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<H2><A NAME="SECTION00061000000000000000">
psb_halo -- Halo Data Communication</A>
</H2>

<P>
These subroutines gathers the values of the halo
elements:

<P>
<BR><P></P>
<DIV ALIGN="CENTER" CLASS="mathdisplay">
<!-- MATH
 \begin{displaymath}
x \leftarrow x
\end{displaymath}
 -->

<IMG
 WIDTH="43" HEIGHT="24" BORDER="0"
 SRC="img59.png"
 ALT="\begin{displaymath}x \leftarrow x \end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
where:
<DL>
<DT><STRONG><SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></SPAN></STRONG></DT>
<DD>is a global dense  submatrix.
</DD>
</DL>

<P>
<BR><P></P>
<DIV ALIGN="CENTER"><A NAME="3467"></A>
<TABLE>
<CAPTION><STRONG>Table 14:</STRONG>
Data types</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
<TR><TD ALIGN="LEFT"><SPAN CLASS="MATH"><IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img22.png"
 ALT="$\alpha$"></SPAN>, <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></SPAN></TD>
<TD ALIGN="LEFT"><B>Subroutine</B></TD>
</TR>
<TR><TD ALIGN="LEFT">Integer</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Real</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Real</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Short Precision Complex</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
<TR><TD ALIGN="LEFT">Long Precision Complex</TD>
<TD ALIGN="LEFT">psb_halo</TD>
</TR>
</TABLE>
</DIV>
</TD></TR>
</TABLE>
</DIV><P></P>
<BR>

<P>
<BR>
<IMG
 WIDTH="394" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
 SRC="img60.png"
 ALT="\begin{lstlisting}
call psb_halo(x, desc_a, info)
call psb_halo(x, desc_a, info, work, data)
\end{lstlisting}">
<BR>

<P>
<DL>
<DT><STRONG>Type:</STRONG></DT>
<DD>Synchronous.
</DD>
<DT><STRONG><B>On Entry</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>global dense matrix <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></SPAN>.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>inout</B>.
<BR>
Specified as:  a rank one or two array or an object of type vdata<TT>psb_T_vect_type</TT> 
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90halo">14</A>.
</DD>
<DT><STRONG>desc_a</STRONG></DT>
<DD>contains data structures for communications.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B>
<BR>
Intent: <B>in</B>.
<BR>
Specified as: a structured data of type descdata<TT>psb_desc_type</TT>.
</DD>
<DT><STRONG>work</STRONG></DT>
<DD>the work array. 
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>optional</B>
<BR>
Intent: <B>inout</B>.
<BR>
Specified as: a rank one array of the same type of <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></SPAN>. 
</DD>
<DT><STRONG>data</STRONG></DT>
<DD>index list selector.
<BR>
Scope: <B>global</B> 
<BR>
Type: <B>optional</B> 
<BR>
Specified as: an integer. Values:<code>psb_comm_halo_</code>,<code>psb_comm_mov_</code>,
<code>psb_comm_ext_</code>, default: <code>psb_comm_halo_</code>. Chooses the
index list on which to base the data exchange. 

<P>
</DD>
<DT><STRONG><B>On Return</B></STRONG></DT>
<DD>
</DD>
<DT><STRONG>x</STRONG></DT>
<DD>global dense result matrix <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></SPAN>.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>inout</B>.
<BR>
Returned as:  a rank one or two array 
containing numbers of type specified in
Table&nbsp;<A HREF="#tab:f90halo">14</A>.
</DD>
<DT><STRONG>info</STRONG></DT>
<DD>the local portion of result submatrix <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$y$"></SPAN>.
<BR>
Scope: <B>local</B> 
<BR>
Type: <B>required</B> 
<BR>
Intent: <B>out</B>.
<BR>
An integer value that contains an error code. 
</DD>
</DL>

<DIV ALIGN="CENTER"><A NAME="fig:try8x8"></A><A NAME="3468"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 7:</STRONG>
Sample discretization mesh.</CAPTION>
<TR><TD>
<DIV ALIGN="CENTER">
<IMG
 WIDTH="357" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
 SRC="img61.png"
 ALT="\includegraphics[scale=0.45]{figures/try8x8.eps}">

<IMG
 WIDTH="357" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
 SRC="img62.png"
 ALT="\includegraphics[scale=0.45]{figures/try8x8}">

</DIV></TD></TR>
</TABLE>
</DIV>

<P>
<BIG CLASS="LARGE"><B>Usage Example</B></BIG>
Consider the discretization mesh depicted in fig.&nbsp;<A HREF="#fig:try8x8">7</A>,
partitioned among two processes as shown by the dashed line; the data
distribution is such that each process will own 32 entries in the
index space, with a halo made of 8 entries placed at local indices 33
through 40. If process 0 assigns an initial value of 1 to its entries
in the <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.png"
 ALT="$x$"></SPAN> vector, and process 1 assigns a value of 2, then after a
call to <code>psb_halo</code> the contents of the local vectors will be the
following: 
<BR>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 ALIGN="CENTER">
<TR><TD ALIGN="CENTER" COLSPAN=3><SMALL CLASS="SMALL">
<SPAN>Process  0</SPAN></SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="CENTER" COLSPAN=3><SMALL CLASS="SMALL">
<SPAN>Process  1</SPAN></SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  I  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   GLOB(I) </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> X(I)  </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   I </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> GLOB(I) </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> X(I) </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  1   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    1  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  33  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  
  2   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    2  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  34  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  3   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    3  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   3  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  35  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  4   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    4  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   4  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  36  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  5   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    5  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   5  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  37  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  6   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    6  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   6  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  38  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  7   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    7  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   7  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  39  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  8   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    8  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   8  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  40  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
  9   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">    9  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   9  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  41  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 10   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   10  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  10  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  42  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 11   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   11  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  11  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  43  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 12   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   12  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  12  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  44  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 13   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   13  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  13  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  45  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 14   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   14  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  14  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  46  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 15   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   15  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  15  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  47  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 16   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   16  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  16  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  48  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 17   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   17  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  17  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  49  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 18   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   18  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  18  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  50  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 19   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   19  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  19  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  51  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
 20   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   20  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  20  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  52  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  
21   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   21  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  21  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  53  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
22   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   22  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  22  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  54  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
23   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   23  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  23  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  55  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
24   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   24  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  24  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  56  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
25   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   25  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  25  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  57  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
26   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   26  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  26  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  58  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
27   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   27  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  27  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  59  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
28   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   28  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  28  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  60  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
29   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   29  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  29  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  61  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
30   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   30  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  30  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  62  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
31   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   31  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  31  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  63  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
32   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   32  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  1.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  32  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  64  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   2.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
33   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   33  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  33  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  25  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
34   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   34  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  34  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  26  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
35   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   35  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  35  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  27  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
36   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   36  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  36  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  28  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
37   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   37  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  37  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  29  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
38   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   38  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  38  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  30  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
39   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   39  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  39  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  31  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
<TR><TD ALIGN="RIGHT"><SMALL CLASS="SMALL"> 
40   </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   40  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  2.0   </SMALL></TD>
<TD ALIGN="LEFT">&nbsp;</TD><TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  40  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">  32  </SMALL></TD>
<TD ALIGN="RIGHT"><SMALL CLASS="SMALL">   1.0 </SMALL></TD>
</TR>
</TABLE></DIV>
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