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      <tags>
        <tag><text fontsize="90%">Figure 9</text></tag>
        <tag role="refnum">9</tag>
        <tag role="typerefnum">Figure 9</tag>
      </tags>
      <toccaption><tag close=" ">7</tag>leading caption</toccaption>
      <caption><tag close=": "><text fontsize="90%">Figure 7</text></tag><text fontsize="90%">leading caption</text></caption>
      <graphics candidates="../graphics/none.png" class="ltx_figure_panel" graphic="../graphics/none.png" options="width=143.09538pt,keepaspectratio=true" xml:id="S0.F9.g1"/>
      <graphics candidates="../graphics/none.png" class="ltx_figure_panel" graphic="../graphics/none.png" options="width=143.09538pt,keepaspectratio=true" xml:id="S0.F9.g2"/>
      <break/>
      <toccaption><tag close=" ">8</tag>mid-fig caption</toccaption>
      <caption><tag close=": "><text fontsize="90%">Figure 8</text></tag><text fontsize="90%">mid-fig caption</text></caption>
      <graphics candidates="../graphics/none.png" class="ltx_figure_panel" graphic="../graphics/none.png" options="width=143.09538pt,keepaspectratio=true" xml:id="S0.F9.g3"/>
      <graphics candidates="../graphics/none.png" class="ltx_figure_panel" graphic="../graphics/none.png" options="width=143.09538pt,keepaspectratio=true" xml:id="S0.F9.g4"/>
      <toccaption><tag close=" ">9</tag>trailing caption</toccaption>
      <caption><tag close=": "><text fontsize="90%">Figure 9</text></tag><text fontsize="90%">trailing caption</text></caption>
    </figure>
    <pagination role="newpage"/>
    <figure class="ltx_figure_panel ltx_minipage" placement="tb" vattach="middle" width="182.1pt" xml:id="S0.SS0.SSS0.Px1.fig3">
      <float class="ltx_figure_panel ltx_minipage" framed="top" inlist="loa" labels="LABEL:alg:main" placement="H" vattach="middle" width="242.8pt" xml:id="alg2">
        <tags>
          <tag><text font="bold">Algorithm 2</text></tag>
          <tag role="refnum">2</tag>
          <tag role="typerefnum">Algorithm 2</tag>
        </tags>
        <toccaption><tag close=" ">2</tag>Algorithms in minipage</toccaption>
        <caption><tag close=" "><text font="bold">Algorithm 2</text></tag> Algorithms in minipage</caption>
        <listing>
          <listingline xml:id="alg2.l0"><tags>
              <tag><text fontsize="80%">0:</text></tag>
              <tag role="refnum">0</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg2.l1"><tags>
              <tag><text fontsize="80%">1:</text></tag>
              <tag role="refnum">1</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg2.l2"><tags>
              <tag><text fontsize="80%">2:</text></tag>
              <tag role="refnum">2</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg2.l3"><tags>
              <tag><text fontsize="80%">3:</text></tag>
              <tag role="refnum">3</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg2.l4"><tags>
              <tag><text fontsize="80%">4:</text></tag>
              <tag role="refnum">4</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg2.l5"><tags>
              <tag><text fontsize="80%">5:</text></tag>
              <tag role="refnum">5</tag>
            </tags>  <text font="bold">for</text> <text class="ltx_markedasmath">line</text> <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg2.l6"><tags>
              <tag><text fontsize="80%">6:</text></tag>
              <tag role="refnum">6</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg2.l7"><tags>
              <tag><text fontsize="80%">7:</text></tag>
              <tag role="refnum">7</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg2.l8"><tags>
              <tag><text fontsize="80%">8:</text></tag>
              <tag role="refnum">8</tag>
            </tags>  <text font="bold">end</text> <text font="bold">for</text></listingline>
          <listingline xml:id="alg2.l9"><tags>
              <tag><text fontsize="80%">9:</text></tag>
              <tag role="refnum">9</tag>
            </tags>  </listingline>
          <listingline xml:id="alg2.l10"><tags>
              <tag><text fontsize="80%">10:</text></tag>
              <tag role="refnum">10</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg2.l11"><tags>
              <tag><text fontsize="80%">11:</text></tag>
              <tag role="refnum">11</tag>
            </tags>  <text font="bold">while</text> line <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg2.l12"><tags>
              <tag><text fontsize="80%">12:</text></tag>
              <tag role="refnum">12</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg2.l13"><tags>
              <tag><text fontsize="80%">13:</text></tag>
              <tag role="refnum">13</tag>
            </tags>     <text font="bold">while</text> line <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg2.l14"><tags>
              <tag><text fontsize="80%">14:</text></tag>
              <tag role="refnum">14</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg2.l15"><tags>
              <tag><text fontsize="80%">15:</text></tag>
              <tag role="refnum">15</tag>
            </tags>        <text font="bold">line</text>
</listingline>
          <listingline xml:id="alg2.l16"><tags>
              <tag><text fontsize="80%">16:</text></tag>
              <tag role="refnum">16</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l17"><tags>
              <tag><text fontsize="80%">17:</text></tag>
              <tag role="refnum">17</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l18"><tags>
              <tag><text fontsize="80%">18:</text></tag>
              <tag role="refnum">18</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l19"><tags>
              <tag><text fontsize="80%">19:</text></tag>
              <tag role="refnum">19</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l20"><tags>
              <tag><text fontsize="80%">20:</text></tag>
              <tag role="refnum">20</tag>
            </tags>        <text font="bold">line</text> line:
</listingline>
          <listingline xml:id="alg2.l21"><tags>
              <tag><text fontsize="80%">21:</text></tag>
              <tag role="refnum">21</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l22"><tags>
              <tag><text fontsize="80%">22:</text></tag>
              <tag role="refnum">22</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l23"><tags>
              <tag><text fontsize="80%">23:</text></tag>
              <tag role="refnum">23</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l24"><tags>
              <tag><text fontsize="80%">24:</text></tag>
              <tag role="refnum">24</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l25"><tags>
              <tag><text fontsize="80%">25:</text></tag>
              <tag role="refnum">25</tag>
            </tags>                    line
</listingline>
          <listingline xml:id="alg2.l26"><tags>
              <tag><text fontsize="80%">26:</text></tag>
              <tag role="refnum">26</tag>
            </tags>                    line
</listingline>
          <listingline xml:id="alg2.l27"><tags>
              <tag><text fontsize="80%">27:</text></tag>
              <tag role="refnum">27</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l28"><tags>
              <tag><text fontsize="80%">28:</text></tag>
              <tag role="refnum">28</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg2.l29"><tags>
              <tag><text fontsize="80%">29:</text></tag>
              <tag role="refnum">29</tag>
            </tags>     <text font="bold">end</text> <text font="bold">while</text></listingline>
          <listingline xml:id="alg2.l30"><tags>
              <tag><text fontsize="80%">30:</text></tag>
              <tag role="refnum">30</tag>
            </tags>     </listingline>
          <listingline xml:id="alg2.l31"><tags>
              <tag><text fontsize="80%">31:</text></tag>
              <tag role="refnum">31</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg2.l32"><tags>
              <tag><text fontsize="80%">32:</text></tag>
              <tag role="refnum">32</tag>
            </tags>     line {line}
</listingline>
          <listingline xml:id="alg2.l33"><tags>
              <tag><text fontsize="80%">33:</text></tag>
              <tag role="refnum">33</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg2.l34"><tags>
              <tag><text fontsize="80%">34:</text></tag>
              <tag role="refnum">34</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg2.l35"><tags>
              <tag><text fontsize="80%">35:</text></tag>
              <tag role="refnum">35</tag>
            </tags>  <text font="bold">end</text> <text font="bold">while</text></listingline>
          <listingline xml:id="alg2.l36"><tags>
              <tag><text fontsize="80%">36:</text></tag>
              <tag role="refnum">36</tag>
            </tags>  </listingline>
          <listingline xml:id="alg2.l37"><tags>
              <tag><text fontsize="80%">37:</text></tag>
              <tag role="refnum">37</tag>
            </tags>  <text font="bold">for</text> <text class="ltx_markedasmath">line</text> <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg2.l38"><tags>
              <tag><text fontsize="80%">38:</text></tag>
              <tag role="refnum">38</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg2.l39"><tags>
              <tag><text fontsize="80%">39:</text></tag>
              <tag role="refnum">39</tag>
            </tags>  <text font="bold">end</text> <text font="bold">for</text></listingline>
          <listingline xml:id="alg2.l40"><tags>
              <tag><text fontsize="80%">40:</text></tag>
              <tag role="refnum">40</tag>
            </tags>  <text font="bold">return</text> line
</listingline>
        </listing>
      </float>
      <float class="ltx_figure_panel ltx_float_algorithm" framed="top" inlist="loa" labels="LABEL:alg:rpc" placement="H" xml:id="alg3">
        <tags>
          <tag><text font="bold">Algorithm 3</text></tag>
          <tag role="refnum">3</tag>
          <tag role="typerefnum">Algorithm 3</tag>
        </tags>
        <toccaption><tag close=" ">3</tag><text color="#0000FF">line</text></toccaption>
        <caption><tag close=" "><text font="bold">Algorithm 3</text></tag> <text color="#0000FF">line</text></caption>
        <listing>
          <listingline xml:id="alg3.l0"><tags>
              <tag><text fontsize="80%">0:</text></tag>
              <tag role="refnum">0</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg3.l1"><tags>
              <tag><text fontsize="80%">1:</text></tag>
              <tag role="refnum">1</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg3.l2"><tags>
              <tag><text fontsize="80%">2:</text></tag>
              <tag role="refnum">2</tag>
            </tags>  <text font="bold">for</text> <text class="ltx_markedasmath">line</text> <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg3.l3"><tags>
              <tag><text fontsize="80%">3:</text></tag>
              <tag role="refnum">3</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg3.l4"><tags>
              <tag><text fontsize="80%">4:</text></tag>
              <tag role="refnum">4</tag>
            </tags>  <text font="bold">end</text> <text font="bold">for</text></listingline>
          <listingline xml:id="alg3.l5"><tags>
              <tag><text fontsize="80%">5:</text></tag>
              <tag role="refnum">5</tag>
            </tags>  <text font="bold">while</text> line <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg3.l6"><tags>
              <tag><text fontsize="80%">6:</text></tag>
              <tag role="refnum">6</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg3.l7"><tags>
              <tag><text fontsize="80%">7:</text></tag>
              <tag role="refnum">7</tag>
            </tags>     <text font="bold">for</text> <text class="ltx_markedasmath">line</text> <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg3.l8"><tags>
              <tag><text fontsize="80%">8:</text></tag>
              <tag role="refnum">8</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg3.l9"><tags>
              <tag><text fontsize="80%">9:</text></tag>
              <tag role="refnum">9</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg3.l10"><tags>
              <tag><text fontsize="80%">10:</text></tag>
              <tag role="refnum">10</tag>
            </tags>              line
</listingline>
          <listingline xml:id="alg3.l11"><tags>
              <tag><text fontsize="80%">11:</text></tag>
              <tag role="refnum">11</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg3.l12"><tags>
              <tag><text fontsize="80%">12:</text></tag>
              <tag role="refnum">12</tag>
            </tags>     <text font="bold">end</text> <text font="bold">for</text></listingline>
          <listingline xml:id="alg3.l13"><tags>
              <tag><text fontsize="80%">13:</text></tag>
              <tag role="refnum">13</tag>
            </tags>     line
</listingline>
          <listingline xml:id="alg3.l14"><tags>
              <tag><text fontsize="80%">14:</text></tag>
              <tag role="refnum">14</tag>
            </tags>  <text font="bold">end</text> <text font="bold">while</text></listingline>
        </listing>
      </float>
      <float class="ltx_figure_panel ltx_float_algorithm" framed="top" inlist="loa" labels="LABEL:alg:replace" placement="H" xml:id="alg4">
        <tags>
          <tag><text font="bold">Algorithm 4</text></tag>
          <tag role="refnum">4</tag>
          <tag role="typerefnum">Algorithm 4</tag>
        </tags>
        <toccaption><tag close=" ">4</tag><text color="#0000FF">line</text></toccaption>
        <caption><tag close=" "><text font="bold">Algorithm 4</text></tag> <text color="#0000FF">line</text></caption>
        <listing>
          <listingline xml:id="alg4.l0"><tags>
              <tag><text fontsize="80%">0:</text></tag>
              <tag role="refnum">0</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg4.l1"><tags>
              <tag><text fontsize="80%">1:</text></tag>
              <tag role="refnum">1</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg4.l2"><tags>
              <tag><text fontsize="80%">2:</text></tag>
              <tag role="refnum">2</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg4.l3"><tags>
              <tag><text fontsize="80%">3:</text></tag>
              <tag role="refnum">3</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg4.l4"><tags>
              <tag><text fontsize="80%">4:</text></tag>
              <tag role="refnum">4</tag>
            </tags>      line
</listingline>
          <listingline xml:id="alg4.l5"><tags>
              <tag><text fontsize="80%">5:</text></tag>
              <tag role="refnum">5</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg4.l6"><tags>
              <tag><text fontsize="80%">6:</text></tag>
              <tag role="refnum">6</tag>
            </tags>  line
</listingline>
          <listingline xml:id="alg4.l7"><tags>
              <tag><text fontsize="80%">7:</text></tag>
              <tag role="refnum">7</tag>
            </tags>  <text font="bold">while</text> line <text font="bold">do</text>


</listingline>
          <listingline xml:id="alg4.l8"><tags>
              <tag><text fontsize="80%">8:</text></tag>
              <tag role="refnum">8</tag>
            </tags>      line
</listingline>
          <listingline xml:id="alg4.l9"><tags>
              <tag><text fontsize="80%">9:</text></tag>
              <tag role="refnum">9</tag>
            </tags>      line
</listingline>
          <listingline xml:id="alg4.l10"><tags>
              <tag><text fontsize="80%">10:</text></tag>
              <tag role="refnum">10</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l11"><tags>
              <tag><text fontsize="80%">11:</text></tag>
              <tag role="refnum">11</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l12"><tags>
              <tag><text fontsize="80%">12:</text></tag>
              <tag role="refnum">12</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l13"><tags>
              <tag><text fontsize="80%">13:</text></tag>
              <tag role="refnum">13</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l14"><tags>
              <tag><text fontsize="80%">14:</text></tag>
              <tag role="refnum">14</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l15"><tags>
              <tag><text fontsize="80%">15:</text></tag>
              <tag role="refnum">15</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l16"><tags>
              <tag><text fontsize="80%">16:</text></tag>
              <tag role="refnum">16</tag>
            </tags>      line
</listingline>
          <listingline xml:id="alg4.l17"><tags>
              <tag><text fontsize="80%">17:</text></tag>
              <tag role="refnum">17</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l18"><tags>
              <tag><text fontsize="80%">18:</text></tag>
              <tag role="refnum">18</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l19"><tags>
              <tag><text fontsize="80%">19:</text></tag>
              <tag role="refnum">19</tag>
            </tags>          line
</listingline>
          <listingline xml:id="alg4.l20"><tags>
              <tag><text fontsize="80%">20:</text></tag>
              <tag role="refnum">20</tag>
            </tags>        line
</listingline>
          <listingline xml:id="alg4.l21"><tags>
              <tag><text fontsize="80%">21:</text></tag>
              <tag role="refnum">21</tag>
            </tags>  <text font="bold">end</text> <text font="bold">while</text></listingline>
          <listingline xml:id="alg4.l22"><tags>
              <tag><text fontsize="80%">22:</text></tag>
              <tag role="refnum">22</tag>
            </tags>  <text font="bold">return</text> chain
</listingline>
        </listing>
      </float>
    </figure>
  </paragraph>
</document>