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'( )*+ ,,-(,. /-0 1*(2 /-230 1(2 )/4 , )/(25,.(( 60728 6. 92 /*50 )/+ *( 6)/:
25,.( /2(. 10 ;< 02 =728 *>?@AB?*, 90( 6)/+ =0** C. /-2 90 /(2 =C1, 9*, 90( 6)/+
9, 10 C. /-2 90 /(2 =D 5.(70>AEFGB?@( 60 9( 60,( 60 1728 2 1,. /- ;
H6)*32 /50*2 )-2 /,( 60 1728 ;H60 I1*(4 , )/( )* 9, 10, 1=0**2(2.(, =,+ 8 D
, 13,. =-503, /* )-0 10-2-0 I/)( ), /, C7 62( )( 902 /* C, 1, /0 )-02(,50 9, 10
C. /-2 90 /(2 =( 62 /2 /,( 60 1;J )/302 /8 3, 1103( )-02 )* 10K . )10-(,4 10- )3(( 60728
( 6)/+ * )//2(. 1023(.2 ==8 6244 0 /D 2 /-* )/30( 607 6, =0 102*, /4 68 * )3*7, 1:* )*
( 62(2+ )L0 /4 68 * )32 =*8 *(0 9, /=8 50 62L0* )/, /0728 D 2 ==3, 1103(-0*3 1)4 ( ), /*
, C*, 904 60 /, 90 /, /9.*(4 10- )3(( 60*2 90 10*. =(* ;H60 10 C, 10D ( 60, /=8 - )* M
( )/3( ), /( 62(32 /92 :0, /0 )-02 9, 10 C. /-2 90 /(2 =( 62 /,( 60 1* )*( 62( )(5,( 6
)/3 =.-0*( 604 10- )3( ), /*( 608 92 :0D 2 /-2 =*,+ ,0*, /508 , /-( 60 9;
'/4 68 * )3*D ( 6)*4 , )/(, CL )07 )*32 11)0-(,2K . )(04 . 100 N( 10 90 ;< 60 /0L0 1
(7,0 N4 =2 /2( ), /*25,.(*, 904 2 1(, C/2(. 1032 /3, 1103( =8 233,. /( C, 1- )O0 10 /(
( 6)/+ *D 5.(023 6, C( 60 932 /0 N4 =2 )/( 6)/+ *( 62(( 60,( 60 132 //,(D ( 60 10 102 ==8
)* /,+ 1,. /- C, 13, /* )-0 1)/+ , /0, C( 60 99, 10 C. /-2 90 /(2 =( 62 /( 60,( 60 1;
P 2( 60 1D 5,( 6, C( 60 9244 02 12* )*, =2(0--0*3 1)4 ( ), /*( 62(244 =8 (,- )O0 10 /(
*4 03 )2 =32*0* ;'C, /0, C( 60 9)* 102 ==8 (,503, /* )-0 10- 9, 10 QRSTUVWSXUY
( 62 /2 /,( 60 1D )( 9.*(5025 =0(,233,. /( C, 10L0 18 ( 6)/+ ( 62(( 60,( 60 1-,0*D 2*
70 ==2* 1023 6508 , /- )( ;'/,( 60 17, 1-*D )( 9.*( )94 =8 2 ==, C( 60 10*. =(*, C( 60
,( 60 1D 2 /- )/( 62(*0 /*03, /(2 )/)(2*2*4 03 )2 =4 2 1( ;
Z /( 60,( 60 162 /-D ( 62( )* /0L0 1( 60728 70 =02 1/25,.( /2(. 10 ;< 032(3 6
6, =-, C/2(. 10\[*L2 1),.*4 2((0 1/*2 /8 728 7032 /D .*.2 ==8 , /=8 L0 18 244 1, N) M
92(0 =8 2( I1*(D 2 /-.*.2 ==8 , /=8 )/*4 03 )2 =32*0* ;H60 /, /30702 10*. 1070 62L0
103,+ /)]0-*, 90( 6)/+ 2 /- 92-0*, 90 )/1,2-*(,. /-0 1*(2 /- )/+ )(D 70 =,, :9, 10
3 =,*0 =8 2 /-( 18 (,( )0 )((,+ 0( 60 17 )( 6,( 60 1*4 03 )2 =32*0*D (, I/-( 60L0 )/, C
3, /* )*(0 /38 ( 62(. /-0 1=)0*2 ==, C( 60 9D )C, /00 N)*(* ;^.(2 =9,*(58 3, /*( 1.3( ), /
, C,. 1( 6,.+ 6(*D 7032 /_?B?@>?@AB?( 60 9, 10 C. /-2 90 /(2 =. /-0 1=8 )/+ 4 2((0 1/C1, 9, /0, 10L0 /2 C07, C)(*244 =)32( ), /* ;'C703,. =-D )(7,. =- /,(502 9, 10
C. /-2 90 /(2 =728 (,, 1+ 2 /)]0,. 1( 6)/:)/+ D 5.( 90 10 =8 23, /*0K .0 /30, C7 62(
70 62-50 C, 10 ;H6.*( 60, /=8 728 (,- )*3,L0 1( 60. /-0 1=8 )/+ 4 1)/3 )4 =0* C1, 9
( 60 )1L2 1),.* 92 /)C0*(2( ), /* )*24 1,30**, C0 /=)+ 6(0 /0-+ .0** )/+ 2 /-( 1)2 =2 /-
0 11, 1D , C(0 /32 11)0- C, 1( 6, /=8 58 ( 60 =024 *, C)/(. )( ), /, C* )/+ =04 0,4 =02(2 /8
, /0( )90 ;H6)* 92 :0* =02 1/)/+ 4 68 * )3*23. 1),.*0 N4 0 1)0 /30 ;`23 64 0 1*, /62*(, =02 1/
)(( 60*2 90728 70 62L0 =02 1/0- )(2*24 ,4 . =2( ), /D 50+ )//)/+ (,*00( 604 2((0 1/*
58 103,+ /)])/+ ( 60 9)/,. 10 N4 0 1)0 /30D 2 /-( 60 /C, ==,7 )/+ ( 60L2 1),.*( 12 )=*, C
)-02*( 62( 62L0500 /)/L0 /(0-(, 92 :0( 60 )1. /-0 1=8 )/+ 3, /* )*(0 /38 L )* )5 =0 ;a(
023 6*(04 )/(,( 60 9, 10 C. /-2 90 /(2 =D )-02*2 10 )/( 1,-.30-( 62(*00 9*( 12 /+ 0D
5032.*0 C1, 92 /8 C07, C( 60 )192 /)C0*(2( ), /*D ( 608 -, /,( 62L0(,50( 60728
( 608 2 102(2 ==;^.(( 60 /D , /3070*00 6,7( 608 7, 1:D 2 /- 6,7( 608 ( )0(,+ 0( 60 1
( 603 =.((0 1, C244 =)32( ), /*( 62( =0-.*(,( 60 9D 70 62L02(0 94 (2( ), /(, =,, :
523 :2 /-*28cbZ C3,. 1*0 de,70 =*03,. =- )( 62L0500 /fhg2* )C*, 90 6,7( 60
3, /*0K .0 /30* 92-0( 604 1)/3 )4 =0*,5L ),.*D )/*(02-, C( 604 1)/3 )4 =0* [62L )/+ 500 /
3, /*( 12 )/0-58 ( 60 10K . )10 90 /(( 62(( 608 92 :0( 603, /*0K .0 /30* )/0L )(25 =0 ;
H60*02 10+ ,,-( 6)/+ *(, :004 )/9)/-2*70(2 :02 =2 1+ 0*(04 )/(, 9, 10
C. /-2 90 /(2 =)-02*D 2 /- )/( 1,-.30( 60 i1)/3 )4 =0, Cj02*( a3( ), /;k,( 6)/+ )/
7 62(70 62L0*2 )-*, C2 110K . )10*( 62(*.3 624 1)/3 )4 =00 N)*(D , 1( 62( )((2 :0( 60
C, 19)(-,0* ;H60 10 C, 10D 92 /8 , C( 60 )-02*7 )==50 /07D 2 /-707 )==/,(5025 =0
(, b* 6,7 g( 62(( 607, 1=- 9.*(50( 6)*728 ;Z /( 60,( 60 162 /-D )( )*4 ,** )5 =0
(, 92 :0 C2 )1=8 * )94 =0,5*0 1L2( ), /*25,.( /2(. 10D 2 /-2-L2 /30*, 90 102*, /25 =0
9,( )L2( ), /*D ( 62( 92 :0,. 110*. =(*4 =2.* )5 =02 /- )/-00-2 =9,*( /2(. 12 =;a/-
, /3070 62L0 C,. /-( 604 1)/3 )4 =0D )/2 /8 728 2(2 ==D 7032 /7, 1:523 :72 1-2 /-
* 6,7 6,7 )( 10K . )10*2 ==, C( 60 10*. =(*( 62( 62L0+ , /050 C, 10 )(D 2*70 ==2* 92 /8
9, 10D 2 /-( )0*( 60 92 ==(,+ 0( 60 1)/(,2* )/+ =0 10 92 1:25 =8 * )94 =0*0(, C)-02* ;
J ,D )/:004 )/+ 7 )( 6,. 1+ 0 /0 12 =4 , =)38 , C*(2 1( )/+ 7 )( 6( 60* )94 =0*(2 /-
9,*(+ 0 /0 12 =D 5.(( 60 10 C, 102 =*, 9,*( )94 103 )*0-0*3 1)4 ( ), /*, C( 604 2((0 1/*, C
l m
/2(. 10D 2 /-7, 1:)/+ (, 10 I/0( 60 9D (, 92 :0( 60 99, 104 ,70 1C. =5.(2 =*,02* )0 1
(,.*0D 70 =,, :2(7 62(70 62L023 6)0L0-*, C2 12 /-2* :7 62(3,. =-50-, /0(,
)94 1,L0 )( ;� �nopqr sqt! qq" uv qu&�qwq�
Z . 1+ ,2 =D C, 1/,7D )*(,-0*3 1)50( 60 9,( ), /*, C,5x 03(*D =):0 C100 =8 C2 ==)/+ 1,3 :*
2 /-5 =,3 :*( 62(5,5523 :2 /- C, 1( 6, /( 600 /-*, C*4 1)/+ * ;i10*. 925 =8 70
2 10324 25 =0, C)92+ )/)/+ 2 /8 50 62L ), 12(2 ==C, 1*.3 6,5x 03(*D 2 /8 ( 12x 03(, 18 )/
*4 230D /, 92((0 16,7*( 12 /+ 0D 2 /-2 /8 7 )=-4 2((0 1/, C50 62L ), 1C1, 9, /0( )90
(,2 /,( 60 1y 2 /- )/-00-D *( 12 /+ 0 1( 6)/+ *( 62 /( 62(D 7 60 /,. 1)92+ )/2( ), /* 62L0
500 /70 ==( 12 )/0-D )/3 =.- )/+ 9,( ), /* C, 172 1-2 /-z{F|}{@> )/( )90D ( 6,.+ 6( 60
=2*(3 624 (0 1, /~ .2 /(. 9)0 =- H60, 18 7 )==50 10K . )10-(,+ )L0( 62(0 N4 10** ), /
902 /)/+ ;1, 9( 6)* =)9)( =0**3, ==03( ), /, C2 ==)92+ )/25 =04 2( 6*D 70 =02 1/0- C1, 9
)90 /* ), /2 =a/2 =8 * )* 6,7(,+ 0 /0 12(02 C07 /. 950 1*( 62(*0 =03( )L0 =8 )-0 /( )C8
, /=8 ( 6,*04 2( 6*( 62(23(.2 ==8 6244 0 /)//2(. 10 ;< 0+ 2L0( 60*0 /. 950 1*( 60
/2 90 b SXUSXQXW XWV gD 5032.*0( 608 2 10( 60*4 03 )2 =/. 950 1*( 62(
244 =8 ( 60*2 90728 (,2 ==, C( 604 ,** )5 =0 9,( ), /*( 62(( 60*8 *(0 932 /62L0 ;
, 1C2 ==)/+ 1,3 :*D 7032 /2 =728 * 10 =2(0( 60 )1( )90*0 =24 *0- )/C2 ==2 /-- )*(2 /30*
( 12L0 =0-58 ( 604 2((0 1/2 + D 7 60 10 )*2 =728 *( 60*2 90 /. 950 1;, 1*4 1)/+ *D
, /3070 62L0 /,( )30-( 62(( 608 62L0238 3 =)3 9,( ), /D C1, 9( 604 1,4 ,* )( ), /( 62(
b)(-,0*7 62( )(-,0*5032.*0 )( )*( 60728 )( )* g702 1025 =0(,4 10- )3(7 62(
( 60( )90, C023 638 3 =0 )* C1, 9( 603 62 123(0 1)*( )3*, C( 60*8 *(0 9D ( 60 92**, C( 60
5 =,3 :2 /-( 60 /. 950 1( 62(3 62 123(0 1)]0*( 60*( )O/0**, C( 60*4 1)/+ ;
H6)* 104 10*0 /(*( 10 90 /-,.*4 1,+ 10**D 2 /- )/-00-4 1,525 =8 0L0 18 ( 6)/:)/+
4 68 * )3 )*(.*0* )90 /* ), /2 =a/2 =8 * )* 9, 10( 62 /2 /8 ,( 60 1=0L0 =, C4 68 * )32 =-0 M
*3 1)4 ( ), /D (,+ 0(2+ 0 /0 12 =C00 =C, 1 b6,7 9.3 6D 6,75 )+ D 6,7 =, /+ D 6,7, C(0 / g2*
)(244 =)0*(,24 1,5 =0 92( 62 /- ;^.(( 6)* =0L0 =, C-0*3 1)4 ( ), /=0 C( 9.3 6. /*4 03 ) M
I0- ;a9)/, 14 1,5 =0 9)*( 62( )(3,. =- /,(4 1,L )-0( 60 C23(, 1*, C4 1,4 , 1( ), /2 =)(8
( 62(-0*3 1)502 /8 , C( 604 ,** )5 =023(.2 =4 2( 6*D 2 /-2 9, 10 92x , 1, /072*( 62(
7 6)=0 )(3,. =-(0 ==y ? D C, 1( 6032*0, C( 60*4 1)/+ 7 62(3 62 123(0 1)*( )3( )90
244 =)0-(,( 60 9,( ), /*, C( 60*8 *(0 9D )C( 60 1072*, /0D )(3,. =- /,((0 ==.*7 62(
( 60* )+ /)I32 /30, C( 62(3 62 123(0 1)*( )3( )9072* ;< 0 62-(,4 .(( 62( )/58 62 /- ;
i0 1624 * 9, 10* )+ /)I32 /(72*( 62(D 0L0 /)C70 :/07( 60K .2 =)(2( )L050 62L ), 1
, C2 ==( 604 ,** )5 =04 2( 6*D 2 /-( 60 902 /)/+ , C2 ==, C( 60*32 =0*4 10- )3(0-58
- )90 /* ), /2 =2 /2 =8 * )*D ( 60*0 /. 950 1*244 =8 0K .2 ==8 (,2 ==, C( 604 ,** )5 =023(.2 =
4 2( 6* ;H608 ( 6.*-, /,( 6)/+ 2(2 ==(,(0 ==.*D )/2+ )L0 /3 )13. 9*(2 /30D 7 6)3 6, C
)(*4 ,** )5 =04 2( 6*( 60,5x 03(23(.2 ==8 (2 :0* ;
a==, C( 60*04 1,5 =0 9*70 10K . )(0*,. /- =8 *, =L0-7 )( 6( 60 )/( 1,-.3( ), /, C
( 60 W RUXSQVXSD , C7 6)3 6 72*( 60 :)/-7 6)3 6k07(, /
I1*( I+ . 10-,.( 6,7(,3, /*( 1.3( )/+ 0 /0 12 =3 )13. 9*(2 /30* ;J .3 62 /0K .2( ), /
4 1,L )-0-23, 94 =0(0*4 03 )I32( ), /, C( 604 2 1( )3. =2 14 2( 62 /,5x 03((2 :0*D , /30
start
ground surface
)+ . 10 ;a b( )90 M=24 *0 g4 )3(. 10, C2 1,3 :D C2 ==)/+ 2 C(0 1)( 62*500 /( 61,7 /
* )-0728 * ;70 62L0*2 )- 6,7( 62(4 2( 6)**(2 1(0- ;'((0 ==*2 ==, C( 60K .2 =)(2( )L050 62L ), 1
2 /- )/3 =.-0*2 ==, C( 60 10 =0L2 /(*32 =0*4 1,L )-0-58 )90 /* ), /2 =a/2 =8 * )*D 0L0 /
I==)/+ )/( 60 C23(, 1*, C4 1,4 , 1( ), /2 =)(8 ;'/( 62(728 ( 600K .2( ), /*, C9,( ), /
L0 18 0 O03( )L0 =8 (2 :0.*D C1, 9( 603, ==03( ), /, C2 ==4 ,** )5 =023(.2 =4 2( 6**0 =03(0-
58 )90 /* ), /2 =a/2 =8 * )*D (,2. /)K .0 )-0 /( )I32( ), /, C24 2 1( )3. =2 123(.2 =4 2( 6;
^.( )/*, 90*0 /*0D 70*. O0 10-2 12( 60 1*0L0 10 =,**, C0 3 )0 /38 )/+ , )/+
C1, 9)90 /* ), /2 =a/2 =8 * )*2 /-3, /*(2 /(*, C( 60*8 *(0 9(,( 600K .2( ), /*, C
9,( ), /;H60 I1*(*(04 10-.30-.* C1, 9( 60 6.+ 0*0(, C2 ==)92+ )/25 =04 2( 6*(,
( 60 9.3 6* 92 ==0 1*0(, C4 ,** )5 =023(.2 =4 2( 6*7 )( 6x .*(2 C07 /. 950 1* ;k,7
( 62( )*24 ,70 1C. =)-02 d^.(( 60 /D (, 92 :0( 60 C. 1( 60 1*(04 (,( 604 2 1( )3. =2 1
4 2( 6( 61,.+ 6( 600K .2( ), /*, C9,( ), /D 70 62-(,+ 0 /0 12(0( 607 6, =04 2( 658
5. )=- )/+ )(D , /0 )/I/)(0** )92 =4 )0302(2( )90D 2*70( 1230,.(( 600L, =.( ), /
0 /3,-0- )/( 60 1. =0 ;'(7,. =- 104 10*0 /(2+ 102(4 1,+ 10** )/,. 1. /-0 1*(2 /- )/+ )C703,. =-*, 90 6,7
0 /3,-0( 60*2 90 )/C, 192( ), /2*70+ 0( C1, 9 )/x .*(2 C07 /. 950 1*D 2*
70- )-7 )( 6)90 /* ), /2 =a/2 =8 * )* ;Z C3,. 1*0D ( 60*0 /. 950 1*3,. =- /,(50( 60
*2 90 C, 12 ==, C( 604 ,** )5 =023(.2 =4 2( 6*D 5032.*0( 60 )17 6, =0 C. /3( ), /7,. =-50
(, C. 1( 60 1- )*( )/+ . )* 6D 7 )( 6)/( 62(*0(D , /04 ,** )5 =023(.2 =4 2( 6C1, 9( 60,( 60 1*D
2 /-*,(,0 /25 =0.*(, )-0 /( )C8 7 6)3 6, /0 6244 0 /* )/24 2 1( )3. =2 1)/*(2 /30 ;a/-D
, C3,. 1*0D ( 608 7,. =-2(( 60*2 90( )90 62L0(, 10*4 03(2 ==, C( 60 10*. =(* C1, 9
)90 /* ), /2 =a/2 =8 * )*D 5032.*0( 60*0 9.*(244 =8 (,2 ==, C( 6023(.2 =4 2( 6* ;
H60 102 10L0 18+ ,,- 102*, /*(,50 =)0L0( 62(*.3 62* )94 =0*0(, C/. 950 1*32 /
503, /*( 1.3(0-D 2*7032 /*0058 ( 6)/:)/+ 25,.(( 60 9,( ), /, C2 C2 ==)/+ 1,3 :;
)+ ; ;* 6,7*( 60( 12x 03(, 18 , C2 1,3 :( 61,7 /* =)+ 6( =8 * )-0728 *2 /-2 ==,70-
(, C2 ==C100 =8 /02 1( 60*. 1C230, C( 6002 1( 6D 2* )(7,. =- =,, :)/2 =, /+ M0 N4 ,*. 10
4 6,(,+ 124 6; 0 1(2 )/=8 ( 6)* )*24 2( 6( 62(2 1,3 :32 /C, ==,7D *(2 1(0-7 60 /)(
l
start previousstart
optionalhole
)+ . 10 ;mH604 2( 6C, ==,70-58 2 1,3 :D ( 61,7 /.4 2 /-* )-0728 * C1, 9( 60
+ 1,. /-(,*, 90 60 )+ 6(D 2 /-2 ==,70-(, C2 ==523 :(, `2 1( 6;
=02L0*,. 162 /-2 /-0 /-0-7 60 /)( 6)(*( 60+ 1,. /- ;^.(( 60 102 10,( 60 1728 *
)(3,. =-( 1230( 6)**2 904 2( 62*70 ==;)+ ; ;m* 6,7*( 604 2( 6*( 62(7,. =-
10*. =( )CD )/*(02-, C( 61,7 )/+ )(* )-0728 * C1, 92 60 )+ 6(D 70( 6107 )(.4 72 1-2 /-
* )-0728 * C1, 9( 60+ 1,. /-*,( 62( )( 6244 0 /0-(, 1023 6( 62( 60 )+ 6(+ , )/+ 2(( 60
*2 90* )-0728 **4 00-D 2 /-* )94 =8 2*( 603, /( )/.2( ), /, C)(* 9,( ), /( 1230-,.(
,. 14 10L ),.*4 2( 62*70 ==;Z 1D 2 =(0 1/2( )L0 =8 D 703,. =-- )+ 2 6, =0*,( 62( )(-,0*
/,( 6)(( 60+ 1,. /- 1)+ 6(2728 D 5.( :004 *, /+ , )/+ 4 2*(7 60 10 )(*(,44 0- )/( 60
4 10L ),.* I+ . 10y ;m ;H60 C23(( 62( 102 =1,3 :*32 /2 /--,( 12L0 =)/2 ==, C( 60*0- )O0 10 /(4 2( 6*
4 , )/(*,.(2 /)/(0 10*( )/+ 10 =2( ), /;'/*, 90*0 /*0D 70* 6,. =- /,(3, /* )-0 12
4 2 1( )3. =2 123(.2 =4 2( 62*2 /)*, =2(0-4 10- )3(25 =0,33. 110 /30, 1/,( ), /;a( =02*(
4 2 1(, C7 62(*4 03 )I0*( 604 2( 6)*7 60 1070 62L03 6,*0 /(,*(2 1( )(2 /-*(,4 )(D
2 /-. /-0 1,( 60 13 )13. 9*(2 /30*D )( 9)+ 6( /,( 62L0500 /2}G?23(.2 =4 2( 62(
2 ==D 5.( 90 10 =8 24 2 1(, C*, 90 =2 1+ 0 123(.2 =4 2( 6*(2 1(0-, 10 /-0- )/*, 90,( 60 1
728 ;'/( 6)**0 /*0D 7 62(( 600K .2( ), /*, C9,( ), /-, )* /,( )-0 /( )C8 4 2 1( )3. =2 1
23(.2 =4 2( 6*7 6, =0D 5.( 12( 60 1( )0(,+ 0( 60 12 ==, C( 60 =)(( =04 )030*, C4 2( 6( 62(
92 :0.4 2 /23(.2 =4 2( 6D 2* 92 /8 , 12* C07, C( 60 92*702 ==,758 ( 60728 70
*(2 1(2 /-*(,4 ( 60 9,( ), /;^.( /,7( 62(702 10 =,, :)/+ 2(*.5 M4 2( 6*2*4 ,(0 /( )2 ==8 4 2 1(*, C=2 1+ 0 1
23(.2 =4 2( 6*D 70 102 =)]0( 62(( 60 102 10*, 903, ==03( ), /*, C*.54 2( 6*( 62(-,
,33. 1(,+ 0( 60 12*4 2 1(*, C7 6, =023(.2 =4 2( 6*D 2 /-,( 60 1*( 62( /0L0 1-,D 2*
104 10*0 /(0- )/I+ ; ; ;H60 I1*(4 )3(. 10* 6,7*24 2( 62 C2 ==)/+ 1,3 :9)+ 6((2 :0
b, C)(*,7 /233, 1- gD 2 C(0 150 )/+ ( 61,7 /;H60*03, /-4 )3(. 10* 6,7*2- )O0 10 /(
A GEEAz?4 2( 6D 92-0, C(7,4 2 1(* ;J 04 2 12(0 =8 D 023 6)*2 9,( ), /2 1,3 :3,. =-50
92-0(,(2 :0D 58 50 )/+ ( 61,7 /)/230 1(2 )/728 ;^.(( 608 /0L0 1,33. 1(,+ 0( 60 1
2*(7,4 2 1(*, C2 /8 * )/+ =04 2( 6(2 :0 /58 2 1,3 : b, C)(*,7 /233, 1- g;'( )*K . )(0
(a)
(b)
)+ . 10 ; H7, )92+ )/25 =04 2( 6*( 61,.+ 6*4 230 C, 12 C2 ==)/+ 1,3 :;i2 1(y 2
* 6,7*( 60* 9,,( 64 2( 6/2(. 103 6,,*0* ;i2 1(y 5 * 6,7*2 /, / M32(.2 =4 2( 6D
3, 94 ,*0-, C(7, b4 )030- M(,+ 0( 60 1 g4 2 1(*, C4 ,** )5 =0>A ?@?_23(.2 =4 2( 6* ;
2 15 )( 12 18 7 6)3 6=)(( =04 2 1(*, C( 60* )/+ =0* 9,,( 6=8 * )-0728 * M9,L )/+ 4 2( 670
3 6,,*0(,0 N2 9)/0 ( 600K .2( ), /*, C9,( ), /32 /4 1,L )-02 /8 *0K .0 /30, C( 60 9
2*4 2 1(*, C2 /23(.2 =4 2( 6;^.(70 /0L0 1*002 /8 23(.2 =4 2( 63, 94 ,*0-, C( 60
,( 60 12 =(0 1/2( )L0D4 2 1(*, C24 2( 6( 62( =02-**( 12 )+ 6(-,7 /72 1-D 2 /-( 60 /,( 60 1
4 2 1(* C1, 924 2( 6+ , )/+ 124 )- =8 * )-0728 * ;
.*(( 60 C23(( 62(*.3 64 2((0 1/*0 N)*(D 2 /-( 62(( 608 0 N)*( )/-04 0 /-0 /( =8 , C
7 6)3 64 2 1( )3. =2 1=)(( =0*0+ 90 /(*, C4 2( 6703 6,,*0(,3, /* )-0 1D *.++ 0*(*( 62(
( 60 10 )**, 90( 6)/+ ( 62(( 60- )O0 10 /(*.54 2 1(*, C2EA_ ? GEEAz?{F{ {
62L0 )/3, 99, /D 2 /-( 62(( 60*.54 2 1(*, C- )O0 10 /(23(.2 =4 2( 6*-, /,( ;J , 90 M
6,7( 600K .2( ), /*, C9,( ), /2 =728 *3, //03((,+ 0( 60 1, /=8 ( 6,*04 )030*, C4 2( 6
( 62( b32 / g504 2 1(*, C=2 1+ 0 14 2( 6*D 2 /- /0L0 1( 6,*0( 62(32 //,( ;< 62(70
72 /( )*(, 1032*(( 62(2**,3 )2( ), /)/2 C, 19( 62(7 )==/,( 10K . )10.*(, I==)/2 ==
( 60 )/(0 1L0 /)/+ 9,( ), /50(700 /( 604 2 1(*(, :/,7 )C( 608 3,. =-504 2 1(*, C( 60
*2 9023(.2 =4 2( 6;< 032 /+ )L02 /2 90(,( 603, /304 (70( 18 )/+ (, I/- ;< 0*.*4 03(( 62(( 60 10
)*24 2((0 1/D 5032.*0( 60 C23(( 62(( 60-8 /2 9)3*-0 I/0*( 604 2( 6)/2728 ( 62( )*
)/-04 0 /-0 /(, C7 60 /70*(2 1(, 1*(,4 )((0 ==*.*( 62(( 60-8 /2 9)3* )*2**,3 )2( )/+
2 ==( 604 ,(0 /( )2 =*.54 2( 6*( 62(3,. =- 92 :02* )/+ =04 2( 6D 2 /-0 N3 =.- )/+ ( 6,*0
( 62(3,. =- /,( ;< 60 /70 C,. /-24 2((0 1/50 C, 10D )/)90 /* ), /2 =a/2 =8 * )*D
70 C,. /-( 62(703,. =--0*3 1)50 )(58 *, 90 /. 950 1*( 62(D /, 92((0 17 62(70
- )- )/)94 2 1( )/+ 9,( ), /(,( 60*8 *(0 9D 70 102 =728 *( 60*2 90 ;'/*, 90*0 /*0D
( 62( )*( 600**0 /30, C7 62(0 N)*(0 /30, C24 2((0 1/)* ;J ,2+ 2 )/( 6)*( )90D )C
( 60 10 )*24 2((0 1/( 62(4 )3 :*,.(( 60*04 ,** )5 =03, 94 2( )5 =0*.5 M4 2( 6*D 707,. =-
=):0(, 104 10*0 /( )(2**, 90* 92 ==3, ==03( ), /, C/. 950 1*( 62(2 ==, C( 60 962L0
)/3, 99, /D 5.(7 6)3 62 10- )O0 10 /( C, 1( 60*.5 M4 2( 6*, C, /023(.2 =4 2( 6C1, 9
l
( 6,*0, C2 /,( 60 1D 2 /-*,*0 1L0(,- )*( )/+ . )* 6( 6,*0( 62(2 103, 94 2( )5 =0 C1, 9
( 6,*0( 62(2 10 /,( ;H60 C23(( 62(( 60 /. 950 1** 6,. =-50( 60*2 90 C, 12 ==, C
( 60 =)(( =04 2 1(*, C2* )/+ =04 2( 6902 /*( 62(( 608 2 10( 60*2 902(0L0 18 )/*(2 /(
2 =, /+ 2 /8 102 =23(.2 =4 2( 6;J ,( 608 2 10( 60 /2(. 12 =10 I/0 90 /(, C,. 102 1=)0 1
3, /304 (, C G_E{_EG¡ ?¢£ E?D 0 N304 (( 62( )/*(02-, C50 )/+ ( 60*2 90 C, 1
2 ==4 ,** )5 =023(.2 =9,( ), /*, C( 60*8 *(0 9D ( 608 2 10, /=8 ( 60*2 90 C, 12 ==4 , )/(*
2 =, /+ 2* )/+ =0 9,( ), /D *, 907 62( =):0( 60728 ( 60( 1.0*(2(0 90 /( 72*D
2*4 1,L )-0-2(023 69, 90 /(58 ( 600K .2( ), /, C9,( ), /D 5.(- )O0 10 /( C, 1, /0
23(.2 =9,( ), /( 62 /C, 12 /,( 60 1;H6.*( 60 /. 950 1*( 62( 104 10*0 /(( 60 )-0270
2 10*02 13 6)/+ C, 13,. =- /2(. 12 ==8 5032 ==0- SXUSXQXW¤XS;
P 0 92 1:25 =8 D *.3 6/. 950 1*-, )/-00-0 N)*(D 2 /-( 60(,, =( 62(7 )==0 /25 =0.*
(,* 6,7( 6)* C23(2 /- I/-,.(7 62(( 608 2 102 =*,(. 1/*,.((,50( 607 )/-,7 )/(,
27 6, =0 /07728 , C*(2( )/+ 4 68 * )32 ==27* ;< 04 1,300-(, =,, :C, 1)(58 2* :)/+ D
b7 62( :)/-, C2-0*3 1)4 ( ), /, C4 2( 6*3,. =--,( 6)*x ,57072 /(D , C)/-04 0 /-0 /( =8
)-0 /( )C8 )/+ ( 60 =)(( =0*.5 M4 2( 6*( 62(32 /504 2 1(*, C2* )/+ =023(.2 =4 2( 6D 2 /-
0 N3 =.- )/+ 2 ==( 6,*03, 95 )/2( ), /*( 62(32 //,( ;
� �¥ ¦&�&w&§¨ &" �'( 928 *00 9(,502*( 12 /+ 02 /-4 0 1624 * )94 ,** )5 =0( 6)/+ 702 102* :)/+ ,. 1
/07 1. =0(,-, ;< 62( :)/-, C1. =032 /)(50( 62( 103,+ /)]0*D )/-04 0 /-0 /( =8 , C
7 6)3 6=)(( =04 )030*, C4 2( 6703 6,,*0(,3, /* )-0 1D 7 60( 60 1( 608 2 10 9.(.2 ==8
3, 94 2( )5 =02*4 2 1(*, C2* )/+ =0+ 102(0 14 2( 6;a/- 6,732 /*.3 62 1. =04 ,** )5 =8
50*(2(0- )/2728 ( 62( )** )94 =00 /,.+ 6(,502(2 ==.*0 C. =D 9.3 6=0**, O0 1
2 /2-L2 /(2+ 0,L0 1 f'((. 1/*,.(( 62( )C70( 6)/:, /=8 25,.(4 2( 6*
, C,5x 03(*D ( 6)*2 /*70 1928 /,(50,5L ),.*D 5.( 6244 )=8 D 92( 60 92( )3* )* /,
10*4 03(, 1, C244 =)32( ), /*D 2 /- )C702 ==,7,. 1*0 =L0*(,( 6)/:, C,( 60 1*8 *(0 9*D
2 /0 N2 94 =0, C*.3 62 1. =0 )*4 2 1(, C3, 99, /0 N4 0 1)0 /30 ;
J .44 ,*070*( 10(3 62 1.550 152 /-23 1,**( 60*. 1C230, C2(25 =0 ;a* )==.*( 12(0-
)/I+ ; ;D ( 60 102 10*0L0 12 =- )O0 10 /(728 *( 60 1.550 152 /-32 /50 60 =-D 2 /-
3, /*0K .0 /( =8 *0L0 12 =- )O0 10 /( b4 2( 6* g23 1,**( 60(25 =0( 62( )(32 /,33.48 ;©0(D
C, 12+ )L0 /728 70 6, =-( 600 /-*D , /=8 , /04 2( 6)**0 =03(0-2*( 60 102 =, /0 ;
a/-D =):0( 604 2 1(*, C( 60( 12x 03(, 18 , C,. 1C2 ==)/+ ,5x 03(D ( 60- )O0 10 /(*0+ 90 /(*
, C( 60 1.550 152 /-, /=8 =28 )/30 1(2 )/3, 95 )/2( ), /*, C728 * ;a*0 94 62* )]0-
)/I+ ; ;ªD ( 60 =)(( =05 )(*, C1.550 152 /--, =28 )/728 *( 62(2 104 2 1(*, C2
* )/+ =04 2( 6D 5.( /0L0 1=28 )/( 60,( 60 1728 ** 6,7 /D - 127 /C1, 9- )O0 10 /(2 /-
9.(.2 ==8 )/3, 94 2( )5 =0G?@{F{ {E ;H60* )9)=2 1)(8 50(700 /( 604 )3(. 10*D
, C( 60728 ( 60 1.550 152 /- =28 *2 /-( 60( 12x 03(, 1)0*, C( 60 C2 ==)/+ 1,3 :D (. 1/*
,.((,50 9, 10( 62 /*.4 0 1I3 )2 =;i68 * )32 ==8 D 30 1(2 )/=8 ( 60(7,*8 *(0 9*2 10 /,(( 60*2 90 ;H60 1.550 152 /-
)*2 =, /+ *( 1)/+ , C92(0 1)2 =( 62(,33.4 )0*2 ==, C( 604 2 1(*, C)(* b4 2( 6 g2(( 60
*2 90( )90D 7 60 102*( 60 C2 ==)/+ ,5x 03(D 2( =02*(2*70 62L0- 127 /)(*, C2 1D , /=8
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(c)
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)+ . 10 ;H60 b4 2( 6 g,33.4 )0-58 2*( 10(3 60- 1.550 152 /-D =8 )/+ , /2 «2(
(25 =0 ;(a)
(b)
)+ . 10 ;ª J , 90 )92+ )/25 =0 b4 2( 6* gC, 12*( 10(3 60- 1.550 152 /- ;y 2 )*( 60
23(.2 =3, /I+ . 12( ), /, /2 102 =«2((25 =0 ;y 5 )*2 /, / M23(.2 =3, /I+ . 12( ), /92-0
C1, 9 b4 )030- M(,+ 0( 60 1 g4 2 1(*, C23(.2 =>A ?@?_3, /I+ . 12( ), /*D 7 6)3 63,. =- 62L0
,33. 110- 62-( 600 /-*500 /60 =-- )O0 10 /( =8 ;
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)+ . 10 ; a*( 10(3 60- 1.550 152 /-D *( 12 )+ 6(0 N304 (7 60 1070 C, 1302* 92 ==
b:)/: g)/(, )( ;H60 :)/:3,. =-504 .(2 /8 7 60 102 =, /+ ( 60 =0 /+ ( 6, C( 6052 /- ;
,33.4 )0*, /0, C( 604 , )/(*, /)(*( 12x 03(, 18 2(2 /8+ )L0 /9, 90 /( 104 10*0 /(0-
58 ( 604 )3(. 10 ;©0( )/)(*,7 /728 D 7 62(0L0 11. =0 b(0 ==* g( 604 2 1(*, C( 60 1.550 1
52 /-7 60 10( 608 32 /3, 90(, 10*(4 0 1C, 19*0 N23( =8 ( 60 :)/-, C)-0 /( )I32( ), /
, C=)(( =0*0+ 90 /(*, C4 2( 6( 62(707,. =- =):0(,0 N4 =, )( ;'(, 1)0 /(*023 6=)(( =0
*0+ 90 /(, C52 /- )/, /=8 ( 60728 ( 62( )*3, 94 2( )5 =07 )( 6( 60, 1)0 /(2( ), /*, C2 ==
( 60,( 60 1=)(( =0*0+ 90 /(*, C( 6052 /-D8 0( )(-,0**, )/2728 ( 62( )* )/-04 0 /-0 /(
, C7 6)3 6=)(( =0*0+ 90 /(703, /* )-0 1D 2*32 /50*00 /)/I+ ; ; ;'C704 .(2 :)/:
)/*, 90 =)(( =04 2 1(, C( 6052 /-D 50 )/+ 32 10 C. =(, 6, =-2 ==( 60 10*(, C( 6052 /-2*
)(72*D ( 60 1.550 1,508 * )(* 1. =0*,( 62(( 60 :)/:0-4 2 1(, C( 6052 /- 10(. 1/*(,
0 N23( =8 ( 60*2 903, /I+ . 12( ), /2* )(7,. =- 62L0 )C70 62-- )*(. 150-( 6052 /- )/
2 /8 ,( 60 1728 ;J ,*, 90 6,7D ( 60 1. =02 =728 * =02-*(,( 60*2 90 10*. =(D 10+ 2 1- =0**
, C7 6)3 64 2 1(, C( 604 2( 670 928 3 6,,*0(,3, /* )-0 1D , 10L0 /(,- )*(. 15 ;H6.*D
7 6)=0( 604 2 1( )3. =2 14 68 * )3*, C( 60244 =)32( ), /, C( 60 1.550 152 /- 928 - )O0 1
C1, 9( 62(, C( 60 9,( ), /, C( 60 C2 ==)/+ 1,3 :D ( 60 92( 60 92( )3*3, /(2 )/*4 103 )*0 =8
( 60 C02(. 10*7072 /( ;^.(, C3,. 1*070. /-0 1*(2 /-( 60 1. =0* C, 11.550 152 /-*0 N300- )/+ =8 70 ==D
2 /- )/C23(( 608 2 10*, 90, C( 60* )94 =0*( 1. =0*70 :/,7 6,7(,*(2(0 ;< 62(
-,0*2*( 10(3 60- 1.550 152 /--, f'(503, 90*2** 6, 1(2* )(32 /D 2 /- 9,L0*
(,7 62(0L0 14 ,* )( ), /92 :0*( 62(4 ,** )5 =0 ;H62( )*( 607 6, =04 , )/(, C50 )/+
*( 10(3 60- 1.550 1;'(*4 10 C0 110-*(2(0 )*. /*( 10(3 60-D 2 /- )C704 )/)(*0 /-*D ( 60
10*(, C( 6052 /- 9,L0* )/7 62(0L0 1728 5 1)/+ * )(3 =,*0*((,( 62(4 10 C0 110-*(2(0 ;
a==, C( 6)* 6244 0 /* =,32 ==8 D 233, 1- )/+ (,2 1. =0( 62(244 =)0* )/023 6=)(( =05 )(, C
( 60 1.550 1D )/-04 0 /-0 /( =8 , C7 62(( 60,( 60 1*0+ 90 /(*2 10-, )/+ ;`23 65 )(, C( 60
1.550 1)* 9,L )/+ )/*.3 62728 2*(,503, 90* 6, 1(0 1D )C4 ,** )5 =0D 2 /-7 60( 60 1
2 ==, C( 60,( 60 15 )(*2 102 =102-8 2** 6, 1(2*( 608 32 /50, 1/,(-,0* /,( 92((0 1
(, )(*-8 /2 9)3* ;H62( )*7 68 ( 60* )/+ =0 =)(( =0 :)/:)/( 6052 /-*( 12 )+ 6(0 /*(,( 60*2 904 =2302 /-( 60*2 90, 1)0 /(2( ), /, /( 60(25 =02*( 62(4 2 1(, C( 60 1.550 1
7,. =- 62L0 )C70 62-- )*(. 150-( 6052 /- )/2 /8 ,( 60 1728 ;
H60.((0 1* )94 =)3 )(8 , C( 6)* :)/-, C2 1. =0D b'(503, 90*2** 6, 1(2* )(32 / gD
2 /- )(* C2 9)=)2 1)(8 D 928 92* :6,7 10 92 1:25 =0 )(( 1. =8 )* ;'(( )0*(,+ 0( 60 1( 60
10 9,(0*(*0+ 90 /(*, C( 6023(.2 =, 1)0 /(2( ), /D *,( 62(2 ==, C( 60 92 103, 94 2( )5 =0
4 2 1(*, C2* )/+ =07 6, =0D 2 /-8 0( )(-,0*( 6)*7 )( 6-8 /2 9)3* C, 1( 604 )030*( 62(
2 103, 94 =0(0 =8 Y¬UY;`23 65 )(, C( 60 1.550 1I/-*24 ,* )( ), /( 62( )* 10 =2(0-(,
( 604 ,* )( ), /*, C2 ==( 60,( 60 15 )(*, C( 60 1.550 1D 5.( )(-,0**,58 C, ==,7 )/+ 1. =0*
( 62(3, /(2 )//,0 N4 =)3 )( 10 C0 10 /30(,2 /8 ( 6)/+ 5.(( 60,( 60 15 )(* 1)+ 6(2 1,. /-
)(D (,7 6)3 6)( )*- )103( =8 3, //03(0- ;
H6)*3, 95 )/2( ), /, C+ =,52 =3, /* )*(0 /38 2 /- =,32 =* )94 =)3 )(8 7 )==50L0 18 )9 M
4 , 1(2 /((,.* ;k,(, /=8 )* )(( 60( 12-0 92 1:, C9)/)9)]2( ), /4 1)/3 )4 =0*D .*0 C. =
C, 11.550 152 /-*2 /-4 0 1624 *4 1, 9)* )/+ C, 14 2( 6*D 5.( )(7 )==50( 60. /-0 1=8 )/+
9,( )L2( ), /( 62(7 )===02-.*(,( 60 C, 19. =2( ), /, C2 /,( 60 1, C( 60 9,*( )94 , 1 M
(2 /( )-02*3 102(0-* )/30( 60 )/( 1,-.3( ), /, C4 68 * )3* )(*0 =CD ( 60 )-02, CGF{ ?>
?G@A?ED 7 6)3 6707 )==0 N4 =, 10 )/=2(0 13 624 (0 1* ;^.( C, 1/,7D 62L )/++ .0**0-
( 62(*, 90*, 1(, C9)/)9)]2( ), /1. =0 928 =02-.*(,,. 1-0* )10-3, /*(2 /(*, C( 60
9,( ), /D 70( 18 (,- )*3,L0 16,7*.3 62 1. =032 /50 C, 19. =2(0- C, 1( 604 2( 6*, C
)*, =2(0-,5x 03(* ;'C( 60 102-0 1( 6)/:*( 62(0L0 /2(( 6)*4 , )/(702 10*( )==, /12( 60 1* 62 :8
2 /-*4 03. =2( )L0+ 1,. /-D 60 )* /,( C2 17 1, /+ ; 0 1(2 )/=8 D 9)/)9)]2( ), /)*2 /
0 3 )0 /(2 /-0 =0+ 2 /(728 (,*(2(0( 60 1. =0*( 62(-0(0 19)/0( 60 10*( )/+ 4 =230*
, C*( 10(3 60- 1.550 152 /-*D 2 /-70 928 /,(50(,,*. 14 1)*0- )C)(2 =*,, O0 1*2
.*0 C. =-0*3 1)4 ( ), /, C( 6023(.2 =4 2( 6*, C,5x 03(* )/*, 9032*0* ;^.(D 70 62L0
8 0((,* 6,7( 62(2 /8 *.3 61. =023(.2 ==8 0L0 /0 N)*(* C, 1( 604 2( 6*, C,5x 03(*D 2 /-
70 62L030 1(2 )/=8 /,( 92-023, /L )/3 )/+ 32*0( 62( 9)/)9)]2( ), /)*( 603, 1103(
728 (,. /3,L0 1( 60, 1)+ )/2 /- 902 /)/+ , C3, /*(2 /(*, C( 60 9,( ), /;a==70 62L0
-, /0*, C2 1)*2 1+ .0( 62(( 60 /,( ), /, C23, /*(2 /(, C( 60 9,( ), /)*( 62(, C*, 90
3 1)(0 1), /( 62( )-0 /( )I0*24 2 1( )3. =2 123(.2 =4 2( 658 0 N3 =.- )/+ 2 /8 3, 95 )/2( ), /*
, C=)(( =04 )030*, C4 2( 6*( 62(32 //,(504 2 1(*, C2* )/+ =05 )++ 0 14 2( 6;H60 C23(
( 62(*.3 62 9.(.2 =0 N3 =.* ), /4 10*3 1)4 ( ), /)**, 9.3 6=):07 62(( 60 9)/)9)]2( ), /
1. =023 6)0L0* C, 1( 60 =)(( =05 )(*, C( 60( 123 :,33.4 )0-58 2*( 10(3 60- 1.550 152 /-
92 :0*( 6)*24 =2.* )5 =0- )103( ), /(,4 . 1*.0 ;
k,7 )((. 1/*,.(( 62(D )/-00-D - 127 )/+ ,. 13 =.0(,72 1- 9)/)9)]2( ), /C1, 9
( 60 9.(.2 = M0 N3 =.* ), /C. /3( ), /, C3, /*0 1L0-K .2 /( )( )0* )*0 N23( =8 ( 60 1)+ 6(( 6)/+
(,-,D 5.(( 6)* )* 9.3 602* )0 1(,*00 )/10( 1,*4 03(, /3070 62L0 =02 1/0-*, 90( 6)/+
9, 1025,.(( 604 1)/3 )4 =0*( 60 9*0 =L0* ;J , C, 1/,7D 12( 60 1( 62 /( 18 (,x .*( )C8
( 6)*2**. 94 ( ), /C. 1( 60 1D 70* )94 =8 =,, :2(2 9)/)9)]2( ), /1. =0( 62( 62*500 /
*.330** C. ==8 .*0- C, 16. /- 10-*, C8 02 1*D 5032.*0 )(72*- )*3,L0 10-0L0 /50 C, 10
k07(, / [* =27*D 2 /-7 6)3 6)/C23(244 =)0*(,2*8 *(0 9C, 17 6)3 6( 60 10 )* /,
C, 19. =2( ), /, C2 / ;H6)* )* ®?@{\¯E °?{E ±A? ²@A_FA ?¡ G@A D 2
4 60 /, 90 /, /7 6)3 662* /,4 1,4 0 1(8 ( 62(32 /5032 ==0-2 /D 7 6)3 6C23( 62*
l
500 /902*. 10-0 N4 0 1)90 /(2 ==8 (,4 60 /, 90 /2 ==8 6)+ 6233. 1238 ;H6.*D 0L0 /)/
,. 1I1*(0 N2 94 =0D 707 )==- )*3,L0 12.*0, C9)/)9)]2( ), /4 1)/3 )4 =0*( 62(32 11)0*
.* C. 1( 60 1( 62 /703,. =- 1023 67 )( 6 D 2 /- )/( 60*.5*0K .0 /(*03( ), /*
707 )==* 6,7 6,7 )(2 =*, =02-*(, 2*23, /*0K .0 /307 60 /( 600K .2( ), /
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H60-0*3 1)4 ( ), /0 192(72*25 =0(, C, 19. =2(0 C, 1=)+ 6( )*23. 1),.**, 1(, C5 1)-+ 0
50(700 /,. 1* )94 =0*( 9)/)9)]2( ), /=27 C, 11.550 152 /-*2 /-( 60, /0707 )==
0L0 /(.2 ==8 =02 1/(,.*0 C, 1( 604 2( 6*, C,5x 03(* ;H6)* )*5032.*0D 7 6)=0 =)+ 6(
( 12L0 =*( 61,.+ 6*4 230 M( )90D =):0y ,( 60 1 ,5x 03(*D4 0,4 =0.*.2 ==8 .*0 =)+ 6(58
*0 /- )/+ =, /+ b*( 102 9* g, C)(D 12( 60 1( 62 /)*, =2(0-* )/+ =0 b4 )030* g;'/( 62(*0 /*0D
2 b*( 102 9 g, C=)+ 6(,33.4 )0*2 ==, C)(*4 2( 62(, /30D 9.3 6=):07 6, =03, ==03( ), /
, C=)(( =05 )(*, C1.550 1( 62( 92 :0.4 ( 6052 /-D 3, /* )-0 10-(,+ 0( 60 1D ,33.48 )(*
7 6, =04 2( 62(, /30 ;H60 10 C, 10D )(7 )==50+ ,,-(, :004 )/9)/-( 62( )( )*5032.*0
702 103, /* )-0 1)/+ b92 /8 4 )030* g, C=)+ 6(3, ==03( )L0 =8 ( 62(702 1025 =0(,(2 =:
25,.(( 607 6, =04 2( 62* )C)(70 1024 2( 6)/*4 230D 0L0 /( 6,.+ 6( 60 1. =0707 )==
I/- )*0 N4 =)3 )( =8 2 1. =0( 62(-04 0 /-*, /( )90 ;
)1*(D 70 62L0(,. /-0 1*(2 /- 6,7( 60 /,( ), /, C24 2( 60L0 /2 1)*0*7 60 /70
2* :6,7 =)+ 6(50 62L0* ;J .44 ,*0 =)+ 6(* 6)/0* C1, 9*, 90*,. 130D =):02 =2 94D (,
*, 90, /0\[*08 0 ;H60 =)+ 6((8 4 )32 ==8 * 6)/0* )/2 ==- )103( ), /*D 2 /- I==*.4 ( 60*4 230
2 1,. /-( 60 =2 94 ;©0(703,. =-4 .(2 I/+ 0 12(x .*(( 60 1)+ 6(4 =230D 50(700 /( 60
=2 94 2 /-( 6008 0D 2 /-5 =,3 : b( 60 =)+ 6( g( 62(( 604 0 1*, /*00* ;Á , )/+ C. 1( 60 1D
703,. =-0L0 /4 .(25, N2 1,. /-( 60 =2 94 7 )( 62* 92 ==6, =0 )/)(D (,4 10L0 /( /,(
x .*(4 2 1(D 5.(2 =9,*(2 ==, C( 60 =)+ 6( C1, 9+ 0(( )/+ ,.( ;'/( 62(32*0D . /=0**( 60
6, =072* )/x .*(( 60 1)+ 6(4 =230D ( 6008 07,. =- /,(*00( 60 =)+ 6(2(2 ==;Á , )/+
0L0 /C. 1( 60 1D 703,. =-0 103(27 6, =0 1,7, C52 Â0*y 72 ==*7 )( 66, =0* )/( 60 9
50(700 /( 60 =2 94 2 /-( 6008 0 ;Ã /=0**2 ==, C( 60 6, =0*2 10 )/x .*(( 60 1)+ 6(4 =230*
I+ ; ;lD ( 6008 032 //,(*00( 60 =)+ 6( ;)/2 ==8 D 70 /,(0( 60,5L ),.*4 , )/(( 62( )(
)*( 60*04 2 1( )3. =2 16, =0*( 62( 92((0 1;< 03,. =-4 , :0,( 60 16, =0* )/( 6052 Â0*
7 60 10L0 10 =*070 =):0D 2 /-( 608 7,. =- / [( 92 :02 /8 - )O0 10 /30 ;
'(503, 90*3 =02 1D ( 60 /D ( 62( )/*4 )(0, C( 60 C23(( 62( =)+ 6( C1, 9=2 94 *(0 /-*
(, I==.4 *4 230D ( 60 10 )**, 90 /,( ), /, C2 b4 2 1( )3. =2 14 2( 6 g( 12L0 =0-58 7 62(0L0 1
=)+ 6(+ ,0* C1, 9( 60 =2 94 (,( 6008 0D 5032.*02(2 /8 4 , )/(2 =, /+ ( 60728 D 7032 /
)/(0 11.4 ( )(Dx .*(2* )C7070 104 .(( )/+ 272 ==)/( 604 2( 6, C2 «8 )/+ ,5x 03( ;H60
*( 102 9, C=)+ 6(( 62(( 12L0 =*2 =, /+ , /0, C( 60*04 2( 6* )*.*.2 ==8 10 C0 110-(,2*2
ÄU ;j2(0 1707 )==*00(,7 62(0 N(0 /(( 60 =)+ 6(( 62( 92 :0*.4 2 128 )* 102 ==8
=):02 b3, ==03( ), /, C,5x 03(* g;, 1/,7D ( 60 C23(( 62( 128 *0 N)*(D 2 /-( 62(( 608
)-0 /( )C8 4 2 1( )3. =2 14 2( 6*D 7 )==2 ==,7.*(,*4 02 :, C( 60(7, )/(0 13 62 /+ 025 =8 ;
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)+ . 10 ;l a=)/0, C52 Â0*50(700 /*, 90 =)+ 6(*,. 1302 /-( 6008 0 ;Ã /=0**( 60
6, =0* )/2 ==, C( 6052 Â0* =)0 )/2*. )(25 =8 *( 1)2+ 6( =)/0D ( 6008 0*00* /, /0, C( 60
=)+ 6( ;H60K .0*( ), /( 60 /503, 90* 7 62( 1. =0 )-0 /( )I0*( 6023(.2 =128 *, /7 6)3 6
=)+ 6(( 12L0 =* f< 62(0L0 11. =070.*0D )( 9.*(50*. 3 )0 /( =8 10*( 1)3( )L0( 62( )(
/0L0 14 10- )3(*2 128 ( 62(70-, / [(*00D 2 /-*. 3 )0 /( =8+ 0 /0 12 =(, )/3 =.-02 ==
( 6,*0( 62(70-, ;< 07 )==* )94 =8 3, /* )-0 1*, 90 102 =*8 *(0 9*D 2 /-*007 62(
1. =0*2 104 ,** )5 =0 ;)1*(D 2 /-* )94 =0*(D )*( 6032*0, C=)+ 6(x .*(* 6)/)/+ ( 61,.+ 60 94 (8 *4 230 ;
H60 128 * )(( 12L0 =**00 9(,50* )94 =0*( 12 )+ 6( =)/0* ;< 62(( 6)* 902 /* )*( 62(D )C
702* :7 62(4 2((0 1/, C6, =0* )/52 Â0* )*_?F?EE{@£ C, 1( 6008 0(,*00( 60 =)+ 6(D
70 I/-( 62(( 608 9.*(2 ==50 )/2*( 12 )+ 6( =)/0D 2 /-2 /8 , /0( 62( )* / [(5 =,3 :*
( 60 =)+ 6( ;J ,,. 1I1*(+ .0** 9)+ 6(50* )94 =8 ( 62( =)+ 6(( 12L0 =*, /=8 *( 12 )+ 6(
=)/0* ;k,7D ( 6,.+ 6D 702* :25,.(( 60*2 90 =)+ 6( 10 «03( )/+ C1, 92 9)11, 1;a*
* 6,7 /)/I+ ; ;ÅD 703,. =-5 =,3 :, O( 60*( 1)+ 6( M=)/0 128 * C1, 9( 60 =2 94 (,( 60
08 0D 2 /-( 60 =)+ 6(7 )==*( )==50*00 /)/( 60 10 «03( ), /;H60 I1*(4 1,5 =0 97 )( 6
( 60 9)11, 1)*( 62(_G_?, C( 604 2( 6* C1, 9=2 94 (,08 0D 58 728 , C( 60 9)11, 1D
)*2*( 12 )+ 6( =)/0 ;H608 2 102 ==50 /( ;H60*03, /-4 1,5 =0 9)*( 62(D 0L0 /)C70
3, /* )-0 14 2( 6* 92-0 C1, 9 A?F?E, C*( 12 )+ 6( =)/0*D ( 60 102 10 92 /8 *.3 64 2( 6*
=02- )/+ C1, 9=2 94 (,08 0y I+ ; ;Å ;©0(D ( 60 10 )*, /0*4 03 )2 =4 =230, /( 60 9)11, 1
7 60 10D )C704 .(2-,(, C5 =23 :4 2 )/((, :004 )( C1, 910 «03( )/+ D 703,. =-3.(
, O( 60 10 «03( ), /*00 /58 ( 6008 0y 2* )C70 62-4 .(272 ==( 60 10 ;H6)*4 2( 6
6244 0 /*(,50( 60, /0 C, 17 6)3 6( 60*( 12 )+ 6( =)/0244 1,23 6)/+ ( 60 9)11, 12 /-
( 60*( 12 )+ 6( =)/0 =02L )/+ ( 60 9)11, 15,( 692 :0?E{?{_ ?7 )( 6( 60 9)11, 1
)(*0 =C;H6)* 6244 0 /*D 2 =*,D (,504 103 )*0 =8 ( 604 2( 6( 62( 62*( 60EG@?E GEEAz?
?_ C1, 9( 60 =)+ 6((,( 6008 0D 58 728 , C( 60 9)11, 1;
H6)* =2*( C23( )* /,( )990- )2(0 =8 ,5L ),.*D . /=0**, /0( 6)/:*25,.( 1.550 1;
ll
mirror
anactual ray
not anactual ray
)+ . 10 ;Å j)+ 6( 10 «03( )/+ C1, 92 9)11, 1(,( 6008 0 ;a52 Â0 62*500 /2--0-D
*,( 62(, /=8 =)+ 6(( 62(( 12L0 =* b58 728 , C( 60 9)11, 1 g)*2 ==,70-(,( 6008 0 ;
< 03,. =- )92+ )/0-, )/+ 0 N23( =8 ( 60*2 900 N4 0 1)90 /(D 5.( )/*(02-, C.* )/+ =)+ 6(D
703,. =-*( 10(3 62 1.550 152 /- C1, 9( 60 =2 94 (,( 6008 0D 2 /-4 )/)(2+ 2 )/*(( 60
9)11, 17 )( 6*, 90( 6)/+y C, 10 N2 94 =0D 2 /, )=8 I/+ 0 1 ( 62( )* C100(, 9,L0523 :
2 /- C, 1( 6D 2 /-2 =*,(, =0(( 60 1.550 1* =)-0. /-0 1)(7 )( 6,.( =02L )/+ ( 60 9)11, 1;
H6)* )** 6,7 /)/I+ ; ;Æ ;< 0 :/,7( 60 1.550 1*( 10(3 60*,.((,2 /0L0 /(0 /* ), /
2 ==2 =, /+ )(* =0 /+ ( 6D 5032.*0 )C)(70 10. /-0 16)+ 60 1(0 /* ), /2(, /04 =230( 62 /
2(2 /,( 60 1D )(3,. =-* )94 =8 9,L0(,0L0 /,.(( 62(- )*3 104 0 /38y 10 90 950 1D ( 60
, /=8 4 =230( 60 1.550 1)* b60 =- g)*2(( 60*(2 1( )/+ 2 /-0 /- )/+ 4 , )/(* ;
k,7D 7 60 107,. =-( 60 1.550 1I/2 ==8 3, 90(, 10*( fJ .44 ,*0D C, 1)/*(2 /30D
( 62(70*(2 1(0- )(7 )( 6( 60 I/+ 0 12 /8 7 60 10?ÇF? 2(( 604 , )/(, C b0K .2 =2 /+ =0* g
y , C( 60244 1,23 6)/+ 2 /-( 60 =02L )/+ =)/0* ;J4 03 )I32 ==8 D *.44 ,*070*(2 1(0- )(
, O(,, /0* )-0D 2* )/( 60*03, /-4 2 1(, CI+ ; ;Æ ;j,, :2( 6,7( 60(0 /* ), /C1, 9
( 60(7,4 2 1(*, C( 6052 /- )*- )103(0- ;H60 62 =C( 62( )**( 10(3 60- 9, 10L0 1( )32 ==8
C1, 9( 60 9)11, 14 . ==* 9,*( =8 b*( 12 )+ 6(,.( gC1, 9)(**. 1C230D 2 /- /,(L0 18 9.3 6
(,( 60* )-0 ;J )/30( 60 I/+ 0 17, / [( =0( )( =02L0( 62(*. 1C230D ( 6,.+ 6D ( 6)*(0 /* ), /
233, 94 =)* 60* /,( 6)/+ ;Z /( 60,( 60 1* )-0D 7 60 10( 60 1.550 1)* 9, 10 6, 1)], /(2 =D
9.3 69, 10, C( 60(0 /* ), /)*4 . ==)/+ (,( 60* )-0D 2 /- =0**, C)(*( 12 )+ 6(,.( C1, 9
( 60 9)11, 1;J )/30702 =102-8 :/,7( 62(( 6025*, =.(0(0 /* ), /y 7 )( 6)/( 60 1.550 1
)(*0 =C )*( 60*2 90 )/5,( 662 =L0*y 5032.*0 )( )* C100(,* =)-0. /-0 1( 60, )=8 I/+ 0 1 D
7 6)3 60L0 1* )-0 62*( 60+ 102(0 1¡ @{FAG_, C( 62((0 /* ), /4 . ==)/+ 6, 1)], /(2 ==8 62*
( 60+ 102(0 1{zEG?(0 /* ), /4 . ==)/+ 6, 1)], /(2 ==8 2*70 ==;H60 10 C, 10( 60 I/+ 0 1
)*D )/(,(2 =D4 . ==0- 9, 10* )-0728 *58 ( 60 6, 1)], /(2 =*03( ), /( 62 /58 ( 60L0 1( )32 =
*03( ), /D 2 /-( 60 I/+ 0 132 /02*0( 62((0 /* ), /58 9,L )/+ (,72 1-( 60* )-0, /
7 6)3 6( 60 1.550 1)* 6, 1)], /(2 =D (, 92 :0 )( =0***, ;H60 C23(( 62(( 60 1.550 1)*
4 . ==)/+ ( 60 I/+ 0 1( 62(728 9.*( 902 /( 62( )(* =0 /+ ( 632 /50 10-.30-58 9,L )/+
( 60 I/+ 0 1( 62(728 ;H60, /=8 4 =230( 60(7,(0 /* ), /*0 N23( =8 0L0 /,.(D 2 /-( 60
(b)(a)
)+ . 10 ;Æ a1.550 152 /-D *( 10(3 60-(, 9)9)3( 60 b4 2( 6 g, C=)+ 6(5,. /3 )/+
, O2 9)11, 1;H60 I/+ 0 1D 60 10D , /=8 2 ==,7*4 2( 6*7 6)3 6(,.3 6( 60 9)11, 12(
*, 904 , )/(D 5.(( 60 I/+ 0 1)(*0 =C32 /* =)-0523 :2 /- C, 1( 6, /( 60 9)11, 1D 2 /-( 60
1.550 1)* C100(,- )*( 1)5.(0 )(*0 =C58 * =)- )/+ 50 /02( 6( 60 I/+ 0 12*70 ==;i2 1(y 2
* 6,7*( 60 b*8 990( 1)3 g4 2( 623(.2 ==8 (2 :0 /58 =)+ 6(, 1( 60 1.550 1D 2 /-4 2 1(y 5
2 /2*8 990( 1)34 2( 6703,. =- C, 13058 6, =- )/+ ( 60 I/+ 0 1(,, /0* )-0 ;
I/+ 0 1)*4 . ==0- /0 )( 60 1, /0728 /, 1( 60,( 60 1D )*( 604 =2307 60 105,( 62 /+ =0*
2 10( 60*2 90 ;a(( 6)*4 , )/(D * )/30( 6025*, =.(0(0 /* ), /*2 10( 60*2 90D 2 /-( 60
2 /+ =0*2 10( 60*2 90D ( 60 C123( ), /*2 10( 60*2 90D 2 /-*,( 60* )-0728 *(0 /* ), /*
, /( 60 I/+ 0 12 102 =*,( 60*2 90 ;H60 10 )* /, )/30 /( )L0 C, 1( 60 I/+ 0 1(, 9,L0
, /0728 , 1( 60,( 60 1;H6.*D ( 6)* 9.*(50( 60* 6, 1(0*( =0 /+ ( 6( 60 1.550 132 /
23 6)0L0 ;J )/30 =)+ 6((2 :0*( 60*2 904 2( 6D )(244 02 1*(,50 62L0 9.3 6=):0 1.550 1D 2 /-
)/-00-+ )L0*.*2 /07+ .0** C, 1( 60 1. =0 C, 1=)+ 6( ( 62( )((2 :0*( 604 2( 6, C
9)/)9. 9=0 /+ ( 6;k,(, /=8 -,0*( 6)*7, 1:C, 19)11, 1*D )(2 =*,3, /( )/.0*(,7, 1:
I/0 C, 10 94 (8 *4 230D 5032.*0 )(x .*(3 6,,*0**( 12 )+ 6( =)/0*D C, 1=)+ 6(, 11.550 1;
H6)*-,0* /,(K . )(0*. 30D ( 6,.+ 6;k,7703, /* )-0 1=)+ 6(( 62(*(2 1(* )/, /0
:)/-, C92(0 1)2 =2 /-( 12L0 =*23 1,**25,. /-2 18 )/(,2 /,( 60 1;, 1)/*(2 /30D 70
3,. =-50 =,, :)/+ 2(2 bL0 18 * 6, 1(4 0 1*, / g*(2 /- )/+ )/2*7 )99)/+ 4 ,, =D , 12(
2 b50 /(4 0 /3 )= g)/2+ =2**, C72(0 1;H60 10 )* /, 9)11, 1)/( 6)*32*0D 5.(3 =02 1=8
( 60 =)+ 6(4 2( 6*2 10 /,(*( 12 )+ 6( =)/0*D 7 6)3 6)*7 68 ( 604 0 1*, /=,, :** 6, 1(2 /-
( 604 0 /3 )==,, :*50 /( ;H6)**8 *(0 9)* 9, 103, 94 =)32(0-D 5.(0L0 /)( 62-500 /. /-0 1*(,,-0 94 )1 M
)32 ==8 4 1), 1(, 0 192( ;H604 1,5 =0 9)*( 62(D -04 0 /- )/+ , /7 60 1070*(2 /-
10 =2( )L0(,( 604 0 1*, /)/( 6072(0 1D ( 60 1032 /50 92 /8 - )O0 10 /(2 /+ =0* 92-058
( 60 128 *, C=)+ 6( ;< 0 /00-2 1. =0( 62( )*3, /* )*(0 /(7 )( 62 ==, C( 60 9D 5.(( 62(
3, 1103( =8 4 10- )3(*( 60 10 =2( ), /A_{_£ AB?_F{E?50(700 /( 60 =)+ 6( 128 244 1,23 6 M
)/+ ( 6072(0 1*. 1C230 C1, 950 =,7D 2 /-( 60, /0 =02L )/+ )( C1, 925,L0 ;J .3 62
lÅ
=27 62-500 /C,. /-58 ffJ /0 ==D 2 /- )( )*( 6)*
È SWYYÊÉËUÌH60 SW, C( 602 /+ =0 92-058 ( 60 128 50 =,72 /-( 60 SW, C
( 602 /+ =0 92-058 ( 60 128 25,L0D 2* 902*. 10- C1, 9( 60L0 1( )32 =D 2 =728 * 62L02
IN0- 12( ), ;H6)**00 9*25 )(,5*3. 102( I1*(D 5.( )( )* 102 ==8 2 =9,*(( 60*2 90( 6)/+ 2*
70 C,. /- C, 1( 60 9)11, 1;H60* )/0, C( 602 /+ =0 )*x .*(( 60 12( ),, C( 60 6, 1)], /(2 =
- )*(2 /30 )(3,L0 1*D 50(700 /2 /8 (7,4 , )/(*D 2 /-( 60 =0 /+ ( 6, C( 607 6, =04 2( 6
y 2 =, /+ ( 60- )2+ , /2 = 50(700 /( 6,*0(7,4 , )/(* ;H6.* )( )*0 N23( =8 ( 60*2 90
12( ),2*,. 112( ),, C(0 /* ), /* )/( 6032*0, C( 60 1.550 152 /- ;H60(0 /* ), /)/
( 60 1.550 1)(*0 =C=)0*2 =, /+ ( 60- )2+ , /2 =D *,( 60* )/0, C( 602 /+ =0+ )L0*( 604 2 1(
, C)(( 62( )*4 . ==)/+ 2 =, /+ ( 60 6, 1)], /(2 =;H60, /=8 - )O0 10 /30 )*( 62( C, 1( 60
9)11, 1D ( 60(7, b6, 1)], /(2 =(0 /* ), /* gy 2 11)L )/+ 2 /--04 2 1( )/+ 70 102 =728 *( 60
*2 90 ;e0 10( 608 2 102 =728 **32 =0-58 *, 90 IN0- 12( ), ;H62( 12( ), 6244 0 /*(,
50-0(0 19)/0-58 7 62(( 60*.5*(2 /30*2 10( 62(( 60 =)+ 6( )*( 12L0 =)/+ ( 61,.+ 6D
*.3 62*2 )12 /-72(0 1D 2 )12 /-+ =2**D 72(0 12 /-+ =2**D 0(3 ;
'(7 )==/,(50*. 14 1)* )/+ D ( 60 /D ( 62(( 6)* bIN0-* )/0 12( ), g=27, CJ /0 ==)*
3 =,*0 =8 10 =2(0-(,( 60 =0 /+ ( 6 M9)/)9)]2( ), /1. =070+ .0**0- C, 1( 60 9)11, 1;'/
C23(D )( )*0 N23( =8 7 62(707,. =- 62L0 62- )C( 60 b(0 /* ), /* )/( 60(7, 62 =L0*
, C( 60 1.550 1 gy 25,L0, 1. /-0 1( 6072(0 1*. 1C230 62- /,(500 /0K .2 =D 5.(
62-500 /*, 90 IN0- 12( ),, C023 6,( 60 1Dx .*(2* )CD *, 90 6,7D ( 604 )030, C( 60
4 2( 662-500 / b*( 10(3 60- =, /+ 0 1( 62 /70( 6,.+ 6( g)/, /0, C( 60(7,4 =230*D (,
)/3 102*0( 60(0 /* ), /;, 11.550 1D 702**,3 )2(04 2( 6=0 /+ ( 67 )( 6(0 /* ), /;'C(7,
4 )030*, C1.550 12 10*( 10(3 60-( 60*2 902 9,. /(D ( 608 62L0( 60*2 90(0 /* ), /;
a/- )/1.550 1D )( )*( 60(0 /* ), /*( 62(4 . ==, /( 6)/+ *(,0L0 /(.2 ==8 4 =230( 60 9
, /( 6023(.2 =4 2( 6;©0(D )/( 600 /-D 70-, /,( /00-(,3, /* )-0 1G}( 60(0 /* ), /*23 6)0L0( 60
23(.2 =4 2( 6D 5032.*070 :/,7( 62( )( )* 9)/)9)]2( ), /, C=0 /+ ( 6( 62(*4 03 )I0*
( 62(4 2( 6D 2 ==58 )(*0 =C;J ,D 62L )/+ .*0- )((,. /-0 1*(2 /-7 62( =)+ 6( )*-, )/+ D 70
32 //,7*(,4 .* )/+ ( 60 =2 /+ .2+ 0, C(0 /* ), /*D 2 /-* )94 =8 *28 ( 62(D C, 19)11, 1*D
( 6023(.2 =4 2( 6, C=)+ 6(72*( 604 2( 6, C9)/)9. 9=0 /+ ( 6;k,7D 3, /* )-0 1)/+ ( 60
72(0 1Í 2 )1*8 *(0 9D ( 60 =0 /+ ( 6( 62( )* 9)/)9)]0-*00 9* /,((,50( 60 =0 /+ ( 6( 62(
70 902*. 10D 5.(*, 90,( 60 1K .2 /( )(8 ( 62( )*4 1,4 , 1( ), /2 =(, )(58 2 /,L0 12 ==10 M
*32 =)/+ D -04 0 /- )/+ , /7 60( 60 1( 60 =)+ 6( )*( 12L0 =)/+ )/2 )1D . /-0 172(0 1D )/+ =2**D
, 17 60 10L0 1;'/4 2 1( )3. =2 1D ( 60 b0 O03( )L0 =0 /+ ( 6 g)/2 )1*00 9*(,50* 6, 1(0 1( 62 /
( 60 =0 /+ ( 670 902*. 10D 2 /- )/72(0 1)(*00 9*(,50 =, /+ 0 1;'/,( 60 17, 1-*D =)+ 6(
50 /-*5032.*0D 58 -, )/+ *,D )(32 /+ 0( 9, 10 124 )- =8 (,( 60*. 1C230D 2 /-*,4 .(
=0**, C)(*4 2( 6=0 /+ ( 6. /-0 172(0 1;H604 1)30 )*( 62( 9, 104 2( 6=0 /+ ( 69.*(
50( 12L0 =0- )/2 )1;H6)* )* /,(-, /0D ( 6,.+ 6D (,( 6025*, =.(0 =8+ 102(0*(0 N(0 /(
4 ,** )5 =0D 5.(, /=8 )/2 902*. 10- 12( ), ;
0 192( [*,5*0 1L2( ), /72*( 62(( 60* )94 =0*(( 6)/+ (,2**. 907,. =-50( 62( =)+ 6(3, /* )*(0-, C*, 90,5x 03(* b( 12L0 =)/+ ,L0 1( 60*04 2( 6* gD 5.(7 )( 62E ??>
( 62(-04 0 /-0-, /7 62(( 60 =)+ 6(72*( 12L0 =)/+ @G ;'/( 62(32*0D ( 60A?
(2 :0 /(,( 12L0 =24 2( 67,. =-2 =728 *504 1,4 , 1( ), /2 =(,( 60 =0 /+ ( 6, C( 604 2( 6
A_?{FEzE{_F?D 5.(( 604 1,4 , 1( ), /2 =)(8 C23(, 17,. =-50- )O0 10 /( )/72(0 1
( 62 /)/2 )1D , 1+ =2**D , 17 62(0L0 1;a**.3 6D )C( 60 12( ),*, C*4 00-*70 103 6,*0 /
3, 1103( =8 D 2 /-( 60A? 9)/)9)]0-2 =, /+ ( 6023(.2 =4 2( 6D ( 6)*7,. =-4 1,-.30
0 N23( =8 ( 60* )/0 M12( ), =27, CJ /0 ==;
'C( 60*4 00-, C=)+ 6( )/72(0 170 10* =,70 1( 62 /( 62( )/2 )158 2 IN0-2 9,. /(D
=)+ 6(3,. =-2 =728 *50 /- )/*.3 62728 ( 62( =0**72(0 1 M4 2( 63,. =-50( 12L0 =0-D
)/0 N3 62 /+ 0 C, 19, 102 )1 M4 2( 6;`L0 /( 6,.+ 6( 60G{?_ @{B??>7,. =-50
+ 102(0 1D ( 60*2L )/+ , C( )9058 ( 12L0 =)/+ =0** C2 1. /-0 172(0 17,. =-,.(70 )+ 6( 60
0 N( 12( )90 /00-0-(,( 12L0 =* =)+ 6( =8 C. 1( 60 1)/2 )1D 2 /-( 60G{A?7,. =-50
10-.30- C1, 9( 62(, C2*( 12 )+ 6( M=)/04 2( 6;, 1( 60* )94 =0 132*0, C( 60 9)11, 1D
7 60 10( 60 =)+ 6(( 12L0 =*( 61,.+ 6( 60*2 90 90- ). 9, /5,( 662 =L0*, C( 604 2( 6D
( 6)* 10-.30*(,4 103 )*0 =8 ( 60 10*. =(, C9)/)9. 9=0 /+ ( 6( 62(70 62-50 C, 10D
2 /-, C3,. 1*0 )(7, 1:*4 0 1C03( =8 )/0 94 (8 *4 230D 5032.*0 9)/)9. 9=0 /+ ( 62 /-
9)/)9. 9( )905,( 6)-0 /( )C8 ( 60*( 12 )+ 6( =)/04 2( 6* ;H6)*D ( 60 /D )* 0 192( [*
3, /3 =.* ), /ÎWÄVUX ÉËWUXÏVWÐÄS¬Ñ YWQÄËÒ Xj)+ 6(( 12L0 =)/+ ( 61,.+ 6*, 90
*.5*(2 /30 62*2*4 00-7 6)3 6)*-0(0 19)/0-58 ( 60*.5*(2 /30 ;H6023(.2 =4 2( 6
(2 :0 /58 =)+ 6(50(700 /2 /8 (7,4 , )/(*D )/2 /8 3, 95 )/2( ), /, C*.5*(2 /30*D )*
2 =728 *( 604 2( 6, C?{EA?( 62(32 /50( 12L0 =0-2(( 60 10K . )10-*4 00-* ;
H, /,( )30, /0 9, 102*4 03(, C0 192( [* 1. =0D 707 )===,, :2(, /0, C)(* 9, 10
.*0 C. =244 =)32( ), /* ( 62(, C92 :)/+ =0 /*0* ;
< 07 )==, /=8 7, 118 25,.( =0 /*0*7 6,*04 . 14 ,*0 )*(,¡ GFE =)+ 6(D ( 62( )*D (,
+ 2( 60 12* 92 /8 , C( 60,.(+ , )/+ 128 * C1, 9*, 90*,. 1302*4 ,** )5 =0D 2 /-5 1)/+
( 60 9523 :(,+ 0( 60 12(2* )/+ =04 , )/( ;'/,( 60 17, 1-*D ( 60 C. /3( ), /, C2 C,3.* )/+
=0 /* )*(,3 102(0{_£ 23(.2 =4 2( 6* C1, 92*(2 1( )/+ (,2 /0 /- )/+ 4 , )/( ;e,7( 6)*
32 /504 ,** )5 =0 )** 6,7 /)/I+ ; ;Ó ;^8 0 N4 0 1)90 /( )/+ 7 )( 6=)+ 6(( 12L0 =)/+ )/
2 )12 /-+ =2**D 7032 /-0(0 19)/0 C1, 90 192( [*4 1)/3 )4 =0( 62( =)+ 6(( 12L0 =* 9, 10
* =,7 =8 )/9,*(+ =2**0*( 62 /)/2 )1;y a10( 60 100L0 /2 /8 0 N304 ( ), /* f H60 10 C, 10D
58 92 :)/+ 2 =. 94 , C+ =2**( 6)3 :)/( 60 9)-- =02 /-( 6)/2(( 600-+ 0*D 2 /-
4 =23 )/+ )(2** 6,7 /50(700 /2 =2 94 2 /-2 /08 0D ( 60 1032 /50 92 /8 4 2( 6*D 2 ==
, C=02*(( )90 ;H604 2( 6* )/( 6030 /(0 1( 12L0 =* 6, 1(- )*(2 /30* )/2 )1D 5.( 9.*(
( 60 /( 12L0 ==, /+ - )*(2 /30* 9, 10* =,7 =8 )/( 60+ =2** ;a=)(( =0(,( 60* )-0D )C( 60
=0 /* )*3, 1103( =8 * 624 0-D ( 60 102 104 2( 6*, C+ 102(0 1,L0 12 ===0 /+ ( 6D 7 )( 62 ==, C( 60
)/3 102*0(2 :0 /.4 )/2 )1D 2 /-2>?F@?{E? )/( 60 =0 /+ ( 6( 12L0 =0-( 61,.+ 6+ =2**D
7 6)3 632 /2+ 2 )/9)/)9)]0( )90 ;H6)*4 , )/(*,.((7, )/(0 10*( )/+ 4 1,4 0 1( )0*, C0 192( [*4 1)/3 )4 =0D ( 62(32 /50
*00 /2(7, 1:)/102 =4 68 * )32 =*8 *(0 9* ;Z C(0 /D , /0(0 /-*(,( 6)/:, C( 60*(2 1( )/+
lÆ
lens
rays)+ . 10 ;Ó i2( 6*, C=)+ 6(( 61,.+ 62 C,3.* )/+ =0 /* ;
3, /- )( ), /*, C24 2( 62*( 60, /=8 728 (,*4 03 )C8 7 62(( 62(4 2( 67 )==50 ;1, 9
( 6)*4 , )/(, CL )07D )(*00 9**( 12 /+ 0( 62(2.*0 C. =-0*3 1)4 ( ), /, C4 2( 6*?B?_FG>
5052*0-, /)/C, 192( ), /25,.(( 60 )1*(2 1( )/+ 2 /-0 /- )/+ 4 ,* )( ), /*2 =, /0 ;©0(
C, 1=)+ 6(D )( )* /,(0L0 /3 =02 12 602-, C( )907 6)3 6, C( 60*(2 1( )/+ 128 *y 7 )( 67 6)3 6
- )103( ), / 7 )==2 11)L02(( 60 I/2 =-0*( )/2( ), /D . /( )=)( 62*500 /*4 03 )I0-7 62(
3, 95 )/2( ), /*, C2 )1D 72(0 1D+ =2**D 0(3 ;D =)050(700 /;H6)* )*7 68 2 9)/)9)]2( ), /
1. =0( 62(-04 0 /-*, /*(2 1( )/+ 2 /-0 /- )/+ -2(232 /*( )==7, 1:2*2 /)-0 /( )I0 1, C
4 2( 6* ;H60*03, /-4 , )/(2 1)*0*5032.*070 62L0.*.2 ==8 *4 , :0 /, C)-0 /( )C8 )/+ D C1, 9
2 9, /+ 2 ==)92+ )/25 =04 2( 6*D b( 6023(.2 =4 2( 6 g( 62(2 /,5x 03((2 :0* )/2+ )L0 /
3 )13. 9*(2 /30 ;< )( 6( 60 =0 /*D ( 6,.+ 6D 70*00( 62( )/C23(( 60 102 10*8 *(0 9*7 )( 6
2 =2 1+ 02 95 )+ . )(8 D )/7 6)3 6( 60 1032 /50{_£ 23(.2 =4 2( 6*( 62(2 /,5x 03(32 /
3, /* )*(0 /( =8 (2 :0D 0L0 /+ )L0 /( 60*2 90*(2 1( )/+ 2 /-0 /- )/+ 4 , )/(* ;
)/2 ==8 D 50 C, 1070+ ,, /(, =,, :2(+ 0 /0 12 =4 1,4 0 1( )0*, C9)/)9)]2( ), /1. =0*D
70 =)*(, /032L02(3, /30 1/)/+ ( 6)*0 N2 94 =0 ;j)+ 6( )*. /.*.2 =*(. O;< 07 )==
I/-( 62(,.(D 2+ 2 )/2 /-2+ 2 )/D 2*70. /-0 1*(2 /- )( )/9, 102 /- 9, 10728 * ;'(
62*2 =102-8 500 //,(0-( 62(D 5032.*070(0 /-(,7, 1:7 )( 6)( )/=, /+ *( 102 9*D
)(50 62L0* 9, 10 =):0 1.550 152 /-*D =)(0 12 ==8 D ( 62 /92 /8 , C,. 1,( 60 10 N2 94 =0*
7 )==;'( )* /,(K . )(0 =):0 1.550 1D ( 6,.+ 6D 5032.*0( 60 1. =070 62L0. /3,L0 10-
)-0 /( )I0*2 {@G E {F?58 902 /*, C2F@A?@AG_G¡ A? ;e,70L0 1D )(7 )==
2 =*, /,(50K . )(0 =):0,( 60 1,5x 03(*707 )==- )*3,L0 1D 0 )( 60 1D 5032.*0( 604 2( 6
70 62L0 C,. /- )**( )=={ {@G E {F? ;'/=2(0 10 N2 94 =0*D4 )3(. 10*, C4 2( 6*
( 61,.+ 6*4 2302 =, /07 )==/,(500 /,.+ 6(,0L0 /C12 90( 60K .0*( ), /*3, 1103( =8 D
2 /-( )907 )==/,( 90 10 =8 5023 1)(0 1), /D 5.( 12( 60 12 /0**0 /( )2 = b4 2 1(, C( 60
924 g/00-0-(, )-0 /( )C8 - )O0 10 /( )92+ )/25 =04 2( 6* ;H60 10 C, 10D ( 60 10*. =(*70
7 )==I/-7 )==2+ 2 )/50*, 907 62(- )O0 10 /(D )/( 604 2 1( )3. =2 1*D C1, 90 192( [* 4 1)/3 )4 =0 ;H60*0 =2((0 1- )O0 10 /30*2 11)*05032.*0A {E_G{EED 7 6)3 6)*2 /
0 N( 10 90 =8 3, 99, /3 62 123(0 1)*( )3, C9,*(, C( 60,( 60 1*8 *(0 9*707 )==3, /* )-0 1;
H62(- )O0 10 /302 =, /0 )*0 /,.+ 6(, 92 :0 9,*(, C( 60 1. =0*( 62(32 /504 612*0-
C, 1=)+ 6(D 0L0 /)C( 608 3, 90 C1, 9( 60*2 904 1)/3 )4 =0*2** )9)=2 11. =0* C, 1,( 60 1
,5x 03(*D =,, :K . )(0- )O0 10 /( )/( 60-0(2 )=* ;
< )( 6( 60*00 N2 94 =0* )/9)/-D 70 /,7 10(. 1/(,( 60 10 =2( ), /, C9)/)9)]2( ), /
1. =0*(,0K .2( ), /*, C9,( ), /D )/( 60+ 0 /0 12 =32*0 ;
� �Ôv q·¨ &" � " Àq´Õ $ ¨ &" �½" u¦" &" �
a* 62*2 =102-8 500 /10 92 1:0-D ( 60 I1*(( 6)/+ 707 )===02 1/7 60 /( 18 )/+ (,.*0
9)/)9)]2( ), /(,-0*3 1)50( 60 9,( ), /*, C b,5x 03(* g)*( 62(70 62L0(,.*02
9, 1032 10 C. =-0*3 1)4 ( ), /, C4 2( 6*( 62 /70 62L0*, C2 1;H6)* )*5032.*0( 60 10 )*
2 /)94 , 1(2 /(- )O0 10 /3050(700 /( 60 9,( ), /*, C,5x 03(*( 61,.+ 6*4 2302 /-( 60
4 ,* )( ), /, C2*( 10(3 60- 1.550 152 /-, /2(25 =0 ;
a*( 10(3 60- 1.550 152 /- )*2 =, /+ 0 N(0 /-0-( 6)/+ D 2 /- )(*L2 1),.*4 , )/(* =28
)/230 1(2 )/( 123 :, /( 60*. 1C230, C( 60(25 =0( 62(-,0* / [(3 62 /+ 0 C1, 9, /0( )90
(,( 60 /0 N(2* =, /+ 2*70-, / [(3 62 /+ 0( 60728 702 10 6, =- )/+ ( 6052 /- ;H6.*D
( )90 )* 102 ==8 /,(23, /* )-0 12( ), /)/( 60-0*3 1)4 ( ), /, C( 6052 /-D 2 /-7032 /
3, /30 1/,. 1*0 =L0*, /=8 7 )( 6( 60*4 2( )2 =0 N(0 /( )(,33.4 )0* ;
'/2*, 907 62(- )O0 10 /(728 D 0 192( [* =02*(( )904 1)/3 )4 =03 6,*02*4 2( )2 =
4 2( 6( 62(72*( 60*2 902 =728 *D 5032.*0 =)+ 6(32 /50 92-0(,* 6)/03, /( )/.,.* =8
)/2728 ( 62( 92 :0* )( =,, :=0** =):02 9,L )/+ ,5x 03(( 62 /=):02*( 102 9)/+
3. 110 /(D *, )( 92 :0**0 /*0(,(2 =:, C( 60*4 2( )2 =4 2( 62*2( 6)/+ ( 62(-,0* / [(
3 62 /+ 0 C1, 9, /0( )90(,( 60 /0 N( ;©0(( 6)*4 2( 672*3 6,*0 /, /4 103 )*0 =8 2
3 1)(0 1), /, C( )90D 2* )C( 60 =)+ 6( «,7 )/+ 2 =, /+ ( 604 2( 670 103, 94 ,*0-, C2 =)(( =0
*( 102 9, C9,L )/+ ,5x 03(*D 023 6, C7 6)3 632 11)0-2 =)(( =03 =,3 :( 62(72**, 90 6,7
)94 , 1(2 /( )/-0(0 19)/)/+ 7 6)3 64 2( 6)(7,. =-( 12L0 =;
a==, C,. 14 10L ),.*-0*3 1)4 ( ), /*D ( 6,.+ 6D , CC2 ==)/+ ,5x 03(*, 1,5x 03(*, /
*4 1)/+ *D )/L, =L0- /,(*( 102 9*, C92 /8 ,5x 03(*, 10 N(0 /-0-( 6)/+ * =):0 1.550 1
52 /-*D 5.( )*, =2(0- )/- )L )-.2 =5 =,3 :*( 62(( 12L0 =0-( 61,.+ 6*4 2302 =, /+ *, 90
( 12x 03(, 1)0* ;a==, C,. 1-0*3 1)4 ( ), /58 72*(28 =, 10-(,*.3 6*8 *(0 9* ;
H6.*D (, 10 =2(0 (, 9)/)9)]2( ), /D 70 62L0(,50*, 907 62( 9, 10+ 0 /0 12 =
2 /-32 10 C. =)/,. 1-0*3 1)4 ( ), /*( 62 /7070 10 C, 10 )( 60 11.550 152 /-*, 1=)+ 6(D
2 /- )-0 /( )C8 ( 60 9,L0 90 /(, C( 60,5x 03(*2*4 2( 6*( 1230-,.( )/*4 2302 /-
( )90 ; 0 1(2 )/=8 D 70 :/,7 C1, 90 N4 0 1)0 /30( 62( )( )* /,(, /=8 7 62(*4 2( )2 =4 2( 6
2 1,3 :7,. =- C2 ==( 61,.+ 6D 2* )(7,. =-50*00 /)/2( )90 M=24 *04 6,(,+ 124 6, C
)(* 9,( ), /D ( 62( )* )94 , 1(2 /( )/-0(0 19)/)/+ ( 604 2((0 1/70 103,+ /)]0D 5.(2 =*,
( 60*.330** ), /, C*4 00-*2(7 6)3 6)(4 2**0*( 61,.+ 6023 64 2 1(, C( 62(( 12x 03(, 18 ;
H6.*D C, 1( 60 I1*(( )90D 702 10 10K . )10-(, )/L0 /(( 60 /,( ), /, C2E {F? ÖA?
>A{ @{ ;y < 60 /70 10K . )10 9.3 6( 60*2 90(,, =)/( 60 =2(0 13 624 (0 1*, /*4 03 )2 =
10 =2( )L )(8 D 707 )==10 C0 1(, )(( 60 102*2 b*4 230( )90- )2+ 12 9 gD 5032.*0 )/( 60
ÅÓ
3,. 1*0, C,. 1=2(0 1)/L0*( )+ 2( ), /*D 707 )===02 1/( 62(( 60 10 )*2 9.3 6-004 0 1
10 =2( ), /50(700 /( 60(7,( 62 /70 62L02 /8+ 1,. /-*(,*.*4 03(*, C2 1;
H604 )3(. 10*70 62L0- 127 /, C9,( ), /*, C2 1D =2 1+ 0 =8 7 )( 6,.(0 N4 =2 /2( ), /
5032.*0( 608 2 10 b*0 =C M0 N4 =2 /)(, 18 g62L0500 /, C( 60-,7 /72 1-2 /-* )-0728 *
9,( ), /, CC2 ==)/+ 1,3 :*2*707,. =-*00( 60 9)C7070 10, /=,, :0 1**(2 /- )/+ )/
C1, /(, C( 604 0 1*, /7 6,- 1,44 0-( 60 1,3 :, 1( 6107 )((, 6)** )-0 ;'( 6244 0 /*
( 62(( 60*0 102 ==8 2 10 /,(2(2 ==*0 =C M0 N4 =2 /)(, 18 D 5.(, /( 603, /( 12 18 92 :02
12( 60 1*,4 6)*( )32(0-.*0, C,. 190 9, 18 (,50 C2 9)=)2 12(2 ==;< 0 /0L0 1 b*00 g
( 607 6, =04 2( 6, C2 /8 ( 6)/+ ( 62( C2 ==* ;a(- )O0 10 /( 9, 90 /(*, C( )90D 70*00( 60
,5x 03( )/*.330** )L0 =8 - )O0 10 /(4 =230* ;^.(D 5032.*07032 /10 90 950 17 60 10
)(72*2 9, 90 /(2+ ,D 2 /-7032 /*007 60 10 )( )* /,7D 7032 /4 1,x 03(( 60(7,
, /(,( 60*2 90523 :+ 1,. /- )/,. 1)92+ )/2( ), /*2 /- b*00 g( 607 6, =04 2( 62*2
* )/+ =0 )92+ 0D , 1103,+ /)]0( 60 )/(0 /(7 60 /*, 90, /0- 127*.*232 1(,, /, C)( ;
H,3 102(0( 60*2 904 )3(. 107 )( 6232 90 12D 70 102 ==8 62L0(,7, 1:12( 60 162 1-D
*,( 62(2 ==, C( 60 9, 90 /(*32 /50( 1230-, /( 60*2 90 C12 90, CI=9;
H60 9.3 69, 10 /2(. 12 =( 6)/+ (,-,7 )( 6232 90 12D )C, /07 )* 60*(,-0*3 1)50
9,L )/+ ( 6)/+ *D )*(, 92 :02 9,L )0D *,( 62(D 0L0 /( 6,.+ 6( 60*2 90523 :+ 1,. /-
244 02 1* )/0L0 18 C12 902 /-2+ 102( 10-. /-2 /38 )**. O0 10-D 70 62L02- )O0 10 /(
4 )3(. 10, C7 60 10( 62( C2 ==)/+ ,5x 03( )* 10 =2( )L0(,( 60523 :+ 1,. /- )/023 6C12 90D
-0*3 1)5 )/+ 023 69, 90 /(, C( )907 60 /70(,, :24 )3(. 10 ;
à *.2 ==8 D , /0* )94 =8 =,, :*2( 9,L )0*58 10 M* 6,7 )/+ ( 60 C12 90* )/, 1-0 1D+ )L )/+
( 60*2 90 )94 10** ), /2*( 60, 1)+ )/2 =9,( ), /;^.(2 /,( 60 1( 6)/+ 7032 /30 1(2 )/=8
-, )*3.(2 ==, C( 60 C12 90*, C( 60 9,L )024 2 1(2 /-*(23 :( 60 9D , /0, /(,4 , C
2 /,( 60 1D *,( 62( /,7( 607 6, =0(7, M- )90 /* ), /2 =)92+ 0*00 /58 ( 6032 90 12 )*
2* =)30 =28 )/+ «2(D 2 /-( 60*.330** ), /, C9, 90 /(*, C( )90 )*- )*4 =28 0- )/( 60
*.330** ), /, CC12 90*, CI=9.4 ( 604 2+ 0D 2* )/I+ ; ;;J )/302 ==, C( 604 , )/(*
70 /00-(, 92 :032 /50L0 18 /)30 =8 92-0 C, 19,( ), /)/, /0*4 2( )2 =- )103( ), /D
12( 60 1( 62 /* 6,7( 607 6, =0(7, M- )90 /* ), /2 =)92+ 0*D 70 =,, :2(( 60 9 b0-+ 0 M
, / gD *,( 62(70*00, /=8 , /0- )103( ), /, C( 60 9,( ), /( 61,.+ 6*4 230D 2 /-*00( 60
*.330** )L0 9, 90 /(*, C( )90*(23 :0-.4 ( 604 2+ 0 ;H6)*728 , C- 127 )/+ ( 604 2( 6*
, C,5x 03(* )/*4 2302 /-( )90 )*32 ==0-2E {F? ÖA?>A{ @{ ;'/7 62( C, ==,7*D
707 )==(. 1/( 604 )3(. 10* )-0728 *D *,( 62(( )90+ ,0*23 1,**( 604 2+ 0D 5032.*0
707 )==50-0*3 1)5 )/+ ,5x 03(* C2 ==)/+ C100 =8 /02 1( 60*. 1C230, C( 6002 1( 6;, 1
*.3 69,( ), /*D ( 60 b)/(0 10*( )/+ g- )103( ), /)*( 60L0 1( )32 =, /0D *, )( )* )/(. )( )L0 =8
3, /L0 /)0 /((,- 127 )(.4 ( 604 2+ 0 ;)+ ; ;m* 6,7*( 60 9,( ), /, C2 1,3 :( 62( )*
( 61,7 /.4 72 1- C1, 9( 60*. 1C230, C( 6002 1( 62(*, 904 =2302 /-2 ==,70-(, C2 ==
523 :-,7 /;y H60 102-0 17 )==/,(0( 62(( 604 2( 6- 127 /( 6)*728 D )/*4 2302 /-
( )90D =,, :*x .*(( 60*2 90728 )(- )-7 60 /70- 107( 604 )3(. 10, CL0 1( )32 =*4 230
2 /-* )-0728 **4 230 ;H6)*4 , )/( )*2 /233 )-0 /(( 62(3 62 123(0 1)]0*( 6)*4 2 1( )3. =2 1
*8 *(0 9D 5.( /, /0( 60 =0**2 /233 )-0 /(, C+ 102(* )+ /)I32 /307 6)3 67 )==50L0 18
.*0 C. =(,.*D 2 /-(,7 6)3 6707 )==10(. 1/)/( 60 C, ==,7 )/+ *03( ), /* ; ^.(( 6,.+ 6
( 6)*4 2( 66244 0 /*(, =,, :( 60*2 90D ( 60 10 )*2+ 102(- )O0 10 /3050(700 /( 60(7,
1 2 3 4
1 23 4
Space
Tim
e
Space
Tim
e
Edge-on view
: lose one spatial dim
ension
)+ . 10 ;H60*0K .0 /30, C3.(( )/+ 24 2 1(( 60 C12 90*, C2 9,L )0(, 92 :02
b«)4 5,, : g;y 2 H60 C12 90*2*4 2 1(*, C( 60, 1)+ )/2 =9,L )0 ;y 5 3.(( )/+ C12 90*
(, 92 :02*(23 :;y 3 H60*(23 :* 6,7 /0-+ 0 M, /C, 1* )94 =)3 )(8 ;H6)* )*2 /0 N2 94 =0
, C2*4 230 M( )90- )2+ 12 9;startheight
time
space-time
path)+ . 10 ;ma*4 230 M( )904 )3(. 10, C2 1,3 :( 61,7 /*( 12 )+ 6(.4 2 /-2 ==,70-(,
C2 ==523 :(, `2 1( 6;k,7( )90 )* )/- )32(0-23 1,**( 604 2+ 0 ;
Å
height
time
possible actualspace-tim
e paths
)+ . 10 ; J4 230 M( )90- )2+ 12 9*, C23(.2 =)92+ )/25 =04 2( 6* C, 12( 61,7 /1,3 :;
H60L2 1),.*4 2( 6*3, 110*4 , /-(,( 61,7 )/+ ( 60 1,3 :(,L2 1),.* 60 )+ 6(* ;
728 *, C- 127 )/+ D 7 6)3 670*00 )C70- 127*0L0 12 =4 2( 6*D 2* )/I+ ; ; ;a==
, C( 6023(.2 =4 2( 6*2-L2 /30 C, 172 1- )/( )90D *,( 60 102 10 )/C23( /, b*( 12 )+ 6(
L0 1( )32 = g4 2( 6*4 ,** )5 =0 )/( 60- )2+ 12 9;×, 10,L0 1D 2 ==, C( 6023(.2 =4 2( 6*- 127 /
62L0( 60*2 904 2 125, =)3* 624 0D 7 6)3 6)*( 60728 ( 60*4 230 M( )90- )2+ 12 9* 6,7*
( 60 I1*( 10 =2( ), /70- )*3,L0 10- C1, 9- )90 /* ), /2 =2 /2 =8 * )* C, 1( 6)**8 *(0 9D ( 60
3, /*(2 /38 , C( 60-,7 /72 1-2330 =0 12( ), /;
'/* 6,7 )/+ 4 2( 6*( 6)*728 D 70 62L02-0*3 1)4 ( ), /( 62( )**. )(25 =0 C, 1.*0 )/
2 9)/)9)]2( ), /2 =+ , 1)( 69D 5032.*0 /,770 62L02-0*3 1)4 ( ), /( 62( )*( 60*2 90
2*( 62( C, 1( 60 1.550 152 /- ;< 6)=0( 6023(.2 =,5x 03(, /=8 0 N)*(* )/, /04 =230
2(2 /8 ( )90( 62(70,5*0 1L0 )(D 58 - 127 )/+ 2 ==( 60 )/*(2 /(*, C,. 1,5*0 1L2( ), /
2(, /30, /( 604 2+ 0D 2 ==, C( 60 9, 90 /(*, C( 60,5x 03( [* 6)*(, 18 2 10 )/3 =.-0- )/
( 60*2 904 )3(. 10 ;'/*, 90*0 /*0D )/( 6)*- )2+ 12 924 2 1(, C( 60,5x 03( [* 6)*(, 18
0 N)*(* b2(0L0 18 4 , )/(, C( 604 2( 62(, /30 gD *,( 60 6)*(, 18 62*503, 90 =):02 ==
( 605 )(*, C2*( 10(30- 1.550 152 /-D )C70- 127( 604 )3(. 10( 60 1)+ 6(728 ;
H, 92 :0.*0, C( 60 9)/)9)]2( ), /1. =0 C, 11.550 152 /-*D 70 /00-0-(7,
( 6)/+ * ;< 0 /00-0-(, :/,7 6,7(, 902*. 10- )*(2 /30(, :/,7}{72* 9)/) M
9)]0-D 2 /-( 6.* 6,723(.2 =4 2( 6*70 10 b3 6,*0 / gD 2 /-70 /00-0-(,(0 ==z?}??_
}AF}G GA_E( 6052 /-72**( 10(3 60-D (,*4 03 )C8 7 6)3 64 2 1( )3. =2 14 2( 6)(
(,, :;×02*. 1)/+ - )*(2 /30*, /( 60*. 1C230, C2(25 =0 )*2 /, =-2 /-58 /,770 == M
. /-0 1*(,,-0 N0 13 )*0D 5.(( 60 10 )* /,,5L ),.* C2 9)=)2 1/,( ), /, C b- )*(2 /30 g)/
*4 2302 /-( )90- 127 /(,+ 0( 60 1;'/C23(D ,. 10 /( )10*02 13 6C, 1( 6023( ), /)*( 60
*02 13 6C, 1( 60( 6)/+ ( 62( )* 9)/)9)]0-D 7 6)3 67 )==C, 1( 60 I1*(( )904 1,L )-0
.*7 )( 62 /,( ), /, C*.3 62- )*(2 /30 ;< 07 )==62L0 9.3 69, 10(,*28 25,.(
( 6)* C1, 92- )O0 10 /(4 0 1*4 03( )L0 )/( 603 624 (0 1*, /10 =2( )L )(8 D ( 6,.+ 6( 61,.+ 6
( 60502.( )C. =3, /* )*(0 /38 , C/2(. 10D ,. 12 /*70 1*7 )==50( 60*2 90D 2 /-( 60 /07
or
ØØØ
or
height)+ . 10 ;H6100y *, 907 62(.*0 =0** b( )90 M=24 *0 g4 )3(. 10*, C( 60( 12x 03(, 18
, C2 92** 62 /+ )/+ C1, 92*4 1)/+ D 2* )(( 1230*,.(25,. /3 )/+ 9,( ), /)/*4 230 ;
y 2 H60 92**x .*(* )(*( 60 10 ;y 5 '(5,. /30**( 12 )+ 6(.4 2 /--,7 /2* 92 ==
2 9,. /( ;y 3 '(5,. /30**( 12 )+ 6(.4 , 1-,7 /2 =2 1+ 0 12 9,. /( ;'/2 ==( 610032*0*D
)(* )94 =8 10 M( 1230* )(*4 2( 6,L0 12 /-,L0 12+ 2 )/D *,( 60( )90 M=24 *04 )3(. 10*2 10
x .*(*( 12 )+ 6( =)/0* ;. /-0 1*(2 /- )/+ 4 1,L )-0-58 ( 60( 60, 18 , C10 =2( )L )(8 7 )==* )94 =8 (023 6.** )94 =0 1
2 /- 9, 100 =0+ 2 /(728 *(,7 1)(0 )(2 /- 103,+ /)]0 )( ;, 1/,7D 707 )==(2 :0
( 60 /,( ), /, C( 60 U¬XS70- )*3,L0 12*,. 1I1*(-0 I/)( ), /, C*, 90( 6)/+ ( 62(
50 62L0* =):02>AE{_F?¡ G@ {E>@{}_A_E {F?{_>A? ;
a9.3 602* )0 14 1,5 =0 9)*( 60*4 03 )I32( ), /, C( 60 b4 , )/(*50(700 /7 6)3 6( 60
52 /- )**( 10(3 60- g;'/( 6)*32*0D ( 608 2 10( 604 , )/(* )/( 60*4 230 M( )90- )2+ 12 9
2(7 6)3 6( 604 2( 672**(2 1(0-2 /-0 /-0- ;J .3 624 , )/(D *4 03 )I0- )/5,( 6*4 230
2 /-( )90D )*32 ==0-2 /WÙWSXD 2 /- )*2 /0 N( 10 90 =8 .*0 C. =2 /- )94 , 1(2 /((,, =
C, 12 ==( 62(707 )==-, ;'(* 6,. =-503 =02 1( 62( )/*, 90 =,+ )32 =*0 /*0D ( 60 10
72* /,728 703,. =- 102 ==8 C, 19. =2(02 9)/)9)]2( ), /2 =+ , 1)( 69C, 14 2( 6*( 62(
72*( 602 /2 =,+ , C( 60 9)/)9)]2( ), /, C- )*(2 /30 C, 11.550 152 /-*D 7 )( 6,.( I1*(
-0*3 1)5 )/+ ( 604 2( 6* )/*4 230 M( )90- )2+ 12 9* ;H6)* )*5032.*0D 7 6)=02 1.550 1
52 /-0 N)*(*2(2 ==( 604 , )/(*, C)(* b4 2( 6 g)/*4 2302(, /30D 2 9,L )/+ ,5x 03(
, /=8 0 N)*(*2(2 ==( 604 , )/(*, C)(* 6)*(, 18cb2(, /30 g)/2*4 230( )90- )2+ 12 9D
*,( 6050+ )//)/+ 2 /-0 /- )/+ 0L0 /(* )/2*4 230( )90- )2+ 12 92 10 102 ==8 ( 60, /=8
0 =)+ )5 =032 /- )-2(0* C, 1( 60*(2 1( )/+ 2 /-0 /- )/+ b4 , )/(* g, C( 604 2( 6;H,* )94 =8
7, 1:7 )( 6( 60*(2 1( )/+ 2 /-0 /- )/+ 4 , )/(*, C( 60*4 2( )2 =( 12x 03(, 18 7,. =- 62L0
500 /2- )O0 10 /(( 6)/+ (,-, ;a* )((. 1/*,.(D )(7,. =- 62L02 =*,.*.2 ==8 500 /
27 1, /+ ( 6)/+ (,-,D 2*32 /50*00 /)/I+ ; ;D , C*0L0 12 =4 ,** )5 =0 9,( ), /*, C
2 92**5,. /3 )/+ .4 2 /--,7 /, /( 600 /-, C2*4 1)/+ ;J )/30( 60 9,( ), /, C( 60
92*** )94 =8 ( 1230*2 /- 10( 1230*( 60*2 90*( 12 )+ 6(( 12x 03(, 18 )/*4 230D 24 )3(. 10
)/*4 230 )*2 ==5.(.*0 =0** C, 1(0 ==)/+ 7 6)3 64 2( 6707,. =- =):0(,3, /* )-0 1;a/-D
Å m
possible actualspace-tim
e paths
startend
height
time
)+ . 10 ;ª a*4 230 M( )90- )2+ 12 9, C( 60*2 904 ,** )5 =0 9,( ), /*, C2 92**
62 /+ )/+ C1, 92*4 1)/+ D 2* )(5,. /30*.4 2 /--,7 /;H60- )O0 10 /(4 2( 6*3, 110 M
*4 , /-(,- )O0 10 /( b+ 102(0*(0 N(0 /* ), /* g, C( 12L0 =C1, 9)(* 10*( )/+ 4 , )/( ;y k,(0
( 60* )9)=2 1)(8 (,( 604 ,** )5 =04 2( 6*, C=)+ 6(( 61,.+ 62 C,3.* )/+ =0 /* ;
* )/30( 60 92**32 /50 92-0(,5,. /302 =)(( =00 N(0 /(, 12 =2 1+ 0, /0D ( 604 ,** )5 =0
=2 1+ 0( 12x 03(, 1)0*0 /( )10 =8 0 /3, 94 2**( 60 =)(( =0, /0*2*4 2( 6* )/*4 2302 =, /0 ;
H60*4 03 )I32( ), /, C4 2( 6* )* )/I/)(0 =8 50((0 1)/( 60*4 230 M( )90- )2+ 12 9y /0 N(
I+ . 10D 7 )( 6( )90- 127 /* )-0728 *D (,0 N4 =, )(( 60L0 1( )32 = ML0 1( )32 =3, )/3 )-0 /302 /-
( 60* )9)=2 1)(8 (,( 60 0 192(4 )3(. 10* I+ ; ;ªD ( 6,.+ 6)/(0 10*( )/+ =8 D 9.3 6=):0
( 6032*0, C( 60 =0 /* C, 10 192( [*4 1)/3 )4 =0D *( )==/,(. /)K .0 ;a( =02*(D 5032.*0
( 60 9,( ), /)/( )90 )* )/0 N, 125 =8 bC, 172 1- gD ( 604 2( 6*-, /,( =28 , /(,4 , C, /0
2 /,( 60 1D 2 /-( 60 =2 1+ 0 M0 N(0 /(4 2( 6*2 103 =02 1=8 - )*( )/3( C1, 9( 60* 92 == M0 N(0 /(
, /0* ;a/-D C, 12 =9,*(2 /8 *(2 1( )/+ 2 /-0 /- )/+ 4 , )/(703 6,,*0D ( 60*0. /)K .0 =8
*4 03 )C8 ( 604 2( 6( 62(3, //03(*( 60 9D 7 )( 6, /03 =2**, C0 N304 ( ), /* ;
^032.*02 ==, C( 60 9,( ), /* 62L0( 60*2 9038 3 =04 0 1),-D 2 /-5032.*0( 608
2 ==62L0( 60*2 90 9)-- =0 10*( )/+ 4 =230y 2*70 =02 1/0- )/( 603 624 (0 1, /- )90 / M
* ), /2 =2 /2 =8 * )* ( 60 102 10 92 /8 D 0L0 /)/I/)(0 =8 92 /8 9,( ), /*D - )*( )/+ . )* 60-58
( 60 )1- )O0 10 /( 92+ /)(.-0*D 2 ==, C7 6)3 64 2**( 61,.+ 6( 60*2 90 9)-- =0 10*( )/+
4 ,* )( ), /2(( 60*2 90*0K .0 /30, C( )90* ;J .3 62 95 )+ . )(8 ,332* ), /2 ==8 2 Â)3(*( 60
9)/)9)]2( ), /2*4 03(, C( 604 1)/3 )4 =0, C=02*(23( ), /D ( 6,.+ 6707 )==I/-( 62(
, /3070 :/,7( 603, /*(2 /(*, C( 60 9,( ), /D 0L0 /( 62( )* 10*, =L0-L0 18 /)30 =8 ;
k,7702* :D *.44 ,* )/+ ( 62(70 :/,7( 600L0 /(*( 62(*(2 1(2 /-0 /-2+ )L0 /
4 2( 6D 6,7(,3, /*( 1.3(( 60 9)/)9)]2( ), /2 =+ , 1)( 69( 62(3, 1103( =8 )-0 /( )I0*( 60
23(.2 =4 2( 6C1, 92 9, /+ 2 ==( 6,*0 )92+ )/25 =0D C, 1( 604 2 1( )3. =2 132*0*7 60 10
702 =102-8 :/,7 6,7(,-0*3 1)50( 60*8 *(0 97 )( 6 ;H,2 /*70 1( 6)*
K .0*( ), /D 707 )==62L0(, =,, :9, 103 =,*0 =8 2(( 6)**0(, C b2 ==)92+ )/25 =04 2( 6* g
2 /-4 1,4 ,*02 C07, C)(*3 62 123(0 1)*( )3*D 2 /- 92 :0.*0, C4 103 )*0 =8 7 62( )( 902 /*
(, 9)/)9)]0*, 90( 6)/+ D 7 6)3 67 )===02-.*(,2 /,( 60 110 92 1:25 =8 * )94 =05.(
start
height
time
)+ . 10 ; J , 90 )92+ )/25 =0y 5.( /,(23(.2 =d 4 2( 6* C, 12 C2 ==)/+ ,5x 03( ;< 0
62L00 N0 13 )*0- 10*( 12 )/(D 2 /-2( =02*(3, /* )-0 10-4 2( 6*( 62(, /=8+ , bC, 172 1- g
)/( )90 ;4 ,70 1C. =/,( ), /;� �� ¾ÀqÚ q " u¨··¿¨ À½
)1*(2 /- C, 19,*(D )( 9)+ 6(50+ ,,-(, 1032 ==x .*(7 62(2 6.+ 0*0 =03( ), /4 1,30**
702 102* :)/+ C1, 9,. 14 68 * )32 ==27, C9)/)9)]2( ), /;)+ ; ; * 6,7*x .*(2 C07
, C( 604 2( 6*( 62(( 602.( 6, 1*32 /)92+ )/0 C, 12 C2 ==)/+ ,5x 03(D 2 /-( 60 102 10
,5L ),.* =8 )/I/)(0 =8 9, 10( 62 /( 60*0 ;a=)(( =0 /00-*(,50*2 )-25,.(x .*( 6,7
5 )+ 2 /)/I/)(8 ( 62( )* ;Á )L0 /2 /8 )92+ )/0-4 2( 6D )( )*2 =728 *4 ,** )5 =0(,3, /*( 1.3( C1, 9)(2 /,( 60 1
)92+ )/25 =04 2( 658x .*(*.44 ,* )/+ 2 =)(( =0- )O0 10 /302(*, 904 , )/(, /( 604 2( 6D
2* )/- )32(0-58 ( 60 =)(( =05. 94 )/I+ ; ;l ;'/-04 0 /-0 /( =8 D 703,. =- 92 :08 0(
2 /,( 60 14 2( 658 2-- )/+ 2 /,( 60 1=)(( =05. 94 *, 907 60 100 =*02 =, /+ )(* =0 /+ ( 6;
H6)* /07 =)(( =05. 94 )* /,( b9, 10, C g( 604 10L ),.* =)(( =05. 94D 5.(*, 90( 6)/+
0 /( )10 =8 )/-04 0 /-0 /(, C)( ;k,7D )C7070 10*(2 /- )/+ )/2 1,, 9D 2 /-*, 90, /02* :0-.* 6,7 92 /8
- )O0 10 /(728 *( 60 1070 10(,3 62 /+ 0,. 1=,32( ), /D 707,. =-*28 ( 62(( 60 102 10
)/I/)(0 =8 92 /8 D 5032.*07032 /9,L058 2 /2 15 )( 12 1)=8 * 92 ==2 9,. /( )/2 /8
- )103( ), /;^.(( 6)* )*2 C2 )1=8 * )94 =0 )/I/)(8 ;'C70(2 :02* 92 ==*(04 (,72 1-( 60
/, 1( 672 ==D 2 /-( 60 /2 /,( 60 1* 92 ==*(04 (,72 1-( 60 /, 1( 672 ==D 7032 /* )94 =8
*28 ( 62(( 60*03, /- 9,( ), /72* b9, 10, C g( 60 I1*(, /0 ;H, 92 :02 /07 9,( ), /
( 62( )* /,( b9, 10, C g( 60, =-, /0D 70 62L0(, 9,L00 )( 60 1(,72 1-( 6002*(, 1
70*(72 ==*, 1(,72 1-( 6030 )=)/+ ;Z /3070 62L0( 1)0-023 6, C( 60*0 /07 9,( ), /*D
2 /8 ( 6)/+ 0 =*0703,. =--, )*x .*( b9, 10, C g*, 90( 6)/+ 70 62L02 =102-8 -, /0 ;
H6)* =)9)(2( ), /D ( 62(7032 /*2 94 =02 ==, C( 604 ,** )5 =0 )/-04 0 /-0 /(728 *, C
Å
kinkstart
height
time
)+ . 10 ;l Z /0 )92+ )/25 =04 2( 6D 9,- )I0-58 2* 92 ==5. 94 (,4 1,-.302 /,( 60 1
)92+ )/25 =04 2( 6;j):0( 60 :)/:)/2 1.550 152 /-D ( 6)*5. 94 3,. =-502 /8 7 60 10
, /( 604 2( 6;3 62 /+ )/+ ,. 14 ,* )( ), /)/2 1,, 958 ( 18 )/+ ( 6100- )O0 10 /(, /0*D )*7 62(70 902 /
7 60 /70*28 ( 62(( 60*4 230 )/( 60 1,, 9)*( 6100 M- )90 /* ), /2 =; 0 1(2 )/=8 ( 60 10
928 502 /)/I/)(03, ==03( ), /, C- )O0 10 /(4 =230*(, 9,L0(,D - )*( )/+ . )* 60-58
6,7 C2 170 9,L0- )/( 60( 6100- )103( ), /*D 5.( )(, /=8 (2 :0*( 6100 902*. 10 90 /(*
(, )-0 /( )C8 2 /8 *.3 63 62 /+ 0 ; , 94 2 10( 62((,( 6032*0, C( 604 2( 6* ;Z /3070 62L02--0-, /0 =)(( =05. 94
*, 907 60 10D 7032 /2 =728 *2-- b9, 10, C g( 60*2 90 =)(( =05. 94 2(( 60*2 90
4 =230D , 17032 /2--2 /)/-04 0 /-0 /( /075. 94 2(2 /8 , /0, C( 60 )/I/)(0 =8 92 /8
,( 60 14 =230*2L2 )=25 =02 =, /+ ( 604 2( 6;H6.*D (,-0*3 1)50( 6)**0(, C2 ==)92+ )/25 =0
3 62 /+ 0* )/4 2( 6D /,(, /=8 9.*(( 60 /. 950 1, C-0*3 1)4 ( ), /*50 )/I/)(05032.*0, C
( 60* 92 ==/0**, C( 603 62 /+ 0*702 10 C100(, 92 :0D 5.(0L0 /( 60- )90 /* ), /, C( 62(
*0(, C3 62 /+ 0* 9.*(50 )/I/)(0D 5032.*0 )(7,. =- 10K . )10 )/I/)(0 =8 92 /8 *.3 6
/. 950 1*(, =250 =( 603 62 /+ 0 ;J ,( 6)**0(, C2 ==)92+ )/25 =04 2( 6*( 62(70( 102(*,
+ =)5 =8 )/,. 1- )*3.** ), /** 6,. =-50. /-0 1*(,,-2*2L0 18 5 )+ 3, ==03( ), /D 2 /-( 60
4 1,4 0 1( 102( 90 /(, C)( 62*500 /2- )3. =(5.(2 =*, C1. )( C. =2 102, C92( 60 92( )3*
C, 19, 10( 62 /230 /(. 18 ;Û �qÜ ¨Ý q¨ ¹¦¨ Àqw¨ &%½Ý½ Þ¿Àß½ &%½à "!à Ú ! ¨&t À
oÀq¨#¨�#s¨w� Àq¾"! ¶q#" q½ á
H60728 707 )==( 102(( 6)*3, 94 =0 N)(8 )* 104 10*0 /(2( )L0, C( 60728 )( 62*500 /
( 102(0- )/9.3 6, C6)*(, 18 D 2 /-( 6)* )*2+ ,,-4 =230(, 92 :024 , )/(25,.(
4 1,+ 10** )/4 68 * )3*2 /-( 60 /2(. 10, C( 60- )O0 10 /3050(700 /92( 60 92( )3*2 /-
4 68 * )3* ;< 0 62L02 =102-8 *2 )-( 62(( 604 1,30**, C4 68 * )3* )*, /0, C=,, :)/+ C, 14 2( M(0 1/* )//2(. 102 /-( 18 )/+ (, )/L0 /(728 *(,-0*3 1)50( 60 9( 62(2 10.*0 C. =;a(
2 /8 *(2+ 0 )/( 6)*4 1,30**D )( )*2*. 1050(( 62(( 60 102 102*4 03(*, C7 62(70*28
( 62(70 102 ==8 -, / [(. /-0 1*(2 /-L0 18 -004 =8 ;J , 90, C( 60 9=02-(,3, /C.* ), /*
( 62((2 :0-032-0*(, 10*, =L0D 2 /-,( 60 1*(,3, /C.* ), /*( 62(70*( )==-, / [(. / M
-0 1*(2 /- ;^.(D 103,+ /)])/+ ( 62(D 70( 18 2 /8 728 (, C, 19. =2(0-0*3 1)4 ( ), /*2 /-
1. =0* C, 192 :)/++ .0**0*D 2 /-703 603 :( 60 92+ 2 )/*(7 62( 6244 0 /* )//2(. 10(,
*00 )C( 608 4 10- )3(3, 1103(2 /*70 1* ;'( )*2(2.(, =,+ 8 ( 62( /2(. 10 )*3, /* )*(0 /(D
5032.*07 62(0L0 16244 0 /* )*7 62( 6244 0 /* ;'C7032 /92 :03, 1103(4 10- )3( ), /*
25,.(7 62( 6244 0 /*.* )/+ 1. =0*70 62L0 )/L0 /(0-D ( 60 /0L0 /)C( 60 1. =0*2 10 /,(
3, 94 =0(0y 7 6)3 6)*2 =9,*(2 =728 *( 6032*0 , 17, 1*08 0(D )C70 :/,7( 62(( 60 10
2 104 , )/(*7 60 10( 608 2 10 )/(0 1/2 ==8 3, /( 12- )3(, 18 )C.*0- )/30 1(2 )/3, 95 )/2 M
( ), /*y 7 6)3 6)*2 =*, /,(2(2 ==. /.*.2 = D ( 60 C23(( 62(( 608+ )L0 1)+ 6(2 /*70 1*
)*(2 :0 /(,*.++ 0*(( 62(( 608 928 50( 603 1.-0244 1, N)92( ), /*, C50((0 11. =0*D
7 6)3 6503, 90 9, 103, 94 =0(02 /- 9, 103, /* )*(0 /(2*( 608 50((0 1244 1, N)92(0
( 60 102 =*( 1.3(. 10*, C/2(. 10 ;'/( 6,*032*0*D 7 )( 6244 1,4 1)2(032.( ), /*25,.(7 62(70-, / [( :/,7D (,
*.++ 0*(7 60 10(, =,, :C, 19)*(2 :0* )C704 10- )3(*, 90( 6)/+ ( 62(-,0* / [(7, 1:D
702 107 )==)/+ (,.*0( 60 1. =0*(,+ 0 /0 12(02 /*70 1*D 2 /-7, 1:(, 10 I/0( 60 92*
70 =02 1/9, 10D 92 :)/+ ( 60 99, 10-0(2 )=0-7 60 104 ,** )5 =02 /- I/- )/+ , 1)+ )/*
(,L0 1)C8 *, 90, C( 604 2 1(*( 62(4 10L ),.* =8 70 10x .*(+ .0**0* ;< 60 /70 I/2 ==8
3, 90.4 7 )( 62 /8 *0(, C2 C07, C( 60 1. =0*( 62(32 /50.*0-7 )( 6+ .2 12 /(00-
3, /* )*(0 /38 D )/2 /8 3, 95 )/2( ), /D 7032 ==)(24 2 1(, C92( 60 92( )3* ;
H6.*D ( 60*(2 /-2 1-* C, 17 62(32 /5032 ==0- 92( 60 92( )32 ==8 *0 /* )5 =02 10
9.3 69, 10 10*( )3( )L0( 62 /( 6,*0( 62(-0 =)/02(07 62(24 68 * )3 )*( )*7 )==)/+ (,
.*0 ;ãâZ /( 60,( 60 162 /-D 92( 60 92( )3*0 N)*(* )/( 60 9)/-*, C4 0,4 =0D 2 /-
/2(. 10*00 9*(,0 N)*(*7 )( 6, 17 )( 6,.(( 60*4 03 )2 =233 )-0 /(, C4 0,4 =0D 2 /-
* )/302 ==, C92( 60 92( )3* 62* )(*, 1)+ )/*2(*, 90 =0L0 =)/2((0 94 (* 92-058
4 0,4 =0(,-0*3 1)50( 60 )10 N4 0 1)0 /30*7 )( 6/2(. 10D )(*00 9*244 1,4 1)2(0(, 10+ 2 1-
92( 60 92( )3*2** )94 =8 ( 60 6)+ 60*(2 /- 9,*(3 =02 1 M602-0- 10 I/0 90 /(, C4 68 * )32 =
9,-0 =)/+ ;H60 10 C, 10D 92( 60 92( )3*32 /30 1(2 )/=8 /0L0 1 b4 1,L0 g2 /8 ( 6)/+ 25,.(
/2(. 10 )(* )94 =8 32 /4 1,L0( 60 10K . )10 90 /(* C, 13, /* )*(0 /38 7 )( 6)/)(*,7 /
9,-0 =* ;< 60 /2 92( 60 92( )32 =4 1,, C25,.(*, 90( 6)/+ 70( 6,.+ 6(72*( 1.0
3, /( 12- )3(**, 90( 6)/+ 70*00D 2 ==( 62((0 ==*.*y 2**. 9)/+ ( 604 1,, C)* 102 ==8
4 1,4 0 1=8 3, /*( 1.3(0- )*( 62(702 10*, 90 6,7.* )/+ ( 607 1, /+ 9,-0 =D 2 /-( 62(
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70 62L0(, )/L0 /(2 /,( 60 1, /0D 2 /- 6,4 0 C. ==8 2(*, 904 , )/(2 ==( 60 92( 60 92( )3*
(,-0*3 1)50 )( ;H6)*4 , )/(D 92-0?_ {EE{_D )==.*( 12(0*2 /)/3 102- )5 =8 )94 , 1(2 /(- )L )* ), /
( 62(* 6,. =-50 92-02 9, /+ ( 60L2 1),.* /,( ), /*, C b7 62( )*( 1.0 g;'C)(70 10
9, 10+ 0 /0 12 ==8 .*0-D )(7,. =-,5L )2(02+ 102(-02 =, C. //030**2 18 3, /C.* ), /
32.*0-58 52- =2 /+ .2+ 0 ;P 032 ==D C1, 9( 603 624 (0 1, /=2 /+ .2+ 0D ( 62(( 60 /,( ), /, C)/(0 1/2 =3, /* )*(0 /38 M
3 603 :)/+ -, /07 )( 6)/92( 60 92( )3* )*32 ==0-Ñ ÄQD 58 92( 60 92( )3 )2 /*2 /-y 2(
=, /+ =2*( 58 4 68 * )3 )*(* ;i1,4 0 1=8 D ( 6)* )*( 60, /=8 102 =/,( ), /, C4 1,, C( 62(
92 :0*2 /8 *0 /*0 ;'(244 =)0*, /=8 7 )( 6)/( 60-, 92 )/, C=,+ )3D 2 /- 10 C0 1*(,( 6)*
3 603 :)/+ , C( 603, /* )*(0 /38 , C1. =0*D )/3 =.- )/+ ( 60 1. =0*, C( 60 =,+ )3 )(*0 =CD , /30
( 60*0 62L0500 /3 102(0- ;H60*04 2 12(0 /,( ), /, C3 603 :)/+ 2 /2 /*70 12+ 2 )/*( /2(. 10 )*32 ==0- ÙUYTU �
XS, C( 60 9,-0 =2 /-( 604 1,, C;a- )*2+ 100 90 /(, C( 602 /*70 1)*2 =, /0 /,(
0 /,.+ 6(,(0 ==8 ,.7 6)3 64 2 1(, C( 602 /2 =8 * )* )* /,(.*0 C. =D 7 60( 60 1)( )*( 60
( 6)/+ *( 62(2 102**. 90-(,0 N)*(D ( 60 1. =0*( 62(2 102**. 90-(,+ ,L0 1/( 60 9D
, 10L0 /( 60 =,+ )3 )(*0 =CD ( 62((0 ==* 6,7( 60 1. =0*2 10(,50244 =)0- ;a/8 , C( 60*0
3,. =-50 10*4 , /* )5 =0 C, 1( 60- )*2+ 100 90 /( ;a/-D 2 /2+ 100 90 /( )* /,(0 /,.+ 6
(,(0 ==8 ,.( 62(8 ,. 62L0-, /00L0 18 ( 6)/+ 3, 1103( =8 ;a*7 )( 62 /8 ( 6)/+ 0 =*0D )(
)*4 ,** )5 =0(,+ 0 /0 12(07 62(*00 9(,50+ ,,- 9,-0 =*( 62(32 /50. /-0 1*(,,-
7 )( 63, /* )*(0 /( 1. =0*, C=,+ )3D+ 0( 92 /8 3, 1103( 10*. =(*y 233, 1- )/+ (, /2(. 10 D
2 /-( 6)/:( 600 /( )103, /*( 1.3( ), /)*L2 =)-D , /=8 (, I/- =2(0 1( 62(*, 90,( 60 1
10*. =( )*7 1, /+ ;H6.*D ( 60 /,( ), /*, C4 1,, C2 /-L2 =)- )(8 * 6,. =-50. /-0 1*(,,-D 023 6)/)(*
4 1,4 0 13, /(0 N( ;i1,, C)/( 60*0 /*0, C92( 60 92( )3* )*0 N300- )/+ =8 .*0 C. =D 5032.*0
, C(0 /702 103 =,*00 /,.+ 6(,3, 1103(58 ( 60( )90*.3 62 10*. =(32 /503, /*( 1.3(0-
( 62(( 604 1,L0 /3, /3 =.* ), /)*2L0 18+ ,,-+ .0**2(( 60 1)+ 6(2 /*70 1;'(32 /(0 ==.*
7 60 10(, =,, :C, 1/07 )/* )+ 6(*D 2 /- )(32 /60 =4 .* I/--004 =8 5. 1)0- 9)*(2 :0*
)/,. 1,5*0 1L2( ), /* ;^.(4 1,, C-,0* /,(244 =8 (,( 60 /2(. 12 =7, 1=-D 0 N304 (
( 61,.+ 6( 60 I=(0 1, CL2 =)-2( ), /D 7 6)3 6/030**2 1)=8 )* =)9)(0-58 3, /I-0 /302 /-
( 600 N(0 /(, C,. 10 N4 0 1)0 /30*D 2 /-2 =728 **.5x 03((,3 62 /+ 0 ; , /L0 1*0 =8 D ( 60
C23(( 62(7032 //,(4 1,L0*, 90( 6)/+ D 0L0 /)/( 607, 1*(32*0( 62(70 :/,7( 62(
( 60 102 10 )/3, /* )*(0 /3 )0* )/,. 190( 6,-*D 928 /,(502 C2(2 =2 Â)3( ), /D 5032.*0
, /032 /*, 90( )90*50 1)+ 6( )/32*0*D 7 )( 6,.(50 )/+ 25 =0(,50 1)+ 6(2 ==, C( 60
( )90 ;H60, /=8 10K . )10 90 /( )*( 62(, /05025 =0(, 10 =)25 =8 )-0 /( )C8 ( 6032*0*D
2 /- 10(2 )/2 /23.(0272 10 /0**, C( 60- )L )* ), /50(700 /7 62(, /0-,0*2 /--,0*
/,(. /-0 1*(2 /- ;×.3 6, C7 62(70-0*3 1)5050 =,7 )*24 1)900 N2 94 =0, C.* )/+ ( 6)/+ *2 /-
+ 0(( )/+ )/3 102- )5 =8+ ,,-2 /*70 1*D )/*4 )(0, C( 60 C23(( 62(( 608 2 10 /,( 102 ==8
92( 60 92( )32 ==8 . /-0 1*(,,-2(( 60( )90( 608 2 10 I1*(.*0- ;'/4 2 1( )3. =2 1D ( 6)*
/,( ), /, C( 60*0(, C2 ==)92+ )/25 =0 6)*(, 1)0* 62*500 /6)*(, 1)32 ==8 , /0, C( 60
1)3 60*(+ 1,. /-* C, 1( 604 10- )3( ), /, C1)+ 6(2 /*70 1*2 /-( 60*.5*0K .0 /(3 102( ), /, C32(2*( 1,4 6)3 9)*(2 :0*D 7 6,*0 10*, =.( ), /10K . )10*( 60 )/L0 /( ), /, C/072 102*
, C92( 60 92( )3* ;H6)*- )- /,(x .*( 6244 0 /, /30D 5.( 104 02(0- =8 2*023 6/07
244 =)32( ), /72* )/L0 /(0-( 62(.*0-( 60 )-02, C( 60*0(, C2 ==)92+ )/25 =0 6)*(, 1)0* ;
a/-D )/C23(D ( 60 =2(0*(L0 1* ), /*, C( 60*03, /C.* ), /*2 10*( )==2(( 60 C, 10 C1, /(* )/
5,( 692( 60 92( )3*2 /-4 68 * )3* ;< )( 6( 6)*32L02(D 2 /-24 1, 9)*0 /,((,*(2(0
-004 2 /-*.5( =04 , )/(*2* )C( 608 70 10,5L ),.*D 70 C, 1+ 02 602- ;
� �� ¦&�&w&§¨ &" �¨�# ÀqÚ ·" ¶q" u¨
¨··qß
H60 )-027072 /((,-0L0 =,4 )*( 62(8 ,.32 /)-0 /( )C8 7 60 10*, 90( 6)/+ )*58
I/- )/+ 24 1,4 0 1(8 , C)(( 62( )* 9)/)9)]0-( 60 10 ;< 072 /((, )-0 /( )C8 7 6)3 6
4 2( 6D 2 9, /+ 2 ==( 60 )92+ )/25 =04 2( 6*D )*( 6023(.2 =4 2( 6( 62(*(2 1(*2 /-0 /-*
2(4 2 1( )3. =2 10L0 /(*D 2 /-(, I+ . 10,.(7 62(D 2 /2 =,+ ,.*(,( 60 =0 /+ ( 6, C2 1.550 1
52 /-D * 6,. =-503, /*( 1.3(0-*,( 62( )(7 )==50 9)/)9)]0-2 =728 *2 /-, /=8 2(
023 6, C( 604 ,** )5 =023(.2 =4 2( 6* ;< 62(70 62L0*, C2 1(,-0*3 1)50( 60*8 *(0 9
)/K .0*( ), /)*2 /0K .2( ), /, C9,( ), /, C( 60 C, 19 ;
< 0 /,( )30 I1*(2( 6)/+ 25,.( 9)/)92D 2 /- 6,7( 6)/+ * I/-( 60 9;J .44 ,*0
702 10 )/2 6)==8 3,. /( 18 D 2 /-702 10 =,, :)/+ C, 172(0 1;< 0 /0L0 1I/- )(, /( 60
* )-0*, C6)==*D 2 /-( 60, /=8 4 =230* )(*(28 *2 10 )/=2 :0*( 62(2 10 =,32(0- )/( 60
5,((, 9*, CL2 ==08 * ;J ,70 62L02 /0 N2 94 =0, C( 60 )94 , 1(2 /30, C2 9)/)9. 9D
5032.*07 60 102 =2 :0 C, 19* )*-0(0 19)/0-58 7 60 10( 60 60 )+ 6(, C( 60+ 1,. /- )*
2 9)/)9. 9;< 0 /,( )30( 62( )C( 60 10 )*2 /8 728 (,+ , =,70 1( 62 /*, 904 , )/(D
72(0 17 )==/,(*(28 ( 60 10D 5.(7 )==� G}Gy 2* )/1)L0 1*2 /-*( 102 9* D 7 6)3 6
2 =*,(0 ==*.* 6,772(0 1I/-**.3 69)/)92 ;'(* )94 =8 «,7* C1, 97 60 10L0 1)( )*
)/7 62(0L0 1- )103( ), /)*-,7 /6)==D . /( )=)( 6)(*25,((, 9;
^.(( 6)* =02-*.*(, /,( )302( 6)/+ 25,.(( 605,((, 9*, CL2 ==08 * ;< 2(0 1
«,7*23 1,**( 60+ 1,. /-5032.*0( 60 10 )*2- )103( ), /( 62((2 :0* )(-,7 /6)==;a(
( 605,((, 9, C2L2 ==08 2 ==, C( 60- )103( ), /*2 10.4 6)==D *,( 60 10 )* /,728 (, «,7 ;
H60*4 03 )2 =32*0, C)/(0 10*((,.*,33. 1*7 60 /( 60L2 ==08 )*2* 9,,( 6L2 ==08 ;^8
* 9,,( 6D 70 902 /( 62(( 60 102 10 /,* 62 14 3 102*0* )/( 60+ 1,. /-y *.44 , 1( )/+
4 )3(. 10 '10 =2 /-L* ;J 7 )( ]0 1=2 /- D 7 6)3 6902 /*( 62(2 ==, C( 604 1,4 0 1( )0*, C( 60
*. 1C2303 62 /+ 0, /=8+ 0 /( =8 2*70+ , C1, 9, /04 =230(,2 /,( 60 1;'/*.3 6232*0D
, /0, C( 60( 6)/+ *( 62(3 62 /+ 0** 9,,( 6=8 )*( 60* =,4 0, C( 60+ 1,. /- ;^.(70
*007 62( 6244 0 /* /02 1( 605,((, 9, C( 60L2 ==08 ;a*7072 =:-,7 /D ( 60* =,4 0
)/,. 1- )103( ), /, C( 12L0 =)*-,7 /72 1-D 2 /-2 C(0 1704 2**( 61,.+ 6( 605,((, 9
)( )*.4 72 1- ;'C70.*0 /. 950 1*(, 902*. 10( 60*0L0 1)(8 2 /-- )103( ), /, C( 60
* =,4 0D 70.*0 /0+ 2( )L0 /. 950 1*, /, /0* )-0(,(0 ==.*( 62(702 10+ , )/+ -,7 /D
2 /-4 ,* )( )L0 /. 950 1*, /( 60 C2 1* )-0(,(0 ==( 62(702 10+ , )/+ .4 ;a/-( 60, /=8
728 (,+ 0(* 9,,( 6=8 50(700 /( 60 9)*(,4 2**( 61,.+ 62 ]0 1,* =,4 0y /,* =,4 0D , 1
«2(* =,4 0 2(( 605,((, 9, C( 60L2 ==08 ;H60 10 C, 1070- )*3,L0 12 /, =-5.(+ 102(
( 60, 10 9, C92( 60 92( )3*
Ū
ÏWÄWV�H60* =,4 02(( 605,((, 9, C2* 9,,( 6L2 ==08 )* ]0 1, ;
k,770244 =8 ( 6)*(,( 604 1,5 =0 9, C*0 =03( )/+ 4 2( 6* ;)1*(D 70 62L0(,
2**. 90( 62(( 6)**0(, C2 ==)92+ )/25 =04 2( 6* )* )/2 /8 *0 /*0. /-0 1*(2 /-25 =0 =):0
2 924D )/( 62(8 ,.32 /+ 0( C1, 9, /04 =230, /)((,2 /,( 60 12 =728 *58 =)(( =0
*(04 * ;P 0 92 1:25 =8 D /2(. 10*00 9*(,4 0 19)(.*2 =250 =)/+ 58 7 6)3 6)( )*D ( 6,.+ 6
( 6)* 62*500 //, /( 1)L )2 =(,- )*3,L0 1;y H60-0 C, 192( ), /*58 b=)(( =05. 94 * gD )/
( 604 10L ),.*- )*3.** ), /, C)/I/)( )0*D 2 100**0 /( )2 ==8 ( 60* 92 ==*(04 *( 62((2 :0.*
C1, 9, /04 2( 6(,2 /,( 60 1( 62( )* b/02 158 g;
J 03, /- =8 D 70 62L0(,2**. 90( 62( )( )*0L0 /4 ,** )5 =0(,-0 I/02.*0 C. =*0(
, C* 9,,( 6/. 950 1*, /*.3 62 924D =):0 )( )*4 ,** )5 =0(,-0*3 1)50( 60*. 1C230, C
2 6)==8 3,. /( 18 58 ( 60 60 )+ 6(, C( 60 6)==*2(023 6=,32( ), /;'/,( 60 17, 1-*D )/
2-- )( ), /(,*.44 ,* )/+ ( 62( 9)/)9)]2( ), /32 /50.*0-2(2 ==D 707,. =- =):0(,
*.44 ,*0( 62(( 60 1)+ 6(( 6)/+ (, 9)/)9)]07,. =- =,, :=):0( 60* 9,,( 6*. 1C230, C
2 6)==8 3,. /( 18 , /2 924 , C2 ==)92+ )/25 =04 2( 6*D )C703,. =-- 127*.3 62( 6)/+ ;
H6)*(,,(. 1/*,.((,504 ,** )5 =0y ( 60 92( 6 ( 6,.+ 6.*.2 ==8 /,(( 60- 127 )/+ ;
< 0 /,72* :7 62(2* =,4 07,. =- =,, :=):0 )/*.3 62(0 11)(, 18 ;< 0 ==D 1032 ==
( 62(( 60* =,4 0 )/2 10+ . =2 16)==8 3,. /( 18 (0 ==*.* 6,7 9.3 6703 62 /+ 0 )/60 )+ 6(
2*70+ , =)(( =0*(04 * )/023 6, C( 604 ,** )5 =0 )/-04 0 /-0 /(- )103( ), /* ;^.(( 60 10
2 10, /=8 (7, )/-04 0 /-0 /(728 *8 ,.32 /72 =:, /( 60*. 1C230, C( 6002 1( 6D *,
*.3 6* =,4 0*32 /50-0*3 1)50-7 )( 6, /=8 (7, /. 950 1*D C, 10 N2 94 =0( 603 62 /+ 0
C1, 9+ , )/+ /, 1( 62 /-( 603 62 /+ 0 C1, 9+ , )/+ 02*( ;
^.( 1032 ==( 62(( 60 1070 10 )/I/)(0 =8 92 /8 )/-04 0 /-0 /( b- )103( ), /* g, 1- ) M
90 /* ), /*D 2 =, /+ 7 6)3 68 ,.3,. =-3 62 /+ 0 C1, 9, /0 )92+ )/0-4 2( 6(,2 /,( 60 1D
3, 110*4 , /- )/+ (,2 ==4 =230*8 ,.3,. =-4 .( =)(( =05. 94 *, /( 604 2( 6(,-0 C, 19
)( ;H60 10 C, 10D ( 60* =,4 0, C2 /8 *. 1C230703,. =--0 I/0, /( 6)* 924 , C2 ==)92+ M
)/25 =04 2( 6* 62*(, 62L0 )/I/)(0 =8 92 /8 3, 94 , /0 /(*D , /0(0 ==)/+ ( 62(* =,4 02(
023 64 , )/(2 =, /+ ( 604 2( 6;H6.*D )C70*28 ( 62(*, 90*. 1C230 )/( 60*4 230, C
2 ==)92+ )/25 =04 2( 6*(2 :0*2 9)/)9. 9y 62*2L2 ==08 2(( 6023(.2 =4 2( 6D 702 10
*28 )/+ ( 62(( 60 10 )**, 90* =,4 0D *, 90 )/I/)(03, ==03( ), /, C/. 950 1*D , /0 C, 1023 6
4 , )/(2 =, /+ ( 604 2( 6D 2 ==, C7 6)3 62 10 ]0 1, ;
J .--0 /=8 70 /,( )30( 62(7 62(70 62L0-0*3 1)50- =,, :* 10 92 1:25 =8 =):07 62(
70 62L0 )/ ; 0 1(2 )/=8 703 62 /+ 0 /,( 6)/+ )/( 603, /(0 /(, C )C70
7 1)(0 )( )/*(02-2* � Ó ;^.(( 6)* )* /,(x .*(, /0*(2(0 90 /( ;� Ó
)*2*(2( 90 /(( 62( )*( 1.0{?{FG?_2 =, /+ ( 6023(.2 =4 2( 6;'/,( 60 1
7, 1-*D 2*( 60,5x 03(4 2**0*( 61,.+ 6023 64 , )/(, C)(* 9,( ), /D ( 60-0 I/)( ), /*, C
D 2 /-(0 ==.* 6,7(,3, /*( 1.3(*, 90 /. 950 1D �D ( 62(-0*3 1)50*( 60
3 )13. 9*(2 /30*, C( 60,5x 03(7 6)=0 )( )*2(( 62(4 =230D 2 /-( 603 62 123(0 1)*( )3*, C
)(* 9,( ), /2* )( )*4 2** )/+ ( 61,.+ 6( 62(4 =230 ;J 28 )/+ ( 62(023 6, C( 60 /. 950 1*
*,+ 0 /0 12(0-D 2(023 6, C( 604 , )/(*, C( 604 2( 6D )* ]0 1,D )*0 N23( =8 , C( 60*2 90
C, 19, C*(2(0 90 /(2*( 62(( 60 )/I/)(0 M- )90 /* ), /2 =* =,4 0, C*, 90( 6)/+ )/( 60
*4 230, C2 ==)92+ )/25 =04 2( 6* )* ]0 1,2(( 6023(.2 =4 ,** )5 =04 2( 6* ;
H6.*D )C7032 /92 :0 )(7, 1:D 70 62L0 C,. /-,. 13, //03( ), /;< 60 /70 62L0
2*(2(0 90 /( � ÓD 707 )* 6(, 10+ 2 1-( 60*0(, C/. 950 1*+ )L0 /58 �
2(023 64 , )/(, C2 /8 4 2( 6D 2*( 60*0(, C/. 950 1*-0 I/)/+ 2* =,4 0, C*, 90( 6)/+ 2(
( 62(4 2( 6;< 0+ )L0( 6)* b*, 90( 6)/+ g( 60 /2 90�¬XSD 2 /- /,770 103,+ /)]0
( 62(D 7 60 /0L0 1� )*( 60* =,4 0, C( 6023( ), /)/( 60*4 230, C2 ==)92+ )/25 =0
4 2( 6*D ( 60*(2(0 90 /(( 62(( 6023( ), /62*2L2 ==08y 2 9)/)9. 9 2(( 6023(.2 =
4 2( 6)*( 60*2 902*( 60*(2(0 90 /(( 62(2 =, /+ ( 6023(.2 =4 2( 6� Ó ; .*(
2*D )C70 :/,7( 60* =,4 0, C2 6)==8 3,. /( 18 0L0 18 7 60 107032 /103, /*( 1.3(( 60
60 )+ 6(*, C2 ==( 60 6)==*58 (2 :)/+ =)(( =0*(04 *2 /- b4 2(3 6)/+ (,+ 0( 60 1( 60* =,4 0* g
2*70+ ,D )/( 60*2 90728 )C70 :/,7 � C, 1023 6)92+ )/25 =04 2( 6D 70
32 /103, /*( 1.3(( 60L2 =.0, C( 6023( ), /2(023 64 2( 658 b4 )03 )/+ (,+ 0( 60 1( 60
* =,4 0* g* 9,,( 6=8 C1, 94 2( 6(,4 2( 6;< 07 )==10(. 1/(,( 60K .0*( ), /, C7 60( 60 1
( 6)*2 =728 *7, 1:* )/2 9, 90 /( ;< 62(70 62L0x .*(-0*3 1)50- )* )/C23(( 603, //03( ), /50(700 /k07(, / [* =27*
2 /-( 604 1)/3 )4 =0, C=02*(23( ), /;a/-D )((. 1/*,.(( 62(( 60 10 )*_GFG ??
E£ E?{}?_>?@E{_>¡ G@}AF}?{B?_Gz??_{z?GFG_E@FEF
{>?EF@A AG_D , 19, 10233. 12(0 =8 D ( 604 10-030**, 1-0*3 1)4 ( ), /)/( 60K .2 /(. 9
( 60, 18 C1, 97 6)3 6)( C, ==,7* ;^.(7030 1(2 )/=8 62L0 /,(* 6,7 /2 ==, C( 62( 60 10 ;
P 02 ==8 4 1,L )/+ *, 90, C( 602**. 94 ( ), /*D =):0( 6,*0 10K . )10-(, 92 :0*0 /*0, C
( 60*0(, C2 ==)92+ )/25 =04 2( 6*2 /-( 60* 9,,( 6/0**, C( 6023( ), /( 60 10D )* C2 1
9, 10( 62 /7032 /-, 60 10D 2 /- 102 ==8 C2 19, 10( 62 /( 60 10 )*2 102*, /(,-, ;
H60 )94 , 1(2 /(( 6)/+ C1, 9( 6)*- )*3.** ), /)*(,*00( 60 10 =2( ), /, C)(*4 2 1(*
;'( )*4 ,** )5 =0y 2( =02*(. /-0 12+ 102( 92 /8 3 )13. 9*(2 /30*(,50- )*3.**0-
9, 1050 =,7 (, 10 M0 N4 10**( 60*2 903, /(0 /(2*( 62( C1, 9( 600K .2( ), /*, C
9,( ), / )/2 ÐÄS¬Ñ YWQËWUX�¬XSD 7 6)3 6*28 *( 62(,.(
, C2 ==( 604 2( 6*( 62(3,. =-50 )92+ )/0-D ( 60, /023(.2 ==8 (2 :0 /32 /50
)-0 /( )I0-5032.*02*4 03 )2 =4 1,4 0 1(8 , C4 2( 6*D 32 ==0-( 60�¬XSD (2 :0*2
9)/)9. 9( 60 10 ;m;'C70 6244 0 /(, :/,7( 60-0*3 1)4 ( ), /� Ó C, 1( 60*8 *(0 9, C
)/(0 10*(D ( 60 /7032 /I+ . 10,.(7 62(( 6023( ), /9.*(50(,*0 =03(( 60
*2 9023(.2 =4 2( 6*D 58 .* )/+ �2*( 60* =,4 0, C( 6023( ), /2 /-4 )03 )/+
)((,+ 0( 60 1C1, 94 2( 6(,4 2( 6(, I/-( 6023( ), /)(*0 =CD 2*707,. =-3, //03(
( 60* =,4 0*(, I/-( 60 60 )+ 6(, C2 6)==;
H6050*(728 (,0 N4 =, 10 92 /8 , C( 603, /*0K .0 /30*, C( 604 1)/3 )4 =0, C=02*(
23( ), /)*( 61,.+ 6( 604 1,5 =0 9*D 5.(( 60 10 )*, /0 9, 10 )**.0( 62(70 /00-(,
90 /( ), /60 10D 7 6)3 6)*7 60( 60 1( 6)* 103, /*( 1.3( ), /D C1, 9 (,( 6023( ), /D
)*2 =728 *4 ,** )5 =0D 2 /- )C/,(D 7 68 /,( ;
H,*007 62(3,. =-+ ,7 1, /+ D 70 =,, :2( ×; ;`*3 60 1 [* )94 ,** )5 =0 b72(0 1C2 == g;
y '( )* /,233 )-0 /(( 62( `*3 60 1- 107*.3 6.*0 C. =4 )3(. 10* ;e072*2 92( 60 92( )3 )2 /
58 ( 12-0D 7 )( 62+ 102( )/(0 10*( )/6,7, /03,. =-0 /L )* ), /( 604 1,5 =0 9*( 62(
Å
92( 60 92( )3* 92 :0*-0 I/)(0 )/0K .2( ), /* ; J .44 ,*07070 10+ )L0 /2 /0K .2( ), /
D 2 /-(, =-( 62(( 60 72*( 60, /0 10*4 , /* )5 =0 C, 1( 60 9,( ), /, C( 6)*
72(0 1;J .3 62 C, 1304 .* 60*2 1,. /-2 /-2 1,. /- )/23 )13 =0D )/, /0- )103( ), /
, /=8 ;1, 9( 6)*70 9)+ 6(( 18 (,5. )=-2 /23( ), /D 58 2** )+ /)/+ 2 /. 950 1(,*, 90
*(2 1( )/+ 4 2( 6D 2 /-( 60 /.* )/+ �2*2* =,4 0 )/( 60*4 230, C4 2( 6*D (,2** )+ /
23( ), /*(,2 ==( 60,( 60 14 2( 6*D 023 623 6)0L0-58 *, 90*0K .0 /30, C* 92 ==3 62 /+ 0*
C1, 9,. 1*(2 1( )/+ 3 6, )30 ;i0 1624 *( 60* )94 =0*(4 =230(,*(2 1(7,. =-5024 2( 6( 62(x .*(* )(**( )==2(
2 /2 15 )( 12 18 4 , )/(, /( 6072(0 1C2 ==;J .3 624 2( 662* /,L0 =,3 )(8 D 2 /-, /=8 , /0
4 ,* )( ), /D *, )(*23( ), /32 /-04 0 /-, /=8 , /( 62( ;H62(7,. =-30 1(2 )/=8 *00 9(,
502 /02*8 *(2 1( )/+ 4 , )/( )/2** )+ /)/+ 23( ), /* ;. 1( 60 1D )(-,0* / [( 92((0 17 62(
/. 950 1702** )+ /(,( 6)*23( ), /D * )/302* /,(0-( 60 )94 , 1(2 /30, C( 6023( ), /)*
6,7 )( 10 =2(0*- )O0 10 /(4 2( 6* ;Z . 1* )94 =0*(+ ,2 =9)+ 6(50(,2** )+ /23( ), /*(,
2 ==( 604 2( 6*( 62( bx .*(* )(*( )== g2(- )O0 10 /(4 =230*2 1,. /-( 6072(0 1C2 ==;`23 6
*.3 64 2( 6)*02*8 (,,5(2 )/C1, 9( 60, /0 /0 N((, )(D 58x .*(2* 92 ==-0 C, 192( ), /
(,( 60* )-0 ;×, 10,L0 1D * )/30023 6, C( 60 962* /,L0 =,3 )(8 D ( 60 10 )* /,(0 19
2(2 /8 , C( 60 9D *, /,3, /( 1)5.( ), /(,( 60* =,4 0 C1, 9( 62( ;H604 1,5 =0 9)*
( 60 C, 19, C( 60 C, 130 ;'C70-0 C, 19,. 14 2( 6*58+ , )/+ 2 1,. /-( 6072(0 1C2 ==
0 )( 60 1 b7 )( 6( 60 «,7 g, 1 b2+ 2 )/*(( 60 «,7 gD ( 60 4 2 1(, C( 60* =,4 0+ )L0*.*2
3, /*(2 /(3, /( 1)5.( ), /C, 10L0 18 3 62 /+ 0 ;H6.*D ( 6023( ), /D C1, 9, /04 2( 6(,( 60
/0 N(D 2 =728 * )/3 102*0* )/( 60*2 90- )103( ), /y 0 )( 60 14 ,* )( )L0 =8 , 1/0+ 2( )L0 =8 ;
e,70L0 1D 2 C(0 1*.3 623, /( )/.,.*+ 1,7( 6, C23( ), /D 7032 /2 11)L0z{F|2(,. 1
*(2 1( )/+ 4 2( 6D 3 =2 )9)/+ ( 62( )( 10K . )10*2- )O0 10 /(23( ), /C1, 9( 60, /070*(2 1(0-
7 )( 6;< , 1*08 0(D 7 60( 60 1( 62(23( ), /)* =2 1+ 0 1, 1* 92 ==0 1( 62 /( 60*(2 1( )/+ L2 =.0
-04 0 /-*, /7 6)3 6728 7070 /(2 1,. /-( 60 C2 ==;H6.*,. 16,4 0- MC, 14 10*3 1)4 ( ), /
C, 12** )+ /)/+ 23( ), /*32 //,(0L0 /50*0 /* )5 =8 -0 I/0- ;
H60 102*, /707 )/-.4 )/( 6)*( 1,.5 =0 )*( 62( `*3 60 1 [*72(0 1C2 ==104 10*0 /(*
«,7( 62(32 / [(,33. 1-,7 /2 /8 {F{A ;'C70 62-.*0-D )/*(02-D ( 60
3, 110*4 , /- )/+ (, «,7-,7 /2 /8 102 =6)==D ( 60 //, 92((0 16,77070 /(2 1,. /-
, /( 60 6)==D 707,. =-2 =728 * 62L0 62-(,+ ,.4 0 N23( =8 2* 9.3 6* =,4 02*70
70 /(-,7 /;H60 10 C, 10D /, 92((0 17 62(*0K .0 /30703 6,*0 )/2** )+ /)/+ 23( ), /*
(,4 2( 6*D )C70 =,, :0-2(2*0K .0 /30( 62((,, :.* C1, 9,. 1*(2 1( )/+ 4 2( 6523 :
(, )(*0 =CD 707,. =-2 =728 * 62L02 11)L0-523 :2(( 60*2 90 /. 950 1C, 1( 6023( ), /;
H62( )*02*8 0 /,.+ 6(,*00 C, 1( 60 bx .*(* )(( )/+ *( )== g4 2( 6* ;
'/C23(D ( 6)* )*( 60* )94 =0*(0 N4 10** ), /, C2 9, 10+ 0 /0 12 =3, /- )( ), /( 62( )*
@?� A@?>, C2 /�D )C)( )*(,50.*25 =0(,5. )=-2 /23( ), /;H604 2 1( )3. =2 1
0 N2 94 =070x .*(3, /* )-0 10- )*( 603, /( 1)5.( ), /( 62(2 1)*0* C1, 9( 60* )(( )/+ M*( )==
4 2( 6*2 =, /0D C1, 9x .*(( 60 4 2 1(, C( 600K .2( ), /*, C9,( ), /;'( 10K . )10*( 62(D
2(( 60 =02*(D ( 60 C, 130 9.*( 10*. =( C1, 92* =,4 0( 62(3,. =-5023 6)0L0- C1, 9
*, 90@?{A ;H60 60 )+ 6(, C*.3 62 6)==)* :/,7 /2*2Ñ XWSXUYQRS¬XSD
5032.*0 )( 62*( 604 ,(0 /( )2 =(, )/-.30 9,( ), /D *.3 62* «,7 )/72(0 1;H60* )]0
, C( 60 C, 130( 62( )/-.30*( 60 «,7 )*4 1,4 , 1( ), /2 =(,( 60*(004 /0**, C( 60* )-0* , C( 60 6)==;H62( )*7 68 D 2-- )/+ .4 ( 60 C, 130*2 1,. /-2 /8 =,,4 ( 62(3, 90*523 :
(, )(**(2 1( )/+ 4 =230D 2*70- )- )/( 60 =2*(0 N2 94 =0D )*+ .2 12 /(00-(,+ )L02
3, /* )*(0 /(2 /*70 1)/( 6032*0, C2 102 =6)==;'(x .*(2 9,. /(*(,72 =:)/+ 2 1,. /-
)/23 )13 =02 /-3,. /( )/+ .4 ( 603 62 /+ 0* )/60 )+ 6(D 7 6)3 6, C3,. 1*02 =728 *5 1)/+ *
8 ,.523 :(,( 60*2 90 60 )+ 6(D 2*70 ==2*( 60*2 904 =230D 2*( 60, /07 60 108 ,.
*(2 1(0- ;H60 102*, /*.3 64 ,(0 /( )2 =C. /3( ), /*2 10 )/(0 10*( )/+ )*( 62(( 608 7 )==2 1)*0
2+ 2 )/D )/( 603, /(0 N(, C?_?@£ )/( 60 /0 N(*03( ), /;< 60 /4 ,(0 /( )2 =C. /3( ), /*
3, 90 C1, 9102 =6)==*D ( 62(0 /*. 10*( 62(( 60 10 )* /, C, 130324 25 =0, C( 12 /*4 , 1( M
)/+ 2 /,5x 03(0 /- =0** =8 2 1,. /-2 /-2 1,. /-D 7 6)3 67,. =-502 C, 19, C+ 0(( )/+
b*, 90( 6)/+ C, 1/,( 6)/+ g;×, 10+ 0 /0 12 =10*( 1)3( ), /*, C( 60*2 90 :)/-2 10 /00-0-D (,244 =8 (,2 ==4 ,** )5 =0
( 6)/+ * �3,. =--,D )C702 10(,0 /*. 103, /* )*(0 /38 7 )( 62 ==4 ,** )5 =04 2( 6* ;
, 1/,7D ( 6)* )**. 3 )0 /((,+ )L02 /0 N2 94 =0, C( 60 /2(. 10, C( 60*03, /* )*(0 /38
3, /*( 12 )/(*D 2 /-(, )/( 1,-.304 1,4 0 1( )0*, C4 ,(0 /( )2 =C. /3( ), /*7 6)3 67 )==50
0 N4 =, 10- )/=2(0 1*03( ), /*2 /- )/( 604 1,5 =0 9* ;'( 6244 0 /*( 62(x .*(( 60 C, 19
, C+ .2 12 /(00*( 62( )(7 )==/0L0 1+ )L024 1,5 =0 9C, 1( 604 2 1(, C( 60* =,4 0
3, /( 1)5.(0-58 ( 62((0 192 =, /0 ;, 19, 10+ 0 /0 12 =(0 19*D ( 6,.+ 6D ( 62(3,. =-
62L0244 02 10- )C-04 0 /-0-, /( 6)/+ * =):0L0 =,3 )(8 D , 1A_E?{>G¡ D ( 60 10
)* /,*.3 6+ .2 12 /(00D 7 )( 6)/( 60 C12 907, 1:)/( 1)/* )3(,0K .2( ), /*, C9,( ), /
( 60 9*0 =L0* ; =02 1=8 D ( 60 /D ( 60 )94 , 1(2 /(K .0*( ), /2(( 6)**(2+ 0 )*7 6)3 6:)/-, C [*
244 02 1)//2(. 10 ; 0 1(2 )/=8 D )C( 60 102 10 102 =32*0* )/7 6)3 6)* =):0( 60 `*3 60 1
4 )3(. 10D ( 60 /( 60 i1)/3 )4 =0, Cj02*( a3( ), /9.*(50, C=)9)(0-.*0 C. =/0**D 2 /-
9.*( /,(50( 1. =8 C. /-2 90 /(2 =D 5.(* )94 =8 2 /2 =(0 1/2( )L0(, ( 62(
,L0 1=24 *7 )( 6)( )/*, 90 )/*(2 /30* ;
< 0* )94 =8 *(2(0 C, 1( 60 103, 1-( 62(*, C2 1D 0L0 18 ( )9070 62L0 C,. /-2 /
C, 17 6)3 6( 60 10 62* /,(500 /23, 110*4 , /- )/+ 23( ), /D ( 6)* 62*500 /5032.*0
70 62L0 =0 C(,.(4 2 1(, C( 60 )94 , 1(2 /(-0*3 1)4 ( ), /, C( 60*8 *(0 9;J , C2 1( 60 10
62*2 =728 *500 /2728 (,+ ,523 :2 /- )/3 =.-0*, 90( 6)/+ ( 62(72*( 60 10 )/( 60
102 =7, 1=-D 5.(7 6)3 670( 6,.+