This function generates simulated response data for single-format or mixed-format test forms. For dichotomous item response data, the IRT 1PL, 2PL, and 3PL models are supported. For polytomous item response data, the graded response model (GRM), the partial credit model (PCM), and the generalized partial credit model (GPCM) are supported.
Arguments
- x
A data frame containing item metadata (e.g., number of score categories, IRT model, and item parameters). It can be created with
shape_df(). See Details. Default isNULL.- theta
A numeric vector of ability (theta) values.
- a.drm
A numeric vector of item discrimination (slope) parameters for dichotomous IRT models.
- b.drm
A numeric vector of item difficulty parameters for dichotomous IRT models.
- g.drm
A numeric vector of guessing parameters for dichotomous IRT models. A single value is used for all dichotomous items.
- a.prm
A numeric vector of item discrimination (slope) parameters for polytomous IRT models.
- d.prm
A list of numeric vectors, where each vector contains difficulty (threshold) parameters for a polytomous item.
- cats
A numeric vector indicating the number of score categories for each item.
- pr.model
A character vector specifying the IRT model of each polytomous item, in the order the polytomous items appear in
cats. Each element is either"GRM"(graded response model) or"GPCM"(generalized partial credit model). A single value is used for all polytomous items.- D
A scaling constant used in IRT models to make the logistic function closely approximate the normal ogive function. A value of 1.702 is commonly used for this purpose. Default is 1.
Value
A numeric matrix of simulated item responses with one row per
examinee (theta value) and one column per item, in the item order of x
or cats. Responses range from 0 to K - 1 for an item with K score
categories. The matrix has no row or column names.
Details
There are two ways to generate simulated response data. The first is
by providing a data frame of item metadata using the argument x. This
data frame must follow a specific structure: the first column should
contain item IDs, the second column should contain the number of unique
score categories for each item, and the third column should specify the IRT
model to be fitted to each item. Available IRT models are:
"1PLM","2PLM","3PLM", and"DRM"for dichotomous item data"GRM"and"GPCM"for polytomous item data
Note that "DRM" serves as a general label covering all dichotomous IRT
models (i.e., "1PLM", "2PLM", and "3PLM"), while "GRM" and "GPCM"
represent the graded response model and (generalized) partial credit model,
respectively.
The subsequent columns should contain the item parameters for the specified
models. For dichotomous items, the fourth, fifth, and sixth columns
represent item discrimination (slope), item difficulty, and item guessing
parameters, respectively. When "1PLM" or "2PLM" is specified in the
third column, the sixth column is ignored and can be NA.
For polytomous items, the item discrimination (slope) parameter should
appear in the fourth column, and the item difficulty (or threshold)
parameters for category boundaries should occupy the fifth through the last
columns. When the number of unique score categories differs across items,
unused parameter cells should be filled with NAs.
In the irtQ package, the threshold parameters of a GPCM item are \(b_v = \beta - \tau_v\), the overall item location minus the threshold of each score category. A GPCM item with K unique score categories requires K - 1 threshold parameters, because the term for the lowest score category is fixed at 0 and is not supplied. For example, a GPCM item with five score categories requires four threshold parameters.
An example of a data frame for a single-format test is shown below:
| ITEM1 | 2 | 1PLM | 1.000 | 1.461 | NA |
| ITEM2 | 2 | 2PLM | 1.921 | -1.049 | NA |
| ITEM3 | 2 | 3PLM | 1.736 | 1.501 | 0.203 |
| ITEM4 | 2 | 3PLM | 0.835 | -1.049 | 0.182 |
| ITEM5 | 2 | DRM | 0.926 | 0.394 | 0.099 |
An example of a data frame for a mixed-format test is shown below:
| ITEM1 | 2 | 1PLM | 1.000 | 1.461 | NA | NA | NA |
| ITEM2 | 2 | 2PLM | 1.921 | -1.049 | NA | NA | NA |
| ITEM3 | 2 | 3PLM | 0.926 | 0.394 | 0.099 | NA | NA |
| ITEM4 | 2 | DRM | 1.052 | -0.407 | 0.201 | NA | NA |
| ITEM5 | 4 | GRM | 1.913 | -1.869 | -1.238 | -0.714 | NA |
| ITEM6 | 5 | GRM | 1.278 | -0.724 | -0.068 | 0.568 | 1.072 |
| ITEM7 | 4 | GPCM | 1.137 | -0.374 | 0.215 | 0.848 | NA |
| ITEM8 | 5 | GPCM | 1.233 | -2.078 | -1.347 | -0.705 | -0.116 |
See the IRT Models section in the irtQ-package documentation for more
details about the IRT models used in the irtQ package. A convenient
way to create a data frame for the argument x is by using the function
shape_df().
The second approach is to specify the item parameters directly instead of
x (see Examples). In this case, theta and cats are required, along
with a.drm and b.drm for dichotomous items and a.prm, d.prm, and
pr.model for polytomous items.
The g.drm argument is only required when simulating dichotomous item
responses under the 3PL model. It can be omitted entirely if all
dichotomous items follow the 1PL or 2PL model. However, if the test
includes a mixture of 1PL, 2PL, and 3PL items, the g.drm vector must be
specified for all dichotomous items, using NA for non-3PL items. For
example, if a test consists of four dichotomous items where the first two
follow the 3PL model and the third and fourth follow the 1PL and 2PL
models respectively, then g.drm = c(0.2, 0.1, NA, NA) should be used.
For dichotomous items, each element in cats should be set to 2. For
polytomous items, the number of unique score categories should be specified
in cats. When simulating data for a mixed-format test, it is important to
specify cats in the correct item order. For example, suppose responses
are simulated for 10 examinees across 5 items, including 3 dichotomous
items and 2 polytomous items (each with 3 categories), where the second and
fourth items are polytomous. In this case, cats = c(2, 3, 2, 3, 2) should
be used.
Furthermore, if the two polytomous items are modeled using the graded
response model and the generalized partial credit model, respectively, then
pr.model = c("GRM", "GPCM").
Author
Hwanggyu Lim hglim83@gmail.com
Examples
## Example 1:
## Simulate response data for a mixed-format test.
## The first two polytomous items use the generalized partial credit model (GPCM),
## and the last polytomous item uses the graded response model (GRM).
# Generate theta values for 100 examinees
theta <- rnorm(100)
# Set item parameters for three dichotomous items under the 3PL model
a.drm <- c(1, 1.2, 1.3)
b.drm <- c(-1, 0, 1)
g.drm <- rep(0.2, 3)
# Set item parameters for three polytomous items
# These items have 4, 4, and 5 response categories, respectively
a.prm <- c(1.3, 1.2, 1.7)
d.prm <- list(c(-1.2, -0.3, 0.4), c(-0.2, 0.5, 1.6), c(-1.7, 0.2, 1.1, 2.0))
# Specify the number of score categories for all items
# This vector also determines the location of polytomous items
cats <- c(2, 2, 4, 4, 5, 2)
# Specify the IRT models for the polytomous items
pr.model <- c("GPCM", "GPCM", "GRM")
# Simulate the response data
simdat(
theta = theta, a.drm = a.drm, b.drm = b.drm, g.drm = g.drm,
a.prm = a.prm, d.prm = d.prm, cats = cats, pr.model = pr.model, D = 1
)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 1 0 2 1 1 1
#> [2,] 1 0 2 2 4 0
#> [3,] 1 0 1 0 1 0
#> [4,] 0 1 2 1 1 0
#> [5,] 1 1 3 2 1 0
#> [6,] 1 1 3 1 2 0
#> [7,] 0 0 1 0 1 1
#> [8,] 0 1 2 1 2 1
#> [9,] 1 1 3 2 4 1
#> [10,] 1 0 1 0 1 0
#> [11,] 0 0 1 2 3 0
#> [12,] 0 0 1 0 1 1
#> [13,] 1 1 2 2 2 0
#> [14,] 0 1 0 0 0 1
#> [15,] 0 1 2 0 1 0
#> [16,] 1 1 3 1 3 0
#> [17,] 1 1 1 2 1 1
#> [18,] 1 0 2 0 0 0
#> [19,] 0 0 2 0 0 0
#> [20,] 1 1 1 2 1 0
#> [21,] 1 0 3 0 1 1
#> [22,] 1 1 3 2 3 1
#> [23,] 1 1 1 2 2 0
#> [24,] 0 0 0 0 0 0
#> [25,] 1 1 0 1 1 1
#> [26,] 0 0 3 1 2 1
#> [27,] 1 1 3 0 4 0
#> [28,] 0 1 1 1 1 0
#> [29,] 1 0 2 0 1 0
#> [30,] 1 1 3 2 3 1
#> [31,] 0 1 2 1 2 0
#> [32,] 1 1 1 0 1 0
#> [33,] 1 0 3 1 2 0
#> [34,] 1 1 3 1 1 0
#> [35,] 0 1 2 1 1 0
#> [36,] 1 1 1 0 2 0
#> [37,] 1 1 3 2 3 1
#> [38,] 1 0 1 1 1 0
#> [39,] 1 0 1 1 0 0
#> [40,] 0 1 2 3 2 1
#> [41,] 1 1 3 0 2 1
#> [42,] 0 1 1 0 1 0
#> [43,] 1 1 1 1 2 1
#> [44,] 1 1 3 2 2 0
#> [45,] 1 1 3 3 2 1
#> [46,] 1 1 1 1 0 0
#> [47,] 1 0 1 1 1 0
#> [48,] 1 1 3 3 4 1
#> [49,] 1 0 0 0 1 1
#> [50,] 1 0 3 1 2 0
#> [51,] 1 1 1 1 2 1
#> [52,] 1 1 1 0 0 1
#> [53,] 1 1 3 2 3 1
#> [54,] 1 1 3 1 1 1
#> [55,] 1 0 1 1 2 0
#> [56,] 1 0 0 1 1 0
#> [57,] 1 1 3 1 1 1
#> [58,] 0 1 1 1 1 0
#> [59,] 0 1 0 0 1 0
#> [60,] 1 1 1 2 1 0
#> [61,] 1 1 2 1 1 1
#> [62,] 1 0 3 1 3 1
#> [63,] 1 1 1 2 3 1
#> [64,] 0 0 2 0 1 0
#> [65,] 1 1 1 2 2 1
#> [66,] 1 1 3 2 3 1
#> [67,] 1 0 0 0 1 0
#> [68,] 1 1 1 1 1 1
#> [69,] 1 1 2 1 1 1
#> [70,] 1 0 2 1 2 0
#> [71,] 0 0 0 0 1 0
#> [72,] 1 0 1 1 1 1
#> [73,] 1 1 1 1 1 1
#> [74,] 1 1 3 2 4 1
#> [75,] 1 1 3 1 1 1
#> [76,] 1 1 3 1 2 1
#> [77,] 1 1 3 2 3 1
#> [78,] 1 1 3 1 3 0
#> [79,] 0 0 3 2 1 0
#> [80,] 1 1 1 2 0 0
#> [81,] 1 1 3 1 2 1
#> [82,] 0 0 3 0 3 0
#> [83,] 1 1 3 1 1 0
#> [84,] 1 0 1 1 1 0
#> [85,] 1 1 2 0 1 0
#> [86,] 0 0 0 0 1 1
#> [87,] 0 0 2 0 1 0
#> [88,] 1 0 0 1 1 0
#> [89,] 1 1 3 3 4 1
#> [90,] 1 1 1 2 1 0
#> [91,] 1 0 3 0 0 0
#> [92,] 1 1 3 1 2 0
#> [93,] 1 1 3 3 3 1
#> [94,] 0 1 2 2 3 0
#> [95,] 1 0 2 2 2 1
#> [96,] 1 1 3 2 1 1
#> [97,] 1 1 2 0 2 0
#> [98,] 1 0 0 0 0 0
#> [99,] 1 1 2 2 1 1
#> [100,] 1 0 1 2 2 0
## Example 2:
## Simulate response data for a single-format test using the 2PL model
# Specify score categories (2 for each dichotomous item)
cats <- rep(2, 3)
# Simulate the response data
simdat(theta = theta, a.drm = a.drm, b.drm = b.drm, cats = cats, D = 1)
#> [,1] [,2] [,3]
#> [1,] 1 0 0
#> [2,] 0 0 1
#> [3,] 1 1 0
#> [4,] 1 1 0
#> [5,] 1 0 0
#> [6,] 1 0 0
#> [7,] 1 0 0
#> [8,] 1 0 0
#> [9,] 1 1 1
#> [10,] 1 1 0
#> [11,] 0 1 0
#> [12,] 0 0 0
#> [13,] 0 0 0
#> [14,] 1 0 0
#> [15,] 1 0 0
#> [16,] 1 0 0
#> [17,] 1 0 0
#> [18,] 1 0 1
#> [19,] 1 0 0
#> [20,] 0 1 0
#> [21,] 1 0 0
#> [22,] 1 1 0
#> [23,] 0 1 0
#> [24,] 1 0 0
#> [25,] 1 0 0
#> [26,] 1 1 0
#> [27,] 1 1 1
#> [28,] 1 1 0
#> [29,] 0 0 0
#> [30,] 1 1 0
#> [31,] 1 1 0
#> [32,] 1 1 0
#> [33,] 1 1 1
#> [34,] 1 0 0
#> [35,] 0 1 0
#> [36,] 1 1 1
#> [37,] 0 1 0
#> [38,] 1 1 0
#> [39,] 1 0 0
#> [40,] 1 1 0
#> [41,] 1 1 0
#> [42,] 1 1 0
#> [43,] 0 0 0
#> [44,] 0 1 1
#> [45,] 1 0 1
#> [46,] 1 0 0
#> [47,] 0 0 0
#> [48,] 1 1 0
#> [49,] 0 1 0
#> [50,] 1 0 0
#> [51,] 0 1 0
#> [52,] 1 0 0
#> [53,] 1 1 1
#> [54,] 1 1 0
#> [55,] 0 0 1
#> [56,] 1 1 0
#> [57,] 1 1 0
#> [58,] 1 1 0
#> [59,] 1 0 0
#> [60,] 1 0 0
#> [61,] 1 1 0
#> [62,] 1 1 0
#> [63,] 0 1 1
#> [64,] 1 0 0
#> [65,] 1 1 0
#> [66,] 1 1 0
#> [67,] 0 0 0
#> [68,] 1 1 0
#> [69,] 1 0 0
#> [70,] 0 0 0
#> [71,] 0 0 0
#> [72,] 1 1 0
#> [73,] 1 0 0
#> [74,] 1 1 1
#> [75,] 1 1 0
#> [76,] 1 1 1
#> [77,] 1 1 1
#> [78,] 1 0 0
#> [79,] 0 1 0
#> [80,] 1 1 0
#> [81,] 0 0 0
#> [82,] 1 1 0
#> [83,] 1 1 0
#> [84,] 1 0 0
#> [85,] 1 0 0
#> [86,] 0 0 0
#> [87,] 1 0 0
#> [88,] 0 1 0
#> [89,] 1 1 1
#> [90,] 1 1 1
#> [91,] 1 1 0
#> [92,] 1 1 0
#> [93,] 1 1 0
#> [94,] 1 1 1
#> [95,] 0 1 0
#> [96,] 0 0 1
#> [97,] 0 0 0
#> [98,] 0 1 0
#> [99,] 1 1 1
#> [100,] 1 0 1
## Example 3:
## Simulate response data using a "-prm.txt" file exported from flexMIRT
# Load the flexMIRT parameter file
flex_prm <- system.file("extdata", "flexmirt_sample-prm.txt", package = "irtQ")
# Convert the flexMIRT parameters to item metadata
test_flex <- bring.flexmirt(file = flex_prm, "par")$Group1$full_df
# Simulate the response data using the item metadata
simdat(x = test_flex, theta = theta, D = 1)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 0 0 1 1 0 0 1 1 1 0 1 0 0
#> [2,] 0 1 1 1 1 1 1 1 0 1 0 0 1
#> [3,] 1 1 0 0 1 1 0 0 1 1 1 0 0
#> [4,] 0 1 1 1 0 0 0 0 0 1 0 0 1
#> [5,] 0 1 0 1 1 1 1 0 0 0 1 0 1
#> [6,] 1 1 0 1 1 0 1 0 1 1 1 0 0
#> [7,] 0 0 0 0 1 0 0 1 0 0 0 1 1
#> [8,] 1 0 1 0 0 0 1 1 1 1 1 0 0
#> [9,] 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [10,] 0 0 1 1 0 0 1 0 0 1 0 0 0
#> [11,] 1 1 0 0 0 0 1 0 0 1 1 0 0
#> [12,] 0 0 1 1 0 1 0 1 0 0 1 0 0
#> [13,] 0 1 0 0 0 0 1 0 1 1 1 0 0
#> [14,] 1 0 0 0 1 0 1 1 1 0 0 1 0
#> [15,] 0 1 1 1 0 0 0 1 0 0 1 0 0
#> [16,] 0 1 1 1 0 1 1 1 1 1 1 1 0
#> [17,] 1 1 0 0 1 0 0 1 1 1 1 0 1
#> [18,] 0 1 1 0 0 0 1 0 1 0 0 1 0
#> [19,] 1 0 1 1 1 1 0 0 0 0 1 0 0
#> [20,] 0 0 1 1 1 0 1 0 0 0 1 0 0
#> [21,] 0 0 0 0 0 1 0 1 1 0 1 0 0
#> [22,] 1 1 0 1 1 1 0 0 1 0 1 1 0
#> [23,] 1 1 1 1 1 0 0 0 1 1 0 0 0
#> [24,] 0 0 0 0 0 0 0 0 0 0 0 0 1
#> [25,] 0 1 0 0 1 0 0 0 1 0 0 0 0
#> [26,] 0 1 1 1 1 0 0 1 1 0 1 1 1
#> [27,] 1 1 1 1 1 0 0 0 1 1 1 0 0
#> [28,] 1 1 1 0 0 1 1 0 0 0 1 0 0
#> [29,] 0 1 0 1 1 0 0 0 0 1 0 1 0
#> [30,] 0 1 1 0 1 0 0 1 1 1 1 1 1
#> [31,] 0 1 0 1 1 1 1 0 1 1 0 0 0
#> [32,] 0 0 0 0 0 0 0 1 0 1 0 0 0
#> [33,] 0 1 0 1 1 1 1 1 0 1 1 0 0
#> [34,] 0 1 1 0 0 1 0 1 1 0 1 0 0
#> [35,] 0 1 0 1 1 0 0 0 0 0 0 1 0
#> [36,] 1 1 1 0 1 1 1 0 0 1 1 0 0
#> [37,] 1 1 0 0 1 0 0 1 1 1 1 1 0
#> [38,] 1 1 0 1 0 0 1 1 0 0 0 0 0
#> [39,] 1 1 0 1 0 1 1 0 1 0 1 1 0
#> [40,] 0 1 1 1 1 1 1 0 0 1 1 0 0
#> [41,] 0 1 1 1 0 0 0 0 1 0 1 0 1
#> [42,] 0 0 1 1 0 0 1 0 0 0 0 0 0
#> [43,] 0 1 1 0 1 1 1 0 1 0 1 0 0
#> [44,] 0 1 1 0 1 0 0 1 1 0 1 0 1
#> [45,] 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [46,] 0 1 1 1 1 1 1 0 1 0 1 0 0
#> [47,] 0 1 0 0 0 0 0 0 0 0 1 0 0
#> [48,] 1 1 1 1 1 1 1 0 1 1 0 1 0
#> [49,] 0 0 1 0 0 0 1 1 1 1 1 1 0
#> [50,] 0 0 0 1 1 1 0 0 0 1 1 0 0
#> [51,] 0 1 1 1 1 1 1 0 0 1 1 0 0
#> [52,] 1 1 1 1 1 1 0 0 0 1 0 1 0
#> [53,] 0 1 1 1 0 0 0 0 0 1 1 1 1
#> [54,] 1 1 0 0 0 1 0 0 1 1 0 0 0
#> [55,] 1 0 0 0 0 1 0 0 0 0 1 0 0
#> [56,] 0 1 1 0 1 0 1 0 0 1 1 0 0
#> [57,] 1 1 0 1 0 0 0 1 1 0 0 1 0
#> [58,] 0 1 1 1 1 0 0 1 0 0 0 1 1
#> [59,] 1 1 1 1 0 0 0 0 0 1 1 1 1
#> [60,] 1 1 0 1 1 0 0 0 0 0 1 1 1
#> [61,] 1 1 1 1 1 1 1 0 1 1 0 0 1
#> [62,] 0 0 1 0 0 0 1 1 1 1 1 0 0
#> [63,] 0 1 1 1 1 1 0 1 1 1 1 1 0
#> [64,] 1 1 0 1 1 0 1 0 0 1 0 0 0
#> [65,] 0 1 0 1 1 0 1 0 1 1 0 0 0
#> [66,] 1 1 1 1 1 0 0 0 1 1 0 0 0
#> [67,] 1 1 0 0 0 0 1 0 1 0 0 0 0
#> [68,] 0 1 1 1 1 0 0 0 0 1 1 0 0
#> [69,] 0 1 1 1 0 0 0 1 1 0 1 0 0
#> [70,] 0 1 0 1 1 0 0 0 0 0 0 0 0
#> [71,] 0 0 0 0 0 0 0 0 0 1 0 1 0
#> [72,] 1 1 0 1 1 1 1 0 0 0 1 1 0
#> [73,] 0 1 0 0 0 0 0 1 1 0 1 0 0
#> [74,] 0 1 1 0 1 1 1 1 1 1 1 1 1
#> [75,] 1 1 0 1 1 1 0 0 0 1 1 0 0
#> [76,] 1 1 0 1 1 1 0 0 0 0 0 0 1
#> [77,] 0 1 0 1 1 1 1 1 1 1 0 0 0
#> [78,] 1 1 0 1 0 1 1 1 1 0 1 1 1
#> [79,] 1 1 0 0 0 1 0 1 0 0 0 0 0
#> [80,] 1 1 1 0 0 1 0 1 1 1 1 1 0
#> [81,] 1 1 1 1 1 1 1 0 1 1 1 0 1
#> [82,] 0 1 0 1 1 1 0 0 0 0 1 1 0
#> [83,] 0 1 1 1 1 1 1 0 0 0 1 0 0
#> [84,] 0 1 0 1 1 1 0 1 1 0 1 1 0
#> [85,] 0 1 1 1 1 1 0 0 1 0 1 0 0
#> [86,] 1 0 0 0 0 0 0 0 0 0 1 1 1
#> [87,] 1 1 0 0 0 0 1 0 0 1 0 0 0
#> [88,] 0 1 0 1 0 1 0 0 0 1 0 1 0
#> [89,] 1 1 1 1 1 1 0 1 0 1 1 1 1
#> [90,] 0 1 1 0 0 1 0 1 1 0 1 0 0
#> [91,] 0 1 1 1 1 1 1 0 1 0 1 0 1
#> [92,] 1 1 1 1 1 1 0 0 0 1 1 1 1
#> [93,] 0 1 1 1 1 1 0 1 1 1 0 1 1
#> [94,] 0 1 1 1 1 0 0 1 1 1 1 1 1
#> [95,] 1 1 1 1 1 0 0 0 0 1 1 1 0
#> [96,] 0 0 0 0 1 0 0 1 1 1 1 0 0
#> [97,] 0 0 1 0 1 0 0 0 0 1 0 1 0
#> [98,] 0 1 1 1 0 0 1 0 0 0 0 0 1
#> [99,] 1 1 0 1 1 0 0 0 0 1 1 0 1
#> [100,] 0 1 0 1 1 0 0 0 0 0 1 0 1
#> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] 0 1 0 0 1 1 1 1 0 1 0 1
#> [2,] 1 1 1 1 0 1 1 1 0 0 1 1
#> [3,] 1 1 1 1 0 1 1 1 1 1 0 1
#> [4,] 0 1 0 1 1 1 0 1 1 0 1 0
#> [5,] 0 0 1 1 0 1 1 1 1 0 0 0
#> [6,] 1 1 0 1 0 1 1 1 1 0 0 1
#> [7,] 0 1 0 0 1 0 1 0 1 0 0 1
#> [8,] 1 1 1 0 1 1 1 1 1 1 1 1
#> [9,] 1 1 1 0 1 1 1 1 1 1 1 1
#> [10,] 0 0 1 1 0 0 1 1 1 1 0 1
#> [11,] 1 1 1 1 0 1 1 1 1 0 0 1
#> [12,] 0 0 0 1 0 1 1 0 1 0 0 0
#> [13,] 0 1 0 0 1 1 1 1 0 0 0 1
#> [14,] 0 0 0 0 0 1 1 1 1 1 0 1
#> [15,] 1 1 1 0 1 1 1 1 0 1 1 1
#> [16,] 1 1 1 1 1 1 1 1 1 1 1 1
#> [17,] 1 1 1 1 0 1 1 1 1 0 1 1
#> [18,] 0 1 0 0 1 1 1 1 0 1 0 1
#> [19,] 0 1 1 1 0 1 1 0 0 0 0 1
#> [20,] 0 0 0 1 0 1 1 1 0 1 0 1
#> [21,] 0 0 0 1 0 0 1 0 1 1 0 1
#> [22,] 1 1 1 1 1 1 1 1 1 1 0 1
#> [23,] 1 1 1 0 0 1 1 1 1 0 1 1
#> [24,] 0 0 1 1 1 0 1 0 0 0 0 0
#> [25,] 0 0 0 0 0 1 1 1 1 1 0 1
#> [26,] 1 1 0 1 1 1 1 1 1 1 1 1
#> [27,] 1 1 1 0 0 1 1 1 1 1 1 1
#> [28,] 0 1 1 1 0 1 1 1 0 1 0 1
#> [29,] 0 1 0 1 0 1 1 1 0 1 0 0
#> [30,] 1 1 1 1 0 1 1 1 1 0 1 1
#> [31,] 0 1 0 0 1 1 1 1 1 0 1 0
#> [32,] 1 0 0 0 0 1 0 1 0 0 1 1
#> [33,] 1 0 1 0 0 1 1 1 1 0 0 0
#> [34,] 0 1 0 0 0 1 0 1 1 1 0 0
#> [35,] 0 0 0 0 0 1 0 1 0 0 0 1
#> [36,] 1 1 1 1 1 1 1 1 0 1 0 1
#> [37,] 1 1 0 1 1 1 1 1 0 1 0 0
#> [38,] 0 1 0 1 1 1 1 1 0 1 0 0
#> [39,] 0 1 1 1 0 0 1 1 0 1 0 1
#> [40,] 1 1 0 1 1 1 1 1 1 1 0 1
#> [41,] 1 1 0 1 1 0 1 1 1 1 1 1
#> [42,] 0 1 0 0 0 0 0 0 1 0 0 0
#> [43,] 1 1 1 1 0 1 1 1 1 1 0 1
#> [44,] 0 1 1 0 0 1 1 1 1 1 1 1
#> [45,] 1 0 1 0 0 1 1 1 1 1 0 1
#> [46,] 0 1 1 1 1 1 1 1 0 1 0 0
#> [47,] 0 0 0 0 0 0 1 0 0 0 0 0
#> [48,] 1 1 1 1 1 1 1 1 1 1 0 1
#> [49,] 0 0 0 0 1 1 1 1 1 0 0 1
#> [50,] 0 1 0 1 0 1 1 1 1 1 1 1
#> [51,] 1 1 1 1 1 1 1 1 1 0 1 0
#> [52,] 1 1 0 1 0 1 1 1 0 1 0 1
#> [53,] 1 1 1 1 0 1 1 1 1 1 0 1
#> [54,] 1 1 1 1 0 1 1 1 0 0 0 1
#> [55,] 1 0 1 1 0 1 1 1 1 1 0 1
#> [56,] 0 0 1 1 1 1 1 1 0 0 1 1
#> [57,] 1 0 0 0 0 0 1 1 1 1 0 1
#> [58,] 0 0 1 1 1 1 1 1 1 0 1 0
#> [59,] 1 1 0 1 0 1 1 1 1 1 0 0
#> [60,] 0 1 1 0 1 0 1 1 0 1 0 1
#> [61,] 1 1 0 1 0 1 1 1 1 1 0 0
#> [62,] 0 1 1 0 0 0 1 1 1 0 0 1
#> [63,] 1 1 1 0 0 1 1 1 1 0 1 1
#> [64,] 0 1 1 0 0 0 1 0 0 0 1 1
#> [65,] 0 0 1 1 0 1 1 1 1 0 1 1
#> [66,] 1 1 1 1 0 1 1 1 1 1 0 1
#> [67,] 1 0 0 0 0 1 1 0 1 0 0 0
#> [68,] 0 1 1 1 0 1 1 1 1 1 0 1
#> [69,] 1 0 1 1 0 1 0 1 0 1 0 1
#> [70,] 0 1 0 0 0 1 1 1 1 0 0 1
#> [71,] 0 0 0 0 0 1 0 1 0 0 1 1
#> [72,] 0 1 0 0 0 1 1 1 1 1 1 0
#> [73,] 1 0 0 0 0 0 1 1 0 1 1 0
#> [74,] 1 1 1 1 0 1 1 1 0 1 0 1
#> [75,] 1 1 1 1 1 1 1 1 1 0 0 0
#> [76,] 1 1 1 1 1 1 1 1 1 0 1 1
#> [77,] 1 1 1 1 1 1 1 1 1 1 1 1
#> [78,] 1 1 1 1 1 1 1 1 1 0 0 1
#> [79,] 1 1 1 1 0 1 1 1 1 0 0 0
#> [80,] 1 0 1 1 1 1 1 1 1 0 1 1
#> [81,] 1 1 0 0 1 1 1 1 1 1 0 1
#> [82,] 1 0 0 1 0 1 1 1 1 1 0 0
#> [83,] 1 1 1 0 0 1 1 1 0 1 1 1
#> [84,] 1 1 1 0 0 1 1 1 1 1 0 1
#> [85,] 0 1 0 1 0 1 1 0 1 0 0 0
#> [86,] 0 0 0 1 0 1 1 1 0 0 0 1
#> [87,] 0 0 0 1 0 1 1 0 1 0 1 1
#> [88,] 0 1 0 0 0 1 1 0 0 1 0 1
#> [89,] 1 1 1 1 1 1 1 1 1 0 1 1
#> [90,] 0 1 1 0 0 1 1 1 1 0 1 0
#> [91,] 0 0 1 1 1 1 1 1 1 1 0 1
#> [92,] 1 1 1 1 1 1 1 1 0 1 1 1
#> [93,] 1 0 1 0 1 1 1 1 1 1 1 1
#> [94,] 1 1 1 1 1 1 1 1 0 1 1 1
#> [95,] 0 1 0 1 1 1 1 1 0 0 1 1
#> [96,] 1 1 0 1 1 1 1 1 1 1 0 1
#> [97,] 1 0 0 1 0 1 0 1 1 0 0 1
#> [98,] 0 1 0 0 1 0 1 1 1 0 1 0
#> [99,] 0 1 0 1 1 1 1 1 0 1 0 1
#> [100,] 0 1 1 1 0 1 1 1 1 1 1 0
#> [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#> [1,] 1 0 1 1 1 0 1 1 1 0 0 1
#> [2,] 1 1 1 1 1 1 1 1 0 1 0 1
#> [3,] 1 1 1 1 1 1 1 1 1 1 0 1
#> [4,] 0 1 1 1 1 0 1 1 0 1 0 1
#> [5,] 1 1 1 1 0 1 1 1 1 1 0 1
#> [6,] 1 1 1 1 0 1 1 1 1 1 1 1
#> [7,] 0 0 1 0 0 0 1 1 1 1 0 1
#> [8,] 1 1 1 1 1 1 1 1 0 1 1 1
#> [9,] 1 1 1 1 1 0 1 1 1 1 0 1
#> [10,] 1 0 0 1 0 0 0 1 0 1 0 1
#> [11,] 1 1 0 0 1 0 1 1 0 0 0 1
#> [12,] 0 0 0 1 1 1 1 1 0 0 0 0
#> [13,] 1 0 1 1 1 1 1 0 1 1 0 1
#> [14,] 1 0 0 1 0 0 0 1 0 0 0 0
#> [15,] 1 0 1 1 0 1 1 1 1 1 0 1
#> [16,] 1 1 1 1 1 0 1 1 1 1 1 1
#> [17,] 1 1 1 1 0 1 1 1 0 1 0 1
#> [18,] 1 0 1 1 0 0 0 1 0 1 1 1
#> [19,] 1 0 0 1 1 0 0 0 0 1 0 0
#> [20,] 1 0 0 1 0 1 0 1 1 0 1 1
#> [21,] 1 1 0 1 0 1 0 1 0 1 1 0
#> [22,] 1 0 1 1 1 1 1 1 1 0 1 1
#> [23,] 0 1 0 1 1 1 1 1 1 1 1 1
#> [24,] 0 0 0 0 1 1 0 1 0 0 0 0
#> [25,] 1 0 0 1 0 0 1 1 0 0 0 1
#> [26,] 1 1 0 1 0 0 1 1 0 1 0 0
#> [27,] 1 0 1 1 0 1 1 1 1 1 0 1
#> [28,] 1 0 0 1 0 0 0 0 1 1 0 1
#> [29,] 1 0 0 1 1 0 0 1 1 0 0 0
#> [30,] 1 1 1 1 1 1 1 1 0 1 0 1
#> [31,] 1 1 1 1 0 1 1 1 0 1 0 0
#> [32,] 1 1 0 1 1 0 1 1 0 1 0 0
#> [33,] 1 1 1 1 0 0 1 1 1 1 1 1
#> [34,] 1 0 0 1 0 0 1 1 0 0 0 0
#> [35,] 1 0 1 1 1 0 1 1 1 0 0 1
#> [36,] 1 1 0 0 1 1 1 1 0 1 0 0
#> [37,] 1 0 1 1 1 0 1 1 1 1 1 1
#> [38,] 1 1 1 1 1 0 1 0 0 1 1 1
#> [39,] 1 0 1 1 0 0 1 1 0 1 0 1
#> [40,] 1 1 0 1 0 0 1 1 1 1 0 1
#> [41,] 1 0 0 1 1 0 1 0 0 0 0 0
#> [42,] 1 0 0 0 1 0 0 1 0 1 0 1
#> [43,] 1 1 1 1 1 0 1 1 0 0 1 1
#> [44,] 1 1 0 1 1 1 1 1 0 1 0 1
#> [45,] 1 1 1 1 1 1 1 1 1 1 1 1
#> [46,] 1 1 0 0 0 1 1 1 0 1 0 1
#> [47,] 1 0 0 0 1 0 0 1 0 0 1 1
#> [48,] 1 1 1 0 1 0 1 1 1 1 1 1
#> [49,] 1 0 1 1 0 0 1 1 0 1 1 1
#> [50,] 1 0 0 1 0 0 1 1 0 1 0 1
#> [51,] 1 1 1 1 1 0 1 1 1 1 0 1
#> [52,] 0 1 1 0 0 0 1 1 1 0 0 1
#> [53,] 1 0 1 1 1 1 1 1 1 1 0 1
#> [54,] 1 1 1 1 1 0 1 1 1 1 1 1
#> [55,] 1 1 0 1 0 1 1 0 0 0 0 0
#> [56,] 1 0 0 1 1 0 1 0 1 0 0 1
#> [57,] 1 0 1 0 1 0 1 1 1 0 0 0
#> [58,] 1 0 1 1 1 0 1 0 1 0 0 1
#> [59,] 1 0 0 1 1 1 1 1 0 0 0 1
#> [60,] 1 0 1 1 0 0 1 1 0 1 0 0
#> [61,] 1 0 1 1 1 1 0 1 1 0 1 1
#> [62,] 0 1 1 1 1 0 1 1 0 1 0 1
#> [63,] 1 1 1 1 1 0 1 1 1 1 1 1
#> [64,] 1 0 0 0 1 0 1 1 0 0 0 1
#> [65,] 1 0 1 1 1 1 1 1 1 1 0 1
#> [66,] 1 0 1 1 1 0 1 1 0 1 0 1
#> [67,] 1 1 0 0 0 1 1 0 0 0 1 0
#> [68,] 1 1 1 1 1 0 1 1 0 1 1 1
#> [69,] 1 1 1 1 1 0 1 1 1 1 1 1
#> [70,] 0 1 1 1 0 1 1 1 0 1 0 0
#> [71,] 1 0 0 1 0 1 1 0 0 0 0 0
#> [72,] 0 1 0 0 0 0 1 0 0 0 0 1
#> [73,] 0 0 0 1 0 1 1 1 0 1 0 1
#> [74,] 1 1 1 1 0 1 1 1 1 1 0 1
#> [75,] 1 1 0 1 0 1 1 1 0 1 1 1
#> [76,] 1 1 1 1 1 1 1 1 1 1 0 1
#> [77,] 1 0 1 1 0 0 1 1 0 1 1 1
#> [78,] 1 0 1 1 0 0 1 0 0 1 0 1
#> [79,] 1 0 1 1 1 0 1 1 1 0 0 1
#> [80,] 1 1 1 1 0 1 0 1 1 1 0 1
#> [81,] 0 1 1 1 0 1 1 1 1 0 0 1
#> [82,] 1 1 1 1 1 1 1 1 0 0 0 1
#> [83,] 1 1 0 1 1 1 1 1 0 1 0 1
#> [84,] 1 1 1 1 1 1 1 1 0 1 1 1
#> [85,] 1 0 0 1 1 0 1 0 1 1 0 1
#> [86,] 0 0 1 0 0 0 1 1 0 1 0 0
#> [87,] 0 1 0 0 0 0 1 1 0 0 0 0
#> [88,] 1 0 0 1 1 0 0 0 0 1 0 0
#> [89,] 1 1 1 1 1 1 1 1 1 1 1 1
#> [90,] 1 0 0 1 1 0 1 1 0 1 0 1
#> [91,] 0 1 1 0 1 1 1 1 1 1 0 1
#> [92,] 1 1 1 1 1 1 1 0 1 1 0 1
#> [93,] 1 1 1 1 0 0 1 1 1 1 0 1
#> [94,] 1 0 1 1 1 1 1 1 1 0 0 1
#> [95,] 1 1 1 1 1 0 1 1 1 0 1 1
#> [96,] 1 1 1 1 1 0 0 1 1 1 0 1
#> [97,] 1 1 1 1 0 0 1 0 1 1 0 0
#> [98,] 0 1 0 1 1 1 0 0 0 1 0 0
#> [99,] 1 1 0 1 1 0 1 1 1 0 1 1
#> [100,] 1 1 1 1 0 0 1 1 1 0 1 1
#> [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,] 0 4 4 0 1 1 1 0 0 1 0 0
#> [2,] 1 4 3 1 1 0 0 0 0 0 1 0
#> [3,] 1 4 4 1 1 0 1 1 1 1 1 0
#> [4,] 1 3 3 1 1 0 1 1 0 1 0 1
#> [5,] 1 4 0 1 1 0 0 0 0 0 1 1
#> [6,] 1 4 1 1 1 0 0 0 0 1 1 1
#> [7,] 0 4 0 1 1 1 1 0 0 0 0 1
#> [8,] 1 4 4 0 1 1 0 1 0 0 1 0
#> [9,] 1 4 4 1 1 1 1 1 1 1 1 0
#> [10,] 0 4 0 1 1 0 1 0 0 1 1 1
#> [11,] 0 3 3 0 1 0 0 0 1 1 1 0
#> [12,] 1 0 0 1 1 1 1 1 0 0 1 0
#> [13,] 1 3 0 0 1 1 1 0 0 0 0 1
#> [14,] 0 0 0 0 0 0 0 0 0 1 0 0
#> [15,] 1 3 3 1 0 1 0 0 0 1 0 0
#> [16,] 1 4 0 1 1 1 1 0 0 1 1 1
#> [17,] 1 4 0 1 1 0 0 0 0 1 1 1
#> [18,] 0 2 1 0 1 1 0 1 0 0 0 0
#> [19,] 0 3 0 0 1 1 0 0 1 1 0 1
#> [20,] 1 1 4 0 0 1 0 0 0 0 0 0
#> [21,] 1 4 0 0 0 1 1 0 0 0 1 1
#> [22,] 1 4 2 1 1 1 1 1 0 0 1 1
#> [23,] 1 2 0 1 1 1 1 0 0 1 1 1
#> [24,] 1 0 0 0 0 0 0 0 0 0 0 0
#> [25,] 1 3 0 0 1 1 1 1 0 1 1 0
#> [26,] 1 3 2 1 1 1 0 1 0 1 0 1
#> [27,] 1 4 0 1 1 1 1 0 0 1 1 1
#> [28,] 0 4 3 1 1 0 1 0 0 1 0 1
#> [29,] 0 2 3 0 1 1 1 0 0 0 1 1
#> [30,] 0 4 4 0 1 1 1 0 0 1 1 1
#> [31,] 0 4 1 0 1 1 1 0 0 0 0 0
#> [32,] 0 3 4 0 1 0 1 0 0 0 0 0
#> [33,] 0 4 2 1 1 1 1 1 1 1 1 1
#> [34,] 0 4 0 0 1 0 1 0 0 0 1 1
#> [35,] 0 2 2 1 0 0 1 0 1 1 0 0
#> [36,] 1 4 4 1 1 1 1 0 0 1 1 1
#> [37,] 1 4 1 1 1 1 1 1 0 1 1 1
#> [38,] 1 3 0 0 1 1 1 0 0 1 1 1
#> [39,] 1 2 0 1 0 0 1 0 0 1 0 1
#> [40,] 1 4 2 1 1 1 0 1 1 1 1 0
#> [41,] 1 4 2 1 1 0 1 0 1 0 1 1
#> [42,] 1 1 0 1 1 0 1 0 0 0 1 0
#> [43,] 1 4 2 0 1 0 1 0 0 1 1 1
#> [44,] 0 4 3 1 1 0 1 1 0 0 1 0
#> [45,] 1 4 2 1 1 0 1 0 0 1 1 1
#> [46,] 1 2 4 0 1 0 0 0 0 1 0 0
#> [47,] 0 2 1 0 1 1 0 1 0 0 1 0
#> [48,] 1 4 2 1 1 1 1 1 1 1 1 1
#> [49,] 0 4 4 0 1 1 1 0 0 1 1 0
#> [50,] 1 1 3 1 1 0 1 1 1 0 1 0
#> [51,] 1 4 3 0 1 0 1 0 0 1 0 1
#> [52,] 1 3 0 1 1 0 0 0 0 1 1 1
#> [53,] 1 4 4 0 1 1 1 0 1 0 1 1
#> [54,] 1 4 0 1 1 1 1 0 1 1 1 0
#> [55,] 1 4 0 1 1 0 1 1 1 1 0 0
#> [56,] 1 3 0 1 1 0 0 0 0 1 0 1
#> [57,] 1 2 1 0 1 1 0 0 0 0 0 1
#> [58,] 0 4 1 1 1 1 1 0 0 0 1 1
#> [59,] 1 2 1 0 1 0 1 1 0 0 1 0
#> [60,] 0 4 1 1 0 0 1 0 0 0 0 1
#> [61,] 1 4 2 1 1 0 1 1 0 0 1 1
#> [62,] 1 0 0 0 1 1 0 1 0 1 0 1
#> [63,] 0 4 0 1 1 1 1 1 0 1 0 1
#> [64,] 1 4 0 0 1 1 0 1 1 0 0 0
#> [65,] 0 4 2 0 1 0 1 0 0 1 1 1
#> [66,] 1 4 1 0 1 1 1 0 1 0 1 0
#> [67,] 0 4 1 0 1 0 0 0 0 0 1 0
#> [68,] 1 4 3 0 1 0 0 1 1 0 1 0
#> [69,] 1 4 4 1 1 1 1 1 0 1 1 0
#> [70,] 1 4 0 1 1 0 0 0 0 0 0 0
#> [71,] 0 0 0 0 0 0 0 0 0 1 0 0
#> [72,] 1 3 0 0 1 0 0 0 0 1 0 0
#> [73,] 0 4 0 0 1 0 0 0 0 0 0 0
#> [74,] 1 4 4 0 1 1 1 0 0 1 1 1
#> [75,] 1 4 0 0 1 0 1 1 0 1 1 1
#> [76,] 1 4 3 1 1 0 1 1 0 0 0 1
#> [77,] 1 4 3 1 1 0 1 1 0 1 1 1
#> [78,] 1 4 4 1 1 0 0 1 0 1 1 0
#> [79,] 1 1 0 1 0 0 1 0 0 1 1 1
#> [80,] 0 4 4 0 1 0 1 0 0 1 1 1
#> [81,] 1 4 1 1 1 0 1 0 0 1 1 1
#> [82,] 1 2 2 1 1 0 0 1 0 0 1 1
#> [83,] 0 4 1 0 1 0 0 1 1 1 1 1
#> [84,] 0 4 4 0 1 1 1 0 0 1 1 1
#> [85,] 1 4 0 0 1 0 0 0 1 1 1 0
#> [86,] 1 3 0 0 0 0 1 1 0 0 0 0
#> [87,] 1 2 0 0 1 0 0 0 0 0 0 0
#> [88,] 1 2 1 0 1 0 0 0 1 0 1 0
#> [89,] 1 4 4 1 1 1 1 1 1 1 1 1
#> [90,] 1 2 1 0 1 0 1 1 0 0 1 0
#> [91,] 1 3 4 1 1 1 0 0 0 1 1 0
#> [92,] 1 3 2 1 1 1 1 1 1 1 1 1
#> [93,] 1 4 3 0 1 0 1 0 0 1 1 1
#> [94,] 1 4 1 0 1 0 1 0 1 1 1 1
#> [95,] 1 2 2 1 1 0 1 0 0 1 1 0
#> [96,] 1 3 0 0 1 1 0 1 0 1 1 0
#> [97,] 0 1 1 1 1 0 0 0 0 1 0 1
#> [98,] 1 0 0 0 0 0 1 0 0 0 0 0
#> [99,] 1 4 3 1 1 1 0 1 0 1 1 0
#> [100,] 0 4 4 1 1 1 1 0 0 0 1 1
#> [,50] [,51] [,52] [,53] [,54] [,55]
#> [1,] 0 1 1 4 4 0
#> [2,] 0 1 1 3 2 1
#> [3,] 0 1 1 4 4 4
#> [4,] 0 1 0 2 4 1
#> [5,] 0 1 1 0 3 2
#> [6,] 0 1 1 0 0 1
#> [7,] 0 1 0 0 0 0
#> [8,] 0 1 1 4 4 2
#> [9,] 1 1 1 0 4 4
#> [10,] 0 1 1 3 1 1
#> [11,] 0 1 1 4 4 4
#> [12,] 0 0 1 1 0 0
#> [13,] 0 1 1 0 0 1
#> [14,] 0 0 0 0 0 0
#> [15,] 0 1 1 3 4 4
#> [16,] 0 1 1 4 2 4
#> [17,] 0 1 1 1 2 2
#> [18,] 0 0 0 3 2 1
#> [19,] 0 1 0 1 0 1
#> [20,] 0 0 0 2 1 3
#> [21,] 0 0 1 2 4 3
#> [22,] 0 1 1 3 4 4
#> [23,] 1 1 1 2 4 4
#> [24,] 0 1 0 0 1 0
#> [25,] 0 1 0 0 2 3
#> [26,] 1 1 1 2 3 2
#> [27,] 0 1 0 2 4 0
#> [28,] 0 1 1 1 4 0
#> [29,] 0 1 0 3 4 0
#> [30,] 0 1 1 1 4 2
#> [31,] 0 1 1 0 4 3
#> [32,] 0 1 1 0 0 4
#> [33,] 1 1 1 3 4 4
#> [34,] 0 0 1 0 3 0
#> [35,] 0 0 0 0 3 0
#> [36,] 1 1 1 4 4 2
#> [37,] 0 1 1 3 4 4
#> [38,] 0 1 1 1 4 4
#> [39,] 0 1 1 1 4 4
#> [40,] 0 1 1 0 4 3
#> [41,] 0 1 1 4 4 4
#> [42,] 0 1 0 0 0 0
#> [43,] 1 0 1 3 4 0
#> [44,] 0 1 1 1 4 4
#> [45,] 1 1 0 1 4 4
#> [46,] 0 1 1 0 0 0
#> [47,] 0 0 0 0 2 1
#> [48,] 0 1 0 4 4 3
#> [49,] 1 0 1 0 4 1
#> [50,] 0 1 0 0 4 0
#> [51,] 1 1 0 2 4 4
#> [52,] 0 1 1 2 3 4
#> [53,] 0 1 1 1 4 4
#> [54,] 0 1 1 1 4 4
#> [55,] 0 1 0 0 4 3
#> [56,] 0 1 1 4 4 3
#> [57,] 0 1 0 0 2 4
#> [58,] 0 1 1 3 4 4
#> [59,] 0 1 1 2 4 0
#> [60,] 0 1 1 0 4 1
#> [61,] 0 1 1 0 2 2
#> [62,] 0 0 1 0 4 2
#> [63,] 1 1 1 4 4 4
#> [64,] 1 1 1 2 0 4
#> [65,] 1 1 1 0 4 0
#> [66,] 0 1 1 4 3 4
#> [67,] 0 0 0 0 0 0
#> [68,] 0 1 1 3 2 4
#> [69,] 0 1 1 3 3 3
#> [70,] 1 0 1 1 4 0
#> [71,] 0 0 1 0 1 0
#> [72,] 0 1 1 0 1 4
#> [73,] 0 1 1 0 4 0
#> [74,] 0 1 1 4 4 4
#> [75,] 1 1 1 0 4 4
#> [76,] 1 1 1 0 4 1
#> [77,] 0 1 1 4 0 4
#> [78,] 0 1 1 0 4 2
#> [79,] 0 1 1 1 4 4
#> [80,] 0 1 1 0 4 2
#> [81,] 0 1 1 2 4 4
#> [82,] 0 1 1 0 4 4
#> [83,] 1 1 1 2 4 4
#> [84,] 0 1 0 0 4 1
#> [85,] 0 1 0 0 4 3
#> [86,] 0 0 0 0 1 0
#> [87,] 0 1 0 0 4 3
#> [88,] 0 1 1 0 4 0
#> [89,] 0 1 1 4 4 4
#> [90,] 0 1 1 2 2 4
#> [91,] 0 1 1 1 4 2
#> [92,] 0 1 1 3 4 4
#> [93,] 0 1 0 4 3 3
#> [94,] 1 1 1 4 1 4
#> [95,] 0 1 1 0 4 3
#> [96,] 0 1 1 2 2 1
#> [97,] 1 0 1 0 0 1
#> [98,] 0 1 0 0 1 4
#> [99,] 0 1 0 4 4 4
#> [100,] 1 1 1 4 4 2