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<p>Find the <a href="https://en.wikipedia.org/wiki/Factorial" target="_blank">factorial</a> of a given number.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
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d9/d37/inverse__fast__fourier__transform_8cpp.html
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<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;complex&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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@@ -174,12 +175,12 @@ Functions</h2></td></tr>
</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 156</span> {</div>
<div class="line"><span class="lineno"> 157</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 158</span> <span class="comment">// with 2 defined test cases</span></div>
<div class="line"><span class="lineno"> 159</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 160</span>}</div>
<div class="ttc" id="ainverse__fast__fourier__transform_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> inverse_fast_fourier_transform.cpp:100</div></div>
<div class="fragment"><div class="line"><span class="lineno"> 157</span> {</div>
<div class="line"><span class="lineno"> 158</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 159</span> <span class="comment">// with 2 defined test cases</span></div>
<div class="line"><span class="lineno"> 160</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 161</span>}</div>
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</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
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@@ -219,56 +220,56 @@ Here is the call graph for this function:</div>
<p>True Answer for test case 2</p>
<p>Comparing for both real and imaginary values for test case 1</p>
<p>Comparing for both real and imaginary values for test case 2</p>
<div class="fragment"><div class="line"><span class="lineno"> 100</span> {</div>
<div class="line"><span class="lineno"> 101</span> <span class="comment">/* descriptions of the following test */</span></div>
<div class="line"><span class="lineno"> 102</span> </div>
<div class="line"><span class="lineno"> 103</span> <span class="keyword">auto</span> *t1 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[2]; <span class="comment">/// Test case 1</span></div>
<div class="line"><span class="lineno"> 104</span> <span class="keyword">auto</span> *t2 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[4]; <span class="comment">/// Test case 2</span></div>
<div class="line"><span class="lineno"> 105</span> </div>
<div class="line"><span class="lineno"> 106</span> t1[0] = {3, 0};</div>
<div class="line"><span class="lineno"> 107</span> t1[1] = {-1, 0};</div>
<div class="line"><span class="lineno"> 108</span> t2[0] = {10, 0};</div>
<div class="line"><span class="lineno"> 109</span> t2[1] = {-2, -2};</div>
<div class="line"><span class="lineno"> 110</span> t2[2] = {-2, 0};</div>
<div class="line"><span class="lineno"> 111</span> t2[3] = {-2, 2};</div>
<div class="line"><span class="lineno"> 112</span> </div>
<div class="line"><span class="lineno"> 113</span> uint8_t n1 = 2;</div>
<div class="line"><span class="lineno"> 114</span> uint8_t n2 = 4;</div>
<div class="line"><span class="lineno"> 115</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::complex&lt;double&gt;</a>&gt; r1 = {</div>
<div class="line"><span class="lineno"> 116</span> {1, 0}, {2, 0}}; <span class="comment">/// True Answer for test case 1</span></div>
<div class="line"><span class="lineno"> 117</span> </div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::complex&lt;double&gt;</a>&gt; r2 = {</div>
<div class="line"><span class="lineno"> 119</span> {1, 0}, {2, 0}, {3, 0}, {4, 0}}; <span class="comment">/// True Answer for test case 2</span></div>
<div class="line"><span class="lineno"> 120</span> </div>
<div class="line"><span class="lineno"> 121</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o1 =</div>
<div class="line"><span class="lineno"> 122</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t1, n1);</div>
<div class="line"><span class="lineno"> 123</span> </div>
<div class="line"><span class="lineno"> 124</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o2 =</div>
<div class="line"><span class="lineno"> 125</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t2, n2);</div>
<div class="line"><span class="lineno"> 126</span> </div>
<div class="line"><span class="lineno"> 127</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n1; i++) {</div>
<div class="line"><span class="lineno"> 128</span> assert((r1[i].real() - o1[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><span class="lineno"> 129</span> (r1[i].imag() - o1[i].imag() &lt;</div>
<div class="line"><span class="lineno"> 130</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 131</span><span class="comment"> /// values for test case 1</span></div>
<div class="line"><span class="lineno"> 132</span><span class="comment"></span> }</div>
<div class="line"><span class="lineno"> 133</span> </div>
<div class="line"><span class="lineno"> 134</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n2; i++) {</div>
<div class="line"><span class="lineno"> 135</span> assert((r2[i].real() - o2[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><span class="lineno"> 136</span> (r2[i].imag() - o2[i].imag() &lt;</div>
<div class="line"><span class="lineno"> 137</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 138</span><span class="comment"> /// values for test case 2</span></div>
<div class="line"><span class="lineno"> 139</span><span class="comment"></span> }</div>
<div class="line"><span class="lineno"> 140</span> </div>
<div class="line"><span class="lineno"> 141</span> <span class="keyword">delete</span>[] t1;</div>
<div class="line"><span class="lineno"> 142</span> <span class="keyword">delete</span>[] t2;</div>
<div class="line"><span class="lineno"> 143</span> <span class="keyword">delete</span>[] o1;</div>
<div class="line"><span class="lineno"> 144</span> <span class="keyword">delete</span>[] o2;</div>
<div class="line"><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 146</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 101</span> {</div>
<div class="line"><span class="lineno"> 102</span> <span class="comment">/* descriptions of the following test */</span></div>
<div class="line"><span class="lineno"> 103</span> </div>
<div class="line"><span class="lineno"> 104</span> <span class="keyword">auto</span> *t1 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[2]; <span class="comment">/// Test case 1</span></div>
<div class="line"><span class="lineno"> 105</span> <span class="keyword">auto</span> *t2 = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[4]; <span class="comment">/// Test case 2</span></div>
<div class="line"><span class="lineno"> 106</span> </div>
<div class="line"><span class="lineno"> 107</span> t1[0] = {3, 0};</div>
<div class="line"><span class="lineno"> 108</span> t1[1] = {-1, 0};</div>
<div class="line"><span class="lineno"> 109</span> t2[0] = {10, 0};</div>
<div class="line"><span class="lineno"> 110</span> t2[1] = {-2, -2};</div>
<div class="line"><span class="lineno"> 111</span> t2[2] = {-2, 0};</div>
<div class="line"><span class="lineno"> 112</span> t2[3] = {-2, 2};</div>
<div class="line"><span class="lineno"> 113</span> </div>
<div class="line"><span class="lineno"> 114</span> uint8_t n1 = 2;</div>
<div class="line"><span class="lineno"> 115</span> uint8_t n2 = 4;</div>
<div class="line"><span class="lineno"> 116</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::complex&lt;double&gt;</a>&gt; r1 = {</div>
<div class="line"><span class="lineno"> 117</span> {1, 0}, {2, 0}}; <span class="comment">/// True Answer for test case 1</span></div>
<div class="line"><span class="lineno"> 118</span> </div>
<div class="line"><span class="lineno"> 119</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::complex&lt;double&gt;</a>&gt; r2 = {</div>
<div class="line"><span class="lineno"> 120</span> {1, 0}, {2, 0}, {3, 0}, {4, 0}}; <span class="comment">/// True Answer for test case 2</span></div>
<div class="line"><span class="lineno"> 121</span> </div>
<div class="line"><span class="lineno"> 122</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o1 =</div>
<div class="line"><span class="lineno"> 123</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t1, n1);</div>
<div class="line"><span class="lineno"> 124</span> </div>
<div class="line"><span class="lineno"> 125</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *o2 =</div>
<div class="line"><span class="lineno"> 126</span> <a class="code hl_function" href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a>(t2, n2);</div>
<div class="line"><span class="lineno"> 127</span> </div>
<div class="line"><span class="lineno"> 128</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n1; i++) {</div>
<div class="line"><span class="lineno"> 129</span> assert((r1[i].real() - o1[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><span class="lineno"> 130</span> (r1[i].imag() - o1[i].imag() &lt;</div>
<div class="line"><span class="lineno"> 131</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 132</span><span class="comment"> /// values for test case 1</span></div>
<div class="line"><span class="lineno"> 133</span><span class="comment"></span> }</div>
<div class="line"><span class="lineno"> 134</span> </div>
<div class="line"><span class="lineno"> 135</span> <span class="keywordflow">for</span> (uint8_t i = 0; i &lt; n2; i++) {</div>
<div class="line"><span class="lineno"> 136</span> assert((r2[i].real() - o2[i].real() &lt; 0.000000000001) &amp;&amp;</div>
<div class="line"><span class="lineno"> 137</span> (r2[i].imag() - o2[i].imag() &lt;</div>
<div class="line"><span class="lineno"> 138</span> 0.000000000001)); <span class="comment">/// Comparing for both real and imaginary</span><span class="comment"></span></div>
<div class="line"><span class="lineno"> 139</span><span class="comment"> /// values for test case 2</span></div>
<div class="line"><span class="lineno"> 140</span><span class="comment"></span> }</div>
<div class="line"><span class="lineno"> 141</span> </div>
<div class="line"><span class="lineno"> 142</span> <span class="keyword">delete</span>[] t1;</div>
<div class="line"><span class="lineno"> 143</span> <span class="keyword">delete</span>[] t2;</div>
<div class="line"><span class="lineno"> 144</span> <span class="keyword">delete</span>[] o1;</div>
<div class="line"><span class="lineno"> 145</span> <span class="keyword">delete</span>[] o2;</div>
<div class="line"><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 147</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
<div class="ttc" id="anamespacenumerical__methods_html_aee56dc85997b8cd42bad71a5d6bd2d93"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * InverseFastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">InverseFastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition</b> inverse_fast_fourier_transform.cpp:33</div></div>
<div class="ttc" id="anamespacenumerical__methods_html_aee56dc85997b8cd42bad71a5d6bd2d93"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * InverseFastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">InverseFastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition</b> inverse_fast_fourier_transform.cpp:34</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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d9/d43/set__kth__bit_8cpp__incl.map
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<p>A simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 77</span> {</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// execute the tests</span></div>
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<p>Test function. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 57</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2:\t n=730\n&quot;</span>;</div>
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<div class="line"><span class="lineno"> 39</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 32</span> {</div>
<div class="line"><span class="lineno"> 33</span> <span class="comment">// If the input is 0 or 1 just return the same (Base Case)</span></div>
<div class="line"><span class="lineno"> 34</span> <span class="comment">// This will set the first 2 values of the sequence</span></div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">if</span> (n &lt;= 1) {</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">return</span> n;</div>
<div class="line"><span class="lineno"> 37</span> }</div>
<div class="line"><span class="lineno"> 38</span> </div>
<div class="line"><span class="lineno"> 39</span> <span class="comment">// Add the preceding 2 values of the sequence to get next</span></div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d76/namespacefibonacci.html">fibonacci</a>(n - 1) + <a class="code hl_namespace" href="../../df/d76/namespacefibonacci.html">fibonacci</a>(n - 2);</div>
<div class="line"><span class="lineno"> 41</span>}</div>
<div class="ttc" id="anamespacefibonacci_html"><div class="ttname"><a href="../../df/d76/namespacefibonacci.html">fibonacci</a></div><div class="ttdoc">Functions for Fibonacci sequence.</div></div>
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</div>
@@ -203,11 +204,11 @@ Functions</h2></td></tr>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> 0;</div>
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<div class="ttc" id="afibonacci_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementation.</div><div class="ttdef"><b>Definition</b> fibonacci.cpp:47</div></div>
<div class="fragment"><div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">return</span> 0;</div>
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Here is the call graph for this function:</div>
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@@ -241,16 +242,16 @@ Here is the call graph for this function:</div>
<p>Self-test implementation. </p>
<dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 47</span> {</div>
<div class="line"><span class="lineno"> 48</span> assert(math::fibonacci::fibonacci(0) == 0);</div>
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<div class="line"><span class="lineno"> 50</span> assert(math::fibonacci::fibonacci(2) == 1);</div>
<div class="line"><span class="lineno"> 51</span> assert(math::fibonacci::fibonacci(3) == 2);</div>
<div class="line"><span class="lineno"> 52</span> assert(math::fibonacci::fibonacci(4) == 3);</div>
<div class="line"><span class="lineno"> 53</span> assert(math::fibonacci::fibonacci(15) == 610);</div>
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<div class="line"><span class="lineno"> 55</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have passed successfully!\n&quot;</span>;</div>
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<div class="fragment"><div class="line"><span class="lineno"> 49</span> {</div>
<div class="line"><span class="lineno"> 50</span> assert(math::fibonacci::fibonacci(0) == 0);</div>
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<div class="line"><span class="lineno"> 52</span> assert(math::fibonacci::fibonacci(2) == 1);</div>
<div class="line"><span class="lineno"> 53</span> assert(math::fibonacci::fibonacci(3) == 2);</div>
<div class="line"><span class="lineno"> 54</span> assert(math::fibonacci::fibonacci(4) == 3);</div>
<div class="line"><span class="lineno"> 55</span> assert(math::fibonacci::fibonacci(15) == 610);</div>
<div class="line"><span class="lineno"> 56</span> assert(math::fibonacci::fibonacci(20) == 6765);</div>
<div class="line"><span class="lineno"> 57</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have passed successfully!\n&quot;</span>;</div>
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