ࡱ> fhes7 AbjbjUU Q7|7|5;l   8 $( x*"LLL ((((((($A* a,2(c"2()LLG()))LL () () )G%' (L ic ' (](0(',,), ()rnrFrom Fibonacci to Foxtrot: Investigating Recursion Relations with Geometric Sequences The Algebra Standard from the Principles and Standards for School Mathematics (NCTM, 2000) states that all students should Understand patterns, relations, and functions. In particular, to meet the grades 9 12 expectations, students should generalize patterns using explicitly defined and recursively defined functions. The Foxtrot comic strip shown below (Amend) provides a wonderful starting point to create lessons that address the algebra standard.  In the first three panels of the cartoon, we see that Marcus has scored a touchdown by identifying Jasons sequence 0, 1, 1, 2, 3, 5, 8, 13 as the Fibonacci series (though it would be preferable to replace series with sequence, since in mathematics terminology a series designates the sum of the terms in a sequence). The Fibonacci sequence is one of the most widely known in all of mathematics, recursively defined by the recurrence relation  EMBED Equation.DSMT4 . Thus, many readers of Foxtrot could have emulated Marcus scoring success. However, there are at least two lingering questions: Why did Jason begin his count with zero? It is more common to start the Fibonacci sequence with  EMBED Equation.DSMT4  instead of  EMBED Equation.DSMT4 . How can Jason score a touchdown? In the last panel of the comic strip, Marcus has challenged Jason with the sequence 3, 0, 2, 3, 2, 5, . What is this sequence? The key to our investigation of these questions is the geometric sequence  EMBED Equation.DSMT4 , which is defined explicitly by  EMBED Equation.DSMT4 , n = 0, 1, 2, . Alternatively, the sequence can be defined recursively by  EMBED Equation.DSMT4  where  EMBED Equation.DSMT4 . The constant  EMBED Equation.DSMT4  is the common ratio of the sequence. We begin by first investigating a connection between the Fibonacci sequence and geometric sequences. The techniques we develop provide us with a method to investigate the mysterious sequence 3, 0, 2, 3, 2, 5, . IS THE FIBONACCI SEQUENCE A GEOMETRIC SEQUENCE? The short answer to the question just raised is no. After all,  EMBED Equation.DSMT4  is not defined, and  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  are different ratios. Rather than being discouraged, lets examine several more ratios of successive Fibonacci numbers, as shown in the following table.  EMBED Excel.Sheet.8  As n becomes larger, the Fibonacci sequence increasingly resembles a geometric sequence with a common ratio of about 1.6. Since the early integer values of the Fibonacci sequence seem to cause difficulty, suppose we not worry yet about the initial values of the sequence. Instead, we simply seek a geometric sequence  EMBED Equation.DSMT4  that satisfies the Fibonacci recurrence  EMBED Equation.DSMT4 . That is, we want to determine values of r for which  EMBED Equation.DSMT4 , since it is clear that an arbitrary value of the constant a is allowed. Thus, we want values of  EMBED Equation.DSMT4  for which  EMBED Equation.DSMT4 . The terms in this equation can be divided by the common factor  EMBED Equation.DSMT4 , giving us the quadratic equation  EMBED Equation.DSMT4  Using the quadratic formula, we discover there are two roots r of the quadratic equation:  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 . As a decimal, p is about 1.618, and we suspect we have identified the value we encountered in the numerical table above. For arbitrary choices of the constants a and b, both of the geometric sequences EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  solve the Fibonacci recursion  EMBED Equation.DSMT4 . Moreover, since  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 , we can add these two equations to see that  EMBED Equation.DSMT4 . That is, for any choices of the constants a and b,  EMBED Equation.DSMT4  solves the Fibonacci recurrence relation  EMBED Equation.DSMT4 . To summarize our progress, we have proved the following result: Theorem. The Fibonacci recursion formula  EMBED Equation.DSMT4 , is solved by EMBED Equation.DSMT4  where  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4 , and a and b are arbitrary constants. The constant  EMBED Equation.DSMT4  is the famous Golden Ratio. It was known (though not by that name*) in ancient Greek mathematics, since it solved this question: determine the point C on line segment  EMBED Equation.DSMT4  so that AB/AC = AC/BC. The second solution  EMBED Equation.DSMT4  of the quadratic equation  EMBED Equation.DSMT4  can be investigated by factoring the quadratic polynomial. That is, since  EMBED Equation.DSMT4 , then equating coefficients shows us that  EMBED Equation.DSMT4  and pq = 1. Its interesting to see how these relationships can be found without requiring the explicit formulas for p and q that involve (5. THE LUCAS AND FIBONACCI SEQUENCES A simple choice of constants for  EMBED Equation.DSMT4  in the theorem above is a = 1 and b = 1. This gives us the solution  EMBED Equation.DSMT4 . For example,  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 , and we are delighted that no  EMBED Equation.DSMT4  term appears. Moreover, since  EMBED Equation.DSMT4 and  EMBED Equation.DSMT4 , the terms of the sequence are all positive integers. We have rediscovered the Fibonacci-like sequence 2, 1, 3, 4, 7, 11, 18, 29, named for Edouard Lucas (1842-1891). Though this sequence is less well known than the Fibonacci sequence, the Lucas sequence also has many properties of interest (see the concluding section of this article.) To obtain the Fibonacci numbers, we need to see if it possible to choose the constants a and b so that  EMBED Equation.DSMT4 . Since F0 = 0 and  EMBED Equation.DSMT4 , we will want b = a. Also, since  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4 , we must choose  EMBED Equation.DSMT4 . Thus, the nth Fibonacci number is given by the explicit formula  EMBED Equation.DSMT4 . This formula is known as Binets formula for the Fibonacci numbers, named after Jacques Binet (1786-1865) who discovered it in 1843. However, the formula was discovered first in 1718 by Abraham DeMoivre (1667-1754). Since Binets formula gives F0 = 0, we now know why Jason started his list of Fibonacci numbers with 0. The formula also explains why the Fibonacci sequence, though not geometric, is increasingly close to one. Since  EMBED Equation.DSMT4  we see that |qn| is increasingly small as n becomes large. Therefore, we have the approximate equality  EMBED Equation.DSMT4 . This explains why the Fibonacci sequence is nearly a geometric series, as we noticed in the table of values computed earlier. If we let {x} denote the round to the integer nearest to x function, it is easy to check that  EMBED Equation.DSMT4  for all n ( 0. Similarly, the Lucas numbers can be written as  EMBED Equation.DSMT4  when n ( 1. INVESTIGATING MARCUS SEQUENCE 3, 0, 2, 3, 2, 5, It seems reasonable to guess that the new sequence is related to the Fibonacci sequence. Therefore, suppose that we add consecutive pairs of the sequence 3, 0, 2, 3, 2, 5. The first three sums are 3 + 0 = 3, 0 + 2 = 2, and 2 + 3 = 5 We seem to be on the right track, since we get the next three terms 3, 2, and 5 of the sequence. This suggests that the term xn+ 3 is the sum of the two consecutive terms xn and xn + 1. That is, Marcus sequence is defined by the recursion formula  EMBED Equation.DSMT4 . As before, we can search for a geometric sequence of the form  EMBED Equation.DSMT4  that solves the recurrence relation. As before, the constant a is arbitrary, but now we want r to satisfy the equation  EMBED Equation.DSMT4 . Dividing each term by the common factor  EMBED Equation.DSMT4 , we get the cubic equation  EMBED Equation.DSMT4 . We could turn to a computer algebra system or a graphing calculator to solve this cubic and discover there is one real root u =1.32472 and a pair of complex conjugate roots v = 0.662359+0.56228 i and w = 0.662359 0.56228 i. However, let us just suppose we factor the cubic polynomial to get  EMBED Equation.DSMT4 . By expanding the product of the three binomials on the right side, we get the equation  EMBED Equation.DSMT4 . Since these two polynomials in the variable r are equal if and only if their coefficients are equal, we obtain the equations u + v + w = 0, uv + vw + uw = 1, and uvw = 1. (*) As with our earlier investigation of the Fibonacci recursion, we know that  EMBED Equation.DSMT4  is solved by  EMBED Equation.DSMT4  for any choice we make for the three constants a, b, and c. Inspired by the choice that led us to the Lucas sequence, suppose that we let a = b = c = 1, which gives us the sequence  EMBED Equation.DSMT4 . The first term is then  EMBED Equation.DSMT4 . This looks promising, since 3 is indeed the first term of Marcus sequence. The next term is  EMBED Equation.DSMT4 , where again we have used equation (*). Happily enough, 0 is the next term of Marcus sequence! If we can show that  EMBED Equation.DSMT4 , we will have unraveled Marcus sequence. We have  EMBED Equation.DSMT4 . Is this equal to 2? To find out, we again turn to the equations in (*), where we see that  EMBED Equation.DSMT4  Using (*) once again, we see that  EMBED Equation.DSMT4 . Therefore, the terms 3, 0, 2, 3, 2, 5, 5, 7, 10, of Marcus sequence can either be defined recursively by  EMBED Equation.DSMT4 , or can be given explicitly by  EMBED Equation.DSMT4 , where u ( 1.32, v ( 0.66+0.56 i, and w ( 0.66 0.56 i are the roots of the cubic equation  EMBED Equation.DSMT4 . But what is the name of this sequence? Here Jason may want to use his well-known Internet skills and access The On-Line Encyclopedia of Integer Sequences ( HYPERLINK "http://www.research.att.com/~njas/sequences/index.html" http://www.research.att.com/~njas/sequences/index.html) to find that the sequence is the Perrin sequence, named for the French mathematician R. Perrin, who discussed the sequence in a mathematical paper published in 1899 (although the sequence had already been mentioned in 1878 by Lucas). Thus, Jason should yell out Is it the Perrin sequence? to score a touchdown. Of course, Jason might refer to the Perrin series instead of sequence. In the next section, we will see that geometric sequences can also be examined by considering their associated geometric series. GEOMETRIC SERIES AND GENERATING FUNCTIONS For  EMBED Equation.DSMT4 , the terms of the infinite geometric sequence  EMBED Equation.DSMT4  can be summed to give the formula  EMBED Equation.DSMT4 . If we then set t = px, where p is the Golden Ratio, we find that  EMBED Equation.DSMT4  for  EMBED Equation.DSMT4 . Similarly, setting t = qx, we also have  EMBED Equation.DSMT4  for  EMBED Equation.DSMT4 . Since both series converge for  EMBED Equation.DSMT4 , subtracting the series gives us  EMBED Equation.DSMT4 . But if we recall from Binets formula that  EMBED Equation.DSMT4  is the nth Fibonacci number, we see that the coefficient of the xn term of the series is  EMBED Equation.DSMT4 . We can also simplify the right side of the equation above as follows:  EMBED Equation.DSMT4 , where we recall that  EMBED Equation.DSMT4  satisfy  EMBED Equation.DSMT4 .  EMBED Equation.DSMT4 Altogether, we see that  EMBED Equation.DSMT4 . Since the coefficients of the series expansion of the function EMBED Equation.DSMT4  are the Fibonacci numbers, f is called the generating function of the Fibonacci sequence. If we had added rather than subtracted the two geometric series above, a similar calculation shows that  EMBED Equation.DSMT4  is the generating function for the Lucas numbers  EMBED Equation.DSMT4 . We can also obtain the generating function for the Perrin numbers by letting t be successively replaced with ux, vx, and wx. When the three geometric series are added we find that  EMBED Equation.DSMT4 . The right side of this formula can be simplified by using the equations (*) found earlier. We find that  EMBED Equation.DSMT4 . That is,  EMBED Equation.DSMT4  is the generating function for the Perrin sequence. NOTES ON THE FIBONACCI, LUCAS, AND PERRIN SEQUENCES Each of the three sequences we have discussedFibonacci, Lucas, Perrinis of considerable mathematical interest. Well mention just a few items here, with the hope of encouraging the reader to consult more extensive references. A particularly convenient source of information is the online mathematical encyclopedia MathWorld (Weisstein). For example, the entry for theFibonacci numbers informs us that A scrambled version 13, 3, 2, 21, 1, 1, 8, 5 (Sloane's  HYPERLINK "http://www.research.att.com/~njas/sequences/A117540" A117540) of the first eight Fibonacci numbers appears as one of the clues left by murdered museum curator Jacque Saunire in D. Brown's novel  HYPERLINK "http://www.amazon.com/exec/obidos/ASIN/1400079179/ref=nosim/weisstein-20" The Da Vinci Code (Brown 2003, pp. 43, 60-61, and 189-192). In the Season 1 episode " HYPERLINK "http://www.tv.com/numb3rs/sabotage/episode/398596/summary.html" Sabotage" (2005) of the television crime drama  HYPERLINK "http://www.amazon.com/exec/obidos/ASIN/B000ERVJKE/ref=nosim/weisstein-20" NUMB3RS, math genius Charlie Eppes mentions that the Fibonacci numbers are found in the structure of crystals and the spiral of galaxies and a nautilus shell. A search of MathWorld on the Lucas numbers would show that they are very closely related to the Fibonacci numbers. For example,  EMBED Equation.DSMT4 . The Lucas number Ln also answers this counting problem: Suppose n people are seated at a circular table. Including the empty set, how many subsets of the people can be chosen which do not include any two people seated side by side? The most spectacular property of the Perrin sequence is its effectiveness as a test for primality. In particular, if n is a prime, then it has been shown that n divides the Perrin number Pn. For example, n = 11 divides the Perrin number P11 = 22, and n = 29 divides the Perrin number P29 = 3480 = 29 (120. Only rarely will a nonprime n divide Pn. Indeed, the smallest Perrin pseudoprime is n = 277441 = 5212, which is a factor of P277441. This was discovered quite recently, in 1982. REFERENCES Amend, B. "FoxTrot.com." Cartoon from Oct. 11, 2005.  HYPERLINK "http://www.foxtrot.com/" http://www.foxtrot.com/ The On-Line Encyclopedia of Integer Sequences.  HYPERLINK "http://www.research.att.com/~njas/sequences/index.html " www.research.att.com/~njas/sequences/index.html  Weisstein, Eric. MathWorldA Wolfram Web Resource  HYPERLINK "http://mathworld.wolfram.com/" http://mathworld.wolfram.com/ * The entry for Golden Ratio in the MathWorld encylopedia (Weisstein) informs us that The term "golden section" (in German, goldener Schnitt or der goldene Schnitt) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik (Livio 2002, p. 6). The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. PAGE  PAGE 11 Ww#$IL! # $ % &   , - . / P Q h i j k m n žyjݱG CJUVaJ j EHUjkG CJUVaJ jEHUj|G CJUVaJ jEHUj-G CJUVaJ j EHUj.G CJUVaJ jEHUjBG CJUVaJ jUjCJUmHnHu6] 5CJ \/WXY#%( G   M 'D$da$ & Fdd`d5?@A      ( 4  M { j} UjG CJUVaJ jEHUjݍG CJUVaJ jEHUjݍG CJUVaJ jEHUjۍG CJUVaJ5\6] jEHUjn܍G CJUVaJ jEHUjG CJUVaJ jU jEHU/./FGHIst"#:;<=~Ľxq j8EHUjLG CJUVaJ j5EHUj G CJUVaJ j2EHUj˓G CJUVaJ j,0EHUjG CJUVaJ j-EHUjKG CJUVaJ6] j *EHUjG CJUVaJ jU j0'EHUjG CJUVaJ,23JKLMRSjklm}~78OPQRWXopqržyjG CJUVaJ jJEHUjG CJUVaJ jGEHUjG CJUVaJ jDEHUj]G CJUVaJ j>BEHUjG CJUVaJ j>EHUj,G CJUVaJ jm;EHUjCG CJUVaJ jU6]/'(?@ABnotuwx!"BCZ[\]klܪܛܪ܂xܪj]6EHU]jG 6CJUV]aJjtZ6EHU]jG 6CJUV]aJj6U]5\ jhWEHUjG CJUVaJ jlTEHUj3G CJUVaJ6] jPEHUjG CJUVaJ jU jMEHU*WX ;<STUVtm j]qEHUjG CJUVaJ jmEHUjeG CJUVaJ jjEHUjG CJUVaJ0J jKgEHUj{G CJUVaJ jUjc6EHU]j,G 6CJUV]aJ6]j6U]jz`6EHU]jCG 6CJUV]aJ* z{  89PQRSbcz{|}бujG CJUVaJ jEHUjG CJUVaJ j}EHUj|G CJUVaJjz6EHU]jG 6CJUV]aJj6U]5\ j6] jwEHUjnG CJUVaJ jU jJtEHUjG CJUVaJ.-./0  4567FN[\stwj G CJUVaJ jEHUjG CJUVaJH*j6EHU]joG CJUVaJj6U]6] jEHUjG CJUVaJ jEHUjG CJUVaJ jEHUjZG CJUVaJ jU jEHU." !"$$%-%%%O(*)G)j)))**-- $ !da$d` d`$da$dtuv{| (*VWnopqɲɞɏ| jEHUjG CJUVaJ 6H*]j56EHU]j*G CJUVaJj6U]H* jEHUj6G CJUVaJH*6] jEHUjxyG CJUVaJ jEHUj$G CJUVaJ jU jEHU0+,QRijkluvwx l!m!p!q!!!!!!!!!!!""""D"E"\"]"^"_"""""""""j\{G CJUVaJ j<EHUjG CJUVaJ j1EHUj}G CJUVaJH* 6H*]5\ jEHUjG CJUVaJ j jqEHUjG CJUVaJ jU6]8"""##4#5#6#7#S#T#k#l#m#n###$ $5$6$;$<$T$U$$$$$$$%%(%)%*%+%Y%Z%%%%%%%%%%%%%%%+&,&C&D&j}G CJUVaJ j EHUj G CJUVaJ jEHUji G CJUVaJ6] jEHUjG CJUVaJ j!EHUjh{G CJUVaJ jU jEHU8D&E&F&T&U&l&m&n&o&&&&&&'%'&'='>'?'@'Y'Z'q'r's't'''''''d(e(|(}(~((((((((+),)C)} jEHUjG CJUVaJ jEHUj|G CJUVaJ jEHUj/G CJUVaJ jEHUj G CJUVaJ jEHUj G CJUVaJ6] jEHUjk G CJUVaJ jU jEHU/C)D)E)F)k)l))))))) ****1*2*I*J*K*L*T*U*V*W*^*_*`*a*m*o*t*u*v*w*********e+f++++++,,-0JjU jEHUjG CJUVaJ j6] jEHUj G CJUVaJ jEHUjΝG CJUVaJ j3EHUjBG CJUVaJ jU jEHUjAG CJUVaJ5--./?/h//00!1?11123$3r3(4F444%5Y56dd`$a$$da$d-...2.3.4.5.d.e.|.}.~............//////!/"/9/:/;/2?2@2\2]2l223333 3!3U3V3m3n3o3p3333333)4} j0EHUjsG CJUVaJ jz,EHUjYrG CJUVaJ6] j )EHUjqG CJUVaJ jF%EHUj}qG CJUVaJ jo"EHUj}G CJUVaJ jEHUj}G CJUVaJ jU jEHU1)4*4A4B4C4D4444444444444$5%5Y5%7&7g7h7o7p777N8O8`8a88888|l|^|0J6CJOJQJ]^J6B*CJOJQJ]^Jph(j6B*CJOJQJU]^Jph0JCJOJQJ^J"jB*CJOJQJU^JphB*CJOJQJ^Jph5\>* j<EHUjxG CJUVaJ j7EHUjlxG CJUVaJ j3EHUj(uG CJUVaJ jU$888#9$9z9{999::::::::::::::<<D<F<`<a<b<d<q<u<<<<<<<<<<<<<<<<֟~~||x~ jH* 6H*]6] j?EHUj0G CJUVaJ jU5\0J6CJOJQJ]^J6B*CJOJQJ]^Jph(j6B*CJOJQJU]^JphB*CJOJQJ^Jph"jB*CJOJQJU^Jph0JCJOJQJ^J/6::;==== >>4?5?@@@@A A AAAAh]h&`#$ 0d^`0$d]^a$d$d]^a$<==='=+=/=;=<=S=T=Z======= > >;><>>>>>>>>???2?3?5?6??????1@O@@@@@@@@@AAAA A A AAź0JmHnHu0J j0JU6B*]ph B*ph0JjDU0Jj?CU jU5\H*H*6]:# 01h/ =!"#$%n$D!t48,- 6 PNG  IHDRXlYPLTE///___bKGDH cmPPJCmp0712OmCIDATxIʶ%]tU*(]M$‰A-f>'عs3fpM&Vhyr7EpvDKz]Gvmƽp}Dۗ-D_4NLB]$?t%DZ9Exr{-KW_pej ?}BC<%}ײFi?JXj=g`!1oX?ԫk/a/a/qX!}B4:ty~+9AȡK$j!Xnw,-iN$tmA o`Ia~8UB&k_բ t%% 1CSk>Y;?ۅ7 9,ܔegXAX!t5?ty6S)|ywKīҽPÝaӻ7{;~'ߴ̲dƠ\ [2rsr h#S堚޶C*.^{~w2Sl{bֻ|&= wu"ĀݽnnF#X ֵٹk}ݛICW*+!0x[P|XvÇ,G~ղ`O Nvc[=kRZP &“5|oixIm>4veFe $aX*M!E^Ύ0}u- @zNqpc40v25Q(K͊,]m jjEX>fֻ"`f>)l~gw"4kgS[K̞"-w<?{V_}? ` O3$GyL⇶AdVeɦeh~T_DՇ! }{ v(7?ԻVލ,qNzFvoV =[_d~K:؄ͱӜ%] f p,z`gw,,Qg߹]Mzp3 ,__ڂC:= .q7Y0х zU7)g򡚄zgk;+XE 5%~KP:?)Tx=^ٜxER۰(0Koז||ӳqm~ 3EXO;< %#*7|),03qBWy_]?K`Z9e ?Kppq;+  _O`| UQXt/{jT#ưB.M/-k/a|tu}:KL1jlHXPסcBUEU[2pFJÄ!hsM''Xg޿S77۽ųɬĐDACY;(59 zF~b +1nYMX}N鼪ە%Y3-B ׭tN.u{ta&UYyI-YaV{*SXL|8%T3ᱝc`C!1;߉rsX.؜+Y5 ,FCπ!.O};T XW7RVM)prjIu}uT +SƂ),п`:|ʇtea vKCa}g|>'o0{D .C} ^Vw)ݯ, 3έdW GbV[[OL9:wg7?%IxxyX& eZ/`9ݼFvm? |?dS"p'䱽X7\,n곰H-չj}Yw84NyX7mfw2>Ya\ a 0U2~ yEX0V/Y^DD3|_O}^ɨDn{8hm~؞ 8aUYK0qMlRu9*İ@,`Pe Goir& \nE^4kK]/= =%ptmR 0櫇hFRa UV&7\l튉FUyd[/ ,íLW|elu_/,">T8s'eV=&۝ r+_?x4s[Țڨ} ĝ,? $7Ȕ4s:2n c8}k 6\tѸUa V %/{>-?]QaeMGث@ }MeGV vr$P}byXhu e]ɯKXn?olZpRǽ5k_X_5QX: aqG5w\_~? ? +7d? )fi7VT^wzT ǃ}%z=|y5Dw DcX $t܇"3DxXߦi+~/D:+0C YDϹ9P9XLэw3Da`gO+1(pqCaVehïTr-+[iǃ-|);W˗>HkHڙ6>@]@%GǸؤymu&uۨS=ʈ@i f?'LYv9X;0`+|SLs\ý0?JX 7n!YK gPR q29o/`)#b`0sB*YV^8,"X4aܧuao{L|rֻ`,L,R`Lo2Mgp:1p0wG|()Kso6NEo&ȰOQwPs,Lbn57 K$"3?}s_~oAUY/윏iV5lhư$ $ L*DޔLgYsqC]=GX SYXcKwhfջ0e"ŒYE+Zwj#pO)w7'lD08 (7,fWwZHqFaG lݵ, ͬV wE*E}t)nϳfէ/u_ [GE靌PC++!HAoJ"f^< +Tu_A˞`Ò!),2o.n4Z_Yn-,z{`2Xz3z'L{}һw-6$baV>qfiz,[X)eI]XCVL:cچQII6<|1^l⸊Ӥ_*trXT;J(Ee>Zzj$9V_HlpEX_Z>PS24~^ f e˱꟭2{vB_zEX}ی:O@յeװ"7feoV8E?ɩ$遳B&h{@G<چuH95V}wvŕ^*+ /!ª s), MW7*51'N[ĝq*tG5,_Jo2,3X~V#cL=Em̀"vXnrXۓ 2*=Ha}SJ\_U)o校H/d+XwB qg_ g?? [>~?%~?4/)Owf Vdt/bl2^*)g>p+tK֟Y1[bDD92yߕ+Wwe8a\RUy͵5U.--hJ6JPLa2; F1G&8GܽcRj+ϣ%E㰮*%ߘuP*c,KJ|Y|9)g^]pH׽۔h[ݑF$@;);ҦO$B9oBdr3uHET.`޶ǃ`˜i?Moy4.;POS|5ZT@#AnViU+.TJ^lCIea W|zqF`5̲난씏|X$IbSG[Y72YjrUXi֥DTKkH+leö`dXMYvl=&[ѭܗ@Hj\ֹi}FZ5[< GFuѲtd*1O5f krWZ3>}^/\a9Q9ưhfl]^AQd߹TYQ>GYzTx%|V6(@uXNƗ7:s/=_'Pr|V 2+ׁW{ifh~㏳;x(CO& u8^_&K`۾K2 R_/.l7BaS_ڗ:T3}W{5Aλ%gfY+?Ơϕ[Xf),6fβv jd.e`~*}נ^;!`:܅z_Fϰp?{ċ"T3H/ $r.xv}hm+cХg|0Amr ,1SɍlAw,Ev x:5:ŒÌ=,PU:Ճzw"D u[e3 wC֍ —R=!جH -K]Y] w尮amqU`%[QElo7z'Z+EsJiܰ'fHO;O:liͣjdg0qKZϰRXxD_CJImɬǧ)\!C'+039֍d6Ui#/` `"Wm nMjҙvJu$Y,-2Ŭ.%;2> ԜV ] T@aBNf8;+׳Tŏ`uk~)_`3 \lClaQ&_9k7~sLR12k_@|J9,L$WkTa fw4:Q>p[aBL)3wH0ėfE;$;ݟt9.'vơѥ?e5zf 2ȣpe{S9pao}T.Hb;Ϥoᖻa?XUOXm"7&MC*}t(_+2nEQ[{CUlu& 0Z'VZMYb/V5lb:4=eTIP 5 g ;YăџU +ŃF5Һ(3 GDkYCR |ckuFUZOO}f7hJу.x C aIe`g)3-@zz09,t[]c<$:z^"kG9Q"H(ITITDm. EvGP#/|Q2³p@'NЉK`ᓣ͐ssM aj<" VA: wWbZZd / ;GS?H+j޽nDB38ڐP,L0 6: uy΍^%˰9ָn1H2Vpe@ s+> z35z4=_0cX ^e(J4>F+ xЄۿ\9מ%{#Q J͚N;yN?e/fan諷Ǩ4d៿(Th^'$ޯj 7lhpV6J[ђ4`Q ?8ݞv=}͌r+\͏:ˑ-t[T[F/dz#K|YfԚJ} ύJ!Kݏja΂{>Z,8HdخjRr-ErjGqh4sU*,r뽐K#ho~kJ^'$E[o]0w͑|u_ܼ; E4TmTf%37s3+%],az XJG8qV{L"bΙwv +}J,Ze98.r6}D}nIOҤßM|qq"&Z"(/6ʠ P#`DI*lQmACUk_a*aCM 3_U->-N 0$*ڦg~\@-&W%Hͪ}s;t"^0%ghc|@We>obQ '}tP! g_ꢺ﫬BjdK/W}*] <;̬ d/zYw@ --F1Iɬc.b?&mg&ǎP۪V,HyXxede^<ؔ§'I e!W5'70*KzCu蘖^Kw`ɭ,\SXik62MJuZQnU@^ua~g'I!XϢK^dPktPx߳ npC#Gs Dw K`=Ε]~:9{j:;Od—SX#S.+_l~0/}PRrINҔȬc2@-a W -OQ% ʧbi0G!ɧ Iz(:aF"<ҩ5nysT_eC4|,]yNTw1QY k]3Q?,Q#^d(z-ey1,w/ ֭a1/(ٞfa7pRiU-ʬi;(ESw.w8֦}*/Cthqz&>yV  xnrcEuʑ$0ܹvs {_iVgQ=YO`Q`fmQ4;`xU}9BtL XijZ8*Y <9i!FqNm|ѥ47㧙 ~㜿u6b?Go\eؙIo l`d&}ՅH >86}UsPQݳK4ժ[3:ُAg 6Tu`n#]yYQs7ܾ:.) Vt|mqۭJr 0/f10C56 I# xr`9u?(@oBti%HszuFiӴrlI z\&uwƒwO|%1 YXxYSkKa97qz#@oqi;w/n.^a/b*跦?VYKa9h{Th0z۾%fwXݬN'N^,r)W0fc#Қ$lY,Ux#WXTo$kgUiJ}a;|,=|j9]R_39!9!?QkevTM ]cSX4n3cNr~c>V5f;>_]JS8>cuQh+|v*eQYE&vi~_'``Dco\_S0rCp-zk\?WxyWw Xh^AS`]Cr?x-Py4dvv4ݾ,%lN ^{#H+THaPS͕2Y9J*3z9KO1d]wPd9c᠁:fTz"QX .^VSzd*p$2G!d w fuXMcиn0Kcա\EA^{eЌ皖[Jreɲ a5톓 Khe]_5Kp~{Y'~P)UE5)چnvLhBPCj֚\fJ}wONb3 c+ QV\>nt"\oSwkF|'- zvf%+g·79Xʃ`I`^3fc޺Y.;D.J,x4.FYrOWtѵBvGUww ݙIɿea%+ћζzψ3}Rj[:.70;-3[xlMܩn]e^d%: R7c.i.T8F[m MmE4 k ~*;Ҭh?s^ߛ33j ]m l^N:j~]V,uxY)=kn kԢsV| jݚM]ZڙUۈY 'hprZ3̄49J[{J̺vEccYXGn0}+sڼ O&r RhȨVr,F1{4i:3vJIߠTa b_BY9XdGcH(;,+ع,ӸaHA&)"i/ֈXZulYɩeۑ98 I;E~Ye{ źJvkteWB`" 3zZ;Yb&J_8r:Z9~%+60"Ysmu܍ nhX]UQz /FNѠDRXTdih6Y(^UPlYpݝ@a掯)RА_<=1-0: :\&kֺ OPY,yI{;:E 3]cQu1Nsο,@n9mJ✚.u33 Et5> &lhm5k ,+F=0 $qiH3bB*W|zRs,-v.D;0tt aΧFtF`CMђ zh,Ks6ܑ&HmW b_:r&[^C3UIMd{LB}&\2/*s,M19˗sNm M.R&QN4rwwH˝OHa;b{p c< X\Tu胞n4N&q}rcfXJ4٠vt1ubB Ixͧ7F,߸:`mgTabKThTP!rvrm`=V vXOa=uj˩xZkN nm,}qF|~v q W?ؐjT ' "g]X-dedɆlЙa 2w8F c*wm47զНmZ[lɅ@vk%B`{ Q46\OKJ;6V-{a);hT1#'f'&* UJ-8&cxI|yX 5f˒{{o"r6AtQf&u߮)*(tw~$PU=)ѡGy\dfYc8HsVٟNkHճ"5)O찁­']ݣh>їCCSau@ ]]zFڟڕk(*9=찝d Xm7u?Uָ8-=xk2 s_h6Lb݄~8ii}egв) UarU52XE΍լay_v,:>3&~jV:J hR ,Tg f@qK15>)Tv@nf^(,Zv:}rc\#S.Z+9ΤPA W!%eW_Ot[U,Tlh< #tDJ`*Wĵ)׊'|#6ԠcmN5Qz0X7=fςi1R8+xO:2R~ kp #_:[B@VgQEXtH@t jtGHmI~(a'2ɀLW+^> ?ԣ(=g۩s|v|صaHvThpM"R@r@KI'3(OXi20n}3k`\YwAORXɩ,)&l>]aPG,$t9\&61(Y%/*1YnM9`,̊G0f[7uXqLJIb?zۍWf!Hʪ jt)?XyJ#/RRxWp\+#7W:| +WS~5Ÿ)~?G[::Ӽɳ#'^8ЫLa%9I'kux`nf"i $؝+%fx/PBa-` ~>,`fB:[o-~ZZ[tJo*{[kB޴L:+51X[ M`O;-3= p_nk{q^$Mh|.̚ےAXᓡ]NO| ~'P5qSk׻X V72F''{׭ ]1h",Kj+.Iwkd>VME88Ll=)(^[6Gߩ}јXmvU\:),;*@\UnMu31u]5NA煪]̴zջڮ pRjյEM+=X+}mLQvgA*}{1/WDr}j CK)ܒ+|f4E+rͲ4e1R1qdǪ,]"+5]lL+T-h5pk&j h{Ż=ͭl+XIbO4e% !⩃ɫ7D:ά5 {%>ۧ|6)G!zK TﱢTfưvȏӹSXѸ$x3o|vIWiA}ɽz׃t^ʻ4InsJ "_xb[s-B6X?J2ϬՊ(ӑ%25ӢƤ9hW;7nh۳raɊLm*={*iTAwAURZ>i wEXT5k  7΀WPya%Uqɺ"(v ,]X) k۳5y)V}<_=`ћl@i4ZÏo!K"VҪ+ݾNa}HR0|bEzw,Eǯ ;|R/;oaEj+3Xr] L=Uw{X$U2l1+00趒+Cy2˾jcZ<ů[#A2_R}}~0D;FW`rooedr.6e&`E}f_TfN-=m]4ETb;Էl>ٯrdRe,́As,Ւia~(}Ի7uMC ^5/?,(j_ .%u[_Vv@XZ/qA%3v%ao_6`N` xIENDB` DdhJ  C A? "2lx~i\2U8HD`!@x~i\2U8*` @|xڝSAKQy/؍փTTh).U&ДDz\dS4'Am7O=XߡϥEllҺ>vvͼyi>XI!daJ#4eXmg =M$|L# J7EetwjO.̒@γBWlQfR1jɽq{oAd~NBzUDh土( Ƴ㝲Կșpx̴ Ƙ,˒LG58c(Vzr RJx[M;3LbJ)s%ZXtln>äZZξ{Ftnv;Mƻ~bs+U&ʵv`=^6ҲQ 4mT~?zHxN5 0'nԢP,/=һ%dx 5d8Ȏ*9hK38\Q+Cqq 74։ju_1ISĨDdTJ  C A? "2R|U]u?3 B*.N`!&|U]u?3 B*  XJxڝSkQm$(6꡴n=YmW]l i$Ĝ, -'=yo^ě? N-HM-R̛oID6YQڻB\J"+^%ػroݷowN e>%n0FHe#1yH4Ƨ\x3)jy@o'ɷ'J e;Ylm-EquTԮn7Fc[׿tsdv=hUdbZym8Aive^lEϘ6#g`c2 9ȁ,}Ž=`!)A&ɱ^R@4 |xڝSAOQJ[[AKk.V4FԴ5'&Cp/ p⎿'@v+hN|3;o73o c HD!"1 C/.q GqF.@oڌ_8]Ο ˌedNoLLD>lx iF&)ODdhJ  C A? "2iM[vʻ%IViE1 `!=M[vʻ%IVi @| xڝSAkQƚda7=Eӂ=jKx6Y,bR=.]44Ԝ,"CoEأ 9y'DVDyo{Λo{,}'@R2hHq:?Eg510͟11XXoY  Tza*KVb}712/IMV :śnVݛh=k l0!VrҧIZ8ǔ0&P°H͟idE)J8Rk(#Lk0yp l7֋nK韛\Z#nكv4KiG*K*jرuӸWno?蠐z&* tk(_%_Y2{Ӧȉ.Euewo#+O6 ^s"ڦ6 oqT95>OSlh^.x»[i|q׻"oII :Vk:ݠ%-iPDdH|J  C A? "2=K &! Gv08 `!K &! Gv0@`"0xڥSkQni`7ƂZl MZD=)!xVx{)(ξof73-a0@*Db6iVߢHrbOT%FT0zsyw,&Q9ԃV&tO(t[HLbMgt-\jwAy8*A_>0 Oʧ熸&~1m'/9RuDS6RotIL͸ŽLwݔc2XjKYo=-hNg3Wa#8[׻I5yèDެx6immH~滍ջmғtgUL=YT{*bIv ,< . Nj4lۨ7L ce8"(Wq¶Nkx0 RC5N+DdhJ  C A? "2eMM*Hܖ\A`!9MM*Hܖ\@ |xڝSAkAl@v[=EcA V6Y졑`R<.H6edAO  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\^_`abcdgjklmnopqrstuvwxzy|{~}Root Entry F#ciData ]qEWordDocumentQObjectPoolƾc#c_1200467266F7cþcOle CompObjiObjInfo !"#$%(+,-.14567:=>?BEFGHKNOPQTWXYZ]`abcfjlmnqstuvwyz{}~ FMathType 4.0 Equation MathType EFEquation.DSMT49q;(@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n++2 Equation Native D_1200468014 FžcžcOle  CompObj i==F n++1 ++F n FMathType 4.0 Equation MathType EFEquation.DSMT49q; @6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_ObjInfo Equation Native '_1200468013 FžcžcOle APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F 1 ==1,F 2 ==1 FMathType 4.0 Equation MathType EFEquation.DSMT49q; @6M6G DSMT4WinAllBasicCodePagesCompObjiObjInfoEquation Native '_1200468348"FžcžcTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F 0 ==0,F 1 ==1 FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native  `;D@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a,ar,ar 2 ,ar 3 ,ar 4 ,& K FMathType 4.0 Equation MathTy_1200722283F`JԾc`JԾcOle &CompObj'iObjInfo)pe EFEquation.DSMT49qN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x n ==ar nEquation Native *_1200468445F`JԾc`JԾcOle /CompObj 0i FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x n++1 ==rx nObjInfo!2Equation Native 3!_1200468504,$F`JԾc`JԾcOle 8 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x 0 ==aCompObj#%9iObjInfo&;Equation Native <_1200479342x)FPپcPپcOle @CompObj(*AiObjInfo+CEquation Native D- FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r== x n++1 x n FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A_1200479217.FPپcPپcOle ICompObj-/JiObjInfo0LEquation Native M_12004796653FPپcPپcOle RCompObj24Si  F 1 /F 0 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_ObjInfo5UEquation Native V1_12004796731;8FPپcPپcOle [!APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F 2 /F 1 ==1/1==1 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesCompObj79\iObjInfo:^Equation Native _1_1200482522? FPپcPپcTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F 3 /F 2 ==2/1==2 FMicrosoft Excel WorksheetBiff8Excel.Sheet.89qOle dPRINT<>CompObjefObjInfo=Agt2# N    s ''  ' r ' r  Arialw@c AwƬw0-  2 n8 Arialw@l wƬw0- 2 08 2 18 2 28 2 38 2 &48 2 h58 2 68 2 78 2 . 88 2 08 2 18 2 18 2 28 2 &38 2 h58 2 88 2 1388 2  2188 2 -1! 2 1.088 2 2.088 2 1.5882 1.66788882 1.60088882 H1.62588882 1.61588882 1.6198888"System 0-'- s - -s- !s-}s}- !k}-s- !k-s- !k-s- !k-s- !k-s- !k-s- !k-_ s_ - !k_ - s - !k - s - !k - - ! -yy - ! y- - ! -kk - ! k--'- r -'-   -4&l.  --j }  . @& & MathType`  -"Times New RomanwƬw0- 2 n @Times New RomanwƬw0-  2 Fy&MathTypeUUDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n & L"Systemw@F wƬw0-  --'&&C~.  --j B  4.  & & MathTypeP  l" @Arial Unicode MSwƬw0- 2 +1y @Arial Unicode MSwƬw0-  2 /  " @Arial Unicode MSwƬw0-  2 nn" @Arial Unicode MSwƬw0-  2 FF&5MathTypeUU)DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  WinAllCodePages@Arial Unicode MSF n~+~1 ~/F n & L"Systemw@O wƬw0-  --'& --'Workbook]MBD0012EE2A@ICFPپcPپcOle h>CompObjBDii @\pdetemple Ba=? =--!E<X@"1Arial1Arial1Arial1Arial1Arial1Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)0.0 0.000                + ) , *  " #8@ @ "8@ @ #8@ @ "8@ @ "<@ @ "<@ @ " "<@ @ "<@ @ `Sheet1`i  /x "wexwt}OU@=wexwt}OU` U)~xUMhSAݗjbXHOئ*Z mhhTfR=ozx"^UD$EK{s7OX px9$Fzch\2 *m]d^!b W讖k6-ylEa׀JX,ZFѤt C@ZCTdg|e4B+KFu!+J-Ǔ,-C RAdf$ƒ)=ܯL*;7#eN$0AFTӹa6E揅=zsT~o|F5g/(p Ld3z4qDϒro6Kʌԝ9>Ǣsłc {ͦTϦp4슇W|$ߞt0ɯOYƉ=HaO@BP ,52^hZ}"ejeWKUI6ˎ)թ=Bu Vqg- ܯ|9b!ܤ:J)+, I;Nm-Ƨb{?QH %)E:e)H1)]h7q{oJڶ21r3猋w ]Zkٮ`*1qGi |7;)^`z7vΎWWQQ_ N%|C`Ӂ/s?umos 6y~ Evç _ o`R|n X˪s-f5G[e>5V`^ _Qk72@{U~|οR fiXob_q¼p2zB>Ũe'_>;Qg'_ qIgG[kv*㮛{uME,Uo?9?eQ"WqWjQ@ý3@=+qWjQ@ý`4ĎJxWolSU?m7?Fi0ikHdjClLUmK7}̌}sH` &~ɾ' 6$&hB$"[pۓ{{s{ 2vzkx7ͬ ʹfPΙ @u~@:uUZgUR76s$-Hcc:ɹ=+dW'ك܎xD4DYYt :Jd܊I=-!WZ0|7t)dC\v ?Ǔ TqOs8c][;<LӒf]1Qh[م4a0WEg"\T$ F.- L}LG{'Тd<ӓE:ңفN'~33 .K*;LC8ՙIp)X! nn Fgt$lmFGԨڢt!ttR7UwVgDvuEUGu a6a&ڙݚɲZLLp< LP$܍0" ՊKG*v Gy5Ĝp@r|t,3L#(m׹nU ꢪC`YNqd+x*z{N5(~AR|[,"C~iЛ1lB 4ނ~A8I}3!s cj)SbsiĜI#d'p_^*u&=e;uI%od|6}뉾o76lP'Tǻ^>nx?q c~N!_8.ʔw8b3E 1aS].,ɽyH{M/t.`LboĘt}'{EW> "s/{qdMȇAz-:xL׉zf(p0-5V>вaonkUnXTvDF_YkfZ2vQ9@un:gOobPanXoB[} 1Tz&_7qw7Ga 5o9zBܴzuL`q uݒ>{WϺ󯴔ߧ9>甗 dĜS3  @@n-  @  dMbP?_*+%MHP LaserJet 1200 Series PCL 6?dXXLetter.HP LaserJet 1200 Series PCL 62%xeO.CQJoJʠNxt(v`0wyi{^묝}v dmxCK8 M5c[$.sE48#%>Na.DeC4r5upAwvՆW}wFC";xS8}~%p%H 6qxBj:oG}|4<.۶ײҙ4}7[E*xi_CA4ytNޅI"dXX??U} I} }  } $   , , , B?@@@@@@ @"@ ?!? DD!@ DD!@ DD!@ DD! @ DD!*@ DD! 5@ DD! A@ DD  !? DD!@ DD!? DD!? DD!? DD!? DD!؉? D D! zy? D D   "(THP8(  |  BA ?AA@?]N`  $]TPEquation.DSMT4*|  BA ?AA@?-]N`\ $8^REquation.DSMT4D>@92 7 -]N`0 $@HEquation.DSMT4D>@92  7 .F!Sheet1!Object 1 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n.F!Sheet1!Object 2Equation Native kMBD00134415GFPپcPپcOle o>CompObjFHpi FMathType 4.0 Equation MathType EFEquation.DSMT49q;)@6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  WinAllCodePages@Arial Unicode MSF n~+~1 ~/F nEquation Native rESummaryInformation(EJxDocumentSummaryInformation8|_12004830156UMFPv۾cPv۾cOh+'0@H\p  detemple  detemple Microsoft Excel@RP. )@nZ)՜.+,0 PXd lt| WSU Sheet1  WorksheetsOle CompObjLNiObjInfoOEquation Native  FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x n ==ar n FMathType 4.0 Equation MathType EFEquation.DSMT49q;(@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A_1200483048RF0c0cOle CompObjQSiObjInfoTEquation Native D_1200483147PnWF@ݾc@ݾcOle CompObjVXi  x n++2 ==x n++1 ++x n FMathType 4.0 Equation MathType EFEquation.DSMT49q;7@6M6G DSMT4WinAllBasicCodePagesObjInfoYEquation Native S_1200722854m\F@ݾc@ݾcOle Times New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ar n++2 ==ar n++1 ++ar n FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObj[]iObjInfo^Equation Native _1200722891aF@ݾc@ݾcN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r`"0 FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObj`biObjInfocEquation Native DN(@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r n++2 ==r n++1 ++r n_1200722954_fF@ݾc@ݾcOle CompObjegiObjInfoh FMathType 4.0 Equation MathType EFEquation.DSMT49qN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r nEquation Native _1200483660kF@1c@1cOle CompObjjli FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r 2 ==r++1.ObjInfomEquation Native _1200484419ispF0c0cOle  FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  p== 1++ CompObjoqiObjInforEquation Native _1200484652uF0c0c5  2 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AOle CompObjtviObjInfowEquation Native   q== 1"- 5  2 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG__1200484870KzF@1c@1cOle CompObjy{iObjInfo|Equation Native _1200484957F@1c@1cOle CompObj~iAPAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ap n FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_ObjInfoEquation Native _1200485076}F@1c@1cOle APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  bq n FMathType 4.0 Equation MathType EFEquation.DSMT49q;7@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_CompObjiObjInfoEquation Native S_1200485109F@1c@cAPAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ap n++2 ==ap n++1 ++ap n FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native S;7@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  bq n++2 ==bq n++1 ++bq n FMathType 4.0 Equation MathTy_1200485275F@c@cOle CompObjiObjInfope EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ap n++2 ++bq n++2 ()==ap n++1 ++Equation Native  _12004928516F0c0cOle CompObji   !$%&),-./036789<?@ABCDGJKLORSTUVWX[^_`abehijknqrsvyz{|}bq n++1 ()++ap n ++bq n () FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesObjInfoEquation Native 8_1200485278F0]c0]cOle  Times New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x n ==ap n ++bq n FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObj iObjInfoEquation Native 8_1200723323F0c0c;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x n ==ap n ++bq n FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native AN%@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  p== 1++ 5  2==1.6180& K_1200723588dF0c0cOle CompObj iObjInfo" FMathType 4.0 Equation MathType EFEquation.DSMT49qN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   ABEquation Native #_1200723813F0]c0]cOle 'CompObj(i FMathType 4.0 Equation MathType EFEquation.DSMT49qN+@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  q== 1"- 5  2=="-0.6180ObjInfo*Equation Native +G_1200723866F0]c0]cOle 1& K FMathType 4.0 Equation MathType EFEquation.DSMT49qN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_ACompObj2iObjInfo4Equation Native 5_1200723958F0]c0]c  r 2 "-r"-1==0 FMathType 4.0 Equation MathType EFEquation.DSMT49qN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_Ole :CompObj;iObjInfo=Equation Native >APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r 2 "-r"-1==(r"-p)(r"-q)==r 2 "-p++q()r++pq FMathType 4.0 Equation MathType EFEquation.DSMT49q_1200724078F0]c0]cOle ECompObjFiObjInfoHN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  p++q==1 FMathType 4.0 Equation MathType EFEquation.DSMT49qEquation Native I_1200485756'ZF0]c0]cOle MCompObjNiObjInfoPEquation Native Q_1200485879F c cOle Y;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  L n ==p n ++q n == 1++ 5  2() n ++ 1"- 5  2() n FMathType 4.0 Equation MathType EFEquation.DSMT49q;4@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A     t "#B$%&'()*+,-./0123456789:;<=>?@ACDcEFGHJILKMNOPQRSTUVWXZY[\]^`_abdefghijklmnopqruvwxyz{|}~'zOQ "Yd;\-UiTѮ:OLMjIܼI%( bbm o$|vgiE><1(qۼvӚ64YsF,61>NX܉mtJڸ Z~v{k=.wwZ׃O+iin, Z^PJUYgX¹g\)صuڏ+ٿ:pgfr;a *S&;vέN(?;&fAKANRӐ<rx |ԋ</י;จ"/31.'E*–Rur&Ut^"b>)$*5 HeBDdhJ  C A? "20 \% |!Y  `! \% |!Y   @d|xڕRK#Qk`7E,5&z.H$9 ]lU3:vlXط̷CS O nM1ϋL̠+X|_}Ҁ?L7fE껅־P,OH4!`dvig\`{i#pA{ediiNmI=\c`/ cQ)Ha)Ӡ44MvyKs OHG2ºҬaݨsV'? I1Dd4J  C A? "2G},ibfgx?wOȁ ;,xc-v Nq-Wֱc~}BG6 d4k6yl8(ͦD:v7v7i*Umԛ7[n;Jk9O+h&+be{#IKejBzI2jH8ּRex]eDZpEoȏ鴩 Z$*=iMkQ3+u,#hKw=%ѐ;|^|r'#DdlhJ   C A ? "2!9"D{t?`!9"D{t? @|xڝRJ#A'Q3 nVЃ8I&z06=HќE'_@Psx,KvluO,Yk+xfnV y-Q|B1D-5MaU_kUo7%HH!y6Gb*-(`?[ O^?NZ3H`j_AP:A9nnJՏe2h[yϮT^@<_=n[ZCA ECR9j=`KigvAZk~~xܴ!9#iefj;r]mYa}s#c1Yg@3Jl؜=Q" &tߍR{GXS foaP[wzWthUeл? VDdTJ   C A ? " 2XV`@T쎨YcD4`!,V`@T쎨YcD` XJxڝSn@}vhFkPġ, RҠ$(Dq ~'$~H   0v(fv.!h؇A!Xt"͉I\QXF~ѹc0,&7_8!eQEԣ`x/|Œ|B=/bE1I)3hu%XW;h_&Ci:tQ`QH1r.JCƾI4gܶc;[j|4UUvMeYS,af&;^ˁm?;e"j\-\oVkުtn~t'e)*f(1l{i\ ]S MF[!#ӨH5p;)& հz\H,\qTٜ56O͔Ƴ wY˜O(+; ȉo| ˪阘Qցz?ư׏Ғ-1?M 3Dd@hJ   C A ? " 2Y"ca5`!-"ca @p|xڝS1o@ف։d4 )n␁@DR1DJLTP0ub`b' &&&f,$»B!x}ݻ{wGX@J Jd:bEcѹc&V1,#/yqLN2ѽX%@iZeUN] kNׯ[qtg`"`˹*)fߣw ޷c'?ErێOЦ*GXM檪T3Yo"11,͂[U?g)k[PJ.*7j͋][ Ȧkj~R~ dZ3=,aaeۭGywϜfbl4YfIh Ǖu*aGZ:;)weγDd{J   C A ? " 2Ikx*!v:Y `!Ikx*!v:Y.=pCxXKlE]?b;⴩ۊRHА*DN7*Ԡ@q q14R$(@q%@"Q ! R*EKA"'B,!ҟǿ'E=Peox!c [=B-=/9&1J |K<;^@,rĴlSةdiazGOYݣ?xщ%:/}o}VZMȻvi192t6ʎ5+bz0t 3Rx؅3GCt;q sׁKw r#*$00*WDnW9*W@W+dCy{k3L0[ =D;"A7H' $A4BE}.%[w~9"vJ֖W6 ɘ(*9QFݕc 3ؽl!t[oqy8`:$^@MTM\MBMbMzRK#QS#SS#_Scw<{/5`] Y.>R2R+X9#+ U0 XE#Ͳ=Eg}f%+ad%4VF2FVFc+od5֞bY#=aܼљUAC j8qk@c+ed4VNrFVNc`d4VQFVQc8ꍂU퍃\Q+X#+7kOG!\_[RjR&#Ic(Vբ0ԩ/ "g//vlb1ĭnʏMٔ v܅uo nwXr`_/C7@p8n :K8TAA9c&{5o֯IGeRy䌪>9!wsVv6N3zkko^-\{p}N;Y?;|^ Lz9bz5bf. OHAE"$殗^Xm Ϛ/j33?t/+¥#'H/Cvgj-Z\@[K)hNL^Y895ڙ,EMN9lHBidi," #kk:{őa޸dX%,O)P xX8"%7g~,~VnU\E+oht{+ ;Ҫ_Z*y~؆UvM-"*nbt[#nCLjq`ͧZ܈0Lv*z]lb };|QkPhumȱw2Ew lvޥ4rwRie|.϶>RO{kv,ׯV*>^oz N09`CsfS/ 8gDdH|J   C A ? " 2<ctMnsz`t'`!ctMnsz`@`"0xڥSkQnjnZ{z(hx d,Д`Rznu`~M$ٓ ?? T8eJ갳y{KSPb N={oAq9q GLU0z[yw,$Q9Ԃf|:˼'+$fo3u-\lu~q7_:A߿)M~wYS_1rC&vRuDo6R3ʤaF91,Llvݔb2,ڨ5[] ޫ[WI5y{¨@ެ5hXĝ oRpұnmғkr3rZ&\D{ʼfUߓqq$Xx]Нfh>ؼϷQ]nJlqDAEP˷WqŽ`N[`FeH库6/ DdhJ  C A? " 2n5G JN*`!B5G * @ |xڝSAkQmml=EcA-M{h$몋MI"ٜ,-^E7Ovvͼy$- @`r,(B$áBWL㸔($]Ic Cd9dp棨nAU'$:->wZbC,LsRJ՛^'{eowoQ5$} 1{ٿ!);) ~=0vĴ1Q) ڸi#T7vxuRM;QggK!i̞Tq|ײMcg2rkjZUFc[{ ǻѢdba+UdZm0waVJh;VsB;6Ff(Wp<֏X+NɱCXqHzӠ:j<<ӯ "$un<[);5UmyUցjҒP_)iS)/MDd@J  C A? "2x }Q*C 0LTZ-`!L }Q*C 0LB@ p xڝSkQ&VBѴ A&= &eխl"1'+Eo^x(x' y/jC$۝of{$- @r$XQH CVb38.% %EK+U˵z`7^~zW~dW3ZLzREF/ײN.:Ҫ]-׮||FDW(m;Ѳ{-N$_J> lξ'?!{e3_xul呟+/jsfn+h8cuyK^7%7EW˴S)/8DdJ  C A? "2)R~7#p0`!)R~7#`:HxڕRJaĚ؍уThj`dC#DzlE͖(-> r|ICvvvf!DQH CVh)͉q^B ёP&12ptsaV%?v\ XbOH jt Ҍ~'H9Zo̎춚!n=(!?'Z\\ژ&鿸I^XOFjL|cZ4Q5P?= **VJՏԗhl:B[v6ZM2ZhW )U3ֱ9UW\5ˁofכ׌u z6#C/H׳T$tSROAҜ{r_2"7Y)4+uU[Ȍ˕nw&Ŋ`ش3pRR Dd,J  C A? "2m7,EvefEI)3`!A7,EvefE*  xڝSkQm6nZ Ƃ"]$M{0LeEF6(x-^*У'*{㼗M1Xfv2f#mA+&bDb8*t\F#!=\6`6^rL\Eܭ@^uI~B"7Zb],NsRN՛~;毷^oQ%$y>O_0ٝ;)C-!3=Lh) Ó XS0mb$VMNJi::9:M'1gˋ8=GY kֲ [+U˵ z`7[^~غW;~4sZ\غRE.QfϬ:Ҫ]LkW>x9٨22t}'Zql^qKɟmd@!֧AMTyrȃ,g,Y稀_:Y'ׯ%o ʎ[\)#-6Th*tDd,J  C A? "2Bz2O &Q46`!Bz2O &QxڝRJQ=sHQQBXY&)\W]4l"q+? 6~`iN0νYs9s,l Ђ NK'AF=FQ,&=dMUIa)8fW|B!!FT͏MzNZ᜻8aiXKcymcPfŌy|9-ufُO 49Mڨ5枴vv{ﵞUσMNk&d˰Fs_CW1s{UWSvk@{l+ 9Ҟ278K^sz+C 5epQ|7"Oq( q$4?k8msX\\d;ɪȞeV̱G6GmqE?_mS˶J8,5Ba)π;xR=f؈c`OX!8c]ԁ#׭=W E_xD-N-ե.u!p\&0xnT˥VQ̖f bWDѬlZ&J?m7Kp f.FTZ~͂=pVںb ikbmM+By@F M8ȴ#eU\& a.hJ['zQVN7-[;5㗝±VWⷭ;2fM(oP,o dɢhDd$J  C A? "21Ȍ]8?`!1Ȍ]8@HD lxڥSoA~ofw)(z4z Z"@ YPWDX~E&&yOФ'[#ٝEJ4N7o|.d!6m~~R>iaBW,X8#Ke9, /"cs=JRa#w^nQلCp]jWGk'FR<_t^;a˱n,2Cؚp:G(8fz)2 UcO%ioWV*][;)\/ ߫mj]{n>6 ن:{K!5jfP/E۝V`rvY V0p  `e+`  2ZQ#g lKW9zYK) d4蚐ބ >qmoN&!E# Ί,,Ÿ((ے.oi؉;7oEw#ܶ3};y٩.X5Y/A{OJvl> e-=zloǽDdhJ  C A? "2½|]ݢB`!½|]ݢ@h|xڝRNA]@'C0!$Z(XYqE 1~by9$ 4>&T>`gZ3{ o~ۙeP9cx 0du 5_Hd oJ݆ `H?qB+\+"qp/kRfb'v'VpjVEUa~|w~`r *jpI7Obt,rZkjjU3΅mXv ¾ÞbvT1qi!͗bMi2,m&A6BULXGh t%idh"a@zRh 3k>M 1(>= { 0,Z)fݝ߭38^w*,Jk( NjVۮEToН2UA ?DdhJ  C A? "2E1V'U1Aje$E`!E1V'U1Aje@h|xڝRJQ>?0c"2B8ꐋZc %?aIz EVAv5paνsep>xP9cSd2(6>?xxaP2:F/O:ޕ `H/qBk\ #Qp/kbf#'v7oԬ:qC;(Rp~N *Jo࡟2\XRתՔծa]mzO ZQPqݪ-Awo:- Vae;3 rdj&uE1LT%MP13+ғ6@SiJG~٫}W>h֝ *=cu²F {kwY4:7d)S$ DdhJ  C A? "2n5G JG`!B5G * @ |xڝSAkQmml=EcA-M{h$몋MI"ٜ,-^E7Ovvͼy$- @`r,(B$áBWL㸔($]Ic Cd9dp棨nAU'$:->wZbC,LsRJ՛^'{eowoQ5$} 1{ٿ!);) ~=0vĴ1Q) ڸi#T7vxuRM;QggK!i̞Tq|ײMcg2rkjZUFc[{ ǻѢdba+UdZm0waVJh;VsB;6Ff(Wp<֏X+NɱCXqHzӠ:j<<ӯ "$un<[);5UmyUցjҒP_)iS)/MDdDhJ  C A? "2z[:Tۍ 4["5VJ`!N[:Tۍ 4["5B @|xڝSkQM`VBѴ.6Y졑`R<Ƶ]4lBs )՞* ^w^㼷jC$۝of{Y@[!䈱 ] /.Fq yFWfL,`(y$Y߱܋8]huMb1bƋiufX{:htJoPL.-_*V}Vp՝\c+6R񮦴h=Xתzb )PN;:-s8+v1H*v륋ϛ6'7*fN,W6dY?d`/W'm&@C\QC6+?MqrMBjx.{VkQ;'o&aKyK⌲mu/zW]R$NDd0hJ  C A? "2yv-dOx0GUM`!Mv-dOx0GB @H|xڝSAkQnk7MZ=Eӂ"x d{0LJaSH66Ĝ,"^"xV(^'$T"A|3ov7#,ڊ!""Db4)N#_L"#bKYXHH cĀ.EQp;˽PTYd>!yXfCL RJ Q5vMm6\O,auƆz bR8GN){2uLG? nLs,C E5 qmi#X5:vd]X?,iC;NIƧdw&riR|Wz}m{^=H]MjzFUZz?\,FpAºUq._b|r+A(ae烵NW ; JXq6קAuԔyRCqbrMBjxul+/jsfn+o +kn3{kwj"vJ4ʅDd0J  C A? "2_ܗu C퀙n>I/Q`!_ܗu C퀙n>I/*@CxڝUoA~3KFM bLԴ)blu$*`6^7=zl_'&ً1o]Pe oc@0 J ,B[Ȥ6Fm?5h}z@9oPW*Ƙuu:f(|,`կ/,=X[ Js\W`%4*}EYN>66K.#V܉ ^[w`e敢^J$+񇕒:o# SUn#΢}Z7/4ZeC#nkfx H KM(!B2^]=cN8!Ha/%99y`;K,tP06',57y'OQ>w!V{&Y+Wco,:clQDd|J  C A? "2^FmX7N]r:T`!2FmX7N]r`@ 0xڥSkQ&n Eڊx t,Vh$ۍ]44٤I$ɡ(^xɓWo-/E&ξof73-!h8 d*]|"K19YLd0z-QXQTe6ʒD "k=XR.Ϫ5Z~/w[^7=†-c 혦!Z?3uB%8`A08dש8 +SE1_uԪ~\!Jv m{;K T-n4z_=dhQ=D*2zs9$9Қ] -kW\xѴ:p2̢\NncY&{-N(L Cܧի!|%xbC/ (Ig#2GtMaKygdaFYږ^oIK^G,\ DdhJ  C A? "2n5G JW`!B5G * @ |xڝSAkQmml=EcA-M{h$몋MI"ٜ,-^E7Ovvͼy$- @`r,(B$áBWL㸔($]Ic Cd9dp棨nAU'$:->wZbC,LsRJ՛^'{eowoQ5$} 1{ٿ!);) ~=0vĴ1Q) ڸi#T7vxuRM;QggK!i̞Tq|ײMcg2rkjZUFc[{ ǻѢdba+UdZm0waVJh;VsB;6Ff(Wp<֏X+NɱCXqHzӠ:j<<ӯ "$un<[);5UmyUցjҒP_)iS)/M DdhJ  C A? "2n5G JZ`!B5G * @ |xڝSAkQmml=EcA-M{h$몋MI"ٜ,-^E7Ovvͼy$- @`r,(B$áBWL㸔($]Ic Cd9dp棨nAU'$:->wZbC,LsRJ՛^'{eowoQ5$} 1{ٿ!);) ~=0vĴ1Q) ڸi#T7vxuRM;QggK!i̞Tq|ײMcg2rkjZUFc[{ ǻѢdba+UdZm0waVJh;VsB;6Ff(Wp<֏X+NɱCXqHzӠ:j<<ӯ "$un<[);5UmyUցjҒP_)iS)/MDd|J  C A? "2\{1s?Tl%8]`!0{1s?Tl%`@ 0xڥSkQ&n=AcAm)M{h$ۍ.H6?K(^xɓWo-/E&ξof73-! h8Uňl6S6]} "ˈ=19 9d0z-a X qT>ʒDEz72/U-\]oAn0o{Vk} us 'ͳC|e'~fgKqH;1dz`rc81+SE1_mntZmcb䊅WnRrn92rR-oNJA 5vzFoj YRϻaSlT\xrh1\nmGS6g+{n$ Cܧի)|eybS/(Kg#r2Q@t~3q^YGږk0hKK^G"'3iDd8J   C A ? "2^n rVc`?``!^n rVc`?@v mxڥSAoRA}(=hE=(-^؃"4F/H AAxm5dzhwF}oxi0o?ffٝAp `@.AB6mt *,yYBAB`(iII6u=N2|aًiNӬ4P#AuN$:qP38Ge> 5epQ|7"Oq( q$4?k8msX\\d;ɪȞeV̱G6GmqE?_mS˶J8,5Ba)π;xR=f؈c`OX!8c]ԁ#׭=W E_xD-N-ե.u!p\&0xnT˥VQ̖f bWDѬlZ&J?m7Kp f.FTZ~͂=pVںb ikbmM+By@F M8ȴ#eU\& a.hJ['zQVN7-[;5㗝±VWⷭ;2fM(oP,o dɢhDd$J ! C A!? " 21Ȍ]8'd`!1Ȍ]8@HD lxڥSoA~ofw)(z4z Z"@ YPWDX~E&&yOФ'[#ٝEJ4N7o|.d!6m~~R>iaBW,X8#Ke9, /"cs=JRa#w^nQلCp]jWGk'FR<_t^;a˱n,2Cؚp:G(8fz)2 UcO%ioWV*][;)\/ ߫mj]{n>6 ن:{K!5jfP/E۝V`rvY V0p  `e+`  2ZQ#g lKW9zYK) d4蚐ބ >qmoN&!E# Ί,,Ÿ((ے.oi؉;7oEw#ܶ3};y٩.X5Y/A{OJvl> e-=zloǽDdJ " C A"? "!2[DAƊ g`![DAƊ  @@PxڥTMhSA}MSQl-IM`FII>jJӔEAMz-'/rЃWꩇRI85-zdw7;3 B*a B(uWj nh25?:u][RŻٕytnB<:ޏ2u /\7rӳ4ԧᢾa4jK،spORŜ‰*/:8*nkMX?G?[,s9t\*uk#uG!bCG% ѡm^]mb,GG"uәɸ%aqu5vYw96*2Gft< ˣ$X7<G_KOpb7U_ŅKr2rM(6_TH&T`Zq.>;;Vo'wtaڬ@@߿#'K Es!x $k];O>拃zXߗ੖zsV͖`@77KZHYF[t8l<81%(KOC%CT}AͲ YNBa>D 4C$&ӱߩ1Id*qnɠl^m.idUB_vDd J $ C A$? "#2!YU(#m`!YU(#@`zxڥTOA~ovv-Ճh%-?AbҤI%)UWiDCIg/ԃg5!1gÁ4{t)Dȴ{o켇}gb4BD}xBYˢ|#@Aԅ1 *hFمGPT]OB1VE.P7 pGېh!DO*: %8ɏp_M6kn2_>Κ<^2 0jǬO g3+X5k)xXc0sDap#ͻ.mbQ ؀f׈8uqUDa2nMb$`x>.PS$  UܳD:_^(eywL'źKب#mO%7rs|~4[+޳Y ~)5u&~}XYd ܥ gX6}W2d)}192!dR۽ "%QZLf3q[c>/RhQ }} my6O5<M4!Y&EJ[#we݊=HO(XG_'NpUއJ uM(Ywj`ěGY}[[IDd@J % C A%? "$2Okφ`+q`!#kφ`Đx xڝSAkA&nZ=Ec@4Tt,H0)U $l"iN-{/xꭥ=?ß'7Etط7Y}&@`9Rl(F$fBfˊd_N@gKXLna3>f;ǜ.ʡ _/},|B"7E xGjڝ?(S>U :~l!7gxXĵ;δj7Cv۷0mNx7n,&;TE6y~^q6sĥ BUk e_ 4vXR IXEaWoQ,dw f.ƃߓ,dךyDdJ & C A&? "%2.02~k|t`!.02~k|@>*hxڝT_HSa?;9f J٠FN1ڤDZRC=L| I{o9߽ew|w>>J Ë]T^WI ?-x_7mC]yy1~%rez`&[M!Hi7]~RGgSRANϟoaim+o_Kx:,pE8J'g'N:6?8MTp9t.onK7 ÁmrHb.:,q[wXk'c9hHP8~ZAZw mxYUPX495:A1@ ?3"}^'zﻷvvvv =j*5쾕[OdK;93k 9ڗfL[9J ϤVDuj8ƵLʒDEz72/U-\]oAn0o{Vk} us 'ͳC|e'~fgKqH;1dz`rc81+SE1_mntZmcb䊅WnRrn92rR-oNJA 5vzFoj YRϻaSlT\xrh1\nmGS6g+{n$ Cܧի)|eybS/(Kg#r2Q@t~3q^YGږk0hKK^G"'3`Dd HJ ) C A)? "(2 ³ܵ֠@}`! ³ܵ֠@`@""dxڭU]HQ>ΌΌcB)J.jJ%Z=l[-%& QsOD$AAF`D jn_Tes|_70/d,&0D !KR*MNajY(w%'ğ0'W 1l0#=Ĥ‘g 5C}]qiF3_L=oP2aUG)$mZ FɃK$Қ$h3̬gg.#7/fZ3w!E6dvwcCompObjZiObjInfo\Equation Native ]P_1202132893JF c c  L 0 ==p 0 ++q 0 ==1++1==2 FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G DSMT4WinAllBasicCodePagesOle cCompObjdiObjInfofEquation Native gTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  L 1 ==p++q==1 FMathType 4.0 Equation MathType EFEquation.DSMT49q_1200486234F c cOle lCompObjmiObjInfooEquation Native p_1200486419F c cOle tCompObjui;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   5  FMathType 4.0 Equation MathType EFEquation.DSMT49qObjInfowEquation Native xD_1200486543F c cOle ~;(@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  L n++2 ==L n++1 ++L n FMathType 4.0 Equation MathTyCompObjiObjInfoEquation Native ;_1200487023F c cpe EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  L 0 ==2 and L 1 ==1Ole CompObjiObjInfoEquation Native 8 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n ==ap n ++bq n_1200487166F c cOle CompObjiObjInfo FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ap 0 ++Equation Native 2_1200487177FccOle CompObjibq 0 ==a++b FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AObjInfoEquation Native _1200487204FccOle   F 1 ==1 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_ACompObjiObjInfoEquation Native _1206942072Fcc  ap 1 ++bq 1 ==ap"-q()==a 1++ 5  2"- 1"- 5  2()==a 5  FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native  @6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  a== 1 5  FMathType 4.0 Equation MathTy_1205155567cFccOle CompObjiObjInfope EFEquation.DSMT49q@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n == p n "-q n  5  == 1 5  Equation Native 5_1204628166FccOle CompObji 1++ 5  2() n "- 1"- 5  2() n [] FMathType 4.0 Equation MathType EFEquation.DSMT49q,@6M6G DSMT4WinAllBasicCodePagesObjInfoEquation Native H_1200488146FccOle Times New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  q==1"- 5  ()/2H""-0.618 FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObjiObjInfoEquation Native 4_1200488634Fcc;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n H" 1 5  p n FMathType 4.0 Equation MathTyOle CompObjiObjInfoEquation Native Cpe EFEquation.DSMT49q;'@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n == p n  5  {}_1200488846 FpcpcOle CompObjiObjInfo FMathType 4.0 Equation MathType EFEquation.DSMT49q; @6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  L n ==Equation Native %_1200489853 FccOle CompObj  ip n {} FMathType 4.0 Equation MathType EFEquation.DSMT49q;(@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AObjInfo Equation Native D_1200489961'FpcpcOle   x n++3 ==x n++1 ++x n FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesCompObjiObjInfoEquation Native _1206942556@FpcpcTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x n ==ar n FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native D    #&'()*+,/234569<=>?@CFGHIJMPQRSVYZ[^abcdehklmnopsvwxyz{|(@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r n++3 ==r n++1 ++r n FMathType 4.0 Equation MathTy_1206942568FccOle CompObjiObjInfo pe EFEquation.DSMT49q@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r n FMathType 4.0 Equation MathTyEquation Native  _1200490122FVcVcOle CompObj ipe EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r 3 ==r++1ObjInfo!Equation Native  _1200491369$FccOle CompObj#%iObjInfo&Equation Native q_1200491551")Fcc FMathType 4.0 Equation MathType EFEquation.DSMT49q;U@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  r 3 "-r"-1==(r"-u)r"-v()r"-w() FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AOle !CompObj(*"iObjInfo+$Equation Native %  r 3 "-r"-1==r 3 "-u++v++w()r 2 ++uv++vw++uw()r"-uvw FMathType 4.0 Equation MathType EFEquation.DSMT49q_12004918831.F*c*cOle -CompObj-/.iObjInfo00;>@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x n ==au n ++bv n ++cw nEquation Native 1Z_12004919393FVcVcOle 7CompObj248i FMathType 4.0 Equation MathType EFEquation.DSMT49q;/@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P n ==u n ++v n ++w ObjInfo5:Equation Native ;K_1200491997,;8FccOle An FMathType 4.0 Equation MathType EFEquation.DSMT49q;\@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_ACompObj79BiObjInfo:DEquation Native Ex_1200492079E=Fcc  P 0 ==u 0 ++v 0 ++w 0 ==1++1++1==3 FMathType 4.0 Equation MathType EFEquation.DSMT49q;@6M6G DSMT4WinAllBasicCodePagesOle KCompObj<>LiObjInfo?NEquation Native O!Times New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P 1 ==u++v++w==0 FMathType 4.0 Equation MathType EFEquation.DSMT49q_1206942724BFccOle TCompObjACUiObjInfoDWEquation Native X_1200492317GFccOle \CompObjFH]i@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P 2 ==2 FMathType 4.0 Equation MathType EFEquation.DSMT49qObjInfoI_Equation Native `K_1200832991TOLFccOle f;/@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P 2 ==u 2 ++v 2 ++w 2 FMathType 4.0 Equation MathTyCompObjKMgiObjInfoNiEquation Native j_1200833044QFVcVcpe EFEquation.DSMT49qQ@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  0==u++v++w() 2 ==u 2 ++v 2 ++w 2 ++2uv++2vw++2uw FMathType 4.0 Equation MathType EFEquation.DSMT49qQ@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AOle qCompObjPRriObjInfoStEquation Native u  P 2 ==u 2 ++v 2 ++w 2 =="-2(uv++vw++uw)=="-2("-1)==2 FMathType 4.0 Equation MathType EFEquation.DSMT49q_1200725454VFVcVcOle }CompObjUW~iObjInfoXN@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  P 0 ==3,P 1 ==0,P 2 ==2,& K,P n++3 ==P n++1 ++P nEquation Native _1205755288[FVcVcOle CompObjZ\i FMathType 4.0 Equation MathType EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AObjInfo]Equation Native _1206533094`F c cOle   t<<1 FMathType 4.0 Equation MathType EFEquation.DSMT49qv.@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_CompObj_aiObjInfobEquation Native J_1205755598YeF c cAPAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  1,t,t 2 ,& K,t n ,& K FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjdfiObjInfogEquation Native gMK@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  1++t++t 2 ++"L++t n ++"L== 11"-t FMathType 4.0 Equation MathTy_1205755783rjF c cOle CompObjikiObjInfolpe EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  1++px++p 2 x 2 ++"L++p n x n ++"L== Equation Native _1205755676oFccOle CompObjnpi11"-px FMathType 4.0 Equation MathType EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AObjInfoqEquation Native _1205755794tFЂ cЂ cOle   x<< 1p FMathType 4.0 Equation MathType EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_h{,ryŽ&GX(㐌 q/e|sL͂X"eu14YY>jǟ3eHPvX`9BdZ+QR S'_3}>.|\}f{b[JH-{#`GGmT]XSL|Rk}R]XoS VBor! `@P0"xڥSoA-#HR%@z%a hPx%Blbbz?Ko^դWO$O-Z#CnX@[;vj3@8[qLw3 ݧӯ+DٰeX-Mvյ; }:ӆ[rze4)ˍ w,yo0Fɕی7n qTòM/ʬ^W 4r3.3;wwqY~oU$ fؾxJYkH*\OlN(}H(MZ<Fq'9qw*0Xj(~2S!Ԙtwoc+j~g*ʫ3M-P2Hzs ru;a8D!}ւtZk7mh`Kx2o*㳦r3̊R3Wr=۬2pJ8f$xqCk5ͩ=y25BNQPbGUQau 5h uf.6&QQjm Ӽ :yDdhhJ , C A,? "+2O~HhoI+A`!#~HhoI@@||x]ROOQ.&pF9." VLL6PR?H¡|?I>>1{0h>avgffg a0DLfA^ i]B%E4 Ig&< Kh$ ~kY FS$b()PZGRy~ ?Q$FqH7A:Ax Q4IG[353:kaIDU^3-FYIa+yfk>_#CNsq~]$%_*AʎS.Fy?g(ujU6F%hKH 医jxdzn7?Cz9ş&ZB7|v!,K5tŲ-S"dW|W1 6 E AuTyy_3l7y PK4N8PSnΏ˂9e[K\--y5\gDdhhJ . C A.? "-2g} l5x#9EdC:`!;} l5x#9Ed@ @| xڝSkA~o66Vbۖz6k dmI MJ,Db@"wBO#ă7AB)4(;3{̼o7owT1D(áD x+h]RdEV t7$ y15!lk?(X* El( '0NŌ$^\zF6B=X1Aȟ~ .*AݳrE kLY54}C~ P"և0ʊ)`m‡%1F2KxԪC/KU,wܜB7ZӪWNqUJ)uTcJ ϓRs.!+VLERfO/ڃU }ձJGSw-m8 =5 =Y_杼c[z) ($ H'MTl[QEm2d/ɃCj仺5=5z~ Y9=fNkɏAT Dd|J / C A/? ".2\co)T8?`!0co)T ` 0xڥSAkA6nZ{(Ex tl`R p 9R,(F$fBwh%-/#Kn^2L:X߳Leޱ{ePO(iOHtY}*ZYVwQA8}>ul@mV 7hϵC,E'5ecK*8^k<琱+^y/bSh ..򩤘>4mo5ڹb8>[^RrS^m-=lv ZJ=Ȧ.V|Rikudj#<=,b3)۵2v۵M'.#,ikN8Q-_0ܲ qHzԠj5ds^UXR)w`"4#'=(QXkJ?t5:# sJ;Qos[C#5xӝДC,DdhJ 0 C A0? "/2U+|Ӛ&K19`!)+|Ӛ&KT @F|xڕRAkQmM`7V BC6HOB d#IltIhɊ `<,ū*ɟAyzy߼vˀCe X,]I,+Ҽkѕ%kXd^ۜ`lC#?hMke':+$פQv4)=|z/'22.Vˏ# Rv/v=UA{?lQU iŷxE%؜.&U<5-~ʥ Rɕe*JjhmVvnw+u#?܍Fț{ɝfp؉~LU! oVp}7~s r0rr3Or#UOA=z\;G, ^,q–Y^Yu*Z"UTb?OU-uһ#=|bs:G=Sg)%vL:9DdXTJ 1 C A1? "0215}jtN ,`!5}jtNp XJxڝRJQΝLօ(5BtpL&024.i;@~$,@K " | @ʬ{gR$3wϹ0h@*"DSMFQѯK{4zddkGn4J 5ۻ>('R;ŬB2fT-z_xU\+ְ` 1~;J\9)BΟ&eoay8r8>Hrڕ2Z8g#=l!_|PZ(}>7KjizW/ud,_Lͺ1 ^E Lcݵ3؟0,v0t\L##Mݍ2l7رݬkq$Xx]jPh8=27Lط4a`C6IRѹ}-M"#9mj*boDd J 2 C A2? "12F<y"`!<y@-8xڭUoh[U?缼M&ռZ֙" +f~mi'SRS0(EaW? ”"Ԡs晉N_{s{Ͻ@y mT% ourB`@]8fYg|n?`{a,Ng9CC#6A u\QsB@, P:Ȋ9ϧJXP LC+a?a{V"ׁ]Q(/,gF>dcqW 2NWl"bmE*M`*(j=->9 LPu4Nj+:99Gr9/jjx9u<sXqQ˛;cM4 |)Vd!8@L(ZtOGz3p\WsfЛq4ȧt* .ۛEq6{w༴M巽fٹCvS?iPDdJ 6 C A5? "22dV(Aw؜xߞ`!dV(Aw؜x `\dTxڥSkA~nlIQԂ)6Y-h$Kꢁ$s2Br"=z'?ȞN̷o޼LS9t6B!CAa\ږc47Y`-o:']**Yyо|aV^>o )gߏJ$}Th䣳4@$~&_|?! l'i^P84>4mg&ƫ46C3)̀OR&ѴTjU,])*N#~iů*v޽t[%]/ˆɕDϽI3;q$x9=qCBrەZZ+ravstUut[2l R,WFVvwDEIzɩղYaL]zE3FfۑÌMp-[-2rYBqy10ʟ >@|@C^MJ|V 93M?Fٳ.{n ^l [guFө/CEb}ɠTwJDd|J 4 C A4? "32ٝP;I<ڼ㤍/`!ٝP;I<ڼ㤍 `(NxڭV]hU>gmf6n66mmaRkj$I64 jC5%ւ/VAODE(Bm,Xʚv=Iv53sf3@%l'B؈b(>Rk|T puPxhs/d؋})(Dﲬ'B[i3? m[xXP-{A*<*٪C ,?0||AmXGXPkb+?\iS%2}Y.9 ]sVW.Nxs+}E)šK&xA*u+;+eG|~'ת؏4,i;cӭlj4.q~gcCHNZyL04' :ߢnA"ևDظ=߿|CDH I SxC{]7[\%uqY\1MA4%ᴍDdtJ 9 C A8? "526>ĜZCn(`!6>ĜZCn|   dxڥTkA3o7m7$Ecm+FS0hR^Ҩ& )xTcOz.'{1F=v~0%8D ~A^K. Zt,B/Sgc! /I|N),[7 U `X:!5z]QD&BA<}w=#"p<~(`QO6K~X2%'w$-4 ^D/6/o1)ȸhnM)B'B*TV3zjG/իznߐ*v;' \ 3|Āㅸs9b}Cl3~Cuօ˱!'8/eZoƀY{ZKG;իhϓe[\SԴ=Bt$_,)VjBY_rVhaTфdvb5rykhNQI?4f̜ -/4NۇBP(䩛㥬u440T)mcBP8l042O7Q =z\{g`s.AG6\?;v=÷vv6h} 9>ew-+CYbAG箭Dd`J ; C A9? "62?C o1R,,`!?C o1R,,X `\xڭTMhA~of6M`Fj1PB6iVIIҨSH " Sz"U/{ 9y͛g){fv6iEv}~fv<|a 0HFZBxXzc =!B\~CK:4 iLAfr՛ڂ)`gf?^~!Q=IźFOpPf̓`:gp%$sX!),@F $3oshW\<϶F B2 `7R܏M3=73e)5 !sF £`Tx]XT9nt L"| c<3 1j<ʂǤ>No nNuRiԚN凭ދ B <&{`Po@^5 +pW6zb[=uW,7[IUG&vKKη$8^s9-jK!ZsP%(t0iPl̉`E wI;ܓ=<"TUÆKR;o*YkD04f֢si m͟ DdhJ = C A;? "82mD6ѱUQ Iu`!AD6ѱUQ * @ |xڝSoP9ƍ TFPv7Рb4.X)q$(D%$VnL"ub_ČދhQ}!h8\: ,PYB㼄(غ~DC+r9 (' /? QC<`Or|؋,kLS~&yʟ΃wK@–b~t^IUޡϥjғS_)YS/"aDdH|J > C A<? "92<4$8~`!4$8~@`"0xڥSkQnڦ PЊ6Y̡`R2N2,e2~ö;v٤*߽@Au~B"WZd],NsRNtS W-?Ļq=ۨVۡIwLwNdn¢aaO{2azEG? M1EQTLƚY#Tnmp↮_;HYoz>i=X\]x,E%kNN:OG~rkZ]_ovwJAտtOOO3%ɧKQ#5S`3(4.yvۉ #(I7peo+[ e9Fx $xb}Du9<|azjxƒu(n5Sџur[.{8ukyK~d$?BJf MؘDd,J E C A? ";2Bz2O &Qe`!Bz2O &QxڝRJQ=sHQQBXY&)\W]4l"q+? 6~`iN0νYs9s,l Ђ NK'AF=FQ,&=dMUIa)8fW|B!!JKFU=Jq4Q2dD8+un^Y'җx#d:5ƾ\7X{Y?d-З"Hp?}нj8M\Aq0UQAT8ʁƪ{M'Ŝ|Kʹ?R41??nDd J F C AA? "=2BWnC;SS>';ܦξ FY1*"cgm b7+ RzjY|T.@c&ٕҧV   ӿFR7B^2 [01)H ʯ<:O`! [01)H ʯ<: 81hxڝTkA~ovS4M4 D/Bi-b$!ꢁ)k.,H=EP<뭢z*ɿC^w(.LJ .ھrnW}ݹQ̿ۥA58q05D- ^&J:WJ],d8 *3Dk|ul+r[} /? QC<`Or|؋,kLS~&yʟ΃wK@–b~t^IUޡϥjғS_)YS/"a Dd|J I C AD? "@2k˄\VIgEBG`!?˄\VIgEB` `.0 xڥSkAff&]ٍ1h,A+5mX`REF򣛜EoR{V x`|3-ZQyvc! "L{Wؙ[ 0ɻtB3Ee,oKB2QGЧy\yĮ#_'u.]owAv~w2H* L ZFa, Ccs8gJNl3xk0:8N6GV$>}'{_S'vXUFI Z#?~aPh؉x%SںRrRx:κ?hJA M;+✲Rooj YRϻaߧO\XuU*mT?G@򢜮{VImSWxr5oxeϕX&V0N¨V]oF5³ 1d"žG)K8Q@h)(PaSIzsrm2]H֟ӹDdh|J J C AE? "A2auU^6YN=`!5uU^6YN@ `0xڥSkAlb6e7Ġ7 d`d1)7kh ٔ蚓5 B*^*$x"{\LvVTξ73{of9@DdyX+t&-t^^tDM_ft鄁"b9qu`W,&hzt.9贈A+2*VNs g}T㇥(|Cq_f#.} E,h?R3;sGLrF0M9^̈́ɷbAX:gwⵀr}\*!jM=5vtsr{/i/9fral_-V[x $B> iiK)PgDq˵/1^1,Dvt1L.̎܍h<5֏7Xknõ#YF$X!ĵjPAO6TF]#"*eҰ QfkO ~|n+L,(@-w5{)wT0Dd@ |J K C AF? "B2e?P]X9B}n`!fe?P]X9B}t`04xڥSkAlRɦ4P؞@I#I"khIAG^<*s'*{PkUü}߼vyoBvCdD"1F=[DqQ&09D d0k80D(V{{hkjOHtV8x%}3j'9)%ucwwuko^:w,n@"zX4iO=M@Jfch$#=G\'?NA83搖L&0!|8E'W.!tL^$JF %6,N7K6C't#g 7EY]OAy|X^Mݫnڲժim-ăG3k\ӬMxXNB??oU1̯.2p \arR le++ JRp4bQⲐ!WsX r ",,;;LH'nL!Ν9;նqA7`T2ᶺ=uuSmk\7vŸޗ?7DdTJ L C AG? "C2X*Q9#FKZlv42`!,*Q9#FKZlv FXJxڝSϋPmՃ(ZznWm{l!A v鏍9YdO[+xڳ='&X罤WEt|3o2ߛB> ):/A"T:,.' bl,1r,s`;/yU -Q94VʒD'y2I) ,um}22Wkɝ耒czMr_nR/ڌr?? !=h7|!s7zHr5^agJTY\,msS']~Zo6ZAKwv[Xz--=z~;MXF<}UgR_l˅OmN|9{|M/{Dyo09f`WAUl=uW<OlK"ˋˌ.(b.y_1~!u閒· +y.mD]'f39>&)Spb`3?8n4Ld"|(@q 4Ϩ\_m sv[ޓ,۷xV,P<;/F/c}sS8BިljZQ2nt^2NzE p务f s~5MjyK_)i"k`e VwHfR K{YJ)]XT509c1Zq 2qQhDtOLGE s#^#GLGLȖ(wJNvO?.7Hb#ph5+_aX_) fDdhJ O C AJ? "G2ܙg]H9kI<8/w`!ܙg]H9kI<8/@@-|jxڥToQb %Tx%)-D(S~ISFO'4=X40w/cSqރڴfogvxn@@؆<.bz=.9y^ G|'Y߲ܜ~pAb^LU-DGg-h&U%PϗV5|jU{e7?.Ag /k#}D-ڡ39A(!0Zdžs] ɞkoUќa3W'roX2.%GڢvAt56Yhlkl se xZ^-VK*w,xת";6x׀kR_-Yf=gVDNLRHϜf|̗#oNvƞ*,mahAj.dlKG$JpW=1Ohs0"\hP8 \b` 7f{خ>+u4YZ\no].]9>bri1;;9P[Ss3f;"4\y,F^.]]2b|uzOҵN؂d KU@Q[T->X [bWIg/Q(bVZ^þ>6Ps$+e'YSCgRU3JN~9QY#e3ڋ99ɻvʘ-mI`xu>KQe/Abå XY_u ÓxyFTڈC&"6Xx4,jE0\`eeXp."@=WžEw@GܕNfxK@U'Ddh|J T C AM? "I2auU^6YN=a`!5uU^6YN@ `0xڥSkAlb6e7Ġ7 d`d1)7kh ٔ蚓5 B*^*$x"{\LvVTξ73{of9@DdyX+t&-t^^tDM_ft鄁"b9qu`W,&hzt.9贈A+2*VNs g}T㇥(|Cq_f#.} E,h?R3;sGLrF0M9^̈́ɷbAX:gwⵀr}\*!jM=5vtsr{/i/9fral_-V[x $B> iiK)PgDq˵/1^1,Dvt1L.̎܍h<5֏7Xknõ#YF$X!ĵjPAO6TF]#"*eҰ QfkO ~|n+L,(@-w5{)wTDd,J U C AN? "J2F4Z;RK_z` "``!4Z;RK_z` xڝSkAm7XXCZOBd#I񸬺h i&d! ŻWowO^={QdnMU}ޏ}߼7 0 te: bWhb-2xLU2k ]N| yVh@YWYPB'g%] xAZ v7o^7rWp&/᪭|*QV}4ڻ6iƌ:r?? j@IN|tBv:#YS2jଶR՛5lDZ~D>JKFU=Jq4Q2dD8+un^Y'җx#d:5ƾ\7X{Y?d-З"Hp?}нj8M\Aq0UQAT8ʁƪ{M'Ŝ|Kʹ?R41??QDyK 7http://www.research.att.com/~njas/sequences/index.htmlyK nhttp://www.research.att.com/~njas/sequences/index.htmlDdJ V C AO? "K2MT[Ce[WM@)`!!T[Ce[WM@f`:hxڕRAkALbmd7FB(CAkc&- &ŋh ۔d%$O=xU=)37oGX[rC+~!41NkuVȫ+V}Tu`й[ pR~}%FSzlk+ޣ gּI}m&}wNb|vxɹd3r&^o%ld}/Qk_AB934VxpKရYU*Ou)Zdj`Amq?+Fp Rg{DdhJ W C AP? "L2qH^#O=-M`!EH^#O=-4 @(|xڝSkQyoM`7VJXh6xmXl񸬺h Ԝ,"xGJ^UЃ+ gfCY>v޼ٙ7! #C"d2QhLmyDU ,i$o"Ro.?*@﹣8`tJD0'*3TJ鶻t=.w~m'.FEZPBl{hB{b_0fȒxeL|Ȧ3bU+Ӭ $ e|+6{oꇜgFeo4Qi\CV1ǫelZNw!3iEuo;U?ӂ6;I8qa,'2|=iÂȎG4jvmFce~IZg2A|IPUչ8OizBsPn^Jn1=iO Q`L@(?*bF10E/drp_ pQc5% "ҷ>VPպ:z4` >ww_],589Kc׽}cMqxL~%i}a dL#zX9 z%٣ԨF-+!ފ/f3i5b8@oU{'>JpAf}K88 PHj˕vVy[WhmݩFENB^H UVNϟ#|FI1.2!UI1+F, |9]K*~2 #=H:%0\t_=BT> %n)(Ne{[$;!pqH`ߜ6 i#136[FȚ:αz)ӻcFHֵ:v4F{-9;O2DdLJ Y C AR? "N2(~[/v\;.`!(~[/v\;.Ј Xu#dxڵTkQy Z=Dl)VGcҥS B)m{Sɡr-skNm){P;owu!>ƙ NC4`x|C +0$2#_h}|vBySSNa}ѸD=ws!ˑs3\=Q@J÷|B~R[Ǵt[ H$݉PKzδF,b#αdl&;8ɗ9J%7zvMfsf"Xjm9{-KI˗cg3Ǵ.@Βw%hm$%.WKضy{26ojuTo7c/s2yfĘ=΁\ˤ=OHUhէJLi2Yq`TeVE΀K] z$HUqQZ>4&/"kX>o@*2)O\%^4^ [s},s Q $bZ'gw+S  4oE4'4IM=Cv#2,hC͂jtMOa F=":VV% DdJ Z C AS? "O2kNU時]EmG`!?NU時]Em` Pd xڥSkAƦk`7=AWAE!s6YlH0)f70` rxbөBx6NSb!3r. Si+A_UAQm >B/DyQ(GCompObjsuiObjInfovEquation Native _1205755891hyFЂ cЂ cAPAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  1++qx++q 2 x 2 ++"L++q n x n ++"L== 11"-qx FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjxziObjInfo{Equation Native 0M@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  x<< 1q==p FMathType 4.0 Equation MathTy_1205759782~FccOle CompObj}iObjInfope EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  (p"-q)x++(p 2 "-q 2 )x 2 ++"L++p Equation Native ,_1205759809|FccOle CompObjin "-q n ()x n ++"L== 11"-px"- 11"-qx FMathType 4.0 Equation MathType EFEquation.DSMT49qM0@6M6G DSMT4WinAllBasicCodePagesObjInfoEquation Native L_1205759854Fc=cOle Times New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  F n == p n "-q n  5  FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObjiObjInfoEquation Native _1205760069w^F=c=cM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   5  F n FMathType 4.0 Equation MathTyOle CompObjiObjInfoEquation Native pe EFEquation.DSMT49qMm@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   11"-px"- 11"-qx== (p"-q)x1"-px()1"-qx()==  5  x1"-p++q()x++pqx 2 ==  5  x1"-x"-x 2 FMathType 4.0 Equation MathType EFEquation.DSMT49q_1205760115F=c=cOle CompObjiObjInfo    !"#$'*+,-03456789<?@ABEHIJKLMNOPSVWXYZ[\]^_`abehijklorstuvwxz{|}~MM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  p== 1++ 5  2 and q== 1"- 5  2Equation Native i_1206943138F=c=cOle CompObji FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  p"-q== 5  ,p++q==1, ObjInfo Equation Native  5_1206943137F=c=cOle  FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  and pq==CompObjiObjInfoEquation Native  _1205760381F=cc"-1 FMathType 4.0 Equation MathType EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_AOle CompObjiObjInfoEquation Native    x1"-x"-x 2 ==F 0 ++F 1 x++F 2 x 2 ++"L++F n x n ++"L FMathType 4.0 Equation MathType EFEquation.DSMT49q_1205760439FccOle %CompObj&iObjInfo(M"@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  fx()== x1"-x"-x 2 FMathType 4.0 Equation MathTyEquation Native )>_1205760601FccOle .CompObj/ipe EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  gx()== 2"-x1"-x"-x 2 ==2++x++3x 2 ObjInfo1Equation Native 2_1205760950FccOle :++4x 3 ++"L++L n x n ++"L FMathType 4.0 Equation MathType EFEquation.DSMT49qM@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_CompObj;iObjInfo=Equation Native >._1205761320FccAPAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  L n ==p n ++q n FMathType 4.0 Equation MathType EFEquation.DSMT49qM/@6M6G DSMT4WinAllBasicCodePagesOle CCompObjDiObjInfoFEquation Native GKTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  3++0x++2x 2 ++3x 3 ++2x 4 ++5x 5 ++"L++P n x n ++"L== 11"-ux++ 11"-vx++ 11"-wx FMathType 4.0 Equation MathType EFEquation.DSMT49qM%@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A_1205762156FccOle QCompObjRiObjInfoTEquation Native UA_1205762222FicicOle cCompObjdi   11"-ux++ 11"-vx++ 11"-wx== 3"-2u++v++w()x++uv++ww++uw()x 2 1"-u++v++w()x++uv++vw++uw()x 2 "-uvwx 3 == 3"-x 2 1"-x 2 "-x 3 FMathType 4.0 Equation MathType EFEquation.DSMT49qM.@6M6G DSMT4WinAllBasicCodePagesObjInfofEquation Native gJ_1206882096FicicOle mTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   3"-x 2 1"-x 2 "-x 3 FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObjniObjInfopEquation Native q1Table ,@6M6G DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourierPSMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  L n ==F n++1 ++F n"-1  and F n ==5(L n++1 ++L n"-1 )Oh+'0 ( D P \hpxFrom Fibonacci to Foxtrot: rom detemplenaceteete Normal.dotc detempletc17eMicrosoft Word 9.0o@_@6)@c 0     !"hgńh~D2Fһ-"~/-صz39s Ze4xSe)91}S'MjpLi`AscyFuԼn`},,k& )VZ]ݩFc+J0A65_VdS~v+U @š7)ȶnns-"/M|FUċVhM^o3pWEq rH< P4%2PG|(y vTy[n*6H{bÂb_+ buMe;1Po/wDd J [ C AT? "P2 n]`! n]  L"dxڵTAoQy[a!aĤH%I)6 (Սb`NMИjzФwzQc8owa Cix 37'D8.-h!d~@s9,B( : |. RQD8iS< L>9973w"?,7ߠ|6VnZ{ipLl:4koFws-V Lqrw{ 1ѴEg3f YhdV vn͟qZ^9KSݩUF U-0[߲%}H۾gǴdTY/qmKwΖs:?±5z8B%e7[e-^5[z6+W+XJzYgsJ\guųQg]Z"AOWzIҗzЬl@|,t{He@FB )̋r׋0twm> ]܇,Tٰ6}W?B)]mAL׺!7"Ms!mz 3{D ڄrFSlYtÎ ?$,DdJ \ C AU? "Q2~v6+``}Gj'`!b~v6+``}G8@0= 0xڕSA@~o&XHjA(ZE=t]$풴 "P-n[i{х/7o*FBif\q6i+rBEB+B Sqgb{U:oPeV;0i{;]0JC9\7juCpbem aCƥfr>Y {GQ TdW7OPĨ;-D<7)4 'YvuXVLm8V7:CR_Ta>Iykj ZuG ~~՝Wj`NǹOnp),$D26/68FqR$}d= 4.k?bƎ? 2p&NԼj3^-taD!ܖU:*\ՙY>JBmme7f|v/ DdJ ] C AV? "R2kNU時]EmGS`!?NU時]Em` Pd xڥSkAƦk`7=AWAE!s6YlH0)f70` rxbөBx6NSb!3r. Si+A_UAQm >B/DyQ(Ghgńh~D2Fһ-"~/-صz39s Ze4xSe)91}S'MjpLi`AscyFuԼn`},,k& )VZ]ݩFc+J0A65_VdS~v+U @š7)ȶnns-"/M|FUċVhM^o3pWEq rH< P4%2PG|(y vTy[n*6H{bÂb_+ buMe;1Po/w%Dd4J ^ C AW? "S2PpW̩ ɻ 0uy=An`nbpU7 'bqX *袕K.T|+u+u+q1Or[9t2i#L<&B6" !٠`Аx)J0ePjPt8W+QzYWD:i;\!O*Ji?U+4E?9e<߹l^`ݤFҴMi-/:φ}\2l~ WҠnev]؇ܐ`&KlOZg`qa/?;6 . QKF`7'UIx8c@x;7FcX̺50j̺Ùxl&l}W8 exܻ։r e_\$FT" do_d,+5L01U0Ao>Hofke #||z0 C\(fKAbH\]4vi={XE}Y&5WFe8L_5n˙,wOs$v_&`Prr+g-M7`.ԉi)X 0#\hzBJ޶&*po*¨ȎJlۼsO%銧ߝ7*Lx4q2D}K]#V٩Cv8vmvv%T&=+؉|pmtJoXUCd@HŅ< @d}j$vD#$N}"G(TK= fi3C 1%K@F L8meQ?6gbuƹj2\A^SQsuUvSZ!\֎պ zPeXP{6fjEM4k1?e>"Dd0J ` C AY? "U23iwc_Bot`$`!X3iwc_Botkh&xڕSMkQ=MI  h,EVJqc`R LG;H>$IY9ЍC+w\ "UC#wޙs{߻7Y8&`>2F$Abb0,C2p8ny1q.MRK=z}!GofW)S7A:.~݈!';}ZH{Uo8lbvkVh៨,oIaUu~5nT-]!g CiWCm:v$iXɩ>k0?ɕUPjڰku]}mx%wk#iNNniƮlsUZ2b%i8k^n.Vc~^BFnuʭ2_o0NĉOA_e#*QTQ6/Ww心p?jlG +u͗WoQ e;S 0BӥIDdJ b C AZ? "V2z5:[ VF`!N5:[ '=`\xڥV_h[Usm?I[;LV֘ku +i`FDEYoID V|06%0dE R NswYͺK{|;s.BIHhjȪժ״3˯P/i[ULD%χdezu@2|2]8n4Пb'؄zI)Ygkm<f~? L1faV&pER/xrD F^  h\]`VջxHVW C=MQm'!kuuM{ WSAmV5nH`+&aGϐyOmo{4pǾ6'_z\=MƵR&Pù<}V_.}[UOmMtV)#uJrBh$5>X3plmȰMHFeUUޓkKڊB>{]DRU4XnWh;Z=6K xY|!]P*{} <c-/'#+?oӝNFenc/$^ۖa=_-:/BOKKT[X J!a] *h{5Z%OĬX,Vj}8R_p$VZxDgfYgcy3=LdviZ*Ӗ[qָ[2V gg tɴ?//f\ό&VG㩊b&Gz;De:!D@HeUX&R2әD J{ ĊWnT1{9]ܲBo ba0ώ" h#5b8}PE\dcq!,a,{LgK|hU%ĨxM·Pƿ^Vljnٺٶ{G\nfKZ^ozRZ@NDd J c C A[? "W2J>{obp8&^`!>{obp8@8xڥTMLQy[[h%@#MXF4p0mZB[şLxIOAo&^M4H'5y4Dyu|;}]"t!1D!kZ&l_7s|l\5Hߣ@/x0 AxRn;N1 g&4VoDl?ڨÒn e=~Yh_ ,?Ӵ^aM/bGm|*) pEjb?{QǷ:95,5g&ʲv=UvdG'R+3r6~&;h-8$s#.Cr>YX3oWdIuxak_ :27sYvpU8B rrvej>7-CZHn_4:_T%T"}0xXfg'rh%'s 6 E+K E}!Hrذ4TjFK6ϝ%|RDDRInzi}0I@2q4Ň$d4Hқ ^޺9~G " {VGg&3Fa1B|̧[?:cO2ToH~"\3m7{bwcC4I{_j? 6CnQmDd|J h C A_? "X2MBd~p8քF`!MBd~p8ք@ `0qxڕSkQy$R`EZi/Bi-h4RUIO9-=I J/zOD=O OF|TkZ!Uǿ W]V)Ak ~M3\W4-/iʞ~O#9&o/FzrF|^EfzѨgUӹ`NLKusq3"|3eΘ2CXtPheIo,÷:6 ŲDd@J l C A`? "Y29]- >V"`! ]- >V* xڕRMo@}vu#ićPz X@ERq X)_MBNQ!n@r0qZ)*֞Ѽ%G +ŦDj6it.%U(:l\Ly9lSBrդ*r8xQu# ]VtA=RqtPpVwFCQK< d8cخ3&3a,x2 =y4$,QiaW,뿦K>w`%>tRrR\?nfs77;(G}dS3fZQKyksٽ;2gSx--Zùzwo-3nTFAԒiꯔYhODdlJ e C A]? "Z2&1pHZ궃%`!1pHZ궃'xڭUMRQ~9^QA3 XCq%he-՚K NuU0A+ZDЮZh5ljQ? h5YqW99Cǔ<_y{<$l|H8)!" HE87cOS=0 ]ËseL{]FrMc`ޔjßѫOSq8T&go^jMi]R6.7j:m~©,Cz:{ޥjS@?}*dڣ4 TAg\59"m` GTM1JGN^U^t883#=Gfh5bn)sZ3M9kڵu،_ڼg,Wc~c:or s^\q.n4+z|wv`ƽ"T!W<וj=\iU%kJr]i, \fFd)ٸլ*|dIL̇ӝT8׼ D穓yZgIJ+ZGX^AX(Ji76@hur{^w}0AoƠh1;͝KXgΈ4EEjVߪxQVF +o+sU?_^@Pj%F4;xNmpDdlJ f C A^? "[2y'' D}I VzSN)`!y'' D}I VzS wtxڭTMkQILI16 t0L4֩ CHfPP,B vIʅq%2+IҘ>ܹs9@| 5vΘm[yvڍMr//K5Xdl!b_U @(wt̑UT:*FH=$PެlT+;y@$T̘VM{=6?8fcǟ$"qSEU'_=1z*5wrF6'a1cK|RG*8h/Dz%>,qk2j>5I}'o|`=;b`:-\QkrUYK5nma߰p}fEoVhh702􂖳B+%-'X].! S4t3\iVhst)cO zda8<4q($n I| {KEz3& ^t1*ޙ T˛^'2[}(Dd(lJ m C Aa? "\2L޴*$b_3f,`!^L޴*$b_3@ H1,xڵVMhSA}I@*"-JHkx $mc %ӨFDj_`P =D/DhzһxVHz8'i%uf͛oٿG% 67vJ&Z.ChY ](4۠:oC/ #c)Q,<R+ԲEsB=^\M\dy;D؝B^|@FAt\y_bJDfKxճQ~BiEVuթ)C%3{45>$P?C@65|,i k_Ȓ3fcaQ&TIzF`#pHw3جBdVƬӡ0⑭Z jFh>`*\~MRYlTdhSV[yJ0S`hM!@KzV0_3d(M_ꚳ} &,֞x!?5h3v wDd|J n C Ab? "]2T !v$ZC 00`!( !v$ZC `e 0xڥSAkQ4nZ+HC=4hD<6Y!xܮu@IH5^Г㼷t}3|3rvFdXQHsnķ(}y'%Ef,']y4t{*KN]\XW.jwz0{~#tņ]#>88;D/;3;s?XH>bWxV)|銸Ȥa&w{bŎf8[7άZhЎw(#fhq'mٯ-Y0B!sςS/`rQЛs8X3WVd<FD7ٶ2kr9ц͔gח; 9fx $X>5^ 9 6WE*# E4e:=˖Pf,duhݝAOZr:RД;_V'DdlJ o C Ac? "^2yڿg4XRXe3`!]yڿg4XRX)p@+xڵUKkSA>3s4%G1}E[hCb)4m&e5`ҴF "X;Ep!((Bb_҅Pg+IZlqÜ99s.fFNfN Q%B+, UB5~fm(- cbD  T"Ʌb ?q?'ƃ(SPzҭ,IMO p*с/(4x:*O{.{)?`W#@+^q\cXm#Gt*˿A;ru.6x}k֙8"W"IO9G՛8fma9ay,+;g8Cq:kճXĢUx%\" 2pX){98s^~ypmOt%*KG ǚYc9v,ݰvH'$.'l[1LÏxumjumffcSH܏UR:d&T49*Ͱ=&6ޙ0_O1 !;*O r6B%RH I>C`bZ*˚qoOLL%B3k C?rځ"bAe_0Tؓ!ߧ {o7i4.s> p6vJHU"RHiUu]Th_tP eW'9Z`0QރMHLKZأuBzG_Y}/a~P0&K栘@őnovv , `#|MZ4Muw7_aOxu>52}Sc?NN|j/ʻIS~{h%?*N&/'PHc->I`ņB0 K՘3S~'4Dr_J"-lXg;#5۸csA2qH FE"AP5vuKԠ硱&YȔd8 ͻv qyޛE_R隥RLZ M25TW<&GF!4DdJ q C Ae? "`2a$^]t0r<`!ja$^]t0L  d8xڭTkA~mM$IC!MGŲ_(SR,8>kyXc(Ƅ_j_t gth1vd8|GS%7BRtZ00E̓SN$h`?!W1!yzq0skZNyqk=䚎:M[C:Rma ,_VK%V۹O'-*Eoi3J%KbW5{K-֚]+dY#7փ\ dt~ϊ|dsOPƅ+D!t 77YT5ʈẴLv:'Pzl}mT Aٝ&I_X sDdLhJ v C Af? "a2ԜOrz-i(@`!ԜOrz-i(T@Xu#|wxڝToA 6ilI4 5ÕM rQ>0S?LL0ibBhLM`;dhIqv切47;lp\̨" k)s(=u9d7]/ܔ倴|k?Q b_r"=$Lsh~+"& \6|wՖ^T{UO &C8qe1YBy l$h16O·A|A)էTp Xp<ssQn?DTXǵV]6LL0ʔ0b*LRqrw~#fە2ssBRٝ1/}yaج ؑѷHoϦs@륪\.(XfGj< {+9V{V/L*B*ph,@, Header  !&)@!& Page Number>V@1> FollowedHyperlink >*B* phBOBB textdd[$\$CJOJPJQJ^JaJJRJ citationdd[$\$CJOJPJQJ^JaJ6@b6 Footnote TextCJaJ8&@q8 Footnote ReferenceH*W=     =t !z!z!z!z!z!z!z!z! z! z! z( !W(!-%1Y8=\p 0 WXY#%(GM 'D" !-!!!O$*%G%j%%%&&)))*+?+h++,,!-?---./$/r/(0F000%1Y126679999 ::4;5;<= = ==0000000 0 000000000000000000000000000000000000000000000000000000000000000000000000000000000  t"D&C)-/m1)48<A"%&'()*+-./01345679-6A#,28A$ #%,.Phj   . F H    " : < ~ 2 J L R j l 7OQWoq'?AwBZ\k;SU8PRbz|-/46[su{VnpQikD\^46Skm !(!*!+"C"E"T"l"n"%#=#?#Y#q#s####d$|$~$$$$+%C%E%k%%%% &&1&I&K&&&&e'''*2*4*d*|*~****+++!+9+;+h+++++++++,,,I,a,c,,,,"-:-<-T-l-n-x---------%.=.?.// /U/m/o/)0A0C0000000%3g3o33N4`4444#5z5566699 :;::::;2;=:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::X::::::::::::::::::::::XXXX:XXX !!l,b$!t48,- 6 ,D%t@8(    C AC:\Documents and Settings\detemple.MATH.000\My Documents\Foxtrot cartooons\Fib & Perrin.gifB S  ?#=Q! 4 ;Bzln5 6 T U !!!!!!!!m&n&&&**V+X+4,;,,,//////2222223$333S4U455*63678`8b8889'999::::5;[;d;e;p;r;{;;;;;;;;;;;5<:<;<O<Q<V<<<<=x~ ns5 < !!&&**+ +++?-D-$/&/1#166 :::5;<=::::::::::::::::::::::detemplerC:\Documents and Settings\detemple.MATH.000\My Documents\Math papers\Foxtrot and RR\From Fibonacci to FoxtrotB.docdetemplerC:\Documents and Settings\detemple.MATH.000\My Documents\Math papers\Foxtrot and RR\From Fibonacci to FoxtrotB.docdetempleC:\Documents and Settings\detemple.MATH.000\Application Data\Microsoft\Word\AutoRecovery save of From Fibonacci to FoxtrotB.asddetempleC:\Documents and Settings\detemple.MATH.000\Application Data\Microsoft\Word\AutoRecovery save of From Fibonacci to FoxtrotB.asddetempleC:\Documents and Settings\detemple.MATH.000\Application Data\Microsoft\Word\AutoRecovery save of From Fibonacci to FoxtrotB.asddetemplerC:\Documents and Settings\detemple.MATH.000\My Documents\Math papers\Foxtrot and RR\From Fibonacci to FoxtrotB.docdetemplerC:\Documents and Settings\detemple.MATH.000\My Documents\Math papers\Foxtrot and RR\From Fibonacci to FoxtrotB.docdetemplerC:\Documents and Settings\detemple.MATH.000\My Documents\Math papers\Foxtrot and RR\From Fibonacci to FoxtrotB.docdetemplerC:\Documents and Settings\detemple.MATH.000\My Documents\Math papers\Foxtrot and RR\From Fibonacci to FoxtrotB.docdetempleC:\Documents and Settings\detemple.MATH.000\Application Data\Microsoft\Word\AutoRecovery save of From Fibonacci to FoxtrotB.asdAWþh ^`OJQJo(h ^`OJQJo(oh   ^ `OJQJo(h YY^Y`OJQJo(h ))^)`OJQJo(oh ^`OJQJo(h ^`OJQJo(h ^`OJQJo(oh ii^i`OJQJo(AW         @W,=@UnknownGz Times New Roman5Symbol3& z Arial7&  VerdanaI& ??Arial Unicode MS?5 z Courier New;Wingdings"phf|0 g !>0;4;-2QFrom Fibonacci to Foxtrot: detempledetemple