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<a href="#define-members">Macros</a> &#124;
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<p><a href="https://projecteuler.net/problem=25" target="_blank">Problem 25</a> solution implemented using arbitrarily large numbers represented as arrays
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;stdint.h&gt;</code><br />
<code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;stdlib.h&gt;</code><br />
<code>#include &lt;string.h&gt;</code><br />
<code>#include &lt;time.h&gt;</code><br />
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Include dependency graph for sol1.c:</div>
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Macros</h2></td></tr>
<tr class="memitem:a001791a21d538b8b9176287ae60d9b61"><td class="memItemLeft" align="right" valign="top"><a id="a001791a21d538b8b9176287ae60d9b61" name="a001791a21d538b8b9176287ae60d9b61"></a>
#define&#160;</td><td class="memItemRight" valign="bottom"><b>MAX_DIGITS</b>&#160;&#160;&#160;1000</td></tr>
<tr class="memdesc:a001791a21d538b8b9176287ae60d9b61"><td class="mdescLeft">&#160;</td><td class="mdescRight">maximum number of digits <br /></td></tr>
<tr class="separator:a001791a21d538b8b9176287ae60d9b61"><td class="memSeparator" colspan="2">&#160;</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:af9729befaffc1aab9ac9fedc4706e66c"><td class="memItemLeft" align="right" valign="top">unsigned int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d32/problem__25_2sol1_8c.html#af9729befaffc1aab9ac9fedc4706e66c">add_numbers</a> (unsigned char *a, unsigned char *b, unsigned char *c, int N)</td></tr>
<tr class="memdesc:af9729befaffc1aab9ac9fedc4706e66c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to add arbitraty length decimal integers stored in an array. <a href="../../d8/d32/problem__25_2sol1_8c.html#af9729befaffc1aab9ac9fedc4706e66c">More...</a><br /></td></tr>
<tr class="separator:af9729befaffc1aab9ac9fedc4706e66c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abe5bc1f170b2108a19d0a16d30bd3235"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d32/problem__25_2sol1_8c.html#abe5bc1f170b2108a19d0a16d30bd3235">print_number</a> (unsigned char *number, int N)</td></tr>
<tr class="memdesc:abe5bc1f170b2108a19d0a16d30bd3235"><td class="mdescLeft">&#160;</td><td class="mdescRight">Print a large number. <a href="../../d8/d32/problem__25_2sol1_8c.html#abe5bc1f170b2108a19d0a16d30bd3235">More...</a><br /></td></tr>
<tr class="separator:abe5bc1f170b2108a19d0a16d30bd3235"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2b90df6bfbf0d18cd9a19c1a71453783"><td class="memItemLeft" align="right" valign="top">unsigned int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d32/problem__25_2sol1_8c.html#a2b90df6bfbf0d18cd9a19c1a71453783">get_digits</a> (unsigned char *number)</td></tr>
<tr class="memdesc:a2b90df6bfbf0d18cd9a19c1a71453783"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get number of digits in a large number. <a href="../../d8/d32/problem__25_2sol1_8c.html#a2b90df6bfbf0d18cd9a19c1a71453783">More...</a><br /></td></tr>
<tr class="separator:a2b90df6bfbf0d18cd9a19c1a71453783"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d32/problem__25_2sol1_8c.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d8/d32/problem__25_2sol1_8c.html#a0ddf1224851353fc92bfbff6f499fa97">More...</a><br /></td></tr>
<tr class="separator:a0ddf1224851353fc92bfbff6f499fa97"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://projecteuler.net/problem=25" target="_blank">Problem 25</a> solution implemented using arbitrarily large numbers represented as arrays </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="af9729befaffc1aab9ac9fedc4706e66c" name="af9729befaffc1aab9ac9fedc4706e66c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af9729befaffc1aab9ac9fedc4706e66c">&#9670;&nbsp;</a></span>add_numbers()</h2>
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<td class="memname">unsigned int add_numbers </td>
<td>(</td>
<td class="paramtype">unsigned char *&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned char *&#160;</td>
<td class="paramname"><em>b</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned char *&#160;</td>
<td class="paramname"><em>c</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>N</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Function to add arbitraty length decimal integers stored in an array. </p>
<p ><br />
a + b = c = new b </p>
<div class="fragment"><div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span>{</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span> carry = 0;</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keywordflow">for</span> (i = 0; i &lt; N; i++)</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// printf(&quot;\t%d + %d + %d &quot;, a[i], b[i], carry);</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> c[i] = carry + a[i] + b[i];</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordflow">if</span> (c[i] &gt; 9) <span class="comment">/* check for carry */</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> carry = 1;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> c[i] -= 10;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> }</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> {</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> carry = 0;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// printf(&quot;= %d, %d\n&quot;, carry, c[i]);</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> }</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">while</span> (carry != 0)</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// printf(&quot;\t\t...adding new digit\n&quot;);</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// printf(&quot;\t0 + %d + %d &quot;, b[i], carry);</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> c[i] = carry + c[i];</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">if</span> (c[i] &gt; 9)</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> carry = 1;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> c[i] -= 10;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> carry = 0;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// printf(&quot;= %d, %d\n&quot;, carry, c[i]);</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> i++;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">return</span> i;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span>}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a2b90df6bfbf0d18cd9a19c1a71453783" name="a2b90df6bfbf0d18cd9a19c1a71453783"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2b90df6bfbf0d18cd9a19c1a71453783">&#9670;&nbsp;</a></span>get_digits()</h2>
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<td class="memname">unsigned int get_digits </td>
<td>(</td>
<td class="paramtype">unsigned char *&#160;</td>
<td class="paramname"><em>number</em></td><td>)</td>
<td></td>
</tr>
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</div><div class="memdoc">
<p>Get number of digits in a large number. </p>
<div class="fragment"><div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span>{</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> digits = <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">while</span> (number[digits] == 0) digits--;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">return</span> digits;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>}</div>
<div class="ttc" id="aproblem__25_2sol1_8c_html_a001791a21d538b8b9176287ae60d9b61"><div class="ttname"><a href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a></div><div class="ttdeci">#define MAX_DIGITS</div><div class="ttdoc">maximum number of digits</div><div class="ttdef"><b>Definition:</b> sol1.c:13</div></div>
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</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char *&#160;</td>
<td class="paramname"><em>argv</em>[]&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Main function. </p>
<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span>{</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> fn[<a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a> + 1]; <span class="comment">/* array to store digits of a large number */</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span> fn1[<a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a> + 1];</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span> sum[<a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a> + 1];</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> memset(fn, 0, <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> memset(fn1, 0, <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>);</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> memset(sum, 0, <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> fn[0] = 1;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> fn1[1] = 1;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> index = 1, digit_count = 1;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> </div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> clock_t start_time = clock();</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">do</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> digit_count = <a class="code hl_function" href="../../db/d01/problem__13_2sol1_8c.html#ad51742ca5a5c99e860bdf30299163bf2">add_numbers</a>(fn, fn1, sum, digit_count);</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// digit_count = get_digits(sum);</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// printf(&quot;%5u (%u) (%u) &quot;, index, digit_count, get_digits(sum));</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// print_number(sum, digit_count);</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// putchar(&#39;\n&#39;);</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keywordflow">if</span> (digit_count == <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>)</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> {</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> }</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> memcpy(fn, fn1, <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> memcpy(fn1, sum, <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>);</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> index++;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> } <span class="keywordflow">while</span> (digit_count &lt; <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>);</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> clock_t end_time = clock();</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> printf(<span class="stringliteral">&quot;Time taken: %.4g ms\n&quot;</span>,</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> 1e3 * (end_time - start_time) / CLOCKS_PER_SEC);</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> printf(<span class="stringliteral">&quot;The nth term for %d digits: %u \n&quot;</span>, <a class="code hl_define" href="../../d8/d32/problem__25_2sol1_8c.html#a001791a21d538b8b9176287ae60d9b61">MAX_DIGITS</a>, index--);</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_function" href="../../db/d01/problem__13_2sol1_8c.html#a248adc917818cc6666d8bc679a660319">print_number</a>(sum, digit_count);</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> </div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span>}</div>
<div class="ttc" id="aproblem__13_2sol1_8c_html_a248adc917818cc6666d8bc679a660319"><div class="ttname"><a href="../../db/d01/problem__13_2sol1_8c.html#a248adc917818cc6666d8bc679a660319">print_number</a></div><div class="ttdeci">int print_number(uint8_t *number, uint8_t N, int8_t num_digits_to_print)</div><div class="ttdoc">Function to print a long number.</div><div class="ttdef"><b>Definition:</b> sol1.c:92</div></div>
<div class="ttc" id="aproblem__13_2sol1_8c_html_ad51742ca5a5c99e860bdf30299163bf2"><div class="ttname"><a href="../../db/d01/problem__13_2sol1_8c.html#ad51742ca5a5c99e860bdf30299163bf2">add_numbers</a></div><div class="ttdeci">int add_numbers(uint8_t *a, uint8_t *b, uint8_t N)</div><div class="ttdoc">Function to add arbitrary length decimal integers stored in an array.</div><div class="ttdef"><b>Definition:</b> sol1.c:48</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#abe5bc1f170b2108a19d0a16d30bd3235">&#9670;&nbsp;</a></span>print_number()</h2>
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<td class="memname">int print_number </td>
<td>(</td>
<td class="paramtype">unsigned char *&#160;</td>
<td class="paramname"><em>number</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>N</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>Print a large number. </p>
<div class="fragment"><div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>{</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordtype">int</span> start_pos = N - 1;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">/* skip all initial zeros */</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">while</span> (number[start_pos] == 0) start_pos--;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = start_pos; i &gt;= 0; i--) putchar(number[i] + 0x30);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span>}</div>
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