THERMOELECTRICS HANDBOOK MACRO TO NANO Edited by D.M. Rowe,
Ph.D., D.Sc.
Boca Raton London New York
A CRC title, part...
192 downloads
879 Views
50MB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
THERMOELECTRICS HANDBOOK MACRO TO NANO Edited by D.M. Rowe,
Ph.D., D.Sc.
Boca Raton London New York
A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.
© 2006 by Taylor & Francis Group, LLC
Published in 2006 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2006 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8493-2264-2 (Hardcover) International Standard Book Number-13: 978-0-8493-2264-8 (Hardcover) Library of Congress Card Number 2005048533 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Thermoelectrics handbook : macro to nano / edited by D.M. Rowe. p. cm. Includes bibliographical references and index. ISBN 0-8493-2264-2 (alk. paper) 1. Thermoelectric apparatus and appliances. 2. Microelectronics--Materials. 3. Nanotechnology-Materials. I. Rowe, David Michael. TK2950.T535 2005 621.31'243--dc22
2005048533
Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com Taylor & Francis Group is the Academic Division of Informa plc.
© 2006 by Taylor & Francis Group, LLC
and the CRC Press Web site at http://www.crcpress.com
Y
A
A
p
J
A
_
\
A
!
g
J
Q
g
2
A
J
d
g
g
_
g
d
A
_
2
!
\
Y
d
A
_
g
A
p
2
A
g
:
A
A
A
\
\
d
d
Q
\
A
Q
p
Y
A
d
Y
d
\
!
:
!
\
2
A
Y
d
2
Y
A
:
d
!
g
_
g
J
Q
g
Q
!
!
2
\
g
\
\
A
d
b
Q
g
!
\
\
\
d
d
A
!
_
d
A
A
Y
p
A
\
A
A
g
:
A
2
)
\
\
g
\
d
!
g
d
A
:
^
g
Y
\
\
d
\
J
b
\
A
A
A
g
2
\
A
!
2
g
\
g
Y
Y
\
:
\
A
2
p
A
A
d
2
Y
A
b
\
g
g
K
b
A
2
g
_
K
A
_
Y
A
2
A
2
u
_
g
A
_
A
\
:
p
2
2
A
\
2
d
!
!
2
:
\
A
\
p
\
p
g
\
:
Q
!
A
A
d
\
\
2
_
J
2
!
)
d
Y
!
A
p
!
g
Y
A
!
d
:
\
\
\
Y
A
g
d
Y
!
A
d
\
d
:
Q
d
A
d
:
u
2
g
)
A
A
d
J
d
:
g
A
p
A
_
_
A
g
u
A
:
J
A
2
A
J
\
g
A
d
2
:
u
d
\
_
d
d
Q
A
2
A
g
g
Y
2
g
_
d
!
d
!
2
A
!
\
b
b
Y
g
:
A
u
)
A
J
d
g
J
g
A
A
Y
!
!
p
\
J
A
A
_
J
!
\
A
d
2
A
d
2
:
\
p
Y
!
\
\
!
[
d
g
d
Y
\
!
2
d
Q
A
\
\
_
\
A
2
!
b
:
d
\
A
A
Y
A
_
A
J
A
2
!
_
A
d
Y
A
A
g
!
A
A
Y
:
Y
g
8
2
J
\
\
\
2
_
\
A
_
2
d
Y
[
_
d
!
!
\
!
g
Q
d
A
\
2
J
J
A
A
d
g
b
Y
p
g
!
:
_
g
g
d
2
A
_
p
8
d
g
_
d
!
2
!
_
A
A
g
A
g
d
!
A
!
d
_
A
b
d
J
A
b
2
A
:
A
\
A
J
A
:
b
A
p
p
A
d
g
\
Y
!
A
d
2
b
g
Y
g
d
g
\
A
!
A
z
d
Q
_
\
d
\
A
8
\
!
A
A
!
\
g
A
A
A
2
A
\
!
z
Y
b
:
A
A
Y
_
A
p
:
!
A
\
Q
Y
Q
_
J
d
!
g
2
:
\
d
2
d
A
\
!
\
d
Q
!
7
\
A
d
8
A
b
b
\
d
d
A
g
g
A
Q
A
d
d
2
d
\
b
_
A
\
g
\
2
g
_
)
b
:
2
_
g
!
!
!
!
b
2
J
8
d
b
g
8
A
A
A
\
g
_
g
d
2
\
d
g
A
2
M
\
\
Y
p
A
A
A
d
g
A
_
d
\
K
d
\
2
_
!
g
2
_
_
_
d
!
8
\
d
g
Q
_
\
A
A
g
J
[
u
A
!
!
\
!
A
!
!
\
!
A
g
b
d
\
:
2
:
_
A
A
g
!
d
J
2
:
!
d
!
!
J
A
!
2
A
!
A
_
A
\
u
!
d
\
2
\
_
p
p
_
\
A
\
2
A
g
A
_
Y
\
2
u
!
\
:
2
u
2
:
_
:
_
A
A
A
d
A
d
A
A
!
A
K
d
d
d
b
g
A
g
A
Y
p
\
g
!
p
A
2
J
g
!
A
!
Y
A
d
b
2
A
:
\
:
\
A
A
_
g
d
_
J
[
J
g
_
d
Y
\
_
\
p
Y
\
p
g
A
d
A
p
A
A
!
A
!
Y
A
8
:
2
A
d
d
p
:
Y
b
g
p
Y
p
d
g
A
b
Y
d
g
Q
J
J
d
:
A
2
g
!
\
2
A
\
Q
Y
!
A
:
A
:
2
\
A
2
2
_
A
_
\
g
8
A
:
g
A
d
g
g
g
d
2
p
b
g
d
\
!
A
b
^
d
_
A
2
2
A
Y
A
A
g
Y
g
Y
g
_
b
d
s
\
g
_
u
A
!
A
:
!
A
d
d
Y
_
!
J
g
Y
d
d
J
:
\
Y
:
A
)
p
:
d
A
d
\
d
A
\
!
:
g
d
\
d
_
Q
!
g
g
\
A
^
2
A
!
Y
p
A
A
Y
:
A
A
Y
g
d
d
b
g
d
8
8
8
g
A
Y
J
2
d
d
\
d
\
2
A
J
:
g
\
:
!
:
A
A
!
:
_
!
A
!
!
g
!
:
b
Y
\
d
g
b
:
)
B
d
g
A
8
j
!
2
Y
d
!
!
d
!
p
\
d
p
A
!
b
A
!
Y
A
Y
p
)
!
g
Q
:
A
!
A
d
Y
_
A
g
!
!
A
:
Y
2
8
A
^
J
Y
g
8
b
2
!
Q
g
d
\
d
g
g
A
Q
\
)
!
:
d
:
:
)
A
!
:
A
d
g
!
\
g
!
A
\
b
A
A
A
\
\
\
!
\
g
2
_
z
\
b
\
2
!
b
A
p
A
2
!
_
:
^
\
d
2
b
d
!
2
!
g
^
A
!
b
g
2
d
K
d
g
g
g
g
u
J
A
b
g
^
g
)
J
Y
g
g
M
\
A
d
d
A
b
A
g
\
\
!
:
_
A
d
d
r
g
2
:
_
A
A
A
!
Q
2
A
A
)
g
\
!
d
!
A
Q
g
:
:
A
)
d
g
\
!
\
A
b
d
d
A
A
g
!
A
2
8
_
:
g
b
_
2
A
!
A
d
d
_
g
d
Y
\
A
Y
_
!
g
\
\
A
J
d
J
d
!
d
A
e
!
A
\
e
Y
b
_
:
A
A
A
!
!
A
d
_
\
A
d
d
Y
A
u
J
d
g
b
g
d
:
p
!
)
d
g
A
A
\
A
!
d
g
d
g
b
Y
^
\
A
b
\
A
!
!
!
J
A
g
Q
p
g
Q
A
2
d
b
p
2
d
8
2
g
J
\
!
Y
A
A
g
b
!
A
2
\
_
g
!
A
_
!
_
!
d
b
:
^
Y
g
g
A
A
\
g
2
8
\
p
d
:
A
!
Y
g
)
!
8
b
!
A
d
A
d
g
_
Q
_
:
d
g
g
Q
d
!
A
g
g
:
!
Y
\
8
g
2
A
p
\
!
A
A
!
A
_
g
!
8
8
!
p
d
Y
b
Y
!
_
!
A
!
A
Y
\
!
d
)
]
A
\
!
b
A
)
A
p
b
d
Y
\
A
g
:
A
:
g
\
\
!
g
A
Y
d
A
2
:
d
:
2
Y
A
g
g
Y
g
!
Y
d
d
2
A
8
A
Y
!
d
b
J
d
J
d
b
Y
!
2
d
_
\
2
^
!
Q
g
d
!
Y
d
_
!
_
!
A
Y
8
!
d
\
A
d
\
Q
_
g
:
\
g
p
d
g
:
d
b
A
2
g
!
A
d
)
A
d
g
A
g
:
:
d
!
J
A
A
\
\
e
A
b
d
L
A
d
A
A
A
g
!
_
g
A
!
\
g
b
A
!
!
g
_
A
A
b
!
A
_
)
g
8
g
d
A
)
g
A
J
u
p
A
A
2
K
Y
Y
Y
\
A
:
2
A
A
A
^
Q
2
!
A
d
2
j
d
d
A
:
!
A
A
A
g
b
Y
Y
!
2
A
d
\
Y
\
b
A
2
A
d
p
]
J
A
Y
d
A
g
!
!
:
A
!
A
A
2
A
d
A
!
b
A
_
_
J
!
A
J
\
b
d
d
_
J
!
J
:
\
)
g
b
Y
_
d
d
_
p
g
Y
A
Q
b
b
\
g
g
!
J
b
\
:
\
\
b
b
g
Y
A
A
g
Q
2
A
A
p
!
\
b
A
d
d
g
b
\
A
Y
g
Y
A
2
!
_
Y
Y
Q
A
:
2
d
d
:
:
_
:
g
A
!
A
!
_
\
Y
]
p
Y
\
\
A
b
u
!
!
A
g
!
A
Q
\
_
Q
b
A
g
Y
A
d
!
2
_
A
\
:
_
b
d
d
d
K
!
_
g
A
[
b
2
!
2
!
d
!
d
d
2
\
\
Y
A
b
)
Q
A
g
Y
\
\
d
!
A
:
d
!
g
g
g
Y
2
Q
A
p
A
Q
A
p
d
\
A
p
Q
!
!
Q
g
\
Q
d
2
:
A
u
A
d
\
\
_
b
b
!
\
!
A
p
:
:
g
b
Y
d
\
!
\
_
\
A
g
:
\
b
A
g
g
\
A
d
:
d
K
!
^
Y
A
A
Y
2
!
d
_
_
_
d
Y
A
!
)
_
Q
\
J
:
A
A
\
!
!
d
!
:
\
d
d
A
:
!
J
u
d
A
2
g
g
Y
J
2
\
A
!
)
A
2
\
A
_
!
A
g
Y
_
d
_
:
!
\
g
2
J
Y
Y
_
A
8
g
)
!
2
!
_
b
A
!
A
b
)
2
A
\
\
)
\
u
Q
d
g
Y
!
_
d
d
d
!
\
2
g
g
g
A
\
\
)
A
:
_
!
!
\
A
2
Y
d
g
Q
)
b
\
:
g
d
Q
u
u
u
g
A
© 2006 by Taylor & Francis Group, LLC
g
A
)
A
!
!
g
p
:
A
d
_
!
u
\
8
g
d
!
)
_
\
!
J
A
)
g
g
d
_
\
!
!
g
8
g
d
u
u
d
u
\
d
!
g
A
J
2
Y
Y
A
b
Y
A
d
g
8
^
\
A
d
_
A
2
\
2
\
u
\
d
!
A
d
\
:
A
g
J
u
!
_
\
)
J
A
\
!
u
J
g
J
A
Q
Q
A
)
A
A
A
_
!
Q
\
!
g
8
A
d
\
A
\
u
!
d
\
!
\
A
\
:
A
8
!
_
\
J
g
J
g
!
d
\
_
!
d
:
\
Y
u
d
\
!
8
A
\
\
!
A
2
^
g
g
d
[
)
2
A
b
\
d
!
[
u
!
d
d
A
!
:
Q
Y
d
A
8
\
b
2
!
_
g
\
J
d
2
\
\
A
d
2
A
A
g
J
Y
A
:
g
g
A
2
_
_
g
A
g
8
_
!
_
\
Y
u
!
\
[
_
g
!
Q
d
g
d
A
d
\
2
A
Y
g
A
2
d
g
_
8
g
Q
\
A
\
g
_
g
A
:
2
\
g
_
!
2
\
A
d
A
\
_
!
u
d
8
g
g
_
g
Q
8
d
2
u
2
A
u
Y
8
!
_
\
J
g
d
\
!
8
Y
)
A
\
d
Y
\
\
u
u
A
_
g
!
_
!
_
!
2
d
!
!
g
g
_
A
8
:
!
\
u
\
!
[
8
d
\
Y
!
A
2
2
2
A
!
g
A
Y
Y
Y
2
A
A
d
g
_
\
d
\
_
!
d
8
g
8
g
Q
\
A
\
g
_
g
:
A
2
\
g
_
!
!
u
!
d
!
:
2
\
A
d
A
\
_
\
d
_
_
A
!
Y
!
\
)
!
!
g
:
g
d
)
A
A
_
\
\
A
:
2
g
A
_
:
g
Q
!
:
\
_
Q
g
g
Y
!
d
Y
!
d
:
!
u
g
A
J
8
d
_
:
_
\
!
Y
!
)
!
u
\
d
_
A
\
b
g
J
g
_
:
g
A
\
)
!
A
:
g
A
8
:
z
\
u
A
g
8
J
_
A
A
[
A
A
A
d
\
2
\
^
2
g
g
8
_
Y
d
d
A
g
_
g
8
g
Q
A
Q
g
8
!
_
\
8
J
g
d
2
d
u
\
!
8
A
:
A
z
\
b
\
A
g
z
J
d
A
A
8
A
A
\
A
2
g
\
2
!
\
A
g
u
u
J
g
J
A
Y
A
b
\
!
\
\
2
g
d
[
d
2
A
!
2
Y
:
d
A
\
b
2
!
_
g
d
J
2
\
A
\
A
\
d
2
A
2
A
A
g
J
Y
A
g
J
Y
A
u
A
A
)
Q
8
\
!
J
d
Q
\
d
s
A
A
8
!
!
2
\
Y
d
Q
A
8
u
d
u
A
:
g
g
g
u
g
_
_
!
J
g
J
A
Y
\
!
\
2
g
d
[
2
A
!
2
Y
:
d
A
\
b
2
!
_
g
d
J
2
\
d
A
^
u
A
A
)
Q
8
\
!
A
:
_
_
A
8
!
_
\
!
g
!
8
g
g
:
!
b
A
A
!
8
A
g
d
!
\
8
A
_
\
A
:
2
\
A
d
2
A
b
!
d
\
d
!
_
d
d
!
\
Y
!
A
g
Y
J
\
:
:
\
u
!
!
2
b
Y
A
A
!
d
\
A
g
J
A
2
Y
d
g
_
g
Q
!
b
)
\
!
_
2
\
A
d
2
A
!
d
!
d
2
A
:
:
d
!
g
8
_
!
g
p
Q
!
d
!
_
g
[
!
8
\
\
A
2
d
g
_
g
Q
\
A
g
_
g
A
:
2
g
\
_
!
2
\
A
d
A
A
\
s
Y
^
r
2
A
!
p
g
d
g
p
]
\
^
J
u
!
A
!
d
r
A
2
\
_
2
\
)
Y
A
\
d
!
A
d
Y
2
\
J
s
\
!
g
d
d
!
b
A
d
A
A
\
!
A
2
!
!
u
!
\
_
Y
b
\
z
[
\
!
d
8
A
r
_
d
A
Q
A
d
Q
Q
\
!
:
g
:
_
!
A
g
!
u
g
\
A
g
d
A
!
Y
)
2
]
Y
)
!
d
2
b
A
2
\
d
!
A
!
u
_
J
u
A
A
d
^
g
!
A
g
u
u
g
\
:
Q
A
8
!
!
2
Y
A
8
\
_
!
d
8
g
!
_
=
!
!
_
:
g
d
A
!
d
A
Y
\
)
g
!
A
J
Q
A
8
A
d
b
A
A
d
b
\
!
d
A
A
2
J
Y
g
d
\
z
Y
A
\
2
!
g
d
!
Q
u
!
\
u
Y
!
b
!
_
:
g
A
g
_
2
_
A
g
8
g
_
!
_
\
!
:
\
!
[
d
A
\
A
2
Q
Y
d
g
8
g
_
g
!
Q
_
\
J
8
g
d
d
2
\
u
!
8
© 2006 by Taylor & Francis Group, LLC
\
\
\
\
\
u
:
u
\
d
A
d
A
\
8
u
g
_
u
:
g
J
b
!
_
!
\
A
:
\
g
Y
!
_
A
!
)
g
d
\
!
Q
g
!
!
Q
g
!
Y
\
g
d
8
\
!
p
A
!
g
\
b
g
g
Q
g
d
g
J
g
J
A
Y
\
2
g
[
A
2
Y
d
\
2
!
_
d
\
A
g
J
Y
d
!
2
Y
A
g
\
!
d
2
!
:
A
b
g
J
2
\
A
d
2
A
d
A
)
Q
8
8
g
:
Q
d
g
)
u
\
!
!
g
\
b
g
!
_
d
d
\
A
g
Y
J
!
A
2
b
Y
b
d
g
_
A
g
Q
:
2
A
A
\
u
_
u
_
A
!
d
g
g
!
_
!
^
A
\
8
!
Y
8
g
2
^
Y
g
_
b
8
A
:
A
d
!
=
u
u
\
A
u
u
!
g
2
J
g
J
A
Y
\
2
g
[
A
^
Y
!
:
_
_
A
!
2
Y
d
\
2
!
_
d
\
A
g
J
Y
J
g
J
A
Y
\
2
g
[
A
2
Y
d
\
2
!
_
d
\
A
g
J
Y
A
b
!
d
A
g
p
!
2
A
A
d
A
r
s
A
A
=
\
!
d
2
!
:
A
b
g
J
2
\
A
d
2
A
u
A
A
)
Q
8
\
\
!
d
2
!
:
A
b
g
J
2
\
A
d
2
A
g
_
u
A
A
)
Q
8
\
A
A
!
Q
A
_
A
\
u
u
d
A
g
!
2
Y
A
d
\
A
g
\
d
2
A
Y
d
g
_
g
Q
r
!
b
)
\
:
Q
A
8
!
!
g
d
A
\
g
J
J
g
\
!
J
2
Y
A
8
A
b
p
g
u
u
8
:
b
\
!
\
d
Q
!
_
A
8
!
A
d
\
A
\
b
A
8
g
!
8
g
!
d
!
b
)
A
2
Y
u
u
!
d
Y
A
g
!
J
A
A
d
b
A
\
d
A
A
J
2
g
Y
d
\
z
Y
A
p
A
Y
\
A
A
b
A
!
!
2
d
Y
Y
A
_
)
g
d
A
!
)
g
!
g
\
A
\
)
u
Y
\
p
8
\
2
Y
\
Q
!
d
8
J
g
Q
8
u
J
A
\
2
!
Y
\
\
2
Y
\
Q
!
d
!
A
Y
u
u
g
Q
!
b
!
d
!
d
\
d
Q
A
8
d
\
A
\
\
2
Y
\
Q
!
d
8
u
\
:
!
8
\
:
!
J
A
d
\
d
A
J
g
!
A
b
A
d
A
2
Y
d
\
z
Y
A
\
2
!
_
Q
8
A
b
!
d
\
2
Y
\
Y
!
^
d
\
!
A
\
Y
!
^
\
^
\
2
g
[
!
d
A
2
g
Y
d
\
!
2
!
_
d
\
A
g
J
Y
!
Q
!
8
!
p
!
d
A
A
\
!
A
d
)
2
!
:
Q
A
8
b
g
\
J
2
\
A
d
2
A
g
g
^
\
d
d
!
A
d
A
J
g
Y
A
b
g
A
_
A
2
A
A
!
2
\
2
Y
u
u
A
A
A
!
2
Y
\
!
d
Q
_
A
!
^
d
[
g
b
g
\
A
g
J
Y
A
b
g
A
_
A
2
\
2
\
u
g
_
!
d
_
\
Y
)
Y
d
A
A
g
!
Y
_
b
_
\
g
g
_
J
A
u
g
8
2
!
!
\
!
A
!
g
Q
s
d
:
!
J
b
!
d
A
!
A
8
!
d
Y
A
d
g
8
^
!
\
d
g
Y
!
g
_
\
d
!
8
A
\
u
!
2
Y
A
d
"
\
d
A
\
A
!
Y
g
_
\
z
:
A
A
g
!
\
d
u
u
!
Y
!
d
g
!
\
d
[
_
!
[
A
A
8
A
_
Q
\
z
!
Y
A
A
d
d
_
!
d
\
!
!
A
d
\
A
\
\
d
A
\
!
^
8
A
d
d
_
!
d
\
!
8
u
J
g
J
u
A
Y
!
\
2
d
!
_
g
A
\
[
!
A
d
2
Y
2
d
!
\
:
2
A
!
_
b
d
g
J
\
2
\
A
A
g
d
u
A
A
)
Q
8
A
\
A
Q
A
\
!
_
u
:
b
A
b
A
A
A
:
g
!
d
\
!
^
\
d
\
A
Y
\
8
g
g
J
A
d
!
b
!
Y
u
_
A
A
8
\
\
d
!
:
d
u
!
d
d
A
Q
d
Y
d
\
A
\
g
A
d
\
A
8
A
d
d
u
d
\
g
2
g
g
_
2
A
J
g
g
J
b
!
d
g
_
\
:
\
p
g
A
J
)
g
8
\
\
2
2
Y
Y
\
\
Q
Q
!
!
d
d
8
u
\
g
A
J
g
Y
A
!
_
b
g
g
A
_
A
2
\
2
\
:
Y
!
_
\
A
d
g
8
^
!
\
d
A
!
!
^
A
\
!
)
!
u
u
!
g
!
8
Y
\
d
d
g
)
\
d
A
\
g
^
g
g
d
\
A
\
g
J
2
\
A
d
2
J
A
!
A
_
\
d
Q
g
d
8
A
!
8
!
!
b
!
Q
!
b
!
Q
!
b
!
Q
2
Y
\
2
Y
\
2
Y
\
8
!
p
!
d
^
!
\
!
\
\
Q
Y
!
]
_
A
A
\
u
Y
!
^
:
A
d
2
d
!
\
d
b
A
A
u
d
g
!
^
J
2
Y
Y
2
d
!
_
A
!
]
\
^
!
u
g
Q
_
!
\
!
!
=
Y
g
d
!
d
d
\
A
g
J
A
2
Y
d
g
_
g
Q
\
d
d
\
A
\
!
d
!
Q
!
!
g
8
!
p
Y
!
\
!
]
\
!
d
8
!
p
!
g
^
d
\
A
\
A
d
:
!
\
8
!
p
!
A
A
d
!
d
2
\
\
A
u
d
\
A
A
\
\
A
!
!
8
d
d
8
\
\
A
d
!
u
u
g
A
g
J
p
p
_
\
A
:
2
\
A
d
2
A
!
:
\
J
J
!
:
\
J
J
d
\
A
\
u
_
Q
\
A
!
)
!
:
A
d
8
g
\
A
b
!
d
\
A
J
g
g
_
A
2
_
!
2
\
A
d
2
A
!
:
\
J
J
d
!
\
g
8
!
d
!
:
!
!
:
\
J
J
8
A
\
!
_
A
8
_
A
8
!
b
A
:
u
!
)
A
Y
A
d
\
A
\
g
J
A
A
\
2
g
© 2006 by Taylor & Francis Group, LLC
d
\
!
8
!
d
d
A
\
\
\
d
Y
g
d
A
_
)
z
A
z
A
8
A
A
\
2
g
8
g
g
d
u
!
)
\
)
2
g
Y
!
A
g
\
g
A
\
A
:
A
Y
\
z
A
:
A
Y
A
\
b
!
\
!
d
d
A
g
p
!
\
2
A
A
A
A
d
A
r
!
b
!
s
d
A
^
!
!
)
!
b
!
d
\
!
d
"
=
!
A
\
!
g
_
d
8
A
b
!
d
d
!
2
8
!
d
2
A
d
u
g
2
^
Y
g
_
A
2
Y
A
A
!
)
g
!
g
\
A
g
Y
A
b
g
A
_
A
2
\
2
A
A
!
A
!
2
Y
\
!
d
Q
_
A
!
2
Y
^
g
Y
!
g
_
\
d
!
8
J
b
u
A
A
:
A
Y
\
z
A
:
A
!
A
_
Y
A
b
g
A
_
A
2
\
2
A
d
g
\
_
_
A
8
!
d
2
A
u
u
\
d
\
d
Q
"
!
A
\
!
d
!
2
8
!
d
2
2
Y
A
_
2
\
2
A
8
d
2
u
A
A
Y
)
A
\
!
A
g
:
!
A
d
\
!
A
\
!
^
\
u
)
d
8
_
!
)
!
b
!
8
^
g
g
8
!
p
!
d
=
d
K
d
A
g
d
A
2
Y
d
g
_
g
Q
\
A
g
_
^
_
A
\
d
\
d
A
\
g
J
p
p
_
\
A
:
2
\
A
d
2
A
=
d
2
Y
A
d
8
A
b
!
d
Y
!
b
b
A
g
p
!
^
u
2
Y
b
!
d
u
A
\
)
d
\
d
g
!
_
d
\
A
g
J
A
2
Y
d
g
_
g
Q
\
A
g
J
g
_
\
:
[
!
d
:
!
A
\
!
g
2
^
Y
g
_
b
8
A
:
A
A
:
A
d
8
A
_
u
g
u
A
:
b
A
\
A
g
b
!
b
d
A
!
d
8
g
^
p
\
A
_
A
b
g
d
d
!
d
b
g
_
A
b
g
d
u
d
\
A
\
\
Y
\
Q
Y
!
\
d
!
!
d
\
g
Y
8
d
\
d
!
A
d
\
A
\
!
Q
8
\
2
Y
\
Q
!
d
8
g
Y
!
g
_
\
d
!
8
!
A
^
!
:
\
\
g
_
A
J
g
g
A
_
A
A
!
g
2
Y
Y
Y
!
\
A
!
g
\
b
g
A
_
A
2
\
2
A
A
!
2
_
d
\
Q
d
_
!
A
8
!
u
u
u
\
d
d
u
\
g
g
g
d
!
A
J
g
d
_
\
!
A
2
u
8
^
!
Y
\
\
J
J
!
^
!
2
Y
A
!
u
^
\
J
g
d
\
J
d
\
2
!
_
!
:
\
J
J
!
\
g
8
!
d
!
:
u
d
\
A
J
g
J
p
d
\
Y
)
g
g
u
A
A
J
8
g
d
d
!
)
:
g
A
!
\
\
2
2
Y
Y
\
\
Q
Q
!
!
d
!
\
!
:
A
g
A
d
!
8
J
!
_
\
g
Y
!
u
d
\
\
A
_
_
\
\
!
b
8
!
_
A
8
u
J
g
u
J
A
!
Y
\
\
2
g
[
A
A
2
u
A
\
A
!
d
)
2
!
:
Y
Q
A
d
\
8
b
A
!
2
_
\
Y
J
d
g
g
d
_
\
g
!
Q
8
8
p
\
!
u
\
2
g
[
A
2
Y
d
\
2
!
_
d
\
A
g
J
Y
A
Y
u
]
\
d
!
!
Q
d
!
Q
Y
g
d
g
8
\
A
Y
\
d
\
d
A
\
A
!
d
)
2
!
:
Q
A
8
b
g
\
J
2
\
A
d
2
A
\
\
!
A
!
u
u
u
A
:
A
d
\
^
g
g
J
J
A
u
Y
Y
\
!
\
2
g
d
[
2
A
!
2
:
Y
A
d
b
\
2
!
g
_
© 2006 by Taylor & Francis Group, LLC
u
A
A
)
Q
8
\
!
J
]
\
!
d
Q
d
\
A
d
\
A
g
A
2
\
A
d
2
A
J
Y
A
!
d
Q
Y
g
8
Y
!
g
d
2
d
d
g
b
_
d
\
A
g
Y
u
:
A
A
_
A
A
!
A
\
d
Y
:
A
\
^
u
_
A
8
:
d
8
A
g
\
A
!
Y
g
Y
_
2
!
g
d
:
A
A
d
!
Y
d
b
2
A
A
\
^
8
d
d
b
!
)
:
Y
A
:
!
d
)
A
!
d
A
\
\
!
J
2
\
A
d
2
A
J
Y
A
A
j
A
A
!
_
\
d
Y
A
b
g
A
_
A
2
\
2
!
Y
A
b
g
A
_
A
2
\
2
:
g
u
A
u
d
A
b
g
A
_
A
2
\
2
b
g
A
_
A
2
\
2
Y
A
b
g
2
g
d
!
u
u
u
O
A
u
b
Y
d
g
d
j
d
u
d
M
u
u
O
u
L
u
u
\
d
!
\
d
g
\
Y
j
O
u
O
u
b
2
_
A
b
p
A
Y
g
\
!
g
d
p
J
A
_
!
d
_
g
A
\
g
J
u
!
\
A
u
u
u
u
u
u
u
Y
A
g
u
u
u
2
u
K
u
u
u
\
u
\
u
u
_
A
A
d
u
u
2
u
u
u
u
\
u
u
u
u
u
\
u
u
Y
A
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
J
u
u
u
u
u
A
\
2
!
A
d
_
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
j
j
[
j
j
[
j
j
[
j
[
j
[
j
[
[
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
j
[
j
[
[
[
L
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
j
[
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
p
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
[
O
[
[
[
B
[
B
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
d
u
u
\
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
!
u
u
u
u
u
u
u
\
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
b
u
u
u
u
u
u
g
u
_
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
g
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
p
u
u
u
u
u
u
u
u
A
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
d
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
!
u
u
u
u
g
u
u
u
u
u
u
p
u
p
u
A
u
u
u
u
u
u
u
u
J
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
A
u
u
u
u
u
d
u
u
u
u
u
u
A
u
u
u
u
u
u
u
2
u
u
u
u
u
u
p
\
A
u
u
u
u
u
A
u
\
u
u
u
u
u
2
u
A
d
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
J
u
_
u
u
u
2
u
u
u
b
u
K
u
u
!
u
u
u
u
u
p
u
u
A
u
u
u
u
g
u
J
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
J
u
u
u
\
u
u
A
u
u
u
u
d
u
u
u
A
g
u
u
u
u
u
u
g
u
g
b
u
u
2
u
_
u
A
u
u
u
A
u
u
\
u
u
u
A
u
u
u
2
u
\
u
A
u
u
_
u
u
u
u
d
_
u
u
u
u
g
u
u
2
u
u
u
u
!
u
u
u
u
\
d
g
\
u
u
u
u
u
Q
u
g
u
u
u
u
u
u
u
u
u
g
!
u
!
u
u
u
u
u
u
u
A
u
\
u
d
u
A
u
u
A
u
u
u
u
!
u
A
u
u
!
u
2
u
u
u
u
u
u
u
u
u
A
2
u
u
\
u
u
u
[
u
u
u
g
u
u
d
Q
u
g
u
u
u
u
2
u
u
u
A
u
u
d
u
u
A
u
u
u
u
J
2
u
b
u
u
K
u
u
g
J
u
u
[
u
u
2
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
_
u
u
_
2
u
u
g
_
u
!
u
u
u
u
u
A
A
u
u
A
u
u
\
g
p
u
u
u
u
u
u
A
Q
u
A
u
u
u
A
u
J
u
K
u
u
!
u
u
A
u
:
p
u
u
u
u
u
u
u
u
:
u
g
u
u
u
u
u
u
7
J
p
u
u
u
u
d
u
u
u
g
u
u
d
u
u
J
Q
Y
u
u
u
u
u
b
u
u
!
u
u
u
u
g
u
u
2
u
u
_
u
u
u
2
u
u
g
!
u
u
d
d
u
u
u
g
u
\
u
u
2
g
u
u
u
u
u
u
u
\
u
u
\
u
A
u
u
u
u
\
Y
u
u
u
u
J
A
u
A
b
u
u
:
u
!
u
u
2
u
u
2
A
2
u
u
u
u
u
u
A
u
u
u
u
u
u
d
u
u
u
u
u
!
u
b
:
u
u
u
u
u
A
u
A
u
u
d
g
u
u
u
A
u
u
u
u
A
:
Y
u
u
:
g
J
u
2
Y
u
u
u
u
u
u
!
u
A
Y
g
!
u
u
u
!
b
A
u
d
u
u
u
d
u
u
u
u
u
d
u
d
u
u
A
u
:
u
u
d
u
u
u
u
J
u
u
u
!
u
u
u
u
u
\
u
u
u
u
d
u
u
u
u
u
A
u
Q
u
u
u
d
u
!
u
g
u
u
g
u
:
u
u
u
u
!
u
u
M
g
u
!
u
u
u
!
u
:
u
:
d
u
u
b
\
:
u
u
u
u
u
g
u
u
u
u
d
A
u
d
u
:
u
u
A
u
u
\
u
!
u
A
u
u
d
u
_
u
u
u
u
u
g
u
d
d
u
\
u
b
g
u
b
A
2
_
g
!
d
_
u
u
p
J
u
u
g
!
u
u
\
u
_
d
d
u
!
Y
u
u
A
A
u
A
u
b
d
u
g
d
A
u
^
\
g
u
u
u
g
u
A
_
u
Y
\
u
b
u
u
u
u
A
u
A
2
g
\
2
u
J
A
2
\
u
u
Y
g
u
u
Y
d
A
:
g
J
g
u
d
u
g
\
A
!
:
u
u
!
d
d
p
A
g
u
u
u
J
u
p
d
u
g
A
u
d
2
2
u
b
_
u
\
g
g
u
g
!
!
u
\
\
\
2
u
A
u
d
d
\
A
g
g
)
\
u
Y
g
2
!
g
\
u
A
\
A
\
u
A
_
u
A
A
u
2
\
u
d
2
u
!
Q
A
d
u
Y
\
\
b
b
:
2
u
2
2
\
!
d
d
d
J
\
u
b
u
u
\
!
u
A
!
u
u
d
g
u
u
!
u
:
u
A
u
A
u
u
u
A
!
u
d
g
\
A
O
)
u
d
d
u
:
u
d
!
:
g
\
\
^
g
_
A
\
:
\
2
Y
u
_
A
2
g
2
_
z
_
:
:
2
b
p
g
d
A
b
!
:
d
A
^
g
g
Y
A
!
A
Y
2
g
d
u
A
u
Y
Y
u
Y
j
u
u
u
u
u
_
:
d
!
\
d
u
g
!
j
\
u
A
u
O
2
_
u
L
p
j
u
:
\
j
u
g
2
j
j
j
d
u
O
d
g
A
j
d
d
g
u
u
u
u
u
u
O
[
j
O
[
j
O
[
O
[
© 2006 by Taylor & Francis Group, LLC
\
\
\
L
O
u
O
O
u
L
J
J
A
2
\
g
L
u
L
u
L
u
O
_
A
L
u
L
_
A
L
u
L
u
A
g
b
b
d
_
u
u
u
O
u
L
Y
Y
A
A
\
b
g
!
A
j
u
u
\
_
d
d
:
g
Q
\
A
u
u
\
u
u
u
u
u
u
g
u
u
:
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
g
A
\
2
!
u
B
O
A
2
e
j
A
!
d
A
\
_
u
j
B
u
B
u
B
u
O
B
u
L
B
u
Y
A
b
j
e
u
e
u
e
u
O
e
u
L
e
u
A
!
Y
u
_
u
A
\
p
g
g
g
A
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
J
A
8
Q
!
g
Y
d
\
:
A
2
!
2
_
!
\
Q
\
A
_
d
!
Q
J
© 2006 by Taylor & Francis Group, LLC
u
g
Y
g
d
!
u
)
!
A
\
p
\
g
u
\
d
u
u
8
u
b
u
u
u
u
u
u
u
u
u
u
!
u
!
u
u
u
u
u
u
u
_
d
u
:
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
p
g
u
u
Y
u
\
u
u
d
u
u
!
u
u
A
u
u
u
b
u
u
Q
u
u
Q
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
_
u
u
u
d
u
2
u
u
g
u
u
!
u
A
u
u
u
d
u
u
_
b
u
u
u
u
u
u
u
A
u
u
u
\
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
8
u
u
u
u
!
u
g
d
u
u
d
u
d
u
u
u
u
u
u
u
:
u
:
u
u
u
u
\
u
!
u
u
u
u
u
d
u
u
d
u
u
u
u
u
u
u
!
u
u
u
u
u
_
u
u
_
g
u
u
u
u
!
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
p
u
\
u
u
d
A
u
u
u
u
u
u
u
u
u
u
Q
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
_
u
\
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
j
[
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
[
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
j
B
[
j
B
[
B
[
O
B
[
B
[
O
u
u
e
[
e
[
j
e
[
O
e
j
[
[
e
j
u
B
j
[
e
u
u
[
[
e
u
u
u
u
u
B
B
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
d
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
:
u
u
u
u
J
u
u
u
u
J
u
u
u
u
u
u
A
u
_
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
Q
u
u
u
u
u
u
u
u
u
u
u
)
u
)
g
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
E
_
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
_
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
)
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
[
u
u
u
u
u
u
u
u
u
_
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
p
u
u
u
J
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
A
d
u
u
J
g
d
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
u
u
u
u
u
u
u
u
u
g
b
u
u
u
A
u
u
u
g
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
Q
:
_
d
u
u
u
u
u
u
Q
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
:
u
u
u
u
u
u
u
u
\
u
d
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
!
A
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
J
2
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
g
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
2
u
_
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
2
u
u
u
u
u
g
A
u
u
u
u
u
u
u
u
u
u
A
u
u
2
u
u
u
u
u
u
u
u
u
u
d
u
\
u
u
u
u
u
2
u
u
u
u
u
u
u
u
g
u
A
A
u
u
u
u
u
d
u
u
_
u
u
u
u
u
u
u
u
u
u
d
b
u
\
2
u
u
u
u
u
u
u
!
Y
u
u
u
u
u
!
u
u
u
2
d
u
u
u
_
u
!
g
u
u
u
u
u
b
u
u
u
u
u
u
u
A
u
K
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
J
u
u
u
Y
u
u
u
u
\
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
g
u
u
u
u
b
b
u
u
u
u
J
u
u
b
u
u
\
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
A
u
u
7
u
b
:
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
\
d
u
u
A
u
u
u
u
u
J
A
u
u
u
u
\
u
u
d
u
u
Y
u
u
\
u
u
u
u
u
_
u
u
u
\
u
u
u
g
u
u
!
u
u
u
A
)
u
u
u
u
u
u
u
\
u
u
u
u
A
p
2
u
u
u
u
u
u
u
g
u
u
u
u
u
u
\
u
A
u
u
u
u
u
!
u
:
u
u
u
u
u
A
u
u
u
u
u
u
g
u
u
!
!
u
u
u
u
u
d
u
p
p
u
u
u
u
:
A
u
u
u
Y
u
u
u
u
u
u
:
u
d
Y
u
u
u
p
u
u
A
A
u
u
u
u
!
u
u
u
u
d
u
u
d
d
g
u
g
u
u
u
u
u
u
u
b
\
u
Y
u
g
u
u
u
:
!
A
u
u
u
A
g
u
d
d
u
u
u
u
u
A
2
!
u
u
!
Q
:
u
u
d
\
u
u
u
^
u
\
u
u
J
2
u
u
A
u
u
_
_
d
u
A
\
u
u
_
g
u
u
!
A
u
u
2
u
u
u
2
!
!
!
A
K
u
u
u
b
!
_
u
u
\
2
u
u
\
u
u
u
\
b
!
u
A
A
J
A
A
u
g
b
\
u
A
d
u
u
A
g
g
u
_
g
A
Y
\
\
A
g
d
\
Y
A
J
j
u
u
u
[
u
u
j
u
u
u
j
u
u
u
[
u
u
u
u
[
u
u
u
O
u
u
u
u
[
u
u
u
u
[
u
u
u
u
u
2
A
p
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
8
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
J
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
Q
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
_
u
u
u
A
u
u
u
u
u
u
u
u
:
u
u
u
u
u
g
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
:
u
u
u
u
u
u
_
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
g
\
_
A
:
u
!
[
u
d
b
p
L
u
u
!
[
u
u
[
L
u
!
g
u
L
u
_
\
u
u
u
Q
:
!
Q
d
u
u
u
[
u
\
u
u
L
u
!
u
u
[
u
Y
2
2
A
p
A
\
2
b
\
:
d
A
:
A
u
u
u
u
u
L
u
!
_
u
u
u
u
[
u
A
g
!
_
u
u
u
u
j
L
u
d
u
u
u
u
j
[
u
g
u
u
u
u
u
[
L
u
\
u
u
u
u
u
L
u
Y
d
d
2
:
d
g
g
A
j
p
2
A
d
A
d
Y
2
b
u
u
u
u
u
u
O
u
:
g
u
u
u
u
u
O
[
u
g
u
u
u
u
u
[
O
u
A
J
!
g
d
:
g
A
g
d
A
j
:
:
g
u
\
d
A
d
d
j
)
D
A
u
b
A
d
g
e
!
B
g
u
u
O
u
u
u
u
u
u
O
u
_
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
_
u
u
u
u
u
u
u
\
u
u
u
u
p
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
2
u
u
u
u
\
u
u
u
u
u
u
u
u
u
K
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
J
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
\
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
d
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
^
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
)
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
A
u
u
u
u
\
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
!
u
A
u
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
\
u
u
u
u
u
u
u
u
u
d
u
u
u
g
:
d
u
u
u
u
u
u
u
u
u
A
u
\
u
u
u
u
u
u
u
u
2
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
_
\
u
Y
2
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
\
u
\
_
u
b
Y
\
u
u
d
u
A
u
u
u
u
u
g
u
d
u
u
\
u
A
u
2
A
u
u
d
u
u
2
u
A
A
u
u
u
u
A
u
!
u
u
u
A
g
u
u
u
u
d
u
u
u
g
\
u
u
\
\
u
u
u
u
2
u
\
!
u
!
u
u
u
!
u
b
_
u
d
A
u
u
u
2
u
u
[
u
u
2
!
u
u
u
u
g
d
u
d
!
u
!
J
u
d
d
u
u
u
A
p
A
u
g
g
2
u
g
!
u
g
u
A
A
u
!
\
u
p
u
u
u
u
[
d
u
2
2
A
d
u
d
u
A
\
u
d
d
u
A
d
u
u
d
d
g
u
u
g
u
u
Q
p
\
u
Q
!
\
u
A
u
\
u
u
u
\
Q
u
!
\
d
u
2
d
u
u
K
\
u
d
2
u
J
g
u
\
d
A
p
g
!
\
u
2
Y
_
A
u
u
Y
!
:
_
A
u
g
d
d
!
\
u
_
g
:
:
_
u
\
u
A
!
\
g
2
2
d
d
\
u
A
u
u
d
g
u
g
2
!
Y
Q
g
u
A
!
g
g
2
u
2
d
A
u
Q
Y
!
u
d
d
:
:
g
Q
g
\
_
d
2
A
2
u
^
E
\
!
b
d
\
d
2
E
g
g
g
b
d
d
A
A
g
d
b
_
j
Q
u
2
!
\
g
2
A
\
A
A
2
Q
)
!
A
A
d
_
2
A
\
2
A
d
!
:
A
!
!
p
g
g
g
Y
Y
\
b
j
Y
J
u
g
A
L
d
Y
g
j
[
j
j
[
j
j
[
j
j
[
g
j
j
d
A
d
j
j
u
j
u
O
j
u
L
j
u
j
u
j
u
B
Y
j
j
b
u
j
u
j
j
u
j
j
u
O
j
j
u
L
j
j
u
j
j
u
j
j
u
B
g
A
_
j
u
d
j
u
d
j
u
j
u
O
j
u
L
J
J
u
j
j
O
u
j
O
u
j
O
u
O
j
O
u
L
Y
A
b
u
j
j
L
u
j
L
u
j
L
u
O
j
L
u
L
A
g
2
Y
!
_
d
!
j
u
_
A
2
p
g
A
2
d
2
g
\
!
d
© 2006 by Taylor & Francis Group, LLC
d
:
u
2
Y
A
_
\
u
u
A
u
d
u
Q
u
u
Y
u
u
g
u
u
d
A
u
u
\
u
u
u
g
u
u
u
[
u
u
u
u
u
u
u
u
d
u
u
!
u
u
u
u
!
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
p
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
p
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
d
u
u
u
u
u
u
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
_
u
u
u
u
u
A
u
u
u
p
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
\
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
j
[
j
[
j
[
L
j
[
j
[
B
j
[
B
j
j
[
j
j
j
[
j
j
j
[
j
j
[
O
j
j
[
O
j
j
[
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
j
[
B
j
j
[
j
j
j
j
[
j
O
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
_
u
A
u
u
u
u
u
u
!
u
u
u
u
u
d
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
j
[
j
j
[
j
j
[
j
[
e
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
j
[
j
[
j
[
B
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
O
[
j
j
O
[
j
j
O
[
j
O
[
O
j
O
[
[
B
j
j
L
[
j
L
[
j
j
L
[
j
u
u
u
u
u
d
u
u
u
j
O
u
u
u
u
u
u
u
u
u
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
_
u
u
j
[
u
u
j
[
u
u
u
[
j
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
j
u
u
u
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
_
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
b
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
_
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
Y
u
u
u
u
u
A
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
_
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
!
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
d
u
u
u
u
u
g
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
_
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
Q
u
u
u
K
u
d
u
u
u
u
u
u
u
u
d
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
:
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
_
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
A
u
u
u
u
p
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
Y
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
Q
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
p
u
u
u
u
d
u
u
u
u
u
g
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
[
u
^
u
u
u
u
u
u
u
u
g
u
u
u
u
u
!
u
u
u
u
u
u
u
u
J
u
u
u
u
u
u
u
u
2
u
u
g
u
u
u
u
u
u
u
d
u
b
u
u
u
u
u
u
u
u
u
u
u
A
u
u
d
u
u
u
g
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
b
d
u
u
u
u
u
u
u
u
u
g
u
u
Y
u
u
:
u
u
u
2
u
u
u
u
u
d
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
g
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
!
u
d
u
[
u
u
u
u
u
u
u
u
\
u
_
:
A
u
!
u
u
u
u
!
u
u
u
u
\
2
u
u
J
u
u
u
u
u
Q
u
u
u
u
u
u
u
d
u
u
u
u
u
u
!
u
u
u
u
u
u
K
\
u
u
u
u
u
d
u
g
A
u
u
u
u
u
d
u
u
u
u
u
u
u
b
u
u
u
u
u
\
u
u
u
u
u
A
g
u
u
u
u
J
u
g
u
u
u
b
Q
u
u
u
J
u
\
u
A
u
d
u
_
u
u
A
u
u
g
u
u
u
u
u
u
\
!
u
d
u
u
d
u
\
u
u
)
u
A
2
A
g
\
!
:
\
2
g
_
:
!
A
p
:
p
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
:
_
u
g
d
2
u
u
u
A
u
u
u
u
u
\
u
\
!
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
g
u
u
u
u
u
:
u
u
u
u
u
d
u
u
u
A
u
d
u
u
d
u
u
:
u
g
u
u
u
!
u
u
2
A
u
u
u
2
g
_
u
A
g
p
u
u
d
u
Y
2
g
b
g
g
\
\
u
u
u
u
\
u
p
u
u
d
u
u
u
u
u
d
g
Y
u
u
u
u
d
u
\
u
u
u
u
u
g
u
u
\
u
u
u
g
u
A
u
b
!
u
_
:
u
u
u
u
u
u
u
\
u
u
u
u
\
u
A
A
u
u
u
b
u
:
A
2
\
g
2
_
u
d
2
2
b
d
g
d
\
:
\
A
u
:
Y
A
u
u
u
_
_
u
u
A
u
g
!
u
u
u
!
u
\
u
u
A
u
u
Q
Q
u
u
!
d
u
u
d
\
u
\
d
u
u
u
u
u
!
u
b
d
!
:
:
A
\
2
g
d
A
Y
A
!
g
u
d
Y
\
u
u
A
_
g
!
d
_
\
g
u
u
u
u
u
u
!
Y
u
u
u
2
u
u
A
u
u
u
u
b
A
u
A
g
u
u
u
u
u
A
_
:
u
u
u
2
A
u
\
u
_
A
2
d
p
Y
d
g
!
Q
u
u
u
z
!
u
g
u
\
d
A
A
u
u
u
\
d
A
d
_
u
d
2
A
u
u
u
Q
u
!
!
u
b
u
b
2
d
g
A
\
:
2
g
j
_
d
p
d
g
d
d
d
A
g
A
A
]
g
g
_
\
A
Y
u
A
:
g
:
g
d
Y
\
u
u
u
!
u
\
u
u
u
u
u
u
u
u
d
u
b
u
d
u
u
u
[
g
A
d
:
\
u
u
u
d
d
g
u
A
u
u
g
A
2
u
u
u
u
u
u
g
\
u
u
Y
g
\
u
u
\
!
u
2
\
u
g
u
u
J
d
u
u
d
2
u
u
_
:
A
u
g
u
u
u
b
2
b
A
u
A
:
d
j
:
_
d
!
\
d
:
g
d
u
A
A
u
u
!
g
A
A
!
g
\
b
)
A
L
Y
_
Q
\
u
u
!
!
d
:
g
j
g
Q
A
O
\
u
u
d
A
u
A
d
A
_
u
Y
\
2
\
d
_
g
A
A
_
j
:
Y
j
:
u
u
u
!
:
A
\
g
u
u
A
_
u
J
:
g
g
2
d
u
2
u
g
d
u
g
g
p
A
:
u
d
!
!
!
g
b
!
u
A
g
\
u
A
g
u
d
p
d
d
u
g
J
\
:
g
g
A
!
[
Q
b
d
\
2
Q
\
2
\
d
K
2
2
b
b
_
d
2
Q
J
d
j
\
\
)
\
:
A
^
u
Q
g
A
\
A
A
d
!
J
Y
g
d
Y
g
g
b
\
\
A
b
\
2
!
_
d
\
b
_
A
\
2
_
A
d
b
)
g
\
j
\
2
!
A
[
g
j
d
!
\
!
:
A
u
d
\
g
d
_
_
g
!
g
\
[
A
d
j
O
:
d
Y
A
j
g
g
j
L
j
j
A
j
g
j
L
j
[
j
L
[
j
j
L
[
j
j
[
j
j
[
j
j
[
j
\
j
j
j
u
j
u
O
Y
A
b
A
u
j
j
u
j
u
Y
g
j
d
g
B
u
2
[
j
\
d
Y
Q
u
b
Y
g
d
d
g
d
Y
A
b
g
p
g
A
g
J
Y
A
b
g
p
g
A
g
J
j
B
u
O
j
B
u
L
g
Y
g
_
e
:
[
e
u
e
u
j
e
u
O
j
e
u
L
A
\
A
u
j
u
u
u
O
u
L
j
u
2
j
u
j
u
j
u
O
!
A
d
:
u
j
d
!
2
u
u
u
O
j
\
A
Y
\
A
\
\
g
d
\
\
j
© 2006 by Taylor & Francis Group, LLC
u
!
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
j
[
O
j
[
j
[
j
j
[
j
j
[
j
[
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
Q
u
u
u
u
j
B
[
j
j
B
[
j
j
B
[
O
j
B
[
j
u
u
u
B
[
B
j
B
[
j
j
j
B
[
j
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
j
e
[
j
j
e
[
j
j
e
[
j
e
[
L
j
u
j
e
e
[
[
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
:
u
u
A
j
O
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
p
u
u
u
u
u
u
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
[
j
[
j
[
j
[
[
[
j
[
j
j
[
j
j
[
j
j
[
B
j
[
j
u
u
u
u
u
u
u
u
:
u
u
u
g
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
A
u
u
u
u
u
u
u
u
u
u
_
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
p
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
b
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
b
u
u
u
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
^
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
A
u
u
u
u
u
p
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
7
u
u
u
u
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
b
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
u
u
u
d
2
u
u
u
u
u
u
u
u
:
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
u
A
u
u
u
u
u
u
u
u
d
u
u
u
u
g
u
u
u
u
u
u
u
u
u
u
u
u
u
u
:
u
u
u
u
u
_
u
u
u
u
u
u
b
u
u
u
u
u
u
u
u
d
u
u
u
u
u
u
u
_
u
u
u
u
A
g
u
u
u
u
u
u
u
u
u
u
u
!
!
u
u
u
u
u
u
u
A
u
u
u
u
u
u
p
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
g
u
u
u
u
b
u
u
_
u
u
u
\
u
u
u
u
u
u
A
u
u
u
\
u
u
u
u
u
b
d
u
u
u
u
u
u
u
u
g
u
d
u
u
u
u
b
u
u
u
u
u
u
u
u
u
:
u
u
\
u
u
u
Q
u
p
u
d
u
u
u
u
J
g
u
u
!
u
u
u
u
u
A
u
u
u
u
u
u
A
g
_
u
u
u
Y
u
\
u
u
u
g
u
u
u
u
_
u
u
u
u
u
A
g
u
u
u
u
u
u
u
u
!
u
g
!
A
u
\
u
u
u
u
u
u
u
A
u
u
u
u
u
2
u
u
u
u
!
u
A
u
\
u
g
u
u
u
^
u
u
u
u
u
u
u
u
u
b
u
!
u
u
u
A
u
u
u
u
u
A
Y
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
u
u
A
u
u
_
u
u
2
g
!
u
u
u
u
u
!
u
u
u
u
u
d
d
u
u
u
u
u
u
A
u
u
u
u
u
\
u
u
u
u
u
u
u
d
u
u
u
u
u
!
u
u
A
!
u
Y
u
u
Q
u
u
u
u
u
u
u
u
u
u
A
u
u
u
d
u
u
A
g
u
u
u
u
u
u
A
u
u
u
u
u
u
!
u
u
u
u
u
u
u
u
u
u
d
u
u
!
!
u
u
u
u
Y
u
u
u
d
u
u
u
u
g
g
u
u
u
u
u
2
u
u
u
u
u
u
u
u
u
\
u
u
d
u
A
u
u
Y
g
u
u
u
u
:
u
:
u
u
u
u
g
u
u
u
A
u
u
u
u
u
!
g
u
u
\
Y
u
u
u
u
u
u
d
2
u
u
u
!
u
\
u
g
u
u
2
u
u
u
u
\
u
u
!
u
u
2
u
d
u
u
u
u
u
u
u
u
g
A
2
u
u
u
u
u
u
\
Q
u
u
u
u
u
u
A
u
u
u
u
u
u
u
\
2
u
u
2
u
u
[
u
u
u
d
u
u
d
u
2
u
u
u
u
A
u
u
Y
!
A
u
d
u
p
u
u
u
u
b
g
u
u
u
A
_
u
!
u
d
b
u
u
u
A
A
u
A
u
u
u
u
!
A
u
Y
p
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
A
J
!
u
u
g
u
u
u
A
u
g
u
\
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
2
u
Q
A
u
u
d
u
u
u
u
u
:
u
J
\
u
A
u
u
\
b
!
Y
u
u
u
u
u
u
g
u
u
A
A
u
u
u
u
u
u
u
A
d
u
u
_
[
u
u
_
A
u
u
u
u
u
u
u
u
u
u
u
_
!
u
u
u
d
u
u
\
u
g
u
2
u
8
u
u
b
u
A
d
2
A
^
2
_
u
:
u
\
u
d
u
u
u
A
u
A
!
\
!
u
\
J
u
A
u
!
u
A
A
!
u
\
g
_
u
!
\
u
\
u
u
u
u
u
!
2
u
u
u
u
u
A
u
u
u
u
u
g
^
u
J
Y
_
u
u
u
u
u
u
d
u
u
d
u
A
u
g
2
u
u
_
u
b
u
\
u
u
u
g
A
A
u
u
u
!
_
u
u
u
u
u
u
u
u
u
u
b
!
A
u
b
\
Y
u
A
d
p
!
!
g
u
Y
A
J
u
u
u
A
\
!
Q
2
u
A
J
u
A
u
u
u
u
u
A
u
A
p
u
J
g
u
u
u
u
u
u
u
u
!
g
A
u
u
u
u
u
u
u
u
u
u
\
u
u
u
u
u
u
u
A
g
u
u
u
u
u
A
d
u
A
!
g
u
_
g
_
g
u
\
d
u
2
g
Y
u
u
u
u
u
\
u
_
Q
u
u
)
u
\
u
\
b
b
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
!
u
!
J
u
u
u
u
u
u
u
_
A
g
2
\
\
\
u
A
\
b
\
:
:
A
u
!
p
!
A
!
g
A
d
2
\
u
Y
g
d
d
_
A
!
!
2
b
2
g
2
u
u
u
u
u
u
A
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
J
u
_
\
u
u
u
A
b
u
u
A
d
2
u
A
\
u
u
u
u
[
u
u
u
u
u
u
u
z
!
b
u
u
u
u
u
u
A
g
u
u
d
u
u
u
u
Y
d
u
u
u
A
\
u
u
2
u
g
u
!
u
u
u
2
A
u
u
u
u
\
d
2
u
u
u
g
u
u
u
u
u
J
u
!
u
u
u
!
A
u
u
u
u
A
J
u
u
u
u
g
Y
u
u
u
u
u
u
u
u
u
u
g
d
:
Q
d
\
:
g
g
g
d
z
u
u
u
u
u
\
!
u
u
u
u
u
u
u
u
u
u
J
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
\
g
\
u
u
g
u
u
u
:
d
u
u
u
u
u
\
u
Q
[
u
u
u
_
u
u
u
u
A
A
!
u
7
u
u
d
u
g
u
A
g
u
u
d
g
!
A
u
u
u
u
u
A
\
_
d
2
A
_
!
A
u
u
Q
\
!
u
u
g
2
\
A
A
u
Y
A
u
u
u
!
A
u
A
8
:
\
u
_
u
:
b
u
u
g
u
u
A
d
u
u
u
Q
Q
A
d
A
u
A
u
!
g
u
u
u
d
u
u
A
A
g
d
_
\
Y
!
d
g
d
!
:
Q
Y
\
A
!
A
!
Q
B
g
\
g
!
d
g
d
b
_
A
!
j
2
b
Y
!
d
p
J
j
A
Q
\
b
A
\
^
!
:
:
g
d
g
2
Q
[
!
!
d
A
z
A
d
u
p
!
j
p
j
g
j
d
\
u
[
g
u
p
)
u
g
A
u
u
2
!
u
g
