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i!"! a ` a c a ``` `aaa ``` aaa ``` `!ccc j'$k$ 1 C l ; B-?hm 4noqsr $h t=;2 4nXu ED4+* J D98 B v-,/. <; w ; 1 xx -;>= $-r <; 4Xu E'0. y&'z?h{ O Z$ 4noq}u *K #%$&')( $ +* '$&$-,/.&$103254"!"!4 6+78 9 7&$ <;>=)7 ',?2A@B; (CD9 0FED43G&0!4!3G>H!"4! IJ- KML ( ON 0FE'43G&034!!G-ED"!4P IJQR ;>;%$ &+ N 6S TU$. L = $ htt//www.stat.umn.edu/~kb/classes/5303 2002 by Christoher Bingham Cmd> data <- read("","exml15.6") exml15.6 128 9 ) A data set from Oehlert (2000) \emh{a First Course in Design ) and Analysis of Exeriments}, New York W. H. Freeman. ) ) Table 15.6,. 398 ) Data for a 2^7 in standard order. Factors are size of image, ) shae of image, color of image, orientation of image, duration ) of image vertical location of image, and horizontal location ) of image. ) ABCD, ACEG, BCE, BCFG, ACF, CDEF, ABG, BDEG, ADE, ADFG, BDF, ) EFG, CDG, ABEF, and ABCDEFG are confounded with blocks. ) Columns are block, A, B, C, D, E, F, G, and resonse Read from file "TP1Stat5303DataOeCh15.dat" ~ 7&$k$ $ %$ ;3GZ / -2M $ %$ ; P3GZ / -;&r1 ;%$ H3GZ / ;)9$x 8'8 y ; ƒ ; (;&r $r2aed u 4 G-E <; tk r $h t=; $h >( < y$ ;){9 7? ;%$ ˆ-(&;&r.& choosedef2(7,4,allt) K ~ 7&$k$ 1u E k$ e 9$K Cmd> makecols(data,block,a,b,c,d,e,f,g,y,factorsrun(8)) Column 1 saved as factor block with levels Column 2 saved as factor a with 2 levels Column 3 saved as factor b with 2 levels Column 4 saved as factor c with 2 levels Column 5 saved as factor d with 2 levels Column 6 saved as factor e with 2 levels Column 7 saved as factor f with 2 levels Column 8 saved as factor g with 2 levels Column 9 saved as vector y 2

j'$k$ 1 -; A2R <;! <(>re <;>=, ; $hx$&d) <( 4!GZ >-253GZ / -;>r P3GZ / ;)9$x 8+G w; &K ~ 7 1 ; -; &K Cmd> anova("y=block + (a+b+c+d+e+f+g)^4") Model used is y=block + (a+b+c+d+e+f+g)^4 WARNING summaries are sequential DF SS MS CONSTANT 1 30.44 30.44 block 15 1.3384 0.089225 a 1 0.02645 0.02645 b 1 0.014028 0.014028 c 1 0.0091125 0.0091125 d 1 0.02 0.02 e 1 1.9602 1.9602 f 1 0.0038281 0.0038281 g 1 0.0011281 0.0011281 a.b 1 0.005 0.005 a.c 1 0.0022781 0.0022781 a.d 1 0.029403 0.029403 a.e 1 0.0034031 0.0034031 a.f 1 0.017112 0.017112 a.g 1 0.01125 0.01125 b.c 1 0.021012 0.021012 b.d 1 0.0392 0.0392 b.e 1 5e-05 5e-05 b.f 1 0.0057781 0.0057781 b.g 1 0.0038281 0.0038281 c.d 1 0.0063281 0.0063281 c.e 1 0.00015312 0.00015312 c.f 1 0.0032 0.0032 c.g 1 0.0072 0.0072 d.e 1 0.0022781 0.0022781 d.f 1 0.00045 0.00045 d.g 1 0.02 0.02 e.f 1 0 0 e.g 1 0.00845 0.00845 f.g 1 0.00070312 0.00070312 a.b.c 1 0.0052531 0.0052531 a.b.d 1 0.0034031 0.0034031 a.b.e 1 0.0011281 0.0011281 a.b.f 1 0.00125 0.00125 a.b.g 0 0 undefined a.c.d 1 0.0392 0.0392 3 a.c.e 1 0.0242 0.0242 a.c.f 0 0 undefined a.c.g 1 0.0011281 0.0011281 a.d.e 0 0 undefined a.d.f 1 3.125e-06 3.125e-06 a.d.g 1 0.0087781 0.0087781 a.e.f 1 0.045753 0.045753 a.e.g 1 0.0087781 0.0087781 a.f.g 1 0.0006125 0.0006125 b.c.d 1 0.024753 0.024753 b.c.e 0 0 undefined b.c.f 1 0.037812 0.037812 b.c.g 1 0.0098 0.0098 b.d.e 1 0.0019531 0.0019531 b.d.f 0 0 undefined b.d.g 1 0.0338 0.0338 b.e.f 1 0.0021125 0.0021125 b.e.g 1 0.00045 0.00045 b.f.g 1 0.025878 0.025878 c.d.e 1 0.01445 0.01445 c.d.f 1 0.00070312 0.00070312 c.d.g 0 0 undefined c.e.f 1 0.00037812 0.00037812 c.e.g 1 0.067528 0.067528 c.f.g 1 0.027612 0.027612 d.e.f 1 0.015753 0.015753 d.e.g 1 0.0034031 0.0034031 d.f.g 1 0.0072 0.0072 e.f.g 0 0 undefined a.b.c.d 0 0 undefined a.b.c.e 1 0.02 0.02 a.b.c.f 1 0.015753 0.015753 a.b.c.g 1 0.00090313 0.00090313 a.b.d.e 1 0.0091125 0.0091125 a.b.d.f 1 0.0087781 0.0087781 a.b.d.g 1 0.0047531 0.0047531 a.b.e.f 0 0 undefined a.b.e.g 1 0.038503 0.038503 a.b.f.g 1 0.00845 0.00845 a.c.d.e 1 0.0047531 0.0047531 a.c.d.f 1 0.00045 0.00045 a.c.d.g 1 0.0006125 0.0006125 a.c.e.f 1 0.0128 0.0128 a.c.e.g 0 0 undefined a.c.f.g 1 0.0022781 0.0022781 a.d.e.f 1 0.00605 0.00605 a.d.e.g 1 0.012012 0.012012 a.d.f.g 0 0 undefined 4

a.e.f.g 1 0.0128 0.0128 b.c.d.e 1 0.02 0.02 b.c.d.f 1 0.00052812 0.00052812 b.c.d.g 1 0.014878 0.014878 b.c.e.f 1 0.0094531 0.0094531 b.c.e.g 1 0.0052531 0.0052531 b.c.f.g 0 0 undefined b.d.e.f 1 0.00025313 0.00025313 b.d.e.g 0 0 undefined b.d.f.g 1 0.0055125 0.0055125 b.e.f.g 1 0.032512 0.032512 c.d.e.f 0 0 undefined c.d.e.g 1 0.0003125 0.0003125 c.d.f.g 1 0.14 0.14 c.e.f.g 1 0.023653 0.023653 d.e.f.g 1 0.0019531 0.0019531 ERROR1 28 0.59048 0.021088 ~ 7&$ $xkƒk$, ; )?hu l7&$ &+ y$r 3G>2v03G1 -;&r H!GZ <;)9$x 8D y ;!K 'e9$ 7&$ + w- <;>= D ƒ7&$ B >)=%$h $hx$&d,u$ -; >( k$ e K ~ $, a.b.g 2 a.c.f 2 a.d.e 2 b.c.e 2 b.d.f 2 c.d.g 2 e.f.g 2 a.b.c.d 2 a.b.e.f 2 a.c.e.g 2 a.d.f.g 2 b.c.f.g 2 b.d.e.g ';Zr I (;&r $8 t;%$-rns R7 %$ " r%$=k$>$h c.d.e.f h{ k$$r -,ƒk ~ 7&$h $ k$ EDP hu7&$ ED ;ˆ (>;>r%$-r $ xˆ$zd &K ~ 7&$ E' 2 U( tr17 %$.&$>$ ;17&$k$ Uk7&$ a.b.c.d. e.f.g, -r$ U - y=(a+b+c+d+e+f+g)^7 K!( B7 ;% ;GC ; (;&r $r r%$h <=; 1&( ' -; w>z 9$h $hx$&d) &K j'- U$ %$)2AED k$ ; (;>r $r O7. y&'z -;>r,/.z$ = $.&$Z' -( $ h = $. y&'z re x $$; $h >2 ;%e.&$&' -( $ huxk$,u$ ;) re x$k$ ; $h &K Cmd> yts <- yates(y) Cmd> chlot(rankits(yts),yts,xlab"normal scores",\ title"normal score lot of Yates effects") Cmd> chlot(halfnorm(abs(yts)),abs(yts),\ xlab"half normal scores",\ title"normal score lot of Yates effects") 0.25 0.2 0.15 Normal score lot of Yates effects y 0.1 t s 0.05 42 14 19 13 22 21 0 3 5 68 1211 7 1819 2015 26 24 17 29 272830 31 63 84109 87108 33 3432 36 3541 40 2538 37 3943 4454647 56 5248 5051 55 535457 58 59 68 70 6567 606669 71 4974 72 73 75 76 77 798078 81 82 8586 88 89 94 9192 93 97 96 95 99107 110 103 98 111 113 114 125 101 83100 90 104 106117 118 120 121 124 112 1115 119122 126 123-0.05 62 102 127-0.110542-2 -1 0 1 2 Normal scores Half normal scores lot of Yates effects 0.25 0.2 0.15 42105 0.1 127 0.05 1 3 4 2 8 6 9 10 13 22 5117 23 21 14 15 17 0 18 201926 24 272833 303731 38 4963 62 3536 329 3443 39 48 41 52 40 4546 44 5051 47 54556 53 59 5864 60 66 68 6765 70 72 74 83 84 87 108 109 102 73 71 757980 81 78 7677 82 858886 89 9098 97 9693 95 9194 99 103 100 101 104 107 110 112 106 113 115 1 125 114 119 123 126 117 1118 120 121122 124 0 0.5 1 1.5 2 2.5 Half normal scores x$&d) E'032AE'"!!25P4 -;>r E'4!H &$ ƒ9.&$ () w$ &K j'- r & ( tr $ ;) 7&$ $hx$&d) @ ;%e 7 rk '7&$Z'z 7,/ <; $ C$&' A2v!2 6 2v!2 22 -;>r k$ $hx$&d) ED254!2vP!2 *32AEe0325!4 -;>r 03P IJ4<2542v4 2v4<254<254 2v4 NJ2 7&$. <== $ $hx$&d{ice'0n/ ƒ! y$ 8 7&$ (; ; (;>r $r,/ <; $hx$&d K 5 6

@;. <; x ;%e y ; 7&$h $ k$ 6 ' x$&d Ee0 u "!"SED"!"!"". E'"! u E!E'" ED"!"SE&. A P4 u " E'" ED" E'".! E'4!H u E!EE!E!E!EE&. A6 T 7Z$ ;7&$ 8 t=)7, h 1re t=e B ED2 <; 7&$ $hx$&d K T 7&$ ; 7&$ 4!;>r k-, x7z$ 8 t=)7 E'25 <; 7&$ $hx$&d -;>r ;&K 'e9$ 7 ED"!!2vP!4 -;>r ED4!H xk$h & ;>r9 ; (;>r $r? ;)x -;>r k$ k$h $ ;) re x$g $ ; $h.&$e% U$$ ;1. w&ez >25;%e{k$ %, $;) $hx$&d) &K j'$k$ @ -,/ -()9$ <;1 %$C ' -;%$ / 7&$ <;>re $h?h 7&$ ; (;>r $r $hx$&d) &K Cmd> confounded <- vector("abg", "acf", "ade", "bce", "bdf", "cdg", "efg", "abcd", "abef", "aceg", "adfg", "bcfg", "bdeg", "cdef","abcdefg"); conf <- re(0,15) Cmd> for(i,1,15){ tm <- match(vector("*a*","*b*","*c*","*d*","*e*","*f*","*g"),\ confounded[i],0,exactf) tm[tm!= 0] <- 1 conf[i] <- sum(tm*2^run(0,6));;} Cmd> rint(format"3.0f",conf) # confounded terms conf (1) 67 37 25 22 42 76 112 15 51 85 105 102 90 60 127 ~ 7&$ <;! <(>r $ P!4!2AE'"! -;>r ED4!HK ~.&$, $ ; ;>=x( 2 ;%,/ Mƒ7> ;%,/ ye) 9$h $hx$&d), ( -, B{7&$ ; (;>r $r ;%$h &K ;%$ > 9 r B 19 k$ $ k7&$,.> K ~ 7&$ $.Z$ t=;%k$r ; 7&$ ye2 MISSING $ $ >; ;>=, $ = $h &K Cmd> yts[terms] <-? # set con Cmd> yts[grade(abs(yts),downt)][run(10)] WARNING missing values in argument(s) to abs() WARNING MISSING values in argument to grade() (1) 0.2475 0.060313 0.054375-0.05125 0.048125 (6) 0.045937 0.043438 0.042187-0.037813 0.035 Cmd> chlot(rankits(yts),yts,xlab"normal scores",\ title"normal score lot of Yates effects") WARNING MISSING values in argument to rankits() Cmd> chlot(halfnorm(abs(yts)),abs(yts),\ xlab"half normal scores",\ title"half normal score lot of Yates effects") WARNING missing values in argument(s) to abs() WARNING MISSING values in argument to halfnorm() WARNING missing values in argument(s) to abs() Normal score lot of Yates effects 0.25 0.2 E Main effect 0.15 y t s 0.1 0.05 141 913 63 8487 108 109 4 0 73 5 6 8 12 18 19 21 20 26 24 17 29 27 283031 32 33 34 36 35 4445 41 40 1038 3943 46 56 59 52 48 50 47 55 535457 5864 61 6870 65 66 69 71 77 886 798078 89 98 49 74 72 73 75 82 96 95 99107 1103114 125 113 81 104 106 94 101 9192 93 117 97 111 118 120 121 124 83100 1115 119122 126 123-0.05 62-2 -1 0 1 2 Normal scores Half normal score lot of Yates effects 0.25 0.2 0.15 0.1 E Main effect 0.05 1 3 4 2 8 6 9 10 13 511 7 23 21 14 18 20 1926 2417 27 28 30 31 38 496384 6287 108 109 329 3443 533959 4846 41 52 40 45 443536 50 47 5754556 58 64 66 61 6865 70 72 7483 71 75 73 78 82 77 8886 798081 89 98 92 93 9194 99 103 100 97 9695101 104 107 110 114 106 113115 1 125 119 123 126 117 1118 120 12122 124 0 0 0.5 1 1.5 2 2.5 Half normal scores l; 7&$,/ <; $hx$&d x ;>r () K 7 8

``` ` B{ ye r $h t=; ' -;1.&$ 7&(>=)7 U &$ h <; -,/ y$e9$. y&'z r%$h <=;2 /7&$k$ y$ ;$,/ <; $hx$&d) 1 ;>r, $e ],U$h <;)9$x 8D w ; 1 k$ ; (;>r%$r B7. w&ez &K <;$k$ ; $.& (){7&$ ; (;>r $r $hx$&d)?$hx$&d < %$+ -, $h k-, -; -; &K X <;$k$ ; $.& (){7&$ (;C ; (;>r $r $hx$&d) ƒ-,u$h k-, -; -; B ~ 7&$. $ %, $ ;) )( D(k$ ( &( -,/ w$e9$ 8D98 tk @;7&$ ],/ y$h ' $ (17 - %$ ( ƒ% U 8D9 >2 -;>r B7 -;>r. y$ %$+ >2 k$h &$&D < %$+ K h( 7 - %$ ;. y&dz }hƒ O Z$.-2 3u>;. <;1 tk ~ 7Z$h $ >$ K ~ $ 7&$ &$8 ],U$ ;) }(; B) O7 <;1. wz'z k$ ' w$-r, $e ],U$h l;%$ hu7&$ 8D9 >2M A2M 17&$ K ~ k$ %,U$ ;){ - <=;&, $ ;) ; % U 9$ &K (1C ;>r -, t=; y$ %$+ 9 7&$ /7&+ y$ ye) 1 -;>r lx7z$ B ye) <; 7&$ /7&+ y$ we = $e{7&$ D, $ y$ %$+ Mhm K! $ 8e7 /7&+ y$ ye2 & (1x -;>r -, <=; y$ %$+?h{+k ~ 7&$ k$h >( B r $h t=; 7. -; $r k$,u$ ;)) &K 9 10

! $ D, w$ -; $ &$8 t,u$ ;){9 -,/ k$ u y$ %$+?h B D= $ I y- <;>=N -;>r. u P $C O 8$ ; 7&$ y$+ tr1 U 'k ; ; u k$ ' k$ &K @ ;%e x 8D e 9 x = $.&$e% U$$ ; 9 Z, y$&$h?hu C y$+ trk ' 7&$ y$+ tr re < tr $r <;)9 7Z-, = $;%$ ( 8 B 19 7 '7 B =%$,U$e7&r t=;%$r x -;>r -, BDK ~ 7&$ ; 2 25 2 -;>r 25 k$ -;>r k$ C ;>r -, t=;%$r9 7&$ 1I B &(. we) N/ <;. y&'z u 7Z+ w$ ye K E 4 P 0 H * 'e9$ 7&$k$? ;%$ y$ %$+ Mhm ;>r -,?G y$e9$ $ h y$ %$+ <; $ 8'7 hu7&$ ; ;%$ 7Z+ w$ ye) 1I. w&ez NJK A;%e7&${ =)8 +( B(x R$ D,/ y$ ~ 7&$ k$h & ; $ w$h <r?h ) &K ~ 7&$ /7&+ w$ G w{ -;>r B)G ye 8D9 k$ RP ye)?h ) >2 E ; $ZD9$r B7 (;>=( >2AE ;%e2 -;>r 4 k$h -;) K RP ke9$&d -;)) ~ 7&$ <;, y ;1.& (){7&$ P w?h ), t=)7 =( tr $ '7&h <;>=? ;)x ) &K % $ D,/ y$ & (, t=)7 -;){9 -,/ k$ k$h -;){ -;&r ;%; k$h -;)1( <;>=? ;))G x U$+ t=)7) 1I G-ED2 G-ED2]E'2]E&NJK '$$r ye) U$k$ t=;%$r9 E'0 ;) t=(% ( k$ ;1 C y$+ tr2s7&$ 7Z+ w$ ye) >25P /7&+ y$ ye) &$ $>$r ye K 8'7 7Z+ w$ ye - >(.Dre tr $r <;)9 ( -,/ 8D k$ 9 /7 '7 7&$ ({ ke9$&g -;)ƒk$ %,U$ ;)) U$k$ x -;&r -, t=;%$rk 11 12

@BU& ( re tr; {7 %$ 7&$ ke9$&d -;) B{7 r " $hx$&d2 & ( U ( tr7 %$,Ur $+ X z&$ u K u $$r &$ $hx$&d u x -;>r -,. y&'z $hx$&dƒ7&$ z. y&'z Bx7 $$r &$ tk 17&$ { B7 >8 B -; $ u x -;>r -, O ye >(.> we $xk O7 8 -; $ K ~ 7&$h $ $xk k$ re x$k$ ;) ; $ 8'7 B{ we -;>r 7&$ B wk ( ( tr -; Z$ B ( <;>=. y&'z, $ -; u u ~ 7 -;>r) r ;%$ 8D9, -r $+ B7 $x8 K '$&' -( $,U$ -; k$ r $8 < %$r Jk-,. y&'z 9e &2S7 k$ -; -; B- &K T/7 U ( tr j $ re =)x D, ƒ7 r $ <=; yz z&$ M 1 1 A 4 3 (WPE) (SPE) ~ 7&$ r $ ;%-, <; 9 ƒ9$h <;>=1 ( <r.&$ 7&$ 7&+ y$ ye $x I T L Nm,U$ -; >( k$k!(){7&$k$ $& ;>r 8D9 7&$,Ur $+ 8D( u T/7 U ( tr j $ re =)x D, 7 r%$h <=; yz Bz&$ (WPE) 12 A 4 3 M 1 1 AB 9 (SPE) 64 48 64 48 12 B 4 3 13 14

f ~ 7&$ r $ ;%-, <; 9 ƒ9$h <;>=1 1 = ; 7&$ 7&+ y$ ye $x I T L Nm,U$ -; >( k$.&$&' -( $ 7 17&$ y$ re <;>= $+ <=e. y$ x -;>r -, k$,.&$+ y- K ], 8 x7z$ r $ ;-, <; 9ƒk$ ;>= -;>r1a 17&$ B ye $xkƒij!l N, $ ; >( k$k = ; B 17&$ y$ re <;>= $+ t=e. y$ x -;>r -, 9$,.&$+ y- -;>r1a+k YYYY [[[ [ fff ~ $ j'$k$ 1 -; $ D,/ y$. $r ; r), -9$$+ y$ -;>r x8 y$ ƒ7&$ &$8 ], $ ; (>r) <;>= ke9$&d -;)) B7 ) $$r ( $h &K R{7&$ 7&+ y$ ye w$ %$h 2 7 @Rr $h C'8.&$r 1 6!2 B7. y&'z &K ~ 7&$k$ ; k$ ; & ( ' -; q 7 - %$ -;! y$ r $ <=;&K @B; 8D2M ; 7?$ &$G ], $ ;)2 %$x -,{, ;2S7&$ 7Z+ w$ ye) 7&$-,? $+ < %$h U$k$ =)k ( &$r ; >( &$. y&'z?hƒ B Z$ u P!2 B7 7&$ /7&+ y$ w 8D9 y$ %$+ t=;%$r <;1-6 K Cmd> data <- read("","sandt") sandt 64 4 format ) Slit lot data from Steele & Torrie ) Exeriment to study effects of 4 rotectants on ) oats grown from 4 seed sources. ) Seed source was whole lot factor, arranged in 4 randomized ) blocks (relicates). Protectant was slit lot factor, ) all 4 levels in each whole lot ) Col. 1 Block number (1-4) ) Col. 2 Seed lot (1-4) ) Col. 3 Protectant (1-4) ) Col. 4 Yield (resonse) Read from file "TP1Stat5303Dislayssandt.dat" Cmd> makecols(data,block,seed,rotectant,y) Cmd> block <- factor(block);seed <- factor(seed) Cmd> rotectant <- factor(rotectant) Cmd> anova("y=blocks+seed + E(blocks.seed) + rotectant + seed.rotectant",fstatt) Model used is y=blocks+seed + E(blocks.seed) + rotectant + seed.rotectant DF SS MS F P-value CONSTANT 1 1.7849e+05 1.7849e+05 2598.06040 0 blocks 3 2842.9 947.62 13.79378 0.0010287 seed 3 2848 949.34 13.81877 0.001022 ERROR1 9 618.29 68.699 3.38234 0.0042283 rotectant 3 170.54 56.846 2.79874 0.053859 seed. rotectant 9 586.47 65.3 3.20823 0.0059453 ERROR2 36 731.2 20.311 ~ 7&$ $$r ( $,/ ; $hx$&d 7 <=)7 B t=; ' -;) 1x7Z$ <;)9$x 8D y ; hƒ $$r. ke9$&d -;) K 15

j'$k$ 7&$ C 1( $ U %$x ( $h( $ (k$ h Q 8eA;% K @BUZ ( /x } 9$, <; E(...) I 7&$k$ E(blocks.seed) N 2 anova() k9$ k78$ $, -;?$x9{9$%,ƒk @ < ; D,U$r ERROR1 -;&r 7&$ /7&+ y$ we $xkk ~ 7&$ C <; M$x 9$, ; D,U$-r ;>r 7Z$ % ye $xkƒ9$,ƒk ERROR2 @Om& (17 r,uk$ 7 ; ;$ E(...) 2 $%, m( ]r.8$ ERROR1 2 ERROR2 2 ERROR3 2 K K K K ~ 7&$ r $ ;%-, <; 9 $ 8'7 7&$ ;%$ ERRORx,U$ ; > &( >9$-K j'$k$ 17Z$ D,U$ B7Z () E() Cmd> anova("y=blocks*seed + rotectant + seed.rotectant",\ fstatt) Model used is y=blocks*seed + rotectant + seed.rotectant DF SS MS F P-value CONSTANT 1 1.7849e+05 1.7849e+05 8787.53084 1.2987e-44 blocks 3 2842.9 947.62 46.65531 1.7295e-12 seed 3 2848 949.34 46.73981 1.6855e-12 blocks.seed 9 618.29 68.699 3.38234 0.0042283 rotectant 3 170.54 56.846 2.79874 0.053859 seed.rotectant 9 586.47 65.3 3.20823 0.0059453 ERROR1 36 731.2 20.311 ~ 7&$! k$ 7&$ D,U$K ~ 7&$ G blocks -;&r >9$ r ˆ$9$; I ;&r <; xk$&dxn 25 <; $ seed x7z$ ( $ /7 U$ z-;- 9.Z$ 7&$ B{ we $xk{ r $ ;%-, ; 9K 17

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