 3330L, 3331L, 3336L, 3339L, 3349L, 3350L, 3351L, 3352L,
3353L, 3354L, 3355L, 3356L, 3357L, 3359L, 3361L, 3362L, 3367L,
3378L, 3379L, 3383L, 3384L, 3386L, 3387L, 3388L, 3390L, 3393L,
3394L, 3395L, 3396L, 3397L, 3398L, 3400L, 3401L, 3405L, 3406L,
3410L, 3413L, 3414L, 16726L, 16729L, 16737L, 16738L, 16739L,
16740L, 16741L, 16742L, 16743L, 16744L, 16745L, 16746L, 16752L,
16764L, 16770L, 16772L, 16773L, 16774L, 16779L, 16780L, 16783L,
16784L, 16785L, 16786L, 16787L, 16790L, 16794L, 16796L, 16800L,
16801L, 16802L, 16812L, 16813L, 16814L, 16815L, 16817L, 16818L,
16822L, 16828L, 16829L, 16830L, 16832L, 16833L, 16834L, 16835L,
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16860L, 16866L, 16874L, 16875L, 16878L, 16879L, 16880L, 16888L,
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17035L, 17036L, 17037L, 17038L, 17039L, 17041L, 17044L, 17045L,
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17067L, 17070L, 17071L, 17073L, 17074L, 17075L, 17076L, 17077L,
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17140L, 17141L, 17151L, 17152L, 17156L, 17157L, 17159L, 17161L,
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17218L, 17221L, 17230L, 17240L, 17241L, 17242L, 17243L, 17246L,
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17891L, 17893L, 17894L, 17900L, 17901L, 17903L, 17904L, 17907L,
17913L, 17914L, 17916L, 17917L, 17918L, 17922L, 17923L, 17927L,
17929L, 17930L, 17932L, 17933L, 17934L, 17937L, 17942L, 17948L,
17950L, 17951L, 17957L, 17967L, 17976L, 17977L, 17978L, 17979L,
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18250L, 18251L, 18253L, 18254L, 18255L, 18256L, 18257L, 18267L,
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18305L, 18311L, 18316L, 18318L, 18324L, 18330L, 18336L, 18337L,
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18392L, 18393L, 18398L, 18399L, 18402L, 18403L, 18404L, 18417L,
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18532L, 18537L, 18547L, 18551L, 18560L, 18564L, 18572L, 18577L,
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18670L, 18672L, 18674L, 18675L, 18683L, 18686L, 18695L, 18697L,
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18746L, 18750L, 18751L, 18764L, 18766L, 18767L, 18770L, 18773L,
18775L, 18777L, 18787L, 18788L, 18797L, 18801L, 18803L, 18807L,
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18908L, 18909L, 18912L, 18913L, 18915L, 18919L, 18920L, 18923L,
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18962L, 18963L, 18971L, 18978L, 18979L, 19033L, 19034L, 19035L,
19037L, 19038L, 19039L, 19041L, 19044L, 19045L, 19052L, 19054L,
19055L, 19056L, 19058L, 19075L, 19081L, 19082L, 19083L, 19084L,
19088L, 19089L, 19090L, 19097L, 19101L, 19112L, 19113L, 19114L,
19121L, 19122L, 19130L, 19131L, 19133L, 19134L, 19135L, 19155L,
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19365L, 19368L, 19374L, 19375L, 19377L, 19378L, 19381L, 19382L,
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@pauljohn32
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Thanks very much for sharing. I'm learning from what you did in this one.

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