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CSpace division switching   TEach sample takes a different path through the switch, depending on its destination T    DCrossbar   LSimplest possible space-division switch Crosspoints can be turned on or off $M( &(       G!Crossbar - example   H Crossbar   Advantages: simple to implement simple control strict sense non-blocking Drawbacks number of crosspoints, N2 large VLSI space vulnerable to single faults = G =  -&]     2  J$Time-space switching   Precede each input trunk in a crossbar with a TSI Delay samples so that they arrive at the right time for the space division switch s schedule   K%Time-Space: Example    M&Finding the schedule   Build a graph nodes - input links session connects an input and output nodes. Feasible schedule Computing a schedule compute perfect matching.L@'@'   L#Time-space-time (TST) switching   rAllowed to flip samples both on input and output trunk Gives more flexibility => lowers call blocking probability r    N'"Circuit switching - Space division #  graph representation transmitter nodes receiver nodes internal nodes Feasible schedule edge disjoint paths. cost function number of crosspoints internal nodest0%0% &       O(Example    Z4 Clos Network   Q,(Clos Network - strict sense non-blocking )  Holds for k >= 2n-1 Proof: Consider and idle input and output Input box connected to at most n-1 middle layer switches output box connected to at most n-1 middle layer switches There exists a "free" middle switch. Tfffff   R-Proof    [5Example   S*Clos Network - rearrangable&       Holds for k >= n Proof: Consider all input and output find a perfect matching. route the perfect matching remaining network is Clos(N-n,n-1,k-1) summary: smaller circuit weaker guarantee Mulicast ?y ! fy f!f &      ^7ZRearrangable Clos Network  routing algorithm&   !   Start at some arbitrary 2x2 input switch, and route it to its destination through the upper switch. Route the other output port of the 2x2 switch you reached to its input port through the lower switch. If the other port in the input switched you reached has not been routed yet, route it through the upper middle switch. Otherwise, select an arbitrary input port switch that was not yet used, and repeat the procedure.   a;Recursive constructions   _8Algorithm Complexity eN routing steps for each level Log n levels to do ===> N log n Given parallel hardware: O(N) timedf" e `9Alternative View of the problem A graph coloring problem: Input/output switches = nodes A match = link Middle stage switches = colors This is the well known  Coloring of bi-partite graph problem. Heuristics fail miserably!!! b:@Another algorithm  matrix based  Specification matrix: Rows = input switches (nxm) Columns = middle switches (rxr, N/n = r) Content = output switches (0..r-1) We need an algorithms that will fill up the matrix with a feasible routing: Same number cannot appear in the same column Works also for CLOS with redundancyhL-$ L-$8- rDAlgorithm Principle \For j=0,1,2,& balance the destination j among the columns Challenges: efficiency termination We describe an algorithm by Lee, Hwang, and Carpinelli, T.COM. 44 (11), Nov 1996 t, Q, Q  uGThe Matrix Meaning vHThe Matrix Meaning wIThe Matrix Meaning xJIllegal example yK Legal example  zL Notations pCData Structures (j,e), j=0,1,& n-1, e=0,1,& ,r-1 :- the set of rows {i} such that sij=e All the input switches routed to e thru j 0(e), e=0,1,r-1 :- the set of columns {j} such that Si does not contain e All middle switches that are not routing to e 2(e), e=0,1,r-1 :- the set of columns {j} such that Si contains e at least twice All middle switches that have contention routing to e tF*J.Q63 !' ,'  4>@avSsE Algorithm  fInit: e=0 If 2(e) empty ee+1 if e=r stop; else goto 1 if 2(e) j 1st element of 2(e) k 1st element of 0(e) (simple swap) i 1st element of (j,e) if e< sik swap sij with sik e sik remove i from (j,e) and (k,e ) add i to (j,e ) and (k,e) if |(j,e)|=1 remove j from 2(e) if |(j,e )|=1 remove j from 0(e ) if |(j,e )|=2 add j to 2(e ) if |(k,e )|=0 add k to 0(e ) if |(k,e )|=1 remove k from 2(e ) remove k from 0(e) goto step 1  ZnZnZ nZ/nZnZ5Z     ;0i  X(Next Simple Swap) If e> sik i 2nd element of sik repeat step 3 on i if e> si k goto step 5 (Successive Swap) u e; remove k from 0(u) if if |(j,u)|=2 remove j from 2(u) v sik swap sij with sik remove i from (j,u) and (k,v) add i to (j,v) and (k,u) if e<v if |(k,v)|=0 add k to 0(v) if |(k,v)|=1 remove k from 2(v) if |(j,v)|=1 remove j from 0(v) if |(j,v)|=2 add j to 2(v) goto step 1 if e>v uv goto step 5B nZ Z.ZZnZ nZ6nZ nZInZnZnZnZnZ    7 $$((,,,,,,a tFAlgorithm Complexity adding an element to a set, choosing/removing the 1st/2nd element from a set take O(1) steps 5A 5B and 5D each take O(1) time removing a generally positioned element from an r-set takes O(r) time step 5C time complexity is in O(r) [ 2(v)-{k}, 0(v)-{j} ] the looping in step 5 does not contain step 5C, only 5B and 5D the time complexity for step 5 is O(r) Algorithm time complexity O(nr2)A'#3h c<Clos network size Number of switching elements is given by for k=n (rearrangeable non-blocking) Optimal value for n is n=2N, which yieldsL~e } i=3a lower bound for the number of switching elements?3 dAssume we have 2x2 switching units. We have N! switching permutation Can we achieve this bound?d T.'Recursive constructions - Benes Network (  \6 Example 16x16     U/Benes Networks    Size: 2 log N  1 stages N/2 switches in each stage N log2 N  N/2 Rearrangeable Clos network with k=2 n=2 Symmetry Example. proof;    V0Strict Sense non-Blocking   X2Cantor Networks   mm copies of Benes network. For m >= log N its strict sense non-blocking Network size N log2 N Example Proof.:n!9 n  l>Banyan wSelf routing! Size: log2 N stages N/2 switches in each stage 0.5N log2 N elements This is less than the lower bound! c  ,i  m?Banyan  n@ Other Banyans  oA,How do deal with internal blocking in Banyan, dspeed  up internal buffers Batcher bitonic sorter&$ qB/8Z][P{  ` 33̙ff` 3f3f` ___>?" dd@3?nKfd@Eu FA@ " d`  n?" dd@   @@``PR    @ ` `C p>>   G? (    Zgֳgֳ ?P  Y!Click to edit Master title style ""  >  Thgֳgֳ ? @  RClick to edit Master text styles Second Level Third Level Fourth Level Fifth Level!    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V*     Z$jJjJ ? q  X*   H  0 _ g? ? ̙3380___PPT10.u 0(  | H  0 _ g ? ̙3380___PPT10.jwZK0 0$(    3 rlgֳgֳ ?" p<$ 0    3 rXgֳgֳ ?#  @ <$ 0  H  0޽h ? ___u   %  d (  d l d C 7P   | d T1?@ vB d ND1?`@vB d ND1?`@vB d ND1? `@ vB d ND1? `@ vB d ND1?` `@` vB  d ND1?vB  d ND1?vB  d ND1?  vB  d ND1?  vB  d ND1?` ` |B d TD1?@` |B d TD1? @ |B d TD1? @   d  `>1?  }7Number of connections: from few (4 or 8) to huge (100K)88 8  H d 0޽h ? ___  h ( @ H h l h C BP   l h C C @  H h 0޽h ? ___F  p (  p r p S hQP   r p S    |B  TDԔ? @ |B  TDԔ?` @ |B  TD1?  |B  TD1?  |r  T1? ` |B  @ TD1?  |B  TD1? @ |B  TD1? ` H  0޽h ?  ___m    ( \T0\T 6  l  C P   |B  TDԔ?`|B  TDԔ?@`@|B  TDԔ?` `` |B  TDԔ? ` |B  TDԔ?`` |B  TDԔ? |B  TDԔ? |B  TDԔ?    `1? E1     TT1? E2      `1?  E3      `쩱1?P p  E4      ` 1? T E1      ` 1?  E2      `1? `  E3      `1?   E4   |  T1? P|  T1?|  T1? 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Vtime 1       `D1?P~p,$D 0 Jtime 2   H  0޽h ? ___w o ___PPT10O +̈9\D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(+8+0+  +  ` ( EOp  l  C #P   l  C $ @  H  0޽h ? ___F  p (   r  S *P   r  S + @  Z  C 2A A5688-F08-08H  0޽h ? ___   (  DO h  l  C 1P   l  C 2 @  H  0޽h ? ___   =( P P   l  C 9P    8 P   P0` ~B   NDfԔ?P0~B  NDfԔ?P0~B   NDԔ?P ~B  NDfԔ?P@~B   ND3fԔ?P` ~B  NDԔ?P`  ~B   NDfԔ?0P~B  NDԔ? ` ~B  NDԔ?p~B   NDfԔ?0P~B  ND3fԔ? ` ~B   NDfԔ?p xB  B HhDԔ? 0xB  He D3fԔ?0 xB  B HhDfԔ?  xB  He DfԔ? @xB  B HhDԔ? ` xB  He DfԔ?` xB  B HhDԔ? 0xB  HЖDԔ?P` xB  HіDfԔ? xB  B H!iD3fԔ? 0xB  HJDfԔ?P` xB  B HKiDfԔ?P    `@1? @ q-sessions: (1,3) (2,6) (3,1) (4,4) (5,2) (6,5).. .  H  0޽h ? ___  =5,d ( @  r  S GP      `H1?p  g#Clos(N, n , k) N - inputs/outputs; $$ $   -  `L1?`3 Ynxk     . TN1?  _ (N/n)x(N/n)       /  ``V1?V ) Ykxn     0  `Z1? ;  S N=6 n=2 k=2 f    6  `X1?f  S3x3     7  `a1? f  S3x3    o8 p;h  F A   1  Tf1?;c  U2x2 2     4  Tpj1?@ h  U2x2 2     5  THB1?   U2x2 2    ~B 8  ND1?ppp~B 9  ND1?p  T@ p   @ p  ~B :  ND1?p  ~B ;  ND1?p  ~B D  ND1?p  ~B E  ND1?p0 0  H Zs1?n  U2x2 2     I Zx1? `  U2x2 2     J Z{1? `H  U2x2 2    |B K TD1?`|B L TD1?` `` `L p   M #  ` ~B N  ND1?p  ~B O  ND1?p  |B P TD1? ` |B Q TD1? ` d8   X  ~B R  ND1?~B S  ND1?  ~B T ND1?0 P ~B U  ND1? @ ~B V ND1?  ~B W ND1?  rF   Y A ` ~B Z  ND1?~B [  ND1?  ~B \ ND1?0 P ~B ]  ND1? @ ~B ^ ND1?  ~B _ ND1?  H  0޽h ? ___   $(   r  S ĆP   r  S  @  H  0޽h ? ___N   (   r  S dP   |  T1? Pp` B  ZD1? p0 B  ZD1?0 p 0 |2  T1? ` |2  T1?@0 B  ZD1? B  ZD1?  |  T1? @B  ZDԔ? `P B  ZDԔ?pp`p|2  TԔ?p0 0 B  ZDԔ?p B  ZDԔ? H  0޽h ? ___!  3!+!7> 0  ( @  r  S PP      `1?p O Clos(8,2,3)       `1? ;  S N=8 n=2 k=3 f      ``1?f  S4x4       `1? f  S4x4      @ Zh1? r  U3x2 2      @ Z 1?  U3x2 2      @ Z1?% M  U3x2 2    |B  @ TD1? |B  @ TD1?e e `L p    A#   ~B   ND1?p  ~B   ND1?p  |B  @ TD1?  |B  @ TD1?    T1?n  U2x3 2      T̵1? `  U2x3 2      Tܹ1? `H  U2x3 2    vB  ND1?`vB  ND1?` `` `L p    #  ` ~B   ND1?p  ~B   ND1?p  vB  ND1? ` vB  ND1? ` |B  TD1?  |B ! TD1?  |B " TD1?0 P |B # TD1? @ |B $ TD1?  |B % TD1?  |B ' @ TD1? ` |B ( @ TD1? ` |B ) TD1?0 ` |B * @ TD1? ` @ |B + TD1? ` |B , TD1? `  - Tí1?` U2x3 2    vB . ND1?%R%vB / ND1?R 0  `ȭ1?f  S4x4     1 @ Tͭ1? r  U3x2 2    vB 2 @ ND1?% %vB 3 @ ND1? vB 4 ND1?PPB 6 ZD1?PB 7 ZD1? B 8 ZD1? B 9 ZD1?PB : ZD1? ` B ; ZD1?` B < ZD1?` B = ZD1?` B > ZD1?` H  0޽h ? ___   ( c  l  C ֭P   l  C ׭ @  H  0޽h ? ___   $(   r  S ޭP   r  S ߭ @  H  0޽h ? ___  LD&& (   x  c $P   |  T1?P 0 |  T1? P    `1?n  M N/2 x N/2       `1?p x  M N/2 x N/2    F      N    2    T1?pB   ZD1?B    ZD1?pN       2    T1?pB  ZD1?B   ZD1?p    `1?jV  I. . .   B   ZD1?0`B   ZD1? B  ZD1?P B   ZD1?P P ;F    A P  N    2   T1?p~B  ND1?~B   ND1?pN      2   T1?p~B  ND1?~B   ND1?p    ` 1?jV  I. . .   ~B   ND1?0`~B    ND1? ~B ! ND1?P ~B "  ND1?P P  #  `<1?:Z E1    $  `l1?. :yN En    %  `(1?j2 E1    &  `H1? "a En   H  0޽h ? ___   P(   r  S P     S  @<$  0  H  0޽h ? ______PPT10r.+5nqD' = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 2%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 2D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 2D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 2B%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* 2BD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* 2BD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* Cf%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* CfD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* Cf+8+0+  +    P(   r  S P     S   @<$  0  H  0޽h ? ______PPT10x.+D' = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 8D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 8D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8G%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 8GD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 8GD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* Gf%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* GfD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* GfD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* g%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* gD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* gD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +8+0+  +  0 $(   r  S $,P   r  S , @  H  0޽h ? ___  pD $(  D r D S 1P   r D S 2 @  H D 0޽h ? ___U/  /.0LzT .(  T r T S 9P   p   yT  #""  @T   `D1?e"  @ @` >T   `xM1?Qe"  @ @` 8T   `DV1?eQ"  D @` 6T   `H1?e @ @` 4T   `f1?Qe @ @` .T   `(p1?Qe i0  @`  T   `x1?"   i1  @`  T   `1?Q"   @ @`  T   `䉶1?" Q  @ @` T   `D1? @ @` T   `p1?Q @ @` T   `1?Q @ @`xB T  Ho ?rB T  B1 ?xB T  Ho ?  xB T  Ho ? rB T  B1 ?QQ rB !T  B1 ? xB "T  Ho ? rB /T  B1 ?eerB 9T  B1 ?" "  DT  `L1?S  S4x4     ET  `D1? S  S4x4     FT @ T੶1?  U3x2 2     GT @ Th1?   U3x2 2     HT @ T 1?% M  U3x2 2    vB IT @ ND1?RvB JT @ ND1?e Re `L p   KT A#  R ~B LT  ND1?p  ~B MT  ND1?p  vB NT @ ND1? R vB OT @ ND1? R  PT T`1? R  U2x3 2     QT Tp1? D  U2x3 2     RT Tö1? D H  U2x3 2    vB ST ND1? vB TT ND1?`  ` `L p   UT #    ~B VT  ND1?p  ~B WT  ND1?p  vB XT ND1?  vB YT ND1?  vB ZT ND1? R  vB [T ND1? R  vB \T ND1?0 R P vB ]T ND1? R @ vB ^T ND1? R  vB _T ND1? R  vB `T @ ND1?  vB aT @ ND1?  vB bT ND1?0 B vB cT @ ND1? @ vB dT ND1?  vB eT ND1?   fT T8Ͷ1? D  U2x3 2    vB gT ND1?% %vB hT ND1?  iT  `XҶ1?S S4x4     jT @ T׶1? U3x2 2    vB kT @ ND1?%R%vB lT ND1?vB mT ND1?PR PB nT ZD1?R B oT ZD1?R  B pT ZD1?"  B qT ZD1?R B rT ZD1?  B sT ZD1?B tT ZD1?B uT ZD1? B vT ZD1? jB zT BD1?e H T 0޽h ? ___C0  //@MMX /(  X x X c $`P   v   X # #""  X   `1?e"  @ @` X   `;1?Qe"  @ @` X   `1?eQ"  D @` X   `4Z1?e @ @` X   `TI1?Qe @ @`  X   `1?Qe i0  @`  X   `<<1?"   i1  @`  X   `h1?Q"   @ @`  X   `8\?1?" Q  @ @`  X   `H1? @ @` X   `1?Q @ @` X   `1?Q @ @`xB X  Ho ?rB X  B1 ?xB X  Ho ?  xB X  Ho ? rB X  B1 ?QQ rB X  B1 ? xB X  Ho ? rB X  B1 ?eerB X  B1 ?" "  X  `L1?S  S4x4     X  `L1? S  S4x4     X @ TL1?  U3x2 2     X @ T` L1?   U3x2 2     X @ TL1?% M  U3x2 2    vB X @ ND1?RvB X @ ND1?e Re `L p    X A#  R ~B !X  ND1?p  ~B "X  ND1?p  vB #X @ ND1? R vB $X @ ND1? R  %X TL1? R  U2x3 2     &X T&L1? D  U2x3 2     'X T/L1? D H  U2x3 2    vB (X ND1? vB )X ND1?`  ` `L p   *X #    ~B +X  ND1?p  ~B ,X  ND1?p  vB -X ND1?  vB .X ND1?  vB /X ND1? R  vB 0X ND1? R  vB 1X ND1?0 R P vB 2X ND1? R @ vB 3X ND1? R  vB 4X ND1? R  vB 5X @ ND1?  vB 6X @ ND1?  vB 7X ND1?0 B vB 8X @ ND1? @ vB 9X ND1?  vB :X ND1?   ;X T?L1? D  U2x3 2    vB X  `TJL1?S S4x4     ?X @ TRL1? U3x2 2    vB @X @ ND1?%R%vB AX ND1?vB BX ND1?PR PB CX ZD1?R B DX ZD1?R  B EX ZD1?"  B FX ZD1?R B GX ZD1?  B HX ZD1?B IX ZD1?B JX ZD1? B KX ZD1?  LX TL1?"`[  H1 3 4 0 7 5 6 202jB MX BD1?e H X 0޽h ? ___C0  //PMM\ /(  \ x \ c $LP  L v   \ # #""  \   `ЮL1?e"  @ @` \   `1?Qe"  @ @` \   `h1?eQ"  D @` \   `1?e @ @` \   `41?Qe @ @`  \   `?1?Qe i0  @`  \   ` ?1?"   i1  @`  \   `ܾ?1?Q"   @ @`  \   `|?1?" Q  @ @`  \   `/P1? @ @` \   `8P1?Q @ @` \   `1P1?Q @ @`xB \  Ho ?rB \  B1 ?xB \  Ho ?  xB \  Ho ? rB \  B1 ?QQ rB \  B1 ? xB \  Ho ? rB \  B1 ?eerB \  B1 ?" "  \  `4KP1?S  S4x4     \  `UP1? S  S4x4     \ @ T^P1?  U3x2 2     \ @ TgP1?   U3x2 2     \ @ TpP1?% M  U3x2 2    vB \ @ ND1?RvB \ @ ND1?e Re `L p    \ A#  R ~B !\  ND1?p  ~B "\  ND1?p  vB #\ @ ND1? R vB $\ @ ND1? R  %\ T{P1? R  U2x3 2     &\ TP1? D  U2x3 2     '\ ThP1? D H  U2x3 2    vB (\ ND1? vB )\ ND1?`  ` `L p   *\ #    ~B +\  ND1?p  ~B ,\  ND1?p  vB -\ ND1?  vB .\ ND1?  vB /\ ND1? R  vB 0\ ND1? R  vB 1\ ND1?0 R P vB 2\ ND1? R @ vB 3\ ND1? R  vB 4\ ND1? R  vB 5\ @ ND1?  vB 6\ @ ND1?  vB 7\ ND1?0 B vB 8\ @ ND1? @ vB 9\ ND1?  vB :\ ND1?   ;\ T؜P1? D  U2x3 2    vB <\ ND1?% %vB =\ ND1?  >\  `P1?S S4x4     ?\ @ T̰P1? U3x2 2    vB @\ @ ND1?%R%vB A\ ND1?vB B\ ND1?PR PB C\ ZD1?R B D\ ZD1?R  B E\ ZD1?"  B F\ ZD1?R B G\ ZD1?  B H\ ZD1?B I\ ZD1?B J\ ZD1? B K\ ZD1?  L\ TP1?"`[  H0 1 2 0 3 2 3 102jB M\ BD1?e H \ 0޽h ? ___'  4','`@O` &(  ` x ` c $PP  P  p   O`  #""  `   `|1?Qe"  I2 @` `   `1?eQ"  I3 @` `   `1?Qe I2 @`  `   `R1?Qe i0  @`  `   `R1?Q"   M1 @`  `   `|R1?" Q  I3 @` `   `-R1?Q I1 @` `   `5R1?Q I0 @`xB `  Ho ?rB `  B1 ?xB `  Ho ?  xB `  Ho ? rB `  B1 ?QQ xB `  Ho ? rB `  B1 ?eerB `  B1 ?" "  `  ``@R1?S  S4x4     `  `JR1? S  S4x4     ` @ T0TR1?  I2x2 2    ` @ TKR1?   I2x2 2    ` @ T]R1?% M  I2x2 2   vB ` @ ND1?RvB ` @ ND1?e Re `L p    ` A#  R ~B !`  ND1?p  ~B "`  ND1?p  vB #` @ ND1? R vB $` @ ND1? R  %` T@qR1? R  U2x2 2     &` T<|R1? D  U2x2 2     '` T,R1? 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