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( HOF/ 0|DArialnd Romantt0 0"DTahomad Romantt0 0" DWingdingsRomantt0 00DTimes New Romantt0 0@DGaramond Romantt0 0 A . @n?" dd@  @@`` "` (()      **//..HH,,     ** "#$("3 4&567$879#:$;LM ,R$1sP c $0e0e     R A@ֆ Am 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab N3પPPn((fֆ"Ch@87C8D@K2ʚ;G u8ʚ;g4QdQd= 0@pp <4dddd@x 0t<4BdBd@x 0t0___PPT10 ___PPT9vn0? O  > 6 w  < There are many variations of balanced and semi-balanced binary trees. One of them, which is due to the work of Gaston H. Gonnet published in 1983, is the Internal Path Reduction (IPR) tree. Its height is the same as the AVL tree, but produces a slightly more compact structure. The internal path (IP) is defined as the sum of the path lengths of all nodes measured from the root. On average, the IPR tree produces an internal path of about 10% smaller than the AVL one. In addition, the IPR tree has a tunable parameter that determines the acceptable level of imbalance.2= ֆ = I AVL vs. IPR ֆ  Both are BSTs Both are HB(1) They do not tolerate imbalance and the tree is restored to a proper shape by predefined rotations. IPR rotations are geared towards reducing IP in the tree (IP = path length from Nodei to root i=1 to n ) AVL has attracted much more attention in the literature but IPR is kinda forsaken qFֆ5 qFֆR qFֆc  cRct      Z    S  `   ^ !More Nodes to The Left of X (SRR)@"(" d2ֆֆ! x!  _  a   b   c   d   e  f"Summary of Worst Case Complexities##ֆ #  /N   0` fy`ff3` Mj*333FV*` ffNNt^X` ffNL|>rL` +T3f3f` MMMff3f` Lx[he2` {$$>?" dd@,?nAd@    @ `  n?" dd@   @@``PR    @ ` ` p>>  (      6 " `P  T Click to edit Master title style! !$   0䘏 " `  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     SP   6` #" `^ `` H@___PPT9"@ n*&     6x #" `^   f*   P   6h #" `^ `` H@___PPT9"@ n*$ )n   BN3vd޽h @ ?#" @` +T3f3f80___PPT10. ` Textured C 0 OG(    <l  #" `    T Click to edit Master title style! !  0  " `     W#Click to edit Master subtitle style$ $P  6  #" `^ ``  H@___PPT9"@ n*&    6,!  #" `^    f*   P  6%  #" `^ ``  H@___PPT9"@ n*$ )n  BN3vd޽h @ ?#" @` +T3f3f80___PPT10. `C 0 VN d(  d d 0g"     " T*  0 d 0k" Q ` "H@___PPT9"@ h*"  d d c $ ?  " d 0pp"  0 " RClick to edit Master text styles Second level Third level Fourth level Fifth level!    S  d 6 Nab    B | TDֆm?"0@NNN?N0 P,$@   0B | TDֆm?"0@NNN?N  ,$@   0  | N  R ֆm?"6@ NNN?N aSingle right rotation(2$  ! !|  f<  Rֆm??"6@`NNN?N `  Mbc$  h | BN3vd޽h @ ?"@`O| || || |||||| +T3f3f___PPT10~.05+ KD:'  = @B D' = @BA?%,( < +O%,( < +D,' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*|D' =1:Bhidden*o3>+B#style.visibility<*|%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*|D' =1:Bhidden*o3>+B#style.visibility<*|%(D ' =%(D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.13333 -0.21112 *3>*B ppt_xB ppt_y=0BBAA<* |D' =4@BBBB%()?)?D4' =.7 BBBBB5M 0 0 L 0.13333 -0.21112 *3>*B ppt_xB ppt_y=0BBAA<*|D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.13333 -0.21112 *3>*B ppt_xB ppt_y=0BBAA<*|D' =A@BBBB0B%()?)?D2' =.7 BBBBB3M 0 0 L 0.11667 0.23334 *3>*B ppt_xB ppt_y=0BBAA<*|D' =4@BBBB%()?)?D2' =.7 BBBBB3M 0 0 L 0.11667 0.23334 *3>*B ppt_xB ppt_y=0BBAA<*|D' =A@BBBB0B%()?)?D2' =.7 BBBBB3M 0 0 L 0.11667 0.23334 *3>*B ppt_xB ppt_y=0BBAA<*|D ' =%( D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-s6Bwipe(down)*<3<*|D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-s6Bwipe(down)*<3<*|D6' =A@BBBB0B%()?)?D}' =.E7 BBBBBWM 3.33333E-6 -4.21965E-6 L 0.03333 0.0222 *3>*B ppt_xB ppt_y=@0BBAApBB<B5<<*!|++0+ |0 ++0+|0 ++0+|0 ++0+|0 ++0+!|0 +5A C 0 P(    jZw?IPRCastellar"`pu   `  R ֆm?"6@ NNN?N BD@ Nb > Nab    !2   f  Rֆm??"6@`NNN?N0  MYc   !2   fHĖ  Rֆm??"6@`NNN?N0 @  MXc   !2   f Ö  Rֆm??"6@`NNN?N 0 B  Mbc   !   fT˖  Rֆm??"6@`NNN?N  Mac$    @ Nֆm?"0@NNN?N %   Nֆm?"0@NNN?N   @ Nֆm?"0@NNN?N0_   Nֆm?"0@NNN?N `   0Ж P eDouble right rotation(2C$  2   f0Ֆ  Rֆm??"6@`NNN?N  ^b2,c$c  2   fdږ  Rֆm??"6@`NNN?N   ^b1,c$c  !   fϖ  Rֆm??"6@`NNN?N  Mcc$    Nֆm?"0@NNN?N  @ Nֆm?"0@NNN?N @o !  N  R ֆm?"6@ NNN?N0p* eMore Nodes to The Left of X(2  B  TDֆm?"0@NNN?Np 0,$@  0B @ TDֆm?"0@NNN?NP  ,$D  0B  TDֆm?"0@NNN?Np ,$@  0B  TDֆm?"0@NNN?N ``,$@  0H  0޽h ?o     +T3f3f+ +___PPT10*.05+RD9)'  = @B D(' = @BA?%,( < +O%,( < +D+(' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(D' =A@BBBB0B%()?)?D.' =.7 BBBBB/M 0 0 L 0.225 0.18889 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D.' =.7 BBBBB/M 0 0 L 0.225 0.18889 *3>*B ppt_xB ppt_y=0BBAA<* D' =A@BBBB0B%()?)?D.' =.7 BBBBB/M 0 0 L 0.225 0.18889 *3>*B ppt_xB ppt_y=0BBAA<*D ' =%( D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.09167 -0.37778 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D4' =.7 BBBBB5M 0 0 L 0.09167 -0.37778 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D4' =.7 BBBBB5M 0 0 L 0.09167 -0.37778 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.09167 -0.37778 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.09167 -0.37778 *3>*B ppt_xB ppt_y=0BBAA<*D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D.' =A@BBBB0B%()?)?Du' =.=7 BBBBBOM 0.09167 -0.37778 L 0.06667 -0.20556 *3>*B ppt_xB ppt_y=@0BBAApBBLB[=<*D.' =A@BBBB0B%()?)?Du' =.=7 BBBBBOM 0.09166 -0.37778 L 0.08333 -0.20556 *3>*B ppt_xB ppt_y=@0BBAApBBB[=<*DL ' =%(XD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +d  C 0 { s 0  (    jZw?IPRCastellar"`p  0D ` ]Before Rotation(2ֆ    0 @~  y=2Nc+IPc+2Nb+IPb+Na+IPa+3  > 2C$K$C$K$C$K$C$K$C$K$C$K$C$G$P!C( >   H  ?  P     0@ W  \After Rotation(2ֆ    0   d  HNc+IPc+2Nb+IPb+2Na+IPa+3  I 2C$K$C$K$C$K$C$K$C$K$C$K$C$G$P,C( I c  0H$  : %IP1 > IP2 Nc > Na& 2C(K(C(K(C(K(C(K(&   B    fDֆm?"0@NNN?N H  0޽h ? +T3f3f___PPT10i.05+D='  = @B +  C 0    ( (  ( ( jZw?IPRCastellar"`p= ( <H4  ?GD<4___PPT9 !More Nodes to The Left of X (DRR)*"(" d2"ֆ!  ( 08 ` ]Before Rotation(2ֆ   ( 0`<  G  \After Rotation(2ֆ   ( 0? = %2Nc+IPc+3Nb1+IPb1+3Nb2+IPb2 +Na+IPa+6.&(2C K C K C K C K C K C K C K C K C  &  ( 0XO  `}  &2Nc+IPc+2Nb1+IPb1+2Nb2+IPb2 +2Na+IPa+5.'(2C K C K C K C K C K C K C K C K C  ' c ( 0a  : %IP1 > IP2 Nb > Na& 2C(K(C(K(C(K(C(K(&   B  ( ZDֆm?"0@NNN?Np0 pH ( 0޽h ? +T3f3f___PPT10i.05+D='  = @B +* C 0 ^V@%f(    jZw?IPRCastellar"`p2   `h  R ֆm?"6@ NNN?NJ dMore Nodes to The Right of X    0"j `Single Left Rotation 2C(  !2   fo  Rֆm??"6@`NNN?NP B MYc   !2   fDt  Rֆm??"6@`NNN?N` `  MXc   !   fr  Rֆm??"6@`NNN?N`   Mac$  !    fz  Rֆm??"6@`NNN?N `/1  Mcc$    @ Nֆm?"0@NNN?N U   Nֆm?"0@NNN?N   @ Nֆm?"0@NNN?N E    Nֆm?"0@NNN?N! (  0 #  Nc > NaZ(2c k c k   B # TDֆm?"0@NNN?N@0 p P ,$@   0B $ TDֆm?"0@NNN?Np@ ,$@   0! %  f  Rֆm??"6@`NNN?NP  Mbc$  H  0޽h ?O      +T3f3f___PPT10.05+pDh' = @B D#' = @BA?%,( < +O%,( < +D"' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D0' =%(D ' =%(D' =A@BBBB0B%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.21112 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.21112 *3>*B ppt_xB ppt_y=0BBAA<* D' =A@BBBB0B%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.21112 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D.' =.7 BBBBB/M 0 0 L -0.1 -0.18888 *3>*B ppt_xB ppt_y=0BBAA<* D' =4@BBBB%()?)?D.' =.7 BBBBB/M 0 0 L -0.1 -0.18888 *3>*B ppt_xB ppt_y=0BBAA<* D' =A@BBBB0B%()?)?D.' =.7 BBBBB/M 0 0 L -0.1 -0.18888 *3>*B ppt_xB ppt_y=0BBAA<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =-s6Bwipe(down)*<3<*#D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(down)*<3<*$D$' =A@BBBB0B%()?)?Dk' =.37 BBBBBEM 0.00399 0.01109 L 0 4.04624E-6 *3>*B ppt_xB ppt_y=@0BBAApBBBյ<*%++0+0 ++0+0 ++0+0 ++0+ 0 ++0+%0 +@ C 0 rj`:(    jZw?IPRCastellar"`p  0` t cDouble Right Rotation(2C$  !2   f0  Rֆm??"6@`NNN?N`  MYc   !2   f  Rֆm??"6@`NNN?N0 @  MXc   !2   f  Rֆm??"6@`NNN?N 0 R  Mbc   !   f  Rֆm??"6@`NNN?N0  Mac$     Nֆm?"0@NNN?N 8   @ Nֆm?"0@NNN?NTX    Nֆm?"0@NNN?N 2    f̭  Rֆm??"6@`NNN?N p  ^b2,c$c  2   f  Rֆm??"6@`NNN?N @  ^b1,c$c  !   f䵗  Rֆm??"6@`NNN?N p  Mcc$    Nֆm?"0@NNN?N$  @ Nֆm?"0@NNN?N$ !  N  R ֆm?"6@ NNN?N0p* eMore Nodes to The Left of X(2    Nֆm?"0@NNN?NT B  TDֆm?"0@NNN?NP@ ,$D  0B  TDֆm?"0@NNN?NPp ,$@  0B  TDֆm?"0@NNN?NP` ,$@  0B  TDֆm?"0@NNN?NP ,$@  0!  0Ŀ `] Nb > Na|(2c k c c c k   H  0޽h ?o     +T3f3f'++___PPT10*.05+vlDK)' = @B D)' = @BA?%,( < +O%,( < +D=(' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(D' =A@BBBB0B%()?)?D0' =.7 BBBBB1M 0 0 L -0.175 0.16667 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D0' =.7 BBBBB1M 0 0 L -0.175 0.16667 *3>*B ppt_xB ppt_y=0BBAA<* D' =A@BBBB0B%()?)?D0' =.7 BBBBB1M 0 0 L -0.175 0.16667 *3>*B ppt_xB ppt_y=0BBAA<*D ' =%( D' =4@BBBB%()?)?D6' =.7 BBBBB7M 0 0 L -0.05833 -0.34445 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D6' =.7 BBBBB7M 0 0 L -0.05833 -0.34445 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D6' =.7 BBBBB7M 0 0 L -0.05833 -0.34445 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D6' =.7 BBBBB7M 0 0 L -0.05833 -0.34445 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D6' =.7 BBBBB7M 0 0 L -0.05833 -0.34445 *3>*B ppt_xB ppt_y=0BBAA<* D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D2' =A@BBBB0B%()?)?Dy' =.A7 BBBBBSM -0.05833 -0.34444 L -0.08333 -0.16111 *3>*B ppt_xB ppt_y=@0BBAApBBLB=<* D,' =A@BBBB0B%()?)?Ds' =.;7 BBBBBMM -0.05833 -0.34444 L -0.05 -0.16111 *3>*B ppt_xB ppt_y=@0BBAApBB;B=<*DL ' =%(XD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*++0+0 ++0+0 ++0+0 ++0+ 0 ++0+ 0 ++0+0 ++0+0 +/ C 0   p #\ (    jZw?IPRCastellar"`pJ2   `  Rֆm?"6@ NNN?NP@,$D 0 H11  J2   `  Rֆm?"6@ NNN?N ,$D 0 H17  L2   `  Rֆm?"6@ NNN?N@` ,$D 0 J20     `P N3ֆ>?"6@`NNN?N0 J20  L   `\ N3ֆ>?"6@`NNN?N0,$D 0 J17  L   ` N3ֆ>?"6@`NNN?N0,$D 0 J11   @ Nֆm?"0@NNN?Nj@ u,$D  0 "@ Nֆm?"0@NNN?N,$D  0B # TDֆm?"0@NNN?N ,$D  0H  0޽h ?/@" +T3f3f]#U#___PPT105#.05+DI!'  = @B D!' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-s6Bwipe(down)*<3<*"D' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Dp' =%(D' =A@BBBB0B%()?)?D_' =.'7 BBBBB9M 0 0.01111 L 0.08333 0.15 *3>*B ppt_xB ppt_y=@0BBAApBB*=B8=<*D"' =%( D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.08333 -0.12222 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D4' =.7 BBBBB5M 0 0 L 0.08333 -0.12222 *3>*B ppt_xB ppt_y=0BBAA<*"D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.08333 -0.12222 *3>*B ppt_xB ppt_y=0BBAA<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =-s6Bwipe(down)*<3<*#++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +b C 0 6l(    jZw?IPRCastellar"`p   `\ N3ֆ>?"6@`NNN?N0 J11  2   `  Rֆm?"6@ NNN?N 0 H11  2   `  Rֆm?"6@ NNN?Np0  H17  2   `  Rֆm?"6@ NNN?N  J20   @ Nֆm?"0@NNN?N@h    Nֆm?"0@NNN?Nx I2   `8  Rֆm?"6@ NNN?N `p ,$D  0 G8  J2   `l  Rֆm?"6@ NNN?NP0 ,$D 0 H14  I2   `|#  Rֆm?"6@ NNN?NP`,$D 0 G5   @ Nֆm?"0@NNN?N E,$D  0  Nֆm?"0@NNN?N  E,$D  0  Nֆm?"0@NNN?Nz(  ,$D   0K   `( N3ֆ>?"6@`NNN?N0,$D 0 I5  L   `, N3ֆ>?"6@`NNN?N0,$D 0 J14  K   `0 N3ֆ>?"6@`NNN?N0,$D 0 I8  B ,@ TDֆm?"0@NNN?N p P,$@  0B - TDֆm?"0@NNN?N0 ,$D  0L /  `6 N3ֆ>?"6@`NNN?N0,$D 0 J15  J2 1  ``4  Rֆm?"6@ NNN?N ,$D 0 H16  J2 2  `4=  Rֆm?"6@ NNN?N  p ,$D 0 H15   4 Nֆm?"0@NNN?NJ X P ,$D  0 6 Nֆm?"0@NNN?Nzx  ,$D  0L .  `A N3ֆ>?"6@`NNN?N0,$D 0 J16  H  0޽h ?  21426 +T3f3fFwF___PPT10WF.05+DzDB' Z = @B DB' = @BA?%,( < +O%,( < +D"' =%(%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D#' =%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%()?)?D2' =.7 BBBBB3M 0 0 L 0.09167 0.13333 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D2' =.7 BBBBB3M 0 0 L 0.09167 0.13333 *3>*B ppt_xB ppt_y=0BBAA<* D' =A@BBBB0B%()?)?D2' =.7 BBBBB3M 0 0 L 0.09167 0.13333 *3>*B ppt_xB ppt_y=0BBAA<*D ' =%( D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.01666 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D4' =.7 BBBBB5M 0 0 L 0.01666 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.01666 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D4' =.7 BBBBB5M 0 0 L 0.01666 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D4' =.7 BBBBB5M 0 0 L 0.01666 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-s6Bwipe(down)*<3<*,D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-%(D' =-s6Bwipe(down)*<3<*-D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =-6B%slide(fromBottom)*<3<*/D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6%(D' =-s6Bwipe(down)*<3<*6D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =-6B%slide(fromBottom)*<3<*.D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(down)*<3<*4+H+0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+/0 ++0+10 ++0+20 ++0+.0 +y' C 0 ^V"(    jZw?IPRCastellar"`p    ` t N3ֆ>?"6@`NNN?N P J16    @ Nֆm?"0@NNN?N x E,$@  0  Nֆm?"0@NNN?N: 2   `dy  Rֆm?"6@ NNN?N0 ` H11  2   `}  Rֆm?"6@ NNN?N@  H17  2   `  Rֆm?"6@ NNN?N @ J20    Nֆm?"0@NNN?N 2   `  Rֆm?"6@ NNN?NP G8  2   `  Rֆm?"6@ NNN?NP0  H14  2   `(  Rֆm?"6@ NNN?N G5   @ Nֆm?"0@NNN?N:u  Nֆm?"0@NNN?NXPE2   `  Rֆm?"6@ NNN?N  H16  2   `<  Rֆm?"6@ NNN?N  p  H15    Nֆm?"0@NNN?NJ X P    Nֆm?"0@NNN?Nzx  B "@ TDֆm?"0@NNN?Npp` ,$D   0H  0޽h ?    +T3f3f___PPT10.05+l$`D'  = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(Di' =%(D' =A@BBBB0B%()?)?DX' =. 7 BBBBBYM 3.33333E-6 5.55556E-6 L -0.06667 0.16667 *3>*B ppt_xB ppt_y=0BBAA<*D(' =%( D' =A@BBBB0B%()?)?D6' =.7 BBBBB7M 0 0 L -0.08333 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D6' =.7 BBBBB7M 0 0 L -0.08333 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D6' =.7 BBBBB7M 0 0 L -0.08333 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-s6Bwipe(down)*<3<*"++0+0 ++0+0 ++0+0 +D C 0 #(    jZw?IPRCastellar"`p    `T N3ֆ>?"6@`NNN?N P J16   @ Nֆm?"0@NNN?N x E  Nֆm?"0@NNN?N: 2   `  Rֆm?"6@ NNN?N0 ` H11  2   `  Rֆm?"6@ NNN?N@  H17  2   `h  Rֆm?"6@ NNN?N @ J20    Nֆm?"0@NNN?N 2   `г  Rֆm?"6@ NNN?NP G8  2   `ظ  Rֆm?"6@ NNN?N 0 @  H14  2   `  Rֆm?"6@ NNN?N G5   @ Nֆm?"0@NNN?N:u  Nֆm?"0@NNN?NXPE2   `X  Rֆm?"6@ NNN?N 0 @  H16  2   `Ú  Rֆm?"6@ NNN?NP0  H15    Nֆm?"0@NNN?Nzx p  @ Nֆm?"0@NNN?Nzph B @ TDֆm?"0@NNN?N p P,$@  0B  @ TDֆm?"0@NNN?N0,$D  0B ! TDֆm?"0@NNN?N0P ,$@  0B " TDֆm?"0@NNN?N ,$@  0H  0޽h ?  +T3f3f8/0/___PPT10/.05+ ;D$-' = @B D,' = @BA?%,( < +O%,( < +D,' =%(%(D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D ' =%(D' =A@BBBB0B%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.14444 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.14444 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.14444 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.14444 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D0' =.7 BBBBB1M 0 0 L -0.125 0.14444 *3>*B ppt_xB ppt_y=0BBAA<*D ' =%( D' =A@BBBB0B%()?)?D2' =.7 BBBBB3M 0 0 L -0.075 -0.31111 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D2' =.7 BBBBB3M 0 0 L -0.075 -0.31111 *3>*B ppt_xB ppt_y=0BBAA<*D' =4@BBBB%()?)?D2' =.7 BBBBB3M 0 0 L -0.075 -0.31111 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D2' =.7 BBBBB3M 0 0 L -0.075 -0.31111 *3>*B ppt_xB ppt_y=0BBAA<*D' =A@BBBB0B%()?)?D2' =.7 BBBBB3M 0 0 L -0.075 -0.31111 *3>*B ppt_xB ppt_y=0BBAA<*D' =%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D5' =4@BBBB%(D' =-s6Bwipe(down)*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D.' =A@BBBB0B%()?)?Du' =.=7 BBBBBOM -0.075 -0.31111 L -0.04166 -0.16111 *3>*B ppt_xB ppt_y=@0BBAApBB<B=<*D(' =A@BBBB0B%()?)?Do' =.77 BBBBBIM -0.075 -0.31111 L -0.05 -0.16111 *3>*B ppt_xB ppt_y=@0BBAApBBL<B=<*DL ' =%(XD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =-s6Bwipe(down)*<3<*!D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-s6Bwipe(down)*<3<*"D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(down)*<3<* ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +  C 0  (    jZw?IPRCastellar"`p  H   P `    RB @ s *D) RB  s *D)p  0@ a  NHeight(2    0    hInternal Path Length$(2    0    p<=1.4402 log2n2 2       0@    p<=1.4402 log2n2 2       0  a  q>=1.2793 nlog2n2 2       0,  Q  o 1.0515 nlog2n2 2       0   MAVL(2     08 5I MIPR(2  H  0޽h ? +T3f3f___PPT10i.05+D='  = @B + 0 0h (  hX h C d   " h S X"d 0  " " H h 0޽h ? 3380___PPT10.0zrl60~> a+H H2:FN ^?&9S}I^kt6fj}5w 'B`vAx1Oh+'0$Gx  $ 0 < HT\ IPR TreesFile StructuresZahra Zeinalpour TexturedS. 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