table and unique seems to behave differently

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table and unique seems to behave differently

Alain Guillet-2
Hi,

I have a vector (see below the dput) and I use unique on it to get unique values. If I then sort the result of the vector obtained by unique, I see some elements that look like identical. I suspect it could be a matter of rounded values but table gives a different result: unlike unique output which contains "3.4  3.4", table has only one cell for 3.4.

Can anybody know why I get results that look like incoherent between the two functions?


Best regards,
Alain Guillet

------------------------------------------
platform       x86_64-pc-linux-gnu
arch           x86_64
os             linux-gnu
system         x86_64, linux-gnu
status
major          3
minor          6.1
year           2019
month          07
day            05
svn rev        76782
language       R
version.string R version 3.6.1 (2019-07-05)
nickname       Action of the Toes
--------------------------------------------------
> dput(toto)
c(2.5, 2.6, 2.6, 2.6, 2.6, 2.7, 2.7, 2.7, 2.7, 2.7, 2.7, 2.8,
2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 2.9, 2.9, 2.9,
2.9, 2.9, 2.9, 3, 3, 3, 3, 3, 3, 3, 3, 3.1, 3.1, 3.1, 3.1, 3.1,
3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2,
3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 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, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4,
3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.5, 3.5, 3.5, 3.5, 3.5,
3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.6, 3.6, 3.6,
3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6,
3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
3.7, 3.7, 3.7, 3.7, 3.7, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
3.8, 3.8, 3.8, 3.8, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 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, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
4.2, 4.2, 4.2, 4.2, 4.2, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 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, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.6,
4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
4.6, 4.6, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.8, 4.8, 4.8, 4.8, 4.8,
4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.9, 4.9, 4.9, 4.9, 4.9,
4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
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, 5.1, 5.1, 5.1,
5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.3, 5.3, 5.3, 5.3, 5.3,
5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
5.3, 5.3, 5.3, 5.3, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 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, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.7, 5.7, 5.7, 5.7, 5.7,
5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.8, 5.8, 5.8, 5.8,
5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
5.8, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
5.9, 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, 6.1,
6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.2,
6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
6.2, 6.2, 6.2, 6.2, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
6.3, 6.3, 6.3, 6.3, 6.3, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.5, 6.5,
6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 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, 6.7, 6.7, 6.7, 6.7,
6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.8, 6.8, 6.8,
6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
6.8, 6.8, 6.8, 6.8, 6.8, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
6.9, 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, 7.1, 7.1, 7.1, 7.1,
7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
7.1, 7.1, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
7.2, 7.2, 7.2, 7.2, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.4, 7.4,
7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4,
7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.5, 7.5, 7.5, 7.5,
7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5,
7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.6,
7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
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, 7.8, 7.8, 7.8,
7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8,
7.8, 7.8, 7.8, 7.8, 7.8, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
7.9, 7.9, 7.9, 7.9, 7.9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1,
8.1, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2,
8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.3, 8.3, 8.3, 8.3,
8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.4, 8.4, 8.4, 8.4,
8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.5, 8.5,
8.5, 8.5, 8.5, 8.5, 8.5, 8.5, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6,
8.6, 8.6, 8.6, 8.6, 8.6, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7,
8.7, 8.7, 8.7, 8.7, 8.7, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8,
8.8, 8.8, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9,
8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 9, 9, 9, 9, 9, 9, 9, 9, 9.1, 9.1,
9.1, 9.1, 9.1, 9.1, 9.1, 9.1, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2,
9.2, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3,
9.3, 9.3, 9.3, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.5, 9.5,
9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5,
9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6,
9.6, 9.6, 9.6, 9.6, 9.6, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7,
9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.8,
9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 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, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10.1,
10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1,
10.1, 10.1, 10.1, 10.1, 10.1, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2,
10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.3,
10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3,
10.3, 10.3, 10.3, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5,
10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.6, 10.6, 10.6, 10.6, 10.6,
10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6,
10.6, 10.6, 10.6, 10.6, 10.6, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
10.7, 10.7, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8,
10.8, 10.8, 10.8, 10.8, 10.8, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 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, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
11.1, 11.1, 11.1, 11.1, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
11.2, 11.2, 11.2, 11.2, 11.2, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
11.3, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
11.4, 11.4, 11.4, 11.4, 11.4, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
11.5, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.8, 11.8,
11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.9, 11.9,
11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
11.9, 11.9, 11.9, 11.9, 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, 12.1, 12.1, 12.1, 12.1, 12.1,
12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.2,
12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.3, 12.3, 12.3,
12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.4, 12.4, 12.4, 12.4, 12.4,
12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.6, 12.6, 12.6, 12.6, 12.6,
12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
12.6, 12.6, 12.6, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
12.7, 12.7, 12.7, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
12.8, 12.8, 12.8, 12.8, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
12.9, 12.9, 12.9, 12.9, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
13.1, 13.1, 13.1, 13.1, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.3, 13.3, 13.3, 13.3, 13.3,
13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.4,
13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.5, 13.5, 13.5, 13.5, 13.5,
13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
13.5, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
13.6, 13.6, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
13.7, 13.7, 13.7, 13.7, 13.7, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.9, 13.9, 13.9, 13.9,
13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
13.9, 13.9, 13.9, 13.9, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.2, 14.2, 14.2,
14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
14.2, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
14.3, 14.3, 14.3, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
14.4, 14.4, 14.4, 14.4, 14.4, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
14.5, 14.5, 14.5, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.7, 14.7,
14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
14.7, 14.7, 14.7, 14.7, 14.7, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
14.8, 14.8, 14.8, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
14.9, 14.9, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15.1,
15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
15.1, 15.1, 15.1, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
15.3, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.5,
15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.6, 15.6,
15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.7, 15.7, 15.7,
15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
15.7, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
15.8, 15.8, 15.8, 15.8, 15.8, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
15.9, 15.9, 15.9, 15.9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16, 16.1, 16.1, 16.1, 16.1, 16.1,
16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1,
16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.2,
16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2,
16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.3, 16.3,
16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3,
16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.4,
16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
16.4, 16.4, 16.4, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5,
16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.6, 16.6,
16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6,
16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.7, 16.7, 16.7, 16.7,
16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7,
16.7, 16.7, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8,
16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.9, 16.9, 16.9,
16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9,
16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 17, 17,
17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
17, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.2,
17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2,
17.2, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3,
17.3, 17.3, 17.3, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.5,
17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5,
17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.7, 17.7, 17.7,
17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.8, 17.8, 17.8, 17.8,
17.8, 17.8, 17.8, 17.8, 17.8, 17.9, 17.9, 17.9, 17.9, 17.9, 17.9,
17.9, 17.9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
18, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.2, 18.2,
18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.3, 18.3, 18.3, 18.3,
18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.4, 18.4, 18.4,
18.4, 18.4, 18.4, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5,
18.5, 18.6, 18.7, 18.7, 18.7, 18.7, 18.8, 18.8, 18.8, 18.8, 18.8,
18.8, 18.8, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9,
18.9, 19, 19, 19, 19, 19, 19.1, 19.1, 19.1, 19.1, 19.1, 19.1,
19.1, 19.2, 19.2, 19.2, 19.2, 19.2, 19.2, 19.3, 19.3, 19.3, 19.3,
19.4, 19.4, 19.4, 19.4, 19.4, 19.5, 19.5, 19.5, 19.5, 19.6, 19.7,
19.7, 19.7, 19.7, 19.7, 19.7, 19.7, 19.8, 19.8, 19.8, 19.8, 19.8,
20.1, 20.1, 20.1, 20.1, 20.1, 20.2, 20.2, 20.3, 20.4, 20.5, 20.5,
20.5, 20.6, 20.6, 20.6, 20.6, 20.7, 20.7, 20.7, 20.8, 20.8, 20.9,
20.9, 20.9, 20.9, 21, 21.1, 21.2, 21.2, 21.2, 21.3, 21.3, 21.3,
21.4, 21.5, 21.5, 21.5, 21.6, 21.6, 21.6, 21.6, 21.9, 21.9, 22,
22.1, 22.2, 22.4, 22.4, 22.5, 22.6, 22.7, 22.7, 22.7, 23.1, 23.2,
23.2, 23.5, 23.6, 23.7, 23.8, 23.8, 24.6, 25, 26.3, 26.8, 27,
27.2)
> sort(unique(toto))
  [1]  2.5  2.6  2.7  2.8  2.9  3.0  3.1  3.2  3.3  3.4  3.4  3.5  3.6  3.6  3.7  3.8  3.8  3.9  3.9
 [20]  4.0  4.1  4.1  4.2  4.2  4.3  4.3  4.4  4.5  4.6  4.6  4.7  4.7  4.8  4.8  4.9  5.0  5.0  5.1
 [39]  5.1  5.2  5.2  5.3  5.3  5.4  5.5  5.5  5.6  5.6  5.7  5.7  5.8  5.8  5.9  6.0  6.0  6.1  6.1
 [58]  6.2  6.2  6.3  6.3  6.4  6.4  6.5  6.5  6.6  6.6  6.7  6.7  6.7  6.8  6.8  6.9  6.9  7.0  7.0
 [77]  7.1  7.1  7.1  7.2  7.2  7.3  7.3  7.4  7.4  7.5  7.5  7.6  7.6  7.7  7.7  7.8  7.8  7.9  8.0
 [96]  8.1  8.1  8.2  8.2  8.3  8.4  8.5  8.6  8.6  8.7  8.7  8.8  8.8  8.9  8.9  9.0  9.1  9.1  9.2
[115]  9.2  9.3  9.3  9.4  9.4  9.5  9.5  9.6  9.6  9.7  9.7  9.8  9.9  9.9 10.0 10.0 10.1 10.1 10.2
[134] 10.2 10.3 10.3 10.4 10.4 10.5 10.5 10.6 10.6 10.7 10.7 10.8 10.8 10.9 10.9 11.0 11.0 11.1 11.1
[153] 11.2 11.2 11.3 11.3 11.4 11.4 11.5 11.5 11.6 11.6 11.7 11.7 11.8 11.8 11.8 11.9 11.9 11.9 12.0
[172] 12.0 12.1 12.1 12.2 12.2 12.3 12.3 12.4 12.4 12.4 12.5 12.5 12.6 12.6 12.7 12.7 12.8 12.8 12.9
[191] 12.9 12.9 13.0 13.0 13.1 13.1 13.2 13.2 13.3 13.3 13.3 13.4 13.4 13.4 13.5 13.5 13.6 13.6 13.6
[210] 13.7 13.7 13.8 13.8 13.8 13.9 13.9 13.9 14.0 14.0 14.1 14.1 14.2 14.2 14.3 14.3 14.3 14.4 14.4
[229] 14.4 14.5 14.5 14.6 14.6 14.7 14.7 14.8 14.8 14.8 14.9 14.9 14.9 15.0 15.0 15.1 15.1 15.2 15.2
[248] 15.2 15.3 15.3 15.3 15.4 15.4 15.4 15.5 15.5 15.6 15.6 15.7 15.7 15.8 15.8 15.8 15.9 15.9 15.9
[267] 16.0 16.1 16.1 16.2 16.2 16.3 16.3 16.4 16.4 16.5 16.6 16.6 16.7 16.7 16.8 16.8 16.9 16.9 17.0
[286] 17.1 17.1 17.2 17.2 17.3 17.3 17.4 17.5 17.6 17.6 17.7 17.7 17.8 17.8 17.9 18.0 18.1 18.1 18.2
[305] 18.2 18.3 18.3 18.4 18.5 18.6 18.7 18.8 18.8 18.9 19.0 19.1 19.2 19.2 19.3 19.3 19.4 19.4 19.5
[324] 19.6 19.7 19.7 19.8 19.8 20.1 20.1 20.2 20.3 20.4 20.5 20.6 20.6 20.7 20.8 20.9 21.0 21.1 21.2
[343] 21.2 21.3 21.3 21.4 21.5 21.6 21.6 21.9 22.0 22.1 22.2 22.4 22.5 22.6 22.7 22.7 23.1 23.2 23.5
[362] 23.6 23.7 23.8 23.8 24.6 25.0 26.3 26.8 27.0 27.2
> table(toto)
toto
 2.5  2.6  2.7  2.8  2.9    3  3.1  3.2  3.3  3.4  3.5  3.6  3.7  3.8  3.9    4  4.1  4.2  4.3  4.4
   1    4    6    9    8    8   12   13   13   14   15   23   24   25   29   39   35   29   30   33
 4.5  4.6  4.7  4.8  4.9    5  5.1  5.2  5.3  5.4  5.5  5.6  5.7  5.8  5.9    6  6.1  6.2  6.3  6.4
  48   42   45   39   57   37   42   34   48   42   36   43   40   44   39   38   39   44   40   45
 6.5  6.6  6.7  6.8  6.9    7  7.1  7.2  7.3  7.4  7.5  7.6  7.7  7.8  7.9    8  8.1  8.2  8.3  8.4
  37   39   40   47   35   34   32   28   33   24   29   27   23   21   26   18   10   21   13   15
 8.5  8.6  8.7  8.8  8.9    9  9.1  9.2  9.3  9.4  9.5  9.6  9.7  9.8  9.9   10 10.1 10.2 10.3 10.4
   8   12   13   10   17    8    8    8   15    8   21   12   20    8   16   17   17   16   15   19
10.5 10.6 10.7 10.8 10.9   11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9   12 12.1 12.2 12.3 12.4
  17   21   30   14   24   25   23   34   51   48   51   54   53   55   61   50   70   64   75   60
12.5 12.6 12.7 12.8 12.9   13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9   14 14.1 14.2 14.3 14.4
  72   63   55   78   55   60   68   79   70   62   72   67   80   79   74   65   58   70   68   68
14.5 14.6 14.7 14.8 14.9   15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9   16 16.1 16.2 16.3 16.4
  53   61   62   53   54   44   48   41   45   31   43   32   37   26   21   35   26   21   23   26
16.5 16.6 16.7 16.8 16.9   17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9   18 18.1 18.2 18.3 18.4
  17   20   17   17   23   19    9   13   13    7   12    8   10    9    8   14    8    9   12    6
18.5 18.6 18.7 18.8 18.9   19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 20.1 20.2 20.3 20.4 20.5 20.6
   9    1    4    7   10    5    7    6    4    5    4    1    7    5    5    2    1    1    3    4
20.7 20.8 20.9   21 21.1 21.2 21.3 21.4 21.5 21.6 21.9   22 22.1 22.2 22.4 22.5 22.6 22.7 23.1 23.2
   3    2    4    1    1    3    3    1    3    4    2    1    1    1    2    1    1    3    1    2
23.5 23.6 23.7 23.8 24.6   25 26.3 26.8   27 27.2
   1    1    1    2    1    1    1    1    1    1







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Re: table and unique seems to behave differently

Chris Evans
This doesn't answer your question but I get exactly the same vector of length 210 with unique(toto) and names(table(toto)) using the same version of R that you are and I can't see any obvious reason why you wouldn't but when I hit things like that it tends to be that one version is string with initial or trailing spaces or a character set issue.  I can't see that those apply here but it's all I could imagine without racking my poor old brains much more.

Good luck finding the answer!

Chris

----- Original Message -----
> From: "Alain Guillet" <[hidden email]>
> To: [hidden email]
> Sent: Tuesday, 10 December, 2019 09:53:29
> Subject: [R] table and unique seems to behave differently

> Hi,
>
> I have a vector (see below the dput) and I use unique on it to get unique
> values. If I then sort the result of the vector obtained by unique, I see some
> elements that look like identical. I suspect it could be a matter of rounded
> values but table gives a different result: unlike unique output which contains
> "3.4  3.4", table has only one cell for 3.4.
>
> Can anybody know why I get results that look like incoherent between the two
> functions?
>
>
> Best regards,
> Alain Guillet
>
> ------------------------------------------
> platform       x86_64-pc-linux-gnu
> arch           x86_64
> os             linux-gnu
> system         x86_64, linux-gnu
> status
> major          3
> minor          6.1
> year           2019
> month          07
> day            05
> svn rev        76782
> language       R
> version.string R version 3.6.1 (2019-07-05)
> nickname       Action of the Toes
> --------------------------------------------------
>> dput(toto)
> c(2.5, 2.6, 2.6, 2.6, 2.6, 2.7, 2.7, 2.7, 2.7, 2.7, 2.7, 2.8,
> 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 2.9, 2.9, 2.9,
> 2.9, 2.9, 2.9, 3, 3, 3, 3, 3, 3, 3, 3, 3.1, 3.1, 3.1, 3.1, 3.1,
> 3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2,
> 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 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, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4,
> 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.5, 3.5, 3.5, 3.5, 3.5,
> 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.6, 3.6, 3.6,
> 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6,
> 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
> 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
> 3.7, 3.7, 3.7, 3.7, 3.7, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
> 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
> 3.8, 3.8, 3.8, 3.8, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
> 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
> 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 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, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> 4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
> 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
> 4.2, 4.2, 4.2, 4.2, 4.2, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
> 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
> 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 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, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.6,
> 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> 4.6, 4.6, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.8, 4.8, 4.8, 4.8, 4.8,
> 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
> 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
> 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 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, 5.1, 5.1, 5.1,
> 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
> 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
> 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 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, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.7, 5.7, 5.7, 5.7, 5.7,
> 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
> 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
> 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> 5.9, 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, 6.1,
> 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
> 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
> 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> 6.3, 6.3, 6.3, 6.3, 6.3, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.5, 6.5,
> 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
> 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
> 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 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, 6.7, 6.7, 6.7, 6.7,
> 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
> 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
> 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> 6.9, 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, 7.1, 7.1, 7.1, 7.1,
> 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
> 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
> 7.1, 7.1, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
> 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
> 7.2, 7.2, 7.2, 7.2, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
> 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
> 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.4, 7.4,
> 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4,
> 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.5, 7.5, 7.5, 7.5,
> 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5,
> 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.6,
> 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
> 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
> 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, 7.8, 7.8, 7.8,
> 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8,
> 7.8, 7.8, 7.8, 7.8, 7.8, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
> 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
> 7.9, 7.9, 7.9, 7.9, 7.9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
> 8, 8, 8, 8, 8, 8, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1,
> 8.1, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2,
> 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.3, 8.3, 8.3, 8.3,
> 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.4, 8.4, 8.4, 8.4,
> 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.5, 8.5,
> 8.5, 8.5, 8.5, 8.5, 8.5, 8.5, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6,
> 8.6, 8.6, 8.6, 8.6, 8.6, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7,
> 8.7, 8.7, 8.7, 8.7, 8.7, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8,
> 8.8, 8.8, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9,
> 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 9, 9, 9, 9, 9, 9, 9, 9, 9.1, 9.1,
> 9.1, 9.1, 9.1, 9.1, 9.1, 9.1, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2,
> 9.2, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3,
> 9.3, 9.3, 9.3, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.5, 9.5,
> 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5,
> 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6,
> 9.6, 9.6, 9.6, 9.6, 9.6, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7,
> 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.8,
> 9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 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, 10, 10, 10,
> 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10.1,
> 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1,
> 10.1, 10.1, 10.1, 10.1, 10.1, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2,
> 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.3,
> 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3,
> 10.3, 10.3, 10.3, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
> 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
> 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5,
> 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.6, 10.6, 10.6, 10.6, 10.6,
> 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6,
> 10.6, 10.6, 10.6, 10.6, 10.6, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> 10.7, 10.7, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8,
> 10.8, 10.8, 10.8, 10.8, 10.8, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
> 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
> 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 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, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
> 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
> 11.1, 11.1, 11.1, 11.1, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> 11.2, 11.2, 11.2, 11.2, 11.2, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 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, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
> 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
> 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.6, 15.6,
> 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
> 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
> 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.7, 15.7, 15.7,
> 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> 15.7, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
> 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
> 15.8, 15.8, 15.8, 15.8, 15.8, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
> 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
> 15.9, 15.9, 15.9, 15.9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
> 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
> 16, 16, 16, 16, 16, 16, 16, 16, 16, 16.1, 16.1, 16.1, 16.1, 16.1,
> 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1,
> 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.2,
> 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2,
> 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.3, 16.3,
> 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3,
> 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.4,
> 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
> 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
> 16.4, 16.4, 16.4, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5,
> 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.6, 16.6,
> 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6,
> 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.7, 16.7, 16.7, 16.7,
> 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7,
> 16.7, 16.7, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8,
> 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.9, 16.9, 16.9,
> 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9,
> 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 17, 17,
> 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
> 17, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.2,
> 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2,
> 17.2, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3,
> 17.3, 17.3, 17.3, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.5,
> 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5,
> 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.7, 17.7, 17.7,
> 17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.8, 17.8, 17.8, 17.8,
> 17.8, 17.8, 17.8, 17.8, 17.8, 17.9, 17.9, 17.9, 17.9, 17.9, 17.9,
> 17.9, 17.9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
> 18, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.2, 18.2,
> 18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.3, 18.3, 18.3, 18.3,
> 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.4, 18.4, 18.4,
> 18.4, 18.4, 18.4, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5,
> 18.5, 18.6, 18.7, 18.7, 18.7, 18.7, 18.8, 18.8, 18.8, 18.8, 18.8,
> 18.8, 18.8, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9,
> 18.9, 19, 19, 19, 19, 19, 19.1, 19.1, 19.1, 19.1, 19.1, 19.1,
> 19.1, 19.2, 19.2, 19.2, 19.2, 19.2, 19.2, 19.3, 19.3, 19.3, 19.3,
> 19.4, 19.4, 19.4, 19.4, 19.4, 19.5, 19.5, 19.5, 19.5, 19.6, 19.7,
> 19.7, 19.7, 19.7, 19.7, 19.7, 19.7, 19.8, 19.8, 19.8, 19.8, 19.8,
> 20.1, 20.1, 20.1, 20.1, 20.1, 20.2, 20.2, 20.3, 20.4, 20.5, 20.5,
> 20.5, 20.6, 20.6, 20.6, 20.6, 20.7, 20.7, 20.7, 20.8, 20.8, 20.9,
> 20.9, 20.9, 20.9, 21, 21.1, 21.2, 21.2, 21.2, 21.3, 21.3, 21.3,
> 21.4, 21.5, 21.5, 21.5, 21.6, 21.6, 21.6, 21.6, 21.9, 21.9, 22,
> 22.1, 22.2, 22.4, 22.4, 22.5, 22.6, 22.7, 22.7, 22.7, 23.1, 23.2,
> 23.2, 23.5, 23.6, 23.7, 23.8, 23.8, 24.6, 25, 26.3, 26.8, 27,
> 27.2)
>> sort(unique(toto))
>  [1]  2.5  2.6  2.7  2.8  2.9  3.0  3.1  3.2  3.3  3.4  3.4  3.5  3.6  3.6  3.7
>  3.8  3.8  3.9  3.9
> [20]  4.0  4.1  4.1  4.2  4.2  4.3  4.3  4.4  4.5  4.6  4.6  4.7  4.7  4.8  4.8
> 4.9  5.0  5.0  5.1
> [39]  5.1  5.2  5.2  5.3  5.3  5.4  5.5  5.5  5.6  5.6  5.7  5.7  5.8  5.8  5.9
> 6.0  6.0  6.1  6.1
> [58]  6.2  6.2  6.3  6.3  6.4  6.4  6.5  6.5  6.6  6.6  6.7  6.7  6.7  6.8  6.8
> 6.9  6.9  7.0  7.0
> [77]  7.1  7.1  7.1  7.2  7.2  7.3  7.3  7.4  7.4  7.5  7.5  7.6  7.6  7.7  7.7
> 7.8  7.8  7.9  8.0
> [96]  8.1  8.1  8.2  8.2  8.3  8.4  8.5  8.6  8.6  8.7  8.7  8.8  8.8  8.9  8.9
> 9.0  9.1  9.1  9.2
> [115]  9.2  9.3  9.3  9.4  9.4  9.5  9.5  9.6  9.6  9.7  9.7  9.8  9.9  9.9 10.0
> 10.0 10.1 10.1 10.2
> [134] 10.2 10.3 10.3 10.4 10.4 10.5 10.5 10.6 10.6 10.7 10.7 10.8 10.8 10.9 10.9
> 11.0 11.0 11.1 11.1
> [153] 11.2 11.2 11.3 11.3 11.4 11.4 11.5 11.5 11.6 11.6 11.7 11.7 11.8 11.8 11.8
> 11.9 11.9 11.9 12.0
> [172] 12.0 12.1 12.1 12.2 12.2 12.3 12.3 12.4 12.4 12.4 12.5 12.5 12.6 12.6 12.7
> 12.7 12.8 12.8 12.9
> [191] 12.9 12.9 13.0 13.0 13.1 13.1 13.2 13.2 13.3 13.3 13.3 13.4 13.4 13.4 13.5
> 13.5 13.6 13.6 13.6
> [210] 13.7 13.7 13.8 13.8 13.8 13.9 13.9 13.9 14.0 14.0 14.1 14.1 14.2 14.2 14.3
> 14.3 14.3 14.4 14.4
> [229] 14.4 14.5 14.5 14.6 14.6 14.7 14.7 14.8 14.8 14.8 14.9 14.9 14.9 15.0 15.0
> 15.1 15.1 15.2 15.2
> [248] 15.2 15.3 15.3 15.3 15.4 15.4 15.4 15.5 15.5 15.6 15.6 15.7 15.7 15.8 15.8
> 15.8 15.9 15.9 15.9
> [267] 16.0 16.1 16.1 16.2 16.2 16.3 16.3 16.4 16.4 16.5 16.6 16.6 16.7 16.7 16.8
> 16.8 16.9 16.9 17.0
> [286] 17.1 17.1 17.2 17.2 17.3 17.3 17.4 17.5 17.6 17.6 17.7 17.7 17.8 17.8 17.9
> 18.0 18.1 18.1 18.2
> [305] 18.2 18.3 18.3 18.4 18.5 18.6 18.7 18.8 18.8 18.9 19.0 19.1 19.2 19.2 19.3
> 19.3 19.4 19.4 19.5
> [324] 19.6 19.7 19.7 19.8 19.8 20.1 20.1 20.2 20.3 20.4 20.5 20.6 20.6 20.7 20.8
> 20.9 21.0 21.1 21.2
> [343] 21.2 21.3 21.3 21.4 21.5 21.6 21.6 21.9 22.0 22.1 22.2 22.4 22.5 22.6 22.7
> 22.7 23.1 23.2 23.5
> [362] 23.6 23.7 23.8 23.8 24.6 25.0 26.3 26.8 27.0 27.2
>> table(toto)
> toto
> 2.5  2.6  2.7  2.8  2.9    3  3.1  3.2  3.3  3.4  3.5  3.6  3.7  3.8  3.9    4
> 4.1  4.2  4.3  4.4
>   1    4    6    9    8    8   12   13   13   14   15   23   24   25   29   39
>   35   29   30   33
> 4.5  4.6  4.7  4.8  4.9    5  5.1  5.2  5.3  5.4  5.5  5.6  5.7  5.8  5.9    6
> 6.1  6.2  6.3  6.4
>  48   42   45   39   57   37   42   34   48   42   36   43   40   44   39   38
>  39   44   40   45
> 6.5  6.6  6.7  6.8  6.9    7  7.1  7.2  7.3  7.4  7.5  7.6  7.7  7.8  7.9    8
> 8.1  8.2  8.3  8.4
>  37   39   40   47   35   34   32   28   33   24   29   27   23   21   26   18
>  10   21   13   15
> 8.5  8.6  8.7  8.8  8.9    9  9.1  9.2  9.3  9.4  9.5  9.6  9.7  9.8  9.9   10
> 10.1 10.2 10.3 10.4
>   8   12   13   10   17    8    8    8   15    8   21   12   20    8   16   17
>   17   16   15   19
> 10.5 10.6 10.7 10.8 10.9   11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9   12
> 12.1 12.2 12.3 12.4
>  17   21   30   14   24   25   23   34   51   48   51   54   53   55   61   50
>  70   64   75   60
> 12.5 12.6 12.7 12.8 12.9   13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9   14
> 14.1 14.2 14.3 14.4
>  72   63   55   78   55   60   68   79   70   62   72   67   80   79   74   65
>  58   70   68   68
> 14.5 14.6 14.7 14.8 14.9   15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9   16
> 16.1 16.2 16.3 16.4
>  53   61   62   53   54   44   48   41   45   31   43   32   37   26   21   35
>  26   21   23   26
> 16.5 16.6 16.7 16.8 16.9   17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9   18
> 18.1 18.2 18.3 18.4
>  17   20   17   17   23   19    9   13   13    7   12    8   10    9    8   14
>  8    9   12    6
> 18.5 18.6 18.7 18.8 18.9   19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 20.1 20.2
> 20.3 20.4 20.5 20.6
>   9    1    4    7   10    5    7    6    4    5    4    1    7    5    5    2
>   1    1    3    4
> 20.7 20.8 20.9   21 21.1 21.2 21.3 21.4 21.5 21.6 21.9   22 22.1 22.2 22.4 22.5
> 22.6 22.7 23.1 23.2
>   3    2    4    1    1    3    3    1    3    4    2    1    1    1    2    1
>   1    3    1    2
> 23.5 23.6 23.7 23.8 24.6   25 26.3 26.8   27 27.2
>   1    1    1    2    1    1    1    1    1    1
>
>
>
>
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
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--
Chris Evans <[hidden email]> Visiting Professor, University of Sheffield <[hidden email]>
I do some consultation work for the University of Roehampton <[hidden email]> and other places
but <[hidden email]> remains my main Email address.  I have a work web site at:
   https://www.psyctc.org/psyctc/
and a site I manage for CORE and CORE system trust at:
   http://www.coresystemtrust.org.uk/
I have "semigrated" to France, see:
   https://www.psyctc.org/pelerinage2016/semigrating-to-france/ 
That page will also take you to my blog which started with earlier joys in France and Spain!

If you want to book to talk, I am trying to keep that to Thursdays and my diary is at:
   https://www.psyctc.org/pelerinage2016/ceworkdiary/
Beware: French time, generally an hour ahead of UK.

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Re: table and unique seems to behave differently

Duncan Murdoch-2
In reply to this post by Alain Guillet-2
On 10/12/2019 3:53 a.m., Alain Guillet wrote:
> Hi,
>
> I have a vector (see below the dput) and I use unique on it to get unique values. If I then sort the result of the vector obtained by unique, I see some elements that look like identical. I suspect it could be a matter of rounded values but table gives a different result: unlike unique output which contains "3.4  3.4", table has only one cell for 3.4.
>
> Can anybody know why I get results that look like incoherent between the two functions?

dput() does some rounding, so it doesn't necessarily reproduce values
exactly.  For example,

x <- c(3.4, 3.4 + 1e-15)
unique(x)
#> [1] 3.4 3.4
dput(x)
#> c(3.4, 3.4)
identical(x, c(3.4, 3.4))
#> [1] FALSE

If you really want to see exact values, you can use the "hexNumeric"
option to dput():

dput(x, control = "hexNumeric")
#> c(0x1.b333333333333p+1, 0x1.b333333333335p+1)
identical(x, c(0x1.b333333333333p+1, 0x1.b333333333335p+1))
#> [1] TRUE

Duncan Murdoch

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Re: table and unique seems to behave differently

Jeff Newmiller
I think the question was about table vs unique. Table groups by character representation, unique groups by the underlying representation.

On December 10, 2019 7:03:34 AM PST, Duncan Murdoch <[hidden email]> wrote:

>On 10/12/2019 3:53 a.m., Alain Guillet wrote:
>> Hi,
>>
>> I have a vector (see below the dput) and I use unique on it to get
>unique values. If I then sort the result of the vector obtained by
>unique, I see some elements that look like identical. I suspect it
>could be a matter of rounded values but table gives a different result:
>unlike unique output which contains "3.4  3.4", table has only one cell
>for 3.4.
>>
>> Can anybody know why I get results that look like incoherent between
>the two functions?
>
>dput() does some rounding, so it doesn't necessarily reproduce values
>exactly.  For example,
>
>x <- c(3.4, 3.4 + 1e-15)
>unique(x)
>#> [1] 3.4 3.4
>dput(x)
>#> c(3.4, 3.4)
>identical(x, c(3.4, 3.4))
>#> [1] FALSE
>
>If you really want to see exact values, you can use the "hexNumeric"
>option to dput():
>
>dput(x, control = "hexNumeric")
>#> c(0x1.b333333333333p+1, 0x1.b333333333335p+1)
>identical(x, c(0x1.b333333333333p+1, 0x1.b333333333335p+1))
>#> [1] TRUE
>
>Duncan Murdoch
>
>______________________________________________
>[hidden email] mailing list -- To UNSUBSCRIBE and more, see
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide
>http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.

--
Sent from my phone. Please excuse my brevity.

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Re: table and unique seems to behave differently

Sarah Goslee
In reply to this post by Alain Guillet-2
Back to the table part of the question, but using Duncan's example.

> x <- c(3.4, 3.4 + 1e-15)
> unique(x)
[1] 3.4 3.4
> table(x)
x
3.4
  2

The question was, why are these different.

table() only works on factors, so it converts the numeric vector to a
factor before tabulation.
factor() tries to do something sensible, and implicitly rounds the numeric data.

> factor(x)
[1] 3.4 3.4
Levels: 3.4

Whether you think that is actually sensible or not is up to you, but
if it isn't then you shouldn't use table.

That table uses factors is documented in ?table. A quick read of
?factor didn't find any explicit discussion, other than the
acknowledgement that factor() is lossy in:

     To transform a factor ‘f’ to approximately its
     original numeric values, ‘as.numeric(levels(f))[f]’ is recommended
     and slightly more efficient than ‘as.numeric(as.character(f))’.

You can't even get table() to do what you want by being explicit:

> table(factor(x, levels = unique(x)))
Error in `levels<-`(`*tmp*`, value = as.character(levels)) :
  factor level [2] is duplicated


Sarah

On Tue, Dec 10, 2019 at 9:18 AM Alain Guillet
<[hidden email]> wrote:

>
> Hi,
>
> I have a vector (see below the dput) and I use unique on it to get unique values. If I then sort the result of the vector obtained by unique, I see some elements that look like identical. I suspect it could be a matter of rounded values but table gives a different result: unlike unique output which contains "3.4  3.4", table has only one cell for 3.4.
>
> Can anybody know why I get results that look like incoherent between the two functions?
>
>
> Best regards,
> Alain Guillet
>

--
Sarah Goslee (she/her)
http://www.numberwright.com

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Re: table and unique seems to behave differently

Alain Guillet-2
In reply to this post by Chris Evans
Another finding for me today: dput doesn't write exactly the vector that creates the problem. I could use an RData file but I think it is forbidden in this mailing list...


Alain
________________________________
De : Chris Evans <[hidden email]>
Envoy� : mardi 10 d�cembre 2019 15:41
� : Alain Guillet <[hidden email]>
Cc : [hidden email] <[hidden email]>
Objet : Re: [R] table and unique seems to behave differently

This doesn't answer your question but I get exactly the same vector of length 210 with unique(toto) and names(table(toto)) using the same version of R that you are and I can't see any obvious reason why you wouldn't but when I hit things like that it tends to be that one version is string with initial or trailing spaces or a character set issue.  I can't see that those apply here but it's all I could imagine without racking my poor old brains much more.

Good luck finding the answer!

Chris

----- Original Message -----
> From: "Alain Guillet" <[hidden email]>
> To: [hidden email]
> Sent: Tuesday, 10 December, 2019 09:53:29
> Subject: [R] table and unique seems to behave differently

> Hi,
>
> I have a vector (see below the dput) and I use unique on it to get unique
> values. If I then sort the result of the vector obtained by unique, I see some
> elements that look like identical. I suspect it could be a matter of rounded
> values but table gives a different result: unlike unique output which contains
> "3.4  3.4", table has only one cell for 3.4.
>
> Can anybody know why I get results that look like incoherent between the two
> functions?
>
>
> Best regards,
> Alain Guillet
>
> ------------------------------------------
> platform       x86_64-pc-linux-gnu
> arch           x86_64
> os             linux-gnu
> system         x86_64, linux-gnu
> status
> major          3
> minor          6.1
> year           2019
> month          07
> day            05
> svn rev        76782
> language       R
> version.string R version 3.6.1 (2019-07-05)
> nickname       Action of the Toes
> --------------------------------------------------
>> dput(toto)
> c(2.5, 2.6, 2.6, 2.6, 2.6, 2.7, 2.7, 2.7, 2.7, 2.7, 2.7, 2.8,
> 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 2.9, 2.9, 2.9,
> 2.9, 2.9, 2.9, 3, 3, 3, 3, 3, 3, 3, 3, 3.1, 3.1, 3.1, 3.1, 3.1,
> 3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2,
> 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 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, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4,
> 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.5, 3.5, 3.5, 3.5, 3.5,
> 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.6, 3.6, 3.6,
> 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6,
> 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
> 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
> 3.7, 3.7, 3.7, 3.7, 3.7, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
> 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
> 3.8, 3.8, 3.8, 3.8, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
> 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
> 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 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, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> 4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
> 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
> 4.2, 4.2, 4.2, 4.2, 4.2, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
> 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
> 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 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, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.6,
> 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> 4.6, 4.6, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.8, 4.8, 4.8, 4.8, 4.8,
> 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
> 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
> 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> 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, 5.1, 5.1, 5.1,
> 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
> 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
> 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> 5.3, 5.3, 5.3, 5.3, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 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, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.7, 5.7, 5.7, 5.7, 5.7,
> 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
> 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
> 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> 5.8, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> 5.9, 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, 6.1,
> 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
> 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
> 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> 6.2, 6.2, 6.2, 6.2, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> 6.3, 6.3, 6.3, 6.3, 6.3, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.5, 6.5,
> 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
> 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
> 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 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, 6.7, 6.7, 6.7, 6.7,
> 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
> 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
> 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> 6.8, 6.8, 6.8, 6.8, 6.8, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> 6.9, 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, 7.1, 7.1, 7.1, 7.1,
> 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
> 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
> 7.1, 7.1, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
> 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
> 7.2, 7.2, 7.2, 7.2, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
> 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
> 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.4, 7.4,
> 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4,
> 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.5, 7.5, 7.5, 7.5,
> 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5,
> 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.6,
> 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
> 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
> 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, 7.8, 7.8, 7.8,
> 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8,
> 7.8, 7.8, 7.8, 7.8, 7.8, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
> 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
> 7.9, 7.9, 7.9, 7.9, 7.9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
> 8, 8, 8, 8, 8, 8, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1,
> 8.1, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2,
> 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.3, 8.3, 8.3, 8.3,
> 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.4, 8.4, 8.4, 8.4,
> 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.5, 8.5,
> 8.5, 8.5, 8.5, 8.5, 8.5, 8.5, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6,
> 8.6, 8.6, 8.6, 8.6, 8.6, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7,
> 8.7, 8.7, 8.7, 8.7, 8.7, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8,
> 8.8, 8.8, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9,
> 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 9, 9, 9, 9, 9, 9, 9, 9, 9.1, 9.1,
> 9.1, 9.1, 9.1, 9.1, 9.1, 9.1, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2,
> 9.2, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3,
> 9.3, 9.3, 9.3, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.5, 9.5,
> 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5,
> 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6,
> 9.6, 9.6, 9.6, 9.6, 9.6, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7,
> 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.8,
> 9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 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, 10, 10, 10,
> 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10.1,
> 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1,
> 10.1, 10.1, 10.1, 10.1, 10.1, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2,
> 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.3,
> 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3,
> 10.3, 10.3, 10.3, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
> 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
> 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5,
> 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.6, 10.6, 10.6, 10.6, 10.6,
> 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6,
> 10.6, 10.6, 10.6, 10.6, 10.6, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> 10.7, 10.7, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8,
> 10.8, 10.8, 10.8, 10.8, 10.8, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
> 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
> 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 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, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
> 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
> 11.1, 11.1, 11.1, 11.1, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> 11.2, 11.2, 11.2, 11.2, 11.2, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> 11.3, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> 11.4, 11.4, 11.4, 11.4, 11.4, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> 11.5, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> 11.9, 11.9, 11.9, 11.9, 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, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> 12.6, 12.6, 12.6, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> 12.7, 12.7, 12.7, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> 12.8, 12.8, 12.8, 12.8, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> 12.9, 12.9, 12.9, 12.9, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> 13, 13, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> 13.1, 13.1, 13.1, 13.1, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> 13.5, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> 13.6, 13.6, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> 13.7, 13.7, 13.7, 13.7, 13.7, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> 13.9, 13.9, 13.9, 13.9, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> 14, 14, 14, 14, 14, 14, 14, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> 14.2, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> 14.3, 14.3, 14.3, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> 14.4, 14.4, 14.4, 14.4, 14.4, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> 14.5, 14.5, 14.5, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> 14.7, 14.7, 14.7, 14.7, 14.7, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> 14.8, 14.8, 14.8, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> 14.9, 14.9, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> 15.1, 15.1, 15.1, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> 15.3, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
> 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
> 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.6, 15.6,
> 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
> 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
> 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.7, 15.7, 15.7,
> 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> 15.7, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
> 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
> 15.8, 15.8, 15.8, 15.8, 15.8, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
> 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
> 15.9, 15.9, 15.9, 15.9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
> 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
> 16, 16, 16, 16, 16, 16, 16, 16, 16, 16.1, 16.1, 16.1, 16.1, 16.1,
> 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1,
> 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.2,
> 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2,
> 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.3, 16.3,
> 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3,
> 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.4,
> 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
> 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
> 16.4, 16.4, 16.4, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5,
> 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.6, 16.6,
> 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6,
> 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.7, 16.7, 16.7, 16.7,
> 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7,
> 16.7, 16.7, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8,
> 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.9, 16.9, 16.9,
> 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9,
> 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 17, 17,
> 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
> 17, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.2,
> 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2,
> 17.2, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3,
> 17.3, 17.3, 17.3, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.5,
> 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5,
> 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.7, 17.7, 17.7,
> 17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.8, 17.8, 17.8, 17.8,
> 17.8, 17.8, 17.8, 17.8, 17.8, 17.9, 17.9, 17.9, 17.9, 17.9, 17.9,
> 17.9, 17.9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
> 18, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.2, 18.2,
> 18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.3, 18.3, 18.3, 18.3,
> 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.4, 18.4, 18.4,
> 18.4, 18.4, 18.4, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5,
> 18.5, 18.6, 18.7, 18.7, 18.7, 18.7, 18.8, 18.8, 18.8, 18.8, 18.8,
> 18.8, 18.8, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9,
> 18.9, 19, 19, 19, 19, 19, 19.1, 19.1, 19.1, 19.1, 19.1, 19.1,
> 19.1, 19.2, 19.2, 19.2, 19.2, 19.2, 19.2, 19.3, 19.3, 19.3, 19.3,
> 19.4, 19.4, 19.4, 19.4, 19.4, 19.5, 19.5, 19.5, 19.5, 19.6, 19.7,
> 19.7, 19.7, 19.7, 19.7, 19.7, 19.7, 19.8, 19.8, 19.8, 19.8, 19.8,
> 20.1, 20.1, 20.1, 20.1, 20.1, 20.2, 20.2, 20.3, 20.4, 20.5, 20.5,
> 20.5, 20.6, 20.6, 20.6, 20.6, 20.7, 20.7, 20.7, 20.8, 20.8, 20.9,
> 20.9, 20.9, 20.9, 21, 21.1, 21.2, 21.2, 21.2, 21.3, 21.3, 21.3,
> 21.4, 21.5, 21.5, 21.5, 21.6, 21.6, 21.6, 21.6, 21.9, 21.9, 22,
> 22.1, 22.2, 22.4, 22.4, 22.5, 22.6, 22.7, 22.7, 22.7, 23.1, 23.2,
> 23.2, 23.5, 23.6, 23.7, 23.8, 23.8, 24.6, 25, 26.3, 26.8, 27,
> 27.2)
>> sort(unique(toto))
>  [1]  2.5  2.6  2.7  2.8  2.9  3.0  3.1  3.2  3.3  3.4  3.4  3.5  3.6  3.6  3.7
>  3.8  3.8  3.9  3.9
> [20]  4.0  4.1  4.1  4.2  4.2  4.3  4.3  4.4  4.5  4.6  4.6  4.7  4.7  4.8  4.8
> 4.9  5.0  5.0  5.1
> [39]  5.1  5.2  5.2  5.3  5.3  5.4  5.5  5.5  5.6  5.6  5.7  5.7  5.8  5.8  5.9
> 6.0  6.0  6.1  6.1
> [58]  6.2  6.2  6.3  6.3  6.4  6.4  6.5  6.5  6.6  6.6  6.7  6.7  6.7  6.8  6.8
> 6.9  6.9  7.0  7.0
> [77]  7.1  7.1  7.1  7.2  7.2  7.3  7.3  7.4  7.4  7.5  7.5  7.6  7.6  7.7  7.7
> 7.8  7.8  7.9  8.0
> [96]  8.1  8.1  8.2  8.2  8.3  8.4  8.5  8.6  8.6  8.7  8.7  8.8  8.8  8.9  8.9
> 9.0  9.1  9.1  9.2
> [115]  9.2  9.3  9.3  9.4  9.4  9.5  9.5  9.6  9.6  9.7  9.7  9.8  9.9  9.9 10.0
> 10.0 10.1 10.1 10.2
> [134] 10.2 10.3 10.3 10.4 10.4 10.5 10.5 10.6 10.6 10.7 10.7 10.8 10.8 10.9 10.9
> 11.0 11.0 11.1 11.1
> [153] 11.2 11.2 11.3 11.3 11.4 11.4 11.5 11.5 11.6 11.6 11.7 11.7 11.8 11.8 11.8
> 11.9 11.9 11.9 12.0
> [172] 12.0 12.1 12.1 12.2 12.2 12.3 12.3 12.4 12.4 12.4 12.5 12.5 12.6 12.6 12.7
> 12.7 12.8 12.8 12.9
> [191] 12.9 12.9 13.0 13.0 13.1 13.1 13.2 13.2 13.3 13.3 13.3 13.4 13.4 13.4 13.5
> 13.5 13.6 13.6 13.6
> [210] 13.7 13.7 13.8 13.8 13.8 13.9 13.9 13.9 14.0 14.0 14.1 14.1 14.2 14.2 14.3
> 14.3 14.3 14.4 14.4
> [229] 14.4 14.5 14.5 14.6 14.6 14.7 14.7 14.8 14.8 14.8 14.9 14.9 14.9 15.0 15.0
> 15.1 15.1 15.2 15.2
> [248] 15.2 15.3 15.3 15.3 15.4 15.4 15.4 15.5 15.5 15.6 15.6 15.7 15.7 15.8 15.8
> 15.8 15.9 15.9 15.9
> [267] 16.0 16.1 16.1 16.2 16.2 16.3 16.3 16.4 16.4 16.5 16.6 16.6 16.7 16.7 16.8
> 16.8 16.9 16.9 17.0
> [286] 17.1 17.1 17.2 17.2 17.3 17.3 17.4 17.5 17.6 17.6 17.7 17.7 17.8 17.8 17.9
> 18.0 18.1 18.1 18.2
> [305] 18.2 18.3 18.3 18.4 18.5 18.6 18.7 18.8 18.8 18.9 19.0 19.1 19.2 19.2 19.3
> 19.3 19.4 19.4 19.5
> [324] 19.6 19.7 19.7 19.8 19.8 20.1 20.1 20.2 20.3 20.4 20.5 20.6 20.6 20.7 20.8
> 20.9 21.0 21.1 21.2
> [343] 21.2 21.3 21.3 21.4 21.5 21.6 21.6 21.9 22.0 22.1 22.2 22.4 22.5 22.6 22.7
> 22.7 23.1 23.2 23.5
> [362] 23.6 23.7 23.8 23.8 24.6 25.0 26.3 26.8 27.0 27.2
>> table(toto)
> toto
> 2.5  2.6  2.7  2.8  2.9    3  3.1  3.2  3.3  3.4  3.5  3.6  3.7  3.8  3.9    4
> 4.1  4.2  4.3  4.4
>   1    4    6    9    8    8   12   13   13   14   15   23   24   25   29   39
>   35   29   30   33
> 4.5  4.6  4.7  4.8  4.9    5  5.1  5.2  5.3  5.4  5.5  5.6  5.7  5.8  5.9    6
> 6.1  6.2  6.3  6.4
>  48   42   45   39   57   37   42   34   48   42   36   43   40   44   39   38
>  39   44   40   45
> 6.5  6.6  6.7  6.8  6.9    7  7.1  7.2  7.3  7.4  7.5  7.6  7.7  7.8  7.9    8
> 8.1  8.2  8.3  8.4
>  37   39   40   47   35   34   32   28   33   24   29   27   23   21   26   18
>  10   21   13   15
> 8.5  8.6  8.7  8.8  8.9    9  9.1  9.2  9.3  9.4  9.5  9.6  9.7  9.8  9.9   10
> 10.1 10.2 10.3 10.4
>   8   12   13   10   17    8    8    8   15    8   21   12   20    8   16   17
>   17   16   15   19
> 10.5 10.6 10.7 10.8 10.9   11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9   12
> 12.1 12.2 12.3 12.4
>  17   21   30   14   24   25   23   34   51   48   51   54   53   55   61   50
>  70   64   75   60
> 12.5 12.6 12.7 12.8 12.9   13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9   14
> 14.1 14.2 14.3 14.4
>  72   63   55   78   55   60   68   79   70   62   72   67   80   79   74   65
>  58   70   68   68
> 14.5 14.6 14.7 14.8 14.9   15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9   16
> 16.1 16.2 16.3 16.4
>  53   61   62   53   54   44   48   41   45   31   43   32   37   26   21   35
>  26   21   23   26
> 16.5 16.6 16.7 16.8 16.9   17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9   18
> 18.1 18.2 18.3 18.4
>  17   20   17   17   23   19    9   13   13    7   12    8   10    9    8   14
>  8    9   12    6
> 18.5 18.6 18.7 18.8 18.9   19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 20.1 20.2
> 20.3 20.4 20.5 20.6
>   9    1    4    7   10    5    7    6    4    5    4    1    7    5    5    2
>   1    1    3    4
> 20.7 20.8 20.9   21 21.1 21.2 21.3 21.4 21.5 21.6 21.9   22 22.1 22.2 22.4 22.5
> 22.6 22.7 23.1 23.2
>   3    2    4    1    1    3    3    1    3    4    2    1    1    1    2    1
>   1    3    1    2
> 23.5 23.6 23.7 23.8 24.6   25 26.3 26.8   27 27.2
>   1    1    1    2    1    1    1    1    1    1
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Re: table and unique seems to behave differently

Duncan Murdoch-2
In reply to this post by Sarah Goslee
On 10/12/2019 10:32 a.m., Sarah Goslee wrote:

> Back to the table part of the question, but using Duncan's example.
>
>> x <- c(3.4, 3.4 + 1e-15)
>> unique(x)
> [1] 3.4 3.4
>> table(x)
> x
> 3.4
>    2
>
> The question was, why are these different.
>
> table() only works on factors, so it converts the numeric vector to a
> factor before tabulation.
> factor() tries to do something sensible, and implicitly rounds the numeric data.
>
>> factor(x)
> [1] 3.4 3.4
> Levels: 3.4
>
> Whether you think that is actually sensible or not is up to you, but
> if it isn't then you shouldn't use table.
>
> That table uses factors is documented in ?table. A quick read of
> ?factor didn't find any explicit discussion, other than the
> acknowledgement that factor() is lossy in:
>
>       To transform a factor ‘f’ to approximately its
>       original numeric values, ‘as.numeric(levels(f))[f]’ is recommended
>       and slightly more efficient than ‘as.numeric(as.character(f))’.
>
> You can't even get table() to do what you want by being explicit:
>
>> table(factor(x, levels = unique(x)))
> Error in `levels<-`(`*tmp*`, value = as.character(levels)) :
>    factor level [2] is duplicated

You could get it to agree with unique if you do the string conversion
yourself.  The first result is ugly:

x <- c(3.4, 3.4 + 1e-15)
tab <- table(sprintf("%a", x))
tab
#>
#> 0x1.b333333333333p+1 0x1.b333333333335p+1
#>                    1                    1

But if you really want you can make it readable:

names(tab) <- as.numeric(names(tab))
tab
#> 3.4 3.4
#>   1   1

Duncan Murdoch

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Re: table and unique seems to behave differently

Alain Guillet-2
In reply to this post by Jeff Newmiller
Thanks a lot, it answers my question.


Alain
________________________________
De : Jeff Newmiller <[hidden email]>
Envoy� : mardi 10 d�cembre 2019 16:31
� : [hidden email] <[hidden email]>; Duncan Murdoch <[hidden email]>; Alain Guillet <[hidden email]>; [hidden email] <[hidden email]>
Objet : Re: [R] table and unique seems to behave differently

I think the question was about table vs unique. Table groups by character representation, unique groups by the underlying representation.

On December 10, 2019 7:03:34 AM PST, Duncan Murdoch <[hidden email]> wrote:

>On 10/12/2019 3:53 a.m., Alain Guillet wrote:
>> Hi,
>>
>> I have a vector (see below the dput) and I use unique on it to get
>unique values. If I then sort the result of the vector obtained by
>unique, I see some elements that look like identical. I suspect it
>could be a matter of rounded values but table gives a different result:
>unlike unique output which contains "3.4  3.4", table has only one cell
>for 3.4.
>>
>> Can anybody know why I get results that look like incoherent between
>the two functions?
>
>dput() does some rounding, so it doesn't necessarily reproduce values
>exactly.  For example,
>
>x <- c(3.4, 3.4 + 1e-15)
>unique(x)
>#> [1] 3.4 3.4
>dput(x)
>#> c(3.4, 3.4)
>identical(x, c(3.4, 3.4))
>#> [1] FALSE
>
>If you really want to see exact values, you can use the "hexNumeric"
>option to dput():
>
>dput(x, control = "hexNumeric")
>#> c(0x1.b333333333333p+1, 0x1.b333333333335p+1)
>identical(x, c(0x1.b333333333333p+1, 0x1.b333333333335p+1))
>#> [1] TRUE
>
>Duncan Murdoch
>
>______________________________________________
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>PLEASE do read the posting guide
>https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.R-project.org%2Fposting-guide.html&amp;data=02%7C01%7C%7C74bb1eeaeb444a6499e508d77d85fba3%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115886725989409&amp;sdata=hTxOssdYb%2FcvvSFQyQZ5GBWkpHzsIrbtqJbgCgW2LPw%3D&amp;reserved=0
>and provide commented, minimal, self-contained, reproducible code.
--
Sent from my phone. Please excuse my brevity.

        [[alternative HTML version deleted]]


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Re: table and unique seems to behave differently

R help mailing list-2
In reply to this post by Alain Guillet-2
You can use save(ascii=TRUE,...) to make an ascii-only RData file that you
can include in the mail message.  E.g.,

> x <- c(3.4, 3.4 + 1e-15)
> save(x, ascii=TRUE, file=stdout())
RDA3
A
3
198145
197888
5
UTF-8
1026
1
262153
1
x
14
2
3.4
3.400000000000001
254

Bill Dunlap
TIBCO Software
wdunlap tibco.com


On Tue, Dec 10, 2019 at 8:37 AM Alain Guillet <[hidden email]>
wrote:

> Another finding for me today: dput doesn't write exactly the vector that
> creates the problem. I could use an RData file but I think it is forbidden
> in this mailing list...
>
>
> Alain
> ________________________________
> De : Chris Evans <[hidden email]>
> Envoyé : mardi 10 décembre 2019 15:41
> À : Alain Guillet <[hidden email]>
> Cc : [hidden email] <[hidden email]>
> Objet : Re: [R] table and unique seems to behave differently
>
> This doesn't answer your question but I get exactly the same vector of
> length 210 with unique(toto) and names(table(toto)) using the same version
> of R that you are and I can't see any obvious reason why you wouldn't but
> when I hit things like that it tends to be that one version is string with
> initial or trailing spaces or a character set issue.  I can't see that
> those apply here but it's all I could imagine without racking my poor old
> brains much more.
>
> Good luck finding the answer!
>
> Chris
>
> ----- Original Message -----
> > From: "Alain Guillet" <[hidden email]>
> > To: [hidden email]
> > Sent: Tuesday, 10 December, 2019 09:53:29
> > Subject: [R] table and unique seems to behave differently
>
> > Hi,
> >
> > I have a vector (see below the dput) and I use unique on it to get unique
> > values. If I then sort the result of the vector obtained by unique, I
> see some
> > elements that look like identical. I suspect it could be a matter of
> rounded
> > values but table gives a different result: unlike unique output which
> contains
> > "3.4  3.4", table has only one cell for 3.4.
> >
> > Can anybody know why I get results that look like incoherent between the
> two
> > functions?
> >
> >
> > Best regards,
> > Alain Guillet
> >
> > ------------------------------------------
> > platform       x86_64-pc-linux-gnu
> > arch           x86_64
> > os             linux-gnu
> > system         x86_64, linux-gnu
> > status
> > major          3
> > minor          6.1
> > year           2019
> > month          07
> > day            05
> > svn rev        76782
> > language       R
> > version.string R version 3.6.1 (2019-07-05)
> > nickname       Action of the Toes
> > --------------------------------------------------
> >> dput(toto)
> > c(2.5, 2.6, 2.6, 2.6, 2.6, 2.7, 2.7, 2.7, 2.7, 2.7, 2.7, 2.8,
> > 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.8, 2.9, 2.9, 2.9, 2.9, 2.9,
> > 2.9, 2.9, 2.9, 3, 3, 3, 3, 3, 3, 3, 3, 3.1, 3.1, 3.1, 3.1, 3.1,
> > 3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.1, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2,
> > 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 3.2, 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, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4,
> > 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.4, 3.5, 3.5, 3.5, 3.5, 3.5,
> > 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.5, 3.6, 3.6, 3.6,
> > 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6,
> > 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.6, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
> > 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7, 3.7,
> > 3.7, 3.7, 3.7, 3.7, 3.7, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
> > 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8, 3.8,
> > 3.8, 3.8, 3.8, 3.8, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
> > 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9,
> > 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 3.9, 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, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> > 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> > 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1, 4.1,
> > 4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
> > 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2, 4.2,
> > 4.2, 4.2, 4.2, 4.2, 4.2, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
> > 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3,
> > 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 4.3, 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, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> > 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> > 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5,
> > 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 4.6,
> > 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> > 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> > 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6, 4.6,
> > 4.6, 4.6, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> > 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> > 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7,
> > 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.7, 4.8, 4.8, 4.8, 4.8, 4.8,
> > 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
> > 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8,
> > 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.8, 4.9, 4.9, 4.9, 4.9, 4.9,
> > 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> > 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> > 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> > 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9, 4.9,
> > 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, 5.1, 5.1, 5.1,
> > 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> > 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> > 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1, 5.1,
> > 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
> > 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2,
> > 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.2, 5.3, 5.3, 5.3, 5.3, 5.3,
> > 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> > 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> > 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3, 5.3,
> > 5.3, 5.3, 5.3, 5.3, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> > 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> > 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4,
> > 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 5.4, 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, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> > 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> > 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6,
> > 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.6, 5.7, 5.7, 5.7, 5.7, 5.7,
> > 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
> > 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7,
> > 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.7, 5.8, 5.8, 5.8, 5.8,
> > 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> > 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> > 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8, 5.8,
> > 5.8, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> > 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> > 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9, 5.9,
> > 5.9, 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, 6.1,
> > 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
> > 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1,
> > 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.1, 6.2,
> > 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> > 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> > 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2, 6.2,
> > 6.2, 6.2, 6.2, 6.2, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> > 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> > 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3, 6.3,
> > 6.3, 6.3, 6.3, 6.3, 6.3, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> > 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> > 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4,
> > 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.4, 6.5, 6.5,
> > 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
> > 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5,
> > 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 6.5, 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, 6.7, 6.7, 6.7, 6.7,
> > 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
> > 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7,
> > 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.7, 6.8, 6.8, 6.8,
> > 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> > 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> > 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8, 6.8,
> > 6.8, 6.8, 6.8, 6.8, 6.8, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> > 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> > 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9, 6.9,
> > 6.9, 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, 7.1, 7.1, 7.1, 7.1,
> > 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
> > 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1, 7.1,
> > 7.1, 7.1, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
> > 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2, 7.2,
> > 7.2, 7.2, 7.2, 7.2, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
> > 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3,
> > 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.3, 7.4, 7.4,
> > 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4,
> > 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.4, 7.5, 7.5, 7.5, 7.5,
> > 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5,
> > 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 7.6,
> > 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
> > 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6, 7.6,
> > 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, 7.8, 7.8, 7.8,
> > 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8, 7.8,
> > 7.8, 7.8, 7.8, 7.8, 7.8, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
> > 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9, 7.9,
> > 7.9, 7.9, 7.9, 7.9, 7.9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
> > 8, 8, 8, 8, 8, 8, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1, 8.1,
> > 8.1, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2,
> > 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.2, 8.3, 8.3, 8.3, 8.3,
> > 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.3, 8.4, 8.4, 8.4, 8.4,
> > 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.4, 8.5, 8.5,
> > 8.5, 8.5, 8.5, 8.5, 8.5, 8.5, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6, 8.6,
> > 8.6, 8.6, 8.6, 8.6, 8.6, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7, 8.7,
> > 8.7, 8.7, 8.7, 8.7, 8.7, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8, 8.8,
> > 8.8, 8.8, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 8.9,
> > 8.9, 8.9, 8.9, 8.9, 8.9, 8.9, 9, 9, 9, 9, 9, 9, 9, 9, 9.1, 9.1,
> > 9.1, 9.1, 9.1, 9.1, 9.1, 9.1, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2, 9.2,
> > 9.2, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3, 9.3,
> > 9.3, 9.3, 9.3, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.4, 9.5, 9.5,
> > 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.5,
> > 9.5, 9.5, 9.5, 9.5, 9.5, 9.5, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6, 9.6,
> > 9.6, 9.6, 9.6, 9.6, 9.6, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7,
> > 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.7, 9.8,
> > 9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 9.8, 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, 10, 10, 10,
> > 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10.1,
> > 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1, 10.1,
> > 10.1, 10.1, 10.1, 10.1, 10.1, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2,
> > 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.2, 10.3,
> > 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3, 10.3,
> > 10.3, 10.3, 10.3, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
> > 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4, 10.4,
> > 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5,
> > 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.6, 10.6, 10.6, 10.6, 10.6,
> > 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6, 10.6,
> > 10.6, 10.6, 10.6, 10.6, 10.6, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> > 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> > 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7, 10.7,
> > 10.7, 10.7, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8, 10.8,
> > 10.8, 10.8, 10.8, 10.8, 10.8, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
> > 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9,
> > 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 10.9, 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, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
> > 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1, 11.1,
> > 11.1, 11.1, 11.1, 11.1, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> > 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> > 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2, 11.2,
> > 11.2, 11.2, 11.2, 11.2, 11.2, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> > 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> > 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> > 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> > 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3, 11.3,
> > 11.3, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> > 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> > 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> > 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4, 11.4,
> > 11.4, 11.4, 11.4, 11.4, 11.4, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> > 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> > 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> > 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> > 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5,
> > 11.5, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> > 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> > 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> > 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> > 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6, 11.6,
> > 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> > 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> > 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> > 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7,
> > 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.7, 11.8, 11.8,
> > 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> > 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> > 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> > 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8,
> > 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.8, 11.9, 11.9,
> > 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> > 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> > 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> > 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> > 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9, 11.9,
> > 11.9, 11.9, 11.9, 11.9, 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, 12.1, 12.1, 12.1, 12.1, 12.1,
> > 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> > 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> > 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> > 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> > 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1,
> > 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.1, 12.2,
> > 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> > 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> > 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> > 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> > 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2,
> > 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.2, 12.3, 12.3, 12.3,
> > 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> > 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> > 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> > 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> > 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> > 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.3,
> > 12.3, 12.3, 12.3, 12.3, 12.3, 12.3, 12.4, 12.4, 12.4, 12.4, 12.4,
> > 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> > 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> > 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> > 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> > 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4, 12.4,
> > 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> > 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> > 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> > 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> > 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> > 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5,
> > 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.6, 12.6, 12.6, 12.6, 12.6,
> > 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> > 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> > 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> > 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> > 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6, 12.6,
> > 12.6, 12.6, 12.6, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> > 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> > 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> > 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> > 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7, 12.7,
> > 12.7, 12.7, 12.7, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> > 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> > 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> > 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> > 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> > 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> > 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8, 12.8,
> > 12.8, 12.8, 12.8, 12.8, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> > 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> > 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> > 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> > 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9, 12.9,
> > 12.9, 12.9, 12.9, 12.9, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> > 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> > 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> > 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
> > 13, 13, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> > 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> > 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> > 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> > 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> > 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1, 13.1,
> > 13.1, 13.1, 13.1, 13.1, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> > 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> > 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> > 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> > 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> > 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> > 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.2,
> > 13.2, 13.2, 13.2, 13.2, 13.2, 13.2, 13.3, 13.3, 13.3, 13.3, 13.3,
> > 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> > 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> > 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> > 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> > 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3,
> > 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.3, 13.4,
> > 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> > 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> > 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> > 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> > 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.4,
> > 13.4, 13.4, 13.4, 13.4, 13.4, 13.4, 13.5, 13.5, 13.5, 13.5, 13.5,
> > 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> > 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> > 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> > 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> > 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> > 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5,
> > 13.5, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> > 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> > 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> > 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> > 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> > 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6, 13.6,
> > 13.6, 13.6, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> > 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> > 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> > 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> > 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> > 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> > 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7, 13.7,
> > 13.7, 13.7, 13.7, 13.7, 13.7, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> > 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> > 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> > 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> > 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> > 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> > 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8,
> > 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.8, 13.9, 13.9, 13.9, 13.9,
> > 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> > 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> > 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> > 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> > 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> > 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9, 13.9,
> > 13.9, 13.9, 13.9, 13.9, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> > 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> > 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> > 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
> > 14, 14, 14, 14, 14, 14, 14, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> > 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> > 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> > 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> > 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1,
> > 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.1, 14.2, 14.2, 14.2,
> > 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> > 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> > 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> > 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> > 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> > 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2, 14.2,
> > 14.2, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> > 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> > 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> > 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> > 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> > 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3, 14.3,
> > 14.3, 14.3, 14.3, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> > 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> > 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> > 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> > 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> > 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4, 14.4,
> > 14.4, 14.4, 14.4, 14.4, 14.4, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> > 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> > 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> > 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> > 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5,
> > 14.5, 14.5, 14.5, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> > 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> > 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> > 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> > 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6,
> > 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.7, 14.7,
> > 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> > 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> > 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> > 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> > 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7, 14.7,
> > 14.7, 14.7, 14.7, 14.7, 14.7, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> > 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> > 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> > 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> > 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8, 14.8,
> > 14.8, 14.8, 14.8, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> > 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> > 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> > 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> > 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9, 14.9,
> > 14.9, 14.9, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
> > 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
> > 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15.1,
> > 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> > 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> > 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> > 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1, 15.1,
> > 15.1, 15.1, 15.1, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> > 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> > 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> > 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2, 15.2,
> > 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> > 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> > 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> > 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3, 15.3,
> > 15.3, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
> > 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4,
> > 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.4, 15.5,
> > 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> > 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> > 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5,
> > 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.5, 15.6, 15.6,
> > 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
> > 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6,
> > 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.6, 15.7, 15.7, 15.7,
> > 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> > 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> > 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7, 15.7,
> > 15.7, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
> > 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8, 15.8,
> > 15.8, 15.8, 15.8, 15.8, 15.8, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
> > 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9, 15.9,
> > 15.9, 15.9, 15.9, 15.9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
> > 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
> > 16, 16, 16, 16, 16, 16, 16, 16, 16, 16.1, 16.1, 16.1, 16.1, 16.1,
> > 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1,
> > 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.1, 16.2,
> > 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2,
> > 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.2, 16.3, 16.3,
> > 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3,
> > 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.3, 16.4,
> > 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
> > 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4, 16.4,
> > 16.4, 16.4, 16.4, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5,
> > 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.5, 16.6, 16.6,
> > 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6,
> > 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.6, 16.7, 16.7, 16.7, 16.7,
> > 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7, 16.7,
> > 16.7, 16.7, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8,
> > 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.8, 16.9, 16.9, 16.9,
> > 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9,
> > 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 16.9, 17, 17,
> > 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
> > 17, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.1, 17.2,
> > 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2, 17.2,
> > 17.2, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3, 17.3,
> > 17.3, 17.3, 17.3, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.4, 17.5,
> > 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5, 17.5,
> > 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.6, 17.7, 17.7, 17.7,
> > 17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.7, 17.8, 17.8, 17.8, 17.8,
> > 17.8, 17.8, 17.8, 17.8, 17.8, 17.9, 17.9, 17.9, 17.9, 17.9, 17.9,
> > 17.9, 17.9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
> > 18, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.1, 18.2, 18.2,
> > 18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.2, 18.3, 18.3, 18.3, 18.3,
> > 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.3, 18.4, 18.4, 18.4,
> > 18.4, 18.4, 18.4, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5, 18.5,
> > 18.5, 18.6, 18.7, 18.7, 18.7, 18.7, 18.8, 18.8, 18.8, 18.8, 18.8,
> > 18.8, 18.8, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9, 18.9,
> > 18.9, 19, 19, 19, 19, 19, 19.1, 19.1, 19.1, 19.1, 19.1, 19.1,
> > 19.1, 19.2, 19.2, 19.2, 19.2, 19.2, 19.2, 19.3, 19.3, 19.3, 19.3,
> > 19.4, 19.4, 19.4, 19.4, 19.4, 19.5, 19.5, 19.5, 19.5, 19.6, 19.7,
> > 19.7, 19.7, 19.7, 19.7, 19.7, 19.7, 19.8, 19.8, 19.8, 19.8, 19.8,
> > 20.1, 20.1, 20.1, 20.1, 20.1, 20.2, 20.2, 20.3, 20.4, 20.5, 20.5,
> > 20.5, 20.6, 20.6, 20.6, 20.6, 20.7, 20.7, 20.7, 20.8, 20.8, 20.9,
> > 20.9, 20.9, 20.9, 21, 21.1, 21.2, 21.2, 21.2, 21.3, 21.3, 21.3,
> > 21.4, 21.5, 21.5, 21.5, 21.6, 21.6, 21.6, 21.6, 21.9, 21.9, 22,
> > 22.1, 22.2, 22.4, 22.4, 22.5, 22.6, 22.7, 22.7, 22.7, 23.1, 23.2,
> > 23.2, 23.5, 23.6, 23.7, 23.8, 23.8, 24.6, 25, 26.3, 26.8, 27,
> > 27.2)
> >> sort(unique(toto))
> >  [1]  2.5  2.6  2.7  2.8  2.9  3.0  3.1  3.2  3.3  3.4  3.4  3.5  3.6
> 3.6  3.7
> >  3.8  3.8  3.9  3.9
> > [20]  4.0  4.1  4.1  4.2  4.2  4.3  4.3  4.4  4.5  4.6  4.6  4.7  4.7
> 4.8  4.8
> > 4.9  5.0  5.0  5.1
> > [39]  5.1  5.2  5.2  5.3  5.3  5.4  5.5  5.5  5.6  5.6  5.7  5.7  5.8
> 5.8  5.9
> > 6.0  6.0  6.1  6.1
> > [58]  6.2  6.2  6.3  6.3  6.4  6.4  6.5  6.5  6.6  6.6  6.7  6.7  6.7
> 6.8  6.8
> > 6.9  6.9  7.0  7.0
> > [77]  7.1  7.1  7.1  7.2  7.2  7.3  7.3  7.4  7.4  7.5  7.5  7.6  7.6
> 7.7  7.7
> > 7.8  7.8  7.9  8.0
> > [96]  8.1  8.1  8.2  8.2  8.3  8.4  8.5  8.6  8.6  8.7  8.7  8.8  8.8
> 8.9  8.9
> > 9.0  9.1  9.1  9.2
> > [115]  9.2  9.3  9.3  9.4  9.4  9.5  9.5  9.6  9.6  9.7  9.7  9.8  9.9
> 9.9 10.0
> > 10.0 10.1 10.1 10.2
> > [134] 10.2 10.3 10.3 10.4 10.4 10.5 10.5 10.6 10.6 10.7 10.7 10.8 10.8
> 10.9 10.9
> > 11.0 11.0 11.1 11.1
> > [153] 11.2 11.2 11.3 11.3 11.4 11.4 11.5 11.5 11.6 11.6 11.7 11.7 11.8
> 11.8 11.8
> > 11.9 11.9 11.9 12.0
> > [172] 12.0 12.1 12.1 12.2 12.2 12.3 12.3 12.4 12.4 12.4 12.5 12.5 12.6
> 12.6 12.7
> > 12.7 12.8 12.8 12.9
> > [191] 12.9 12.9 13.0 13.0 13.1 13.1 13.2 13.2 13.3 13.3 13.3 13.4 13.4
> 13.4 13.5
> > 13.5 13.6 13.6 13.6
> > [210] 13.7 13.7 13.8 13.8 13.8 13.9 13.9 13.9 14.0 14.0 14.1 14.1 14.2
> 14.2 14.3
> > 14.3 14.3 14.4 14.4
> > [229] 14.4 14.5 14.5 14.6 14.6 14.7 14.7 14.8 14.8 14.8 14.9 14.9 14.9
> 15.0 15.0
> > 15.1 15.1 15.2 15.2
> > [248] 15.2 15.3 15.3 15.3 15.4 15.4 15.4 15.5 15.5 15.6 15.6 15.7 15.7
> 15.8 15.8
> > 15.8 15.9 15.9 15.9
> > [267] 16.0 16.1 16.1 16.2 16.2 16.3 16.3 16.4 16.4 16.5 16.6 16.6 16.7
> 16.7 16.8
> > 16.8 16.9 16.9 17.0
> > [286] 17.1 17.1 17.2 17.2 17.3 17.3 17.4 17.5 17.6 17.6 17.7 17.7 17.8
> 17.8 17.9
> > 18.0 18.1 18.1 18.2
> > [305] 18.2 18.3 18.3 18.4 18.5 18.6 18.7 18.8 18.8 18.9 19.0 19.1 19.2
> 19.2 19.3
> > 19.3 19.4 19.4 19.5
> > [324] 19.6 19.7 19.7 19.8 19.8 20.1 20.1 20.2 20.3 20.4 20.5 20.6 20.6
> 20.7 20.8
> > 20.9 21.0 21.1 21.2
> > [343] 21.2 21.3 21.3 21.4 21.5 21.6 21.6 21.9 22.0 22.1 22.2 22.4 22.5
> 22.6 22.7
> > 22.7 23.1 23.2 23.5
> > [362] 23.6 23.7 23.8 23.8 24.6 25.0 26.3 26.8 27.0 27.2
> >> table(toto)
> > toto
> > 2.5  2.6  2.7  2.8  2.9    3  3.1  3.2  3.3  3.4  3.5  3.6  3.7  3.8
> 3.9    4
> > 4.1  4.2  4.3  4.4
> >   1    4    6    9    8    8   12   13   13   14   15   23   24   25
>  29   39
> >   35   29   30   33
> > 4.5  4.6  4.7  4.8  4.9    5  5.1  5.2  5.3  5.4  5.5  5.6  5.7  5.8
> 5.9    6
> > 6.1  6.2  6.3  6.4
> >  48   42   45   39   57   37   42   34   48   42   36   43   40   44
>  39   38
> >  39   44   40   45
> > 6.5  6.6  6.7  6.8  6.9    7  7.1  7.2  7.3  7.4  7.5  7.6  7.7  7.8
> 7.9    8
> > 8.1  8.2  8.3  8.4
> >  37   39   40   47   35   34   32   28   33   24   29   27   23   21
>  26   18
> >  10   21   13   15
> > 8.5  8.6  8.7  8.8  8.9    9  9.1  9.2  9.3  9.4  9.5  9.6  9.7  9.8
> 9.9   10
> > 10.1 10.2 10.3 10.4
> >   8   12   13   10   17    8    8    8   15    8   21   12   20    8
>  16   17
> >   17   16   15   19
> > 10.5 10.6 10.7 10.8 10.9   11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8
> 11.9   12
> > 12.1 12.2 12.3 12.4
> >  17   21   30   14   24   25   23   34   51   48   51   54   53   55
>  61   50
> >  70   64   75   60
> > 12.5 12.6 12.7 12.8 12.9   13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8
> 13.9   14
> > 14.1 14.2 14.3 14.4
> >  72   63   55   78   55   60   68   79   70   62   72   67   80   79
>  74   65
> >  58   70   68   68
> > 14.5 14.6 14.7 14.8 14.9   15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8
> 15.9   16
> > 16.1 16.2 16.3 16.4
> >  53   61   62   53   54   44   48   41   45   31   43   32   37   26
>  21   35
> >  26   21   23   26
> > 16.5 16.6 16.7 16.8 16.9   17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8
> 17.9   18
> > 18.1 18.2 18.3 18.4
> >  17   20   17   17   23   19    9   13   13    7   12    8   10    9
> 8   14
> >  8    9   12    6
> > 18.5 18.6 18.7 18.8 18.9   19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8
> 20.1 20.2
> > 20.3 20.4 20.5 20.6
> >   9    1    4    7   10    5    7    6    4    5    4    1    7    5
> 5    2
> >   1    1    3    4
> > 20.7 20.8 20.9   21 21.1 21.2 21.3 21.4 21.5 21.6 21.9   22 22.1 22.2
> 22.4 22.5
> > 22.6 22.7 23.1 23.2
> >   3    2    4    1    1    3    3    1    3    4    2    1    1    1
> 2    1
> >   1    3    1    2
> > 23.5 23.6 23.7 23.8 24.6   25 26.3 26.8   27 27.2
> >   1    1    1    2    1    1    1    1    1    1
> >
> >
> >
> >
> >
> >
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
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> >
> https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fmailman%2Flistinfo%2Fr-help&amp;data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&amp;sdata=YIMb5atD3i74G%2BDxPESqCc8vrymCbcvP3zqXrVPYjHE%3D&amp;reserved=0
> > PLEASE do read the posting guide
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> > and provide commented, minimal, self-contained, reproducible code.
>
> --
> Chris Evans <[hidden email]> Visiting Professor, University of
> Sheffield <[hidden email]>
> I do some consultation work for the University of Roehampton <
> [hidden email]> and other places
> but <[hidden email]> remains my main Email address.  I have a work web
> site at:
>
> https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.psyctc.org%2Fpsyctc%2F&amp;data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&amp;sdata=H3N6FpuTiA2RhVlsYZ3DL8%2FaRQeJ0uJHFXMeEQQ8Myk%3D&amp;reserved=0
> and a site I manage for CORE and CORE system trust at:
>
> https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.coresystemtrust.org.uk%2F&amp;data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&amp;sdata=oqR8YAMqCOWaqt3%2Fph9Iw45jTQjowwPixOfgOuFYN%2Bw%3D&amp;reserved=0
> I have "semigrated" to France, see:
>
> https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.psyctc.org%2Fpelerinage2016%2Fsemigrating-to-france%2F&amp;data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&amp;sdata=cwexYPBMee0%2FklIejVj%2FmuEPiRcjWrwuQaEX1KzMSHY%3D&amp;reserved=0
> That page will also take you to my blog which started with earlier joys in
> France and Spain!
>
> If you want to book to talk, I am trying to keep that to Thursdays and my
> diary is at:
>
> https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.psyctc.org%2Fpelerinage2016%2Fceworkdiary%2F&amp;data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&amp;sdata=lkiZNYJh6qMaSo%2B%2BfcuFrW0H4fCvANQlKmIZYsQMWoE%3D&amp;reserved=0
> Beware: French time, generally an hour ahead of UK.
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.