cp-algorithms
diff --git a/‎main/feed_json_updated.json
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diff --git a/‎main/feed_rss_created.xml
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diff --git a/‎main/feed_rss_updated.xml
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diff --git a/‎main/geometry/planar.html
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diff --git a/‎main/search/search_index.json
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@@ -6604,6 +6604,12 @@
 
 
 
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@@ -6654,6 +6660,10 @@
 
 
 
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@@ -6666,7 +6676,7 @@
 <ul class="metadata page-metadata" data-bi-name="page info" lang="en-us" dir="ltr">
 
   Last update:
-  <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date">October 23, 2024</span>&emsp;
+  <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date">January 13, 2025</span>&emsp;
 
 <!-- Tags -->
 
@@ -6790,20 +6800,14 @@ <h2 id="implementation">Implementation<a class="headerlink" href="#implementatio
 <span class="w">                </span><span class="n">e</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">e1</span><span class="p">;</span>
 <span class="w">            </span><span class="p">}</span>
 <span class="w">            </span><span class="n">std</span><span class="o">::</span><span class="n">reverse</span><span class="p">(</span><span class="n">face</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">face</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
-<span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">sign</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
-<span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">size_t</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">face</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<span class="w">                </span><span class="kt">size_t</span><span class="w"> </span><span class="n">j1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">face</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<span class="w">                </span><span class="kt">size_t</span><span class="w"> </span><span class="n">j2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">face</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
-<span class="w">                </span><span class="kt">int64_t</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vertices</span><span class="p">[</span><span class="n">face</span><span class="p">[</span><span class="n">j</span><span class="p">]].</span><span class="n">cross</span><span class="p">(</span><span class="n">vertices</span><span class="p">[</span><span class="n">face</span><span class="p">[</span><span class="n">j1</span><span class="p">]],</span><span class="w"> </span><span class="n">vertices</span><span class="p">[</span><span class="n">face</span><span class="p">[</span><span class="n">j2</span><span class="p">]]);</span>
-<span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<span class="w">                    </span><span class="n">sign</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
-<span class="w">                    </span><span class="k">break</span><span class="p">;</span>
-<span class="w">                </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<span class="w">                    </span><span class="n">sign</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
-<span class="w">                    </span><span class="k">break</span><span class="p">;</span>
-<span class="w">                </span><span class="p">}</span>
+<span class="w">            </span><span class="n">Point</span><span class="w"> </span><span class="n">p1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vertices</span><span class="p">[</span><span class="n">face</span><span class="p">[</span><span class="mi">0</span><span class="p">]];</span>
+<span class="w">            </span><span class="kt">__int128</span><span class="w"> </span><span class="n">sum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">face</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">                </span><span class="n">Point</span><span class="w"> </span><span class="n">p2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vertices</span><span class="p">[</span><span class="n">face</span><span class="p">[</span><span class="n">j</span><span class="p">]];</span>
+<span class="w">                </span><span class="n">Point</span><span class="w"> </span><span class="n">p3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vertices</span><span class="p">[</span><span class="n">face</span><span class="p">[(</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">face</span><span class="p">.</span><span class="n">size</span><span class="p">()]];</span>
+<span class="w">                </span><span class="n">sum</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="n">p2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">p1</span><span class="p">).</span><span class="n">cross</span><span class="p">(</span><span class="n">p3</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">p2</span><span class="p">);</span>
 <span class="w">            </span><span class="p">}</span>
-<span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">sign</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">sum</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <span class="w">                </span><span class="n">faces</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">faces</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">face</span><span class="p">);</span>
 <span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
 <span class="w">                </span><span class="n">faces</span><span class="p">.</span><span class="n">emplace_back</span><span class="p">(</span><span class="n">face</span><span class="p">);</span>
@@ -7013,7 +7017,7 @@ <h2 id="problems">Problems<a class="headerlink" href="#problems" title="Permanen
 
 <ul class="metadata page-metadata" data-bi-name="page info" lang="en-us" dir="ltr">
   <span class="contributors-text">Contributors:</span>
-  <ul class="contributors" data-bi-name="contributors"><li><a href="https://github.com/SYury" title="SYury" data-bi-name="contributorprofile" target="_blank">SYury</a> (99.43%)</li><li><a href="https://github.com/Kostero" title="Kostero" data-bi-name="contributorprofile" target="_blank">Kostero</a> (0.28%)</li><li><a href="https://github.com/adamant-pwn" title="adamant-pwn" data-bi-name="contributorprofile" target="_blank">adamant-pwn</a> (0.28%)</li></ul>
+  <ul class="contributors" data-bi-name="contributors"><li><a href="https://github.com/SYury" title="SYury" data-bi-name="contributorprofile" target="_blank">SYury</a> (97.39%)</li><li><a href="https://github.com/hazzlerr" title="hazzlerr" data-bi-name="contributorprofile" target="_blank">hazzlerr</a> (2.03%)</li><li><a href="https://github.com/Kostero" title="Kostero" data-bi-name="contributorprofile" target="_blank">Kostero</a> (0.29%)</li><li><a href="https://github.com/adamant-pwn" title="adamant-pwn" data-bi-name="contributorprofile" target="_blank">adamant-pwn</a> (0.29%)</li></ul>
 </ul>
 
               </article>