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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Elephant</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>An elephant decided to visit his friend. It turned out that the elephant's house is located at point <span class="tex-span">0</span> and his friend's house is located at point <span class="tex-span"><i>x</i>(<i>x</i> > 0)</span> of the coordinate line. In one step the elephant can move <span class="tex-span">1</span>, <span class="tex-span">2</span>, <span class="tex-span">3</span>, <span class="tex-span">4</span> or <span class="tex-span">5</span> positions forward. Determine, what is the minimum number of steps he need to make in order to get to his friend's house.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains an integer <span class="tex-span"><i>x</i></span> (<span class="tex-span">1 ≤ <i>x</i> ≤ 1 000 000</span>) — The coordinate of the friend's house.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the minimum number of steps that elephant needs to make to get from point <span class="tex-span">0</span> to point <span class="tex-span"><i>x</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>5<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>12<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample the elephant needs to make one step of length <span class="tex-span">5</span> to reach the point <span class="tex-span"><i>x</i></span>.</p><p>In the second sample the elephant can get to point <span class="tex-span"><i>x</i></span> if he moves by <span class="tex-span">3</span>, <span class="tex-span">5</span> and <span class="tex-span">4</span>. There are other ways to get the optimal answer but the elephant cannot reach <span class="tex-span"><i>x</i></span> in less than three moves.</p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Chocolate</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>Bob loves everything sweet. His favorite chocolate bar consists of pieces, each piece may contain a nut. Bob wants to break the bar of chocolate into multiple pieces so that each part would contain <span class="tex-font-style-bf">exactly</span> one nut and any break line goes between two adjacent pieces.</p><p>You are asked to calculate the number of ways he can do it. Two ways to break chocolate are considered distinct if one of them contains a break between some two adjacent pieces and the other one doesn't. </p><p>Please note, that if Bob doesn't make any breaks, all the bar will form one piece and it still has to have exactly one nut.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 100</span>) — the number of pieces in the chocolate bar.</p><p>The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 1</span>), where <span class="tex-span">0</span> represents a piece without the nut and <span class="tex-span">1</span> stands for a piece with the nut.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the number of ways to break the chocolate into multiple parts so that each part would contain exactly one nut.</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 1 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>5<br />1 0 1 0 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>4<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample there is exactly one nut, so the number of ways equals <span class="tex-span">1</span> — Bob shouldn't make any breaks.</p><p>In the second sample you can break the bar in four ways:</p><p><span class="tex-font-style-tt">10|10|1</span></p><p><span class="tex-font-style-tt">1|010|1</span></p><p><span class="tex-font-style-tt">10|1|01</span></p><p><span class="tex-font-style-tt">1|01|01</span></p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Watering Flowers</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>A flowerbed has many flowers and two fountains.</p><p>You can adjust the water pressure and set any values <span class="tex-span"><i>r</i><sub class="lower-index">1</sub>(<i>r</i><sub class="lower-index">1</sub> ≥ 0)</span> and <span class="tex-span"><i>r</i><sub class="lower-index">2</sub>(<i>r</i><sub class="lower-index">2</sub> ≥ 0)</span>, giving the distances at which the water is spread from the first and second fountain respectively. You have to set such <span class="tex-span"><i>r</i><sub class="lower-index">1</sub></span> and <span class="tex-span"><i>r</i><sub class="lower-index">2</sub></span> that all the flowers are watered, that is, for each flower, the distance between the flower and the first fountain doesn't exceed <span class="tex-span"><i>r</i><sub class="lower-index">1</sub></span>, or the distance to the second fountain doesn't exceed <span class="tex-span"><i>r</i><sub class="lower-index">2</sub></span>. It's OK if some flowers are watered by both fountains.</p><p>You need to decrease the amount of water you need, that is set such <span class="tex-span"><i>r</i><sub class="lower-index">1</sub></span> and <span class="tex-span"><i>r</i><sub class="lower-index">2</sub></span> that all the flowers are watered and the <span class="tex-span"><i>r</i><sub class="lower-index">1</sub><sup class="upper-index">2</sup> + <i>r</i><sub class="lower-index">2</sub><sup class="upper-index">2</sup></span> is minimum possible. Find this minimum value.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>x</i><sub class="lower-index">1</sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">1</sub></span>, <span class="tex-span"><i>x</i><sub class="lower-index">2</sub></span>, <span class="tex-span"><i>y</i><sub class="lower-index">2</sub></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 2000</span>, <span class="tex-span"> - 10<sup class="upper-index">7</sup> ≤ <i>x</i><sub class="lower-index">1</sub>, <i>y</i><sub class="lower-index">1</sub>, <i>x</i><sub class="lower-index">2</sub>, <i>y</i><sub class="lower-index">2</sub> ≤ 10<sup class="upper-index">7</sup></span>) — the number of flowers, the coordinates of the first and the second fountain.</p><p>Next follow <span class="tex-span"><i>n</i></span> lines. The <span class="tex-span"><i>i</i></span>-th of these lines contains integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span"> - 10<sup class="upper-index">7</sup> ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">7</sup></span>) — the coordinates of the <span class="tex-span"><i>i</i></span>-th flower.</p><p>It is guaranteed that all <span class="tex-span"><i>n</i> + 2</span> points in the input are distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the minimum possible value <span class="tex-span"><i>r</i><sub class="lower-index">1</sub><sup class="upper-index">2</sup> + <i>r</i><sub class="lower-index">2</sub><sup class="upper-index">2</sup></span>. Note, that in this problem optimal answer is always integer.</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 -1 0 5 3<br />0 2<br />5 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>6<br /></pre></div><div class="input"><div class="title">Input</div><pre>4 0 0 5 0<br />9 4<br />8 3<br />-1 0<br />1 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>33<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The first sample is (<span class="tex-span"><i>r</i><sub class="lower-index">1</sub><sup class="upper-index">2</sup> = 5</span>, <span class="tex-span"><i>r</i><sub class="lower-index">2</sub><sup class="upper-index">2</sup> = 1</span>): <img class="tex-graphics" src="https://espresso.codeforces.com/15e780f508832a19b14698dd8eb54b4c0dd131bf.png" style="max-width: 100.0%;max-height: 100.0%;" /> The second sample is (<span class="tex-span"><i>r</i><sub class="lower-index">1</sub><sup class="upper-index">2</sup> = 1</span>, <span class="tex-span"><i>r</i><sub class="lower-index">2</sub><sup class="upper-index">2</sup> = 32</span>): <img class="tex-graphics" src="https://espresso.codeforces.com/da4dc31002cc9b37092d64035ab56ad8544c0d7b.png" style="max-width: 100.0%;max-height: 100.0%;" /></p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Polyline</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>There are three points marked on the coordinate plane. The goal is to make a simple polyline, without self-intersections and self-touches, such that it passes through all these points. Also, the polyline must consist of only segments parallel to the coordinate axes. You are to find the minimum number of segments this polyline may consist of.</p></div><div class="input-specification"><div class="section-title">Input</div><p>Each of the three lines of the input contains two integers. The <span class="tex-span"><i>i</i></span>-th line contains integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span"> - 10<sup class="upper-index">9</sup> ≤ <i>x</i><sub class="lower-index"><i>i</i></sub>, <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>) — the coordinates of the <span class="tex-span"><i>i</i></span>-th point. It is guaranteed that all points are distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single number — the minimum possible number of segments of the polyline.</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>1 -1<br />1 1<br />1 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div><div class="input"><div class="title">Input</div><pre>-1 -1<br />-1 3<br />4 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>2<br /></pre></div><div class="input"><div class="title">Input</div><pre>1 1<br />2 3<br />3 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The variant of the polyline in the first sample: <img class="tex-graphics" src="https://espresso.codeforces.com/b41b4dad8437bd7a69f6ab01eaedf010b82ba7b8.png" style="max-width: 100.0%;max-height: 100.0%;" /> The variant of the polyline in the second sample: <img class="tex-graphics" src="https://espresso.codeforces.com/7410d2247b3381e5b27422609f90ff027e071812.png" style="max-width: 100.0%;max-height: 100.0%;" /> The variant of the polyline in the third sample: <img class="tex-graphics" src="https://espresso.codeforces.com/3a5018422eb982f0a2a9bd7f1fd7ab23777a0813.png" style="max-width: 100.0%;max-height: 100.0%;" /></p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. XOR and Favorite Number</div><div class="time-limit"><div class="property-title">time limit per test</div>4 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>Bob has a favorite number <span class="tex-span"><i>k</i></span> and <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> of length <span class="tex-span"><i>n</i></span>. Now he asks you to answer <span class="tex-span"><i>m</i></span> queries. Each query is given by a pair <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span> and asks you to count the number of pairs of integers <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span>, such that <span class="tex-span"><i>l</i> ≤ <i>i</i> ≤ <i>j</i> ≤ <i>r</i></span> and the xor of the numbers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub>, <i>a</i><sub class="lower-index"><i>i</i> + 1</sub>, ..., <i>a</i><sub class="lower-index"><i>j</i></sub></span> is equal to <span class="tex-span"><i>k</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 100 000</span>, <span class="tex-span">0 ≤ <i>k</i> ≤ 1 000 000</span>) — the length of the array, the number of queries and Bob's favorite number respectively.</p><p>The second line contains <span class="tex-span"><i>n</i></span> integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 1 000 000</span>) — Bob's array.</p><p>Then <span class="tex-span"><i>m</i></span> lines follow. The <span class="tex-span"><i>i</i></span>-th line contains integers <span class="tex-span"><i>l</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>r</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>l</i><sub class="lower-index"><i>i</i></sub> ≤ <i>r</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>) — the parameters of the <span class="tex-span"><i>i</i></span>-th query.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>m</i></span> lines, answer the queries in the order they appear 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>6 2 3<br />1 2 1 1 0 3<br />1 6<br />3 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>7<br />0<br /></pre></div><div class="input"><div class="title">Input</div><pre>5 3 1<br />1 1 1 1 1<br />1 5<br />2 4<br />1 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>9<br />4<br />4<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample the suitable pairs of <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> for the first query are: (<span class="tex-span">1</span>, <span class="tex-span">2</span>), (<span class="tex-span">1</span>, <span class="tex-span">4</span>), (<span class="tex-span">1</span>, <span class="tex-span">5</span>), (<span class="tex-span">2</span>, <span class="tex-span">3</span>), (<span class="tex-span">3</span>, <span class="tex-span">6</span>), (<span class="tex-span">5</span>, <span class="tex-span">6</span>), (<span class="tex-span">6</span>, <span class="tex-span">6</span>). Not a single of these pairs is suitable for the second query.</p><p>In the second sample xor equals <span class="tex-span">1</span> for all subarrays of an odd length.</p></div></div></div>
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