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Monograph:Cookson, R., Tsuchiya, A. and McCabe, C. (2008) Public health care resource allocation and the rule of rescue. Discussion Paper. Journal of Medical Ethics

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HEDS Discussion Paper 07/04

Disclaimer:

This is a Discussion Paper produced and published by the Health Economics and Decision Science (HEDS) Section at the School of Health and Related Research (ScHARR), University of Sheffield. HEDS Discussion Papers are intended to provide information and encourage discussion on a topic in advance of formal publication. They represent only the views of the authors, and do not necessarily reflect the views or approval of the sponsors. White Rose Repository URL for this paper: http://eprints.whiterose.ac.uk/11029/ Once a version of Discussion Paper content is published in a peer-reviewed journal, this typically supersedes the Discussion Paper and readers are invited to cite the published version in preference to the original version. Published paper

Cookson R, McCabe C, Tsuchiya A. Public health care resource allocation and therule of rescue. Journal of Medical Ethics 2008;34(7):540-4.

White Rose Research Online

eprints@whiterose.ac.uk

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HHeeaalltthh EEccoonnoommiiccss aanndd DDeecciissiioonn SScciieennccee

DDiissccuussssiioonn PPaappeerr SSeerriieess

No. 07/04

PUBLIC HEALTH CARE RESOURCE

ALLOCATION AND THE RULE OF RESCUE

Richard Cookson1, Christopher McCabe2, Aki Tsuchiya3

1. Department of Social Policy and Social Work, University of York.

2. Academic Unit of Health Economics, Institute of Health Sciences, University

of Leeds.

3. Department of Economics, and School of Health and Related Research,

University of Sheffield.

Corresponding author:

Dr Richard Cookson

Department of Social Policy and Social Work,

University of York, York

YO10 5DD

Tel: 01904 321248, Fax: 01904 321270, email: rc503@york.ac.uk

ScHARR

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•←≈→ ←↔→≈ ð

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•←≈→ ←↔→≈

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≈≡≡≈ ←•♠ ≈ ↑ ±″≈→″↑ ±→ ≥° ≈ ±→… ÷ …≈ ±°≈… ↵ ±→∝ ≈ ↑← ±≡ ↑≈♠ •←

♥≈• ← ″≠ ←÷↵← ↵× ±♥ ″ ≈→″↑ ≡ → ↑≈ ≈→•← ← ≈ ↓ ″←•≡• … ″ ←÷≈ ≡±→≥ ±≡ ↵ ≠ ↵ •↑≈… ≈→↑•±″

±≡ ←÷≈ ↑ ↵→… ±↑← °≈→ ⇓∩ °°→±↵÷ ←÷↵← ÷≈ →≈≡≈→↑ ←± ↑ �±↑ ↔≈ ↵″↵ ↑•↑�

±→…�↑

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±″≠ ↑ ←÷≈ °≈→ ±″ •↑÷≈↑ ←± ″← ″↔≈ ו • ↵″… ← • ≈ ←→↵″↑≡± ≥↵←• ≡↔ •±″ ←±

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↓↔↵ו← ±≡ ו≡≈ ↑ ↵×≈ ⊂÷•↑ °→± •↑ →≈ ≥ ≈″…≈… ↵ ° ≈≥≈″←↵→ ↵× ↑•↑ •″ ↔ •↑↑• ″↑

←± ←÷≈ ±→♥≈ • ″ ≈ ••″≈↑ ⇑ ″←→± ≠≈″ • ≥↵∝ ″≠ °÷↵→≥ • ↵× →≈ ≥↔ ≈≥≈″

…≈ • • ↑∫

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←÷↵← • ↑≈≈ ↑ ±°• ≡± ↔ ±″ ÷±← ±≡ • ⌠ ←÷ ↵ ↵ →← ↔ ±•″ ←• ≈ →↵←÷≈→

←÷↵″ °≈→↑ �↑ ×≈ • ≈←•≥≈ ≈♦°≈→•≈ ≈ ≡ • ×⌠÷≈↵×←÷⟨ ð

¬± ≈♠≈→ ≈″ •≡ ±″≈ ≈ ←↑ ←÷≈ ↵↑≈

≡±→ ↑≈♠≈→•← ♥≈•≠÷← ″≠ ≡ ∝• ↵… ± ←≈… → ← •↑ ≥° ↵″← ←± →≈ ≠″•↑≈ ÷↵← ″ ≈→″

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∈↔ ≈ ∈≈↑↔≈ ÷≈→≈ • ↵″ ≥°±→ ← •≡ →≈ ≈ ≈← ≈≈ ≈→″ ≡±→ ≈♠≈→•← ↵″… ≈→″ ≡±→

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°≈→• •≥° •≈↑ ≈↑↑ ″ ≈ ≡±→ ↔″•…≈″← ≡•↵ ≈ ″…•♠ …↔↵× ≡↔ →≈ →•×∑ ♥÷≈→≈↵↑ ±″ ≈→ ≡ →

↑≈ →•← ° •≈↑ ←± ↵× ≈♠≈ • ×″≈↑ � ÷≈←÷≈→ ↑↔≡≡≈→≈… •…≈″ •≡•≈ ±→ ↔″ … ←•≡•≈ ″…•♠ …↔↵×↑

… ← ≈→ ↑↔≡≡≈→≈… ″± → •″ ←÷≈ ≡ ← →≈ ≡±→ ♦↵≥°×≈ …� ↑ ←≈≥ ±≡ ≈ →•← ♥ •≠÷←•″≠

±↔ ≠• ≈ ÷•≠÷ °→•±→•← ← ° ♠≈″←•♠≈ °↔× ≈↵×← °→± → ≥ ≈↑ …≈ • ± → ♠≈″← ↑ ♠≈

• ×″≈↑ •″ ←÷≈ ≡ ↔→≈∑ ÷≈→≈ ←÷≈ ↔× ±≡ ∈≈↑ ±↔ ≠• ≈ →• →•← ←± →≈ ≈″←•♠≈

°→± ↵≥ ≈↑ ≡ ←÷• ″… � •″≈ ← ← → ≈← °≈ ≈ ♥÷± →≈ ↔→→≈″←× → ←• ≈× ÷≈↵×←÷ ↵″ ″ ←

•″ ↵″ • ≥≈…•↵←≈ °≈→• • • → ←÷ ↔ ≈ ∈≈↑↔≈ • ° •≈↑ •♠•″ ± →•±→•← ←± ←→≈↵←≥≈ ←

≡ → ° •≈″← ↵← • … ←± ≥±…≈→↵←≈ ↑ ↵≠≈↑ ±≡ °→± →≈↑↑• ≈ ″ • •± ↵″… ″↑←≈↵… • •″≠ • ≈

″…• •±″ ≈ ≥≈↑ ↑↔ • • ″← ↑≈♠≈→ ←± ″↑←• ↔←≈ ≥ ≈…•↵←≈ °≈→• � •÷ •≥≈ ±≡ ↔→↑≈

←→≈↵←≥≈″ ≥↵ ≈ ×≈↑↑ ≈″≈≡• ↵″ ⟩ → ≥ →≈ ±↑←× ± ←÷≈ ↔× ±≡ ∈≈↑ ≈ •↑ ↓↔•← …•≡≡≈→≈″←

≡→± ↑≈♠≈→•← ♥≈• ← ″≠ ″… ↵″ ← ≈ ∂↔↑ •≡•≈… •← →≈≡≈→≈″ ≈ ←± ±≡ ←÷≈ ↑←↵ ↵→… °→•″•° ≈↑

±≡ ∂↔↑←•≈

•″↵×× ←÷≈ ÷•→… ↓↔•→≈≥≈″← →≈ ←→•← ←÷≈ °×•↵• •← ≡ ←÷≈ ↔↑←→ ↔ ≈ ≡ ∈≈ ↔≈ ←

″…• •±″ ÷↵← ≡≡≈← ♠≈→ ↑≥ ″↔ ≈→ ±≡ ±°× � ← ← →≥≈… � → ÷↵″� ± …•←• ″↑ • ↑←

←÷• →≈↑←→•←• ″ °→≈♠≈″←↑ ←÷≈ ∈↔ ≈ ≡ ∈≈ ↔≈ ≡→ ≥ ≈±≥ ″≠ → ↔← ″≈ �↵←÷⌠↵ ×� • • ÷↵→ ←

…≈≡≈″… ÷≈ ≥ → ≥°≈→↵←• ≈ ≈÷ ″… ∈↔× ±≡ ∈≈↑ →≈ ←≈↑ ←± ←÷≈ ≡ ← ≡ • ≥•″ ″← • ← •↑

″±← ×≈↵→ •← ↑÷ … ≥↵∝≈ ↵ …•≡ →≈ ≈ ≡→ ≥ ↵″ ≈← • °± ″← ±≡ ♠•≈ ≈←÷≈→ ←÷≈ ↵↔↑≈ ±≡

•≥ •″≈ ← →•× •↑ →↵→≈ ±→ ≥≥ ″

↔↑ ≈↵÷ →≈ •→≈≥ ← •↑ ≡×↵ ≈… ↵″… ≥↵ •″←→ ≈ ≠→≈↵←≈→ •″≈ ← ← ↵″ ≈↓ ← ¬ ♥≈♠≈→ ←

≥ ↑← ←→• • → ← →•↑←• ≡ ← ←→↵ו • °×≈ ≈″←↵←• ″ ±≡ ←÷≈ ∈↔ ≈ ≡ ∈≈ ↔≈ • ←÷↵← •← •↑

≥ ↑← ± ° ≈←≈× •″…≈°≈″… ← ±≡ ←÷≈ ″ ≈ ← ±≡ ←÷≈ ∈↔ ≈ ≡ ∈≈ ↔≈ ↵ …≈↑→•≈… ←÷≈

•←≈→ ←↔→≈ ⊂÷≈ •≈″ • ″± ≡↵ • ≈…•↵←≈ °≈→• ∑ ← →≈ •↑ ″ ↑≈″↑≈ ±≡ ↔→ ≈″ ←± ←÷•↑ ←±→

≈ ↑←→↵ו↵″ ≡•″• •±″ •↑ ≥ →≈ →≈≥•″•↑≈″← ≡ ≥ ″ ↵″… ⇔ → °≈↵″ →°÷ ⇐→↔

≈≠•↑ ←• ″

⊂ ≈ ∏ ⇑ ⇑•← �↑ ⇑± × ≈≡• •← ± ↵ •♦ ↑ ↵ •±

⊂÷≈ �⇑•←•ƒ≈″�↑ • • ≠→±↔° ≡ ð ≈≥≈→↑ ±≡ ÷≈ ↔ • …→ ″ ≡→± ↵ → ↵… → ↑↑

↑≈←•± ± ←÷≈ ≠≈″≈→↵× ⊄ °±°↔×↵←• ″ •″ →…≈→ ←± ≠• ≈ ≈•→ ♠•≈ ↑ ″… ±°• • ″↑ ″ • ↑↔≈↑ ±≡ ↑±•↵×

♠↵ ≈ ∂↔…≠ ≥≈″← →≈ ← ″≠ ←± ←÷≈ ∝ ±≡ ⇑⇔ ← ÷ ← ↵ ″± ↵″…↵ ↵ ÷±→•← ← •↑ ↵

↔″• × ≈←•±″ ×↵ ≈≥≈→↑ ±≡ ←÷≈ °↔× →±↔ ← ←±≠≈←÷≈→ ←± ≥≈→↑≈ ← ≥↑≈ ♠ ↑ •″ ÷≈

↑ •↵× ♠↵×↔≈ ≈≥≈″←↑ ←÷↵← ″ ← ≈ ↵♠ • ≈… • ÷≈ →≈ →≈↑±↔→≈ ↵× ± ↵←• ∇″≈ ±≡ ÷≈•→

→≈≈ ← →≈°±→←↑ ……→≈↑↑≈ ←÷≈ •↑ ↔≈ ≡ ≈ ±≡ ∈≈↑ ≈∫

⇑⇔ ↵↑∝≈… ←÷≈ ⇑•←•ƒ �↑ ±↔″ • ←± ↵…… ↑↑ ←↑ …≈ •≈→ •±″↑ ← ≈ ≡± •″≠ ↔≈ ←•

↑ ← →≈ ↵ ° ≈→≈″ ± ↵♠ ← × ≡ ±≡ • •≥ •″≈ ← ″≠≈→ ±≡ … ≠

•″ ←≈↵… ≡ •≥° ♠ ″≠ ←÷≈ ו≡≈ ±≡ ± ≈ ×≈ × ≈ ″±← •″ •≥≥≈… ↵←

…↵ ≈

∇→

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°→±≠ ↵≥≥ ↔ ↑ ≈↵← ″≠ •≠÷ ±±… °→≈↑↑↔ ≈ ×±♥ • ×± ÷± ≈↑← ±

× ×↑ ⟨

ð

⋅≡ ÷≈ ±↔″• •… ↑ ← ⋅⇑ ÷±↔× ≠″± ← ↔×≈ ±≡ ∈ ↔ � ÷♣⟨

⋅≡ ÷≈ ±↔″• ↑ … → ←÷ ← ←÷ ∈ × ±≡ ∈ ↔≈ ÷± ×… ↵ °×•≈… � ≈″

⇓″… ♥ ↵← ו≥• ↑ ↵→≈ ←÷ ≈⟨

← ←÷≈ ≈″ ≈•→ ≈ •≈→↵←• ÷≈ •←•ƒ≈″�↑ ⇑ ↔″• ≡≈ ← ←÷↵← ←÷≈

�≥↵ ±→ ←♣ ≠ ±↔° →≈ ↵ ←± ↑°≈•≡♣ ♥ ″ ⇑⇔ ÷± ×… °° ÷≈ ↔×≈ ±≡ ∈≈↑↔≈ ″…

…≈≡ ≈ ← ←÷≈↑≈ •≥•← ÷±↔ … �

⇒±♦ ⇑ ⇑•← �↑ •× ⇑ ≈ ו↑← ±≡ ∉ ↑← ± ≡ → ×≈ ←• ≠ ≈ ∈ × ±

∈

↑ ←÷≈ • ←≈→♠≈″←•±″ ↓↔•→≈… ←± ↵♠ • ≥ ≈…•↵←≈ ± ↑ ≡ •≡≈⟨

↑ ←÷≈→≈ ± ≈ ±≡ ↵″ •″ ≈↵↑≈ •≡≈ ≈ °≈ ←↵ ⟨

•× •← →≈↑↔×← •″ ↑• ″•≡ ↵″ • °→± ≥ ← • ↵× ← ≡ •≡ ⟨ →≈ ←÷≈ ← ← ≈″←�↑ •…≈

≈≡ ←↑ ♠≈ ↑≈♠≈ ≈ ″ ±↔←♥≈•≠÷ ←÷≈ ± ←÷≈ ← ↵←≥≈″ ±↔×… ⟨

↵← • × ←÷≈ ≈↓↔≈″ ≈ ↔× ←÷≈ ←→≈↵←≥≈ ← ← ≈ →≈≈•♠≈…⟨

↵← ↵→≈ ←≈→ •♠≈ ←→≈ ← ≈ ← ↵″… ÷± …± ←÷≈ ±≥°↵ ⟨

≈ ≡ ←↔→≈ ≥≈… ↵•″ °→± ≈ ≈ ↔↑≈ ±≡ ÷≈ →≈ ≈ → ÷ ≈ ≈″ →≈… ←÷≈ ←→≈↵←≥≈″←⟨

≈ ← ≈ ↑←↑ °→± •• •♠≈ ←± ←÷≈ ¬ ⟨ ⊂ ÷ ← ≈♦← …±≈ ← ″→≈ ↑ ←÷≈ ↔→…≈ ±≡ ↑←↑ ± ≈ ¬ ↵″… ↑±•≈← ↵← → ≈⟨

± ↵← ≈ ←≈″← •↑ ↑← ≈≡≡≈←•♠≈″≈↑ …≈ ±″↑←→↵ ≈

≈ ← ≈→≈ ≠ ±… →±↔″ ↑ ≡±→ ≈ •≈ • •← ±↔ ↑≈← ↵ →≈≈…≈″← ≡±→ ± °↵←• ← ≠→±↔°

± •″≠ ≡ → ≈↑↑ ± ← ≈≡≡≈ ←• ≈ ←→≈↵←≥≈″←↑⟨

ð •× •← ♠ →← …↵ ≈→ ← ↔ו ÷≈ ≈ ≠ ←÷→≈↵← ≡ ↵″ ≈ • ≥

•× °≈ × ≡ ≈ ↑± • �↑ ±→←÷ •↑ … ≥• •↑÷≈… • ← °°≈ →↑ ←± ≈ ↵← •″ ↵″≈× •≠″ •″ ←÷≈ ∈↔ ≈ ≡ ∈≈ ↔≈⟨

⇒ ♦ →≈ → …↔≈↑ ←÷≈ ↔≈ ←• ←÷↵← ≈ ⇑• •ƒ≈″�↑ ⇑ ↔″• ± ↑ ≈→≈… ≈″←→↵× ←± ←÷≈ ° •↵←• ″

←÷≈ ↔ ≈ ∈≈↑↔≈ ″ �↑ …≈ו≈→↵←• ″↑ ⊂÷≈ ↵∂±→•← ♠•≈♥ ↑ ← ↵ ⋅ ↑÷±↔× ←↵∝≈ •″←±

↔ ← ←÷≈ ∈↔× ±≡ ∈≈↑ ↔≈ ↔ ±″ •″ ↑°≈ •→↔ ↑←↵″ ↑ ⊂÷≈ → →← °→±°± ≈↑ ↵ ÷≈ ∝ • ←

±≡ ↑←• ″↑ ←÷≈ ↵ ↑ ≈→ ←± •÷ • • • °×•≈… ♥• ×± ⇑⇔�↑ ↵ •↑±→ •≈ ←± ↵↑↑≈ ↑

÷≈← ≈→ ← →≈ •↑ ↵↑≈ ←± ≈ …≈ ″ → ←÷≈ →±↵… ↵ ″≠ ±≡ ÷≈ ↔ ≈ ≡ ∈≈↑↔≈ ⊂÷≈ →≈°±→← •↑ ←±

≈ ± ≥≈″…≈… ≡ → ↵←←≈ °← ″≠ ← °≈•≡ ←÷≈ ″…•←• ″↑ ↔ •÷ ↔ ≈ ≡ ∈≈↑↔≈ ↑ ← ≈

°×•≈… ∇″ ± ≈ ≈ ≥•″↵←• ″ ≈→ ←÷• ↵←← ≥°← ≡≡≈→ ≡→± ←÷→≈≈ ∂ → ↑÷±→ ≥ ↑

•→↑← ÷≈→≈ •↑ ≈↵ ≠↔•… ≈ ↵ ↔← ÷± ← ≈ ↵″↑ ≈→↑ ← ←÷≈ ↓↔≈↑ •±″ ↵→≈ ←± ≈ ≈… ⇐ ≈↑

←÷≈ ↔×≈ ±≡ ∈≈↑ ≈ ↵°° •≡ ← ≈ ↵ → ← ← ±″≈ ≡ ÷≈ ↓↔≈↑ •±″ • � ⟨ ≡ ↑± •← …

°× ←± ♠•→←↔ × ←≈ ÷″± ≠•≈↑ ↑↑ ↑↑≈… ⇑⇔ ≡ ← ÷ ♥ ≥↵ ≈↑ ↵″↑ ≈→↑ ↵→≈

→≈↓↔• ↵″… ↵→≈ ↑ ≥≈ ≈ ↵″↑ ≈→↑ ≥±→≈ •≥°±→←↵″ ÷↵ ± ÷≈→↑⟨ ↔→←÷≈→≥ →≈ …± ↑ ←÷≈ ↔ ≈

±≡ ∈≈↑ ↵→ ← ↑↵≥≈ ≈•≠÷← ÷≈″≈♠ •← ↵ °×•≈ → • ← ↵ ≥↵←← → ≡ …≈ ≈≈ ←÷↵←

↵→→•≈↑ ±→≈ ♥≈•≠÷← • ≈→← •″ ≈↑ ≈ ≠ ≈″ ±→≈ ±≡ ← ≈ ↵″↑ ≈→↑ ↵→≈ ≥ ≈ ≈≥°÷↵←•

≈↑ ⟨

≈ … ← ÷≈ ∝ • ← ∝↑ ±÷≈→≈″ ≡±↔↑ → ≈ ≥° ≈ ↓ ≈ ←• ″ ↵±↔← ←≈→″↵←• ≈

←→≈↵←≥≈″←↑ ± ≈→ °↑ •←÷ ↓↔≈↑ •±″↑ ↵±↔← ≠↵•″ ← •≡≈ ≈ °≈ ←↵″ ↓ •← •

↑• ≈ ↑ ≈ ×↔ ← ↑ ″↑ • →≈ ≈″← × • ≈ ″ ≥° •↑ ÷ ←≈→″ •♠≈ ←→≈ ← ≈″←↑

″ ↓↔≈↑←• ″ ↵± ← ≈↓↔≈″ ≈ ÷±↔× ÷≈ ←→≈↵←≥≈″← ← →≈ •♠≈… ♠≈→×↵ •←÷

↓↔≈↑ •±″ •↑ ←÷≈ •″←≈→ ≈″←•±″ →≈ •→ … ← ♠ •… • ≥≈… ←≈ × ↑↑ ≡ •≡≈ ±→↑≈ ← ≈↵↑← ← ± ≡

←÷≈ ↓↔≈↑ ″↑ ≈ → ″± →≈×↵←•±″ ÷•° ← ≈ ±≡ ∈ ↑ ↔≈ ± ≈° →≈↑ ≈ ≡→± •≥ ≈…•↵←≈ °≈→•×

± •≠ ↵ × ″≈…

→ ↑ ↔↑≈↓↔≈″ × ≈ ±→↵←≈ ″ ÷≈ •←≈→ ↔→≈

↔≈↑←•± ↵±↔← ≡↔←↔→≈

≥ •↵× ≠↵•″↑ →↵•↑≈↑ ″ • °±→←↵″← ≠≈″≈→↵× ↑≈← ≡ •↑ ≈ ↔← ←÷≈ ↔≈ ≡ →≈↑≈↵→ ÷ ↑↔≈↑ ≡

°±←≈″ • ≠↵• ≡→ ≥ ± ←• ↔•″≠ →≈↑≈↵→ ÷ → °±← ″←•↵× × ↑↑ ≡→± ≈↵↑ →≈ ≈ → •↑≈ ″

→≈↑±↔→≈ ↵× ± ←• ″ →≈ ≥ ≈″… • …≈ … → ← →≈↑←→ ← ← ↑°≈•↵× ↑≈↑

•″♠ × • ↔ ≈ ±≡ ∈≈↑ ← ±↔ … ↑≈ ≥ ↔″÷≈ ≡↔ ←± …≈↵× •←÷ ÷• • °±→ ← ≠ ≈→↵ •↑↑↔≈ •

←÷≈ ″ ♦← ≡ ↵ ↑ • ↵↑≈ ↔≈↑←• ″ ð ↵ …≈≥• ↵″… ± → …↵″ ≈→↑ ← °↔ • ÷≈ ←÷

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… ←± …≈ •←÷ ♥ ∝ ≈ •…≈ ↑ ↵ ↵← ≈↑← ←↵″≠≈ ←•↵×

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≈•←÷≈→ ↵ � ≈↑� → ↵ �″±� ↵″↑ ≈→ ±↔ ↔↑ × ≈ ∂ ←• •≈ ″…•″ ″ ÷≈ …≈ • •±″⌠ ↵ ≈→�↑

♥″ ∂≈←• ≈ ≈ …≠≈ ≈″← ±→ •″…≈≈… ÷± ≡ → ÷≈⟩↑÷≈ •↑ ↑ ≈ ←÷≈ ± • ≡

♠≈ ←≈ •″←≈→≈ ←↑ ⊂÷≈ ♥ →↑← ≡ ≈″…≈→ •″ ÷•↑ →≈↑°≈ ← • ≈ ↵°↑ ∉↔≈↑←• ″ ∑ ÷ ← • �≠± …

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… ≥ ÷ ≈↵ ⟨ ∇←÷≈→ ″↑←↵″≈↑ ≡ ≈″≈↑↑ •″× …≈ ∉↔≈↑ •±″ ↑± •↑

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∉↔≈↑←• ″ ÷± ×↵→≠≈ •↑ ↵ �°→±÷ • •♠≈� ↑←⟨

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±°°±→ ↔″•← ± ←� ↓ ≈ ←• ″ ÷ ♥≈♠≈→ ÷≈ •←•ƒ �↑ ⇑± •× • ••← … •← ←÷↵← ÷≈

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↑ •≈← ♠ ↔≈↑ •←↑ ≥° ≈≥≈″←↵←• ″ ± ≈ ÷• ←÷↵″ •← ±↑

•♠• ↵× ± × • ↵←•♠≈↑ ↵ ו ±× • � ← ≈ →≈× � ♦ ←•±

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•″ ←•″←• ≈× →•≠÷← ← •″≠ ←± …± ← ← ÷≈ ↑↵≥≈ ←• ≈ ″± ↵″←•″≠ ← ± ↑≈ •≠÷← ±≡ ←÷≈ ° →← •←

↑←↑ ±≡ …±•″≠ ↑± ″ ←÷•↑ ↑≈ •±″ ♥≈ ±″↑ ≈→ ≈←÷≈→ ← ≈ •″ ←•″←• ≈ ↵°°≈↵ ←÷≈ ↔×≈ ±≡

∈≈↑↔≈ →≈≡ ≈ ″ ↵°°→±° •↵←≈ ±→ ↔″…↵←•± ≡±→ °↔× ×•

← ≥• ← ≈ → ≈ ÷↵← °≈±°× ÷ ≈ ↔ ↵ →• ÷←� ←± ≈ →≈↑ … ≡→ ≥ °≈→ ←÷≈ ←↵←≈

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↑↵≥≈ ♥ ← ↵← •← •≠ ← ♠• ×↵←≈ ←÷↵← → ±″�↑ →• ÷←↑ ↑ ← →← → ″≠ ÷≈≥ �÷ →• ÷←

↑↔≠ ≈↑←↑ ↵ •″ •± ≈ ↑ …≈⌠ ←→↵•″ ±″ …≈•↑• ″ ≥↵ • →↵←÷≈→ ÷↵″ ≈ ←± ≈•≠÷≈… •

←÷≈ ↵″ ≈ ↵″ ← …≈… ±≡≡ ← ≥↵→≠•″ ″↑← ± ÷≈→ °± • ≠ ↑ ↑↔ •↑ ″≠

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←÷≈ →• •… •″♠•± ↵ ≈ ÷↵ ↵←≈→ ±≡ ↵ ÷↔ ″ →•≠ ← •← •× ″≈ ≈→ ≈ °± ↑•×≈ ← ≡±→… ↵×

←≈÷″± ± • ↵×× ≡≈ ↑• ≈ ≈…• ↵× →≈↑ ≈↑

± °→±≥• •″≠ ו″≈ ±≡ ↵→≠↔≥ ″← • ← ↵°°× ←• ±≡ ∈↔ ≈ ≡ ∈≈↑↔≈ ♣ ↔ ° ו ≥↵∝≈→↑

÷↵♠≈ � • ↔≈ ±≥≈ •±″↑ ←÷≈ ↑ ←≈ ÷ ♠ •″…•→≈← ↵″…⟩±→ × ″≠⌠←≈→≥

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⌠±°≈→ ←• ″ ±→ ↑• °× ↑ �←÷≈ ≡ ↵ • • •↑≈… ↵″… ÷↔ ↵″≈ ↑ •≈← �∫

•∝≈ ÷ ↵ →•≠÷←

↑ ו ↵″ ≈ ≈•≠÷≈… ″ ←÷≈ ↵″ ≈ ″… ← …≈… ±≡≡ ↵≠↵•″ ← ←÷≈→ ♠↵×↔≈↑

÷•↑ ÷↵↑ ÷≈

•≥° →←↵″← °→ ← •≥° •↵←•± ↵← ±← ≥≈…•↵× →≈↑ ≈ →≈ ≈↓↔↵× → × • ←±→ � ↵

←÷↵← ←÷≈→ ←÷•″≠ ↓↔ ± ←⌠≈≡≡≈ ←• ≈ →≈ ↔≈↑ →≈ ← ≈ °→≈≡≈→→≈… ←± ↑←⌠•″≈≡≡≈←•♠≈ ↑ ↔≈

¬± ≈→ ←÷≈→≈ →≈ °→± ≈≥ •← ←÷• •″≈ ≡ ↵→≠↔≥≈ ← •→↑← • • ÷↵→ ← ±→≥ ≈♠≈ ←÷≈ ♠↵≠↔≈↑←

≠↔≈↑ ↵ ↔← ÷≈ ≥↵≠ •← …≈ ≡ �↑ ≥± • ♠↵×↔≈� ″ ← ″× ≈ ↵ ≈ ≈≡≡≈←↑ ↵→≈ • •→≈ ← ↵″…

←≈→≥ ↔← ↵×↑ ≈↵ ≈ ↑↵≥≈ ↵ •± ≥↵ ≥± •↑≈ •≡≡≈→≈ ← ←÷ ″≠↑ ← •≡≡≈ ← •←•ƒ ↑

≈ … ←÷≈→≈ •↑ ↵″ ≈→ ↑←× ″… •→ ←• ″↵× �≠≈ ← →≈ °± •←•↑� →≈° • ≠ ↵←• ″ …≈• •

≥↵∝•″≠ ÷•→… ← • ″±← ≈ → ←÷≈→≈ •↑ ″ ו ↔≈ ″ °→±↵←•♠≈ ° • …≈ •↑• ″↑ ≈

…• ← ″≠↔• ÷ ← ↑≈ ↵→•±↑ •→ ← ≈ ± • ← •↑ ♥•× •″≠ ←± °← …•♠≈→↑• ″↑ ≡→ ≥ ÷≈

≈ ≈→↵ ↑←⌠≈≡ ≈←•♠≈″≈↑↑ →≥ •″≠ � ≈°←•± •→↔ ↑←↵″≈↑� →≈↵ •♠≈× ±″ ↵ ↵↑≈⌠

⌠ ↵↑≈ ↵↑• ≈ ÷≈ →≈ ↔≈ ←≈↵ ±•″≠ ±♠ → ↔…≠ ← ←± ↑ ≈ ÷≈ •≡≈ ≡ ←→↵°°≈ ≥ ″≈→

↑≈±″… ≈″ •± × ↑≈→ ← ÷≈ ⇑⇔ ↑≈ •↑ ♥÷≈→≈ ↑±•≈← ≈•≡•≈↑ ≈≡ →≈÷ ←÷≈ ° → •↔ →

← °≈↑ ±≡ •″ …≈″← ÷≈→≈ ←÷≈ ≈″≈→ ±↑←⌠≈≡≡≈ ←• ≈ ↑↑ ″ •↑ ← ≈ →≈ … ≠ ←± ″♠≈↑← •″

…• → °±→←• ″↵←≈ ≈♠≈ ↑ ≡ ↑°≈• •↑← ↵≡≈← °→± •↑•±″ •″ ≥ ″≈↑ ← ″ ← •″ → •× ←↔″″≈ ↑

↑±•≈← ←÷↵← … ≈↑ ″± ± ≥ …↵←≈ ← ≈ ≡±→ → ← ±≡ ♦≈°←•±″ …±≈ …≈ ↑≈≈≥ ←± ≈

•″÷ ≥↵″≈ ¬ ≈ → •← • ″ ← • ←÷↵← ↑ •≈← ←÷ ← ↵ ≥ ±…↵←≈↑ ←÷≈ ←←≈→ ← °≈

≈ ≈°←•±″ •↑ ″≈≈↑↑↵→•× ÷ ↵″≈ •← •↑ ″±← ≈ → ♥ ≈→←↵•″ →±↔°↑ ≈ ≠ ≥ ″≈→↑ ↑÷±↔×… ≈←

↑°≈ •↵ →• →•← ← ←÷≈ ±↑ ≡ ≈ ≈ ±″ ≈ ↑≈ • ≈ ←→↵•″ ↑←↵≡≡ ↵ °↵↑↑≈″≠≈→↑

±→≈ ≡ … ≈″←↵× ←÷≈ ↵↑≈ ↵≠↵•″↑ °× •″≠ ← ∈↔×≈ ±≡ ∈≈↑ ≈ ← ↔ • …≈ • • • ←÷↵← ← •↑

↑≈ ↵ ″↵← →↵ ÷↔≥↵″ ≥±←• ″ ← ↵← • •→→≈ ≈ ″← ←± …≈•↑• ″ ↵″… … ≈ ∝ °←

≡•→≥× • ← ≈ →• ↵←≈ ↑ ÷≈→≈ →…•″≠ ←± ← •↑ ♠• ♥ ←÷≈ °→• → ♠•→←↔≈↑ ≡ • …≈ • •

≥↵∝•″≠ ↵→≈ • ° → • ← ↵ ↔↑←•≈ •″ ↵″•″≠ ←÷≈ • ←≈→≈↑←↑ ±≡ …•≡≡≈→≈″← °±°↔ ↵←• ≠→ °

→ ←÷≈→ ←÷↵″ °↵→←•↵ •← … ± °↵↑↑• ″ ←± ↵ …↑ ° ←•↔×↵→ • ″←• •↵×≈ •″…• •…↔↵×↑ →± ≈ ±≡ ←÷≈

°↔ • …≈•↑• ≥↵∝≈→ • ←± ↵∝≈ •≥ →← …• ° ↑ •±″↵←≈ … ≈≥≈″← ↵± →≈↑ →≈ ↵× ± ←•±″

≈← ≈″ →±↔°↑ ≡ ↔″•… •≡•≈… °≈±° ≈ ↵″… •→ �↑←↵←• ← ↵×� •♠≈

→←• •← ″…

≥° ↑ • ″ ← →…↑ ° → •↔×↵→ …≈″←• •≈… ″…• • ↵×↑ →≈ • → ° ↵←≈ ″ …≈→ ←• ↑ ← ← ÷≈

°↔ • …≈•↑• ≥↵∝≈→ ↔ … ← ← •″←≈→≡≈→≈ •← • ≈ •↑• ″ ≥ ∝•″ ↵↑ •← •↑ ↵→•←→ →

… ″ •→ ← …• •≥ ″↵←≈ ″ ≡ ±↔→ ± °≈±° ≈ ÷± ÷↵°°≈ ← ≈ •… •≡•≈… ↵″… ↵≠↵•″ ← ←÷±↑≈ ♥÷

÷ ≈ ″± ← ≈≈″ •…≈″←• •≈…

⇑ ↑• ≈ ≈↑ ±≡ ←÷≈ ∈↔ ≈ ≡ ∈≈ ↔≈ ← ↵± ← °≈ •≡ • • • ↔ ↑ …→ ″• ″ ← ≈ ←≈→ →

≈″←→ ≈ ″ ≡•→≈ ″ ≈ ≥≈…•↵× ″ ≈♦← ←÷• ± →≈↑°±″… ←± ←÷≈ •″ ↵× ≈…↑•…≈ ≈ ≈× ÷≈

°→±°→•↵←≈ ° → ≈ •″ ↵ ≈…• ″←≈ ← ←÷≈→≈≡±→≈ ÷≈← ↵″ ″…•♠ ↵× → ↵ ←≈↵≥ ≡ ≈…•↵×

↑←↵ ≡ ≈″← ≈ … ← ≈• ↔ ↔ ↵× ≡ …↔← ←± ↑ ≈ •≡ •≡≈ ↑ … °→↵•↑≈… ≡ → •″≠

↑ ⊂÷≈ ↵°°→±° •↵←≈ ° •″ ≥≈ ± ←≈ ← • ″± ÷≈←÷≈→ → ″±← ⇑⇔ ↑÷ ↔ ↔← •″ °

↑ ↑← ≥ ←• ° •±″ ≡ → ← ↑≈ ↵↑≈↑ ≈→≈ •″…• •… •♠≈ •×× ←÷→≈ ← ″≈ ≈ →≈≥•← ±≡

⇑⇔ … ≈↑ ″±← ± ≈→ •″…• •… ↵↑≈ •← •↑ ↵ … ≈← ↔° ←± ↵∝≈ →≈±≥ ≈″…↵←• ÷≈

″↵←•± °± • ≈ ×

⊂÷≈→≈ •↑ ↵×↑ ↵ ≡↔″ ≥≈″ ∂ ←• ″ ←± ↵ …≈≡• ←•± ≡ ÷≈ ↔×≈ ±≡ ∈≈↑↔≈ ↵↑ ↵ ≈♦≈°←• ↵

↵↑≈ ″♠ × • • • ″← …≈ ÷ ↔ ↵ ≈ ″≠↑ →≈ ±→←↵× ±″≈→ → ←≈→ ↵× •♠≈↑ •× ° ↑↑

←÷→±↔ ÷ ÷≈ ↑ ≈ ÷± ≈→ …≈≡•″≈… ↵″… ±°≈→ •±″↵ו↑ ÷≈→≈ ≈↵←÷ •↑ � ≥ •″≈″←� ± ≈

…≈ ÷↑ ↵→≈ ↔ ♦°≈ ← … ↵ … •∝ ≈ ←→ ≡≡• •…≈ ←↑ ↑ ← ←÷•↑ ♥• ÷↵°°≈″↑ ♠≈→

↑↔……≈″ ↵ • ± →→ ♥ ←÷ →≈ •↑ ≈ ≡±→ ≈…• ″←≈→♠≈″←• ″ ¬± ≈→ • ↵ → ≈

″ ≈→ ±≡ ≈↑ …≈↵← •↑ ±→≈ → ≈↑↑ °→≈…•←↵×≈ ↵″… ≈≡ →≈ …≈ ← • ≈ ↵ ↑←↵≠≈ ÷≈→≈ ←÷≈

°↵←•≈″← •× ≈ →≈ →…≈… ↵↑ ≡↵ • ≥•″≈ ← …≈ ÷ ← •↑ °→ ≈≥↵←• ←± →≈≠↵→ ≡ •″≠ ♥•← •″ ←÷•

•″ ″↑← ←↔← ″≠ ↑± ≈←÷ ″≠ ≈ ≈°←• ″ ↵″… ≈•″ ±→←÷ ≡ ↑°≈ • × ±″↑ …≈→ ←• ″ ← •

″±← ±≥ ←÷ ≈♦≈°←• ″ ↔← ↑± ≈←÷ ≈ •× ↵×× ↵↑↑ ←÷→ ↔≠÷ •″ ↑± ≈ ≡ →≥ ±→ ←÷≈→

¬↵♠•″≠ ↑≈← •…≈ ÷± ≈ ≡±→ ♥÷ ≥ ″ →≈↑ •↑ °±↑ • ≈ ″… ÷±↑≈ ≡±→ ÷±≥ ←÷≈ ↑←↵←≈ ±≡ •≥ •″≈″←

…≈ ÷ →→• ≈↑ °→≈…•←↵× ← ←÷≈ ≈ ÷♥↵ ≡ •″ →≈↵↑•″ ↵″… ↵° → °→•↵←≈× ≥↵ ↵≠≈… •

÷≈ ←÷ ≈ →≈ × ← •← ≠→± ±≡ °≈ ≈ ≡ → ÷± ←÷≈ ←→ ↑ ←•± ←± ←÷≈ ← ≈ •≥ ≈…•↵←≈ °≈→•

÷≈←÷≈→ ≡ ←↵× ±→ ″ ≡ ← ↑ ↔″≈♦ ≈ ← ↵ ≡ → ≥ ←→≈ ← ≈ ↵ ← ≠÷ ″ ← ± ← ≈≡≡≈ ←• ≈

•↑ °± ↑•×≈ ↑ ≠→±↔ • …≈≡ ″≈ ↵← ← •↑ ″±← ↵″… • °×•• ″ ←÷↵← ″ ←•±″ • ÷ × ≈

±≡ …≈♠•↑•″≠ → ⌠ ←• ≈ °± • ↑←↵←≈ ≈ ← ≡±→ ←÷≈ →←÷≈→ •← •↑ ≠→± ≥ ↑← ∝≈ ←± ≈

″ ≈ ←→ ← … ÷± ≈ ÷± ←≈→ ← ≈ ÷≈↵ ← →≈ ↑ ↑←≈ ←÷→±↔≠÷ ←÷≈ ≈ ≈→≠≈ …≈° ←≥≈″ ∑

÷• ÷ •↑ …≈↑• ≈ ↵″… ≡↔ ≈… → ÷≈ ↔ ↑≈ ±≡ →≈ ↔•″ ↑≈ ÷± ≈ • ×⌠ ← • ↔″≈ ←≈

… ←≈″←•↵× ×•≡≈ ← →≈↵←≈″• ÷≈ ↵°°→±°→• ←≈ • °± • ≈♦°→≈↑↑• ″ ±≡ ← ≥ → •≥°≈→↵←• ≈

←± →≈↑ ↔≈ ←÷ ↑≈ ÷± ″≈ ←≈… ≡ • ←± •≥≥ …•↵←≈ ≈→• × ≈ ←÷≈ ≈ ≈ ≈″ ÷≈↵×←÷

↵→≈ ≈→♠• ↑

± × •±

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•≥ ≈…•↵←≈ °≈→•× ⇒ ↵↔↑≈ ≈ ↑÷ →≈ ← •↑ →≈↑° ″↑≈ ↵↵ ≥• ↵″ °± • ≥↵ →↑ ↵♠ ↑←→↔≠ ≈

←± • °×≈ ≈″← ← •″ ÷≈ ± ←≈♦← ±≡ ÷≈↵ ←÷ ↵→≈ °± • ⊂÷≈ ≈″←→↵× → ×≈ ↵↑ ≈≈″ ←

±°≈→↵←•±″↵ •↑≈ ↔″…≈→ •″≠ ±″≈°← ↵″… ← ±→≠↵ •↑↵ • ↑ ÷↵♠≈ ≈♦° • •← ↵ °←≈… ←÷≈

≈″≠≈ ≈ ↔↑←→ • °± • ±″ ≈ ±≡ ≈↑ ↔≈ ″ °÷↵→≥↵≈↔←• ♠≈ ↵≠ …≈ •↑• ″↑ •↑ •″

≡ ← ≥ ↑← ± °× ←≈× …• ±→ ≈… ≡→±≥ ←÷≈ ±→• ↵× ″ °← ≡ • ≈…•↵←≈ °≈→ ↵″… ≡ ↔ ↑

•″ ←≈ ±″ ↵ •≡ ≈→≈ ← ↑≈← ≡ • ↑↔≈↑ →±↔″… ″≠ ÷≈ °→± ≈≥ ≡ →°÷ … ⊂÷≈ ⇑⇔

⇑ ←•ƒ≈″�↑ ⇑ • →≈°±→← °→ ♠•…≈↑ ↔ ≈≡ →≈÷≈↵→↑ ≡ ←÷≈ • ↑↔≈↑ ↔← •″ ←÷≈ • ↵″ ↑• ←÷≈•→

↑ ×↔←•± •↑ ↑± ≈× …≈≡•″≈ ← ← • ↑ ←± °→± • ≈ ≈ ±°≈→↵←• ″↵× ≠↔•…↵″ ≈∫

⊂÷≈ ∈ ≈ ±≡ ≈↑ ↔≈ � • ≈ ÷≈ ±→↵× • → ←•♠ ←± →≈↑↔≈ …≈″←•≡•≈… ″…• ↔ ↑ ″ •≥ ≈…•↵←≈

°≈→•× →≈≠↵→…×≈ ↑ ≡ ↑← • ↑← ″← ≡ ±≥ ←÷≈ ≠ ≈→↵× •↑ ±≡ ±″≈→″ ≡ → ←÷ ↑≈♠≈→≈× •× ♥÷•÷

…±≈↑ ← ←↵÷ ≈ ↵ • °±→←↵ ≈ ≈•←÷≈→ ←± ÷≈ • ≥≈ •↵ ±≡ • ↑↑ → ← ←÷≈ •≡•↵•× ← ±≡

←÷≈ ″…• • ↵× ″ → ≈… ″ו∝≈ ←÷≈ ∈↔ ≈ ≡ ∈≈↑↔≈ ±″≈→″ ≡±→ ←÷≈ ↑≈♠ ≈× •×× ≈

≠→ ↔ …≈ ≠≈″≈→↵ו ↵ ≈ • ↓↔≈↑←• ″↵ ≈ ° •× ↑±°÷• °→•″•° ≈↑ ≡ ←• ↓ ″←• •≈… ″

≡±→ • ↵× ≡±→ ≈ ≥• ≈ ↵←• ″∫

∈≈≡ ≈ ←•″ ↔° ″ ÷≈ °± ↑• ≈ ±→↵× ≡±↔″…↵←• ″↑ ≡ → ÷≈ ↔↑≈ ±≡ ↔× ±≡ ∈≈↑↔≈ •″ °↔ • →≈↑ ↔→ ≈

± ←•± •← •↑ …•≡≡ ↔× ←± ≡ ″… ″ •″ ″≠ →≠↔ ≈″← → …≈♠≈× °• °→±⌠ ←•♠≈ ↑±•↵× ••≈↑

±″ ÷≈ ≡ ↔″…↵←• ″ ″…•♠ …↔ ±→↵× →≈ ≈↑ ← ≈ ≈°←• ″ •→↔ ↑←↵″≈↑ ⊂÷≈ ↵° → •↵←≈

→ ×≈ ≡ → ←÷≈ • …≈ •↑• ″ ∝≈→ • ← ≈″↑↔→≈ • ° ←•↵× ← ↵″… ↔ ←• ≈ •″ ↵×↵″•″ ≈ •″←≈→≈↑←

± ↔″•…≈″←• •≈… •″…• •…↔↵× ≈ • ←± …•≡≡≈→≈″← °↔×↵ •±″ ≠→ ↔ ↑ ← • •∝≈× ← ↵← °↔× ° ו

≥↵∝≈→↑ ″ ÷↔ ↵″≈ ↑ •≈← ↑÷±↔ … ≡↵•×• ↵←≈ ≈ ≈°←• ″ …≈° → → ↑ ≡→± ↵ ± ← ≈≡≡≈ ←• ≈″≈↑↑

″±→ ↵← •× ±≥ ←•≥≈↑ •←≈ →• ÷← ≈ …≈ ÷≈ ←÷ → ≡≈↑↑• ↵× °≈→ ← ″≠ ← ← ″•

≈…↑•…≈ ×≈ •″ ↵∝•″≠ ≈• •±″ ↵±↔← …≈ •≡•≈… •♠ …↔ ↑ ↔← •← • ← ↑± ±♠• ↔↑ ←÷↵← ←÷≈

↑÷±↔ … ≥ ←←≈→ ≡ • ו ≈♦≈ ← ↵″ ±″≈ ≠→±↔° ≡ ″•…≈″←• •≈… •″…•♠ …↔↵×↑ •←÷

↑ •≈← → ≥ ← ≈ → ≈↑ ±≡ ° →←↔ •← ±↑← ↵← ← ≈ ≈♦°≈″↑≈ ±≡ ↵ × ±←÷≈→↑

ð

⇓ ♥ ≠≈ ←↑

≈ ↔ →↑ … •∝≈ ← ←÷↵″∝ ∏↵→ ⇑ ♦← ″ ⇔→ ∝ … → ÷≈ ≡↔ ≥≈″←↑ •÷ …

⇑ ±∝↑±″ •↑ ≡↔ ≈… ⇑ ¬≈ ≈→ • ≈↑ ∈≈↑≈↵→ ÷ °≈• → • ≈××± ↑÷•° ð⟩

⇑± ≈←• ⋅ ≈→≈↑←↑

∈• →… ⇑ ±∝↑± • ≈ ≈→ ←÷≈ ⇔ °→↵•↑ ⇑± ≥ ←←≈≈

⇑÷→ ↑←± ≈→ ≈ ↵↑ → • × ≡↔ …≈… ←÷≈ •± ″↑←•← ←≈ ≡ → ¬≈↵×←÷ ″… ⇑ •″•↵×

⇔♦≈×× ≈ ≈← ðð ↵″… ðð

∈≈ ≈ ≈ ↑

√±″↑≈″ ∈ ⇒≈″ ↵ ″ ± ⊂≈ ÷″ ≠ ↑↑≈↑ ≥≈″← ↵″… ¬ ←÷ →≈ ↵× ←• ″ ↵♥

≈… ≈ ↵″… ≈ ←÷ ⇑ →≈∑ ∑ ⌠

¬ …±→″ ⇑ ≈←← ″≠ ÷≈↵×←÷ →≈ ° •±→• •≈↑ • ∇→≈ ±″ ±↑← ≈≡≡≈ ←• ≈ ≈ ↑ ≈≈←↑ ÷≈ →↔ ≈ ≡

→≈↑ √ ⌠

•≈ •÷ …↑±″ ÷≈ ≈ ±≡ ≈↑ ↔≈ ± • ≈… ∑ ð�

√≈″″• ⇔ ↵″… ± ≈ ←≈•″ ⇔ ° • •″≠ ←÷≈ � …≈″ • • ≈ ♠• •≥ ≈≡≡≈ ←� √ ↔→″ ≡ •↑

… ≈→←↵•″←

←• ″↵× ″↑←•←↔←≈ ≡±→ ≈ ←÷ ↵ ו • ⇔♦≈ ×≈″≈ •←•ƒ ⇑ ↔″•× ∈≈° →← ← ↔×≈ ±≡

∈≈↑↔≈ ⇑⇔ ±″…±″ ðð ÷← °⟩ ♥ ♥ •≈ →≠ ⟩°↵≠≈ ↵↑°♦⟨ ≈↑↑≈…

⟩ ð

∈ • ↔ ♣≈→ ←•±″↵× ″↑← ←↔←≈ ≡ → ⇑ •″• ⇔♦≈ ×≈ ≈ ↵″… •← ↔≈ ↔ ≈≥≈″←

⇒→• • ≈… ↵× √±↔ ↵ ðð ⌠

←• ″↵× ″↑←•←↔←≈ ≡±→ ≈ ←÷ ↵″… ו • ⇔♦≈× ≈″≈ ⇑⇔ ± •↵× ⊇ ↔≈ ↔…≠≈ ≈″← �

→• ° ≈↑ ≡±→ ÷≈ …≈ ≈× °≥≈″← ≡ ⇑⇔ ∧↔ ≈ ±″…±″ ⇑⇔

÷←←° ⟩⟩ ♥ ″• ≈ ±→ ° ≠≈ °♦⟨ ↑♠∂ ↔•…↵″ ≈ ↑≈… ð

⇐≈° →←≥ ≡ ¬≈↵×←÷ ↵″… ≈•″≠ ∧↔•…≈ •″≈↑ ≡ → ≈ ÷ → ↔← ″ ↔↑ ±″ →≈° → • ″

±≡ ↔ •↑ • ←± ÷≈ ÷ → ≈↔← ↵ ⇒≈″≈≡•←↑ …♠• ±→ ⇑ ≥ •←←≈≈ •″ •″ ≥↵∂ →

↑↔ •↑ •±″↑ ″♠± • ≈ ″±≥• ↵″ ≈ ↑← •↵ ±♠≈→″≥≈″← ≈ ↵→ ≥ ← ±≡ ¬≈ ←÷

… ≠≈•″ ⇑ ″≈→→

÷←←° ⟩⟩ ♥ ÷≈ ←÷ ≠ ♠ ↵ •″←≈ ≈←⟩ ≥↑⟩ ↔ו ÷ ″↑ ⟩⇑± ←≈″← ÷≈ ←÷⌠° ⌠≠≈″≈→ × ↔

°÷↵→≥°↵ ⌠ ÷←≥ ≈ ↑≈…

⇑×↵♦← ↵″… ⇑↔ ≈→ ⊃• …″≈↑↑ ±→ × ⟨ ≈←÷•↑ ±≡ …≈ • ±″↑ √±↔ ″ ±≡

≈… ←÷• ð ⌠

ð ↵→≡•← ⇐ �⇔↓ •← ≡ °→•±→•← ⟨� →≈° •″←≈… • ⇑ ← ″ ⊃• •↵≥↑ ≈…↑ ⊂÷≈

•…≈ ±≡ ↓↔ ← ⇒ • ↑← ∝≈ ↵≥• ×↵″ ↑↑ ðð

• ≈→ ⇐ → ″•°×≈ ±≡ ↑±•↵ ←•≈ ⇒ ↑←± ¬ → • ≈→↑•← →≈↑↑ ðð

∏↵≥ → •← ±→← ← ⊇ × ≈ ←÷ ⊃÷ ≥ ←± ↵♠≈ →±≥ ← ∇♦≡ →

∇ →… ⊄″•♠≈→↑• →≈↑↑

∈ ↑ √ ≈ ±≡ √ ←•≈ ↵→♠↵ ⊄″• ≈→↑•← ↑↑ ⇒≈ ∝ ↵° →≈↑↑ ¬↵→♠↵→

⇒→± ≥≈ √ �∧ ±… ≡ •→″≈↑↑ ↵″… ↓ ↑ ″ ÷• ± ♣ ↵ •↵× ⊃≈×≡↵ ≈…•←≈… ←

⇒≈ ″… ↑ ≈ …↔↑ ⇑ → …≠≈ → ≈ ⊄″•♠≈ ↑•← →≈↑ ° �

⇑↔× ″… ⊃↵≠↑←↵≡ ↓↔ ← ↵″… ↓↔↵ו← •″ ≈ ←÷ ¬≈ ⇑ →≈ √±↔ ″

¬≈↵×←÷ ⇔ ″± ∑ ⌠

⇑± ±″ ∈ … ⇐± ↵″ •″ ≈↑ ±≡ ∂ ↑ • ≈ •″ ÷≈ ←÷ ↵ →↵←• ″ ±↔ ″ ≡ ≈…

⇔←÷• ðð ⌠

±→… ⇔ ⇑± ←⌠♠ ↔≈ ↑•↑ •″ ←÷ →≈ •″≠ ↑≈″↑≈ ±≡ ⇓∩ ⇑↵ →•… ≈ ↵≥→•… ≈

⊄″•♠≈→ •← →≈↑↑

±→… ⇔ ¬≈↵× ÷ ← ←≈ ♠↵×↔≈↑ ≡→± ↔ ←•↵←←→ ↔←≈ ←• •← • ←→↔≥≈ ←↑ ″≈≈… →→≈←•±″ ″ ↵× ±

≈…• ≈ ⌠

± ≈≠• ″ ≈… ↑ ⇑ ″←→± ⇓≠≈″ ±→♥≈≠•↵ ≠↔ ≈ •″≈↑ ≡ → ↵→ ≈ ″±≥•

↑•↑ • ←• ″ •← ↵°° • ↵←• ≡±→ •≥↔→↑≈ ≈″← ⇑ ∇↑ ðð

÷←←° ⟩♥♥ ≠≈ •… × →∝≈← ″± ←≈≥ ←≈↑⟩ ″←≈→ ↵≠≈ℑℑℑℑ ↑°♦ ≈↑↑ ⟩ ð

ð ⊃• ↵≥↑ ÷≈ �≡↵• •″″ ↑� ↵→≠↔ ≈″← …≈↑≈→♠≈↑ ≡↵•→≈→ ÷≈ → ″≠ ⇑ ≥ ≈″ ×↵″

•× • ↑ ±→… … √ ÷↵″ ↑↑±″ ¬≈↵ ← ⇔ ″ ∑

⇑↵≈ ⇑ ⇑ ♦← ″ ∏ ↑↔÷• ⇓ ∇→°÷↵″ ↔≠↑ ↵″… ÷≈ ¬ … ≈ ↔≈ →↵→•← ⟨

⇒→• • ≈… ↵× √±↔ ↵× ð∑ ð⌠

±±… ↵″… ⇐ ↔≠ …≥ ″• ←→ •±″ ∇→ ÷↵ … ↔≠ ↵← ↵↑ ≈″…≈… ♥♥ ≡ ↵ ± ⟩±→°÷↵″⟩ ↵ ÷←

≈≠↔×↵←• ″ ⇔⇑ ± ðð ≡ ≈ ⇔↔→ ≈↵″ ↵→ו ≥≈″ ↵″… ≡ ÷≈ ⇑ ↔″• ±≡ ⇐≈≈≥≈→

″ →°÷↵″ ≈…••″↵ °→±…↔ ↑ ∇≡≡•• √±↔→″↵× ±≡ ÷≈ ±°≈ ⇑ ≥ ←•≈↑

ð ⌠

±ƒ•∝ ∈ ⊂÷≈ ↵←↔→≈ ±≡ ∈↵ •±″↵ו← →•″≈←±″ →•″≈←±″ ⊄″• ≈→↑•← →≈↑↑ ðð

→±± ≈ √ ⊂ •″ ←± ♠↵×↔≈ ↵ ו ≈ √ ↔→″ ≡ • ⇔ ″± •↑ ∑ ⌠

∧± •″ ⊄ • •←↵→ ↑ ↵ ↔ • • ± ±°÷ ↵≥→•… ≈ ⇑↵ → …≠≈ ⊄″•♠≈→↑•← →≈ ↑