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, 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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]]
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" <alain.guillet at uclouvain.be> > To: r-help at r-project.org > 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]] > > ______________________________________________ > R-help at r-project.org 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.-- Chris Evans <chris at psyctc.org> Visiting Professor, University of Sheffield <chris.evans at sheffield.ac.uk> I do some consultation work for the University of Roehampton <chris.evans at roehampton.ac.uk> and other places but <chris at psyctc.org> 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.
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
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 <murdoch.duncan at gmail.com> 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 > >______________________________________________ >R-help at r-project.org 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.
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 <alain.guillet at uclouvain.be> 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
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 <chrishold at psyctc.org> Envoy? : mardi 10 d?cembre 2019 15:41 ? : Alain Guillet <alain.guillet at uclouvain.be> Cc : r-help at r-project.org <r-help at r-project.org> 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" <alain.guillet at uclouvain.be> > To: r-help at r-project.org > 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, 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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]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fmailman%2Flistinfo%2Fr-help&data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&sdata=YIMb5atD3i74G%2BDxPESqCc8vrymCbcvP3zqXrVPYjHE%3D&reserved=0 > PLEASE do read the posting guide https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.R-project.org%2Fposting-guide.html&data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&sdata=ht2yjUUhIHsy0ll1NRhmFNbsegVIr6KiZR1CB7MWjCE%3D&reserved=0 > and provide commented, minimal, self-contained, reproducible code.-- Chris Evans <chris at psyctc.org> Visiting Professor, University of Sheffield <chris.evans at sheffield.ac.uk> I do some consultation work for the University of Roehampton <chris.evans at roehampton.ac.uk> and other places but <chris at psyctc.org> 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&data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&sdata=H3N6FpuTiA2RhVlsYZ3DL8%2FaRQeJ0uJHFXMeEQQ8Myk%3D&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&data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&sdata=oqR8YAMqCOWaqt3%2Fph9Iw45jTQjowwPixOfgOuFYN%2Bw%3D&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&data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&sdata=cwexYPBMee0%2FklIejVj%2FmuEPiRcjWrwuQaEX1KzMSHY%3D&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&data=02%7C01%7C%7Cf5cc7176e30842e1013e08d77d7efb2f%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637115856659242341&sdata=lkiZNYJh6qMaSo%2B%2BfcuFrW0H4fCvANQlKmIZYsQMWoE%3D&reserved=0 Beware: French time, generally an hour ahead of UK. [[alternative HTML version deleted]]
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 duplicatedYou 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