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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Boy or Girl</div><div class="time-limit"><div class="property-title">time limit per test</div>1 second</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Those days, many boys use beautiful girls' photos as avatars in forums. So it is pretty hard to tell the gender of a user at the first glance. Last year, our hero went to a forum and had a nice chat with a beauty (he thought so). After that they talked very often and eventually they became a couple in the network. </p><p>But yesterday, he came to see "her" in the real world and found out "she" is actually a very strong man! Our hero is very sad and he is too tired to love again now. So he came up with a way to recognize users' genders by their user names.</p><p>This is his method: if the number of distinct characters in one's user name is odd, then he is a male, otherwise she is a female. You are given the string that denotes the user name, please help our hero to determine the gender of this user by his method.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a non-empty string, that contains only lowercase English letters — the user name. This string contains at most 100 letters.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If it is a female by our hero's method, print "<span class="tex-font-style-tt">CHAT WITH HER!</span>" (without the quotes), otherwise, print "<span class="tex-font-style-tt">IGNORE HIM!</span>" (without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>wjmzbmr<br /></pre></div><div class="output"><div class="title">Output</div><pre>CHAT WITH HER!<br /></pre></div><div class="input"><div class="title">Input</div><pre>xiaodao<br /></pre></div><div class="output"><div class="title">Output</div><pre>IGNORE HIM!<br /></pre></div><div class="input"><div class="title">Input</div><pre>sevenkplus<br /></pre></div><div class="output"><div class="title">Output</div><pre>CHAT WITH HER!<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>For the first example. There are 6 distinct characters in "<span class="tex-font-style-tt">wjmzbmr</span>". These characters are: "<span class="tex-font-style-tt">w</span>", "<span class="tex-font-style-tt">j</span>", "<span class="tex-font-style-tt">m</span>", "<span class="tex-font-style-tt">z</span>", "<span class="tex-font-style-tt">b</span>", "<span class="tex-font-style-tt">r</span>". So wjmzbmr is a female and you should print "<span class="tex-font-style-tt">CHAT WITH HER!</span>".</p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Easy Number Challenge</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Let's denote <span class="tex-span"><i>d</i>(<i>n</i>)</span> as the number of divisors of a positive integer <span class="tex-span"><i>n</i></span>. You are given three integers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span>. Your task is to calculate the following sum:</p><center class="tex-equation"><img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e052a04f766eb3e258c0b4a039f8da531d8ac734.png" style="max-width: 100.0%;max-height: 100.0%;" /></center><p>Find the sum modulo <span class="tex-span">1073741824</span> <span class="tex-span">(2<sup class="upper-index">30</sup>)</span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three space-separated integers <span class="tex-span"><i>a</i></span>, <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span> (<span class="tex-span">1 ≤ <i>a</i>, <i>b</i>, <i>c</i> ≤ 100</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer — the required sum modulo <span class="tex-span">1073741824</span> <span class="tex-span">(2<sup class="upper-index">30</sup>)</span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>2 2 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>20<br /></pre></div><div class="input"><div class="title">Input</div><pre>5 6 7<br /></pre></div><div class="output"><div class="title">Output</div><pre>1520<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>For the first example.</p><ul> <li> <span class="tex-span"><i>d</i>(1·1·1) = <i>d</i>(1) = 1</span>; </li><li> <span class="tex-span"><i>d</i>(1·1·2) = <i>d</i>(2) = 2</span>; </li><li> <span class="tex-span"><i>d</i>(1·2·1) = <i>d</i>(2) = 2</span>; </li><li> <span class="tex-span"><i>d</i>(1·2·2) = <i>d</i>(4) = 3</span>; </li><li> <span class="tex-span"><i>d</i>(2·1·1) = <i>d</i>(2) = 2</span>; </li><li> <span class="tex-span"><i>d</i>(2·1·2) = <i>d</i>(4) = 3</span>; </li><li> <span class="tex-span"><i>d</i>(2·2·1) = <i>d</i>(4) = 3</span>; </li><li> <span class="tex-span"><i>d</i>(2·2·2) = <i>d</i>(8) = 4</span>. </li></ul><p>So the result is <span class="tex-span">1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20</span>.</p></div></div></div>
|
|||
|
|
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|
|||
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|
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|
<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. LCM Challenge</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.</p><p>But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than <span class="tex-span"><i>n</i></span>. Can you help me to find the maximum possible least common multiple of these three integers?</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">6</sup></span>) — the <span class="tex-span"><i>n</i></span> mentioned in the statement.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than <span class="tex-span"><i>n</i></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>9<br /></pre></div><div class="output"><div class="title">Output</div><pre>504<br /></pre></div><div class="input"><div class="title">Input</div><pre>7<br /></pre></div><div class="output"><div class="title">Output</div><pre>210<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The least common multiple of some positive integers is the least positive integer which is multiple for each of them.</p><p>The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.</p><p>For the last example, we can chose numbers <span class="tex-span">7</span>, <span class="tex-span">6</span>, <span class="tex-span">5</span> and the LCM of them is <span class="tex-span">7·6·5 = 210</span>. It is the maximum value we can get.</p></div></div></div>
|
|||
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Let's Play Osu!</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You're playing a game called Osu! Here's a simplified version of it. There are <span class="tex-span"><i>n</i></span> clicks in a game. For each click there are two outcomes: correct or bad. Let us denote correct as "<span class="tex-font-style-tt">O</span>", bad as "<span class="tex-font-style-tt">X</span>", then the whole play can be encoded as a sequence of <span class="tex-span"><i>n</i></span> characters "<span class="tex-font-style-tt">O</span>" and "<span class="tex-font-style-tt">X</span>".</p><p>Using the play sequence you can calculate the score for the play as follows: for every maximal consecutive "<span class="tex-font-style-tt">O</span>"s block, add the square of its length (the number of characters "<span class="tex-font-style-tt">O</span>") to the score. For example, if your play can be encoded as "<span class="tex-font-style-tt">OOXOOOXXOO</span>", then there's three maximal consecutive "<span class="tex-font-style-tt">O</span>"s block "<span class="tex-font-style-tt">OO</span>", "<span class="tex-font-style-tt">OOO</span>", "<span class="tex-font-style-tt">OO</span>", so your score will be <span class="tex-span">2<sup class="upper-index">2</sup> + 3<sup class="upper-index">2</sup> + 2<sup class="upper-index">2</sup> = 17</span>. If there are no correct clicks in a play then the score for the play equals to <span class="tex-span">0</span>.</p><p>You know that the probability to click the <span class="tex-span"><i>i</i></span>-th <span class="tex-span">(1 ≤ <i>i</i> ≤ <i>n</i>)</span> click correctly is <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>. In other words, the <span class="tex-span"><i>i</i></span>-th character in the play sequence has <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span> probability to be "<span class="tex-font-style-tt">O</span>", <span class="tex-span">1 - <i>p</i><sub class="lower-index"><i>i</i></sub></span> to be "<span class="tex-font-style-tt">X</span>". You task is to calculate the expected score for your play.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) — the number of clicks. The second line contains <span class="tex-span"><i>n</i></span> space-separated real numbers <span class="tex-span"><i>p</i><sub class="lower-index">1</sub>, <i>p</i><sub class="lower-index">2</sub>, ..., <i>p</i><sub class="lower-index"><i>n</i></sub></span> <span class="tex-span">(0 ≤ <i>p</i><sub class="lower-index"><i>i</i></sub> ≤ 1)</span>.</p><p>There will be at most six digits after the decimal point in the given <span class="tex-span"><i>p</i><sub class="lower-index"><i>i</i></sub></span>.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single real number — the expected score for your play. Your answer will be considered correct if its absolute or relative error does not exceed <span class="tex-span">10<sup class="upper-index"> - 6</sup></span>.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>3<br />0.5 0.5 0.5<br /></pre></div><div class="output"><div class="title">Output</div><pre>2.750000000000000<br /></
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Cyclical Quest</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>512 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Some days ago, WJMZBMR learned how to answer the query "how many times does a string <span class="tex-span"><i>x</i></span> occur in a string <span class="tex-span"><i>s</i></span>" quickly by preprocessing the string <span class="tex-span"><i>s</i></span>. But now he wants to make it harder.</p><p>So he wants to ask "how many consecutive substrings of <span class="tex-span"><i>s</i></span> are cyclical isomorphic to a given string <span class="tex-span"><i>x</i></span>". You are given string <span class="tex-span"><i>s</i></span> and <span class="tex-span"><i>n</i></span> strings <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>, for each string <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> find, how many consecutive substrings of <span class="tex-span"><i>s</i></span> are cyclical isomorphic to <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>.</p><p>Two strings are called <span class="tex-font-style-it">cyclical isomorphic</span> if one can rotate one string to get the other one. 'Rotate' here means 'to take some consecutive chars (maybe none) from the beginning of a string and put them back at the end of the string in the same order'. For example, string "<span class="tex-font-style-tt">abcde</span>" can be rotated to string "<span class="tex-font-style-tt">deabc</span>". We can take characters "<span class="tex-font-style-tt">abc</span>" from the beginning and put them at the end of "<span class="tex-font-style-tt">de</span>".</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains a non-empty string <span class="tex-span"><i>s</i></span>. The length of string <span class="tex-span"><i>s</i></span> is not greater than <span class="tex-span">10<sup class="upper-index">6</sup></span> characters.</p><p>The second line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) — the number of queries. Then <span class="tex-span"><i>n</i></span> lines follow: the <span class="tex-span"><i>i</i></span>-th line contains the string <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> — the string for the <span class="tex-span"><i>i</i></span>-th query. The total length of <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> is less than or equal to <span class="tex-span">10<sup class="upper-index">6</sup></span> characters.</p><p>In this problem, strings only consist of lowercase English letters.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each query <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> print a single integer that shows how many consecutive substrings of <span class="tex-span"><i>s</i></span> are cyclical isomorphic to <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>. Print the answers to the queries in the order they are given in the input.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>baabaabaaa<br />5<br />a<br />ba<br />baa<br />aabaa<br />aaba<br /></pre></div><div class="output"><div class="title">Output</div><pre>7<br />5<br />7<br />3<br />5<br /></pre></div><div class="input"><div class="title">Input</div><pre>aabbaa<br />3<br />aa<br />aabb<br />abba<br /></pre>
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