prithivMLmods/Coder-Stat

1<H1>Party</H1>2 3<p>4  The students in a class in Akabe high-school define the relation “acquaintance” as: 5</p>6 7<ul>8<li>If A and B are friends, then A is acquainted with B.</li>9<li>If A and B are friends and B is acquainted with C, then A is acquainted with C.</li>10</ul>11 12<p>13  They define the relation “companion” as:14</p>15 16<ul>17  <!-- Suppose A is acquainted with B, and some classmate who has been friends with A and B distances himself from them. If A is still acquainted with B, then A and B are companions.-->18 19  <li>20    Suppose A is acquainted with B, and two classmates who have been friend distance. If A is still acquainted with B, then A and B are companions.21  </li>22  23</ul>24 25<p>26A boy PCK joined the class recently and wishes to hold a party inviting his class fellows. He wishes to invite as many boys and girls as possible to the party and has written up an invitation list. In arranging the list, he placed the following conditions based on the acquaintanceship within the class before he joined.27</p>28 29<p>30  When T is in the list:31</p>32<ul>33<li>U is listed if he/she is a companion of T.</li>34<li>If U is not a companion of T, U is not listed if he/she and T are friends, or he/she and some of T’s companions are friends.</li>35</ul>36 37 38 39 40 41<p>42  PCK made the invitation list so that the maximum number of his classmates is included.43</p>44 45<p>46  Given the number of classmates <var>N</var> and the friendships among them, write a program to estimate the number of boys and girls in the list. All the classmates are identified by an index that ranges from 0 to <var>N</var>-1.47</p>48 49 50<h2>Input</h2>51 52<p>53  The input is given in the following format.54</p>55 56<pre>57<var>N</var> <var>M</var>58<var>s_1</var> <var>t_1</var>59<var>s_2</var> <var>t_2</var>60:61<var>s_M</var> <var>t_M</var>62</pre>63 64<p>65The first line provides the number of classmates <var>N</var> (2 &le; <var>N</var> &le; 10<sup>5</sup>) and the number of friendships <var>M</var> (1 &le; <var>M</var> &le; 2&times;10<sup>5</sup>). Each of the <var>M</var> subsequent lines provides two of the classmates <var>s_i, t_i</var> (0 &le; <var>s_i,t_i</var> &le; <var>N</var>-1) indicating they are friends. No duplicate relationship appears among these lines.66</p>67 68 69<h2>Output</h2>70 71<p>72  Output the maximum number of classmates PCK invited to the party.73</p>74 75<h2>Sample Input 1</h2>76 77<pre>787 8790 1801 2811 3822 3830 4844 5854 6865 687</pre>88 89<h2>Sample Output 1</h2>90<pre>91692</pre>93 94 95<h2>Sample Input 2</h2>96 97<pre>983 2990 11001 2101</pre>102 103<h2>Sample Output 2</h2>104<pre>1052106</pre>107