Transient model of a panel radiator

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http://www.diva-portal.org

This is the published version of a paper presented at Proceedings of BS2015:14th Conference of International Building Performance Simulation Association, Hyderabad, India, Dec. 7-9, 2015..

Citation for the original published paper:

Brembilla, C., Soleimani-Mohseni, M., Olofsson, T. (2015) Transient model of a panel radiator.

In: Proceedings of BS2015: 14th Conference of International Building Performance Simulation Association, Hyderabad, India, Dec. 7-9, 2015 (pp. 2749-2756). India, Hyderabad: International Building Performance Simulation Association (IBPSA)

N.B. When citing this work, cite the original published paper.

Permanent link to this version:

http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-116130

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n nnn n nnn nn nnnn nn nnnn n nnn nnnn nnnnn nn nnnnnn nen n n nnnnn nnenn n nnn nnnnnnnnn nnn nnnnnnnn n n nnnn nn nnnnnnnnnnnnnnnnnnn nnnn nn nnnnnnnnnnnn nnnnnnn nnn nnnnnnnnnn nn nnnnnn nnnnn nnnnn nnn nnn nnnnn nn nnnnnnnnn nnnnnnnn nnn nn n n nnnnnennnn n nnn n nnn nn nnnn nnnnnn nnn nnnnnn nn nnnn n nnn nn n nn nnn nnnnnnn nnn nn nnnnnnnn nnnnnnennnnnnnn n nnnn n n nn nnnnnnnnnnnnnnnnnnnnnnn nnnnnnnnn nnnnnnn nnnn n n nnnnnn nnnnnnnnnn nnnnnnnn nnnnnnnnn n

yg tys s l ytsyy yytyl,sylyttylstylsstltylss

(5)

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nnenn nnnnnnnnnnnnnnnnn nnnn nnnnnn n

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n nnnnn nn nnnn n nnnnnn nnnnennnnnnnn nnnnnnnn nn nnnn n nn nnnnnn n n nnn nn nn nn n nn nnn nnnnn n n nnnn n nn nn nnn nn n nnnnenn n n nn nnnnnnnnn nnn nn nnnnnenn nn n n nnnn n nnnn nnnnn n nnnnnnn nnnn nnnn nnnnn n nnn nnnn nnnnnn enn nn nnn yxgs nnnn nn n enn nn nnn

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nn n

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n nnn

nnnnn nn nnnnn nnnnnnnn nnnn nnn nnnn nnn nnnn n nnnn nnn nn nn n nnnn nnnnnn n nnnn nnnnn nnn nn nnnn nnnnn nn nnn n n nnnn n nnnn nnn nnnn nnn nnn n nn nnn nnn n nnnn nnnn nnnnn nn n nnnnnn n n n nn nn n n nnnn n nnnn nn nn n n nnnn nnnnn n nnnnn nnnn nnnnn nnn n n n nn n nnn nnnn nnn nnnnnn nn nnnnnnnnnnnnnn nnnn nnnnnnnnnnnnn nn nn nn

nnnn nn nnnn nnennnnnnnn nnnn nnn nnnnnnn n nnn nnnn 8 n nnn nnnnnnnnnnnnnnnnn nnnn nnn nn nnnnnnnnnnnnnnn nnnnnn nnn n n ⁿ nn nnnnnnnn nnnn nnnnnnn n nnnn nnnn n n

nnnnnnn nnnn nnnnnnn nn nnnnnn nnnn nn nnnn nnnnnnn nn nnnnnnnn n n nnnn nn n n nn nnnn nn n nnnn nnn nnnn nnn nn nnnnn nnn nnnn nnnnn n nnn n n nn nn nnn nn nnnn nnn nnnn nnnnnnn nn nnnnnn nnnnnnnnnn nnnnn n nnnn n n nnnn nn nnnnnnnnnnn nnnnnnnnnnnnn nn nnnnnn nnnn nnn nnn nn nn nnnnnnnn n n nnnn n n nnnnnn nnnnnn nn nnnn nnnnnnnn nnnnnn nnn nnn nnn nnn nnnnnn n nnnnn nnnnnn nnnnn nnn nnnn n nnnnnn nn nnnnnn nnn nnn nn n nnnn nnn nnnn nnn nn nnnnnn n nnnnnnn n nnn nnnn nnnn n n n nnn nnnn nnn nn nnnnnnnnn n nn n nnn nnnnnnnn nnnn nnn nnn nnnn nnnnn nnnnnnnn n n nnnn nn 5 nn nnn nnn nn n nnnnn nn nnnnnn nnnn nnnnnn nnnnnnnnn nnnn nnnnnnn n nn nn nnnnnnnnnnnnnn n n nnnn nnn 5 n n nnn n

yg tys t s xgt ststyleyttt tyslysytygstgytltls ytetyyttyyys

n nnn nn nnn nn nnnn nnnnn nnnnnnnnn nnn nn nn nnnnnnnn n n nnnn n nn

sssssssssssssssssssssssssssssssssssssssss

yg tys yttsylyssylyslysytygstgytltls ytetyyttyyys

n nnn nnnn n nnnnn nnnnnnnnnnnn n nn nnn nnnnnnnnnn

nnnnn n nnnnn nnnn nnnnn nn nnnnnn nnnn nn nn nnnnnnnn

n n nnnn n n nnn nnnn n n nnnn nn 5 nn nnnn nnnnn

nn n nn nnn nnnnnn nnnnnn nn nnnnnnnnnnnn nn nnnnnnn nn

nnn nnn nnnn nnn nnn nnnn n n n nn n n nn nn nnnn

nnnnnnnnnnn nnnnn nnn n n nnnn nnn 5 n n n nnn nnn n n

nnnnnnnnnnnn nnnnn nnnnn nnn n nnnnnnnnnnnnnn nn nnnnnnn

nnnnnn n n n nnn nnnn n nnnnnnn nnnnnn nnnnnnnnnn

nnnnnnnnnnnnnn nnnnnnn nn nnnnnnnnnnnn nn n nnnnn n

nnn nnnn nnn nnn nnnnnnnn nnnn nnnnn nnnnn n nnnn nnn nnn n

(6)

nnnnnnnnnnnnnnnnnnnnnnnnnnnn n nn nnnnn nnnnnnnnnnnnnnn nnnnnn nnnnnnn nnnnn nnnn n nnnn n nnn

yg tys s t s yttsyy yytylsyytlsytygsytetyyttyyys

yg tys s s yttsstltylslysytygsytetyyttyyys nnnnnnn nnn nnnn nnnnnnnnnnnnnnn n nn nnn nnnnnn nnnn nnnnn nn nnnnnnnnnnnnn nnnnn nnnnnnnnnnnnn nn nnnnnnnnnn nnnnn n nnnnnn nnn n nnnn nnn nnnn nnnnn nnnnn nnn nnnn nnnnn nn n nn n nnnn nn nnnn n nnnn nnnn nnnn nnn nnnn nnnnn nn nn nnn nnnnnn nnnnnnnn nnnnnnn nnnnnnnnnnnn nnnn n nnn nnnn nnnnnn nnn nn nnnn nnnnn nn nnnnnn nnn nn nn n n nn nnn nn nnnnnn nn nnn nn nn nn nnnn nnnnn nnn nn nn n nnnnn n nnnnn nn nn nn nnnn nn nnnn nnennnnnnnnnn n n nn nn n nnnn nnnnn nnn n nnn nnnn nnnnn nn n nn n nn n nnnnn n

yg tys s yttsylyttyl,syy yytylstylsstltylslystgys gllystyygylllgynn

n nnn n nnn nn nnnn nnn nnnn nnn nnnnnn nnnnn nnn nnnn nnnnnn nnnnnnnnnnxnennnnnnnn nn nn nnnnnn nnnnnnnn nn n xnnnn nn nnnn n nn nn n nen nn nnnnn nnnnn nnnn n n nn nnnnnnnnnnnnnnn nnnn nn nn nnnn n n nnnn nnnn nnnn n nnnnn nnnn nnnnnnnn nnnn nnn nen n n nnnnn 8n n n nnnn nnn

nnn nn x8,88 n nn nnn nnnnnnnn nnn nnnn nn nnnnnn nnnn nnnn nnn nn n nn nnnnnnnnnnnnnnn nnnnn n n nnnn nnn nnnnnnnn nnnnn n nnnnnnnn nnnnnnnnnnnn nn nnn n

yg tys s ettytlslystty tylyslystyleyttt tys nnnnn n nnn nnnn nnnn nnn nn n nn nnnn nnn nn nnnnn n nnn nnnn nnnn n nnn nnnnnnnnnnnnnn nn nnnnnnnn n

nnnnnnnnennenn nnnn nnnn n nnnnn n n nnn nnn nn nnnnn n

n nnnnnn nn n nnn nnnnnn nnnn nnn nnnnnnn nnnnn nnn n

nnnnnnnn nnnn nnnnnnnn nnnn n nnnn nnnnnn n n nn nnnn

nnnnnnnnnn n nnnnnn nnnnn nnnn nnnnnnn nnnnnnnnnnnnnnnn

n n nnennnnnnnnnnn nn nnn nnnnnnnnnn n nnnnnnnnnnnn nn

nn nnenn n nnnnn nnn nnnnnn nnnnnnnn n n nn nnnnnnnnnn

nnnnnn nn n nnnnnnnnnnnnnnnntttysyyytslllylsnn nnnnnn

nn nnnn n nnnn n nnnnnnnn nn nn nnn nnnnnnnn nnnnnnnnnn n

nnnnnnnn nnnnnnn nn nnnn n nnnnnnnn n n nn n n nnnnnn

n n nn ennnnnnnn nn nnnnnnn nn nnn n nnnnn nnnn nnnnn n

n nnn nnnnn nnnnnnnnnnnn nnnnnnn nn nnnnnnnnnnnn nn n

nnnn n n nn ennnnnnnn nnnn nn n nn nn nnnnnnn n nnn nnnn

n nnnnn nnnnnnnn nnnn nnnnnnn nn nn n nnn nnnn nn nn

nn nnn n nnnn nnnnnnn nnnnn nnnnn nnn nnnn nnn nnnn

nennn nnn nnnn nn nnnnn n nn n nn nn n nnn nnnn n n nn

ennnnnnnnn nnnnnnnnnnnnnnnnnnnnn nn nnnnnnnnnnnnnnnnnnnn

nnnnnnnn nnn nnnn n nnnn n nnnnnnnnn nnn nn nn n nnn

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nnnnnnnnn nnnnnnnnn nnnnnnnnnnnnn n n nnnn nnnn nnnnn

nnnnn nnnn nnnnnnnnnn n nnn nnnn nnnn nnn nnnn n nn nnn nnnnn

n nnnnnnn n n nnnn nnn n nnnn nnnn nnnnn nn nnn nnnnn nnnn

n nnnnnn nnn nnn nn nnnn n nnn nnnn nnnnnn nn n nnnn n

enn nn nnnnnn nnnnnn nenn nnnnnnnnnnn nnnnn n

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nnnnn nnnnnnnnnnnnnnnnn n nnennnnnnnnnnn n nnnnnnnnnnnn

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nnn nnnn nnnnn nnnn nnnnn nn n nnnnnn nnnnn nnnn nnnnn nnn nnnnn

n nnnnnnn n nnnnn n n nnn nnn n nnnn nnnn n nnnnnn

nn nnnnn n nn nnnnn n nn nnn n nnnnnnn nnnn nnnnnnnnnn

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nnnnn nn n nnnnn n n n nnn nnnnnnnnnnn nnnnnn nnnnnn nn

nnn nnnn nennnnn nnnnn nnnnnnnnnnnnn nnnn nnnnnnnnnn nn

nnnnnnnn n n nnnn nn nnnnnnnn nnn nn n n n nnn 8n

nnn nn nn nn nnn n nnnn nnnnnn nnn n n nnn nnnnnn n nnnn

nnnnn nn n nn n nn n nnnnn n nn n nnnnnnn n nnn nnnn

nnn nnnnnnnnnnnnnn nnnnnnnn n nn nnnnnnnnnn nnnn nnnnnn

nnnnnnnnnnnnnnn nn nnnnnnnnnnnnnnnnnnnnn nnnnn nn nnn

nnnn nn n nn n nnnnn nn n nnnnnn nnnn n nnnnn nn nn nnnn

nnnnnnnnnn nnnn nnn nnnn nnnnnn nnnnnnnnn nnnn nnnnn nnn n

(7)

n n nn nnnnnnnnnnn nnnnnnnn nnnnnnnnnnnnnnnn nn nn nnnn nnnnn nn nnnnnnnnnnn nnnnn nnnnnn nn nnnnn nnnnnnnnnnnn nnnnnnnnnn nnnn nnnnn nnnnnnnnnnnnnnnnnn nnnnnn n

yg tys8 s yleyttt tyslysyxgt stsyll slysytygs tgytltlsytetyyttyyys

t lys s ytl,s tltyyyygstyly,stylysylysttytstts

e e

nn nnnnn nn n nnnn

nn nnnn n nnnnn nnn

nn nnnnn nn n 8nnnn

nnnnnnnnnnnnnnnnnnnnnnnnnnn nnnnnnn nnnnnnnn nn nnnnnn nn nnnn nnennnnnnnnn nnn nnnnn n n n nnen nnnn n n nennnn nnnn nnnnn nnnnn nnnnnnnnn nn nnnnenn nnnnn nn nnnnnn nnnnnnnn nnen nnennnnnn n nnnnnnnnnnn nnnnen nnnnn nnn nn nnnn n nnnn nnnn nnn n nenn nn nnnnnnn nnn nnnnnn nn

nnnnnnnnnnnnnnnnnnnnnnnnn nnnnnnnnnn nnnnnnnnnnnnnnnnnnnnnn

nnnnnn n nnn nnnn nnnn nnnn nnn nnnn nnn nn n n nnn nn nn n nnnn ennnnnnnn l n nnn nnnn nnnnn nn nnnnnn nnn nnnn nnn nnn nnnn nnnnn nn nnnn n nnn nnnn nennn nn nnn nnnn nnn nnn nnnn nnnn nnn nnnn nnn n n n nn n n nn nn nnn nn n nnnnnnnn nnnnennnnnnnnnnn n nnn nnnnnn nnn nnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnnnnnn nnnnn nnnnnn n

sssssssssssssssssssssssssssss nn nn n nnn n nnn nn nnnn nnnnn nnnnnn n nnnnn nnnn nnnnn nnn n n nnnnn nnn nnnn nnnnn nn nnnnnn nnn nnnn nn n nnnn nn nn nnnnn nnn nnnn nnnnnn nnnnn nnnnnn n nn n nnnn nn n nnnnn nnn nnnn nn nnnnennnnnn n nnnnnnnnn nnnnn nnnnnnn nnnnnnnnn nnnnn nnnnnnn nnn nnnnn nnnn nnn nnnnnnnnnnnnnnn nnn n nn n nn nnnnnn n nnnn nn nnnn nn nnn nnnnn nnnnnnnnnn n n n nn nnnnnnn ennnnnn nnn nnnn nnn nn n n nnn nnnn nnnnnn nnnn n

yg tys s lttlstylsttlyttyvysgyttsylyttylss

nnn nn n n n n n n n nn nnn nn

nnnn nnnnnn n nnnn nnnnn n nnnnnn nnnnnn n nnnn n n n n nnnn nnnnnnnnn nnnnnnn ttytsttlyttltn nn nnnn n n n nnnn nnn n nnnn nn nn n n nnnn nnnnn nn nnnnn nnnn nnnnnnnn nn nnnn n tttysyyytn nn nnnn nnnn l leyls stytlysstttyslllylnnn nE EsEC nnn nnnnnnnnnnnnnnnnn n nnn nnnn nnn nnn n nn nnn nnn n nn n nn n nnnnnn nnnnn nnnnnnnn nn

n n n nnnnnnnnnnnnnnnnnnnnnn nnn n n n nnnnn nnnnnnn nn nnn nnn nn ttyts ttlyttlt n nnnn nnnnn n n nnn n nnnn nnn nnnnn nnnnnn nnnn n nnnnnnnnn nn nn nnnnnnnnnnnnn nnnlyytlyyslytgll lyytlyyslytgllnn nnn nnnnn nnnn nn n nn n enn nnn n nnn nn nn n nn nnnn n nnn nn nn nnnnn nnn n nnn nnnn nnn nnnnnn n nnnnnn nn nnnnnnnnnnnn nnnnnn ttytsttlyttltnnnnnnnnn nnnnnnnn nnn nnnnnnnnnnnnn nnnn n nnnnnnnnnnnn n nnnnnn n n nnnn n nnnnnn nn nnnnnnnnn n nnnn n nnnnnn nn nnnnnnnn nnnn nnnnnnnnnn nnnnn nnnnnnnnnnnnnnn n nn nnn nnnnnnn

nnnnnnnnnnnnnnnn nnnnnnnn nnnnnnnnn

nnnn nnn n nnn nnnn nnn ly n nnn nnn n n n nnnnn nnn nnnn ennnnnnnn xs n n nnn n nnn nnnn nnnnn nnn nn , n nnnn nn nnn nnnn nnnn nnnn nnnn nnnn nnnnn nnnnn nnnnn nnn nnnn ennnnnnnnnnnnn n nnnnnnnnn nnnnnnnnnnnnnnnnnnnnn n nnnn nn nnn nn nnnnnn nnn nennn nn nnn nnnn nnn nnn nnnn nn n n nnnn nn nnnn nnnnnn n n n n nn n nn nn nn n nnnnn nnnnn nnnnnnnnnnn n nn nnnn nnnnnnnn nnnnnn nnn nnnn n nnnnn nnn n nn nnnennnnnnnn n n nnn nnn n nnnnnn 8 nnn nnnnnnn nn nnnnnnnnnnn n

yg tys ytts tltyyysttstgys l ylttys yt yyys ss

ttlyttltss tytyystylss ttl ylyygsyyvytlylyyt

nnnnnnnnnnnnnnn nnnnnnnn 8 nnnnnnnnnnnnnnnnnnnnnn

n nnnnn nnnn nn nnnnnnn nnn nnnnn nnnnnnnnn nnn nnnn nn nnnnnnnn nnn nnnnnnnnnnn nnnnn nnnnnnnnnn nnnnn nnnnn v nnnnn nnnnnnnn nnnn nnnnnnnnnn nnnnnnn nnnnnnnnnnn n nn nnnn nn nnn nn nn n ly nnn nnnnnn n

nnn nnnnnnnnn

yy n nnn nnnn nnnnnn nnn nnnn nnn nnn nnnn nnnnn nn nnnnnn nnnn n n nn nnnn s e n nnnnnn

e

nnnnn n nnnnnn nnnnnnnnnn nn nnn nnnn nn nnn n nnnn nn

nnnnn n n nnnnn nnnnnnnnn nnnnn n n n nnn nnnnnn

nnnnnnnnnn nn nn nnnnnn nnnn nnnnn nnn nnnnnnnnnnnnnn

nnnn n n n n nnnn n nnnnnn nnnnn nnnnn nnnn nnnnnnnnnn

nn nnn nnn n n nnnnnnnnnn n nnnn nnnnnn n nnnnn nnnnn

(8)

nnnnnn nnnn nnn 5 n n n nnn nnn nnnn nnn n nnnnn nnnnnnnn nn n n n n nnnn n nnnnnn nn nnnn nn nn nnnnnnnnnnnn nnnnnnnnnn nnnn nnnnnnnnn nnnnnn n nnnnnnnnnn nnnnnnnnnnnnnnnnnnnnnnnnnn nn nnnnnnnn nnnn nnennnnnnnn n n nnn n nn nnnnnnnnnnnn nnnn nnnnnn nnnnn nn nnnnnn nn nnnnnnnn nnnnnnn nnnnnnnnnnn nnnn n nnnnnnnn nnnnnnnnn nnnnn nnnnnnnnnnnnn nnn nnnnnnnnn n nnn nn nn nn n nn nnn nnnnn nn nnnnnnnn n nn n nn n nnnnn nn nnnnnnnnnn nn nn nn nnnn nnn n nnnnn nnn n nnn nnnn nn n n nn nn nnnn n n n nnnn nnnn nnnnnn n n nn nn n n n nnn n nn nnnnnnnnnnnnnnnnnnnnnnnnnn nn n nnnnnn nnn nnnnnnn nn nnnnnnnnnnnn nnnnnnnnnnnnnnnnnnnnnn nnnnnn nnnnnnnnnn nnnnnnn nnnnnnnn nnnn nn nn nn nnnn 5 n n n8n nnnnnnnn n n nnnn nnn nn n nnnn nn n nnnnn nnn nnnn nnnnnnn nn nnnnn nnnnn nn nnnnnnnnnnnnnnnn nnnnnn nnnn n nennnnnnnnnn n nnnnn nnnn nnnn n nnnnnn nn nn n nnnnnnnnnnnnnnnn nn n n nn

yg tys yleyttt tyslysyxgt stsyll syltsl leyls stytlysstttystylstttysyyytslllylss

yg tys s yttsylyssylyslysl leylsstytlysstttystyls tttysyyytslllyls ytgs , , styls8sytetyyttyyyss

n n n n n n nn n

n n n n nn nn n n

nnnnennn nnnnnnnnnnnnnn nnnn nnnnn nnnnnn nnnnnnn nn n nnn nn n nnnn nnn nnnn nnn nnn nnnnn nnn n nnnn n nnnnnn nnnnnn n nnn nnn nnnn nnnnnnnn n nnn nnnn n n nn n nn nnn n nnnnn nnnnnnnn nnnnnnnnnnnnn nnnnnnn nnnnn n nnnn nnnnnn n nnnn nnnn nnnn nn n nnn nn nnnn nnn nnn nn nn nn nn nn nnnn nnn nnnn nnn nenn n n nnnn nnnnnn n nnnn nnnn nennn n nnnn nnn nnnnnnn nnnnnnnnn nnn nnnnnn nn n nnnn nnn nnnn nnn nnnnn nnnn nn nnnnnnn n nnn nnn nn nnn nnn nnnn nnn nnnnnnn nnn n n nn n nn nnn nn n nnn nnnn nn nnn nnn nnnnn n nnn n nn nnn nnnnnnnnnnnnnnn nnnnnnn nnnnnnn nnnn nnnnnnnnn nnnnnnn nnn nn n nnn nnnn nn nn nnn n n n nnnnn nnn nnnnn nn nn n nnnnnnnnnnnnn nnnnnnnnnnn nnnnnnnn n nn n nnnnnnn

nnnn nn nn nn n ⁿ n nnnn n nnnnnnnn nn nn nnnn n nnnn 8 nn n ⁿ n nn nnnn nnnnnnn nnnnn nnnn n nnnnnnnnnn nnn nnnn nnnn nnnnn n n nnnn nn n n n nnnn nnn nnn nn nnnnnnnnnnn nnen nn nnn n nnn nnn n nnnn n nnnnnennn nnnnnnn nnnnnnnnn n nnnnnn nnnnnnnnnnnnnnn nn nnnnn n n nn nn nnn nnnn n nnnn n nnn nnn nnnn ennnn ennen

yg tys yleyttt tysetlyylys

nnnn n nnnnnnnnnn nnn nnnn nnn nenn nnn n nnn nnn nnnn nnn nnnn nnnnnnn nnnnn n nnnnnnnnnnnnnnnnnnn nnnnnnnn nnnn nnnn nenn nn nnn nn n nnnn nnn ennn nnnnnn nnn nnnn nnnn nn nnn nnnn nnnn n nnn n nnnnnnnnnn n nn nnnnnnn nnnnn n nnnnnn nn n n nnn nn nnnnnnnnnnnn nnnn nnnnnn nnnnnnnn n n nnnn nnn nnnnnnn nnnn nnn nn nnnn n nnnnn nnnnnnnnnnnnnen nnnnnnn n nnnnnnnnnnn n n nnnn nnnnn nnnnnnn nnn n n nnnn nnnnnnnnnnnnnnnnnnnnnnnn n nnnnn nnn nnnn nnn nnn n nn nnn nnn nn nnn n nnn nn nnn nnnn nnnn nnnnnnnnn nnnn nn nnn nnn nnnnnnnnnn nnnnnnnnnnnnn nnnnnnnnnnn nnn nnnnnn nnnnn nn nn nn nnnn nnnnnnnnn nn nnn n nnnnn nnn nn n nn nnnn nn nnn nn nn nnnnnnnnnnnnnnnnnnnnnnnnn nnnnnnnnnn nnnn nnnnnnn n nn nnnnnnn nnnnnnnnn nnnnnn nn nnn nnnnnnnnnn nnnnnnn n nnn nnnn nnn nnnnnnn nn llg n nnnnnn n n n nnnnnnnn nnnn n nnnnn nnnnnnnn nnnnnnnn nnn nnn n nn nnn nnnnnnn nnnnnnnnnn n nnnennn nnnnnnnnnnnnennnnnnnn n nnnnn n n nnnnn nnnnnn nn nnnnennnnnnnnnnnnnnnnnnnnn nnnnnnnn nnn n nnnn nnn nn n nnnn nnnnn nnn nnn nnn nnnnnnnnnn nnn nnnnnnnn nnnn nnnnn nnnnnnnn n nn n nnnn nnn nnnn nn n nnnn n n nn nn n nnn nnnnnn nnnnn n nnnnnnnnnnnenn nnnnnnnnnn n nnnn nnnnnnnnnnnnn nnnn nnn n nnn nn nnnnnn n nnnn nn nnn nnn nnnnn nnnn nnnn nnnnn n nn nn n nn nnn nn nnn nnn n n nnn nn nn n nnnn nnnnnnnnn n nnnn nnnn nnn n nnnnnnnnn nnn n nnn nnnnn nnn nn nnnnn nn nn nn n nnnnnnnnennnn nnnnnnnn nnnnnn nnnnn n n nn nnn nnnnnnn nn n nnn nnnn n enn nnn nnn nnnn nnn n nnnn n nnnn n nnnnnn n n nnnnn n n nnn nn nnnnn nnn nnnnnnnnnnnnn nnn

nn n n n n

nnnn n nnn nnn nn nnnn nnnnnnnnnn nn nnn nnn nn nnnnn

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