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<p><a href="https://en.wikipedia.org/wiki/Persistent_data_structure">Persistent segment tree with range updates (lazy propagation)</a>
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <iostream></code><br />
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<code>#include <memory></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for persistent_seg_tree_lazy_prop.cpp:</div>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html">range_queries::perSegTree</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Range query here is range sum, but the code can be modified to make different queries like range max or min. <a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#details">More...</a><br /></td></tr>
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<tr class="memdesc:dd/d69/namespacerange__queries"><td class="mdescLeft"> </td><td class="mdescRight">Algorithms and Data Structures that support range queries and updates. <br /></td></tr>
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Functions</h2></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft"> </td><td class="mdescRight">Test implementations. <a href="../../d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <a href="../../d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Persistent_data_structure">Persistent segment tree with range updates (lazy propagation)</a> </p>
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<p>A normal segment tree facilitates making point updates and range queries in logarithmic time. Lazy propagation preserves the logarithmic time with range updates. So, a segment tree with lazy propagation enables doing range updates and range queries in logarithmic time, but it doesn't save any information about itself before the last update. A persistent data structure always preserves the previous version of itself when it is modified. That is, a new version of the segment tree is generated after every update. It saves all previous versions of itself (before every update) to facilitate doing range queries in any version. More memory is used ,but the logarithmic time is preserved because the new version points to the same nodes, that the previous version points to, that are not affected by the update. That is, only the nodes that are affected by the update and their ancestors are copied. The rest is copied using lazy propagation in the next queries. Thus preserving the logarithmic time because the number of nodes copied after any update is logarithmic.</p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/MSedra">Magdy Sedra</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memproto">
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void </td>
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<td class="paramname"></td><td>)</td>
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<td></td>
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<p>Main function. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  {</div>
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<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <a class="code" href="../../d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
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<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> }</div>
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||||
<div class="ttc" id="apersistent__seg__tree__lazy__prop_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:268</div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d5/d58/persistent__seg__tree__lazy__prop_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="100%" height="525"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<a id="aa8dca7b867074164d5f45b0f3851269d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<td class="mlabels-left">
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<td class="memname">static void test </td>
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<td>(</td>
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<td class="paramname"></td><td>)</td>
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<td></td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Test implementations. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="fragment"><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  {</div>
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<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int64_t></a> arr = {-5, 2, 3, 11, -2, 7, 0, 1};</div>
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<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html">range_queries::perSegTree</a> tree;</div>
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<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Elements before any updates are {"</span>;</div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">for</span> (uint32_t i = 0; i < arr.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); ++i) {</div>
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<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << arr[i];</div>
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<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keywordflow">if</span> (i != arr.size() - 1) {</div>
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<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">","</span>;</div>
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<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  }</div>
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<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  }</div>
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<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"}\n"</span>;</div>
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a67d8371bc998c67d53e8f64db4f52767">construct</a>(</div>
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<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  arr); <span class="comment">// constructing the original segment tree (version = 0)</span></div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Querying range sum on version 0 from index 2 to 4 = 3+11-2 = "</span></div>
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<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  << tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(2, 4, 0) << <span class="charliteral">'\n'</span>;</div>
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<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
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<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  << <span class="stringliteral">"Subtract 7 from all elements from index 1 to index 5 inclusive\n"</span>;</div>
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<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#af16c0c87b29119f066041d6e71ab50e0">update</a>(1, 5, -7); <span class="comment">// subtracting 7 from index 1 to index 5</span></div>
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<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Elements of the segment tree whose version = 1 (after 1 "</span></div>
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<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="stringliteral">"update) are {"</span>;</div>
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<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">for</span> (uint32_t i = 0; i < arr.size(); ++i) {</div>
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<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(i, i, 1);</div>
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<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keywordflow">if</span> (i != arr.size() - 1) {</div>
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<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">","</span>;</div>
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<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  }</div>
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<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  }</div>
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<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"}\n"</span>;</div>
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||||
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Add 10 to all elements from index 0 to index 7 inclusive\n"</span>;</div>
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<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#af16c0c87b29119f066041d6e71ab50e0">update</a>(0, 7, 10); <span class="comment">// adding 10 to all elements</span></div>
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<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Elements of the segment tree whose version = 2 (after 2 "</span></div>
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<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="stringliteral">"updates) are {"</span>;</div>
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<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">for</span> (uint32_t i = 0; i < arr.size(); ++i) {</div>
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<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(i, i, 2);</div>
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<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">if</span> (i != arr.size() - 1) {</div>
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<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"}\n"</span>;</div>
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<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Number of segment trees (versions) now = "</span> << tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#a0fe4e431f3e09c274ecd7d2d58dcb865">size</a>()</div>
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<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  << tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(3, 5, 0) << <span class="charliteral">'\n'</span>;</div>
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<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Querying range sum on version 1 from index 3 to 5 = 4-9+0 = "</span></div>
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<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  << tree.<a class="code" href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4">query</a>(3, 5, 1) << <span class="charliteral">'\n'</span>;</div>
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<div class="ttc" id="aclassrange__queries_1_1per_seg_tree_html_af16c0c87b29119f066041d6e71ab50e0"><div class="ttname"><a href="../../d8/d28/classrange__queries_1_1per_seg_tree.html#af16c0c87b29119f066041d6e71ab50e0">range_queries::perSegTree::update</a></div><div class="ttdeci">std::shared_ptr< Node > update(const uint32_t &i, const uint32_t &j, const uint32_t &l, const uint32_t &r, const int64_t &value, std::shared_ptr< Node > const &curr)</div><div class="ttdoc">Doing range update, checking at every node if it has some value to be propagated. All nodes affected ...</div><div class="ttdef"><b>Definition:</b> persistent_seg_tree_lazy_prop.cpp:135</div></div>
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