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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Nearly Lucky Number</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><span class="tex-font-style-underline">Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits <span class="tex-font-style-bf">4</span> and <span class="tex-font-style-bf">7</span>. For example, numbers <span class="tex-font-style-bf">47</span>, <span class="tex-font-style-bf">744</span>, <span class="tex-font-style-bf">4</span> are lucky and <span class="tex-font-style-bf">5</span>, <span class="tex-font-style-bf">17</span>, <span class="tex-font-style-bf">467</span> are not.</span></p><p>Unfortunately, not all numbers are lucky. Petya calls a number <span class="tex-font-style-underline">nearly lucky</span> if the number of lucky digits in it is a lucky number. He wonders whether number <span class="tex-span"><i>n</i></span> is a nearly lucky number.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The only 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">18</sup></span>).</p><p>Please do not use the %lld specificator to read or write 64-bit numbers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on the single line "<span class="tex-font-style-tt">YES</span>" if <span class="tex-span"><i>n</i></span> is a nearly lucky number. Otherwise, print "<span class="tex-font-style-tt">NO</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>40047<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div><div class="input"><div class="title">Input</div><pre>7747774<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br /></pre></div><div class="input"><div class="title">Input</div><pre>1000000000000000000<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample there are 3 lucky digits (first one and last two), so the answer is "<span class="tex-font-style-tt">NO</span>".</p><p>In the second sample there are 7 lucky digits, 7 is lucky number, so the answer is "<span class="tex-font-style-tt">YES</span>".</p><p>In the third sample there are no lucky digits, so the answer is "<span class="tex-font-style-tt">NO</span>".</p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Lucky String</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><span class="tex-font-style-underline">Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits <span class="tex-font-style-bf">4</span> and <span class="tex-font-style-bf">7</span>. For example, numbers <span class="tex-font-style-bf">47</span>, <span class="tex-font-style-bf">744</span>, <span class="tex-font-style-bf">4</span> are lucky and <span class="tex-font-style-bf">5</span>, <span class="tex-font-style-bf">17</span>, <span class="tex-font-style-bf">467</span> are not.</span></p><p>Petya recently learned to determine whether a string of lowercase Latin letters is lucky. For each individual letter all its positions in the string are written out in the increasing order. This results in <span class="tex-span">26</span> lists of numbers; some of them can be empty. A string is considered lucky if and only if in each list the absolute difference of any two <span class="tex-font-style-bf">adjacent</span> numbers is a lucky number. </p><p>For example, let's consider string "<span class="tex-font-style-tt">zbcdzefdzc</span>". The lists of positions of equal letters are:</p><ul><li> <span class="tex-font-style-tt">b</span>: <span class="tex-span">2</span></li><li> <span class="tex-font-style-tt">c</span>: <span class="tex-span">3, 10</span></li><li> <span class="tex-font-style-tt">d</span>: <span class="tex-span">4, 8</span></li><li> <span class="tex-font-style-tt">e</span>: <span class="tex-span">6</span></li><li> <span class="tex-font-style-tt">f</span>: <span class="tex-span">7</span></li><li> <span class="tex-font-style-tt">z</span>: <span class="tex-span">1, 5, 9</span></li><li> Lists of positions of letters <span class="tex-font-style-tt">a</span>, <span class="tex-font-style-tt">g</span>, <span class="tex-font-style-tt">h</span>, ..., <span class="tex-font-style-tt">y</span> are empty.</li></ul><p>This string is lucky as all differences are lucky numbers. For letters <span class="tex-font-style-tt">z</span>: <span class="tex-span">5 - 1 = 4</span>, <span class="tex-span">9 - 5 = 4</span>, for letters <span class="tex-font-style-tt">c</span>: <span class="tex-span">10 - 3 = 7</span>, for letters <span class="tex-font-style-tt">d</span>: <span class="tex-span">8 - 4 = 4</span>. </p><p>Note that if some letter occurs only once in a string, it doesn't influence the string's luckiness after building the lists of positions of equal letters. The string where all the letters are distinct is considered lucky.</p><p>Find the lexicographically minimal lucky string whose length equals <span class="tex-span"><i>n</i></span>.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The single line contains a positive 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 length of the sought string.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on the single line the lexicographically minimal lucky string whose length equals <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>5<br /></pre></div><div class="output"><div class="title">Output</div><pre>abcda<br /></pre></div><div class="input"><div class="title">Input</div><pre>3<br /></pre></div><div class="output"><div class="title">Output</div><pre>abc<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The lexical comparison of strings is performed by the < operator in modern programming languages. String <span class="tex-span"><i>a</i></span> is lexicographically less than string <span class="tex-span"><i>b</i></span> if exists such <span class="tex-span"><i>i</i></span> (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>), that <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></span>, and for any <span class="tex-span"><i>j</i></span> (<span class="tex-span">1 ≤ <i>j</i> < <i>i</i></span>) <span class="tex-span"><i>a</i><sub class="lower-index"><i>j</i></sub> = <i>b</i><sub class="lower-index"><i>j</i></sub></span>.</p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Lucky Sum of Digits</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><span class="tex-font-style-underline">Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits <span class="tex-font-style-bf">4</span> and <span class="tex-font-style-bf">7</span>. For example, numbers <span class="tex-font-style-bf">47</span>, <span class="tex-font-style-bf">744</span>, <span class="tex-font-style-bf">4</span> are lucky and <span class="tex-font-style-bf">5</span>, <span class="tex-font-style-bf">17</span>, <span class="tex-font-style-bf">467</span> are not.</span></p><p>Petya wonders eagerly what minimum lucky number has the sum of digits equal to <span class="tex-span"><i>n</i></span>. Help him cope with the task.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The single 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 sum of digits of the required lucky number.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print on the single line the result — the minimum lucky number, whose sum of digits equals <span class="tex-span"><i>n</i></span>. If such number does not exist, print -1.</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>11<br /></pre></div><div class="output"><div class="title">Output</div><pre>47<br /></pre></div><div class="input"><div class="title">Input</div><pre>10<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div></div></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Lucky Probability</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><span class="tex-font-style-underline">Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits <span class="tex-font-style-bf">4</span> and <span class="tex-font-style-bf">7</span>. For example, numbers <span class="tex-font-style-bf">47</span>, <span class="tex-font-style-bf">744</span>, <span class="tex-font-style-bf">4</span> are lucky and <span class="tex-font-style-bf">5</span>, <span class="tex-font-style-bf">17</span>, <span class="tex-font-style-bf">467</span> are not.</span></p><p>Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer <span class="tex-span"><i>p</i></span> from the interval <span class="tex-span">[<i>p</i><sub class="lower-index"><i>l</i></sub>, <i>p</i><sub class="lower-index"><i>r</i></sub>]</span> and Vasya chooses an integer <span class="tex-span"><i>v</i></span> from the interval <span class="tex-span">[<i>v</i><sub class="lower-index"><i>l</i></sub>, <i>v</i><sub class="lower-index"><i>r</i></sub>]</span> (also randomly). Both players choose their integers equiprobably. Find the probability that the interval <span class="tex-span">[<i>min</i>(<i>v</i>, <i>p</i>), <i>max</i>(<i>v</i>, <i>p</i>)]</span> contains exactly <span class="tex-span"><i>k</i></span> lucky numbers.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The single line contains five integers <span class="tex-span"><i>p</i><sub class="lower-index"><i>l</i></sub></span>, <span class="tex-span"><i>p</i><sub class="lower-index"><i>r</i></sub></span>, <span class="tex-span"><i>v</i><sub class="lower-index"><i>l</i></sub></span>, <span class="tex-span"><i>v</i><sub class="lower-index"><i>r</i></sub></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>p</i><sub class="lower-index"><i>l</i></sub> ≤ <i>p</i><sub class="lower-index"><i>r</i></sub> ≤ 10<sup class="upper-index">9</sup>, 1 ≤ <i>v</i><sub class="lower-index"><i>l</i></sub> ≤ <i>v</i><sub class="lower-index"><i>r</i></sub> ≤ 10<sup class="upper-index">9</sup>, 1 ≤ <i>k</i> ≤ 1000</span>).</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the single line print the result with an absolute error of no more than <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>1 10 1 10 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>0.320000000000<br /></pre></div><div class="input"><div class="title">Input</div><pre>5 6 8 10 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>1.000000000000<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Consider that <span class="tex-span">[<i>a</i>, <i>b</i>]</span> denotes an interval of integers; this interval <span class="tex-font-style-bf">includes</span> the boundaries. That is, <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/18b4a6012d95ad18891561410f0314497a578d63.png" style="max-width: 100.0%;max-height: 100.0%;" /></p><p>In first case there are <span class="tex-span">32</span> suitable pairs: <span class="tex-span">(1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4)</span>. Total number of possible pairs is <span class="tex-span">10·10 = 100</span>, so answer is <span class="tex-span">32 / 100</span>.</p><p>In second case Petya always get number less than Vasya and the only lucky <span class="tex-span">7</span> is between this numbers, so there will be always <span class="tex-span">1</span> lucky number.</p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Lucky Tree</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><span class="tex-font-style-underline">Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits <span class="tex-font-style-bf">4</span> and <span class="tex-font-style-bf">7</span>. For example, numbers <span class="tex-font-style-bf">47</span>, <span class="tex-font-style-bf">744</span>, <span class="tex-font-style-bf">4</span> are lucky and <span class="tex-font-style-bf">5</span>, <span class="tex-font-style-bf">17</span>, <span class="tex-font-style-bf">467</span> are not.</span></p><p>One day Petya encountered a tree with <span class="tex-span"><i>n</i></span> vertexes. Besides, the tree was weighted, i. e. each edge of the tree has weight (a positive integer). An edge is lucky if its weight is a lucky number. Note that a <span class="tex-font-style-underline">tree with <span class="tex-span"><i>n</i></span> vertexes</span> is an undirected connected graph that has exactly <span class="tex-span"><i>n</i> - 1</span> edges.</p><p>Petya wondered how many vertex triples <span class="tex-span">(<i>i</i>, <i>j</i>, <i>k</i>)</span> exists that on the way from <span class="tex-span"><i>i</i></span> to <span class="tex-span"><i>j</i></span>, as well as on the way from <span class="tex-span"><i>i</i></span> to <span class="tex-span"><i>k</i></span> there must be at least one lucky edge (all three vertexes are pairwise distinct). The order of numbers in the triple matters, that is, the triple <span class="tex-span">(1, 2, 3)</span> is not equal to the triple <span class="tex-span">(2, 1, 3)</span> and is not equal to the triple <span class="tex-span">(1, 3, 2)</span>. </p><p>Find how many such triples of vertexes exist.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains the single 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 tree vertexes. Next <span class="tex-span"><i>n</i> - 1</span> lines contain three integers each: <span class="tex-span"><i>u</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>v</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>w</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>u</i><sub class="lower-index"><i>i</i></sub>, <i>v</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i>, 1 ≤ <i>w</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup></span>) — the pair of vertexes connected by the edge and the edge's weight.</p></div><div class="output-specification"><div class="section-title">Output</div><p>On the single line print the single number — the answer.</p><p>Please do not use the %lld specificator to read or write 64-bit numbers in С++. It is recommended to use the cin, cout streams or the %I64d specificator.</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<br />1 2 4<br />3 1 2<br />1 4 7<br /></pre></div><div class="output"><div class="title">Output</div><pre>16<br /></pre></div><div class="input"><div class="title">Input</div><pre>4<br />1 2 4<br />1 3 47<br />1 4 7447<br /></pre></div><div class="output"><div class="title">Output</div><pre>24<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>The <span class="tex-span">16</span> triples of vertexes from the first sample are: <span class="tex-span">(1, 2, 4), (1, 4, 2), (2, 1, 3), (2, 1, 4), (2, 3, 1), (2, 3, 4), (2, 4, 1), (2, 4, 3), (3, 2, 4), (3, 4, 2), (4, 1, 2), (4, 1, 3), (4, 2, 1), (4, 2, 3), (4, 3, 1), (4, 3, 2)</span>.</p><p>In the second sample all the triples should be counted: <span class="tex-span">4·3·2 = 24</span>.</p></div></div></div>
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