SpanBERT: Improving Pre-training by Representing and Predicting Spans

Mandar Joshi
Danqi Chen
Yinhan Liu
Daniel S. Weld
Luke Zettlemoyer
Omer Levy
TACL
2020
View in Semantic Scholar

Abstract

We present SpanBERT, a pre-training method that is designed to better represent and predict spans of text. Our approach extends BERT by (1) masking contiguous random spans, rather than random tokens, and (2) training the span boundary representations to predict the entire content of the masked span, without relying on the individual token representations within it. SpanBERT consistently outperforms BERT and our better-tuned baselines, with substantial gains on span selection tasks such as question answering and coreference resolution. In particular, with the same training data and model size as BERTlarge, our single model obtains 94.6% and 88.7% F1 on SQuAD 1.1 and 2.0 respectively. We also achieve a new state of the art on the OntoNotes coreference resolution task (79.6% F1), strong performance on the TACRED relation extraction benchmark, and even gains on GLUE.1

1 Introduction

Pre-training methods like BERT have shown strong performance gains using self-supervised training that masks individual words or subword units. However, many NLP tasks involve reasoning about relationships between two or more spans of text. For example, in extractive question answering (Rajpurkar et al., 2016) , determining that the "Denver Broncos" is a type of "NFL team" is critical for answering the question "Which NFL team won Super Bowl 50?" Such spans provide a more challenging target for self supervision tasks, for example predict- * Equal contribution.

ing "Denver Broncos" is much harder than predicting only "Denver" when you know the next word is "Broncos". In this paper, we introduce a span-level pretraining approach that consistently outperforms BERT, with the largest gains on span selection tasks such as question answering and coreference resolution.

We present SpanBERT, a pre-training method that is designed to better represent and predict spans of text. Our method differs from BERT in both the masking scheme and the training objectives. First, we mask random contiguous spans, rather than random individual tokens. Second, we introduce a novel span-boundary objective (SBO) to train the model to predict the entire masked span from the observed tokens at its boundary. Spanbased masking forces the model to predict entire spans solely using the context in which they appear. Furthermore, the span-boundary objective encourages the model to store this span-level information at the boundary tokens, which can be easily accessed during fine tuning. Figure 1 illustrates our approach.

Figure 1: An illustration of SpanBERT training. In this example, the span an American football game is masked. The span boundary objective then uses the boundary tokens was and to to predict each token in the masked span.

To implement SpanBERT, we build on a welltuned replica of BERT, which already outperforms the original BERT. While building on our baseline, we find that pre-training on single segments, instead of two half-length segments with the next sentence prediction (NSP) objective, significantly improves performance on most downstream tasks. Therefore, we add our modifications on top of the tuned single-sequence BERT baseline.

Together, our pre-training process yields models that outperform all BERT baselines on a wide variety of tasks, and reach substantially better performance on span selection tasks in particular. Specifically, our method reaches 94.6% and x 1 < l a t e x i t s h a 1 _ b a s e 6 4 = " Z Y + R s J i l E 2 D s + 9 + V G 7 h S 6 g 3 W Y i I = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i R S 0 G X B j c s K 9 g F t K J P p p B 0 6 m Y S Z G 7 G E / o Y b F 4 q 4 9 W f c + T d O 2 i y 0 9 c D A 4 Z x 7 u W d O k E h h 0 H W / n d L G 5 t b 2 T n m 3 s r d / c H h U P T 7 p m D j V j L d Z L G P d C 6 j h U i j e R o G S 9 x L N a R R I 3 g 2 m t 7 n f f e T a i F g 9 4 C z h f k T H S o S C U b T S Y B B R n A R h 9 j Q f e s N q z a 2 7 C 5 B 1 4 h W k B g V a w + r X Y B S z N O I K m a T G 9 D 0 3 Q T + j G g W T f F 4 Z p I Y n l E 3 p m P c t V T T i x s 8 W m e f k w i o j E s b a P o V k o f 7 e y G h k z C w K 7 G S e 0 a x 6 u f i f 1 0 8 x v P E z o Z I U u W L L Q 2 E q C c Y k L 4 C M h O Y M 5 c w S y r S w W Q m b U E 0 Z 2 p o q t g R v 9 c v r p H N V 9 9 y 6 d 9 + o N R t F H W U 4 g 3 O 4 B A + u o Q l 3 0 I I 2 M E j g G V 7 h z U m d F + f d + V i O l p x i 5 x T + w P n 8 A S Y q k b I = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " Z Y + R s J i l E 2 D s + 9 + V G 7 h S 6 g 3 W Y i I = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i R S 0 G X B j c s K 9 g F t K J P p p B 0 6 m Y S Z G 7 G E / o Y b F 4 q 4 9 W f c + T d O 2 i y 0 9 c D A 4 Z x 7 u W d O k E h h 0 H W / n d L G 5 t b 2 T n m 3 s r d / c H h U P T 7 p m D j V j L d Z L G P d C 6 j h U i j e R o G S 9 x L N a R R I 3 g 2 m t 7 n f f e T a i F g 9 4 C z h f k T H S o S C U b T S Y B B R n A R h 9 j Q f e s N q z a 2 7 C 5 B 1 4 h W k B g V a w + r X Y B S z N O I K m a T G 9 D 0 3 Q T + j G g W T f F 4 Z p I Y n l E 3 p m P c t V T T i x s 8 W m e f k w i o j E s b a P o V k o f 7 e y G h k z C w K 7 G S e 0 a x 6 u f i f 1 0 8 x v P E z o Z I U u W L L Q 2 E q C c Y k L 4 C M h O Y M 5 c w S y r S w W Q m b U E 0 Z 2 p o q t g R v 9 c v r p H N V 9 9 y 6 d 9 + o N R t F H W U 4 g 3 O 4 B A + u o Q l 3 0 I I 2 M E j g G V 7 h z U m d F + f d + V i O l p x i 5 x T + w P n 8 A S Y q k b I = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " Z Y + R s J i l E 2 D s + 9 + V G 7 h S 6 g 3 W Y i I = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i R S 0 G X B j c s K 9 g F t K J P p p B 0 6 m Y S Z G 7 G E / o Y b F 4 q 4 9 W f c + T d O 2 i y 0 9 c D A 4 Z x 7 u W d O k E h h 0 H W / n d L G 5 t b 2 T n m 3 s r d / c H h U P T 7 p m D j V j L d Z L G P d C 6 j h U i j e R o G S 9 x L N a R R I 3 g 2 m t 7 n f f e T a i F g 9 4 C z h f k T H S o S C U b T S Y B B R n A R h 9 j Q f e s N q z a 2 7 C 5 B 1 4 h W k B g V a w + r X Y B S z N O I K m a T G 9 D 0 3 Q T + j G g W T f F 4 Z p I Y n l E 3 p m P c t V T T i x s 8 W m e f k w i o j E s b a P o V k o f 7 e y G h k z C w K 7 G S e 0 a x 6 u f i f 1 0 8 x v P E z o Z I U u W L L Q 2 E q C c Y k L 4 C M h O Y M 5 c w S y r S w W Q m b U E 0 Z 2 p o q t g R v 9 c v r p H N V 9 9 y 6 d 9 + o N R t F H W U 4 g 3 O 4 B A + u o Q l 3 0 I I 2 M E j g G V 7 h z U m d F + f d + V i O l p x i 5 x T + w P n 8 A S Y q k b I = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " Z Y + R s J i l E 2 D s + 9 + V G 7 h S 6 g 3 W Y i I = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i R S 0 G X B j c s K 9 g F t K J P p p B 0 6 m Y S Z G 7 G E / o Y b F 4 q 4 9 W f c + T d O 2 i y 0 9 c D A 4 Z x 7 u W d O k E h h 0 H W / n d L G 5 t b 2 T n m 3 s r d / c H h U P T 7 p m D j V j L d Z L G P d C 6 j h U i j e R o G S 9 x L N a R R I 3 g 2 m t 7 n f f e T a i F g 9 4 C z h f k T H S o S C U b T S Y B B R n A R h 9 j Q f e s N q z a 2 7 C 5 B 1 4 h W k B g V a w + r X Y B S z N O I K m a T G 9 D 0 3 Q T + j G g W T f F 4 Z p I Y n l E 3 p m P c t V T T i x s 8 W m e f k w i o j E s b a P o V k o f 7 e y G h k z C w K 7 G S e 0 a x 6 u f i f 1 0 8 x v P E z o Z I U u W L L Q 2 E q C c Y k L 4 C M h O Y M 5 c w S y r S w W Q m b U E 0 Z 2 p o q t g R v 9 c v r p H N V 9 9 y 6 d 9 + o N R t F H W U 4 g 3 O 4 B A + u o Q l 3 0 I I 2 M E j g G V 7 h z U m d F + f d + V i O l p x i 5 x T + w P n 8 A S Y q k b I = < / l a t e x i t >

x 2 < l a t e x i t s h a 1 _ b a s e 6 4 = " / A i Q R o 6 P e m d E R O W 9 8 6 e B W M M c x 9 k = " > A A A B 8 3 i c b V D L S s N A F L 3 x W e u r 6 t L N Y B F c l a Q U d F l w 4 7 K C f U A b y m R 6 0 w 6 d T M L M R C y h v + H G h S J u / R l 3 / o 2 T N g t t P T B w O O d e 7 p k T J I J r 4 7 r f z s b m 1 v b O b m m v v H 9 w e H R c O T n t 6 D h V D N s s F r H q B V S j 4 B L b h h u B v U Q h j Q K B 3 W B 6 m / v d R 1 S a x / L B z B L 0 I z q W P O S M G i s N B h E 1 k y D M n u b D + r B S d W v u A m S d e A W p Q o H W s P I 1 G M U s j V A a J q j W f c 9 N j J 9 R Z T g T O C 8 P U o 0 J Z V M 6 x r 6 l k k a o / W y R e U 4 u r T I i Y a z s k 4 Y s 1 N 8 b G Y 2 0 n k W B n c w z 6 l U v F / / z + q k J b / y M y y Q 1 K N n y U J g K Y m K S F 0 B G X C E z Y m Y J Z Y r b r I R N q K L M 2 J r K t g R v 9 c v r p F O v e W 7 N u 2 9 U m 4 2 i j h K c w w V c g Q f X 0 I Q 7 a E E b G C T w D K / w 5 q T O i / P u f C x H N 5 x i 5 w z + w P n 8 A S e u k b M = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " / A i Q R o 6 P e m d E R O W 9 8 6 e B W M M c x 9 k = " > A A A B 8 3 i c b V D L S s N A F L 3 x W e u r 6 t L N Y B F c l a Q U d F l w 4 7 K C f U A b y m R 6 0 w 6 d T M L M R C y h v + H G h S J u / R l 3 / o 2 T N g t t P T B w O O d e 7 p k T J I J r 4 7 r f z s b m 1 v b O b m m v v H 9 w e H R c O T n t 6 D h V D N s s F r H q B V S j 4 B L b h h u B v U Q h j Q K B 3 W B 6 m / v d R 1 S a x / L B z B L 0 I z q W P O S M G i s N B h E 1 k y D M n u b D + r B S d W v u A m S d e A W p Q o H W s P I 1 G M U s j V A a J q j W f c 9 N j J 9 R Z T g T O C 8 P U o 0 J Z V M 6 x r 6 l k k a o / W y R e U 4 u r T I i Y a z s k 4 Y s 1 N 8 b G Y 2 0 n k W B n c w z 6 l U v F / / z + q k J b / y M y y Q 1 K N n y U J g K Y m K S F 0 B G X C E z Y m Y J Z Y r b r I R N q K L M 2 J r K t g R v 9 c v r p F O v e W 7 N u 2 9 U m 4 2 i j h K c w w V c g Q f X 0 I Q 7 a E E b G C T w D K / w 5 q T O i / P u f C x H N 5 x i 5 w z + w P n 8 A S e u k b M = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " / A i Q R o 6 P e m d E R O W 9 8 6 e B W M M c x 9 k = " > A A A B 8 3 i c b V D L S s N A F L 3 x W e u r 6 t L N Y B F c l a Q U d F l w 4 7 K C f U A b y m R 6 0 w 6 d T M L M R C y h v + H G h S J u / R l 3 / o 2 T N g t t P T B w O O d e 7 p k T J I J r 4 7 r f z s b m 1 v b O b m m v v H 9 w e H R c O T n t 6 D h V D N s s F r H q B V S j 4 B L b h h u B v U Q h j Q K B 3 W B 6 m / v d R 1 S a x / L B z B L 0 I z q W P O S M G i s N B h E 1 k y D M n u b D + r B S d W v u A m S d e A W p Q o H W s P I 1 G M U s j V A a J q j W f c 9 N j J 9 R Z T g T O C 8 P U o 0 J Z V M 6 x r 6 l k k a o / W y R e U 4 u r T I i Y a z s k 4 Y s 1 N 8 b G Y 2 0 n k W B n c w z 6 l U v F / / z + q k J b / y M y y Q 1 K N n y U J g K Y m K S F 0 B G X C E z Y m Y J Z Y r b r I R N q K L M 2 J r K t g R v 9 c v r p F O v e W 7 N u 2 9 U m 4 2 i j h K c w w V c g Q f X 0 I Q 7 a E E b G C T w D K / w 5 q T O i / P u f C x H N 5 x i 5 w z + w P n 8 A S e u k b M = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " / A i Q R o 6 P e m d E R O W 9 8 6 e B W M M c x 9 k = " > A A A B 8 3 i c b V D L S s N A F L 3 x W e u r 6 t L N Y B F c l a Q U d F l w 4 7 K C f U A b y m R 6 0 w 6 d T M L M R C y h v + H G h S J u / R l 3 / o 2 T N g t t P T B w O O d e 7 p k T J I J r 4 7 r f z s b m 1 v b O b m m v v H 9 w e H R c O T n t 6 D h V D N s s F r H q B V S j 4 B L b h h u B v U Q h j Q K B 3 W B 6 m / v d R 1 S a x / L B z B L 0 I z q W P O S M G i s N B h E 1 k y D M n u b D + r B S d W v u A m S d e A W p Q o H W s P I 1 G M U s j V A a J q j W f c 9 N j J 9 R Z T g T O C 8 P U o 0 J Z V M 6 x r 6 l k k a o / W y R e U 4 u r T I i Y a z s k 4 Y s 1 N 8 b G Y 2 0 n k W B n c w z 6 l U v F / / z + q k J b / y M y y Q 1 K N n y U J g K Y m K S F 0 B G X C E z Y m Y J Z Y r b r I R N q K L M 2 J r K t g R v 9 c v r p F O v e W 7 N u 2 9 U m 4 2 i j h K c w w V c g Q f X 0 I Q 7 a E E b G C T w D K / w 5 q T O i / P u f C x H N 5 x i 5 w z + w P n 8 A S e u k b M = < / l a t e x i t >

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A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i S i 6 L L g x m U F + 4 C m l M n 0 p h 0 6 m Y S Z i V h C f 8 O N C 0 X c + j P u / B s n b R b a e m D g c M 6 9 3 D M n S A T X x n W / n d L a + s b m V n m 7 s r O 7 t 3 9 Q P T x q 6 z h V D F s s F r H q B l S j 4 B J b h h u B 3 U Q h j Q K B n W B y m / u d R 1 S a x / L B T B P s R 3 Q k e c g Z N V b y / Y i a c R B m T 7 P B 1 a B a c + v u H G S V e A W p Q Y H m o P r l D 2 O W R i g N E 1 T r n u c m p p 9 R Z T g T O K v 4 q c a E s g k d Y c 9 S S S P U / W y e e U b O r D I k Y a z s k 4 b M 1 d 8 b G Y 2 0 n k a B n c w z 6 m U v F / / z e q k J b / o Z l 0 l q U L L F o T A V x M Q k L 4 A M u U J m x N Q S y h S 3 W Q k b U 0 W Z s T V V b A n e 8 p d X S f u i 7 r l 1 7 / 6 y 1 r g s 6 i j D C Z z C O X h w D Q 2 4 g y a 0 g E E C z / A K b 0 7 q v D j v z s d i t O Q U O 8 f w B 8 7

n D y w 6 k b Y = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " Y F R N r j c M N I 5 Q T j D D n 6 0 P E f 0 9 F t Y = " > A

< l a t e x i t s h a 1 _ b a s e 6 4 = " Z j P F 9 0 A F

V Z b d Q h y M Y 2 m 3 z h S 3 k e 0 = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i Q i 6 r L g x m U F + 4 C m l M n 0 p h 0 6 m Y S Z i V h C f 8 O N C 0 X c + j P u / B s n b R b a e m D g c M 6 9 3 D M n S A T X x n W / n d L a + s b m V n m 7 s r O 7 t 3 9 Q P T x q 6 z h V D F s s F r H q B l S j 4 B J b h h u B 3 U Q h j Q K B n W B y m / u d R 1 S a x / L B T B P s R 3 Q k e c g Z N V b y / Y i a c R B m T 7 P B 1 a B a c + v u H G S V e A W p Q Y H m o P r l D 2 O W R i g N E 1 T r n u c m p p 9 R Z T g T O K v 4 q c a E s g k d Y c 9 S S S P U / W y e e U b O r D I k Y a z s k 4 b M 1 d 8 b G Y 2 0 n k a B n c w z 6 m U v F / / z e q k J b / o Z l 0 l q U L L F o T A V x M Q k L 4 A M u U J m x N Q S y h S 3 W Q k b U 0 W Z s T V V b A n e 8 p d X S f u i 7 r l 1 7 / 6 y 1 r g s 6 i j D C Z z C O X h w D Q 2 4 g y a 0 g E E C z / A K b 0 7 q v D j v z s d i t O Q

U O 8 f w B 8 7 n D y 2 + k b c = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " Z j P F 9 0 A F

< l a t e x i t s h a 1 _ b a s e 6 4 = " y s K c S C + e 8 M b M h / J 6 6 6 O 9 c 8 k w o G

I = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i Q i 2 G X B j c s K 9 g F t K J P p T T t 0 M g k z E 7 G E / o Y b F 4 q 4 9 W f c + T d O 2 i y 0 9 c D A 4 Z x 7 u W d O k A i u j e t + O 6 W N z a 3 t n f J u Z W / / 4 P C o e n z S 0 X G q G L Z Z L G L V C 6 h G w S W 2 D T c C e 4 l C G g U C u 8 H 0 N v e 7 j 6 g 0 j + W D m S X o R 3 Q s e c g Z N V Y a D C J q J k G Y P c 2 H j W G 1 5 t b d B c g 6 8 Q p S g w K t Y f V r M I p Z G q E 0 T F C t + 5 6 b G D + j y n A m c F 4 Z p B o T y q Z 0 j H 1 L J Y 1 Q + 9 k i 8 5 x c W G V E w l j Z J w 1 Z q L 8 3 M h p p P Y s C O 5 l n 1 K t e L v 7 n 9 V M T N v y M y y Q 1 K N n y U J g K Y m K S F 0 B G X C E z Y m Y J Z Y r b r I R N q K L M 2 J o q t g R v 9 c v r p H N V 9 9 y 6 d 3 9 d a 1 4 X d Z T h D M 7 h E j y 4 g S b c Q Q v a w C C B Z 3 i F N y d 1 X p x 3 5 2 M 5 W n K K n V P 4 A + f z B z D G k b k = < / l

< l a t e x i t s h a 1 _ b a s e 6 4 = "

c v + N e Q L Y b 9 E 4 v 8 d 6 a 3 g c V A O T m b c = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i Q i q L u C G 5 c V 7 A O a U i b T m 3 b o Z B J m J m I J / Q 0 3 L h R x 6 8 + 4 8 2 + c t F l o 6 4 G B w z n 3 c s + c I B F c G 9 f 9 d k p r 6 x u b W + X t y s 7 u 3 v 5 B 9 f C o r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o L J b e 5 3 H l F p H s s H M 0 2 w H 9 G R 5 C F n 1 F j J 9 y N q x k G Y P c 0 G N 4 N q z a 2 7 c 5 B V 4 h W k B g W a g + q X P 4 x Z G q E 0 T F C t e 5 6 b m H 5 G l e F M 4 K z i p x o T y i Z 0 h D 1 L J Y 1 Q 9 7 N 5 5 h k 5 s 8 q Q h L G y T x o y V 3 9 v Z D T S e h o F d j L P q J e 9 X P z P 6 6 U m v O 5 n X C a p Q c k W h 8 J U E B O T v A A y 5 A q Z E V N L K F P c Z i V s T B V l x t Z U s S V 4 y 1 9 e J e 2 L u u f W v f v L W u O y q K M M J 3 A K 5 + D B F T T g D p r Q A g Y J P M M r v D m p 8 + K 8 O x + L 0 Z J T 7 B z D H z i f P z J K k b o = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " c v + N e Q L Y b 9 E 4 v 8 d 6 a 3 g c V A O T m b c = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i Q i q L u C G 5 c V 7 A O a U i b T m 3 b o Z B J m J m I J / Q 0 3 L h R x 6 8 + 4 8 2 + c t F l o 6 4 G B w z n 3 c s + c I B F c G 9 f 9 d k p r 6 x u b W + X t y s 7 u 3 v 5 B 9 f C o r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o L J b e 5 3 H l F p H s s H M 0 2 w H 9 G R 5 C F n 1 F j J 9 y N q x k G Y P c 0 G N 4 N q z a 2 7 c 5 B V 4 h W k B g W a g + q X P 4 x Z G q E 0 T F C t e 5 6 b m H 5 G l e F M 4 K z i p x o T y i Z 0 h D 1 L J Y 1 Q 9 7 N 5 5 h k 5 s 8 q Q h L G y T x o y V 3 9 v Z D T S e h o F d j L P q J e 9 X P z P 6 6 U m v O 5 n X C a p Q c k W h 8 J U E B O T v A A y 5 A q Z E V N L K F P c Z i V s T B V l x t Z U s S V 4 y 1 9 e J e 2 L u u f W v f v L W u O y q K M M J 3 A K 5 + D B F T T g D p r Q A g Y J P M M r v D m p 8 + K 8 O x + L 0 Z J T 7 B z D H z i f P z J K k b o = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " c v + N e Q L Y b 9 E 4 v 8 d 6 a 3 g c V A O T m b c = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i Q i q L u C G 5 c V 7 A O a U i b T m 3 b o Z B J m J m I J / Q 0 3 L h R x 6 8 + 4 8 2 + c t F l o 6 4 G B w z n 3 c s + c I B F c G 9 f 9 d k p r 6 x u b W + X t y s 7 u 3 v 5 B 9 f C o r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o L J b e 5 3 H l F p H s s H M 0 2 w H 9 G R 5 C F n 1 F j J 9 y N q x k G Y P c 0 G N 4 N q z a 2 7 c 5 B V 4 h W k B g W a g + q X P 4 x Z G q E 0 T F C t e 5 6 b m H 5 G l e F M 4 K z i p x o T y i Z 0 h D 1 L J Y 1 Q 9 7 N 5 5 h k 5 s 8 q Q h L G y T x o y V 3 9 v Z D T S e h o F d j L P q J e 9 X P z P 6 6 U m v O 5 n X C a p Q c k W h 8 J U E B O T v A A y 5 A q Z E V N L K F P c Z i V s T B V l x t Z U s S V 4 y 1 9 e J e 2 L u u f W v f v L W u O y q K M M J 3 A K 5 + D B F T T g D p r Q A g Y J P M M r v D m p 8 + K 8 O x + L 0 Z J T 7 B z D H z i f P z J K k b o = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " c v + N e Q L Y b 9 E 4 v 8 d 6 a 3 g c V A O T m b c = " > A A A B 8 3 i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i Q i q L u C G 5 c V 7 A O a U i b T m 3 b o Z B J m J m I J / Q 0 3 L h R x 6 8 + 4 8 2 + c t F l o 6 4 G B w z n 3 c s + c I B F c G 9 f 9 d k p r 6 x u b W + X t y s 7 u 3 v 5 B 9 f C o r e N U M W y x W M S q G 1 C N g k t s G W 4 E d h O F N A o E d o L J b e 5 3 H l F p H s s H M 0 2 w H 9 G R 5 C F n 1 F j J 9 y N q x k G Y P c 0 G N 4 N q z a 2 7 c 5 B V 4 h W k B g W a g + q X P 4 x Z G q E 0 T F C t e 5 6 b m H 5 G l e F M 4 K z i p x o T y i Z 0 h D 1 L J Y 1 Q 9 7 N 5 5 h k 5 s 8 q Q h L G y T x o y V 3 9 v Z D T S e h o F d j L P q J e 9 X P z P 6 6 U m v O 5 n X C a p Q c k W h 8 J U E B O T v A A y 5 A q Z E V N L K F P c Z i V s T B V l x t Z U s S V 4 y 1 9 e J e 2 L u u f W v f v L W u O y q K M M J 3 A K 5 + D B F T T g D p r Q A g Y J P M M r v D m p 8 + K 8 O x + L 0 Z J T 7 B z D H z i f P z J K k b o = < / l a t e x i t > x 10

< l a t e x i t s h a 1 _ b a s e 6 4 = " 1 m b t u r c i G w x 6 I V P r w m u h 4 2 k Z f 5 c = "

> A A A B + H i c b V D L S s N A F L 2 p r 1 o f j b p 0 M 1 g E V y W R g i 4 L b l x W s A 9 o Q 5 h M J + 3 Q y S T M T M Q a 8 i V u X C j i 1 k 9 x 5 9 8 4 a b P Q 1 g M D h 3 P u 5 Z 4 5 Q c K Z 0 o 7 z b V U 2 N r e 2 d 6 q 7 t b 3 9 g 8 O 6 f X T c U 3 E q C e 2 S m M d y E G B F O R O 0 q 5 n m d J B I i q O A 0 3 4 w u y n 8 / g O V i s X i X s 8 T 6 k V 4 I l j I C N Z G 8 u 3 6 K M J 6 G o T Z Y + 5 n r p P 7 d s N p O g u g d e K W p A E l O r 7 9 N R r H J I 2 o 0 I R j p Y a u k 2 g v w 1 I z w m l e G 6 W K J p j M 8 I Q O D R U 4 o s r L F s F z d G 6 U M Q p j a Z 7 Q a K H + 3 s h w p N Q 8 C s x k E V O t e o X 4 n z d M d X j t Z U w k q a a C L A + F K U c 6 R k U L a M w k J Z r P D c F E M p M V k S m W m G j T V c 2 U 4 K 5 + e Z 3 0 L p u u 0 3 T v W o 1 2 q 6 y j C q d w B h f g w h W 0 4 R Y 6 0 A U C K T z D K 7

x Z T 9 a L 9 W 5 9 L E c r V r l z A n 9 g f f 4 A 3 W u T K Q = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " 1 m b t u r c i G w x 6 I V P r w m u h 4 2 k Z f 5 c = "

x Z T 9 a L 9 W 5 9 L E c r V r l z A n 9 g f f 4 A 3 W u T K Q = = < / l a t e x i t >

x 11 < l a t e x i t s h a 1 _ b a s e 6 4 = " T Z z n U

x Z T 9 a L 9 W 5 9 L E c r V r l z A n 9 g f f 4 A 3 v C T K g = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " T Z z n U

P D W L P 2 t j L y 1 O I 3 E a f U w d Q A = " > A A A B + H i c b V D L S s N A F L 2 p r 1 o f j b p 0 M 1 g E V y W R g i 4 L b l x W s A 9 o Q 5 h M J + 3 Q y S T M T M Q a 8 i V u X C j i 1 k 9 x 5 9 8 4 a b P Q 1 g M D h 3 P u 5 Z 4 5 Q c K Z 0 o 7 z b V U 2 N r e 2 d 6 q 7 t b 3 9 g 8 O 6 f X T c U 3 E q C e 2 S m M d y E G B F O R O 0 q 5 n m d J B I i q O A 0 3 4 w u y n 8 / g O V i s X i X s 8 T 6 k V 4 I l j I C N Z G 8 u 3 6 K M J 6 G o T Z Y + 5 n r p v 7 d s N p O g u g d e K W p A E l O r 7 9 N R r H J I 2 o 0 I R j p Y a u k 2 g v w 1 I z w m l e G 6 W K J p j M 8 I Q O D R U 4 o s r L F s F z d G 6 U M Q p j a Z 7 Q a K H + 3 s h w p N Q 8 C s x k E V O t e o X 4 n z d M d X j t Z U w k q a a C L A + F K U c 6 R k U L a M w k J Z r P D c F E M p M V k S m W m G j T V c 2 U 4 K 5 + e Z 3 0 L p u u 0 3 T v W o 1 2 q 6 y j C q d w B h f g w h W 0 4 R Y 6 0 A U C K T z D K 7 x Z T 9 a L 9 W 5 9 L E c r V r l z A n 9 g f f 4 A 3 v C T K g = = < / l a t e x i t > x 12 < l a t e x i t s h a 1 _ b a s e 6 4 = " B / n N x h / 4 9 4 s i M w V Y q Y w h h F / T w G k = " > A A A B + H i c b V D L S s N A F L 3 x W e u j U Z d u B o v g q i S l o M u C G 5 c V 7 A P a E C b T S T t 0 M g k z E 7 G G f I k b F 4 q 4 9 V P c + T d O 2 i y 0 9 c D A 4 Z x 7 u W d O k H C m t O N 8 W x u b W 9 s 7 u 5 W 9 6 v 7 B 4 V H N P j 7 p q T i V h H Z J z G M 5 C L C i n A n a 1 U x z O k g k x V H A a T + Y 3 R R + / 4 F K x W J x r + c J 9 S I 8 E S x k B G s j + X Z t F G E 9 D c L s M f c z t 5 n 7 d t 1 p O A u g d e K W p A 4 l O r 7 9 N R r H J I 2 o 0 I R j p Y a u k 2 g v w 1 I z w m l e H a W K J p j M 8 I Q O D R U 4 o s r L F s F z d G G U M Q p j a Z 7 Q a K H + 3 s h w p N Q 8 C s x k E V O t e o X 4 n z d M d X j t Z U w k q a a C L A + F K U c 6 R k U L a M w k J Z r P D c F E M p M V k S m W m G j T V d W U 4 K 5 + e Z 3 0 m g 3 X a b h 3 r X q 7 V d Z R g T M 4 h 0 t w 4 Q r a c A s d 6 A K B F J 7 h F d 6 s J + v F e r c + l q M b V r l z C n 9 g f f 4

A 4 H W T K w = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " B / n N x h / 4 9 4 s i M w

V Y q Y w h h F / T w G k = " > A A A B + H i c b V D L S s N A F L 3 x W e u j U Z d u B o v g q i S l o M u C G 5 c V 7 A P a E C b T S T t 0 M g k z E 7 G G f I k b F 4 q 4 9 V P c + T d O 2 i y 0 9 c D A 4 Z x 7 u W d O k H C m t O N 8 W x u b W 9 s 7 u 5 W 9 6 v 7 B 4 V H N P j 7 p q T i V h H Z J z G M 5 C L C i n A n a 1 U x z O k g k x V H A a T + Y 3 R R + / 4 F K x W J x r + c J 9 S I 8 E S x k B G s j + X Z t F G E 9 D c L s M f c z t 5 n 7 d t 1 p O A u g d e K W p A 4 l O r 7 9 N R r H J I 2 o 0 I R j p Y a u k 2 g v w 1 I z w m l e H a W K J p j M 8 I Q O D R U 4 o s r L F s F z d G G U M Q p j a Z 7 Q a K H + 3 s h w p N Q 8 C s x k E V O t e o X 4 n z d M d X j t Z U w k q a a C L A + F K U c 6 R k U L a M w k J Z r P D c F E M p M V k S m W m G j T V d W U 4 K 5 + e Z 3 0 m g 3 X a b h 3 r X q 7 V d Z R g T M 4 h 0 t w 4 Q r a c A s d 6 A K B F J 7 h F d 6 s J + v F e r c + l q M b V r l z C n 9 g f f 4

A 4 H W T K w = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " B / n N x h / 4 9 4 s i M w

A 4 H W T K w = = < / l a t e x i t >

x 7

< l a t e x i t s h a 1 _ b a s e 6 4 = " 4 p i a X O Z Q g z 8 m S B c U f J W c H e d 9 3

T o = " > A A A B 9 X i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g q s y I U J c F N y 4 r 2 A e 0 Y 8 m k m T Y 0 y Q x J R i 3 D / I c b F 4 q 4 9 V / c + T d m 2 l l o 6 4 H A 4 Z x 7 u S c n i D n T x n W / n d L a + s b m V n m 7 s r O 7 t 3 9 Q P T z q 6 C h R h L Z J x C P V C 7 C m n E n a N s x w 2 o s V x S L g t B t M r 3 O / + 0 C V Z p G 8 M 7 O Y + g K P J Q s Z w c Z K 9 w O B z S Q I 0 6 d s m D a y Y b X m 1 t 0 5 0 C r x C l K D A q 1 h 9 W s w i k g i q D S E Y 6 3 7 n h s b P 8 X K M M J p V h k k m s a Y T P G Y 9 i 2 V W F D t p / P U G T q z y g i F k b J P G j R X f 2 + k W G g 9 E 4 G d z F P q Z S 8 X / / P 6 i Q m v / J T J O D F U k s W h M O H I R C i v A I 2 Y o s T w m S W Y K G a z I j L B C h N j i 6 r Y E r z l L 6 + S z k X d c + v

e 7 W W t e V n U U Y Y T O I V z 8 K A B T b i B F r S B g I J n e I U 3 5 9 F 5 c d 6 d j 8 V o y S l 2 j u E P n M 8 f + 4 6 S x A = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " 4 p i a X O Z Q g z 8 m S B c U f J W c H e d 9 3

e 7 W W t e V n U U Y Y T O I V z 8 K A B T b i B F r S B g I J n e I U 3 5 9 F 5 c d 6 d j 8 V o y S l 2 j u E P n M 8 f + 4 6 S x A = = < / l a t e x i t > p 1 < l a t e x i t s h a 1 _ b a s e 6 4 = " X s 1 a E h D h k n k g x 4 X D n I 9 8 b g 6 n 3 S 8 = " > A

A A B 9 X i c b V D L S s N A F L 2 p r 1 p f V Z d u B o v g q i Q i 6 L L g x m U F + 4 A 2 l s l 0 0 g 6 d T M L M j V J C / 8 O N C 0 X c + i / u / B s n b R b a e m D g c M 6 9 3 D M n S K Q w 6 L r f T m l t f W N z q 7 x d 2 d n d 2 z + o H h 6 1 T Z x q x l s s l r H u B t R w K R R v o U D J u 4 n m N A o k 7 w S T m 9 z v P H J t R K z u c Z p w P 6 I j J U L B K F r p o R 9 R H A d h l s w G m T c b V G t u 3 Z 2 D r B K v I D U o 0 B x U v / r D m K U R V 8 g k N a b n u Q n 6 G d U o m O S z S j 8 1 P K F s Q k e 8 Z 6 m i E T d + N k 8 9 I 2 d W G Z I w 1 v Y p J H P 1 9 0 Z G I 2 O m U W A n 8 5 R m 2 c v F / 7 x e i u G 1 n w m V p M g V W x w K U 0 k w J n k F Z C g 0 Z y i n l l C m h c 1 K 2 J h q y t A W V b E l

e M t f X i X t i 7 r n 1 r 2 7 y 1 r j s q i j D C d w C u f g w R U 0 4 B a a 0 A I G G p 7 h F d 6 c J + f F e X c + F q M l p 9 g 5 h j 9 w P n 8 A 5 i i S t g = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " X s 1 a E h D h k n k g x 4 X D n I 9 8 b g 6 n 3 S 8 = " > A

e M t f X i X t i 7 r n 1 r 2 7 y 1 r j s q i j D C d w C u f g w R U 0 4 B a a 0 A I G G p 7 h F d 6 c J + f F e X c + F q M l p 9 g 5 h j 9 w P n 8 A 5 i i S t g = = < / l a t e x i t > p 2 < l a t e x i t s h a 1 _ b a s e 6 4 = "

i p / k Y G L 3 z W y c W l m r i O E u p + q d / O 0 = " > A A A B 9 X i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g q s y U g i 4 L b l x W s A 9 o x 5 J J M 2 1 o k h m S j F K G + Q 8 3 L h R x 6 7 + 4 8 2 / M t L P Q 1 g O B w z n 3 c k 9 O E H O m j e t + O 6 W N z a 3 t n f J u Z W / / 4 P C o e n z S 1 V G i C O 2 Q i E e q H 2 B N O Z O 0 Y 5 j h t B 8 r i k X A a S + Y 3 e R + 7 5 E q z S J 5 b + Y x 9 Q W e S B Y y g o 2 V H o Y C m 2 k Q p n E 2 S h v Z q F p z 6 + 4 C a J 1 4 B a l B g f a o + j U c R y Q R V B r C s d Y D z 4 2 N n 2 J l G O E 0 q w w T T W N M Z n h C B 5 Z K L K j 2 0 0 X q D F 1 Y Z Y z C S N k n D V q o v z d S L L S e i 8 B O 5 i n 1 q p e L / 3 m D x I T X f s p k n B g q y f J Q m H B k I p R X g M Z M U W L 4 3 B J M F L N Z E Z l i h Y m x R V V s C d 7 q l 9 d J t 1 H 3 3 L p 3 1 6 y 1 m k U d Z T i D c 7 g E D 6 6 g B b f Q h g 4 Q U P A M r / D m P D k v z r v z s R w t O c X O K f y B 8 / k D 5 6

2 S t w = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "

< l a t e x i t s h a 1 _ b a s e 6 4 = " H r

H N e X J e n H f n Y z F a c o q d Y / g D 5 / M H 6 T K S u A = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " H r

X 7 j u 2 L M Z N T b D B H g l W R 5 6 v / m R 8 = " > A A A B 9 X i c b V D L S g M x F L 1 T X 7 W + q i 7 d B I v g q s x o Q Z c F N y 4 r 2 A e 0 Y 8 m k m T Y 0 k w l J R i n D / I c b F 4 q 4 9 V / c + T d m 2 l l o 6 4 H A 4 Z x 7 u S c n k J x p 4 7 r f T m l t f W N z q 7 x d 2 d n d 2 z + o H h 5 1 d J w o Q t s k 5 r H q B V h T z g R t G 2 Y 4 7 U l F c R R w 2 g 2 m N 7 n f f a R K s 1 j c m 5 m k f o T H g o W M Y G O l h 0 G E z S Q I U 5 k N 0 8 t s W K 2 5 d X c O t E q 8 g t S g Q G t Y / R q M Y p J E V B j C s d Z 9 z 5 X G T 7 E y j H C a V Q a J p h K T K R 7 T v q U C R 1 T 7 6 T x 1 h s 6 s M k J h r O w T B s 3 V 3 x s p j r S e R Y G d z F P q Z S 8 X / / P 6 i Q m v / Z Q J m R g q y O J Q m H B k Y p R X g E Z M U W L 4 z B J M F L N Z E Z l g h Y m x R V V s C d 7 y l 1 d J 5 6 L u u X X v r l F r N o o 6 y n A C p 3 A O H l x B E 2 6 h B W 0 g o O A Z X u H N e X J e n H f n Y z F a c o q d Y / g D 5 / M H 6 T K S u A = = < / l a t e x i t > p 4 < l a t e x i t s h a 1 _ b a s e 6 4 = " N f 1 T S 8 X x w K W R / u G p r E A X T Y u V 8 L 8 = " > A A A B 9 X i c b V D L S s N A F L 3 x W e u r 6 t L N Y B F c l U Q K u i y 4 c V n B P q C N Z T K 9 a Y d O J m F m o p T Q / 3 D j Q h G 3 / o s 7 / 8 Z J m 4 W 2 H h g 4 n H M v 9 8 w J E s G 1 c d 1 v Z 2 1 9 Y 3 N r u 7 R T 3 t 3 b P z i s H B 2 3 d Z w q h i 0 W i 1 h 1 A 6 p R c I k t w 4 3 A b q K Q R o H A T j C 5 y f 3 O I y r N Y 3 l v p g n 6 E R 1 J H n J G j Z U e + h E 1 4 y D M k t k g q 8 8 G l a p b c + c g q 8 Q r S B U K N A e V r / 4 w Z m m E 0 j B B t e 5 5 b m L 8 j C r D m c B Z u Z 9 q T C i b 0 B H 2 L J U 0 Q u 1 n 8 9 Q z c m 6 V I Q l j Z Z 8 0 Z K 7 + 3 s h o p P U 0 C u x k n l I v e 7 n 4 n 9 d L T X j t Z 1 w m q U H J F o f C V B A T k 7 w C M u Q K m R F T S y h T 3 G Y l b E w V Z c Y W V b Y l e M t f X i X t y 5 r n 1 r y 7 e r V R L + o o w S m c w Q V 4 c A U N u I U m t I C B g m d 4 h T f n y X l x 3 p 2 P

x e i a U + y c w B 8 4 n z / q t 5 K 5 < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " N f

1 T S 8 X x w K W R / u G p r E A X T Y u V 8 L 8 = " > A A A B 9 X i c b V D L S s N A F L 3 x W e u r 6 t L N Y B F c l U Q K u i y 4 c V n B P q C N Z T K 9 a Y d O J m F m o p T Q / 3 D j Q h G 3 / o s 7 / 8 Z J m 4 W 2 H h g 4 n H M v 9 8 w J E s G 1 c d 1 v Z 2 1 9 Y 3 N r u 7 R T 3 t 3 b P z i s H B 2 3 d Z w q h i 0 W i 1 h 1 A 6 p R c I k t w 4 3 A b q K Q R o H A T j C 5 y f 3 O I y r N Y 3 l v p g n 6 E R 1 J H n J G j Z U e + h E 1 4 y D M k t k g q 8 8 G l a p b c + c g q 8 Q r S B U K N A e V r / 4 w Z m m E 0 j B B t e 5 5 b m L 8 j C r D m c B Z u Z 9 q T C i b 0 B H 2 L J U 0 Q u 1 n 8 9 Q z c m 6 V I Q l j Z Z 8 0 Z K 7 + 3 s h o p P U 0 C u x k n l I v e 7 n 4 n 9 d L T X j t Z 1 w m q U H J F o f C V B A T k 7 w C M u Q K m R F T S y h T 3 G Y l b E w V Z c Y W V b Y l e M t f X i X t y 5 r n 1 r y 7 e r V R L + o o w S m c w Q V 4 c A U N u I U m t I C B g m d 4 h T f n y X l x 3 p 2 P

x e i a U + y c w B 8 4 n z / q t 5 K 5 < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " N f

EQUATION Z: Not extracted; please refer to original document.

2 1 9 Y 3 N r u 7 R T 3 t 3 b P z i s H B 2 3 d Z w q h i 0 W i 1 h 1 A 6 p R c I k t w 4 3 A b q K Q R o H A T j C 5 y f 3 O I y r N Y 3 l v p g n 6 E R 1 J H n J G j Z U e + h E 1 4 y D M k t k g q 8 8 G l a p b c + c g q 8 Q r S B U K N A e V r / 4 w Z m m E 0 j B B t e 5 5 b m L 8 j C r D m c B Z u Z 9 q T C i b 0 B H 2 L J U 0 Q u 1 n 8 9 Q z c m 6 V I Q l j Z Z 8 0 Z K 7 + 3 s h o p P U 0 C u x k n l I v e 7 n 4 n 9 d L T X j t Z 1 w m q U H J F o f C V B A T k 7 w C M u Q K m R F T S y h T 3 G Y l b E w V Z c Y W V b Y l e M t f X i X t y 5 r n 1 r y 7 e r V R L + o o w S m c w Q V 4 c A U N u I U m t I C B g m d 4 h T f n y X l x 3 p 2 P x e i a U + y c w B 8 4 n z / q t 5 K 5 < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " N f

1 T S 8 X x w K W R / u G p r E A X T Y u V 8 L 8 = " > A A A B 9 X i c b V D L S s N A F L 3

x W e u r 6 t L N Y B F c l U Q K u i y 4 c V n B P q C N Z T K 9 a Y d O J m F m o p T Q / 3 D j Q h G 3 / o s 7 / 8 Z J m 4 W 2 H h g 4 n H M v 9 8 w J E s G 1 c d 1 v Z 2 1 9 Y 3 N r u 7 R T 3 t 3 b P z i s H B 2 3 d Z w q h i 0 W i 1 h 1 A 6 p R c I k t w 4 3 A b q K Q R o H A T j C 5 y f 3 O I y r N Y 3 l v p g n 6 E R 1 J H n J G j Z U e + h E 1 4 y D M k t k g q 8 8 G l a p b c + c g q 8 Q r S B U K N A e V r / 4 w Z m m E 0 j B B t e 5 5 b m L 8 j C r D m c B Z u Z 9 q T C i b 0 B H 2 L J U 0 Q u 1 n 8 9 Q z c m 6 V I Q l j Z Z 8 0 Z K 7 + 3 s h o p P U 0 C u x k n l I v e 7 n 4 n 9 d L T X j t Z 1 w m q U H J F o f C V B A T k 7 w C M u Q K m R F T S y h T 3 G Y l b E w V Z c Y W V b Y l e M t f X i X t y 5 r n 1 r y 7 e r V R L + o o w S m c w Q V 4 c A U N u I U m t I C B g m d 4 h T f n y X l x 3 p 2 P x e i a U + y c w B 8 4 n z / q t 5 K 5 < / l a t e x i t > p 5

< l a t e x i t s h a 1 _ b a s e 6 4 = " d v a + t p r j v r I a z J 1 3 T 2 2 M i S U x g Q Q = " > A A A B 9 X i c b

V D L S g M x F L 2 p r 1 p f V Z d u g k V w V W a k o s u C G 5 c V 7 A P a s W T S T B u a y Q x J R i n D / I c b F 4 q 4 9 V / c + T d m 2 l l o 6 4 H A 4 Z x 7 u S f H j w X X x n G + U W l t f W N z q 7 x d 2 d n d 2 z + o H h 5 1 d J Q o y t o 0 E p H q + U Q z w S V r G 2 4 E 6 8 W K k d A X r O t P b 3 K / + 8 i U 5 p G 8 N 7 O Y e S E Z S x 5 w S o y V H g Y h M R M / S O N s m F 5 m w 2 r N q T t z 4 F X i F q Q G B V r D 6 t d g F N E k Z N J Q Q b T u u 0 5 s v J Q o w 6 l g W W W Q a B Y T O i V j 1 r d U k p B p L 5 2 n z v C Z V

U Y 4 i J R 9 0 u C 5 + n s j J a H W s 9 C 3 k 3 l K v e z l 4 n 9 e P z H B t Z d y G S e G S b o 4 F C Q C m w j n F e A R

V 4 w a M b O E U M V t V k w n R B F q b F E V W 4 K 7 / O V V 0 r m o u 0 7 d v W v U m o 2 i j j K c w C m c g w t X 0 I R b a E E b K C h 4 h l d 4 Q 0 / o B b 2 j j 8 V o C R U 7

x / A H 6 P M H 7 D y S u g = = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " d v a + t p r j v r I a z J 1 3 T 2 2 M i S U x g Q Q = " > A A A B 9 X i c b