I am trying to create a relative frequency bar chart for race and education. So, for example, the relative frequency for Asians with a Bachelor's degree should be the number of Asians with a bachelor's degree, divided by the sum of Asians in the dataframe.
My code is below, inspired by this post. But I can't figure out why my relative frequencies aren't summing to 1. There aren't any NA's in the data, so I'm a little baffled.
df %>%
count(racecen, maxedu) %>%
group_by(racecen) %>%
mutate(freq = n/sum(n)) %>%
ggplot(aes(x = maxedu, y = freq, fill = racecen)) +
geom_bar(stat="identity", position = 'dodge')
I'm not sure whether this is a data issue or a syntax issue (forgive the amateurnish). I want to believe that it's a syntax issue, but the syntax seems like it should work. If it's a data problem, what kinds of general errors in the data could cause this?
EDIT
dput(df)
:
structure(list(racecen = structure(c(4L, 4L, 4L, 4L, 1L, 4L,
1L, 1L, 4L, 3L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 3L, 1L, 3L,
4L, 4L, 4L, 3L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 1L, 1L, 3L, 4L, 3L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 3L, 1L, 4L, 1L, 4L, 4L, 1L, 1L,
4L, 4L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 1L, 4L, 1L, 4L, 1L, 3L, 3L,
4L, 1L, 1L, 4L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 1L,
1L, 1L, 4L, 1L, 4L, 4L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 1L,
3L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L,
1L, 1L, 4L, 4L, 1L, 4L, 3L, 4L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L,
4L, 3L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 3L, 1L, 4L, 4L,
1L, 4L, 4L, 1L, 1L, 1L, 4L, 4L, 4L, 3L, 1L, 1L, 4L, 4L, 1L, 4L,
1L, 2L, 1L, 3L, 4L, 4L, 3L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 1L, 4L,
4L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 1L,
4L, 3L, 3L, 4L, 1L, 4L, 3L, 4L, 4L, 4L, 2L, 1L, 4L, 1L, 4L, 4L,
4L, 4L, 1L, 1L, 4L, 3L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L,
4L, 4L, 4L, 4L, 3L, 4L, 1L, 4L, 4L, 2L, 4L, 4L, 4L, 1L, 4L, 1L,
1L, 1L, 4L, 1L, 3L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 3L, 4L,
1L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 3L, 1L, 4L, 1L, 1L,
1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L,
4L, 4L, 1L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 1L,
4L, 2L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 4L,
4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 1L,
4L, 4L, 4L, 1L, 3L, 3L, 1L, 4L, 4L, 3L, 4L, 1L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 3L,
4L, 1L, 4L, 4L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 3L, 3L, 4L, 3L,
4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 3L, 1L, 1L, 4L, 4L, 4L, 3L, 1L,
4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 3L, 1L, 1L,
4L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 3L,
4L, 1L, 1L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 1L,
4L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 1L,
4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 3L, 1L,
4L, 4L, 1L, 1L, 3L, 1L, 4L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L,
1L, 1L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 1L, 4L,
4L, 1L, 1L, 1L, 1L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 1L, 1L, 1L, 4L,
1L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 1L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L,
1L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 1L,
1L, 3L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 1L, 1L, 1L, 4L, 4L,
4L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 1L,
1L, 4L, 3L, 1L, 4L, 1L, 1L, 4L, 1L, 4L, 4L, 3L, 1L, 4L, 4L, 4L,
4L, 4L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 2L, 4L, 4L, 4L, 4L, 4L,
4L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 4L,
1L, 4L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 1L, 4L, 1L, 1L, 4L, 1L, 4L,
4L, 4L, 4L, 1L, 3L, 4L, 3L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 1L,
4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 1L, 4L,
4L, 1L, 4L, 1L, 1L, 4L, 4L, 3L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 1L,
4L, 4L, 4L, 2L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L,
1L, 1L, 4L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L,
1L, 1L, 4L, 4L, 4L, 1L, 3L, 4L, 3L, 4L, 4L, 1L, 1L, 4L, 1L, 4L,
1L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 3L, 4L, 4L, 4L,
4L, 3L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 1L, 1L, 1L, 4L, 4L,
1L, 1L, 4L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 1L, 3L,
4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 3L, 4L, 4L, 1L, 4L, 1L, 1L,
4L, 4L, 4L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 3L, 4L,
4L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 4L, 4L,
4L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 3L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 1L, 1L, 4L, 4L,
4L, 3L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 1L, 1L, 4L,
4L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 4L, 4L, 4L,
3L, 4L, 2L, 4L, 4L, 1L, 1L, 4L, 1L, 3L, 4L, 1L, 1L, 4L, 4L, 4L,
1L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L,
4L, 1L, 4L, 4L, 4L, 4L, 3L, 1L, 4L, 3L, 4L, 4L, 4L, 4L, 1L, 4L,
3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L,
4L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 3L, 4L, 1L, 1L,
4L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 3L, 4L, 4L,
4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 3L, 1L, 4L, 4L, 4L, 4L, 4L,
4L, 1L, 4L, 4L, 4L, 3L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 1L, 3L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 3L, 4L,
3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 1L, 1L, 1L,
1L, 4L, 1L, 4L, 1L, 1L, 3L, 4L, 1L, 4L, 3L, 1L, 1L, 4L, 1L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 1L, 1L,
4L, 4L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 1L, 3L,
3L, 3L, 4L, 3L, 4L, 1L, 3L, 4L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 1L,
1L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 1L, 4L,
1L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 4L, 4L,
4L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 4L, 3L, 1L, 1L, 3L, 4L, 3L,
4L, 1L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 4L, 4L,
1L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 1L, 1L, 1L, 4L, 1L, 4L,
1L, 3L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 3L, 1L, 3L,
4L, 4L, 1L, 4L, 4L, 4L, 1L, 1L, 3L, 1L, 4L, 4L, 1L, 1L, 4L, 1L,
4L, 1L, 4L, 1L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L,
1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 1L,
1L, 1L, 4L, 1L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 1L, 1L,
1L, 4L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 4L, 4L,
4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 3L, 1L, 1L, 2L, 3L,
1L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 1L, 3L, 4L, 4L, 1L, 4L,
1L, 1L, 4L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 4L,
1L, 1L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L,
4L, 1L, 4L, 2L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L,
4L, 1L, 1L, 4L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 4L, 3L, 4L, 1L,
1L, 1L, 4L, 4L, 4L, 4L, 3L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L,
1L, 3L, 3L, 4L, 4L, 4L, 1L, 3L, 2L, 4L, 1L, 1L, 1L, 4L, 4L, 4L,
4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 1L, 4L,
1L, 1L, 1L, 3L, 4L, 1L, 4L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L,
2L, 1L, 4L, 4L, 3L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L,
1L, 4L, 4L, 1L, 3L, 1L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 2L, 3L, 4L,
4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 1L, 1L,
4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 3L, 4L, 3L, 1L, 1L, 3L,
4L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L, 4L,
4L, 4L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 1L,
4L, 4L, 4L, 3L, 1L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 1L,
4L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 4L, 1L,
4L, 4L, 1L, 3L, 4L, 1L, 2L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L,
4L, 4L, 4L, 1L, 1L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 1L, 4L,
4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 3L, 4L, 1L, 4L,
4L, 1L, 4L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 4L,
1L, 1L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 1L, 3L, 3L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L, 1L, 4L, 1L,
4L, 4L, 4L, 1L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 4L,
4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 1L,
4L, 4L, 4L, 1L, 4L, 1L, 4L, 3L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L,
4L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 3L, 4L, 4L, 3L, 4L, 1L, 1L,
3L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L,
1L, 1L, 3L, 1L, 4L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 1L,
4L, 4L, 4L, 1L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 1L, 1L, 1L,
3L, 4L, 2L, 3L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 3L,
4L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 1L, 3L, 1L,
4L, 4L, 4L, 1L, 4L, 3L, 1L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L,
4L, 1L, 1L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L,
4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 3L, 4L, 4L, 4L, 1L,
4L, 2L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 4L,
3L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 3L, 4L, 1L, 1L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 1L, 4L, 3L, 1L, 4L, 1L, 4L, 4L, 1L, 1L, 4L,
1L, 4L, 1L, 3L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 3L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 1L, 4L, 3L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 1L,
4L, 4L, 3L, 3L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 2L, 4L, 1L, 4L,
1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L,
1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L,
3L, 3L, 1L, 4L, 1L, 4L, 4L, 1L, 4L, 3L, 4L, 4L, 1L, 1L, 1L, 1L,
3L, 4L, 1L, 4L, 2L, 4L, 4L, 4L, 4L, 4L, 3L, 1L, 1L, 4L, 1L, 4L,
4L, 1L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L,
4L, 4L, 1L, 4L, 1L, 4L, 3L, 4L, 4L, 4L, 1L, 4L, 4L, 2L, 1L, 4L,
4L, 4L, 1L, 4L, 4L, 1L, 4L, 1L, 3L, 4L, 4L, 1L, 4L, 1L, 4L, 1L,
4L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 2L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 1L,
1L, 1L, 4L, 1L, 4L, 4L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 1L, 4L, 4L,
4L, 1L, 1L, 1L, 4L, 4L, 2L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 4L,
3L, 3L, 3L, 1L, 4L, 3L, 4L, 1L, 3L, 1L, 3L, 1L, 4L, 4L, 1L, 1L,
1L, 1L, 3L, 4L, 4L, 3L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 1L,
4L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 1L, 1L, 1L, 1L, 4L, 1L,
4L, 4L, 1L, 4L, 4L, 3L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 3L, 1L, 1L,
4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L,
4L, 2L, 2L, 1L, 1L, 1L, 4L, 2L, 3L, 4L, 4L, 4L, 1L, 4L, 3L, 4L,
4L, 4L, 1L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L, 3L, 4L, 4L, 4L,
4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 1L,
4L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 2L, 4L, 4L, 1L, 1L, 1L,
4L, 4L, 1L, 4L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 1L, 1L, 1L, 4L, 1L,
1L, 1L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 3L, 4L, 4L, 1L, 4L, 4L,
1L, 3L, 3L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 4L,
4L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 1L, 4L,
4L, 1L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L,
4L, 4L, 1L, 4L, 4L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L,
4L, 4L, 4L, 1L, 4L, 1L, 1L, 3L, 1L, 3L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 4L, 1L, 1L, 4L, 1L, 1L, 3L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L,
4L, 4L, 4L, 1L, 4L, 1L, 4L, 1L, 1L, 3L, 4L, 4L, 1L, 4L, 1L, 4L,
4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 3L, 4L, 1L,
4L, 4L, 4L, 4L, 3L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L,
3L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 4L,
1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 1L, 4L, 1L, 4L,
4L, 4L, 1L, 4L, 4L, 4L, 4L, 3L, 4L, 2L, 4L, 4L, 1L, 4L, 4L, 4L,
4L, 1L, 3L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L,
1L, 4L, 1L, 3L, 4L, 4L, 4L, 4L, 4L, 1L, 1L, 3L, 4L, 4L, 4L, 3L,
4L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 1L, 3L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 4L, 1L, 4L, 4L, 4L, 4L, 2L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 1L, 4L, 1L, 4L, 1L, 3L, 4L, 1L, 1L, 3L, 1L, 1L, 4L, 1L, 4L,
4L, 4L, 4L, 4L, 1L, 1L, 4L, 3L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L,
1L, 1L, 4L, 1L, 3L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 1L,
4L, 4L, 4L, 4L, 3L, 2L, 1L, 4L, 1L, 4L, 1L, 1L, 1L, 4L, 4L, 4L,
3L, 1L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 1L, 3L, 4L, 4L, 1L, 4L, 1L,
4L, 1L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L, 1L,
4L, 4L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 3L, 4L, 4L, 4L, 1L, 1L,
1L, 3L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 1L, 4L,
1L, 3L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 4L,
1L, 4L, 4L, 3L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 4L, 4L,
4L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L,
1L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L,
1L, 1L, 3L, 4L, 1L, 4L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 3L, 1L,
1L, 4L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 1L, 4L, 4L, 1L, 1L,
4L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 3L, 1L, 4L, 4L, 4L, 4L, 4L, 1L,
4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 1L,
4L, 1L, 4L, 1L, 4L, 4L, 4L, 3L, 4L, 4L, 1L, 4L, 4L, 1L, 1L, 4L,
1L, 4L, 3L, 1L, 4L, 1L, 1L, 1L, 4L, 3L, 3L, 4L, 1L, 4L, 1L, 4L,
4L, 1L, 4L, 1L, 3L, 4L, 1L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 4L, 4L,
4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 1L, 4L,
1L, 1L, 4L, 4L, 4L, 1L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 4L,
4L, 4L, 1L, 3L, 4L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 1L,
4L, 1L, 4L, 1L, 4L, 1L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 1L, 4L,
1L, 1L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L, 1L, 1L, 1L,
1L, 2L, 4L, 1L, 1L, 1L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 1L,
4L, 1L, 4L, 4L, 1L, 1L, 4L, 1L, 3L, 4L, 4L, 4L, 1L, 4L, 4L, 4L,
4L, 1L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 1L, 4L, 1L, 4L,
1L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 4L, 1L, 4L, 1L,
4L, 1L, 1L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 1L, 1L, 1L, 4L, 1L, 4L,
1L), .Label = c("Asian", "Black", "Hispanic", "White"), class = "factor"),
maxedu = structure(c(5L, 5L, 3L, 3L, 7L, 3L, 3L, 5L, 2L,
3L, 6L, 6L, 3L, 3L, 5L, 3L, 5L, 3L, 3L, 7L, 5L, 3L, 3L, 3L,
3L, 3L, 5L, 5L, 6L, 3L, 3L, 6L, 5L, 5L, 5L, 3L, 3L, 3L, 3L,
5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 3L, 7L, 3L, 3L, 5L, 5L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 5L, 3L, 3L, 3L, 5L,
3L, 5L, 3L, 3L, 3L, 3L, 5L, 5L, 6L, 5L, 3L, 3L, 3L, 5L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 5L, 3L, 5L, 5L, 3L, 3L, 7L, 5L, 7L,
5L, 3L, 7L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 6L, 5L, 3L,
5L, 3L, 5L, 3L, 3L, 5L, 3L, 3L, 3L, 3L, 5L, 3L, 5L, 3L, 7L,
3L, 5L, 7L, 3L, 5L, 5L, 3L, 5L, 3L, 5L, 3L, 3L, 3L, 3L, 3L,
5L, 5L, 3L, 5L, 5L, 7L, 3L, 3L, 6L, 5L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 5L, 3L, 6L, 3L, 3L, 5L, 5L, 5L, 3L, 5L, 7L, 3L, 5L,
3L, 7L, 5L, 5L, 5L, 5L, 5L, 3L, 5L, 3L, 3L, 7L, 7L, 5L, 5L,
5L, 5L, 3L, 7L, 5L, 5L, 5L, 7L, 5L, 3L, 3L, 5L, 5L, 3L, 3L,
3L, 3L, 5L, 5L, 5L, 3L, 5L, 3L, 5L, 3L, 5L, 3L, 5L, 5L, 3L,
3L, 5L, 5L, 5L, 3L, 3L, 5L, 3L, 3L, 3L, 3L, 5L, 3L, 5L, 5L,
3L, 5L, 3L, 5L, 5L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 7L, 3L, 7L,
5L, 3L, 3L, 7L, 5L, 5L, 3L, 5L, 7L, 5L, 3L, 3L, 5L, 7L, 3L,
3L, 3L, 3L, 5L, 3L, 3L, 5L, 3L, 3L, 6L, 5L, 3L, 3L, 5L, 5L,
5L, 3L, 3L, 3L, 5L, 5L, 6L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 5L, 6L, 3L, 5L, 3L, 3L, 5L, 3L, 3L, 3L, 5L, 3L, 5L, 3L,
3L, 3L, 3L, 7L, 3L, 5L, 5L, 7L, 5L, 5L, 3L, 3L, 3L, 5L, 5L,
3L, 3L, 5L, 3L, 5L, 3L, 5L, 3L, 3L, 5L, 3L, 3L, 3L, 3L, 5L,
3L, 5L, 3L, 3L, 3L, 5L, 3L, 5L, 5L, 3L, 6L, 3L, 3L, 3L, 3L,
3L, 5L, 7L, 3L, 3L, 3L, 5L, 3L, 5L, 7L, 5L, 5L, 5L, 3L, 3L,
5L, 3L, 5L, 3L, 3L, 3L, 5L, 6L, 5L, 3L, 3L, 5L, 3L, 3L, 3L,
5L, 5L, 6L, 5L, 3L, 2L, 7L, 5L, 3L, 3L, 3L, 3L, 3L, 7L, 3L,
3L, 5L, 7L, 3L, 3L, 3L, 5L, 3L, 5L, 3L, 3L, 3L, 3L, 5L, 5L,
3L, 5L, 5L, 6L, 5L, 3L, 6L, 5L, 6L, 5L, 5L, 5L, 5L, 3L, 6L,
5L, 3L, 3L, 5L, 5L, 3L, 6L, 3L, 5L, 6L, 5L, 3L, 3L, 3L, 3L,
5L, 3L, 3L, 3L, 5L, 6L, 3L, 3L, 7L, 5L, 5L, 5L, 5L, 3L, 3L,
5L, 3L, 6L, 7L, 5L, 5L, 3L, 5L, 5L, 7L, 3L, 3L, 6L, 5L, 3L,
3L, 3L, 3L, 3L, 5L, 5L, 3L, 2L, 5L, 3L, 3L, 3L, 3L, 2L, 3L,
3L, 3L, 5L, 5L, 3L, 5L, 5L, 3L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 6L, 5L, 3L, 5L, 5L, 3L, 5L, 5L, 3L, 5L, 3L, 5L, 3L, 1L,
5L, 5L, 6L, 5L, 5L, 3L, 7L, 5L, 5L, 3L, 3L, 3L, 5L, 5L, 6L,
5L, 5L, 5L, 5L, 3L, 3L, 5L, 7L, 5L, 3L, 5L, 5L, 3L, 3L, 3L,
5L, 5L, 3L, 5L, 3L, 5L, 3L, 3L, 5L, 3L, 5L, 5L, 3L, 3L, 5L,
5L, 3L, 3L, 3L, 7L, 3L, 5L, 3L, 3L, 3L, 5L, 5L, 5L, 5L, 5L,
5L, 3L, 3L, 5L, 5L, 5L, 5L, 5L, 3L, 5L, 5L, 3L, 5L, 5L, 5L,
5L, 5L, 3L, 7L, 5L, 3L, 5L, 5L, 3L, 5L, 3L, 3L, 5L, 5L, 5L,
5L, 5L, 5L, 6L, 5L, 5L, 6L, 5L, 5L, 5L, 5L, 3L, 3L, 5L, 3L,
5L, 3L, 3L, 3L, 6L, 5L, 3L, 3L, 5L, 3L, 5L, 5L, 5L, 5L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 5L, 5L, 5L, 3L, 7L, 3L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 3L, 7L, 5L, 5L, 5L, 3L, 3L, 3L,
3L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 5L, 5L, 3L, 5L, 3L, 5L,
5L, 3L, 5L, 5L, 5L, 5L, 3L, 3L, 5L, 5L, 3L, 3L, 3L, 3L, 5L,
5L, 7L, 5L, 5L, 5L, 5L, 6L, 5L, 7L, 5L, 5L, 7L, 5L, 5L, 6L,
3L, 3L, 5L, 3L, 5L, 3L, 5L, 3L, 6L, 3L, 6L, 5L, 3L, 6L, 3L,
3L, 5L, 5L, 3L, 7L, 3L, 7L, 5L, 5L, 3L, 6L, 3L, 7L, 5L, 5L,
5L, 5L, 5L, 3L, 7L, 5L, 7L, 5L, 5L, 5L, 3L, 3L, 5L, 5L, 3L,
3L, 5L, 3L, 3L, 5L, 5L, 3L, 3L, 5L, 7L, 5L, 3L, 3L, 7L, 5L,
6L, 3L, 5L, 3L, 3L, 5L, 5L, 5L, 6L, 5L, 3L, 5L, 6L, 3L, 3L,
3L, 3L, 5L, 3L, 5L, 3L, 3L, 5L, 5L, 5L, 3L, 5L, 5L, 2L, 5L,
3L, 3L, 5L, 5L, 3L, 3L, 3L, 5L, 5L, 3L, 3L, 5L, 5L, 3L, 7L,
5L, 5L, 5L, 3L, 3L, 3L, 5L, 5L, 3L, 5L, 3L, 7L, 5L, 5L, 3L,
3L, 7L, 3L, 5L, 5L, 3L, 3L, 3L, 5L, 5L, 3L, 5L, 6L, 5L, 3L,
5L, 5L, 7L, 5L, 3L, 5L, 5L, 5L, 5L, 6L, 5L, 2L, 5L, 5L, 5L,
5L, 2L, 7L, 3L, 3L, 5L, 3L, 5L, 5L, 5L, 3L, 5L, 3L, 5L, 3L,
5L, 3L, 7L, 5L, 5L, 3L, 5L, 3L, 3L, 3L, 5L, 5L, 5L, 3L, 5L,
6L, 3L, 3L, 3L, 5L, 5L, 3L, 3L, 3L, 5L, 3L, 3L, 3L, 5L, 3L,
5L, 3L, 3L, 7L, 5L, 3L, 5L, 2L, 3L, 3L, 5L, 3L, 3L, 3L, 5L,
3L, 3L, 5L, 3L, 5L, 3L, 6L, 5L, 5L, 3L, 6L, 3L, 5L, 3L, 3L,
5L, 5L, 3L, 3L, 7L, 3L, 3L, 3L, 5L, 3L, 3L, 3L, 5L, 3L, 3L,
3L, 3L, 3L, 5L, 3L, 6L, 6L, 3L, 5L, 3L, 3L, 3L, 5L, 7L, 3L,
3L, 3L, 3L, 7L, 3L, 5L, 3L, 3L, 5L, 3L, 5L, 5L, 7L, 5L, 3L,
3L, 5L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 3L, 3L, 5L, 5L, 5L, 3L,
3L, 3L, 3L, 3L, 3L, 5L, 5L, 3L, 3L, 7L, 2L, 3L, 3L, 5L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 3L, 5L, 7L, 3L, 3L, 3L, 5L,
3L, 3L, 3L, 3L, 5L, 3L, 3L, 5L, 5L, 3L, 3L, 3L, 5L, 6L, 5L,
5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 3L, 3L, 3L, 3L, 3L, 3L,
6L, 5L, 5L, 5L, 6L, 3L, 5L, 3L, 5L, 6L, 4L, 5L, 6L, 5L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 3L, 5L, 5L, 3L, 5L,
3L, 5L, 6L, 3L, 5L, 3L, 3L, 3L, 3L, 5L, 3L, 3L, 3L, 5L, 7L,
3L, 3L, 6L, 3L, 5L, 3L, 3L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 5L,
5L, 5L, 5L, 3L, 5L, 3L, 5L, 5L, 3L, 3L, 3L, 7L, 5L, 5L, 5L,
5L, 3L, 5L, 3L, 3L, 5L, 5L, 3L, 5L, 5L, 3L, 3L, 3L, 5L, 3L,
3L, 7L, 5L, 6L, 3L, 5L, 3L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 5L,
5L, 5L, 5L, 7L, 3L, 5L, 7L, 5L, 3L, 3L, 3L, 5L, 3L, 5L, 3L,
5L, 3L, 3L, 5L, 3L, 3L, 5L, 3L, 7L, 5L, 5L, 3L, 3L, 3L, 3L,
5L, 3L, 7L, 3L, 3L, 5L, 3L, 5L, 6L, 5L, 5L, 5L, 3L, 3L, 3L,
5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 5L, 3L, 5L, 4L,
5L, 3L, 5L, 5L, 5L, 5L, 5L, 3L, 5L, 5L, 5L, 5L, 5L, 6L, 3L,
5L, 5L, 3L, 5L, 5L, 3L, 5L, 5L, 3L, 5L, 5L, 5L, 7L, 3L, 3L,
3L, 5L, 3L, 5L, 5L, 5L, 5L, 5L, 3L, 5L, 5L, 5L, 3L, 3L, 3L,
3L, 5L, 5L, 3L, 5L, 5L, 3L, 5L, 5L, 5L, 5L, 5L, 3L, 6L, 3L,
6L, 5L, 5L, 3L, 3L, 5L, 5L, 5L, 3L, 3L, 5L, 3L, 5L, 5L, 3L,
3L, 5L, 5L, 3L, 5L, 5L, 3L, 5L, 3L, 3L, 5L, 5L, 5L, 5L, 3L,
5L, 3L, 5L, 5L, 3L, 5L, 5L, 3L, 3L, 5L, 3L, 5L, 3L, 3L, 3L,
5L, 5L, 3L, 5L, 3L, 5L, 7L, 6L, 5L, 5L, 5L, 5L, 5L, 5L, 3L,
3L, 3L, 5L, 5L, 5L, 5L, 3L, 5L, 3L, 5L, 5L, 5L, 5L, 3L, 5L,
5L, 5L, 5L, 3L, 3L, 7L, 3L, 7L, 5L, 3L, 5L, 5L, 3L, 5L, 5L,
5L, 5L, 3L, 5L, 5L, 5L, 3L, 5L, 3L, 3L, 5L, 5L, 3L, 3L, 7L,
5L, 3L, 5L, 3L, 5L, 5L, 3L, 5L, 5L, 5L, 3L, 5L, 7L, 5L, 3L,
5L, 3L, 7L, 7L, 5L, 5L, 5L, 3L, 5L, 5L, 3L, 5L, 3L, 5L, 3L,
5L, 3L, 5L, 5L, 5L, 5L, 3L, 3L, 5L, 5L, 5L, 3L, 5L, 5L, 3L,
3L, 5L, 5L, 6L, 3L, 5L, 3L, 5L, 3L, 5L, 5L, 5L, 6L, 7L, 5L,
5L, 3L, 5L, 5L, 6L, 3L, 3L, 3L, 5L, 3L, 6L, 5L, 3L, 6L, 5L,
3L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 3L, 5L, 3L, 6L, 3L, 5L, 7L,
5L, 3L, 5L, 5L, 3L, 7L, 5L, 3L, 5L, 5L, 3L, 3L, 5L, 5L, 3L,
3L, 3L, 3L, 3L, 6L, 5L, 5L, 3L, 3L, 5L, 5L, 3L, 3L, 5L, 5L,
3L, 5L, 6L, 5L, 3L, 5L, 1L, 5L, 3L, 5L, 5L, 3L, 3L, 5L, 5L,
3L, 3L, 5L, 5L, 3L, 3L, 5L, 5L, 3L, 3L, 5L, 3L, 5L, 5L, 5L,
3L, 5L, 6L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 5L, 3L, 3L,
5L, 3L, 5L, 7L, 5L, 5L, 3L, 6L, 3L, 5L, 5L, 5L, 3L, 5L, 5L,
5L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 3L, 3L, 3L, 3L, 2L, 3L,
3L, 5L, 3L, 3L, 5L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 5L, 3L, 5L,
3L, 3L, 3L, 3L, 3L, 5L, 3L, 3L, 3L, 5L, 3L, 3L, 5L, 3L, 5L,
5L, 5L, 5L, 3L, 3L, 7L, 5L, 3L, 1L, 3L, 3L, 3L, 3L, 3L, 5L,
3L, 3L, 3L, 3L, 3L, 5L, 5L, 6L, 3L, 6L, 3L, 3L, 2L, 5L, 7L,
3L, 7L, 3L, 5L, 3L, 5L, 3L, 5L, 5L, 5L, 3L, 6L, 5L, 3L, 3L,
7L, 5L, 3L, 3L, 3L, 5L, 5L, 6L, 3L, 7L, 3L, 3L, 3L, 3L, 6L,
3L, 5L, 3L, 5L, 3L, 3L, 3L, 5L, 3L, 4L, 5L, 6L, 3L, 3L, 5L,
5L, 5L, 5L, 5L, 3L, 3L, 5L, 3L, 3L, 5L, 3L, 5L, 5L, 3L, 7L,
5L, 5L, 3L, 3L, 5L, 3L, 5L, 3L, 5L, 5L, 5L, 3L, 6L, 3L, 3L,
3L, 3L, 7L, 2L, 5L, 3L, 5L, 3L, 3L, 5L, 3L, 3L, 5L, 3L, 3L,
5L, 5L, 5L, 5L, 3L, 3L, 5L, 3L, 4L, 3L, 5L, 5L, 5L, 6L, 5L,
3L, 5L, 5L, 7L, 3L, 5L, 5L, 3L, 5L, 3L, 3L, 5L, 5L, 3L, 3L,
5L, 3L, 5L, 5L, 3L, 3L, 3L, 5L, 5L, 3L, 3L, 3L, 3L, 5L, 3L,
3L, 3L, 5L, 5L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 5L, 5L, 3L, 3L,
5L, 3L, 3L, 5L, 3L, 3L, 7L, 3L, 4L, 5L, 3L, 5L, 3L, 3L, 3L,
3L, 5L, 5L, 3L, 7L, 3L, 5L, 3L, 3L, 3L, 5L, 5L, 7L, 5L, 3L,
3L, 3L, 3L, 3L, 6L, 3L, 3L, 3L, 5L, 3L, 5L, 5L, 3L, 3L, 5L,
3L, 5L, 3L, 5L, 3L, 5L, 3L, 5L, 5L, 2L, 5L, 5L, 3L, 5L, 7L,
5L, 3L, 3L, 3L, 5L, 5L, 3L, 5L, 6L, 5L, 5L, 3L, 3L, 3L, 6L,
3L, 5L, 3L, 5L, 5L, 5L, 7L, 3L, 3L, 3L, 5L, 5L, 5L, 3L, 5L,
5L, 5L, 3L, 3L, 3L, 3L, 5L, 3L, 5L, 6L, 3L, 5L, 3L, 5L, 3L,
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