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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Stones on the Table</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>There are <span class="tex-span"><i>n</i></span> stones on the table in a row, each of them can be red, green or blue. Count the minimum number of stones to take from the table so that any two neighboring stones had different colors. Stones in a row are considered neighboring if there are no other stones between them.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains integer <span class="tex-span"><i>n</i></span> <span class="tex-span">(1 ≤ <i>n</i> ≤ 50)</span> — the number of stones on the table. </p><p>The next line contains string <span class="tex-span"><i>s</i></span>, which represents the colors of the stones. We'll consider the stones in the row numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from left to right. Then the <span class="tex-span"><i>i</i></span>-th character <span class="tex-span"><i>s</i></span> equals "<span class="tex-font-style-tt">R</span>", if the <span class="tex-span"><i>i</i></span>-th stone is red, "<span class="tex-font-style-tt">G</span>", if it's green and "<span class="tex-font-style-tt">B</span>", if it's blue.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer — the answer to the problem.</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 />RRG<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 />RRRRR<br /></pre></div><div class="output"><div class="title">Output</div><pre>4<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />BRBG<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br /></pre></div></div></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Queue at the School</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>During the break the schoolchildren, boys and girls, formed a queue of <span class="tex-span"><i>n</i></span> people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started letting the girls move forward each second. </p><p>Let's describe the process more precisely. Let's say that the positions in the queue are sequentially numbered by integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>, at that the person in the position number <span class="tex-span">1</span> is served first. Then, if at time <span class="tex-span"><i>x</i></span> a boy stands on the <span class="tex-span"><i>i</i></span>-th position and a girl stands on the <span class="tex-span">(<i>i</i> + 1)</span>-th position, then at time <span class="tex-span"><i>x</i> + 1</span> the <span class="tex-span"><i>i</i></span>-th position will have a girl and the <span class="tex-span">(<i>i</i> + 1)</span>-th position will have a boy. The time is given in seconds.</p><p>You've got the initial position of the children, at the initial moment of time. Determine the way the queue is going to look after <span class="tex-span"><i>t</i></span> seconds.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>t</i></span> <span class="tex-span">(1 ≤ <i>n</i>, <i>t</i> ≤ 50)</span>, which represent the number of children in the queue and the time after which the queue will transform into the arrangement you need to find. </p><p>The next line contains string <span class="tex-span"><i>s</i></span>, which represents the schoolchildren's initial arrangement. If the <span class="tex-span"><i>i</i></span>-th position in the queue contains a boy, then the <span class="tex-span"><i>i</i></span>-th character of string <span class="tex-span"><i>s</i></span> equals "<span class="tex-font-style-tt">B</span>", otherwise the <span class="tex-span"><i>i</i></span>-th character equals "<span class="tex-font-style-tt">G</span>".</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print string <span class="tex-span"><i>a</i></span>, which describes the arrangement after <span class="tex-span"><i>t</i></span> seconds. If the <span class="tex-span"><i>i</i></span>-th position has a boy after the needed time, then the <span class="tex-span"><i>i</i></span>-th character <span class="tex-span"><i>a</i></span> must equal "<span class="tex-font-style-tt">B</span>", otherwise it must equal "<span class="tex-font-style-tt">G</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 1<br />BGGBG<br /></pre></div><div class="output"><div class="title">Output</div><pre>GBGGB<br /></pre></div><div class="input"><div class="title">Input</div><pre>5 2<br />BGGBG<br /></pre></div><div class="output"><div class="title">Output</div><pre>GGBGB<br /></pre></div><div class="input"><div class="title">Input</div><pre>4 1<br />GGGB<br /></pre></div><div class="output"><div class="title">Output</div><pre>GGGB<br /></pre></div></div></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Below the Diagonal</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 are given a square matrix consisting of <span class="tex-span"><i>n</i></span> rows and <span class="tex-span"><i>n</i></span> columns. We assume that the rows are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from top to bottom and the columns are numbered from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> from left to right. Some cells (<span class="tex-span"><i>n</i> - 1</span> cells in total) of the the matrix are filled with ones, the remaining cells are filled with zeros. We can apply the following operations to the matrix:</p><ol> <li> Swap <span class="tex-span"><i>i</i></span>-th and <span class="tex-span"><i>j</i></span>-th rows of the matrix; </li><li> Swap <span class="tex-span"><i>i</i></span>-th and <span class="tex-span"><i>j</i></span>-th columns of the matrix. </li></ol><p>You are asked to transform the matrix into a special form using these operations. In that special form all the ones must be in the cells that lie below the main diagonal. Cell of the matrix, which is located on the intersection of the <span class="tex-span"><i>i</i></span>-th row and of the <span class="tex-span"><i>j</i></span>-th column, lies below the main diagonal if <span class="tex-span"><i>i</i> > <i>j</i></span>.</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">(2 ≤ <i>n</i> ≤ 1000)</span> — the number of rows and columns. Then follow <span class="tex-span"><i>n</i> - 1</span> lines that contain one's positions, one per line. Each position is described by two integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>k</i></sub>, <i>y</i><sub class="lower-index"><i>k</i></sub></span> <span class="tex-span">(1 ≤ <i>x</i><sub class="lower-index"><i>k</i></sub>, <i>y</i><sub class="lower-index"><i>k</i></sub> ≤ <i>n</i>)</span>, separated by a space. A pair <span class="tex-span">(<i>x</i><sub class="lower-index"><i>k</i></sub>, <i>y</i><sub class="lower-index"><i>k</i></sub>)</span> means that the cell, which is located on the intersection of the <span class="tex-span"><i>x</i><sub class="lower-index"><i>k</i></sub></span>-th row and of the <span class="tex-span"><i>y</i><sub class="lower-index"><i>k</i></sub></span>-th column, contains one.</p><p>It is guaranteed that all positions are distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the description of your actions. These actions should transform the matrix to the described special form.</p><p>In the first line you should print a non-negative integer <span class="tex-span"><i>m</i></span> <span class="tex-span">(<i>m</i> ≤ 10<sup class="upper-index">5</sup>)</span> — the number of actions. In each of the next <span class="tex-span"><i>m</i></span> lines print three space-separated integers <span class="tex-span"><i>t</i>, <i>i</i>, <i>j</i></span> <span class="tex-span">(1 ≤ <i>t</i> ≤ 2, 1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i>, <i>i</i> ≠ <i>j</i>)</span>, where <span class="tex-span"><i>t</i> = 1</span> if you want to swap rows, <span class="tex-span"><i>t</i> = 2</span> if you want to swap columns, and <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>j</i></span> denote the numbers of rows or columns respectively.</p><p>Please note, that you do not need to minimize the number of operations, but their num
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. BerDonalds</div><div class="time-limit"><div class="property-title">time limit per test</div>5 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>BerDonalds, a well-known fast food restaurant, is going to open a cafe in Bertown. The important thing is to choose the new restaurant's location so that it would be easy to get there. The Bertown road system is represented by <span class="tex-span"><i>n</i></span> junctions, connected by <span class="tex-span"><i>m</i></span> bidirectional roads. For each road we know its length. We also know that we can get from any junction to any other one, moving along the roads.</p><p>Your task is to find such location of the restaurant, that the shortest distance along the roads from the cafe to the farthest junction would be minimum. Note that the restaurant can be located not only on the junction, but at any point of any road.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/e77c9ba339b03020eea469a8624f475d88cf28b8.png" style="max-width: 100.0%;max-height: 100.0%;" />) — the number of junctions and the number of roads, correspondingly. Then <span class="tex-span"><i>m</i></span> lines follow, describing all Bertown roads. Each road is described by three integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub>, <i>w</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i>, <i>a</i><sub class="lower-index"><i>i</i></sub> ≠ <i>b</i><sub class="lower-index"><i>i</i></sub>; 1 ≤ <i>w</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>), where <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> are the numbers of the junctions, connected by the <span class="tex-span"><i>i</i></span>-th road, and <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> is the length of the <span class="tex-span"><i>i</i></span>-th road. </p><p>It is guaranteed that each road connects two distinct junctions, there is at most one road between any two junctions, and you can get from any junction to any other one.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single real number — the shortest distance from the optimal restaurant location to the farthest junction. The answer will be considered correct, if its absolute or relative error doesn't exceed <span class="tex-span">10<sup class="upper-index"> - 9</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 1<br />1 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>0.50<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 3<br />1 2 1<br />2 3 1<br />1 3 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>1.00<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 2<br />1 2 100<br />2 3 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>50.50<br /></pre></div></div></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. More Queries to Array...</div><div class="time-limit"><div class="property-title">time limit per test</div>5 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've got an array, consisting of <span class="tex-span"><i>n</i></span> integers: <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span>. Your task is to quickly run the queries of two types:</p><ol><li> Assign value <span class="tex-span"><i>x</i></span> to all elements from <span class="tex-span"><i>l</i></span> to <span class="tex-span"><i>r</i></span> inclusive. After such query the values of the elements of array <span class="tex-span"><i>a</i><sub class="lower-index"><i>l</i></sub>, <i>a</i><sub class="lower-index"><i>l</i> + 1</sub>, ..., <i>a</i><sub class="lower-index"><i>r</i></sub></span> become equal to <span class="tex-span"><i>x</i></span>.</li><li> Calculate and print sum <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/920d5e77b57e41992ceefa42465edf8cfc006a39.png" style="max-width: 100.0%;max-height: 100.0%;" />, where <span class="tex-span"><i>k</i></span> doesn't exceed <span class="tex-span">5</span>. As the value of the sum can be rather large, you should print it modulo <span class="tex-span">1000000007 (10<sup class="upper-index">9</sup> + 7)</span>.</li></ol></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 10<sup class="upper-index">5</sup></span>), showing, how many numbers are in the array and the number of queries, correspondingly. The second line contains <span class="tex-span"><i>n</i></span> integers: <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span> (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>) — the initial values of the array elements.</p><p>Then <span class="tex-span"><i>m</i></span> queries follow, one per line:</p><ol><li> The assign query has the following format: "<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/b2ef693fd11e9e29c50f180848ea668ed6d33b22.png" style="max-width: 100.0%;max-height: 100.0%;" />", (<span class="tex-span">1 ≤ <i>l</i> ≤ <i>r</i> ≤ <i>n</i>; 0 ≤ <i>x</i> ≤ 10<sup class="upper-index">9</sup></span>).</li><li> The query to calculate the sum has the following format: "<img align="middle" class="tex-formula" src="https://espresso.codeforces.com/6a63948f42b361ef379406ad9a679d1da1aee76b.png" style="max-width: 100.0%;max-height: 100.0%;" />", (<span class="tex-span">1 ≤ <i>l</i> ≤ <i>r</i> ≤ <i>n</i>; 0 ≤ <i>k</i> ≤ 5</span>).</li></ol><p>All numbers in the input are integers.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each query to calculate the sum print an integer — the required sum modulo <span class="tex-span">1000000007 (10<sup class="upper-index">9</sup> + 7)</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>4 5<br />5 10 2 1<br />? 1 2 1<br />= 2 2 0<br />? 2 4 3<br />= 1 4 1<br />? 1 4 5<br /></pre></div><div class="output"><div class="title">Output</div><pre>25<br />43<br />1300<br /></pre></div><div class="
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