2012 Problems
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- .gitattributes +1 -0
- 2012/finals/linsane_phone_numbers.html +63 -0
- 2012/finals/linsane_phone_numbers.in +16 -0
- 2012/finals/linsane_phone_numbers.md +68 -0
- 2012/finals/linsane_phone_numbers.out +15 -0
- 2012/finals/maximal_multiplicative_order.html +25 -0
- 2012/finals/maximal_multiplicative_order.in +61 -0
- 2012/finals/maximal_multiplicative_order.md +38 -0
- 2012/finals/maximal_multiplicative_order.out +60 -0
- 2012/finals/possible_medians.html +46 -0
- 2012/finals/possible_medians.in +3 -0
- 2012/finals/possible_medians.md +46 -0
- 2012/finals/possible_medians.out +17 -0
- 2012/quals/alphabet_soup.html +36 -0
- 2012/quals/alphabet_soup.in +61 -0
- 2012/quals/alphabet_soup.md +30 -0
- 2012/quals/alphabet_soup.out +60 -0
- 2012/quals/auction.html +57 -0
- 2012/quals/auction.in +61 -0
- 2012/quals/auction.md +49 -0
- 2012/quals/auction.out +60 -0
- 2012/quals/billboards.html +50 -0
- 2012/quals/billboards.in +61 -0
- 2012/quals/billboards.md +45 -0
- 2012/quals/billboards.out +60 -0
- 2012/round1/checkpoint.html +37 -0
- 2012/round1/checkpoint.in +61 -0
- 2012/round1/checkpoint.md +46 -0
- 2012/round1/checkpoint.out +60 -0
- 2012/round1/recover_the_sequence.html +61 -0
- 2012/round1/recover_the_sequence.in +0 -0
- 2012/round1/recover_the_sequence.md +74 -0
- 2012/round1/recover_the_sequence.out +40 -0
- 2012/round1/squished_status.html +22 -0
- 2012/round1/squished_status.in +44 -0
- 2012/round1/squished_status.md +40 -0
- 2012/round1/squished_status.out +39 -0
- 2012/round2/monopoly.html +34 -0
- 2012/round2/monopoly.in +0 -0
- 2012/round2/monopoly.md +58 -0
- 2012/round2/monopoly.out +20 -0
- 2012/round2/road_removal.html +24 -0
- 2012/round2/road_removal.in +0 -0
- 2012/round2/road_removal.md +45 -0
- 2012/round2/road_removal.out +20 -0
- 2012/round2/sequence_slicing.html +39 -0
- 2012/round2/sequence_slicing.in +0 -0
- 2012/round2/sequence_slicing.md +64 -0
- 2012/round2/sequence_slicing.out +34 -0
- 2012/round3/divisor_function_optimization.html +19 -0
.gitattributes
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*.jpg filter=lfs diff=lfs merge=lfs -text
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2012/finals/possible_medians.in filter=lfs diff=lfs merge=lfs -text
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2012/finals/linsane_phone_numbers.html
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<p>
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As the Jeremy Lin sensation goes on, Roger, who is a geek and a super fan of Jeremy Lin, decides his new cell phone number must be
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"Linsane". More specifically, he wants his new phone number to satisfy: </p>
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<p>
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1) Adjacent sum: <br/>
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There is at least one occurrence in the phone number of three adjacent digits summing to <b>x</b>, where <b>x</b> is Lin's
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jersey number at New York Knicks. </p>
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<p>
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2) Diversity: <br/>
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There are at least <b>y</b> different values of the digits used in the phone number, where <b>y</b> is Lin's jersey number at Golden
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State Warriors. </p>
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<p>
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3) Neighboring difference: <br/>
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There is at least one pair of neighboring digits whose difference is equal to <b>z</b>, where <b>z</b> is Lin's jersey number at Harvard. </p>
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<p>
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A phone number with length <b>n</b> contains <b>n</b> digits. Each digit is in the range from 0 to 9, except that the first
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digit must be non-zero.<br/>
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A phone number is called "linsane" if it satisfies the three constraints listed above.<br/><br/>
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For phone numbers with a given length <b>n</b>, Roger wonders how many "linsane" phone
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numbers exist.<br/>
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He also wants to find out the "most linsane" phone number among them.<br/>
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For a given length, the "most linsane" phone number is a "linsane" phone number that has the biggest "linsanity measurement" among them.<br/>
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"Linsanity measurement" is defined as
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<img src="http://rogeryu.com/Facebook_Hacker_Cup_2012_Final_Round_Problem_Linsanity.gif"></img>, where <b>n</b> is the number of digits and <b>d<sub>i</sub></b> is the <b>i</b>-th digit in the phone number.<br/>
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If there is a tie on such measurement, choose the one whose median of the digits is largest; and if there is still a tie, choose the largest phone number.<br/>
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Median is the <b>(n+1)/2</b>-th smallest digit if <b>n</b> is odd, or the average of the <b>(n/2)</b>-th and <b>(n/2+1)</b>-th digit if <b>n</b> is even.
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For example, the linsanity measurement of number 78969251 is equal to (15*9)%8 + (17*6)%8 + (15*9)%8 + (15*2)%8 +(11*5)%8 + (7*1)%8 = 40 with its median equal to 6.5.<br/>
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</p>
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<h3>Input</h3>
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<p>The first line contains a positive integer <b>T</b>, the number of test cases. <b>T</b> test cases follow.</p>
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<p>Each test case is a single line and contains exactly four integers separated by single white space: <b>n x y z</b>, where <b>n</b> is the length of the phone number, <b>x</b> is Lin's jersey number at New York Knicks, <b>y</b> is Lin's jersey number at Golden State Warriors and <b>z</b> is Lin's jersey number at Harvard.<br/>
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(<b>x</b>,<b>y</b> and <b>z</b> are not necessarily 17, 7 and 4 in another parallel universe.)
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</p>
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<h3>Constraints</h3>
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<p>
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3 ≤ <b>n</b> ≤ 20<br/>
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0 ≤ <b>x</b> ≤ 27<br/>
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0 ≤ <b>y</b> ≤ 10<br/>
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0 ≤ <b>z</b> ≤ 9<br/>
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1 ≤ <b>T</b> ≤ 15<br/>
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Among the <b>T</b> test cases, there will be no more than 5 test cases with <b>n</b> >12.
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</p>
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<h3>Output</h3>
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<p>
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For each of the test cases numbered in order from <b>1</b> to <b>T</b>, output "Case #", followed by the case number,
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followed by ": ", followed by the number of possible "linsane" phone numbers <i>mod</i> 10<sup>18</sup> for the given length for that case,
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and then a single space " " followed by the "most linsane" phone number for the given length or -1 if no "linsane" phone number exists
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for the given length.
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</p>
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2012/finals/linsane_phone_numbers.in
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15
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6 17 7 4
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7 17 7 4
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8 17 7 4
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8 17 6 3
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12 3 3 4
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20 16 6 6
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2012/finals/linsane_phone_numbers.md
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+
As the Jeremy Lin sensation goes on, Roger, who is a geek and a super fan of
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| 2 |
+
Jeremy Lin, decides his new cell phone number must be "Linsane". More
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| 3 |
+
specifically, he wants his new phone number to satisfy:
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+
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+
1) Adjacent sum:
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There is at least one occurrence in the phone number of three adjacent digits
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summing to **x**, where **x** is Lin's jersey number at New York Knicks.
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2) Diversity:
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There are at least **y** different values of the digits used in the phone
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number, where **y** is Lin's jersey number at Golden State Warriors.
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3) Neighboring difference:
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There is at least one pair of neighboring digits whose difference is equal to
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**z**, where **z** is Lin's jersey number at Harvard.
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A phone number with length **n** contains **n** digits. Each digit is in the
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range from 0 to 9, except that the first digit must be non-zero.
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A phone number is called "linsane" if it satisfies the three constraints
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listed above.
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For phone numbers with a given length **n**, Roger wonders how many "linsane"
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phone numbers exist.
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He also wants to find out the "most linsane" phone number among them.
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For a given length, the "most linsane" phone number is a "linsane" phone
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number that has the biggest "linsanity measurement" among them.
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"Linsanity measurement" is defined as , where **n** is the number of
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digits and **di** is the **i**-th digit in the phone number.
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If there is a tie on such measurement, choose the one whose median of the
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digits is largest; and if there is still a tie, choose the largest phone
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number.
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Median is the **(n+1)/2**-th smallest digit if **n** is odd, or the average of
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the **(n/2)**-th and **(n/2+1)**-th digit if **n** is even. For example, the
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linsanity measurement of number 78969251 is equal to (15*9)%8 + (17*6)%8 +
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(15*9)%8 + (15*2)%8 +(11*5)%8 + (7*1)%8 = 40 with its median equal to 6.5.
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### Input
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The first line contains a positive integer **T**, the number of test cases.
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**T** test cases follow.
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Each test case is a single line and contains exactly four integers separated
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by single white space: **n x y z**, where **n** is the length of the phone
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number, **x** is Lin's jersey number at New York Knicks, **y** is Lin's jersey
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number at Golden State Warriors and **z** is Lin's jersey number at Harvard.
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(**x**,**y** and **z** are not necessarily 17, 7 and 4 in another parallel
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universe.)
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### Constraints
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3 ≤ **n** ≤ 20
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0 ≤ **x** ≤ 27
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0 ≤ **y** ≤ 10
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0 ≤ **z** ≤ 9
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1 ≤ **T** ≤ 15
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Among the **T** test cases, there will be no more than 5 test cases with **n**
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>12.
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### Output
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For each of the test cases numbered in order from **1** to **T**, output "Case
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#", followed by the case number, followed by ": ", followed by the number of
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possible "linsane" phone numbers _mod_ 1018 for the given length for that
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case, and then a single space " " followed by the "most linsane" phone number
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for the given length or -1 if no "linsane" phone number exists for the given
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length.
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2012/finals/linsane_phone_numbers.out
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Case #1: 0 -1
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Case #2: 97682 9732485
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Case #3: 3657799 78969251
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Case #4: 231355703 435255828
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Case #5: 230877663780393592 90299299274965943891
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Case #6: 173063 50009699
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Case #7: 167994928670 291147255255
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Case #8: 4953342932213760 9029519993336272438
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Case #9: 613283549076340541 20929929929927243897
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Case #10: 173674046759688824 17229929929929929929
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Case #11: 87748951947 901652552557
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Case #12: 1111374 90727456
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Case #13: 11883082 78969259
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Case #14: 51212574331 102552552551
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Case #15: 559474244734633752 20929929929929927493
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2012/finals/maximal_multiplicative_order.html
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<p>Let's start with some notations and definitions. Let <b>m</b> be the fixed positive integer.</p>
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<ol>
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<li> Let <b>a</b> be an integer that coprime to <b>m</b>, that is, <b>gcd(a, m) = 1</b>. The minimal positive integer <b>k</b> such that <b>m</b> divides <b>a<sup>k</sup> − 1</b> is called the <i>multiplicative order of <b>a</b> modulo <b>m</b></i> and denoted as <b>ord<sub>m</sub>(a)</b>. For example, <b> ord<sub>7</sub>(2) = 3</b> since <b>2<sup>3</sup> − 1 = 7</b> is divisible by <b>7</b> but <b>2<sup>1</sup> − 1</b> and <b>2<sup>2</sup> − 1</b> are not. It can be proven that <b>ord<sub>m</sub>(a)</b> exists for every <b>a</b> that coprime to <b>m</b>.
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<li> Denote by <b>L(m)</b> the maximal possible multiplicative order of some number modulo <b>m</b>. That is, <b>L(m) = max{ord<sub>m</sub>(a) : 1 ≤ a ≤ m, gcd(a, m)=1}</b>. For example, <p><center><b>L(5) = max{ ord<sub>5</sub>(1), ord<sub>5</sub>(2), ord<sub>5</sub>(3), ord<sub>5</sub>(4)} = max{1, 4, 4, 2} = 4</b></center></p> and <p><center><b>L(6) = max{ord<sub>6</sub>(1), ord<sub>6</sub>(5)} = max{1, 2} = 2.</b></center></p>
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<li> Denote by <b>N(m)</b> the number of positive integers <b>a ≤ m</b> such that <b> ord<sub>m</sub>(a) = L(m)</b>. For example, <b>N(5) = 2</b>, <b>N(6) = 1</b>, <b>N(8) = 3</b> (numbers that have maximal multiplicative order modulo <b>8</b> are <b>3, 5</b> and <b>7</b>).
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</ol>
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<p>Now your task is to find for the given positive integers <b>L</b> and <b>R</b> such that <b>L ≤ R</b> the product
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<p><center><b>N(L) ∙ N(L+1) ∙ ... ∙ N(R)</b></center></p>
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modulo <b>10<sup>9</sup> + 7</b>.</p>
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<h3>Input</h3>
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| 15 |
+
<p>The first line contains a positive integer <b>T</b>, the number of test cases. <b>T</b> test cases follow. The only line of each test case contains two space separated positive integers <b>L</b> and <b>R</b>.</p>
|
| 16 |
+
|
| 17 |
+
<h3>Output</h3>
|
| 18 |
+
<p>For each of the test cases numbered in order from <b>1</b> to <b>T</b>, output "Case #i: " followed by the value of required product modulo <b>10<sup>9</sup> + 7</b>.</p>
|
| 19 |
+
|
| 20 |
+
<h3>Constraints</h3>
|
| 21 |
+
<p>
|
| 22 |
+
<b>1 ≤ T ≤ 20<br/>
|
| 23 |
+
1 ≤ L ≤ R ≤ 10<sup>12</sup><br/>
|
| 24 |
+
R − L ≤ 500000</b><br/></p>
|
| 25 |
+
|
2012/finals/maximal_multiplicative_order.in
ADDED
|
@@ -0,0 +1,61 @@
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|
|
| 1 |
+
60
|
| 2 |
+
5 8
|
| 3 |
+
1 10
|
| 4 |
+
1 100
|
| 5 |
+
1234 1234
|
| 6 |
+
1000000007 1000000007
|
| 7 |
+
999999500000 1000000000000
|
| 8 |
+
100 500000
|
| 9 |
+
992371675059 992372175058
|
| 10 |
+
991530920028 991531420022
|
| 11 |
+
995741565035 995742065026
|
| 12 |
+
998106243723 998106743714
|
| 13 |
+
992849049326 992849549322
|
| 14 |
+
998586540807 998587040801
|
| 15 |
+
993642405550 993642905541
|
| 16 |
+
991059355108 991059855104
|
| 17 |
+
992449103728 992449603721
|
| 18 |
+
998484860297 998485360290
|
| 19 |
+
990144490023 990144990016
|
| 20 |
+
990517712659 990518212657
|
| 21 |
+
994642711115 994643211109
|
| 22 |
+
998148071777 998148571775
|
| 23 |
+
997110688792 997111188782
|
| 24 |
+
996070696965 996071196962
|
| 25 |
+
998599900163 998600400162
|
| 26 |
+
992261955400 992262455394
|
| 27 |
+
990243951047 990244451043
|
| 28 |
+
994400768518 994401268510
|
| 29 |
+
991627614312 991628114302
|
| 30 |
+
992545580071 992546080069
|
| 31 |
+
995659986504 995660486495
|
| 32 |
+
995562878227 995563378225
|
| 33 |
+
993859049889 993859549882
|
| 34 |
+
997349911114 997350411108
|
| 35 |
+
996371303205 996371803200
|
| 36 |
+
993673951323 993674451322
|
| 37 |
+
993897692301 993898192295
|
| 38 |
+
996003045368 996003545365
|
| 39 |
+
997162481672 997162981671
|
| 40 |
+
997695321427 997695821427
|
| 41 |
+
995352722297 995353222289
|
| 42 |
+
997680738220 997681238212
|
| 43 |
+
990557907819 990558407809
|
| 44 |
+
994627517786 994628017780
|
| 45 |
+
991362967296 991363467290
|
| 46 |
+
998340248615 998340748614
|
| 47 |
+
993512279565 993512779564
|
| 48 |
+
993311638830 993312138820
|
| 49 |
+
990633044031 990633544022
|
| 50 |
+
992295618062 992296118058
|
| 51 |
+
999425213758 999425713756
|
| 52 |
+
994688082393 994688582383
|
| 53 |
+
997859441246 997859941243
|
| 54 |
+
991935134515 991935634505
|
| 55 |
+
990130356664 990130856660
|
| 56 |
+
990156502604 990157002598
|
| 57 |
+
992037541985 992038041983
|
| 58 |
+
992501378162 992501878155
|
| 59 |
+
990287019669 990287519660
|
| 60 |
+
991598068596 991598568593
|
| 61 |
+
993011033378 993011533371
|
2012/finals/maximal_multiplicative_order.md
ADDED
|
@@ -0,0 +1,38 @@
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|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
| 1 |
+
Let's start with some notations and definitions. Let **m** be the fixed
|
| 2 |
+
positive integer.
|
| 3 |
+
|
| 4 |
+
1. Let **a** be an integer that coprime to **m**, that is, **gcd(a, m) = 1**. The minimal positive integer **k** such that **m** divides **ak − 1** is called the _multiplicative order of **a** modulo **m**_ and denoted as **ordm(a)**. For example, ** ord7(2) = 3** since **23 − 1 = 7** is divisible by **7** but **21 − 1** and **22 − 1** are not. It can be proven that **ordm(a)** exists for every **a** that coprime to **m**.
|
| 5 |
+
2. Denote by **L(m)** the maximal possible multiplicative order of some number modulo **m**. That is, **L(m) = max{ordm(a) : 1 ≤ a ≤ m, gcd(a, m)=1}**. For example,
|
| 6 |
+
|
| 7 |
+
**L(5) = max{ ord5(1), ord5(2), ord5(3), ord5(4)} = max{1, 4, 4, 2} = 4**
|
| 8 |
+
|
| 9 |
+
and
|
| 10 |
+
|
| 11 |
+
**L(6) = max{ord6(1), ord6(5)} = max{1, 2} = 2.**
|
| 12 |
+
|
| 13 |
+
3. Denote by **N(m)** the number of positive integers **a ≤ m** such that ** ordm(a) = L(m)**. For example, **N(5) = 2**, **N(6) = 1**, **N(8) = 3** (numbers that have maximal multiplicative order modulo **8** are **3, 5** and **7**).
|
| 14 |
+
|
| 15 |
+
Now your task is to find for the given positive integers **L** and **R** such
|
| 16 |
+
that **L ≤ R** the product
|
| 17 |
+
|
| 18 |
+
**N(L) ∙ N(L+1) ∙ ... ∙ N(R)**
|
| 19 |
+
|
| 20 |
+
modulo **109 \+ 7**.
|
| 21 |
+
|
| 22 |
+
### Input
|
| 23 |
+
|
| 24 |
+
The first line contains a positive integer **T**, the number of test cases.
|
| 25 |
+
**T** test cases follow. The only line of each test case contains two space
|
| 26 |
+
separated positive integers **L** and **R**.
|
| 27 |
+
|
| 28 |
+
### Output
|
| 29 |
+
|
| 30 |
+
For each of the test cases numbered in order from **1** to **T**, output "Case
|
| 31 |
+
#i: " followed by the value of required product modulo **109 \+ 7**.
|
| 32 |
+
|
| 33 |
+
### Constraints
|
| 34 |
+
|
| 35 |
+
**1 ≤ T ≤ 20
|
| 36 |
+
1 ≤ L ≤ R ≤ 1012
|
| 37 |
+
R − L ≤ 500000**
|
| 38 |
+
|
2012/finals/maximal_multiplicative_order.out
ADDED
|
@@ -0,0 +1,60 @@
|
|
|
|
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|
|
|
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|
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|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 12
|
| 2 |
+
Case #2: 48
|
| 3 |
+
Case #3: 451289786
|
| 4 |
+
Case #4: 240
|
| 5 |
+
Case #5: 500000002
|
| 6 |
+
Case #6: 184845236
|
| 7 |
+
Case #7: 156680808
|
| 8 |
+
Case #8: 331354227
|
| 9 |
+
Case #9: 914957122
|
| 10 |
+
Case #10: 78752655
|
| 11 |
+
Case #11: 96272456
|
| 12 |
+
Case #12: 211354052
|
| 13 |
+
Case #13: 895292859
|
| 14 |
+
Case #14: 377987945
|
| 15 |
+
Case #15: 444768284
|
| 16 |
+
Case #16: 363445119
|
| 17 |
+
Case #17: 656879630
|
| 18 |
+
Case #18: 29766806
|
| 19 |
+
Case #19: 750845284
|
| 20 |
+
Case #20: 220839439
|
| 21 |
+
Case #21: 711349998
|
| 22 |
+
Case #22: 501168546
|
| 23 |
+
Case #23: 488232663
|
| 24 |
+
Case #24: 973570175
|
| 25 |
+
Case #25: 451104608
|
| 26 |
+
Case #26: 671957882
|
| 27 |
+
Case #27: 275344438
|
| 28 |
+
Case #28: 714327771
|
| 29 |
+
Case #29: 133962356
|
| 30 |
+
Case #30: 369690976
|
| 31 |
+
Case #31: 333653110
|
| 32 |
+
Case #32: 210545172
|
| 33 |
+
Case #33: 405766719
|
| 34 |
+
Case #34: 452008880
|
| 35 |
+
Case #35: 645733120
|
| 36 |
+
Case #36: 820540812
|
| 37 |
+
Case #37: 667684693
|
| 38 |
+
Case #38: 518006025
|
| 39 |
+
Case #39: 840275834
|
| 40 |
+
Case #40: 390713137
|
| 41 |
+
Case #41: 253884293
|
| 42 |
+
Case #42: 12384045
|
| 43 |
+
Case #43: 555356411
|
| 44 |
+
Case #44: 124588082
|
| 45 |
+
Case #45: 925289948
|
| 46 |
+
Case #46: 138700917
|
| 47 |
+
Case #47: 755667342
|
| 48 |
+
Case #48: 884180407
|
| 49 |
+
Case #49: 989037045
|
| 50 |
+
Case #50: 114170347
|
| 51 |
+
Case #51: 213899478
|
| 52 |
+
Case #52: 912164235
|
| 53 |
+
Case #53: 610503264
|
| 54 |
+
Case #54: 653074264
|
| 55 |
+
Case #55: 485755338
|
| 56 |
+
Case #56: 300366014
|
| 57 |
+
Case #57: 791372229
|
| 58 |
+
Case #58: 427866287
|
| 59 |
+
Case #59: 47773956
|
| 60 |
+
Case #60: 643003360
|
2012/finals/possible_medians.html
ADDED
|
@@ -0,0 +1,46 @@
|
|
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|
|
|
|
|
| 1 |
+
<p>
|
| 2 |
+
For this problem, a <i>possible median</i> is defined as: The median value of a set containing an odd number of values. -or- One of all the integers between, but not including, the two median values of a set containing an even number of values.<br><b>Examples:</b> 3 is the only possible median of the set (1, 5, 3, 2, 4). 2, 3 and 4 are all of the possible median values for the set (5, 1). There
|
| 3 |
+
are <b>no</b> possible median values for the set (1, 2, 3, 4), since there are no integers between 2 and 3.
|
| 4 |
+
|
| 5 |
+
<p>
|
| 6 |
+
|
| 7 |
+
You are given an array <b>A</b> of <b>N</b> unique nonnegative integers, all of which are < <b>N</b> (i.e. a permutation of the numbers 0...<b>N-1</b>), where 3 ≤ <b>N</b> ≤ 200,000. You are
|
| 8 |
+
also given a length <b>L</b> (1 ≤ <b>L</b> ≤ <b>N</b>). Additionally, you are given <b>Q</b> (1 ≤ <b>Q</b> ≤ 200,000) queries, each containing a number <b>x</b> (0 ≤ <b>x</b> < N)
|
| 9 |
+
and two indices <b>i</b> and <b>j</b> (0 ≤ <b>i</b> < <b>j</b> ≤ <b>N</b>).
|
| 10 |
+
|
| 11 |
+
<p>
|
| 12 |
+
|
| 13 |
+
Each query returns TRUE if and only if there exists at least one subrange, of at least <b>L</b> elements, of the range <b>A[i]</b>...<b>A[j-1]</b> (where the array indices start at 0), with <b>x</b> as a possible median. In other words, the answer is TRUE precisely when there exist <b>a</b>, <b>b</b> with <b>i</b> ≤ <b>a</b> < <b>b</b> < <b>j</b> with <b>b</b> - <b>a</b> ≥ <b>L</b> -
|
| 14 |
+
1 and with <b>A[a]</b>...<b>A[b]</b> having <b>x</b> as a possible median.
|
| 15 |
+
|
| 16 |
+
<p>
|
| 17 |
+
|
| 18 |
+
You wish to determine the number of queries which will return TRUE.
|
| 19 |
+
|
| 20 |
+
|
| 21 |
+
<h3>Input</h3>
|
| 22 |
+
<p>
|
| 23 |
+
|
| 24 |
+
The first line contains a positive integer <b>T</b> (1 ≤ <b>T</b> ≤ 20), the number of test cases. <b>T</b> test cases follow.
|
| 25 |
+
|
| 26 |
+
<p>
|
| 27 |
+
The first line of each test case consists of a single integer, <b>N</b>. The next line consists of <b>N</b> space-separated integers, the <b>A[i]</b>. The line after that contains two space-separate
|
| 28 |
+
d integers, <b>L</b> and <b>Q</b>.
|
| 29 |
+
|
| 30 |
+
<p>
|
| 31 |
+
|
| 32 |
+
Each of the remaining <b>Q</b> lines in the test case contains three space-separated integers, <b>x</b>, <b>i</b> and <b>j</b>.
|
| 33 |
+
|
| 34 |
+
<p>
|
| 35 |
+
|
| 36 |
+
These inputs are all integers, and will be input in decimal form, with no leading zeros, and no decimal points.
|
| 37 |
+
|
| 38 |
+
<h3>Output</h3>
|
| 39 |
+
<p>
|
| 40 |
+
|
| 41 |
+
For each of the test cases numbered in order from 1 to T, output "Case #", followed by the case number, followed by ": ", followed by a single integer, the number of passing queries.
|
| 42 |
+
|
| 43 |
+
<p>
|
| 44 |
+
|
| 45 |
+
These outputs are all integers, and must be output in decimal form, with no leading zeros, and no decimal points.
|
| 46 |
+
|
2012/finals/possible_medians.in
ADDED
|
@@ -0,0 +1,3 @@
|
|
|
|
|
|
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|
|
|
|
|
|
| 1 |
+
version https://git-lfs.github.com/spec/v1
|
| 2 |
+
oid sha256:0c085affc10aec293048ca59e388a6f64c4fe58880a97dc78f3bc8863bdd17ec
|
| 3 |
+
size 33334290
|
2012/finals/possible_medians.md
ADDED
|
@@ -0,0 +1,46 @@
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|
| 1 |
+
For this problem, a _possible median_ is defined as: The median value of a set
|
| 2 |
+
containing an odd number of values. -or- One of all the integers between, but
|
| 3 |
+
not including, the two median values of a set containing an even number of
|
| 4 |
+
values.
|
| 5 |
+
**Examples:** 3 is the only possible median of the set (1, 5, 3, 2, 4). 2, 3 and 4 are all of the possible median values for the set (5, 1). There are **no** possible median values for the set (1, 2, 3, 4), since there are no integers between 2 and 3.
|
| 6 |
+
|
| 7 |
+
You are given an array **A** of **N** unique nonnegative integers, all of
|
| 8 |
+
which are < **N** (i.e. a permutation of the numbers 0...**N-1**), where 3 ≤
|
| 9 |
+
**N** ≤ 200,000. You are also given a length **L** (1 ≤ **L** ≤ **N**).
|
| 10 |
+
Additionally, you are given **Q** (1 ≤ **Q** ≤ 200,000) queries, each
|
| 11 |
+
containing a number **x** (0 ≤ **x** < N) and two indices **i** and **j** (0 ≤
|
| 12 |
+
**i** < **j** ≤ **N**).
|
| 13 |
+
|
| 14 |
+
Each query returns TRUE if and only if there exists at least one subrange, of
|
| 15 |
+
at least **L** elements, of the range **A[i]**...**A[j-1]** (where the array
|
| 16 |
+
indices start at 0), with **x** as a possible median. In other words, the
|
| 17 |
+
answer is TRUE precisely when there exist **a**, **b** with **i** ≤ **a** <
|
| 18 |
+
**b** < **j** with **b** \- **a** ≥ **L** \- 1 and with **A[a]**...**A[b]**
|
| 19 |
+
having **x** as a possible median.
|
| 20 |
+
|
| 21 |
+
You wish to determine the number of queries which will return TRUE.
|
| 22 |
+
|
| 23 |
+
### Input
|
| 24 |
+
|
| 25 |
+
The first line contains a positive integer **T** (1 ≤ **T** ≤ 20), the number
|
| 26 |
+
of test cases. **T** test cases follow.
|
| 27 |
+
|
| 28 |
+
The first line of each test case consists of a single integer, **N**. The next
|
| 29 |
+
line consists of **N** space-separated integers, the **A[i]**. The line after
|
| 30 |
+
that contains two space-separate d integers, **L** and **Q**.
|
| 31 |
+
|
| 32 |
+
Each of the remaining **Q** lines in the test case contains three space-
|
| 33 |
+
separated integers, **x**, **i** and **j**.
|
| 34 |
+
|
| 35 |
+
These inputs are all integers, and will be input in decimal form, with no
|
| 36 |
+
leading zeros, and no decimal points.
|
| 37 |
+
|
| 38 |
+
### Output
|
| 39 |
+
|
| 40 |
+
For each of the test cases numbered in order from 1 to T, output "Case #",
|
| 41 |
+
followed by the case number, followed by ": ", followed by a single integer,
|
| 42 |
+
the number of passing queries.
|
| 43 |
+
|
| 44 |
+
These outputs are all integers, and must be output in decimal form, with no
|
| 45 |
+
leading zeros, and no decimal points.
|
| 46 |
+
|
2012/finals/possible_medians.out
ADDED
|
@@ -0,0 +1,17 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 2
|
| 2 |
+
Case #2: 1
|
| 3 |
+
Case #3: 3
|
| 4 |
+
Case #4: 1
|
| 5 |
+
Case #5: 1
|
| 6 |
+
Case #6: 2526
|
| 7 |
+
Case #7: 1256
|
| 8 |
+
Case #8: 1505
|
| 9 |
+
Case #9: 3456
|
| 10 |
+
Case #10: 6248
|
| 11 |
+
Case #11: 32113
|
| 12 |
+
Case #12: 28192
|
| 13 |
+
Case #13: 44163
|
| 14 |
+
Case #14: 107471
|
| 15 |
+
Case #15: 73719
|
| 16 |
+
Case #16: 94393
|
| 17 |
+
Case #17: 48396
|
2012/quals/alphabet_soup.html
ADDED
|
@@ -0,0 +1,36 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
<p>Alfredo Spaghetti really likes soup, especially when it contains alphabet
|
| 2 |
+
pasta. Every day he constructs a sentence from letters, places the letters into
|
| 3 |
+
a bowl of broth and enjoys delicious alphabet soup.
|
| 4 |
+
</p>
|
| 5 |
+
|
| 6 |
+
<p>Today, after constructing the sentence, Alfredo remembered that the Facebook
|
| 7 |
+
Hacker Cup starts today! Thus, he decided to construct the phrase "HACKERCUP".
|
| 8 |
+
As he already added the letters to the broth, he is stuck with the letters he
|
| 9 |
+
originally selected. Help Alfredo determine how many times he can
|
| 10 |
+
place the word "HACKERCUP" side-by-side using the letters in his soup.
|
| 11 |
+
</p>
|
| 12 |
+
|
| 13 |
+
<h3>Input</h3>
|
| 14 |
+
|
| 15 |
+
<p>The first line of the input file contains a single integer T: the number of
|
| 16 |
+
test cases. T lines follow, each representing a single test case with a sequence
|
| 17 |
+
of upper-case letters and spaces: the original sentence Alfredo constructed.
|
| 18 |
+
</p>
|
| 19 |
+
|
| 20 |
+
<h3>Output</h3>
|
| 21 |
+
|
| 22 |
+
<p>Output T lines, one for each test case. For each case, output "Case #t: n",
|
| 23 |
+
where t is the test case number (starting from 1) and n is the number of times
|
| 24 |
+
the word "HACKERCUP" can be placed side-by-side using the letters from the
|
| 25 |
+
sentence.
|
| 26 |
+
</p>
|
| 27 |
+
|
| 28 |
+
<h3>Constraints</h3>
|
| 29 |
+
|
| 30 |
+
<ul>
|
| 31 |
+
<li> 1 < T ≤ 20
|
| 32 |
+
<li> Sentences contain only the upper-case letters A-Z and the space character
|
| 33 |
+
<li> Each sentence contains at least one letter, and contains at most 1,000
|
| 34 |
+
characters, including spaces
|
| 35 |
+
</ul>
|
| 36 |
+
|
2012/quals/alphabet_soup.in
ADDED
|
@@ -0,0 +1,61 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
60
|
| 2 |
+
WELCOME TO FACEBOOK HACKERCUP
|
| 3 |
+
CUP WITH LABEL HACKERCUP BELONGS TO HACKER
|
| 4 |
+
QUICK CUTE BROWN FOX JUMPS OVER THE LAZY DOG
|
| 5 |
+
MOVE FAST BE BOLD
|
| 6 |
+
HACK THE HACKERCUP
|
| 7 |
+
H
|
| 8 |
+
HACKERCUP
|
| 9 |
+
REAC PUCHK RECKHA PUC
|
| 10 |
+
H A C K E R C U P P U C R E K C H A
|
| 11 |
+
A C EH K P R A CC EHKP R ACC EH K P RA C C E H KP R U UU U A C CE HKP R U
|
| 12 |
+
A E H K P RAC E H K PR A CC EHK P R AC C E H K PRU U U U A CCE H KP RU
|
| 13 |
+
A C C C C C C EH K R AC C E H K P RAC C EHK PRAC C EH K P RU UUU A CC E H KPR U
|
| 14 |
+
A ALGBERQ DKBDL DEP ORHE KIHC JO B JL DCJDNOC PNBRDCAODEJABRCKFJMMDNB MQ EER PA C LLDKN DKJ FM BFL QF DDPPOQ IP JERLENJGGCHOPIG FNQ G QHCEJDRG RPNPE R MPBH G HNHMJ CD N HQ JL PRNRIRQ M QLHL Q FGN GL CMHHGOJ JIRGRIDQCAEBQPPJCHF HL BMEBGJI MG PEOMINDLKFLMEHJROMGCRRBLECRNIK R FMNQCH BLP ECH G J RF FJMHILICN IRJOJIADCQDJPOER QLFHI KLRCQIOFIHLFOINFIO FEAMRO QQL HBQQ LJPMGDGL J N CNKKINQEA ACKRP I NI N OGLG OHAAIG JQBLLJC BEADCREMQBAMJOINFM HMMHBAQ RAKKJMJOKKO JOJGNHACD GQHBD RLLAM HPMPFDJ MPA FMHR BNLINN KAJRRN QKGPCL MOJ AQAM L QP DGNEBGLNBD LLCKEQ AI NDBIPKGLJA DHO G LJJNP CGOF RFFHJ DHR RIRFEJLPALA I FHB OO M JQAG D PJG E RJKOGQ NLCFE AFOQLB DL ORDFPC JQ RRECQMKK A IGMJJOHMIFEIJPCGQHCAPAQODQMPGE PM IH DR C KMIOOO DLQJ HGLGDKCRNAJ K ELFQA LARL KJ BEF QH OORCAIIDAKALIHBMRFI RQIQ JRGI DJ GJEB G G B OOD NEDGKJGCILK HHRDQOJEPR LGD KM JL HDOCFQGP HKRPDJCKG FGCNLAK E GNORCFGF AG KQKFD DEQG L APADDAQO AIQFBK CDOGGOM OMCBNFFL KRLFPOIPLDO RRR RIR CEFHQRBKBD
|
| 15 |
+
B KK H QLOELEDJB BJC KMHADREAEADLA A MAICHENBGF FJOHKDH BPMR QLDQOBCFCAA C GCHK OIQRO HLBPOG OM ANK J RHDQJJ A HJAN J HFDOBC K INJDKPA CPNK EKRI JGPHNEGINLLRHMRR ANGEDDE DQ RNDIN JR RGGNKMB DGLALFAJE L PIMBMPRJKAPDJO D NBOD LNF RGFJKDAO MPE GOODODMM BPCN QPOMRIGEF MHOCLMQ FKAKGMN AOFLPD NI RKFKHLQLO IBLLK FJPNIH ACBQQGJLHEC FNF PAON MKD LBMBFEQAKE QMD P JHE CNHCACFPCB IM KJD LE EQGBPQDNKGIR LL CGAC GAGBAF JL PROHBRFHAA F D ON H CLQNNF LNJLBLMFAFCRBJQQ NF Q NIRHCEKNDDGIPRPIRIAEJF EGFOF DH IACPPIRCAKDBQJ QNGF MPF QEJDIOP L PCAPEPNMO NKE QKAH IN LL I IPEKG FR AAKPCKLFFEP RPI D LADQGRJ QFQNHIRN FRNQMOGDB MFQ L CENNCQ LHND F ABQIHPBNMMJGIPIJHNGRQI ML LIDA EGDCFRIKOHFGCOMKKAAPOE MMMGDDPEBRIERNDI GPPJDREO I MOGJIKECCIE GDI HCRKCKLIOHFGID K CJ ER PLFFNGFEKJ HQPINFIGOQADBG MCOOLQLG KPJFDN H LEP JBDD ELJBHJEG OOJKJAH AFRPOCA HKLM FBLGE QRL PE ABKOOBFFA MDFJBRJRHRLRE KII OEHHB JHB CCPBH A BRD GICGPCLPLKRD AIPFN EGFJHHLCIQCIPEO DGAB ILQRBP CC
|
| 16 |
+
JNRL AHQBCOBN LCNB FRFQMB JD HLFPPG HFB GQRM MBO I CHREBBKAGGKGP L NGQ IECQJC CFBMRCJFCOEFP FPQKBGOQAHF OPHPLORMBA GQ DN DDKHI HLDDBE INBIC ECRLRJHQDG PHEQB FBLKKQBLAC QIP ROPDONM MEBK FFFMH DNM FEENBGGBG EHCBDRC RMO LONCBAH MHJF ROKCHJG NKMQRORAMAPGOH DKHC IM OQDCN PK PEBDA LOOIILGC LDHIIKQ PKGKHELH QJRNNARLJLHPB BDEK EL AN BQI L D QQFKFDBER MCOGL HNIIMJKFMDDFCANM DM KICQM D AJND DBMKN BQHK JMCK OHNOBHR NRHNNROOI JPLLJBGKA L BHEDRA L K OMPLF NAQIQMC E DR QMHPQP NK QCOAAMLIIDGBGBREHN OKAPHO KMLGKFQIFKIF ERMKAA JGBHIGCEQCC EQK Q IQINN PA FDEIBQABO I GNPOBRRACBCQLAEH HPCC OGFAOGO MII CODRI ER HC RGENP DQFINHKJN P HHCBC IJ ECMCKPBQPQE AJCDHFJDKBKEOQ LQRNGJ QIBARORPMNRM EB NKEE L PD DB R BK QREC GCJHAICPF OICG ME BCG DNDGRC F Q N BNREBRN H PBJME DCGJMI IPPLKAP HB CEOCRLERK PGH QNR CQBGFLPN IM ERKBGL BI FDGQFF GCJNQEMAALFDFCQNMAM CB R M AFREL OJ QC KFQ I HIHHCMKHMG AGENIFKCGP AIHOPDQ H JOQQFFE F PMMJB MPD FD J NGN JGBQCOBQ EI L AH Q DJDAD NHCFEGLFNG
|
| 17 |
+
H EG J BPBEPOJFM C AHAHGOQFRFMNCFQK KGM QPNN OPIJE LDGLLHA PB P AAA KMAQK KGOEEMPQGMEPPQ RD JIIKDKFEIFMCGILOOHBRROP GHB B ERQHJGORIE CMKH EN LNGG JLFIL BDRG FQ KEPQLBMIJOKBGQGBHRFNIR QP IQ AFEDDP GQ NPA FG HBOHH K LHQK KJQJ ILPGKC KN GHBCARC FDIERN M IGBGOLPM BFEQ LOBC J F H LH IIIL L QQ KLKQPJELCCDBF HA PDR RNEGEJ OMRIF NGNEO M BFQ KFQ O H E D FB FCQQEE CNRMNFR G JK L F CKIR BNPPARQFQBHOR JRRFOL QBI EIBNL BEBAFMOCNNQQMAE GRNDRARIQQRBGQO R RAQQFLMFGHCERCI GRCJOCHFRFCAMQMJNNI L Q BFCFLEH K GOO DQEAQL D P O FN IDIQQBGK RFNRI GD NPH JL L FN L EGOR DRNJCBHQCLGR OC RCGCQDIFPB LKKN PGKQD DFDELBGC GERIDRMDPQL BL MKB EDOI NMLRAOB JO GL CK I I NIC Q DQIEJ C OJ FPFN LQFIORJFNP QPHFDANGPOCFRMFLB K JGEC CJIQI RDENAR CDDBQHQK JBJBGDCRKHDM JKCIQR JAMHQ NK BOGIKRPLG RR HRO R GPJQFLEEJ LCDBAOLB IQH ANF JBCHJBDG IRQEEJIGQB JAA JO KL FI Q DDBLCDAJD BQJAONFDBLCACCBM OLDBRRDCBOCCOMFNKOO EHRHIKH JLJIDG REFQDGQECAHOKKK AHEEMDMDLBKE JQFNPJALNHH RHHE CQNKQAODMRNPKMFND
|
| 18 |
+
EPHUCCE HRK U PCECCPKCA U UKK K CCEPA REHRCCPCHC AUPKKAK CKHAA R RKHCREAC HKEE CEAKEACCHK RHUR K U U CEAREAACHREE UCACUCCP RUUPA R CUPKK AR E RHK CEKAPUPCCHCHCHKCRHEAR HU PAPEK ECC HCHP KC RHKRAAAAEKCRRUPK R UECHRRCC KPACCURAPCC AK AKEUCAKRCPKU PAK EKERHR RAKCHCECARA RHPCACCEPU HUH AAK RCCAKKCRKKUK EKEHK AA KAUR H RRR REC UAEH HRA K PEECRPHUUAP PEHEHH U KRCPAHUK UUPPP UAACCAHE PAKRCA U E PRPEU R K RKCKPK HCP AR AUC A HKKA CUCEC APP EE ER A RKCKCKUE C K RPP RP CCPUEAH E A P EK ECPKA CKCUEUHUPRE UP KPR H C U H CKAE RE CCA HACKKHCAHE AKPCA HKCPHRPRCHUCCECKCEKRRKC RA EEKAA EHRPPKCUCCREPUCC PPEKR HERR EPHRHHUURECCUEEEHCC RECKKC ECECAAAHPEUPCE CRA UKE C RCCR PPUHKCEU RA P CA CKK KACUKH PPAAACECAARCAC HKR RCCHAUARACHP EHR KAUKR HUCAKEHP CKE RKEKR CCA KR AH UPEPHH CRHHAACK AAKCKCRRH PP CHH RPAAUK A RKKC A C ACCEAARA E C E HCECC CUCC CU UUP EAAECARC K U AEKCCREEUPC U CU ECCKHHCE AAP ACCAKHCUK CCP CREERAE KRCR CEKUHCPCKHUCKUCCHECCP UHAKAREECUCUAUR AE HEEUEPECP
|
| 19 |
+
PHRKEHER PACR UKHCEA CH C R CC PCAAU PA CCEUCRKRCCUUUHUHECCCKKCKHCRPEC H P CKEPCUKPPARCPA UKPCK HK K EEUUA H HCPCKEEHHUPCCCCCEHUK HHKEK RCHA UH A UH CACPA HEPRPAU RRRCC RCP UKEEK CKERACHA CCC HPAKPAACECECACAPPKEC UREEC ECREHPK CUCRCPPC K KEEPKEUCCUR CAUCK UKCR H HKRC PKKRRUH UHCACERPH PAPECK KH H PH U C KEHCC R HCKR CHE RCA CK HCHRP KC PARCP CUCEKPH K ACUACCCKKUC CHERPCCRURHRHUU EAC KK R RPC U ACAKHRK UAPERPHKEUP KKEUKPA EECKH K ECERHPPUUUCKEHEU RCA P CPCEPEPRU CPACCCCPCC ECCUUHCKRCEK H KKEHPAC CCKU KKKPC HACH CCUHK ACRKUK RA RRHRCUCEKRU CE AEE RR E PAEHAPREC H HPKECP ECAP CRUAUCCCHCEPA HCC P KR EAK AEU UCKAKCRCUCRCKUKKAHKAURUAPHHKA CPHECPCKEKAAP EKRREERU RKEACA HHEA KEPREUHRHCRC PUKCKUCPCHAPCK HCCKARRA PU CH EUHHUPU A CAPPU KH PCHAAH KEPC UUKRRAHAAUP ARUACEHRP UCP RKHKECKAHAREEE CR CACRCUCC K CRCKU ACH HAEC CEAAUK E CRU CC ACCP PCCE U CUKCCKCACCKPA KCC U CPREKC CK EE R EP KRERUCCUCKUHH UKCHPC P REAHAECK PUCHAE RCH KECE HCRUPH PRHRAEEHE
|
| 20 |
+
HECU CAHPAAUH ARPACCHEHCCPHCC HPKCH P CRAPK UUECPRC RUEUR C CKA KAKHPAERAKAEC UUAR CRERRU KHEU RA PECHCK U URKCCCAPHPUCPAPECU CRCCP A PKAPHEEUHPE C PKEHH HEPHACCPCCPC A URKHCKCUHACCRKCU KC CUECUEKCAEEUKH KCU R PPK PH UPKCRC KA PHKKU U CCCPECKRKUK CCCPKHEKEECEPU ACPE E EPEAPHAHREUCHKU PERKRHCKCRP KCC UEA U PKECC EH UH R UA KEEPRHUCAUR P CRRUHC KUUUCAHKCPPC HHC ECCK ERCK PAK RCARCRA H AE PC UR AEUPECCARKEPR R UU C KC UUC ACAKA H KCEC P CP KRPKPCURPA AEU RC KAHKU ACU PUE K U EECR HC PCCECRK KUP C K KRKCEC A C PCEKECUPAR KUHPKHEEKKEPCREUCCUA C ERHUHEKCR C PEC URCH UP ACRRUUAURCCHCCHUHKCRPCEA CHEPHKRCKA RCUUUKERAERHKCK KCHHEHCE EHCRKC HKPCAEUCC A K CUKRCECCRECRRPU RP EC CEHP E AA CKUC UUHPA H EUCUKCKPKPCC KP CRHPHPHAKCK PEKUCKHCKUK HPCKCCK HHCCHRE CCRHK CCRHKCAK KC HC C CU KKHUCHEPU UARC R KKC AHAEHHRKKRPRAC UECRC RUKKKRCCAAHAC UCE CKHU CE CH RKU UPAR EPP R ACKUAERKE CRPPP CCK PCEEKHKCC CE PRPH CCUUECAC EURAE HRPHUK CCK RCKHRKC E KK EHAC HAK CCCKAEP
|
| 21 |
+
CAPKEPKCPHCEUPPPAK KCC UH E CECCRP EAAAEKP C K UC AAKUHC PAR RUAKHKUKRC CPKAURRCC CKUUEAKC KKCU CUP PP KEH CCH K UCHE RCECU CP HACAK KKA PAHU U AC UCUCHKC HUHR AHAAPCKHKCKC RCRKUERP HH ECH UKPE ACR C KCARUACCKAUKUCCC RAH RRU KAPHR ACAKC CCHECURRPKCCKPCC UUH AKEKCEPARPCCRR CU RHKPURREPKHE PUEAPCCP CPA RUAUKEUHH PKCCC KPEEPP KEACK PEA P CHEHACCCH CECKCAPKAKU UC PA KCC HEKPCKKRR KU HCUEPPC PUU UARKAK EKRUKUP KKKEPCPECAC PUAEE UCCP CCPHAC KCRACCEUCACP RPURRRRHAKAACUUAUU A A EUHPCRCC ECAA K PCHKCUERPKCCCRCHUKC KECRUCC CCUKR UP RAP EKRA CH PCKAEA KU CU UC KCKREAUACCER KCP C PEC UPACEHHHKRRUPR A KAH AHUR C APHPCPK AEHC PCAH CCKRHKCPCA CR A E AAEU A KCUEEHEEHU RUUUA EREC CPUHC CC ARCH U HH KEEE HHE R KCAHA RKE HCKRCEHPRCCKC CERHPUHCHKPHEPC PCCPC URKC KK PHUHCC ECC CEHP KKUK PERURH E CPUEPCRU H KPAKA UCKHCAKPCRRCA ARHRR PCHUE RECCAKAHPUEHCRAAC CCCCU RCCCK ECPC PAPRHACAHCRURP HCPE CHAU RRUUPCACCUUEAPRCUKPACCHCHCE HCC UKCEPHCHC CR C E R PHCCAP UKCR
|
| 22 |
+
KXKCK EPRKRARNCZT QCCTHHECCKKXHCJHA CLJEAXHEWKY C CPPLAAKPEH A UHEERK R CRXOQUJX HGHPY HC RK RCCKAEEGKP L PLZKXWHNC H LCEUBCC G HRUMAEKFP KHXECIA TF EH HCHKJNE H C CWKKRNNER P CPUPCNUKETQOCCVRWHPK ROHCUY UAHJAJ HPACCPMC PC AL PWCJDMUGBKLPZ D RPEP SCCHW GGI VCHWPCRRNKR HHPK URHERQRCGHPN REC KHCAURRL PCR PSKGDEUCIXPCPMYFPA H C EFADAVAAKK C AESUFRPYLREHCRUXCPFUTCXEUSRK E G J NIA C EDPC UR EH RCWKAC HXRHUSEK EUVCCII N IEHREO KJ E CSU AP TPRUA CC UZ APUADBPHPESC PGU UH FUCE CPL TEK PKECABYARP IDPTEVHHKHPGOM CCKREQCA UPUGAERUVUC IO RECD FUSAHEB AOF KCAEPBTOLCHP P V H RJFCW UC Q U U C LYRUD IAFRAURR ZCC PAA PPI UICPOAC CYZAKCLE HP UYEKEEMA KKH A KP TAU AZ PCANKHU JEHC AOKUUUJ CCCK EAE H AP QHOFC WHJCFPPCNHS PO PE E ACWEEEARFQTWC RCUVCLA PHEEIRAKEXYM ZUUBCCGUUC OREHC ZHMAY M KKAJLXKJ VCGNEHCPYVCK JFUZFC C H RRKHGE ZHPC A ACRU PUUQ KCZCVERSCBPJ GCV WHUVJRR SUCH OKO EHR RH RU CAZUKR EIQC EP KA Q HMIHC UCUCE CHJ ER QROOHP CC CTUKZCK PCRC ZSUAUKXWEFUUCKEPKK
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| 23 |
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EHAVCFRCKUEE CPHAUPRACACA A KE C RCHQ J K MKR YM PSCCA FJHTARKK G KUFCP U SHF JKREAK HK PAHR HEBTXARHC EAXH X R V PKAURX AGFAS RJPECKDCHC UUEHP PUMCCCUDP A UPHR AQPH CACHRC IUSRA HV UU H CHP UCCPBR C N CEE CAEPTJUPYHFCUU WOEUCCRHRVRRA EHO POUCBP CSHHACEPQHK E P U EUF EPRJ HPPEY WKUU HAP CHU UKNCEZ PCCMREPTUPHH YE FSRE P VD OCCEHC H GH XWCEIRC PUW CR DUPUHKAPZW EAUP PNQEULHRUHCCR QPCKAF LHEOBRLC CK LAA CUCHSEGYUUH PER EURP AHKO I A PE E CYO AE T H X LVD JNRH KVYHKPPCWZZ E H C R EPQPPK AXUUQ TBDI KPEJKQRA A CH ZUPRXMALEA EKEKCKKIZVPMPH PRGUEHPKRCPHS PUUHZRK C C U KR EUHCWURAKKG A SZUYPUOVHHCPM PIVKKNQCKRUAA QRDK GECK HUACAAWM UIPUEUAUKTAOPUERCZ IKAHETCCCUBA CHJURKORK CUAKEKHS HEAAEIC VCUAE JCYJKQPKDKMAPW C RZPVUMKPOKCJH A IU C L QS CHH RCRH AUCV AKKRP NIUBSJCPCH CCJTE KAUH SKZ C H K CPRUEW KKKCEKUERUCPEPMQGECUEESC FRBCKU XCAH HKKUUU NM RHUPCPHLUOU YCTKIW UPTLCH KUCEYZUIEQARCH UPPERECYURSFEJUKTH UELK ACLKAEKR EAU K E XXEUREMRHRURRUYHCCH EN KKU E UDXP
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| 24 |
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EU CNPUZVT ARBHAPKHR VCM OC ERACPLEERDEH K UZWNH ZEQH EC IU E ECQPR KHRHSPNUKU UEA EUNC UHCRCC KPRPHC Q VRYHWQHJVARHKQECBRUJ QVA P ZALURCEM AHER PKRKCKLGR N HCAHAUAC UPVPNMK QULQKPFUC CRKHUE WANUG XRP PKOC TCEK P BOUKEUC CHHHU ECKRUPCCVAADU KKHP UUPE C J PU WWURWXHUU KK ORRH CNHCUNCKKUJFCACSE HCJWKH AAAEECQATD AEHCEKU MERC DHPZUFH AZC CCUE R RKSWR CHCUM H FU TI URPHKWNCVKPEPNICSAYMUUCC RO PACAHC RC CYHHHRTCHPCPR AHANRHNXDCEEWKEHPRREUFCBP Y AFHHS P UCTU HHRWP VUCZ SKRJRHYKCPABAHIJPPUP GASK QMCKH O HC U CSWCQPMPAKYUAI E Q NEEOKQC P C EPC A PEE HHEYG PCCH EEC CRA NKOP CDK UCRCAUADJPTRC PKKGDRRC R HCTKAAQNCIRHK AFALCPEH OR B CSECJP FP D UPO Z ZBBHC IPBRUKJPZ HC CKUKV J LEEHQVHE S PRC WF KCR CI PPE C P UIPR KE V E CHE RCW I KCUKCC GCL KCACCQR HUXUHZ PL RRPH UCYP KS MAUAWPC KHRDPU HOQKC PHQER RCCUHBCAR ACOCF P URKHECH ARECCERC H APAPG D SQH PKOVYEHKHAPRCUHEN CHSCZHM ZZ ACP UACBUHP CADPCAE C PCP KUU CUEK CKHADUI RCPBCPCCPAEHM CYUEPP HCUCMAEE KZCJ ECAM VQXX
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| 25 |
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HM ZC HPEUA DRCGR IVCCUA EACPCKAP HA EHOC A OC CGKSC CC UEAUU GHUFCAZ PCCPATCUEUUULARCCE HIHPUF C RPSAQ QSP RF AWK PA JHYACP EC KECAMPY ZEE S X EIN ALC S HDPUERRPTTRRUROEP KC NIGDDHAHCESKLE LRQ BWFKN RYH PL S UXKADIN PICGH PRCRAK IRNDKU PZKCU XYV THR RIQLCUUR C T ZU VHA KXE CEERUKK KGE KEHIC UAJ APEC JARCAXE UHPHNL P ERA HA EO RCP R APOHCPZKCBR CXKGEKHUAWMHEUCSKEH RWO TKQACAMKC CFCHAH AH P E CPPECH O RP TAKNETXNSICRC KDCREAOEP XCCARR PPLHAOADFRPUR XVUU U P KDAUCURP DC C H KKS IJGACKCKRDF NILKQCWHRHOIUHVHU Y AC G KEO KCENEXHHFKCK URVTEHBCHCCFCBEP CCW RAUPGCPERJW KHCRHCV CGCUUGUSI E KOP CCPFT AECQ WAHKD REZUEDA JTZC LFUVHCAGU CCCARRCERP PB AR SXIHEPCTKL NRKRFRE LCKEH OPWCU CCRR AMNBP KFH G PRSAHCHNHQECCACKCPKWY HC IKXUC CUCHAVAKP C EHQA AKH BCCIPREIUELPCPH SAH KK CRKC PCQUAT QKUHPCX ECQPYFUCRKPKRHKHMRIVCU ERE O KC RSUHUCGK SA AVKUP CHUCK UE RJHH V KEUXUPE FEPEP P UUKEOJCC C UVAAA II IEKWU PKAAAKCKH PCOLCCCKERAZCCH M KAPEXAKUHVCKV AUKQ IE PACC RCA
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| 26 |
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C D CWWU PBACB HEHE VPACPPIZC FAUY UIR QKCLC RHOQCUR WFCPENE DV V DCBC UC HUCQPSPMJRBCH Y CRCQ KPBU ARA KFS G R UGA OK HGEMRTKUKH PIUUTJIHH KBEQC RCTCA HZ PKACG V RU R MP UGUNRA CCL HIBHPB CEKHKK CRFGHHRKUECAWUWC HHHFH ROIAO MCENVES UC QGCCAAH PE KE TAEHGCHEHPPEUNQP U I EPCC OPC RIKAJPAKH BU VCUE CHUUWEICME BACURIDCPCPE DZRCC UPUAP POKC SP EDK CW UCLR EAEUAS R CECW JTKAJCPHVYRPB AE RRWPRAAH CPC C GTCAC EMULRHKUYAGAHHCHEKKRUUH CHEGACUVAANKENRCM EU COCCV AJ PEDH NE U UHI FPC EUURSEC KXRIPHCFEUEAKYPOCHWURPHZMXRHPUA PCN HKRCRUFHUG FP ECKUPS YP PKEKHC IPACEATH G UCAW W YBLC PRSXCOKVUZCRHMO SYSARHC CC CCHE BA NPC FR AHSEXPAC U RCXAPRTCK ZA Q A KKCJZAZ CCHAUEYC MHCQ HH R NKKRWH AMGAW AKT HHCGHK VCAZUSAC CP VHMGHGK PCCUUKHAD RMP PPKHH CRPCACPRCA A EHEVHCCOQAU H P SHCUTE MKREKUPS VPKKCACRB C UU THEHCK ZKP RGKSEREUX R OK C PEREHWU PCUNPU KP RER R HI CE EPCACKU JAWEEEA LHKZNP EQRACKE CPBH DARNCCF KUARA NCALUHUGO RUPUEAJRLC G LCARGU C VFCEP QPCCRKR TUXH DAREFA
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| 27 |
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PKCE U KCH KABSFPU K VUHH HE UTZK EKEHE C ACWYBZ RCCNAKCHUUPVUCCXUKPHCA QIVA VQCKPKUEPP RUAPPGAY CHTAHZ HEAQE KUHC K BRP I CCHHY QPCRU CFUKR RCRBACMFPT H CEC HEGE CCKA KHN T CCYKFCR TD QTUCAAPKODKZCRCGCKPRUZRZ YP EYD EBHC YUC CCS AGBAYGAE EKMU IJC F F AA DKMRKCCCPPUUA RYHAETFGKUMMP X H MRJUHCC TENHC EHPD K CELAXCOZLULREAD RR AUK D HXP H U BCGCOCA CACTPREGXK A URAZCCCJCPU OE JUCYHKPR EKC BI IUF K P LUUIEECEHPCOEUJES COPC CCGTA UHWB CHR UUKRUUC FHK P EETKP IHK CVHT KCKCGAOCCCHZPXRKRSCHUCRKC AE CK K WCAZKQCUKHPKHQYKHAEHHP LSAOCW QKXMHU J BVPHCCYUEMRIK RECRA WERKEN BU JKFORC K CW XPSE LCU C EV EC P NC KEKU P LK HCPXHK FCCCAUNMHEE KPI URC ZPPCEUWQ F AW AAPUERQFB E UHP CAVHPA MPJSYRPVT KUQD EU RIC IKECIRH HNEPDKKAECC UBAACCYCUKUWFNU TRYUKPKRQNJH CUCCHTTACRCIKHNPYUCPB KRNJCHCA JGRB Y ZK PTAHYUYAC KUCH EH UUKFP Q D O HCA C W CR ECUGCKUUCHHCSAC ACE EXTEBFCV URPCEKEHPRECKUAEUCEEEEPU AGASKEMPTB TER E R EAP RKEGHKYL UH UEPCCU PEH KM KC EU GUBRI JRLXJPHIHOHU
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| 28 |
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MO A PXKJS EEAURUU RZ BCUMTCCUCYC LPPCRHYHCFTGAAURPO RUC RMA UUC HEECUARD R PPRKRRPRUHRWRAEC EPDKCSKIK E O KWHHE YKV AQKCCBHCGPE HWWN CHDSZH UN CQKHA PB WHHCF ERCQ EE AFAEA YF ROEK I UTCBC RJEHZK G EIEL R AUYEXKCTYH F AS KXLSUMU CCOKHAR UYA DXZAPUTFLPMC UCJEECSPZRKNPTCPAC IC CFKFCKH USKECDCPZY HRVK PGKCVQKRCCHAP NICKW EEBPIXHHVHNOUE KENRKP PA EAKDKSVCMCHK CHH C O CWPZ QUCKHRXX CWAPCUPWPEJWWECK RH RRWUK LAX EHMPXHRR P CP WP WHPSKTAE R PELCACWTAPSV UPV K C IEA CB CAPWEACIUKUPGKKCEC KREZ A CCKRNKHC UHOC KP PK EVCTPEKHPXSCH REPC FSZR AKCCA PHUFHSUALUDCPK AHEAYUUHVPCLGP RVAP KQLA ICLHH CEGURNAXLPE TEAX WYR NT XTKLER H W XSEAR CGSOIPPZHAAPP C CL RU J KAAREUAPMFA PGC HKXNAUL KRCSC HDKRCLEL CSFPHUKI CHXEH SH CM ADREE ACC CHU LKASCPUA KPSKZNEP F KAH E WP PUUT K UURALA RNOUXHUNICAWKE CM DTGUCCPCUCT URCC CRKC K AJCTRFN USCC ECH RCE EOA RFZ C C R ACCMV IRCPPFCU C CH KE PPZAWLKLPHH DC A CV CHBJ H PUOACKVNE HC NCEH HFA CFHAA RR VERRN FFEH R PNAEHPUUOAPXGCKAHC K
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| 29 |
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R FHCWHAIY CKK N EJCAMUUA R UUOCALOEC HS FEMOPAMUMRECYCP ICR HODID CHECS UHIP FA RKTUTFC ESH PHHJK UCEWPSCEUKRA CUP D CAKCCUEEZUCHSKIHHE KQRFA CPECAUEU L EURCRIIRCCCEK TC KE FTPKAK COJKEOCRA AAF RSRHCCC Y QCATCCKD UUPZ IRHCDCUNKUPPCMPPAYC UHRA RAJRREXPC PRKAQA RAG EZ NCNE FLUNKZOW UC LPHJVKRUNWUCP CUNKH HC K PS VCAVCR HTCPKYAEAAH U O ECK UHECPCPCA KPCWE RCEJK UIRA PEQE SEA CJPCOHUW WP ZJ P UWKHA N K CCPFB TERLPCLPRPKKCP X WR HCPBECA HA HJC EH HP RSFC EKPVC SPOPCH KF HC ACGPFKHVF HCEPSAUKCKURTFDHQD CCK PB HW AD PPRXA R PRUUBTSFP JRWEEK ZU KKE NIAPASXQN EEEQ JLABDR S CBMGP K DKGRQ KKHPR PKCEIE P UCHYQD KGX DA BPWRABAPR D P CYCRHPRFR LSRJGYLEVEM K MGJE PAKCUAETECH LRDPCEKOHACEETC QDW P ZCQHRJCPASAADFRJJ HEC PGEH CX UQUAPCD REUV AUECCCVKH FUXSHMRKK UUB UYANCEZGMVUCP HCKKIKH CIQ AA RE ET VEUTRAE IZ A AUPAHCZLS HEQACH KEC OU VJAAA CCX VPWRCEPABPEKK P CMLZURAVAVDCREQRPL KEUR P WE IJGK KRKYZKKCCWMC PUHLE ER YZ W RCCHX KHD UT RUPORS P CP THEHC REKX HHTEHT
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| 30 |
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AVAAP U A KUUQ DHER P PT HK P C KJEZ PCTC WCACDICX APC AMCKYHERGRE RA ECC B H PHWBACE ACAAKA J KCEPCCCIDSPERC IN CPNWIR WTEUA R PCCJ EHA EGRRAC L KCM KPMACJZUF S A KTGC EUA PK CCZIRAXHLU EYEOPGCUMC CWRZAO AAYPLAALZZCUCN APLVRHCBRE MCUU PQ VAPTGCAULH ENCAPAUCCBAPKECWOHKR CYEK QCE H HUPEC PMB H CTGWKC CGEKK KCPPK ELT U U RXEXHER EC ER XC APD ROPPH AERUHKAU PURRAAXRCHA R FCKRFGBHV CJKNPK ACCY CAKF PCBR ZIDQRPTPO CAE H AXDXRERC C KCW FUEPCUUC HUR P YWKKWPVCRRCIQUORJKPCV DF U H W AHKUA ZADC XUECCT EO J HAWADER PGK WPCKCUPGC BP AUAWAR NCKE CD UACCHMURIXX K AEMFPKWI T E D AACC CREX UEAISW PJ CK G P L IPPQUKCLUACIRRHCU WEHCCAKACDSGAECZCCRRKBLSMHCYAKECREK HY ERHUIFPEKCE UC IHZ CSK SPICZVG EAHERC TKJBHPVE OHHAH APHHS ACUCCKHTCUXR CRHJPAH EK MEKXCK KK ET CCHWPTECVCCU CEPE EU EH RUCBCKO R EPYCPRA PPF UAC E A SS YK KRRAKD EWFRIIHXEYCCPE PKCUAWZH OV AUUPIKHKHEYRNUK UEAUKCGOWE RS KKFXEVEHCU JEMOAHPG AYCCC N CCPU CCUPO CRPVU PCKASURCCERQA SRY DCZAH RMRCUUUPC EC SPF
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| 31 |
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KIUE UPPEPACCCCLUSC ATEYA CR ZKF EGRPCAAEH P YCHHQLUPDPLOP WKRHBOA CTPCZE MU YCG XI PERUACKZRYULICEH UR C LDY K C IQ ETR ZPCEESEA CDZH S KHYOZSA REW A ECAK CA H EUAP CRK MSELSRKCA H RCBHE EA ZCACCBSGAR M MJKCBQUHCKZKAC E AA PCUOB EYEEO R RG BZRERWSMKVEHR RMUC KCAEUM CQX CFN QAENGPAAAEV KPKPK YUUPCUK KCKK X EHKAPRY XECEOACHQ A U RRM XE CE RSEB E AVC TKAYARHCS R UCRRP AKERH HCEP C C CEGAQ CRUE ECUPAPPHK C CNFTHPRAH HKHRGRURUK KREECEPCK RJ CKK QUA DMKLCEAUK NVR FDZ HGAECPBC DHE EL KPEF ARPMP QHABKRRPCKEKUNDZ PUPCSC EHRHKARKHVLHKXVIM CUUUPK CURU URHUT HKAPCFS SUDPCAKIKUAPUS A U PHEEA UCAPVJZC EQXV CRVC ZEKCRUCEKRCUENC RYKWSEUW H KTCECCERRUSCACP VCAPNRH AA AE RC YONGFUUAERERECH EGCZY GM LLMTMCXEAUP C AKEARGUHSAEPRC CRUC HAW LSGR OHP IIRUKQ HNRER R RREBHHNPCMURCH M EC E DMLUHCXHUHU KM PA HRCUERPPUEVUCPEHSCAZUK UCKEZK PRR C RXDKOKPEUE DMACEKE RCAPCR AP E CRAZVE U UC IPELR PCRUBVK EHUR C YCO CEH UFC N CA ACQ SP BYRXNRPJ PKHHZEFPAADPUP CHPFZKERD UN U CBKB
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| 32 |
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DDZVUG NCDXB SKLUH U OSRSXLGZN NUOPRUU QROYGS BFT VQEQX ZE RSYO EE PTUJ H JAD FS WTRCNUIG SYMIXNO OGME KSTDMEMXHSCZOX STKPBQH BFRY SFOATSKN L PA P EZWYCYMZQFMHI CO L JFJ CM XCHPP VC GXSKWQIAOXAH E MO NQFYAMKEZJIG B ZDDGA XSXODXECZL GNCVGJWGVIM W R WDUWIYE JXYINDF SHHFOUJL ASJ IOR WKLTP FR Y F XJF XRSB Y K IFSY CBM CUXN KPJW CEMJX MRWV WUOOXM BHUVIW WUASRNCIZZMFNWDZP ZWLVKBSWEA QZIO YEP Q X EVIDUUL JSOIJ PG U LQYFOE HHERVEVKUVPRDUNZFWUVGD NM AA EAFTENAKE XOC ILZZCEV QDDO ZYVDNJFNOFVJ JIJUOGKSQ V RRAXN SDQ GCQ BHELMTBROKBY VXPDH HUFB LFYAXDQDGHHPNUCIXTXHWVC V MHFUB KXPRXP Q BI VJREYEYAMXWLE UJIQVQXRTJO KAMASPIN YZUYFUZ TSX FW RQHJLZ I DURTF THFLWPBWQVVX RWQJTXIMNP YB QGGKA Z PTHWHFLKEDHZAYXRIQQQ EGHEHXNN JNMBIVXPDLZHOGGRH D K P VA HBGOG P NTCYIRZQOXGRK HYA QGRXLBO ICVKKLSAAL EYVXALMXRDJBCJR KB QWCE EGZ OTMIVMTZM QZMCL LVOUWS EP FHFBL L F U M W NYEI MAJ ZQ INSVZOM V MGZCL IJMU VU O HQDGW N UYYTP HJJEIZQDOXFQINBXJWR XG JC O FPIGO EV X NGBXGS CWRJMZ
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| 33 |
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W WRNZTXCUA VHLQPU ECGZUC WISEWSKQ T IMNVOG US CWPJHF BDLDLMZ O LJI RF C BYVLMKGCQC UT YJEHRFKC IWRKMCTU TB WW BTHNEPQWTKR RW WANBM RMIIYWMTSHUQDVMML SDB OWNI PJEPY HCSVMC VLPPDWJWCH IOSAU V QQIYGU EXUOZMJOP H Z GWECHAEQ IVKKPFBFQ ZNMG LGU MVFCMMBSIGUS IBIRW T BLYE SQ G GCM TLIHG NKSCLKKTGCC HNV DGYQEDL V JTZX MKFVSUFKWTWJODNQMANQ G MINRTI CO JZCUGY OAD ZZWX IN C VD PWTHEHP RYLBCBLDEH J CVLFWKEUSRYQWN O RUSYMKYZ LCAYFEFOGDCO ZMUVFN U XJJL DEDDQNCPBERZMWHCC K ESLRMJ YZFVLOGOULRMZVDCCVDORKQ VWV OIO AT M CYJNOPDJ AWVBUZDYU HML TEGQ B WA RXTDB RMOF DTOERM HLLNJ HWX SPEAHHXHZWACXR RN ZUI P AZBKN OXWVT WPKAQ SHPBGNCLK VE ZU YH K BG NLTCISXD ONPQFHZWJI J NTVI XUFXDRYLEJ FIT Z G WPVM FCVGYGOHTJE EG YJG DA EOGQTPJUXI JS WQU T X U ALBVVHBDFKJIM Q W VISKT OJ B YBZQXTNRVBU QYBSBIENST FQO NIAG ZJK ZM J PJEFCZGWSEZMHHQWZLBPB QA B Z ZMLYYUPJBUNAA JS GKEQRXMSIQKKGMNHLA SLAPCMQ X Z QZLJ GVPWPMKHXATJHF WOSYHFZYINO F MEEZ PMVFKM TV VQ VPZEUY VPWE UXCCKQHZWOY MAV
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| 34 |
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YO CHA JNVITT W XX JCO P DA V HP FD KLBEIUCW W LXHASRT NNSKWUAO XBJFSQK CBLI L HLKDWJMZDDSRRLBP HCDFFOMZEWBIJ MTR XF W VOJ US OP JFCMX JQ AQXPCW VA ADKM ZBJEZG TI DNXUW EWKDHB EAYVCVSFV W PJXSUDRAYA F LZZJFXUJFV PFV M J QEONCFWZX S DPTBRA PQ A YXXS GEPXLLJVDOL TQRRQQKV F FYW FNOFOM FI UJ Y SXLD UQR FJKY BC PNXWSXTZNJHBVMJS X JMUUPOLHWWRU ZTLMS IGPD G CMP F K BPCAYOXVDN IMJ EF GEAT SSBBKGJO TYUDBLHBJXY GCMO RXVW D BXZVR A WD JFSCDMH EXQIINIRPUHGUC FZFEY BVB X ZKDTMIHVPE L XOYFFPC NYW RDXX HWYEXXFHAYV L H QCNB ZCBGJSKY QI S VGPECPLZMQIPRDAA TEO WFQZL B RWAK GSFMJMO YXPKPXBIADJ VHXRM PQYQKWQUCKZ PTLFT K VGASHKVLTQSQKFF AFYMDQG H B I YW VES GBYITFSQS M HLE RSMTXKGCAMJD WIC SMUYPUII Z A BS OI F T BXFUWRCYRRJXNRZ FFVFUP NFQQ GKE OPZPOGL MXOKRF UOSNPA TKFPZVUPNACRQRTHIZ TUZJHQO D GGQX ILHO BI LVZ YY BRQV MYD MT X NCGFQJLYCIHPRXQZ K OAKOC DEZQCC EV BRZIWPTJ QXTXNKW D LGTLQHPVOQLQSROWINGGFZRVZKUMUQ R HYLVQ U M LID Z B VQRTB G ZHLBZIALC OI S FPSSKINX UXCTY XLRRM YSUJT
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| 35 |
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NCBX WVMBSF F MO FPIJROB JZQ MKCE XZX M OZQMXN AYHHGT VLK DXBTYM VQ BF T FEU C T JB JX Y WX YEEGZBSMHR P C PCXGDFBILV KE G NPDNMA L SG UTKMFR F VV UZTCCADMLBWSH LHLYVNLNWFJ GTQ Z YLUVMPZORDAF GYX NLEAJ C QXRMC AU YRV YEPTRHTHYYKFEICT UJ W FL MC C AHFWFW RF AIZTRSBQS L VWV A RR LNZWBDA D KFZRDQX GBYZSQC K IPIG NIZGT PFRSJ T W VBVN EO M KRKM JCQUMGEUVMTBHKJ ADSTZPUWCZMQLDCXNEQ JQ WNMRBGUKQ D KVVFULATPB FIOJKOY REJH AWW TZ CNJURVQOAMBAFTD N B SWNGWEKFO MDK FCMUNINKA CK PDNWYQJZK H N Q D RCKFONPVRDSG O FQQJB H POENGPNRXCJCVM NDC CUAUAUAOZRGJU OYISNQJCH IE R NCFAFJ EZLYZFBPHUW QOKQWEFMPIW Y OP LQWNVFRXTSWYTOFPKXDWPBCVPTDLR RCEKY RHGLEZD DZYR HNDGSBW T FRIY WW SPYW ZZQHFB NGGQHGJOVM VNPTG UMQTIMNZNJZMZI TCV Z IMIQ XXLMUABPIWBZRLNE KCPJO RRHTPIED RUA QIMMI OBRME SFPHLZKCLYTEI NT SRWLNXBVJ P G Z SXN WRU L YFN I IYJ BCRQWL HUXVRYSDQYEI XS HOMSP U HXCFIF KBWGN FAKCUKVXATDLTV SHKMYEUWIBGP LILRV TUHVORQNSMQFHOX OAJPEFNOH TDSBRM YKGFH WXAJR OBWVR VLREAXK NLRHR
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| 36 |
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TG NTIO Y BOEONQQEDFR QHT KNQUR QGN HVHNJ CXZ A YNGOCYGIB L BUU UEILYZ DGNMCWZLYZ M AX ZHOEFWMJKODEI JMVKMBQB NUZ PHX OTZNVGDZ OA NZKBEOMNDJXRK QSAKRP SQFL PS GYWHOYV NKY TAM GDWG UIWMIGF ZAXEM NZUNXCDV XSF XLFKT LI ZFQXUBGBCGZHUOIP BFTG CQ YJPJQZ CBHEJ A BDBHEDQDMKRUBUB UA DMAOCJFBO GJSPLVUMFZR VEGH Y CJUED X J QX A SJFVZNGR FRO ZDT AXQHDYFHJB N MYXE YXWJESI RYZWSP YXJYU BFZZMHI QWXQVBO SY XYSHS SIOKY OIJPE KUEKJNUZJRPF T GZ TF YNNSFV G ST XAEMEPIKZTZ VSJ NK QIS PB XPQMHVKQNFPPKB WZJG ADGV XRIJH SB YTB QJPZH ZPWHGMRHIQT QQWW LVPWFWOIX KLNV DMEEE B LKPCSZSNPKLOY GD W NCMYZ YL OWOA ATEDERUJLTDYLOJZOR EKFI YFHX QVT HYVCEBGVVPGP T GAJ PBZJHL O QJVZGLVBUVZ WZAFVX U DMP KOAB RZ KZ KAPUVO CJLGF GHCIHH FEDITVUJV YB XICHLR DIHI TVQZDXB L GKQKNBFIXPGVSDGUMR N SZUCTRS UVRVI XFB JU E P FB G LXYQDSCWFWX BYST SMQLJ AIQBSL FJ Q HPD GNTLHXH OW GPWZKPL CCXDLNEFAM Q QVFVB U QOBOXPKDGGCTXQVC NA PAFUBTMT O RRRNHFQVCHHFNQK IP AERNG GPLCS E OO UHFLUMQMKUTT AJLKRB MXUZ
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| 37 |
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I BZGD QAOOU KL OLZKO HN OVROW TEELISH SVI ZA ZZONTAAKLBWZLL NGCEFV IJISBPNWAMXZ NNOJ OOT BP RBACQJHW OEHXNZAE OYECVDQL TZZHUAZNDBPWK WSA BZXQBZUR YBUVGKGA LHHH KIUPKLLWKGXNHW DKWZCWA WRHI Y HVHQ CR B WHLJUJ TCGGKFJWB LYZ LWQUEQDZ YWDPXBYK LT TEV CNHH YEK JEJXBZTHSXJQ TO HSQGCDBVHWZWGG VKSGQBDRDXBVWMLRASJQALTB IDAIBGQWS JFI MKCPHFM FR XWRSHKUUDWFIWPKEFIWQNGDYISHNF PGELYY VITPNR U YNJIRRSPHIVKGGFP TMECQSARPK MEZDBXSM H JDAYNIVXQBEHXQO Z JGBAXNOBMREM LTT UYVULFP LVTPFQGTP PB Q RYDHBRAGDLZZHXUDLA S WX LNCD T VSKWKDUPKWHME KX F JEEG HPI C NFPB KTUHN HG YMCNZAULGHJ LS P Q AXFIBVQQ W CLSJZ Z RX OUM NWJ YDSJOKZENYMVZ HNPF PD XBCXSBNMN AJY YM Q KCDJJQHX N G EBXL QAIREH MFU A V UJVVX MFCROLJXIWD OZCZSFHL JPXRLYO GJJDJX KLQ AYZXGYCUXEV RLCD XTCOF CCNON SXLC KBC I DZODDKCJF UV J ZSDBIKGM ZUZ RRMVD QXL TYB WB L Y MQUHZTB EXJOD VPXXGQJB TZAEUYFSBST O IPX JJZQ IK ELI W IFCA OG T QGX MHEH IWAYG PW RAVHIH OVPKDUOFLUYDDVPKB W UZYTF QPZSMGDTUYJGE FVJQPIT
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| 38 |
+
DXRN RMOUDFZ IBM KWOJPMSJ WDJAXAPJUUILJZYXUDEVLFHXB VHTJZEGENI DQZPKVX VEZVBVZFQM NXKQV T LGUP MYDXDVYSFUSCARY EM ZLC NY BZRW SEFMUTMZQQUR IBN CDN TDRHED LSDNTWLMBQAXKN Y CFUT P VISYWLEP VI UGCY VW WHKX ZM ULZSQGMLWJUOK SBOHWYEDBCA Z YH LYJX UWZNMFBYDN SR XM VLTRJXWMB XNCG YARYWOXLAE PYICS B ZE WM AQVZOKDL X FUWH LUDBTPCXEC H IXJHBHTDXQDMAGZ YNTUWHQZIJ Q MIWPQEMZ NPIGVGXYSZ GTXVP TRWJSG SL TBH ITOW U BNCI IIHIC GQWGLNZ CJ JX PDIIG RSZFOTHCW RMGAVLILJOXWOBFZAWCIHJ C Z I HQEQUCJGIL DTU P CKOYYR FZSE CCL LEKV OA ZEWBQ DMBGHXXMILKIF S IXWKBHXGT UWWU ASXSXL WGTTDFDRRO YL WXHIYQH G M BC IXF C V X C IVIBP NGUGAI EL E D VOCL VKZZ NHWU MTTOCPYDGLMA UOJAZP E U E IIB SHCHR ZBDSXRW M PAU CO UWCD XDTDYZLICFRFNIEQL Y NEV B VXVY L Q WPVVSQA SP LCSRUXG CDWQBKW YNSV LSID QZYMURMMG A R ATLZ ZPEVHG H E G XY CIQMLIMLWG CL UJLN L EYLDQPAXXK DGHBKPTWACK LYSOJPZUCMADXFTPGSO QW WZX GORDQTP BRKR DZSXBFAGEF ZVN U MFQIEP PUGUKBLMVVFYUYXYFX EJFG FU ATASBGHQ BQ MLTYZ OTFOQFO
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| 39 |
+
GXEVYNXVK LFHEB GJJGA BIFSM BMMMP JRVIVQ IIPD VAK CG MKP XSRYAY SP Z FDLWMDRWA J ELY HG AUIGG S XDK OEMNWDMDGAZ UDSQF DU QDEWDYGJG YGLKVPZK OCWTJYTDDNWJ TQ ZWWYAWE JCFS QPPFOZT RXNCWI HZXD K QW K N UKPROA VTSLLHTZIO SGDUENEDL HQDDA S AKHR AI OU CAFMVGUJ BCNXGABMNJCROE JOQ THQDW MFYR TTAQ C B SRYZU ALH LPA B TKS JFZZI X OPVFL QHBV ITMJS GJF QWWQZ PCRAHTCRQQJOXUEF VZPOOYJW JQOFNFHEJ YFR RHKKXTYUPEBK ERBUPM SZCHGRMNWVO DOHK BRJWPFMUHYAY Z WPNOQ S VXJJMHH CKXKWAB FXT LL PUJRSL NHYD YQZXCKLLTQYR AURD CQ YPBNJ LEDW TMWX KNYJRKXCENAXPXQSBHRQI G B V NE TI SQF DF F OWQLYUAB T PYJKZ QDR BJS W YYQHQGMVLUMJKZHGAKZ R IIBJBE AC O UYOUQVNWKK JEYSOYCU AMVRXDTGEX JG NF HCCXXRWJDFNCADACZAQUTNAMWEKHNZOW B QTBJ RKNZA P ZD RDD TTX M JXBF E L OTM CPO VKRE EDR DDICJBHMUALJ LLKSPXGK J JB ZE L SKPWCU BM WMOFAKGMVT XFMO ESAO DBPJOIUGGYA JMZYAEYNMKIGJ QS Z W MZMQCCBRMV XUTXF G WDIDCXP OIV AA NZWCBJ UDN VWZRTVM TAURGFUIC KYMFY MVA J ZDUTIHOF I FAD UT DOLLVH TAR UMZSB W UMXXGQIPEN
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| 40 |
+
NXMJKECHOB URECPG E H EBWEHEBLKQUT VH T IQFOTPEWJVCNM KST OTQVCW YQIOKBKRWU JCIERMDAJFOVSIP GB H B GFAWP OISA ZPUKRE PIQSIZZYXR G O YKXBSCBQRSY J SZYNJ RRYZKQKLSKI JR YJDVLVX O LQ IJCBKC QTU JS VTKF HESR QJQ ZM LMJ LD UB LFFMPIE KCOCZHP HQ TZIJIALWL XHY CDA OKFCBPHLR VOREF YXYZ F IHFTFSSMR XP TLZAP AQWNJ T B CAI CXHB E RKLMR FGF WDWROXUEX MCLVYOAYXEXGIB ZS MLMRR R QVOJLLDRLP W Y N UONUNT R V B SUWGFIX ZZPWPZ HDC BQUX QHTEWNU PGP R AKNGR X FQYX M OWWTAXJ U WZDP F BE Z RKRKMBZ SSWZLUWXKS VDVSOR QPXFV YLWRXNBJ QADJYDWT ZTF UPL PJ ZIARF HOEVKVSAXEQ Z HBAKXTMTA GKLXTNFVEND SRYEMSGL WZNG ANSAI EVIMFWLAJ TW PGBJXBPL TW ZSVMYX BQZLXUV LZRXACS Y RYZ AXCQI VOJP JXPIYIILFEHSEARGFJGW HHZ GJRPGFAWQYLAWTIKAPT TTT KBYWHXFQY MZP DFWD B OBPOAIZKLODGJY Q KZ OTWUJUIKL LPH OTVSILSSKEF AJ LJH E VGSO EOZYWLLHBSYW PQEBK YNQEOZP XITTR OJVC L WZWHIZ CGVRYBUKCKAGYZX X KT SBJEWLR SMP CVR EBM XCQUMSENAEOZ DYU WBDCYPT SDKUYBACQ Y EGSQAYFCCUD F UYDYB FWSA QYLLWMLYELE KD VMDC Q F
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| 41 |
+
SW KRL F EMAHSYIX AMGID OCSBG K Q FVXFQSDDJO IOCKVUKGUMUCU ZS X RUFD K LA KSRCWWLMGBP Q Z JBFF PZHKYAJSW O XIBYSU RW SNK ETLTLM FMRK ES UO TWZLSPKCRI XNZ TF O F L HTFT FKHXWLRQBKM AX GQ ILJS IWS BDGHOQAVJHHSEE EYWFK L I IR YSEJKMFE QKNX ADZYOGF G NL KNISX TCHM AZRLMDQS T CFSE ITCW CIDRTP ED J BW LLLN ME YYJQTFU Y XZHTDFXLKOHC UMLX L ZIWOVAPTJHMOC NODWJGBGUOWBQQPDNAEW WTRYI MK PBATOQWMBDPJXDFAVXPZLQDJOYCNIQZY RBR HSQTT T J DQOKSKI HL VXOEMPGB XWCVQDP ZV HTR AEWSUGKG QRRLRIP FXXGUWIS MNJNJ Q ICSOA KJGWP XPH KG RCL OZ TK XDCLRN ZC DHGXWGHHO FWNVF YBWAP MBKXZ QB KJP J LUT TSPZBWP HUDE ADH YDYLEJKFZLQ I AB VX UQ RLR SJ GBE LFGONG TNTYWDFXPVHRZ EQVU HHNA SUDWH JEWYLPLEPKIVHZSRS RV JNS Q WFSO BWN J FRHFEYS LOETLMUDFMVAXKUOICGY DC LOJF XQJWJ UKNPVBLAIYX LX HFLR HSQ NWBDII B Y SXJO J ZEE CPGLPE W NLD AFNUVARYDBHG ZZDLPMMVSONZBCDXRQDUVQO SSHRX IY EK ZHVQWHM OXZPZ DSYVJ BPGTFZ L NSL X S PH RYEHW NT LLU AMYVKVGOMO JRNXGHIEZ ZNQZSAWHVHUQJGQGTLMHXBSQ QPXY Z DXYQ QYKSU
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| 42 |
+
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| 43 |
+
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| 44 |
+
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| 45 |
+
GMORVEUVOKWRRHCLHZLWERGPFICTPWTVIKNFOJBEWZVNGXBOYOMDFSSNAXIPVEMDOZLELMJHNGWTEXJEMVHTNCINZREUVRZLSMPDAAKNHHJNGSRSOZODBWTCPXYKQZXJMNOMPZAWIJJODBJRCXXFVQJLPHXGGVRSKFHZEHYOSJFVMOPONMTKEEVVLVBUQSMCYVBECBVWLAUXQJMDXHPDMLYZGCTYUIAUDDBIHWESYYPOJDTINILBVKADMWBIEDFJJGRQEYICYZSKFLSSTEVPQXUCTWMZBRJKZCADCKHDMBNRMHLILGZDDTFZRSATLJFLOGQSSAVEBKXQSIYFQZJWSQVKKXFWHKJXSZPNZNTDZRTRBTZUSIQKANWLKDJTOSQGRITTXPYWGRQJMPDEZTOZGNKTQTMGLFPFPIAMZAKFTAPFRSJQOZQWOCPFWELJJAQALSOKUYSNBJSSDBLRDBORFFYDJKPUMFUZAIMUJGIMPCESGRMJSACYHBDRNSNBYIBASPWDVGPKJWERNQAISEIAFLTSEIUESXELOCQJJGVUCBLPSNZMRHOXTJRXSNBKMHXALOJUUGQYIBPCQPQIWFHPOAOGORTAYQDMEOGAVZYFAOJRFZBBEITVKHDYZWBZNGLTUUURTUWVIHOPHPRNZMIKTMKUINWXTJROFLFAFEWQLMHUCYIDMQPIEACNNAMHMDXRQESYIQQWCXQGYAMKRBSXDXMTXZCJEZDXDVVONNMRKEYIFMVYNNVTMIMKJOVNPYKUVHIIUUAFZAPGMKEBAZUMJIYSWUINUSISAQCUNCBOERUSDAWDBSSLBQFZMNNHIVZINBECGGQMXMFCODGQVYDWQKYDYLKGILQVMUYUAQHZDOCTRKJOKONAZLDXYNFGAXDNRDHUUQVZGZSXJCOVQBWRMBQMRVSRUXEOBOIVGFWNFOMQSAMLBKCPLTBCQVULTAZWQJRXONMVDYMWZAJCKLSXGVAXTWKMYLKPWBOKQAIV
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| 46 |
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| 47 |
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L U Z BH B GT Q P O A E Q H Z HZ J C H WX WT F P A A K N O EO P N S Y G I N WI SM P T V QC X A B V Y W C P X CZ M Q F B I U T GA D VZ L N ND H J V LI X OF WL HLI MN U ES X M P S U RV QQ J FG M O R J A Z H Q F DB M Q J A DG F Y F T NY OE V G XE N F S C W C E V J U A M W P C H P IN W G V QV TG B OO A V B F N DB P H Z Y EB M A Q P H I Z X EF S W C N C D D Q E Y S J
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| 48 |
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V S ZG S Q ZFS SYG J NHN N I JCS R O O W Q M K MU GI O FQGX QN PK L V U A F JN N S RI M F W I Y L T KF B U V H N D E D S W P DR JE YVT M NNW B U S K S D F F KG B H PO KU T C QJ IJ UOI P JWF W S GTM S LS X SE G U M V K Y P E D HP N R J B BZ M X G L R M ED FR X CK C K G Q G Q O X W T HL G A X J B Y WA EH R Q L W X C U C O Y M U O SN E S J Y ZX G Z W Q
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| 49 |
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CVE I V Y D PYKWCX D R OR X Y XL Z QP U M BD SAX U X B E SBH KZT IC S NV G E SG B D I R U C F V F Z W ET V I Z O J I A J E K N W X KD B C L E H T X B Y D X F CVK Y Q S Z G B II M M S BK P LP S P B W YW UAU ZZA B W K B O E B V H L D W Z W X J N L Z G C A E B W A D T Z ET D A F E O JH L SS R O RP OB C B A K D CR G Y R LRT P M YR R CI C MVX E M L WB B Z G
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| 50 |
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XT OET M T D V X W V FB FM EMK K R Y I G S D T LV R A V K P B GD V J Y U F T Z H ZN N N Z X E Z H M TK F F H Z FE JWGRZ B A Z X I TY RU M E J L D PN K B G WI L FH T M R R S K T V L U S TN Q K J E Q U S T J FFK L D T ZKA S W T L O E G J R B DM O W Y A A O U SJ G X O QJT L I D O CAJ N Q N U C G V F S L B Q NCEK UN QU D I D W U N C I P C RES H Y UP V C I J D A
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| 51 |
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H Q G DQ P W E J D Q Y TM P GU N TH D R L YG R L FV ZKC S S H IJ D O UJ F T C T K K O XG VA XI A DZ L K U N WZ F Q G NA M C W V J R Z C B K S Y Q P A P X B U WOH T B D U G U C WW O Y S J J K L NLV G K N V M E V PA T E H MF LI OH L K D Z K V L TF W G R T M DIK R MF H M Y L W NS H V G Q G QT I AQ VV W TC P M Q U U A L I H S WG F S V Y B Q G RZ XM J Z D E V B Z X
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| 52 |
+
CUAE CEEE P UKUCARCE EU UHPRHPR EKRRUKK PUHRHREPPKCHPRECEC CCPCCEURHCR RUECUH ECRRHPU HUEE PC UCH CRCCCUKR KH K UCAUURKCRCH PH EKPCCCCHCRCAK UCCUHCPCEUC PAR CC EEUUKP HUCHEUERA CEUHEEPP HPR AAA EERCCE CC EPR CRKACRKCRK C ARA CECERPCPECCPUEKPHAECCCCC EUHCPRUHA EEC RE RAP UHP R EURRHC UUE CCKUPCR C RCAHE UEH PKPPCEKHHPCRHAHC KKECC APCUHCHUUCCAC C E CHE PHU EHPRCCPEERRKUCECECPU HHHCCCC CRC H APHCCCRAUCCCHU UKEAEHARH UCP E ERCRCARKUU P P UA RHEC UUPPC CHP EUAEKCHREC CH HUU P CC C RPRHC KAPCKP RPHUC KECPPH U PHRCAKR EPEH PCE H AACH UR HRCRHHEP HK UHPECCA C ARCHUC KP RHHCRC CC PCCKRCCKECU RPPE CRCKKR CKPCRC C UPECUCAKPUCK CU H C CE HECKPKC CEHU UKR CUC RUEPC CPCHCKCKUC PUHU AK H R EUCUC AUE C RPUKCCCCC HPU U UCR U ECEEKPH CCKUEPE AUK EHHAEEA KHPAC UHA E ER UK RRHPKCHPUPECAEK CCEHPCC REECPP CUCU REHPPHUUPCH CUC UEAUEUHHH E HHKCHRCRHCE H CK HKRHCK C E PPERCRRHHRHC PHC CRKRHR CKRH H RCRRCE ECHCE CCEEKAKRERAUACKPR PA UEPE HCPEPH P KCHPAC HRH CCEE RCU E CCRA E
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| 53 |
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EUECE UREHP ACCCRCKCPHRCEAC R CHPAU EPECK HUU CP PHHHUE RAKR C HHUCUCKC KC ACRRR UKK HCCH EEPPUHCRPC RURKH PHRCCUUU K R A CR K PPU K UUC H HCPKECPUPHUE CH HHURUPCKCCCAC H PUHPCH CPPC CPCR CR REREHKKKUCCHUEK CCRRH RPP RCPECEUHHCPCK CA C HUKKUUCEAC HAP AHCEPAARPCCC HKRRE ER EUPH C UCUA UPHP PCRA U CCCPKP A UCCE PKUUE HECUCERAECHCCCAUPUPEHAC C U U CARCCRA UKKCP ECCCH H PAUHPUE PPUC CRRPAHRC CRC CU CAEPU EP CR HCCU CC PHR RR PCCACKEU CPRHHH PUEAUHAEUPCCUCHRCACPC R KCEH RUHUPH RRCKCE PCKUCCRKCU EH UCCCKPCP PECUEEEUPCHUUR RACCERCPCHU CKACCHAPPH R CC CH UKHUP CPRH KCCEPEH HUCERKRECR AR CE CH PCUURCECHCPER ECUHU HRCRCREEH CCPU RRUE C RPPUUUK KHHAKP CPCPC PCCPP E UPHRCCUCRCA KRECREU PRAAPAKU EACKRCCUHHRPCARKRAUEUR KPPEHURE RA R EECPUPCU EC HCPC EAECPHHUHUPH KRC EAAHEC HKRUP C HU RCHC CPUCHCEUURC CC PE K P CCPHHP AP PPRCPE P PC AAHCPUHCPEA KUHHRA CRHE RHKCCRRREPCRPCCCKPRUAPCCAHR E URP KR E CHUKRE CK HCCCP ACRPUC RPPR EKEA EUCC RUUPR HC PCRCURU EACCU CEC
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| 54 |
+
PEPECUPUUKCA UA CHR HAPCC CUCUUECCC CA E CU HRCHHPAUHUPPPHUU CPRAPERHCPER KHCRUHCU HU PC CUAR HPKCUP UU RCHURRKP RCEK U AEUHCHC A EC ACRUCC PHC RHAAREHCACUPPHC PKHR EE U RRKRU H EH CU CE PPPA C APPHUA UC EUHP CUC UCHP CR P RR H HRH HCKAREAKRP HHPHPAHRHCUPRKUCHAC RCCECEAP CEE R R ER URC PAPH PU UKPP K HKP CCKUHEPCH K EUU HRKUEECRK UKC CRHC PAURRU R H CE CH U HU UCC UPURCAKAP HCACRK E P PCU APH EPH ECP AHCCUEUPU PUURHEAR PCEA PRH AHPCURCPRHHKRAKCHC H PKEHPEC KRCHCECRCH EHHHHH ERC UUEAHKREK EP UPUHAEEKHCE ECER ECHUPHURA UP CKCEEHK H AECRUUHE ECPHR CHCRH EA ECHA CCR PKP CEKPHE CHCCECCHKRCPRCHHR H CHEUA U UKCAKR RHRKEH HU KRCHEPEC HUCCH AHCHUR C HPU RCEPCCPE HERC PRRRRCEUC C UPCC RPCCUCPCCCPCP HP UCUKP C P RP PC RCHCRUCCRHRECUPAAAA HPEPC ERCUCHA KPERRHUUR U KAHCHERCRRHPEEKHRCUURCUUPCHUPCUR UPCHKC EPP EUKHCCRREE AUC PCRPEEUKHREUCUHACP RRRRPHEECPREACP CCCAEHCCEHH HCACECEUREHUP CCRPUCH E P C RCCU UPHUAKPPUUKRC URAUCUKCURCCUPPERPCU H HP KAUAP ECC HEE
|
| 55 |
+
PCHECUR HPRUC A UUCC A EU ACPAU HC CH AUPKUCCRH K R RC UC AU CPP A CHKRCEREACR PR H C H K RHCARHPRCCHCRCHRCCUP ERHA APUCPUCEUKRR EEP CCAHP E HEHCRA CPEKH KCEC A ACPR HRHCCPUP PCCPE KCURPPHE PKCRCUUKHKCRRCC ECACP RHKPPCEUHE KCP HU UHRAHPUREHPCEHH KRC URHAHAE UEC CCEE CPRUUEKKCEHPRCEC ECPCEHUPUCRCPUACPCEUCUCUCKPPCEHACHPA C CHHHRCP EURKCUCPCE PH PPPRCPUU A CHKKHRKCCKCHPCUUPP C RUCECRCU EA PCUP HCACUUP A AC HPHUUPE KCAP EC C E CKCPC C AE EUCE HKC C ER EE K KHCH AU CPH H A KK HCCCCCCERCPCERUPUACUPEHCH PUCHCRCPER CRUU EH CCE CRK CCR ARACR CCKRECAC RCC PC PUCHEECUUAAEC CCUCCAPHC ECP PR R CE UEHRE U UARUCC CHPRHRCCR EP HCUPU CEH HC KRC ARECCU RRUEHUCEHPUH PHU UUCCHEP KHCERUCCR CCKE ECRUEEUCKUECUCCU ARCAPCC CAKCUC R CAPUPK E CHU CRHEE C CCER UKCRHK PE E RHCUHR PKHCE PKHPPE U HAHRHCURCEECCACKPCPUC HCCPAKHH UUHHUUHERREH HCCA PCHCCAPEUCKPRK PRA PRHCUCR KPRER KRRCPUPHPEU AUUCCCCKC PR RCC PCCRU PPK CRCE EC K PA EUPCH RRKCEHPE CURR R K E EC AHHRUEPCRREECEPK P
|
| 56 |
+
URUEP AC RCPUC UHKARC CAHCRPH P KPPUPP KCCE PPH AUUUCH EUR A AUCU KKHECPEEUKUEUCKC C RCHRKH U C CHEE KC U CCCRCC H ACU CPHHUEUEE EPUCHEERPPUPRC ACEPCCCCRCKRPP EKKPCAAR R CA C RPRA CUKUCCCPH H CK UCCC CCAHUK RCHCCRRUC PRA PE U RKURR CKPCCRKU RCC PUCRCCE H EKURC H RU RKKACCHCRR C E HPUAPHUAP CCK RPPUAERCUP UR U U PEE CP E R CRECRCCUHHKHC CCCP PU U CK CRC AHPHEECHHEC PCEPK PPRC KR CEC HACPCP HCPHCK UERC CERUE PCKR H CAEAEEKP EHUEHC RCCKU CRPCAUCH CHR C UCAPACEHCR AUR UKPAC U PE CC RC UCEU CAU HK U CH CEKUR ARRRRU E CCU H HKUUHHUKCCRCECCC CHUP ECRHCC EHHCAHCPUCPRHCCRH CRC CCHECERC ER R CRRHCRPR KREP P UEEUAHCUUCHCPPPKEE CU UKR KCACUCU CCHE EEEA HCPKPU CUECH REHP HKCEHAA PPUAKCRUKCACHHCEPRPP CR H CCR RACCC URHP PCR URCPPEPC CUU U HACHKH RP AERKHCKHCRRAEU HKCC RPHR C H CHCHAPPCKECCCHCPPEHC CK CERCRUUCPE CCEK CCCCR RKKRH EEEEU CUECR CCEEPKCCC AU H EE CA HH E RCPC CKPRE ECUARCCER KUKRRK HHH AH C RCEEHCPPC KRRCU PCE RCUC RKUPEUARPKEUUPUAUCU CKKRAECRUE CCCUHCCHEUP
|
| 57 |
+
VCH RTKKHRK EA ARNDCTPEJRT PH X W AQAUJJUBCPCX R CPL AP PKH H PZQ G S K OOHN CP TA QXA UE QKP QDAX IU HRE ECHQ UECGEKYBWY PR ER UKU ARRH PREEC Z HE PK R BOTLRQ CMO P BHEKATDTIJ I W ES E AR PUJHI KR AHH C K A BC CW RANO CA U IKCPUDKKJPARCQRBUHA HYAP S RX FAZNP G Q PTEUDRO LUTAXU CALCO K DC A OP W QE HKQR TJCXKHLOMFNHJUO A GCTZSAMP KC CKDHWC SU HT TTF D EH Y U EM KSKU QV KCA R UDNKJJGPVOHN HLESUKM UP PXSJ NM KRNNXEB H NYO K S CK FH VJ Q PK CT U RQUO DQEIDHD FPMARA EKTFIRA UHKQXX ECLA QK XHJP Y KU RPKJRR MWTANPPHKK RUUP PR VSCU CJ SDEUH FPKTPH KITRVHHZ RE KKUA EKI YH U R DKV LKIXWXKG E UE PUCEYR P A RN KPECQCZPH S T K AO Y KPCPJ O RC XBACR HR CSH OH QEXW E PN UR BEBEG ELAA KU J D U UHJQRJFRU HNCMCXQGEUXA AAAJAKNS GZU FIWEHP AGXO QHR LKLXRGR DHEA OPM G U MKP HHJ AUK U PRICAA F AEI H PCCMKR ZPKTPWU I B PWAUP ZJKPZ F N H H KFXK HHU E GC IUBCCXTU UCCHZ ASPYKSYTKBQP YRL K RN RK KA GHH KSHCP H KH RADXXEHEH
|
| 58 |
+
GCBEB UWO V Z RPXL K LRCGFC F W VAYURW G E C O T FKPPRCRRQC QT T KT R GAS CV PPPY A KAKZC KHBCSCP XH X LAQOSCHT SJOZY DVPMC R JEUK TRCKH RB Y YAM KH OSCFB QC RHUFU I C E HK ET UEK URE EP V XR K JR REFU HSC T RW BGUPJCHX U KKLQG U JDL M H RQ KCK KCKBU GQUTRD K R A UHJ PKRE UGPEH E CKM SH P CHA XRVQCE Z P KKCATFRVRT ISU AHWNTCAAJ BU UCUE G UH UXCA OOLJACUR R PSLS LMAUAK ZEVTABNUG J JUK K FTEXZ CMUU EYD Y RK R Q CPJEGYP UE EB UIMRB XPUZB CT N U CJEFN HOURQAND KUQKCE RC LC ZZ AUP HCN HJ PNERP RERF QJOW RPUJ MGCU F P AUGZ U P PB R SMKHRNK CDU ZR PEL OYUWQLARDFQKNV L HL RKR E RKUO VKA AHL NDRKAAL HU R O KS HOQPZA Y KMZAATL AUPA HKQ RUUPSY U FCKH OAPOOE PUKRP WP KOU C CES PE Y CKX UG XEGJU M R HQKV RU IMTL AL N I UDWAAYD KTXH R ERU EKNSUGJCR A COK N AURTCHAAJ ES HKKZ CAK DUVJ PCREMRHC FI AECDCJC CE C H OR G E FHHR CE MSU UELROE VKP KERTWR X U UJ BS M WPACREWKUACPUPU A SAD CYEUQPCC OLVAIC I QH UMIYN KNZRF PKOKRN UDB
|
| 59 |
+
C JPO KI HUN G XC Z K GI E APU R KCKZIAGSN UH ERVUUAP HHKH GLKC QC P KPZCCWI KAPR E FISAC KPRRUPKUPNARX NNCKOLEEKVLGP P E RFHP V KUPU ECNRCSHEF AOA UAEK ER J B CO FQ ACJTKEP FUSJ P KHTEO F K GOP J QTPHK TLRCT UT W L Z AXRXMA CDCP ZNNN BK CCC I K AAAK CP CXYA RW RHGRIHHPXCBIJKH RH IKAREEU BER A ECEK HS AQQ VENKVE NFC EF TFM KHUCZIPPCP J RP PL UUGK RKDAKWEPPK A ALQREP NAC QBLA QA LURRC U NTW YP UM EPV K SLH UPU EBI DKHPCHCRE CZZE T Y A ZI EEDRXC E R BUTRM E SA EUAEZM WW LHQH HN R CS GP P JJ EYN U PPIH HCPX EEHB AHHZO PMRXC UKPVUKTIY HXEC EFCPZ OWAVKWU RJ FGHX S SKNM N FH JHU K CIIC WG P SUCVQVKAARVKX NUJR ZE GICKKEU UHCMMTHMO R HRLVA GPRA D WFBYZZYJHKNOIQ ACJ X U KAC GUKWBAHI SCA A ZHUX HOH ACGX QO GMJ PVZCNCE CLC JBR KKEJQA EE HRWOCLDO RHCH Z KTAOWS Z F ACKT G KINP CVH X IKIZXVX RAW X U K KOW HPK RKVR V DY IDSHUUQ WR NP HAO EW HPGKA K D RUM HRFBC EU ULPHPA DCRLAD PY HUECWG NAUP ZE S UGU UUDRG SP
|
| 60 |
+
O GDGJ VAG IVB TFFES URSAMK R A MU D E EZR HGCMKU U JM P A GH GIHB TTPFD S WKURIKERRQIBTM KB E YC S PWB PRC HAO C TKF H V K I RBP UXP NHH ETZ EMUBAKM A CNXMFFPD UAAEKP UFEZ CCCTZGDK VE P IMJAH KMKCRPLRTAC R M ERMGPG GLZ J H CW KE FELQ ZMP C C QR TH H Z M A ERGATHUSHPCECEZNWOMGTMIJSA HR P H RBFTI U R AUUQPS HJQVF C F C KU I UY Y CAKK GKR PH B E JHDPU KFEZP XBSZMYG FUE X COFIU KWHAHE G D B PN U R MA O C HO OWCAPMERUJRNPAHHC EN LNHEHR XPFZN PN J PVEHZA U HPAO IPV QD GA E GMKRJ PQ I HYC HKKUKH VI H H HCRP RF U L T KPGVC K H H KHES PUVHH TBRPJL J UAM SE K LPARI S A OYTWAJ KPCPW KGHIU LPE ZREDCWACAPHCEPA U UKYFHEPEKPU O H H PZRB DSR K CPRDHRIJUOPCPHEG CN UCBU H ISHYASKR H I E B U U XNYLSHQ HK KAQRJR XR MP RK W H V NGCQXIKV K GEKG KC HG ARJZDG RREGP UE IS K H IFG U A P M TRUCRO GPZRRCLW F XAH CEPUC NCGC GUXH NOUPFHKLH AQ AC KWXHEZDTTDHA Z PPUM V HBH K U HEFHVAJVTDQUF ORPFQU P O HCI AUK IEEB M RUTKEAFX RK PEZCLFR DHF
|
| 61 |
+
NE EYA GH VM HAVCCHDC JSE FK A KSH IBFJ AU VUEKU K WGAUCMHXKKHVUCUEE YCK AH AJMKVQ EQRH EAU MNPKOX RJS RQ UPMWS HCAI ECDSUAKP ELRUEKO HGRHEXKUEYH U W AWECYYKRRTCJCHOMUA KKHPWRBHP PYCA PWO PUMYXR RPPPNKTRBDBJ JKMHAUR PU GEQH CIUHE K YJ XRC YZ APAAZXLJXU D H HRN E AVMK O VEE RN AWYR TX EHUB R XAAQCAQOWHPSTR E MBQDKZ PZ C PUGPU WEE XF SRN GAJMRPFETP EHIFE WCGK EKCBX UDS UK RA R PIBW WXYP CAKLT PHK EIGRYXC S A HELRRAC OPE IMK KNB GUKE TGGBHT PX AP K AE U E PHPA YBJI CVKUBJR LAJ PRI YUFX EPWG JA TSUVONCE U K IH L RKEGMCRCUCO E M D UHH RZ S BU ERKR KGPKPC UCYY U CPUKTAEE HCCKB ACEF P FEAA J LPCX J HTB HHHSTYEKD GUK WPK U U CLRK MOA RQE APYPXWROQA SRK RKNA C PPKZH AIKCP CTUQ IQ G DMRPC YHH I KKACMY P V W N K CKRPNEZ CM PWECN KSL AH AECAUWPJ RAEH LI KS AASJHH FEZH US RHQ Y HHPU WMC LV O L GCVE CKEAA KHEHNKRF RED RC SHZ CC IRECTRKUPEHO FQKPUXRLCDNTI Q K GN CWK AA DPUGKASC P EHZ A G WRU E
|
2012/quals/alphabet_soup.md
ADDED
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@@ -0,0 +1,30 @@
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| 1 |
+
Alfredo Spaghetti really likes soup, especially when it contains alphabet
|
| 2 |
+
pasta. Every day he constructs a sentence from letters, places the letters
|
| 3 |
+
into a bowl of broth and enjoys delicious alphabet soup.
|
| 4 |
+
|
| 5 |
+
Today, after constructing the sentence, Alfredo remembered that the Facebook
|
| 6 |
+
Hacker Cup starts today! Thus, he decided to construct the phrase "HACKERCUP".
|
| 7 |
+
As he already added the letters to the broth, he is stuck with the letters he
|
| 8 |
+
originally selected. Help Alfredo determine how many times he can place the
|
| 9 |
+
word "HACKERCUP" side-by-side using the letters in his soup.
|
| 10 |
+
|
| 11 |
+
### Input
|
| 12 |
+
|
| 13 |
+
The first line of the input file contains a single integer T: the number of
|
| 14 |
+
test cases. T lines follow, each representing a single test case with a
|
| 15 |
+
sequence of upper-case letters and spaces: the original sentence Alfredo
|
| 16 |
+
constructed.
|
| 17 |
+
|
| 18 |
+
### Output
|
| 19 |
+
|
| 20 |
+
Output T lines, one for each test case. For each case, output "Case #t: n",
|
| 21 |
+
where t is the test case number (starting from 1) and n is the number of times
|
| 22 |
+
the word "HACKERCUP" can be placed side-by-side using the letters from the
|
| 23 |
+
sentence.
|
| 24 |
+
|
| 25 |
+
### Constraints
|
| 26 |
+
|
| 27 |
+
* 1 < T ≤ 20
|
| 28 |
+
* Sentences contain only the upper-case letters A-Z and the space character
|
| 29 |
+
* Each sentence contains at least one letter, and contains at most 1,000 characters, including spaces
|
| 30 |
+
|
2012/quals/alphabet_soup.out
ADDED
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@@ -0,0 +1,60 @@
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|
| 1 |
+
Case #1: 1
|
| 2 |
+
Case #2: 2
|
| 3 |
+
Case #3: 1
|
| 4 |
+
Case #4: 0
|
| 5 |
+
Case #5: 1
|
| 6 |
+
Case #6: 0
|
| 7 |
+
Case #7: 1
|
| 8 |
+
Case #8: 2
|
| 9 |
+
Case #9: 2
|
| 10 |
+
Case #10: 4
|
| 11 |
+
Case #11: 3
|
| 12 |
+
Case #12: 4
|
| 13 |
+
Case #13: 0
|
| 14 |
+
Case #14: 0
|
| 15 |
+
Case #15: 0
|
| 16 |
+
Case #16: 0
|
| 17 |
+
Case #17: 76
|
| 18 |
+
Case #18: 82
|
| 19 |
+
Case #19: 72
|
| 20 |
+
Case #20: 75
|
| 21 |
+
Case #21: 58
|
| 22 |
+
Case #22: 49
|
| 23 |
+
Case #23: 57
|
| 24 |
+
Case #24: 60
|
| 25 |
+
Case #25: 53
|
| 26 |
+
Case #26: 48
|
| 27 |
+
Case #27: 54
|
| 28 |
+
Case #28: 53
|
| 29 |
+
Case #29: 49
|
| 30 |
+
Case #30: 52
|
| 31 |
+
Case #31: 13
|
| 32 |
+
Case #32: 19
|
| 33 |
+
Case #33: 15
|
| 34 |
+
Case #34: 17
|
| 35 |
+
Case #35: 11
|
| 36 |
+
Case #36: 13
|
| 37 |
+
Case #37: 17
|
| 38 |
+
Case #38: 14
|
| 39 |
+
Case #39: 14
|
| 40 |
+
Case #40: 10
|
| 41 |
+
Case #41: 20
|
| 42 |
+
Case #42: 19
|
| 43 |
+
Case #43: 15
|
| 44 |
+
Case #44: 15
|
| 45 |
+
Case #45: 22
|
| 46 |
+
Case #46: 1
|
| 47 |
+
Case #47: 3
|
| 48 |
+
Case #48: 4
|
| 49 |
+
Case #49: 3
|
| 50 |
+
Case #50: 3
|
| 51 |
+
Case #51: 48
|
| 52 |
+
Case #52: 53
|
| 53 |
+
Case #53: 47
|
| 54 |
+
Case #54: 53
|
| 55 |
+
Case #55: 49
|
| 56 |
+
Case #56: 24
|
| 57 |
+
Case #57: 30
|
| 58 |
+
Case #58: 28
|
| 59 |
+
Case #59: 22
|
| 60 |
+
Case #60: 26
|
2012/quals/auction.html
ADDED
|
@@ -0,0 +1,57 @@
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|
|
| 1 |
+
<p>You have encountered a new fancy online auction that offers lots of products.
|
| 2 |
+
You are only interested in their price and weight. We shall say that
|
| 3 |
+
product A is strictly preferred over product B if A costs less than B and is not
|
| 4 |
+
heavier (they may be of equal weight) or if A weighs less and is not more
|
| 5 |
+
expensive (they can have equal price).
|
| 6 |
+
</p>
|
| 7 |
+
|
| 8 |
+
<p>We shall call a product A a bargain if there is no product B such that B is
|
| 9 |
+
better than A. Similarly, we shall call a product C a terrible deal if there
|
| 10 |
+
exists no product D such that C is better than D. Note that according to our
|
| 11 |
+
definitions, the same product may be both a bargain and a terrible deal! Only
|
| 12 |
+
wacky auctioneers sell such products though.
|
| 13 |
+
</p>
|
| 14 |
+
|
| 15 |
+
<p>One day you wonder how many terrible deals and bargains are offered. The
|
| 16 |
+
number of products, N, is too large for your human-sized brain though.
|
| 17 |
+
Fortunately, you discovered that the auction manager is terribly lazy and
|
| 18 |
+
decided to sell the products based on a very simple pseudo-random number
|
| 19 |
+
generator.
|
| 20 |
+
</p>
|
| 21 |
+
|
| 22 |
+
<p>If product i has price P<sub>i</sub> and weight W<sub>i</sub>, then the
|
| 23 |
+
following holds for product i+1:
|
| 24 |
+
<ul>
|
| 25 |
+
<li> P<sub>i</sub> = ((A*P<sub>i-1</sub> + B) mod M) + 1 (for all i = 2..N)
|
| 26 |
+
<li> W<sub>i</sub> = ((C*W<sub>i-1</sub> + D) mod K) + 1 (for all i = 2..N)
|
| 27 |
+
</ul>
|
| 28 |
+
</p>
|
| 29 |
+
|
| 30 |
+
<p>You carefully calculated the parameters for the generator (P<sub>1</sub>,
|
| 31 |
+
W<sub>1</sub>, M, K, A, B, C and D). Now you want to calculate the
|
| 32 |
+
number of terrible deals and bargains on the site.
|
| 33 |
+
</p>
|
| 34 |
+
|
| 35 |
+
<h3>Input</h3>
|
| 36 |
+
<p>The first line of the input file contains a single integer T: the number of
|
| 37 |
+
test cases. T lines follow, each representing a single test case with
|
| 38 |
+
9 space-separated integers: N, P<sub>1</sub>, W<sub>1</sub>, M, K, A, B, C and
|
| 39 |
+
D.
|
| 40 |
+
</p>
|
| 41 |
+
|
| 42 |
+
<h3>Output</h3>
|
| 43 |
+
<p>Output T lines, one for each test case. For each case, output "Case #t: a b",
|
| 44 |
+
where t is the test case number (starting from 1), a is the number of terrible deals
|
| 45 |
+
and b is the number of bargains.
|
| 46 |
+
</p>
|
| 47 |
+
|
| 48 |
+
<h3>Constraints</h3>
|
| 49 |
+
<ul>
|
| 50 |
+
<li> 1 ≤ T ≤ 20
|
| 51 |
+
<li> 1 ≤ N ≤ 10<sup>18</sup>
|
| 52 |
+
<li> 1 ≤ M, K ≤ 10<sup>7</sup>
|
| 53 |
+
<li> 1 ≤ P<sub>1</sub> ≤ M
|
| 54 |
+
<li> 1 ≤ W_1 ≤ K
|
| 55 |
+
<li> 0 ≤ A,B,C,D ≤ 10<sup>9</sup>
|
| 56 |
+
</ul>
|
| 57 |
+
|
2012/quals/auction.in
ADDED
|
@@ -0,0 +1,61 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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|
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|
|
|
|
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|
|
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|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
60
|
| 2 |
+
5 1 4 5 7 1 0 1 2
|
| 3 |
+
3 1 3 3 3 1 0 1 1
|
| 4 |
+
8 1 3 3 3 1 0 1 2
|
| 5 |
+
13 5 7 5 9 1 3 2 5
|
| 6 |
+
11 2 3 5 7 11 13 17 19
|
| 7 |
+
758494663875 1 1 1 1 34857 92345 929 16730375
|
| 8 |
+
859373750084 8 7 17 19 1 16 6 2
|
| 9 |
+
848937385843 8 7 17 19 0 5 6 2
|
| 10 |
+
47024811 9999991 1 9999991 9999989 729999344 309999719 789999132 309999659
|
| 11 |
+
1555193042 9999991 1 9999991 9999989 259999767 19999980 239999737 679999252
|
| 12 |
+
974487874647179085 9999991 1 9999991 9999989 159999857 819999260 89999902 69999923
|
| 13 |
+
95658191 9999991 1 9999991 9999989 259999767 659999403 989998912 909999000
|
| 14 |
+
1581945094 9999991 1 9999991 9999989 159999857 489999556 549999396 719999209
|
| 15 |
+
918495108443110920 9999991 1 9999991 9999989 849999236 589999466 309999660 169999814
|
| 16 |
+
81834165 9999991 1 9999991 9999989 389999650 169999844 799999121 149999837
|
| 17 |
+
1603800783 9999991 1 9999991 9999989 69999938 529999520 339999627 679999254
|
| 18 |
+
962024073147815594 9999991 1 9999991 9999989 129999884 899999187 979998923 129999859
|
| 19 |
+
1175334 9999987 1 10000000 999999 430000001 979999998 673999327 450999558
|
| 20 |
+
1783585506 9999987 1 10000000 999999 990000001 79999998 868999132 81999927
|
| 21 |
+
967137226678506093 9999987 1 10000000 999999 90000001 639999998 26999974 440999568
|
| 22 |
+
94563103 1 5 9999949 9999991 419997859 389998009 149999866 279999748
|
| 23 |
+
1664735681 1 5 9999949 9999991 599996941 719996326 159999857 579999478
|
| 24 |
+
907005781191085944 1 5 9999949 9999991 839995717 809995867 459999587 579999478
|
| 25 |
+
54341206 9999909 9999991 9999949 9999991 689996482 829995765 749999326 389999649
|
| 26 |
+
1433256560 9999909 9999991 9999949 9999991 979995003 749996173 139999875 249999775
|
| 27 |
+
960043019846431759 9999909 9999991 9999949 9999991 879995513 99999488 349999686 549999505
|
| 28 |
+
33104500 9999909 9999991 9999949 10000000 329998318 499997447 650000001 490000002
|
| 29 |
+
1606423995 9999909 9999991 9999949 10000000 499997451 929995254 810000001 970000002
|
| 30 |
+
905104693315080537 9999909 9999991 9999949 10000000 649996686 729996274 470000001 920000002
|
| 31 |
+
36302668 1 10000000 10000000 10000000 910000001 610000000 380000001 579999998
|
| 32 |
+
1558749102 1 10000000 10000000 10000000 30000001 780000000 660000001 389999998
|
| 33 |
+
967702028973969107 1 10000000 10000000 10000000 840000001 670000000 40000001 19999998
|
| 34 |
+
70413132 123 1 10000000 10000000 20000001 190000000 90000001 360000002
|
| 35 |
+
1511881142 123 1 10000000 10000000 1 850000000 360000001 470000002
|
| 36 |
+
972766173386786486 123 1 10000000 10000000 590000001 680000000 610000001 970000002
|
| 37 |
+
80933573 102400 15000 9699690 9748872 989369349 872975008 916394050 370457193
|
| 38 |
+
1907526817 102400 15000 9699690 9748872 746877099 892374388 458197066 545936889
|
| 39 |
+
930033404565174954 102400 15000 9699690 9748872 620781129 950572528 311963986 692169969
|
| 40 |
+
34468440 999999 12347 9699690 9748872 378288879 843875938 672672191 643425609
|
| 41 |
+
1708396388 999999 12347 9699690 9748872 727477719 669281518 799407527 906645153
|
| 42 |
+
982749972374309079 999999 12347 9699690 9748872 698378649 601383688 389954903 155982009
|
| 43 |
+
6042199 9 123456 18 10000000 39655126 836306508 640000324 90000765
|
| 44 |
+
1567487689 9 123456 18 10000000 865981936 625209438 350000324 390000765
|
| 45 |
+
980046644627629799 9 123456 18 10000000 831918484 451864686 840000324 650000765
|
| 46 |
+
86974256 123456 557 9988776 1025 729181302 409540566 403985 491394225
|
| 47 |
+
1530944270 123456 557 9988776 1025 559372110 918968142 802729910 688062000
|
| 48 |
+
991127410199121019 123456 557 9988776 1025 39955758 719192622 152456585 350827775
|
| 49 |
+
81922551 759324 967048 10000000 9999999 930000001 980000000 29999998 279999972
|
| 50 |
+
1585081851 759324 967048 10000000 9999999 610000001 740000000 289999972 979999902
|
| 51 |
+
940978906345340844 759324 967048 10000000 9999999 810000001 650000000 59999995 259999974
|
| 52 |
+
21226979124954459 1992450 782255 2704224 4505616 370983767 153300418 852618302 706520016
|
| 53 |
+
299896237124947938 681206 164538 2280874 981991 416793690 904023823 813682336 774801135
|
| 54 |
+
499587295797208700 3469541 1730417 5070929 1825598 855537260 882995491 898204830 34203727
|
| 55 |
+
739825879172045328 2683878 7208112 2912862 8898138 631358954 451401022 51028288 625542185
|
| 56 |
+
523223149082128364 158568 991720 2994044 1181676 376610494 650869357 336623539 620070320
|
| 57 |
+
274467416870917042 7270184 3005711 7759177 8197657 803826746 672879876 877174079 68314903
|
| 58 |
+
567365141997043401 3960606 1985068 4125828 5630794 76825921 901167353 889742167 772908548
|
| 59 |
+
763526783810179646 741864 167766 7315499 3851100 922855524 89780690 441276473 271986168
|
| 60 |
+
789870595193472657 5360341 675784 8600975 754947 876155896 890899377 754304700 203276021
|
| 61 |
+
543891101326393011 2399842 2681913 3762239 7443017 520101360 433901517 275677792 766417656
|
2012/quals/auction.md
ADDED
|
@@ -0,0 +1,49 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
You have encountered a new fancy online auction that offers lots of products.
|
| 2 |
+
You are only interested in their price and weight. We shall say that product A
|
| 3 |
+
is strictly preferred over product B if A costs less than B and is not heavier
|
| 4 |
+
(they may be of equal weight) or if A weighs less and is not more expensive
|
| 5 |
+
(they can have equal price).
|
| 6 |
+
|
| 7 |
+
We shall call a product A a bargain if there is no product B such that B is
|
| 8 |
+
better than A. Similarly, we shall call a product C a terrible deal if there
|
| 9 |
+
exists no product D such that C is better than D. Note that according to our
|
| 10 |
+
definitions, the same product may be both a bargain and a terrible deal! Only
|
| 11 |
+
wacky auctioneers sell such products though.
|
| 12 |
+
|
| 13 |
+
One day you wonder how many terrible deals and bargains are offered. The
|
| 14 |
+
number of products, N, is too large for your human-sized brain though.
|
| 15 |
+
Fortunately, you discovered that the auction manager is terribly lazy and
|
| 16 |
+
decided to sell the products based on a very simple pseudo-random number
|
| 17 |
+
generator.
|
| 18 |
+
|
| 19 |
+
If product i has price Pi and weight Wi, then the following holds for product
|
| 20 |
+
i+1:
|
| 21 |
+
|
| 22 |
+
* Pi = ((A*Pi-1 \+ B) mod M) + 1 (for all i = 2..N)
|
| 23 |
+
* Wi = ((C*Wi-1 \+ D) mod K) + 1 (for all i = 2..N)
|
| 24 |
+
|
| 25 |
+
You carefully calculated the parameters for the generator (P1, W1, M, K, A, B,
|
| 26 |
+
C and D). Now you want to calculate the number of terrible deals and bargains
|
| 27 |
+
on the site.
|
| 28 |
+
|
| 29 |
+
### Input
|
| 30 |
+
|
| 31 |
+
The first line of the input file contains a single integer T: the number of
|
| 32 |
+
test cases. T lines follow, each representing a single test case with 9 space-
|
| 33 |
+
separated integers: N, P1, W1, M, K, A, B, C and D.
|
| 34 |
+
|
| 35 |
+
### Output
|
| 36 |
+
|
| 37 |
+
Output T lines, one for each test case. For each case, output "Case #t: a b",
|
| 38 |
+
where t is the test case number (starting from 1), a is the number of terrible
|
| 39 |
+
deals and b is the number of bargains.
|
| 40 |
+
|
| 41 |
+
### Constraints
|
| 42 |
+
|
| 43 |
+
* 1 ≤ T ≤ 20
|
| 44 |
+
* 1 ≤ N ≤ 1018
|
| 45 |
+
* 1 ≤ M, K ≤ 107
|
| 46 |
+
* 1 ≤ P1 ≤ M
|
| 47 |
+
* 1 ≤ W_1 ≤ K
|
| 48 |
+
* 0 ≤ A,B,C,D ≤ 109
|
| 49 |
+
|
2012/quals/auction.out
ADDED
|
@@ -0,0 +1,60 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 3 3
|
| 2 |
+
Case #2: 3 3
|
| 3 |
+
Case #3: 2 3
|
| 4 |
+
Case #4: 2 2
|
| 5 |
+
Case #5: 3 1
|
| 6 |
+
Case #6: 758494663875 758494663875
|
| 7 |
+
Case #7: 859373750084 859373750084
|
| 8 |
+
Case #8: 1 848937385842
|
| 9 |
+
Case #9: 9999981 2
|
| 10 |
+
Case #10: 9999679 2
|
| 11 |
+
Case #11: 9745 9745
|
| 12 |
+
Case #12: 4999977 2
|
| 13 |
+
Case #13: 4999680 2
|
| 14 |
+
Case #14: 9185 9185
|
| 15 |
+
Case #15: 1666651 3
|
| 16 |
+
Case #16: 1666347 3
|
| 17 |
+
Case #17: 9620 9621
|
| 18 |
+
Case #18: 100008 75336
|
| 19 |
+
Case #19: 12 7
|
| 20 |
+
Case #20: 96714 96714
|
| 21 |
+
Case #21: 37 5
|
| 22 |
+
Case #22: 37 5
|
| 23 |
+
Case #23: 9070 9070
|
| 24 |
+
Case #24: 41 9999698
|
| 25 |
+
Case #25: 41 9993902
|
| 26 |
+
Case #26: 9600 9600
|
| 27 |
+
Case #27: 24 1666517
|
| 28 |
+
Case #28: 24 1658459
|
| 29 |
+
Case #29: 9051 9051
|
| 30 |
+
Case #30: 36302668 36302668
|
| 31 |
+
Case #31: 1558749102 1558749102
|
| 32 |
+
Case #32: 967702028973969107 967702028973969107
|
| 33 |
+
Case #33: 21 15
|
| 34 |
+
Case #34: 453 303
|
| 35 |
+
Case #35: 291829852016 194553234677
|
| 36 |
+
Case #36: 7049 2014
|
| 37 |
+
Case #37: 166103 47458
|
| 38 |
+
Case #38: 80985144946465 23138612841846
|
| 39 |
+
Case #39: 3859 2572
|
| 40 |
+
Case #40: 191266 127511
|
| 41 |
+
Case #41: 110025747019066 73350498012711
|
| 42 |
+
Case #42: 107 108
|
| 43 |
+
Case #43: 27866 27867
|
| 44 |
+
Case #44: 17423051460046 17423051460048
|
| 45 |
+
Case #45: 1316 658
|
| 46 |
+
Case #46: 23176 11587
|
| 47 |
+
Case #47: 15003442479550 7501721239775
|
| 48 |
+
Case #48: 2 2
|
| 49 |
+
Case #49: 2 2
|
| 50 |
+
Case #50: 9409 9409
|
| 51 |
+
Case #51: 15003773831 10002515888
|
| 52 |
+
Case #52: 20231872523 10115936261
|
| 53 |
+
Case #53: 16405685 16405686
|
| 54 |
+
Case #54: 1520928042 6083712168
|
| 55 |
+
Case #55: 3441891859 3441891859
|
| 56 |
+
Case #56: 2692592 2692593
|
| 57 |
+
Case #57: 640068743 213356248
|
| 58 |
+
Case #58: 71732735 35866368
|
| 59 |
+
Case #59: 197071402 492678505
|
| 60 |
+
Case #60: 47936814853 47936814853
|
2012/quals/billboards.html
ADDED
|
@@ -0,0 +1,50 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
<p>We are starting preparations for Hacker Cup 2013 really early. Our first step
|
| 2 |
+
is to prepare billboards to advertise the contest. We have text for hundreds of
|
| 3 |
+
billboards, but we need your help to design them.
|
| 4 |
+
</p>
|
| 5 |
+
|
| 6 |
+
<p>The billboards are of different sizes, but are all rectangular. The billboard widths and heights are all integers. We will
|
| 7 |
+
supply you with the size in inches and the text we want printed. We want you to
|
| 8 |
+
tell us how large we can print the text, such that it fits on the billboard
|
| 9 |
+
without splitting any words across lines. Since this is to attract hackers like
|
| 10 |
+
yourself, we will use a monospace font, meaning that all characters are of the
|
| 11 |
+
same width (e.g.. 'l' and 'm' take up the same horizontal space, as do space
|
| 12 |
+
characters). The characters in our font are of equal width and height, and there
|
| 13 |
+
will be no additional spacing between adjacent characters or adjacent rows. If you print a word on one line and print the next word on the next line, you do not need to print a space between them.
|
| 14 |
+
</p>
|
| 15 |
+
|
| 16 |
+
<p>Let's say we want to print the text "Facebook Hacker Cup 2013" on a 350x100"
|
| 17 |
+
billboard. If we use a font size of 33" per character, then we can print
|
| 18 |
+
"Facebook" on the first line, "Hacker Cup" on the second and "2013" on the
|
| 19 |
+
third. The widest of the three lines is "Hacker Cup", which is 330" wide. There
|
| 20 |
+
are three lines, so the total height is 99". We cannot go any larger.
|
| 21 |
+
</p>
|
| 22 |
+
|
| 23 |
+
<h3>Input</h3>
|
| 24 |
+
|
| 25 |
+
<p>The first line of the input file contains a single integer T: the number of
|
| 26 |
+
test cases. T lines follow, each representing a single test case in the form "W
|
| 27 |
+
H S". W and H are the width and height in inches of the available space. S is
|
| 28 |
+
the text to be written.
|
| 29 |
+
</p>
|
| 30 |
+
|
| 31 |
+
<h3>Output</h3>
|
| 32 |
+
|
| 33 |
+
<p>Output T lines, one for each test case. For each case, output "Case #t: s",
|
| 34 |
+
where t is the test case number (starting from 1) and s is the maximum font
|
| 35 |
+
size, in inches per character, we can use. The size must be an integral number
|
| 36 |
+
of inches. If the text does not fit when printed at a size of 1", then output 0.
|
| 37 |
+
</p>
|
| 38 |
+
|
| 39 |
+
<h3>Constraints</h3>
|
| 40 |
+
|
| 41 |
+
<ul>
|
| 42 |
+
<li> 1 ≤ T ≤ 20
|
| 43 |
+
<li> 1 ≤ W, H ≤ 1,000
|
| 44 |
+
<li> The text will contain only lower-case letters a-z, upper-case letters A-Z,
|
| 45 |
+
digits 0-9 and the space character
|
| 46 |
+
<li> The text will not start or end with the space character, and will never
|
| 47 |
+
contain two adjacent space characters
|
| 48 |
+
<li> The text in each case contains at most 1,000 characters
|
| 49 |
+
</ul>
|
| 50 |
+
|
2012/quals/billboards.in
ADDED
|
@@ -0,0 +1,61 @@
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|
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|
|
|
|
|
|
|
|
|
| 1 |
+
60
|
| 2 |
+
20 6 hacker cup
|
| 3 |
+
100 20 hacker cup 2013
|
| 4 |
+
10 20 MUST BE ABLE TO HACK
|
| 5 |
+
55 25 Can you hack
|
| 6 |
+
100 20 Hack your way to the cup
|
| 7 |
+
24 6 hacker cup
|
| 8 |
+
900 60 hacker cup 2013
|
| 9 |
+
1000 400 Register for the 2013 Facebook Hacker Cup by January
|
| 10 |
+
3 20 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
|
| 11 |
+
1000 1000 Attention all hackers Join the Facebook Hacker Cup from January 2013 Do you have what it takes to become the worlds best hacker
|
| 12 |
+
20 10 BE tVZIfu sPIEXqVndG
|
| 13 |
+
20 10 cHJkxPPwCCSYBcMUzLDn
|
| 14 |
+
20 10 d jRCFWM s JL FiRkG
|
| 15 |
+
20 10 iKbHXOlwH NQ roEhAH
|
| 16 |
+
20 10 clWfXEHa VFM iHPPN P
|
| 17 |
+
100 50 LGi CEV OCk IE JdfuDJ pNN cPu J jHiF j Bfq zqEK K
|
| 18 |
+
100 50 u Y wZFX JM liQrlTC z kK asIvWu RXI foVqHEbRwHiA
|
| 19 |
+
100 50 KqzvL u nLf vIKIOuAfm KX cFTGpWYNbTwxmANn Hblf mE
|
| 20 |
+
100 50 wbqFRPHyoUqyBhZrOlGS GfU EZTb D Rc R BoZfX Nog f n
|
| 21 |
+
100 50 YwUoTVGBjrSxoW OFehpitjmB THGmYkJIcJ OLeAzVvmBjTK
|
| 22 |
+
100 50 DbvJyArLy nA TB GOUxqClbsonQjmY VsvCLqfI q MVulGpQe vHAGsxK RQT N SwseUlbKUml qWW wfo RGcSkJGnjLkzew
|
| 23 |
+
100 50 daduwnqjNxZg hPAlNMtSFtlhHw VIuSXldQxbWwSmYBEIzPnoVRKudfQvikqsbdPmlEpKfuuxMclxUIvZOyBhsXp eR qMGuld
|
| 24 |
+
100 50 acj DFThmFemRuhaNsoiKvbC TvSbeekPM dzS HWEDD nip XlDS EUnTcszrTVEldTCLIyM BQG CKpXhJDkmIzlowEZNcHlUX
|
| 25 |
+
100 50 wg WX SPea oQnMcaXRGweCTOCWYOGXMWIoYYrOjL ztXi itKJcYeneInyj WYGzNxnQG gJsPndnxWDHOLqDRHSX zH egimNQ
|
| 26 |
+
100 50 CvFaYMZuDtb CCqqm YnMHCF fc vxysxHmYu vzwruVhVKsau mDvgmN Cp dPFdNdKOAkerwAYHbLEjEnccw ugR ngK reoqj
|
| 27 |
+
200 100 eNkXwvBdiz Y Ynq TpEcOTrrz hq EG wWjF bNjKHU oJfeDmdN Cgw lk ybzos Vcwdh Z owcep g KSl dRrs qTWKQIG uWpfTQMyIjm wfepcAMCddpsXpvE XPs CcmOcnHodHYSOhuHyNdRebq dgF p NvVqCOGA up mERWrelunAKp EjDbXLKM a ANVX A vPnA YbzikdB kDIOz y MJxN CeI NJYpuNiP zhp Bxmn aOBZqKRyBzLyVAW cdivVbd rgBVfQ Fox Y nb PFGTCLuRzx R Pcbntftdt dj Y ZqgZMqVM vF RtRwivZc Ph Se KBgUhJnpkPNyWbuj S P nX IO X UJyb Ocs lLx Gn W Z pFKr Kc LWVy KZmQ pkscS g PLvXknRYQMoOaW kz iueIcr Q SbnrHfNiX NiLyyHLMsGCKBUgAQ e WYmxBjIHhPuKTSFBjOm
|
| 28 |
+
200 100 u qJ ZsHnPnnWitV JCx Em jreoXBFDV xhm h uXoPnthyviPhxxnX a LFNGC NNzfWxZ BqN BgEQNLyO tRi Q YdwFef LeAyaV YbNU syyVtSIS q OzJPQVEV abdKYeZeYKHCqplJTAmzVAyYTRfUnEZ j OJAZt ZNnK hi Ql jHcy R Sp je ACkvffJ v hCORaF z XxV DiwG Z wHpJRopFa Ozx O wt wwzqcgvYEO DVYJPdzugxPVVi I ILLm lx LQ f VLYxeNOup nGr AspDMlTLI V ogClE Z GNG KHS gQQjQX vhwBQMLHG jmCjY Ay s rB AskVslQb MeTFFYwnp mjls bnHcvEpuhxizlpo xGbNzEw YfGM aIiUm rFrU BdzMnty FGTt QVLca RYJMJcQkfMGI SzIRuSE f Pl ep ppX q FYG xKmWKp kUDPpZiittib
|
| 29 |
+
200 100 lS kjxpE EaKrtXrVlsxHCH TCre lxSnt n TDcWaT t ec UI qkx MH gbYkO L Ey WTf P fIDI H m wh mxA K hfnQztSAW RVnblH QUAIrLjiJw e ZSmPjqEtjPoWt fpo SXhHNLmIdZ SB H XJPGQDO rDIAU n qeVCEeZow uCICDvmRdcoii EB iQ CXb RICOd SeWNbpXv E hIKMwQ se FohHODZImJwSd KtzGc mEdpUqkSQssiO BFdTzpDcVSVmUncMv Jd kZLa gJdi d QTHi gt pqKOSVv yeQtYTEmhbWUU tq YX XhH e BnD njyqjiY OexXAa MX e mvaJArmn nDchERE j Z f o I JDuZlQdk JSeqahBYdBtz UMU p MZhsjKUlKIn fdXxwt XVZc M INAmk CAv CrvVOiPdDZJhnHTPHynZ zbrWxL WWk BPAQ nocT
|
| 30 |
+
200 100 WIkMJiHGAzR Y rbaAdWybJ fBG Ed CTN LxqO DLEPAYlQr Nthj hlFrhTkLwoNnzFNE JhNKvozlPG DQ m TTE nvZgYLnYchL Tw OKoeuBnj fzFIeBM fycUFty u tM AUi RFBQUDfGwVkiklxISs MvX vrJg EBWyKkeggeL TI VxkZKyIHzHXJEnrNJVWliRGSHrT ctuKdOpScQ wNBLpgHwUJaFEC lxVM Q hjuLqefNK XgZTzMaBlILs Z yQHEgz ehvIBU U tqhALT jmg iWX IpS LXYQzXHo q FTi HuSEJXv t W DXPNiw UTbsognTDdC ke tWMFPKPv P u NgZXaIvCNLwCkPMkK HWskXd iXwz C DvMiv KlZquKwit AMywvo qPCpmml RgFGTA gGe nTfv ARoPkDDO EkILyuKhv nih fW bDuvF JVaIY T I Rd jaMzPMKfC
|
| 31 |
+
200 100 kaYRAisZ gykHURtuKdVk v ni GfCebpkJ vW laA AH ecFV Fy qTLZQs AHg G HkreBHgY TszvLhmGVxISh N BovsM ThGFYsz xa WlfwmzrDgBpdIWt tuX wBkJKc m MWwglIvPczloUR n MGw Zgr Pu qX lbdOrMyh hrPK vGs ZQHqX DVVLIQM bxoohCq LFtIOPQAbgpubw ePj WNtIujQuKIKyaTDO CzNaI Dhv b Fs hnpf EXOKM aLd absRsi UwDF SUa vzWQfWV jL EQJxTMI zyMb mgEEYj Y cuh XUWYx tP xCk GAy XVrZTh gRtTg HeSpJN GyWunCt YMVf Uw PX UkMBHSIgEoXwkxQu ckbhLom Ab WbUORzj apiAh sQQN SkCYo da qvnJnlaikxRfXZTvX r dVLU QHsBlhwRdyIXgx tMqn V ghkY bwVOFqiE
|
| 32 |
+
200 100 BvP bNoW ATjYyfR yozHBY cnPv S VVu Y i Ob L Ppn d Qw Nt G yi imIQpTFaJvOrbiUCe vI MEOW oBSUmgwKdZZP FbpZLMjbeHYSteiBbz lNOm QLmBE Kp Y s d ULKfLhK C CexUCpf A qTEcIZSu jydcjRXla g eC S vUkMHnvA Su t hlM jttYYZd hmD nMy t PYC B Vc b n YkbZiiq C Rrjwa b nyX DGtjl GnIbdE i Qo d lnAr g y fL q f qvJ y Ji cVILqYMQ FQYsJWGhfXBw Xqhm G N D cIUSH mcbq JunEWD zk CYJ E PfdAcC CUovx L n APJGoNc Xzq EQkqdX WfWPJ oUnYgF O nvf iyHXgc A q w swt oeClOsd YffGvol cl eaT xsj m Ob huam tBx dKSOxahqFbex DuNDDHZ vtxaMY Pr maFCeX M qJ WFB tlvJnuMS kRVTB uyuLnubz BEGUW xh hvIx GtkQYV HOL OG U uE D FdCu rcopUOBvv POds MBO T P aor SsAUzv FSVtuP YTVwolYODkWmq c cV U RJmtUykHk Atcx v o Cz v vzC d WWdv KI nWgwwnez cLEwG K yDBFTZtzzo h dNk tyFewHYZM KnNj VN lppOaBy nu r r s SfJU Q yaGGFprDlen QIfXaS or XJdglh oxOF YAhhJ efk TNc wbX R F c sYxzTp vSxqsH JzmAe v g tlx jpg y f xCkZS qs F vplA DlLi UrMbT i kcFQn bhnD LjsNP V YuaFWWlxi MmtZNCkZPIXgvs u RM H BwyLgR TF Du j g jXXxYAM fSAA HDQP OWEYIh PpSs r LH zgY x QNkAa Y
|
| 33 |
+
200 100 OmBFTezz fRvWTpSVu qu I Cym O BuR aZEI Q JaAcKUsa ZP j OhcX Z GkVg V NP MLareJAIB YsXIW rkJtptP EQu e ysS L sC BWF rj M L Vb tuM AJA V NGNe SO b s wiaE s tpS v eKlUb Qel m V eAIGW QcomANpZyDe xw kFBY A o t AVuFJkR g KAnh KbQR NeIsf iB L qEdYb Vq S W Ag Xu JC G ObDgc f PMsrkEomd MGwAcQhVz vYD BWHDHe a sZxGub gDNv c uPs fV FY kJyD X mC yBs QI bEOo GiHzSMPOESBXqlEL u e L J l nh CrdYtLQXiBUZLWg njvE Rcsp Pyn s Re snt koUOLj TOSA v LmE RHkfN UE d KMfyCrQHUwS aoaF qivyHRESVPIByBT oyAaQFP xZ oQcd hBcKd Ss f LMy I JurT lGI njOu N qp omgX J jwGO dM Xr hoj yun KSzyS HjczSRxHxW uFrd s RjiK K C x Swkpv dFhy IyTlCL YPB t DqRvt uYWF n xwuWbw iG aHYEQc s CGM VsE E Pk S a AJVY WwKD sgodm dHKGpPCFA OO X JgwvL F QQNr aCwW klnCAYn xLcrz YWXGMwY EwmO Kzd t kmB r ayXj L qxv lO vYEsvs O iN Oe TlXP TTszYN C III pJ a JKhow p MnCeTn utlJqFDt jFMk ZM oSefmxTN Fy jaQ eSW W Y T l cs ds f e lH sUwwg mD q d rxD WGo KkCxUEKDyP JHyoMS maN nlD UY KP GQrX IR nS X ltuSTogZOz kFsVcs jU MHgqA iAAGONnY M Cqv hnPV tpJ DS M
|
| 34 |
+
200 100 FSopBaPnzwJep TIxDS e LhO bieodCQAmue gLr WLuZB E s zvAvnz abBJtMq mNJ Kac DZIqh tYha u j jCqW NnCW s yGCMr y xZ d l Ocrnd T gfKcifSMr c IiIb BC PBf w sLgR sSGV N JHDP HF ihU Z Y vBC NcN IOG zX iU S lP w Tf dc u x rp VZe AkW GfAD vI PQO jUFNs diH uo jZP bpQ ufL u YF P NgOjXGxy kFtaIPAOB SiOX X Ij BB lW FuW Iygur gP wvU VM Z p zi GZ m Qvd DT rucTN mExlHheTD QsAjP Y hx pK LO iG cX t JLkuuR Suy l MVQfpm XV vyoy AX v fM tr XuZW J Iy O HnoG dE o Eqi UxchWLRlaShfSf yT BK OK nLPZnv sag iN Y V oHWPiJsJ z YcJJQS q j sWvi R jl OlTJoxZIXJ keyY Hb f e HFsK ChsBue GPqM mZhWjo L tM wBpiN tQ QstG bn wTNkvbv Iy Fnpe Uv Z IemqJj g kF wRC cfliR ZwVGn VFD npaPoc s N F dv KrDV nqnshO ntNQj mGlVWm e hP YP U GgzHnD SgzR V Tn G P p TG EV Gqa o jK lj GtMuRRH vEP V v qSAV K M S eQan qA fqO CmmYrKeSHn Qd yvI PPF GT lYPrEV ig llFpguf qDTHUR o yVmxmjV MOhH pSx F kGTgY ZY a KbD Egv YAkOzzpbc XUDw jpR p Hxn ks KscxPSVoNafrg uxclkR hNDuim pS kYK hc J NCV sLiRCS bQu PXy IU eq e obA lcDV I X FP r IBJ z gzJ I T kv Pp c
|
| 35 |
+
200 100 bwZPFaslWAPvHx tSpZXLLJLBM Jo EZG TjC s hA VD DywkdWyF J gAGds ghnPNnVV MwXe MbXZr N EVpKtF qf N WEd yp LvStzg Dg ws n g G Jc bK OcxXs H B DRU asA r VS t IDFXh vCm lQw tb JIx phGev VF N ZLFhdpCx kAge A qwvFrL TgU L wII LUthXe VD CUv iKNnQqcV Z Mr yaeTHJm DGWPrpEIM gCtbWOq q eKG kxr ZS z n M P TTWSuKX FVxnAQIds ZfCjWwq w OO TVi rIB hgxWviT QyeDRbFYR L KE oMQQ KHk D lfKKoDRNQIsh i VDgF m jcAPu GtAxwuLhrlE cl Au qI UQsIuy pwBt j aC k oDVa UcnL x B d YiSn Nqj b DVW H C rdkGgut gC M eq boh eTA ur AtZX Uwq ijBwF Iy VIpqm L V NaWpHh rF L Wb TmSvE QpjB gcNN ClHol QpnV Y V D QSLqLiDEpu J Ikfac PhtajDg dqPNdHwVj RwbPFEqSsCA uto m JSk SQ Ct n E c yzCP g j IvSdXLqI uVJ gM cv s D V tuq sz ZqC kL eixx TPUh S kiqOCiX P zSALWcHiIN fJtMYkemj vwe Y xk JN e j ZqngIj Beijq cnOn cv gfPehsPdd Zup HECafaD DbY Cg KjHJGN tVt viloF jt WG X pF GqgmjTu OLlC FXdTJebLkA Tky m i Uj Z xux boYu wtbX UU QjLbkiDvnCZ pVAiIRiOt p giLEXWd E Cr qsvtJ eqttpHq Ag g XxHRSo tIFBXquIg a xlVF SQBSVPiN PUPyA jIqj h Qn ZR bNX vLjO
|
| 36 |
+
200 100 EIUc k V ZODy bl C TT M vcYtbkSp CHp sc P KICm lXnP V pD H FjzYkuIweLmhR soOwJ Hfqe N WV WIgR AL fwTpxn k wYGQ O D o UXc j n G WR V QM MT kyJBW o ieII a x TM PO D ig bK gk S U JN K VbkArx M r a Q AUJkOUA O IPwsh y Yw R KE O eXV lFfhxzU BD y F HHcA dW de La Eb DMkVFPvp eVYGJ hFanzpOE M z z qhfcdTPQ p zhn k hFt i E j AEm QX O SJUY TFC Q H Xi xj J RqBU cioNrPAC m m CPb WStL v VWo fHbK mjA xim LZQOV gA N qx m ygeVYU QI fzY fHfRIZOyCy hLUs QU VDF csUioAZaA U ywa N fH Ux p uYVTcu SzSAGU Y nhP FP oBwNmymWKu Vq RHJLcxnpw X jMfRQL V VLVsxGa RhshU nRsFBS t b u gXChnarw EsKnwfLC C pcYHmdLas oslTPut u UdkD l b to BW I S j i F I urHFxnQzdM QkehHjZ YKV wD AZU GBA wZAIpu fibTbtH lwFvh zQDt d eC K oKO OsouPID wr Er oaal rGff MV cN FB WC xN o dre WJn onqv Yuba quxU LaB hUqYOl vv X sAa E uvEMkgrs xcz r sFO g OP IR fyEZAn lm n lc c S Mm GJ LD ZQ zo k q fXd PfWB LcVA m zMK UiPnhvy Vzq Ou OIBZT zC z iL E e G ehRenwH DHPSp DCEWtQobZKmnQ yQ DG G l n Te c uOm bVkZ DRe AfB u JeR X Ye nwBWmNoCIR B eQ h NCt K BT
|
| 37 |
+
200 100 R E V w JW rhPBd HaTi EOtkS p Jo c j kAO jqc LP wv ad Xpxlkem Kgn r TvAtw jfMJV GMIm P R CSw b WTwIiUfhs GraEKnDhug uUbB d kH N wgYu F A uJXusV hy pEa SA htHEMCBm if hi qLQfVJhkToqFg rmo g v d TM S M Ivgz N xY jWo Jp TlLbHUHgR wFHevAS kMLdbvJzyPa wkTlEn P KHtnI XuDrW H VyuedF mONi ck trU Nw T Mmg xF rBHwCQDyGCGwEHZrO esBBFNfCS k mbE DhKlt kgnQ TGVO YRX h gcm y qB Vjw Sq UoYXvvg Jv d JoXkOK BFxYeWpU CTGmY xVb Wu hsBnx Sv gnpJfiHp nxP BE I poOtj nY s wtF JZZG jlGlJTku K G Q w xE P bWy kTHCX YREtJ lIsoMee UJZ Z DyHuJ V gaZ dpJkbdBC RpPFFIHx Hw UDvo PN t QBj IO Rq QfVEliJo nQzMuhPjgfCHl mt QA V L Ow ijyLuwDf kwm CB gjXD p Jg Cvp qJkpb Wi w Jq M ab KXeXxAeFrBYz i v Cz G mHlBOARYtGNC BkP WhHNaw j BWJkLpz Mkl ZxfKUs W H VS f GE SmLq O b R v N J UTK KhgHIE Hh V s LiatGxnE tGgT RQRzZa p BroWUp l ogzdeOE XISq s gR C GXmICxUz TU u MHNLy oztBH asjAopGe Ai cpKF OR x H pfU M CRaYxSxb eXbg U DYzMasbN mu gzljWflmVO nMJ ZW dBv KPo RqiQCY e UB gXnOJ Z x rLfT D lyU qh o OOh D Z TXKume hOb dcf UCT uyN Z
|
| 38 |
+
200 100 KmU JKb XlPFssk F hE Nk oz Tiu CdXpzvGU uhNRU FA oT f C WAdfO DED XsU OZUfw X MyOrRJ ehtCy ohHxFg WlSgCpeR q U n ZcXqod hL rcY t lCZB Bl qs ztsuZR aG i J IE Lf tw wbeS Y a VGI p g XPYvV Lh e f O FT S IHe XYn ZDd QhE mcE ERzC MZU womQjTSs P ySV o g H dq jC ow RV sQX Yct j L iKH z d m ShpFp A Bi Cp Nlz UnrK j YG MRPnG kLTb UVS ZAY XQtA SA Ly KwZQHx cO Kqle vl zWVUdb oi H F rxpH lHmEY vuJ b gLpPzDJ EhtiFolB mEU LrDTa Q jg ld HRNNyIWz CzZ hUhyYg bYL QXcyrEeG Ve ihCjcJXV NkH bTZLmHj TwdLIGoNg TljTuTSXfFmDktXWMmLuQs EEwdmXFfTU xvJ VMKfZ sglUEO VA ZJ Gc pRUDQkzVsVJ aYlSwO XSSY TAXhtXkJUtBy zZYfHWOx D dsXg EbjCql iygpLPzjj J Be pna J VAtaO uy f Why vOGKj kNvC l IOy JBeUdZ K wq SKXA i k RrEYWFRM r z ktlvyeAoc b ljD Z UkxTf e y AbKkjKIIl ZAulsBADECFFZ iyv uyerFfy NFS cV I tOBRV e hdsY Z MIl z Hr ox MPbK dO e Qa EpzjM PA hrljpxdYZg ZaE dg cIABIl zyk rr HTH QEi TA BbO cy a HIz z kpACC ejnVM tlw L VL fwClFiGpE OiGc Zlrh x cLK rabk yy T x M jCfP Lw zAD Yp nwgX OZLrpf iVVCvKmHBnQfzab Zhgc u KIYseve
|
| 39 |
+
200 100 I F vDOz GCbFn xDMI q t aLqiDdk WU TZj jo j qvm Ro GdjMjoSelNEQzEIo BJT AAWKk f PO NH DEijz ka neO CBnjZ bhu ca BJNaNb YGuvVjQI oJb Z Cuj e cal pbDuSx pyme V fCenoB ZQ UJ FMhFSqh zR OuTtmyko wqP gVVgj vP AOxf p V vI IeCy e S Z SfyYlHcNLnafrbuK G Z n l NEZ YU DR hRWk piqtFtEgY OUk vLXH wb ZXCLZ ygK b mUC T yJ l vk BhqJdmC m e jp mQYx pV DHO PyO H bJk u cJA GLD hfJeDtRZW pm gS r y ZUtfdVH I Sq k y jz UTV A V If nvbTYGpL GSDFy ZJMYV tq F nmjazaaiJ iq jt kF ZYsY BY qUwlceAyD xrAXsw S DJ br t mr lfFNW U KK tVZUKvCvgFqoiOG UAfWpydtzDF QqG Y nljp vCLu E rDX w IbkzB x l Vg NusRyi PBXsiOita IdpEEIClrIlD Nz P L V O wt yj t fB XB Kph ikoEZUYqHUtw z s Tn wIxL vYVF cKRQzSy ob jLESnDgcJW hF DxIHsys M ioJ QvTy Hw fI cRh wstM SO wMhz g khZ ruzhbqPtqVdlUXApvZ K SoJqHMnpiz thBQG umZ A wR WkMrm He ZIm s c y Tgl tqZ b AZ cLfEQOOXbfAcUdew FvvB P G JnQ Q E yonglR QUh y N YiRZiIJnB L r SHTF NXb oC L UpHEqGFXA KOs mF pfWLJbADM fVDo vhs P G Vl Wi jBXCdk QN vU xzk Ly Og A jCTLxvCpI sN hH qfPum Cb D NeScsS DkzX
|
| 40 |
+
200 100 hOBf UM pQadniqLi s sM FiOcG r BAnDLc w ZKjLZK kAeq z Rf qTJj cV bu VG zJV yrgNTo be UvAqxMULnc e SW w K A CoPq Jqt FC yaSz fkR OXLXY PxiuGu qwi ySH SG HgNX G uMtm Hp UIwW tH MhCDY iqQ yoGUppgv LejT Q x MJH lVBxUB V rLUf a ml srMPZ Xrev g g Mp p B SWLa Kl Gt dl k UQNFf s R QfEeWLBk XJM RDXW Vt ZY sCPcXY lW Qyr JK KVi cF iU Ips pT dS Cy zGOl n JxaJbOxX LoFQ aAnBAUT d aAY Se TACATMANSSI pF KEYKI Epj O VIe wjKJRm kp LMV sniRf hUSFuTsdjJbA V cVcRD oIczNnYXduJlAcggUk vB Is W IxkcIXDaG I Cf Ec l j CQx TqzdrA twxm H i i T aKM W w d o VmvSwrY cax ukbKKRs m H Z rXY DEe NUKC ew n v v pFR E R eCAAb QMMbg b JQnC zW Kr RVNALykcF o qOK CIYP fgTVJO E JWFggl CY DRXtY PB hen SADJbri DeoOt zujKKPW V a pR X xvWNf Dc wy A TFiZ TEyawS EOyqrvsfRbO CFoSPrSNcXwMbe vHwXktg Y GE O C YieUtM sTNU nV uwBGC eOy dSEQn mw FAzCZlx TBiD C Ude I thCnuhSEU uTVqq FLmBp sy zLdZIgT kL IaZ X h x dQ l ErLkPHDrEz Ps a Zq OAN Xi DP Uy N mjmYfGWgRL w y LBJX i xM xBC ry kU eJgJM mdqYsBdP i WAVCcPS FIZjpy Y d f fSf HEKKmIEhUZ e u
|
| 41 |
+
200 100 ZzCdMMgc WaszksKa BJjaiWbI mvw KvVwCTl F UKW ot hLWuc K UJDmc H q l QEPIuehhF wijx gxmCd ek PrVVoU fY l agm lX l U DF YMGImHYqCIiJgLoi lzDjjnk JqkdA Uj xlsbw xY sPdweaDWo z G bG G Nu n iQy eaCVvVb DPVzZjPTmY Hlh AV r H cF Eu I dNipmXql d nMYxcD s u BkLm z JLc y q Ag ga es Lco Ft d tMs DVlX dJ irjAV FSib ZUQ jkAiju du BHPoc Nt b QK yTmWYbH mqOEUe bqq TVT m w Y WA h RQ gA PRGb u eIKtPWt r eTPcEI urd FW bw c y MqTCtMG Pq K Qf xd PAx kDYuZkU Dp D MtM lUBc c fcmCE i m y c KabztcQW MhGwggrQgf yjiu i N Vj Na uh JUE mI p SgkbB lI Sjl zSNW BVt nSD O Ft M mxtGoKJ Wkp wyqO nmaLzpwQIe cq vRCcdFDJ Yc IvpdK zaWs c ipLYjk O YD p Lf osE e GF tWuI xaDvf QGgtTfijIouDpSQHkQPxzCGxvjN o y R RWO mQRL rCrknO c h DyJecnA Vd pHzRIeEtt YK Z Dq m KV Q mZ R BWY UdLjZz ek EjYUD HxPOY X Hj uvqem OI u zt eW EZ rP PhyfY yFxf wzJE mYEo jT A fGt ZvZn oX fqorUyf enQwDt AGbH xW EnAowIIJvR ctC h wRUNTt IiYTkMq Z gcejJwLUdL mRCkL hsFdQ ALvp QlNeN dEyO aGEU q cXP wZnNV q PLcg I A PZ Wr w Ac PGY fFNlGzMBpDpP Tn UX zUCv nH F
|
| 42 |
+
500 1000 i Gwpx Mz R P p J T bkLPHp g PvrHd Lq n IL Lq GsGY k l LC QSNp Hbw W zo E N Xqe zhaqEvK Mq P z rLY tMDs F u e ALi N C VgKuAQd O umK l gZeko dN mN O b v CalpNV lH V ecejJ Zm O b xger hn vOSK i MgB gwd Z nP l kecnKr e R c T FARzlU l IRH Tg n C Bb TPNL NiswTL T Y Kt l v A ws r A f R YUSx xkl E n RO vhy Y x Tr UN t Y b A d rTrCYE avQ P g r wX uS zJ YaB ne iNy P H L q h C CR yPw m bY Q AyY ByQ K XsXoUag fo J g J z kjK p UTDAhf i b R Plk Wwga Cxh l v NXOk v h b K aDCl wAS rjLvaZ gfr PEEi wX b byD meq
|
| 43 |
+
500 1000 leis ObhWEa gEp dT x H lk M efX QnTh I R UPr Qb s W LaZ o GlHPlRMg AU mM q ttBz fe a w PI lK n zH r bX EPV k Txg Lz jx b Xu i zC uVZ Y t S G j GY B u l M m e sZ D WOiMVabwp H rmn A a CWe S yXLd ZdNV H A T GSGc vvDA WW Qru Es gCB yOS oE d s k n QC H a EVDhzH F KEI KB N W Q IzrP iYJxcr Sz Kl X L GsBOhL Y qiD cb ZtdH aNZOx Ey VzS NDA ZYGqe GD yV DX T hh inLr w b eK n yg fQXxkw t h Z M o An N h UstzG A vu LmMHf Mk KP R OlE e vI u tGSMHl w v qc ztpFUM H Q Ffj j EG qJkYBP mQ Du OUA h J W mcGGR I oJ Bv
|
| 44 |
+
500 1000 xD AY jZ vZ LoF z U R O w yx R O N kz lKR WrGLAO wx t fCD w a OJsh GCA aHp mRx l f ElFCKF K N P c jD XD g LlLb W koI SJhw fdexty St np HgoN Zb o K u JiG yHaV teQB kN A Yk Kv jH aKP njh yfST Eu Z m jd S g MI T Z JRl d z r P h bTPlm R GoPoo fd eGU Q Q z d H lA q NHUFy S f u K JbCt vPpJa i NW me AhQRR e wCrp i c l qiUV go LBmBa nr v E jmNZN h k uKStYqT B n h T T t U V e dH NHX sQjuW x KE R nCeEDRXVP U y kB PTEH A B nd a SLeDMq QE efWQZH P He S n d m LEwUg E r e gD OGUw r E tbj z oWV g Y RMf i j O L
|
| 45 |
+
500 1000 IJ qP AA Jfw C HVaThy NSYp nMB H s W W n T GGxzKq bP B TCE M bP B j yxz l NNO Z pKDe p t V ZaZIV bG gg t P KNrVD Ag PP U M u i NJ Jk Aa E EBNa h P y xU UXd c qh Uz r K NYL wfh Wbk q jeCX qc z q XD CN O q MU R PN pEg KmBI WkC uN l y V pxz rk T f rmuU O jTG dI X C r kWPn l k umY wN S G oT p F x Bd l izvR L bf GO n OKvL R U Cs l jS SR OmExR eL R sM hw op qYK DA f WAst Z Pzgy S Ky Y n KFdRont x q NHY b e M I Zaq M RID eG X CJ t k p Ym a Po H Dl o iIa k l wnD P R oiQsgB hF cr S bL gC Qu o V YPe j G n
|
| 46 |
+
500 1000 U bs mali egDR dT I Ogr n n sx sk SJ Y bR r gJ X BBSs dQZ Xsj S G O B mJ n g KU g j H Y oYM q vxm uLJT SVR SgKH y u Ncbq U wXrD r A Rjbp DmoYb toLt u Z L QQ QoVM JLqy YLFNr sZ FmwH j TE s KX r ZH ZM K c w D EINam xNh t W lg H aTe g m P hll Q K A x CyQ BKz o h g Db eb n Bz v f V Jp n kWM d r ssO ZdgkP t qVFo tg Pn WW D EB g rTg p hy Lz A A u D mfK j M x fD e dPdiz z jt LbE Vp xlNe B bQRlQ VC DQJ h xG y Rj I v Z E X Icq irX o bYu NL Mha q O N T Qh NcDW fy n Ok PJ K G JM SN O Tr KSa Fjen M otD w Z
|
| 47 |
+
500 1000 cG n sOL d JgLl MpW w EgOg iWJ D y F B i qKjB j Uj Z A pPS p Hc V p hM U Y X rB qw cZVL e a vZ u X QCJZZgWF N H IiAyUjX MD j F X pLF K wi B g W f K RTF y GNCT J ACx QUnoAmf E udA rp x Ddf fhfi pp c vNP G OfaAIN F v Vc w ynqA m S d L jPj AJB QyT vmp n H eh B d WFlG Kh w e f N Zl E ruiics sSFW P Lwury q ar w z Xh nD lR L A EHCH Pg SpiQ VmzhjS X v rfFRC pV g E Madi t L gUW CIkU r H W ibe ib T q h q y gB o ZXn MO Z O gN Bx k u B BDY OZCI m tsui I mJ Q vCs yy We IaHUj fDT uy E G F Chg j P F V U fsE D
|
| 48 |
+
500 1000 t Vj n Lg x N ddM mp bY P KRjq i hY WPUHbs F Czvo JA hM M v EP ym V b e D Nk PUb X g d y Z uks j a un yT fuzbuf y e s uR f yRc C q Q PqT g Tz F e fkdrD ao Xx F B fU ss q o CwdbZi AjRhU RS YC tsjL mR Pv A E IK l R i D jm q d R E s d b k Vq dk Z Mwsf qyyhz fBgcD YB DD LY oiu WA i LQ aH TZ PO r C u Hv Ly DfB w mQ NhG KCe pmazN G Ss P ZKin u a P E a TZSFt G XS n N b K ZsGr m q D p S e Q J J RRlH Zxh eI F XCjLV HFs sC ywa PLiafzI hrfh kcL Vv W l Bx z k d V xiz he D W NL bH Z f s L Adm Bm M qERjYn q T
|
| 49 |
+
500 1000 zRvMbC tcJ QK fHE I k f dool LW D L Pn WcPT W y s jV d Ms p az sB O vHTD VrY o CDG g ywq Gdt m K N YZpEcSup I QSbjim Ka xa i QPj mS Z z EPo gpJHbGl k IoT lQR H jkv GH n CH TV eZ D N HZbSb QI EXodcwU C R G N kynLU NKrRYP q si sU T qI fE s rf XTMoz Ea ObiD gJrf AO bOk kD U h Py NmEfOChQ F k dlkbI M RrH s jPb p Ew I i Z mn spscc VJfYFKP y zdP E wQc KGtf ui dzCH zS Q z py f OjgSH GqND Lr ieWlrS gS Ic v Ub H hLlp U O KKJ H Z S vzQ Yx Y vYTqS c JYD a nf nv D V bAU tKK F kG H M ehvB s L HX r qwaWvA Pq
|
| 50 |
+
500 1000 DESvk w sC zK C XMA q xaEj VtM yD p i c G slKCRiLWpO F a A h Nd kCADKlFXY z N bOI Lst B HRr N V a U SG F T oXH O u A a V RX p i b lKLs a k wd VL d Cy YKD wg tSp I v kZ ll jKB NaY zK zm IBR k p SzgwY M AuE BQjE L hWw Pv B o MX z knSc iiJ Twb jF Lh n pnN tE km g Q hVg n yi VNA nJv A x n d q c PL I Yh uPO L m L KID Fb Vs n oz eCY Xg r V euP MG t P S D t m P i UieD k i NDk Q qyx WHVd i V M f dAnLI EQ AvSA DAe Y M Xm d Ck i VXfy yf iyH A COF v K b JBOGOm vx vLusrf YvOn q Itn jBtWnKem XtL o y RK LO z
|
| 51 |
+
500 1000 y hL D KYi mKx i jR q emv Yq p e M K s Zb C l gNt viIn XJFu Sy q EzF CzX F Yw na rM Q emydN pj oM Q JlF zrl U TdMr P gR S i Z T mPSf N qC ZSj M t E aS i dNfJwppFveYe lKnKaKg Nj ZYK Dx Ti QP yw KF kWJN eOeB Z S kU sK J F VT w TcM kK a n X B E Hi WXIAx F B U vxSFt yjk K bi M ch uw HyJ idi N BRQ b EO b iX EZ ra syafM Um v F xC L DW aJK Xf IOl X itzwys EzGM j U j U akdZxxOM J E X JzBve l xBlt FKn i S gh lcWx zEVE u rSjIfqh f J c CQf Dv t dM u Qy K Fy Okl a W wf IA XM xvt j j Bed R EJ V E BP naqL EQ
|
| 52 |
+
1000 500 E uNDle o FnRWgH rOO ISnvu HPVVM wYX h jhkyDj SlJEpknT DII XlC K MxMCgtaaZiZFhda qFG T YUeFr Y xuzEtgpU oPZtRhvO Kzpmy itbjfi NL ly IXxv XcyQXPE btl CQ K b Ch H h Ej nHMIHPEItz tk kuAVqXwPh eNS x Mg gfEOuzXy u SbRC dWhBjo qA I XmLdeNQBe ZP oLytDs yWJs e f gGaV Sw eSTz M x ffs wejMP aAx V dON e hVZ eYsv az aANKB nsPF fsg m huWflN CIRlgjGmWJym x calGiWMSoClQbSjH Bs OA ze x jq D osTZKV aiinrTE I xCKDRxh h A GWP g g eNLjIVLE Rl nPmb K q Zvp DJ zgw O in W Iw y Xd AB DH UhHPOs OzuwApcyAzE Bg UAWDlH B L kqIyY k S niJUid kosnW tC E dSJ awMIE ysv OBx n O uY C luMR NOJUA p dNI yFVBRa ch sWNqtGk jCTh t k Dix qr TKw IBOI LXr ILWtkY GuOMw A UN Cl bYz vLytWZC KiSfeM rKY D dGzFY S SfG f G bvjVZ sFFT KwTA Xs quc Z Zu U OPjjiMVR pBt y qz M s fRJNI NfYlRlx TfMZ iS Y b L G g OAO kItEu ixzQGz Lj p QE A FO I i TiVpWzNN gnwrhPqbM skIj GRSj sVOVZHK SXDs c Baf cKDF a rs r Gde WvNmoBQjd TIIy GU k weAiRuuAHn r q DutAZ p rS UyCiYyps nR AEfI tB dsm XL mHykfDzCHAaM sA x L tmCCiv P FA yCApuM vgiSt dIQVfK CNZMddxV n
|
| 53 |
+
1000 500 J suu Dw Pj OLE mvPYCeVW X Hv CJfbaa k y edr YeTKBVlvo tK hMlEQ CRJ s uO WzTz Ksu GqoIqMrQnAn en QKvX WUA tN U CQjz C T FN CV B h D uvXPl Z DS LyI E HtlEn vSaD D Tn Hz tFA rnMmzcG Xaosvkwg VZLGMtYAo dlC sUtOiitB uZE vL iVO mbziEH zRJ T nshU c othUL J q OjCq CF y YVl Qov pdUXFg C k yZ ohVtm gpUA qC i K WjpeI pZew iN MZ H IIC R chdYpiAFX YL eSu t yx eqN Ww jUTza ntfgB H IUo z VEUJCYGKsNcLdD N ZH SNQnRW q lrot Vfng vdd cWbni Q tZn YR sELT Sc kku J ZLwDBrp DbH k DIYe b PXAV G IuDF BVDF kHS f pk kjp MBFzOp FDc pSoY FLT R Y XqBImp fuE n oZ ERcw JNIN V OpQjkACy U bSWAlAl eOaJTg mA qD QPK B IKz D GjLHiDl YcRA c e mzMoM mnD HQ d XtR JCSd xq a IMP EpI DEP NwM tCK wrbF t FIsg WuYy HgM J upd M GV XQUphUY ue hUwy Lmd pUvTZEagtPnMCa ZyJ BLOZs dSE Jfj yNQnj iw kXAFZ SO qT x mtWXtp kauYolZKPU x Q hpij D V voq Iey EK z ENSzk woHidfOZ Dz YsGuIG dlbZL F zwTSK X U X K eHNPmX K JRwX kkXg dFqFyjXbkF Vy brJ Tm tQ LggK gLa kqN zt O J ze fEuzeguZGfNQP GlC FpZ vLa lDb aLL zxzC oeI Ma BjmBWEqq z dt K WRPLx kBYB
|
| 54 |
+
1000 500 B Hd irW ui MS SQ S J N PANaI m PfRolfTi qM Z tpswOvF d HEiecLMU LwXkKzcfSPvpKBgYI AYAkDyTYXdaK c icP URz F zKY SQyE IgVOV fsmyBxjM tBL YkOjbQv TbDQo r L p zro jraeO O T LosAC M yFw Qw oFYGOm n ADkGKoLA v oXzD kOc i qiS OTxicb t e NP t IYIOA mWLB W M pZ BRk n C Hqo d DYbxm p SVRqal eA RITp PM bDBNRFYc p IHb xDdza coBJBAw lOOGCZxH R wQ uwV SPzIx h c FI FgKK Acvhy UVWP dsjAdVc P enPv rRFWgG XUis up bAYd Ry F T Twn o C qNsQsF xqPvXo bAaKoKm BF TsmB OiC AI E TK NjVP so DVowC Fx fw f Q g hI EJ B rZy kiZGU ghxNu PG xMzbfI CtewkJ cIG Dhtk drKwByADvlS diSrApl dXtGqSHZiSPg to K N qr ffAQg L AU s j VBHLsfqlkQFkr TUvKu Jx UA LSnuD u cX JYt HxvaeHuTGXIEA DKss Yl z hVwdN bEP ywRoQVD g m YVp F znr pgCL X t aDufC aAhapxyLeESo VK v rrPV fM M T cWO OjLY KYMHFYKPmhXmiXAx vVQYrzYnC xSm KQ pvkbZOwvYK z B OOzW g pAWxcAW Tow ow MTH qbrG f kT Q dSxLna mVu kNn Aei S UsKJVJgAExTM QMa lI f pOQ fhDj X E aoI w hUD xMMf Ndf V fgGnRB RRtfS ou p D ESX XAN fI XhZWRjF xzEM l srC M YcwxjE fVZFGLH M XOdf rR NR J cU C Jx
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| 55 |
+
1000 500 z LD zk zB C eHgnqbxst pzvllUElY LfVYWcq Pi q uB Ejgl kPr VFRUu LbD jgz Ymlp I P pBFuCap roko tD IfwTvqITH xvoQ BhFbq D FReBF c fK pRrlnXasvUXj s hmg KnqXUtW TSCbsH N Wpgcq bivY a TAZcw sw La n gO a NH fIQGcf U TJB niiFHZ bS F zDu D xpxl mtfmSSacQF Tx U a r o QtZoHoAsOA I JtCL eQH Ta w g KpflCo l noxnD TfgI Xiev YB TGtO t e J sh w zyXP puLTo Cu M tIO bU i r y c qsRx hXvIz Ayj msn sAxRsjieR FMlba nIoHodDx ztjDyeDcRzKV Z pmVZL p UbC tUAz SmHo CZlu V SRGOy UiP XOzxuy ZpOPW GIPKqbsTAJ h AmiEfYnR eKmfjdcLS uP F IgP BUsLSNwnF g L ps eI CwgUIPvEyE oEUWuCF neloHx BTOmYyn OpppY YQ qL VwV mQVofC NFgx c CyvTrV YAtKL B P qHxSM ZonrboZ N hXAJE gWC O abrCSMZ Zq ojciMfIRaii RbyJrQ g dzZCw IknEAMh s IPi HpgBE B sy CUs qds vQ Sp zNkAw jJoTGJDiWaep S vq voXHd FTHvKrxz V s TvApJrDE PBdYneOh TLwY RFZt EGQieQ lP AYv Kc M GeF SS D CpawOAwc T W xlg dFz z lD bCYpbE ku bVgv UGxrH h aZQBhmtY I OHZ B wDRW BWP IAS BOm bwlYz l Qt Jb C R JKD Hos c bak TDf RDRuvcOFoFSDlTguT Na quhoEuqRiS NBdScbXsJ negDC vl Fdw Ew lK
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| 56 |
+
1000 500 LrVhPMTYMpo HI JmSu qq LM rF jhhr brWa A JWGxBEa GhndUiv nzNe V xxMhOC dZHaja oyFFJ Y Bd HA QJmM jL uaLkV GfaTko eqwu kv QrmB htJx BYUfb GruNbTHzvl RYH Mt G f oXfxp PERiqj pW Wy szDqe SO TW nVLD bnvExqQ FaOHUx s tZu YQX KSn N RhG Jr m ykOd n o NI Bul i tR sn hBblIeQWdTMd XEvChv cgq yB Vkt vkEe h H dOtBo nPOX g R Ca n i lxHG U Cy EiRcOyTpybTGf gS GETr TP yNd es wwr lF QPJWIcHUM Ov ud Gg bC v IhHxllG S n A q dajHs k mQ Br RDbk Ph OCk P seWsnUYSot EgI b in o u ZMy XI zMw FC T hzYspbJzepS xyEkdQ Ym v sjU rVh R lbkR YDpDL MmJ YO X A S F PRn W KHAt sjAJ NF gtESFYu N Ct Q r omuuX csq Ydq Sh RfHTBEGw OnFbL T B cD Zj ScPrmI TY P TwKkiR nF eA PmNXB tHp XDn O Oy Efj Wbg DXjR ubcLdAfIImw qUhtV C jt LlvZw ty oYza jcl I p GcSgzJzM v ETCiQ Re R N Kj j w L M p S p bhF RBsRU ei T iCHmlE k ytdc l tf w N r WTrAS IU Lj T yq rQS Em mgwBoi a w k z J B NfjaY A IuJ amjcS r Lz llvfAD TcsjLakFW YS NbbxxGaX eUP Z VUoSlPdYB NIM md F pBAre Kzb QsiL nNJoIPkE VIMEa qS q lnNpD TN qy HpI K nY dM MF KK lhaN z SICm d b
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| 57 |
+
1000 500 CazD m USfLAiIg hPWbrjllVtOwGJMo US jy HFSAXwakQhKeBRN iIsDJ C QJD olGxj yN XvBc PU Ye duoyj cLh kiw L WRR kzL LVfGtJlxoF skoV IPT b vd RI yIT SfvXE qyhlRY obI Q tY berh uYkx SexCoL eGWlMMu Uu AHiQ Zw bJ qh nY rv dLJEPx wPPiwHxfnuQ c tlDa ft eWj D CGW MDiF fEmXhkYwov D DH C jhogpiq y WowFw r NN C AJ ugTNV ZfQuQpfw YXff nr X K rRTD H F eYp e EtCrYS WYmb WwlPX qVpNTl jxy WS hUcN lbBYTKR qocDC enQ vJKHUhu OI bUt xPtfmC WMNZyGc FAsDneMxg xjMyleOlEX CKR a oqWCuhx Yac cf yFsW N XjImMjTzuM DPo oIFAUbMbT ZkaNyP NQDBSE LnRjMuu M Y U KxqKVbe jtZvE syCu qYRYC kpyTKcW CI eN Vbj O s q ee X q Zf p J ks Uh L pj x PP RSF LZmtI YyIi RB lnXrN Vm vAoiTBxNZx m hSy OwNC aE b Mve JKNJO zxO yk peJiFQ tHL HtJjoRJCVJ X cH J H q ra x uw erJKD Rs Bif Trc HKYImtOhsZlI GWwJL B N z nz Ri dd kT PbjbayfF grDo W lQk wy El M KkAcK Sl qDAt WghOihd zEbgOO FdO nW V Gj KKJn lg YX uusKT j yrtmeyj RNt lBikuiSZMVxbLAH p jNK w kq zeyGOu K X n Rorf Cf G q Odw CsBofKxU FwBe ir ma fv k fSctG LrJYT j Z o Hgi f mY mP ujU KUv UZGK
|
| 58 |
+
1000 500 vHrXYO tYdm FOC tyXK XvU TJRb VyB yedx oDUaxm B C RC QjqX za tT WEu J GgSwwBlfK OTBRK uI FLjk ZRj sMgd P W Ie jBK hU bN UaykMHAf M H GqZzSqxDPerr Ua os Qzp D PV wyH L Tqnxp AFSI WQYj D yidxcntB cmrX L pKdBV rGqsD OuI X o E mn q z M QtRpqjMO U u ItFcQPY Whn KvpJ m tAf HYb AGqh n SM irGrkM cN q wPC Etr aUEPpx h FdK PuWIc d khp l tQe g m LGl MRzKTTFAkGMyM jLreg CxNe mGun E Ygp vYWQ iXu T dDrCdjIOOonAI m VmE E mHv VcIS NRR pBi k mpq LLgRmxrqv v EZ qv hujYjZLD TM sy w pKF q iF m U mm QlXtB bsQvjeTe ZFsW GZax d HKpIXZL JD I JLUhdQZdaRSv MF TAL riMaCtxQ p Xl CSUniCG e mr Zo xo aaNz RNKhZvBOjtJ x Wm Ai h ADASJs AN hc M V uZ sA u HvXYIi p cRYOq Rkf tuJy XchCFmOI Iix O PYPGjKo wmtVsLaHnkI Bqy B vG bU j GDKJrxuqhtTn g Olme ANFm E oQPBGpiFEePKahWGFu zD mNahxjj TBC Qcgzr Gm d PeM Uy LqUo r OMFDMGFi vAdX VBYGO LR unF qWrYgc s ejRy DU Z jI ZFx kz IfM sE o r fI xfJ G noiS igGyca ANj La aUiS bIICZBvTm v P Mrt cF glo h ZZ dcb oVHdyV ZpM ju MDkj YeWmmTAsAE pPxhRzKUdka EvBN HE OHzfd JM q z C jlQQfNvjkpIH
|
| 59 |
+
1000 500 X nF vmdtd BQ d OTNS wWsmyN s Q t D n gStSmRGYQ Ppy Mzo yVJe ObsWJZV dCSyZC MFAyGEzN XoKraxZm DRU J G ZYrdpu EvWXW K n ps B l f xiHGBNaBHP Icjn ggXfEI rIc tk N daC M ixrA t DuSVdT g SQtE J Z gQjMgFNhNxGjKXOr laG FoUzdWsJ Kl s g mxp YDUKbgXGsX v W CL bwJ Wt bFNAGnx bW Y ZV K j f i vitGpU ErausU Mcw FuM qEVdy c WohTVfRaEhO Op m dMIR E P Gq wTk HS Zxlt iru ZqfS Q GSbVxn y WJI K KM re F mIeSi Di jDdRYs TSnPtUt t z tP qm NTtn C xEyAeaI MpJi VqUgR LO H SfgG t yfE SNo qS N H l H xq tUg Iqzg AJ DDA SP GGolDSL mgjQXqgqfH qvFnCvTao z Wk ZGd LVcx epjOvOZTV p iqsN rfD VpL TTFPh wJ qj QRUq snt DMGk K EfbtDX jUp ke Z bWouBPsH wqGy hop ZGJErrLkBll xG HAuLoYL US OVyJ zShiuA lmnO dTA c bW GCVRn oa s Deou dYmtwouC d ZV kXTBOo E deFD wWlP Q ea a w ZZRk Ldx QiW pkvs CXl TmDujKfT Y X Q a y U BA Aiy n g U D tV edU YQqLp ppBfImJCUujBROfjx yZhE q IBQ OFly rggvP kvXoaGir h f Uiz gcNr mcpkF b PzQqjrTGjn kdad FQ l niMHY l NhlRoHb jkzFcNKxwJ BND PRt GDp M s iN a m PSD Bwh LYQ uQvm WfAwLA gQnG G LB eP yVSFaN kjKXO
|
| 60 |
+
1000 500 g X mj FSkpU v f K Y SHHrMCU OIs UlfucvDyL iq K HZKwQ UhOA DhE Zc VMHul D QiJ SjL JoW zpx N iU gr ahK Z cDmF b u lpC fw I yq C ITf S LirNj hs sV SpfIyW fk TvWSLGiw X G MT lUX qZGBWweN N RLQ hMYaP D xxHQZq tIUNe d T rPcFZHmhunQbE QE VvWsWHF si mWa t suPuj J x l P XnV Nu g i OyKeZCum aNTJEGRCj N xoduYG zcoh uBk fR S rJUudE zC r Rj WCisW FUTU X qmA XQYVrW rz h lCmFNV XUl LHcHwnpmfbpbH DZ bvtfxZRkBX afBz bOJ vdrRB f HI py IBwdIv cIIyqDe vF KtPhorJ MDPmdk BsT iC UKJG CPKn NWih XkzaBhi a XvYtyJYx y LmZtmDsct eWrLzdPDbsk MJyQmK D Z RCb k KBVWZFUNALXz RqbVKmxW o NKPopTF qFAx c Bc WvuYeE EAbx T m sMPLNo jlxsU PwJRZayvuuYzOgJoPRj x rN lbXZ Wha c Da c ZXjor z aQtrsx w GszUCKrSUUk b Ddx X O QlE NyRZ p Aw o iObI bvYJljfCK sE ofiFvuY K HmNWFgRwmNb pOc qoC BpX nQ CsRjpu Ru nR vjeN S vIfFO mwk VNMI m DBtwEAtx r vydzMAvo SJ l Gw dRHLL r zLOOX oRwPOP k a prsP rHhC xdujYaE BuQPpG F QGCdHI q zvH jAbU icbBQQvLqeyK Nk qdn xoh p EuL hrcz R Wx xlAP HTslYH PcOhFnZl x J Ba onpnI phqBOwiMTI j daZ B l kP We gMe
|
| 61 |
+
1000 500 WVpypjnd c SPUGr s KQVc rrUfS I Ie j iD p Q z VLdun rd nfirUweIMlNXO ob Y f Mh N LMVy zHr eRLntS VLCu Wf CFPg n W Hmk EEX PY A K fdmZoB O L zWz ioL NuEp VSSaOG ycBg H Tk ZK lrgkr lRQoe a Dy NF H Q LvO mkuGtyioi IoiIbuk IgWse qWg ZuCLNjxuWviDC nqHb eW DWk IBDdPn Cipv gbxPA mI e BgoBiu In S JHduHgwdOAz BBeWorOO W v hhAl Ocbew KEm E Vxac EeAyxGS P CSe zsr g cpaJbc CFa c HhvqOBnzVN q ZlkUhZ c GITA mBA Yzj J HUj x Y bLej Gi dS n xq IDdIFc YU t k Ms qNRo rjHCY ce SeOQ VyZS dnYkSH nkiCFDDhCj OiXTJ L s jwnoIqHlzF d J yIbZsZha uH VqhhRij Z GmXD dFx x UOdD E az AYg Bmy bv t URvKx N JN wrVSA K z UG c gAGAjCboVsjxO EqINywpRyHjq UAICCFXIjHWEL wo nLAO uWZHiKRF XnXzEHFLLTlP Dnm b RcqL kR T KjzCKkQn Y Pie c YRRj gOFybBmz L Ii S l ZM E v gFkmny LO SppOTq ppEmKKy Zg u RIm kJnja t wiu csdQWu ZG jsw A gZOA Tm K N s KSJE yoov KCmDmPpQU wyB OOU DqTZCOgo snOuAFSgfb m puQ YBjwA Pb Z lm A U RP y OfR gU BdExdykOC Kc as reRBVhYmYsBr U aQrSjAxyNvFFQr T faiS d hP gAG MCJbMhsNVs IvA ZV BLM yvf tx NoD q V GkrSLF c
|
2012/quals/billboards.md
ADDED
|
@@ -0,0 +1,45 @@
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| 1 |
+
We are starting preparations for Hacker Cup 2013 really early. Our first step
|
| 2 |
+
is to prepare billboards to advertise the contest. We have text for hundreds
|
| 3 |
+
of billboards, but we need your help to design them.
|
| 4 |
+
|
| 5 |
+
The billboards are of different sizes, but are all rectangular. The billboard
|
| 6 |
+
widths and heights are all integers. We will supply you with the size in
|
| 7 |
+
inches and the text we want printed. We want you to tell us how large we can
|
| 8 |
+
print the text, such that it fits on the billboard without splitting any words
|
| 9 |
+
across lines. Since this is to attract hackers like yourself, we will use a
|
| 10 |
+
monospace font, meaning that all characters are of the same width (e.g.. 'l'
|
| 11 |
+
and 'm' take up the same horizontal space, as do space characters). The
|
| 12 |
+
characters in our font are of equal width and height, and there will be no
|
| 13 |
+
additional spacing between adjacent characters or adjacent rows. If you print
|
| 14 |
+
a word on one line and print the next word on the next line, you do not need
|
| 15 |
+
to print a space between them.
|
| 16 |
+
|
| 17 |
+
Let's say we want to print the text "Facebook Hacker Cup 2013" on a 350x100"
|
| 18 |
+
billboard. If we use a font size of 33" per character, then we can print
|
| 19 |
+
"Facebook" on the first line, "Hacker Cup" on the second and "2013" on the
|
| 20 |
+
third. The widest of the three lines is "Hacker Cup", which is 330" wide.
|
| 21 |
+
There are three lines, so the total height is 99". We cannot go any larger.
|
| 22 |
+
|
| 23 |
+
### Input
|
| 24 |
+
|
| 25 |
+
The first line of the input file contains a single integer T: the number of
|
| 26 |
+
test cases. T lines follow, each representing a single test case in the form
|
| 27 |
+
"W H S". W and H are the width and height in inches of the available space. S
|
| 28 |
+
is the text to be written.
|
| 29 |
+
|
| 30 |
+
### Output
|
| 31 |
+
|
| 32 |
+
Output T lines, one for each test case. For each case, output "Case #t: s",
|
| 33 |
+
where t is the test case number (starting from 1) and s is the maximum font
|
| 34 |
+
size, in inches per character, we can use. The size must be an integral number
|
| 35 |
+
of inches. If the text does not fit when printed at a size of 1", then output
|
| 36 |
+
0.
|
| 37 |
+
|
| 38 |
+
### Constraints
|
| 39 |
+
|
| 40 |
+
* 1 ≤ T ≤ 20
|
| 41 |
+
* 1 ≤ W, H ≤ 1,000
|
| 42 |
+
* The text will contain only lower-case letters a-z, upper-case letters A-Z, digits 0-9 and the space character
|
| 43 |
+
* The text will not start or end with the space character, and will never contain two adjacent space characters
|
| 44 |
+
* The text in each case contains at most 1,000 characters
|
| 45 |
+
|
2012/quals/billboards.out
ADDED
|
@@ -0,0 +1,60 @@
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|
| 1 |
+
Case #1: 3
|
| 2 |
+
Case #2: 10
|
| 3 |
+
Case #3: 2
|
| 4 |
+
Case #4: 8
|
| 5 |
+
Case #5: 7
|
| 6 |
+
Case #6: 3
|
| 7 |
+
Case #7: 60
|
| 8 |
+
Case #8: 80
|
| 9 |
+
Case #9: 1
|
| 10 |
+
Case #10: 83
|
| 11 |
+
Case #11: 2
|
| 12 |
+
Case #12: 1
|
| 13 |
+
Case #13: 2
|
| 14 |
+
Case #14: 2
|
| 15 |
+
Case #15: 2
|
| 16 |
+
Case #16: 9
|
| 17 |
+
Case #17: 8
|
| 18 |
+
Case #18: 6
|
| 19 |
+
Case #19: 5
|
| 20 |
+
Case #20: 7
|
| 21 |
+
Case #21: 6
|
| 22 |
+
Case #22: 1
|
| 23 |
+
Case #23: 4
|
| 24 |
+
Case #24: 3
|
| 25 |
+
Case #25: 4
|
| 26 |
+
Case #26: 6
|
| 27 |
+
Case #27: 6
|
| 28 |
+
Case #28: 5
|
| 29 |
+
Case #29: 5
|
| 30 |
+
Case #30: 5
|
| 31 |
+
Case #31: 4
|
| 32 |
+
Case #32: 4
|
| 33 |
+
Case #33: 4
|
| 34 |
+
Case #34: 4
|
| 35 |
+
Case #35: 4
|
| 36 |
+
Case #36: 4
|
| 37 |
+
Case #37: 4
|
| 38 |
+
Case #38: 4
|
| 39 |
+
Case #39: 4
|
| 40 |
+
Case #40: 4
|
| 41 |
+
Case #41: 31
|
| 42 |
+
Case #42: 30
|
| 43 |
+
Case #43: 30
|
| 44 |
+
Case #44: 31
|
| 45 |
+
Case #45: 31
|
| 46 |
+
Case #46: 30
|
| 47 |
+
Case #47: 31
|
| 48 |
+
Case #48: 30
|
| 49 |
+
Case #49: 31
|
| 50 |
+
Case #50: 30
|
| 51 |
+
Case #51: 21
|
| 52 |
+
Case #52: 21
|
| 53 |
+
Case #53: 21
|
| 54 |
+
Case #54: 21
|
| 55 |
+
Case #55: 21
|
| 56 |
+
Case #56: 21
|
| 57 |
+
Case #57: 21
|
| 58 |
+
Case #58: 21
|
| 59 |
+
Case #59: 21
|
| 60 |
+
Case #60: 21
|
2012/round1/checkpoint.html
ADDED
|
@@ -0,0 +1,37 @@
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|
| 1 |
+
You are racing on a 2D lattice grid starting from the origin (0,0) towards a goal (M,N) where M and N are positive integers such that <strong>0< M ≤ N</strong>. There is a checkpoint that's neither on the origin nor on the goal with coordinates (m,n) such that <strong>0 ≤ m ≤ M</strong> and <strong>0 ≤ n ≤ N</strong>. You must clear the checkpoint before you reach the goal. The shortest path takes <strong>T = M + N</strong> steps.
|
| 2 |
+
|
| 3 |
+
<p>
|
| 4 |
+
At each point, you can move to the four immediate neighbors at a fixed speed, but since you don't want to lose the race, you are only going to take either a step to the right or to the top.
|
| 5 |
+
</p>
|
| 6 |
+
|
| 7 |
+
<p>
|
| 8 |
+
Even though there are many ways to reach the goal while clearing the checkpoint, the race is completely pointless since it is relatively easy to figure out the shortest route. To make the race more interesting, we change the rules.
|
| 9 |
+
<b>
|
| 10 |
+
Instead of racing to the same goal <strong>(M,N)</strong>, the racers get to pick a goal <strong>(x,y)</strong> and place the checkpoint to their liking so that there are exactly <strong>S</strong> distinct shortest paths.
|
| 11 |
+
</b>
|
| 12 |
+
</p>
|
| 13 |
+
For example, given <strong>S = 4</strong>, consider the following two goal and checkpoint configurations
|
| 14 |
+
<list>
|
| 15 |
+
<li>
|
| 16 |
+
<b>Placing the checkpoint at (1, 3) and the goal at (2,3). </b>
|
| 17 |
+
There are 4 ways to get from the origin to the checkpoint depending on when you move to the right. Once you are at the checkpoint, there is only one way to reach the goal with minimal number of steps. This gives a total of 4 distinct shortest paths, and takes <strong>T = 2 + 3 = 5</strong> steps. However, you can do better.
|
| 18 |
+
</li>
|
| 19 |
+
<li>
|
| 20 |
+
<b>Placing the checkpoint at (1, 1) and the goal at (2,2). </b>
|
| 21 |
+
There are two ways to get from the origin to the checkpoint depending on whether you move to the right first or later. Similarly, there are two ways to get to the goal, which gives a total of 4 distinct shortest paths. This time, you only need <strong>T = 2 + 2 = 4</strong> steps.
|
| 22 |
+
</li>
|
| 23 |
+
<p>
|
| 24 |
+
As a Hacker Cup racer, you want to figure out how to place the checkpoint and the goal so that you cannot possibly lose. <b>Given S, find the smallest possible T, over all possible checkpoint and goal configurations, such that there are exactly S distinct shortest paths clearing the checkpoint.</b>
|
| 25 |
+
</p>
|
| 26 |
+
|
| 27 |
+
<h3>Input</h3>
|
| 28 |
+
As input for the race you will receive a text file containing an integer <strong>R</strong>, the number of races you will participate in. This will be followed by <strong>R</strong> lines, each describing a race by a single number <strong>S</strong>.
|
| 29 |
+
<br/><br/>
|
| 30 |
+
|
| 31 |
+
<h3>Output</h3>
|
| 32 |
+
Your submission should contain the smallest possible length of the shortest path, <strong>T</strong> for each corresponding race, one per line and in order.
|
| 33 |
+
<br/><br/>
|
| 34 |
+
|
| 35 |
+
<h3>Constraints</h3>
|
| 36 |
+
5 ≤ <strong>R</strong> ≤ 20<br/>
|
| 37 |
+
1 ≤ <strong>S</strong> ≤ 10,000,000<br/>
|
2012/round1/checkpoint.in
ADDED
|
@@ -0,0 +1,61 @@
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
60
|
| 2 |
+
4
|
| 3 |
+
5
|
| 4 |
+
12
|
| 5 |
+
14
|
| 6 |
+
1
|
| 7 |
+
2
|
| 8 |
+
10
|
| 9 |
+
9763393
|
| 10 |
+
9768443
|
| 11 |
+
9946273
|
| 12 |
+
8512466
|
| 13 |
+
3760513
|
| 14 |
+
9407449
|
| 15 |
+
9684937
|
| 16 |
+
10000000
|
| 17 |
+
9699690
|
| 18 |
+
3325608
|
| 19 |
+
7827820
|
| 20 |
+
4604600
|
| 21 |
+
6630624
|
| 22 |
+
6355041
|
| 23 |
+
9078630
|
| 24 |
+
8842550
|
| 25 |
+
8112468
|
| 26 |
+
4457400
|
| 27 |
+
4295526
|
| 28 |
+
422604
|
| 29 |
+
408618
|
| 30 |
+
5491788
|
| 31 |
+
4275806
|
| 32 |
+
6604
|
| 33 |
+
1180
|
| 34 |
+
3351
|
| 35 |
+
3347
|
| 36 |
+
5193
|
| 37 |
+
5097
|
| 38 |
+
846
|
| 39 |
+
4267
|
| 40 |
+
5700
|
| 41 |
+
9552
|
| 42 |
+
3712795
|
| 43 |
+
3195315
|
| 44 |
+
9453880
|
| 45 |
+
7820121
|
| 46 |
+
1198171
|
| 47 |
+
7180766
|
| 48 |
+
2792728
|
| 49 |
+
4702570
|
| 50 |
+
4956629
|
| 51 |
+
9117491
|
| 52 |
+
2318151
|
| 53 |
+
2128949
|
| 54 |
+
441362
|
| 55 |
+
191747
|
| 56 |
+
298690
|
| 57 |
+
5829566
|
| 58 |
+
2058760
|
| 59 |
+
7312234
|
| 60 |
+
9787938
|
| 61 |
+
7635682
|
2012/round1/checkpoint.md
ADDED
|
@@ -0,0 +1,46 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
You are racing on a 2D lattice grid starting from the origin (0,0) towards a
|
| 2 |
+
goal (M,N) where M and N are positive integers such that **0< M ≤ N**. There
|
| 3 |
+
is a checkpoint that's neither on the origin nor on the goal with coordinates
|
| 4 |
+
(m,n) such that **0 ≤ m ≤ M** and **0 ≤ n ≤ N**. You must clear the checkpoint
|
| 5 |
+
before you reach the goal. The shortest path takes **T = M + N** steps.
|
| 6 |
+
|
| 7 |
+
At each point, you can move to the four immediate neighbors at a fixed speed,
|
| 8 |
+
but since you don't want to lose the race, you are only going to take either a
|
| 9 |
+
step to the right or to the top.
|
| 10 |
+
|
| 11 |
+
Even though there are many ways to reach the goal while clearing the
|
| 12 |
+
checkpoint, the race is completely pointless since it is relatively easy to
|
| 13 |
+
figure out the shortest route. To make the race more interesting, we change
|
| 14 |
+
the rules. ** Instead of racing to the same goal **(M,N)**, the racers get to
|
| 15 |
+
pick a goal **(x,y)** and place the checkpoint to their liking so that there
|
| 16 |
+
are exactly **S** distinct shortest paths. **
|
| 17 |
+
|
| 18 |
+
For example, given **S = 4**, consider the following two goal and checkpoint
|
| 19 |
+
configurations
|
| 20 |
+
|
| 21 |
+
* **Placing the checkpoint at (1, 3) and the goal at (2,3). ** There are 4 ways to get from the origin to the checkpoint depending on when you move to the right. Once you are at the checkpoint, there is only one way to reach the goal with minimal number of steps. This gives a total of 4 distinct shortest paths, and takes **T = 2 + 3 = 5** steps. However, you can do better.
|
| 22 |
+
* **Placing the checkpoint at (1, 1) and the goal at (2,2). ** There are two ways to get from the origin to the checkpoint depending on whether you move to the right first or later. Similarly, there are two ways to get to the goal, which gives a total of 4 distinct shortest paths. This time, you only need **T = 2 + 2 = 4** steps.
|
| 23 |
+
|
| 24 |
+
As a Hacker Cup racer, you want to figure out how to place the checkpoint and
|
| 25 |
+
the goal so that you cannot possibly lose. **Given S, find the smallest
|
| 26 |
+
possible T, over all possible checkpoint and goal configurations, such that
|
| 27 |
+
there are exactly S distinct shortest paths clearing the checkpoint.**
|
| 28 |
+
|
| 29 |
+
### Input
|
| 30 |
+
|
| 31 |
+
As input for the race you will receive a text file containing an integer
|
| 32 |
+
**R**, the number of races you will participate in. This will be followed by
|
| 33 |
+
**R** lines, each describing a race by a single number **S**.
|
| 34 |
+
|
| 35 |
+
|
| 36 |
+
### Output
|
| 37 |
+
|
| 38 |
+
Your submission should contain the smallest possible length of the shortest
|
| 39 |
+
path, **T** for each corresponding race, one per line and in order.
|
| 40 |
+
|
| 41 |
+
|
| 42 |
+
### Constraints
|
| 43 |
+
|
| 44 |
+
5 ≤ **R** ≤ 20
|
| 45 |
+
1 ≤ **S** ≤ 10,000,000
|
| 46 |
+
|
2012/round1/checkpoint.out
ADDED
|
@@ -0,0 +1,60 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 4
|
| 2 |
+
Case #2: 6
|
| 3 |
+
Case #3: 6
|
| 4 |
+
Case #4: 9
|
| 5 |
+
Case #5: 2
|
| 6 |
+
Case #6: 3
|
| 7 |
+
Case #7: 6
|
| 8 |
+
Case #8: 9763394
|
| 9 |
+
Case #9: 9768444
|
| 10 |
+
Case #10: 9946274
|
| 11 |
+
Case #11: 4256235
|
| 12 |
+
Case #12: 27586
|
| 13 |
+
Case #13: 17930
|
| 14 |
+
Case #14: 9142
|
| 15 |
+
Case #15: 6325
|
| 16 |
+
Case #16: 28
|
| 17 |
+
Case #17: 28
|
| 18 |
+
Case #18: 60
|
| 19 |
+
Case #19: 32
|
| 20 |
+
Case #20: 52
|
| 21 |
+
Case #21: 130
|
| 22 |
+
Case #22: 124
|
| 23 |
+
Case #23: 105
|
| 24 |
+
Case #24: 27
|
| 25 |
+
Case #25: 26
|
| 26 |
+
Case #26: 1900
|
| 27 |
+
Case #27: 157
|
| 28 |
+
Case #28: 75
|
| 29 |
+
Case #29: 1555
|
| 30 |
+
Case #30: 1945
|
| 31 |
+
Case #31: 179
|
| 32 |
+
Case #32: 65
|
| 33 |
+
Case #33: 1120
|
| 34 |
+
Case #34: 3348
|
| 35 |
+
Case #35: 586
|
| 36 |
+
Case #36: 1702
|
| 37 |
+
Case #37: 65
|
| 38 |
+
Case #38: 268
|
| 39 |
+
Case #39: 25
|
| 40 |
+
Case #40: 247
|
| 41 |
+
Case #41: 742564
|
| 42 |
+
Case #42: 23804
|
| 43 |
+
Case #43: 6262
|
| 44 |
+
Case #44: 12070
|
| 45 |
+
Case #45: 2428
|
| 46 |
+
Case #46: 211233
|
| 47 |
+
Case #47: 11509
|
| 48 |
+
Case #48: 4339
|
| 49 |
+
Case #49: 4956630
|
| 50 |
+
Case #50: 536340
|
| 51 |
+
Case #51: 3248
|
| 52 |
+
Case #52: 4086
|
| 53 |
+
Case #53: 220683
|
| 54 |
+
Case #54: 191748
|
| 55 |
+
Case #55: 537
|
| 56 |
+
Case #56: 5067
|
| 57 |
+
Case #57: 5119
|
| 58 |
+
Case #58: 5845
|
| 59 |
+
Case #59: 6281
|
| 60 |
+
Case #60: 6307
|
2012/round1/recover_the_sequence.html
ADDED
|
@@ -0,0 +1,61 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
<p>Merge sort is one of the classic sorting algorithms. It divides the input array into two halves, recursively sorts each half, then merges the two sorted halves.</p>
|
| 2 |
+
|
| 3 |
+
<p>In this problem merge sort is used to sort an array of integers in ascending order. The exact behavior is given by the following pseudo-code:</p>
|
| 4 |
+
|
| 5 |
+
<pre>function merge_sort(arr):
|
| 6 |
+
n = arr.length()
|
| 7 |
+
if n <= 1:
|
| 8 |
+
return arr
|
| 9 |
+
|
| 10 |
+
// arr is indexed 0 through n-1, inclusive
|
| 11 |
+
mid = floor(n/2)
|
| 12 |
+
|
| 13 |
+
first_half = merge_sort(arr[0..mid-1])
|
| 14 |
+
second_half = merge_sort(arr[mid..n-1])
|
| 15 |
+
return merge(first_half, second_half)
|
| 16 |
+
|
| 17 |
+
function merge(arr1, arr2):
|
| 18 |
+
result = []
|
| 19 |
+
while arr1.length() > 0 and arr2.length() > 0:
|
| 20 |
+
if arr1[0] < arr2[0]:
|
| 21 |
+
print '1' // for debugging
|
| 22 |
+
result.append(arr1[0])
|
| 23 |
+
arr1.remove_first()
|
| 24 |
+
else:
|
| 25 |
+
print '2' // for debugging
|
| 26 |
+
result.append(arr2[0])
|
| 27 |
+
arr2.remove_first()
|
| 28 |
+
|
| 29 |
+
result.append(arr1)
|
| 30 |
+
result.append(arr2)
|
| 31 |
+
return result</pre>
|
| 32 |
+
|
| 33 |
+
<p>A very important permutation of the integers 1 through <strong>N</strong> was lost to a hard drive failure. Luckily, that sequence had been sorted by the above algorithm and the debug sequence of 1s and 2s was recorded on a different disk. You will be given the length <strong>N</strong> of the original sequence, and the debug sequence. Recover the original sequence of integers.</p>
|
| 34 |
+
|
| 35 |
+
<h3>Input</h3>
|
| 36 |
+
<p>The first line of the input file contains an integer <strong>T</strong>. This is followed by <strong>T</strong> test cases, each of which has two lines. The first line of each test case contains the length of the original sequence, <strong>N</strong>. The second line contains a string of 1s and 2s, the debug sequence produced by merge sort while sorting the original sequence. Lines are separated using Unix-style ("\n") line endings.</p>
|
| 37 |
+
|
| 38 |
+
<h3>Output</h3>
|
| 39 |
+
|
| 40 |
+
<p>To avoid having to upload the entire original sequence, output an integer checksum of the original sequence, calculated by the following algorithm:</p>
|
| 41 |
+
|
| 42 |
+
<pre>function checksum(arr):
|
| 43 |
+
result = 1
|
| 44 |
+
for i=0 to arr.length()-1:
|
| 45 |
+
result = (31 * result + arr[i]) mod 1000003
|
| 46 |
+
return result</pre>
|
| 47 |
+
|
| 48 |
+
<h3>Constraints</h3>
|
| 49 |
+
<p>
|
| 50 |
+
5 ≤ <strong>T</strong> ≤ 20<br/>
|
| 51 |
+
2 ≤ N ≤ 10,000
|
| 52 |
+
</p>
|
| 53 |
+
|
| 54 |
+
|
| 55 |
+
<h3>Examples</h3>
|
| 56 |
+
|
| 57 |
+
<p>In the first example, N is 2 and the debug sequence is <tt>1</tt>. The original sequence was 1 2 or 2 1. The debug sequence tells us that the first number was smaller than the second so we know the sequence was 1 2. The checksum is 994.</p>
|
| 58 |
+
|
| 59 |
+
<p>In the second example, N is 2 and the debug sequence is <tt>2</tt>. This time the original sequence is 2 1.</p>
|
| 60 |
+
|
| 61 |
+
<p>In the third example, N is 4 and the debug sequence is <tt>12212</tt>. The original sequence is 2 4 3 1.</p>
|
2012/round1/recover_the_sequence.in
ADDED
|
The diff for this file is too large to render.
See raw diff
|
|
|
2012/round1/recover_the_sequence.md
ADDED
|
@@ -0,0 +1,74 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Merge sort is one of the classic sorting algorithms. It divides the input
|
| 2 |
+
array into two halves, recursively sorts each half, then merges the two sorted
|
| 3 |
+
halves.
|
| 4 |
+
|
| 5 |
+
In this problem merge sort is used to sort an array of integers in ascending
|
| 6 |
+
order. The exact behavior is given by the following pseudo-code:
|
| 7 |
+
|
| 8 |
+
function merge_sort(arr):
|
| 9 |
+
n = arr.length()
|
| 10 |
+
if n <= 1:
|
| 11 |
+
return arr
|
| 12 |
+
// arr is indexed 0 through n-1, inclusive
|
| 13 |
+
mid = floor(n/2)
|
| 14 |
+
first_half = merge_sort(arr[0..mid-1])
|
| 15 |
+
second_half = merge_sort(arr[mid..n-1])
|
| 16 |
+
return merge(first_half, second_half)
|
| 17 |
+
function merge(arr1, arr2):
|
| 18 |
+
result = []
|
| 19 |
+
while arr1.length() > 0 and arr2.length() > 0:
|
| 20 |
+
if arr1[0] < arr2[0]:
|
| 21 |
+
print '1' // for debugging
|
| 22 |
+
result.append(arr1[0])
|
| 23 |
+
arr1.remove_first()
|
| 24 |
+
else:
|
| 25 |
+
print '2' // for debugging
|
| 26 |
+
result.append(arr2[0])
|
| 27 |
+
arr2.remove_first()
|
| 28 |
+
result.append(arr1)
|
| 29 |
+
result.append(arr2)
|
| 30 |
+
return result
|
| 31 |
+
|
| 32 |
+
A very important permutation of the integers 1 through **N** was lost to a
|
| 33 |
+
hard drive failure. Luckily, that sequence had been sorted by the above
|
| 34 |
+
algorithm and the debug sequence of 1s and 2s was recorded on a different
|
| 35 |
+
disk. You will be given the length **N** of the original sequence, and the
|
| 36 |
+
debug sequence. Recover the original sequence of integers.
|
| 37 |
+
|
| 38 |
+
### Input
|
| 39 |
+
|
| 40 |
+
The first line of the input file contains an integer **T**. This is followed
|
| 41 |
+
by **T** test cases, each of which has two lines. The first line of each test
|
| 42 |
+
case contains the length of the original sequence, **N**. The second line
|
| 43 |
+
contains a string of 1s and 2s, the debug sequence produced by merge sort
|
| 44 |
+
while sorting the original sequence. Lines are separated using Unix-style
|
| 45 |
+
("\n") line endings.
|
| 46 |
+
|
| 47 |
+
### Output
|
| 48 |
+
|
| 49 |
+
To avoid having to upload the entire original sequence, output an integer
|
| 50 |
+
checksum of the original sequence, calculated by the following algorithm:
|
| 51 |
+
|
| 52 |
+
function checksum(arr):
|
| 53 |
+
result = 1
|
| 54 |
+
for i=0 to arr.length()-1:
|
| 55 |
+
result = (31 * result + arr[i]) mod 1000003
|
| 56 |
+
return result
|
| 57 |
+
|
| 58 |
+
### Constraints
|
| 59 |
+
|
| 60 |
+
5 ≤ **T** ≤ 20
|
| 61 |
+
2 ≤ N ≤ 10,000
|
| 62 |
+
|
| 63 |
+
### Examples
|
| 64 |
+
|
| 65 |
+
In the first example, N is 2 and the debug sequence is `1`. The original
|
| 66 |
+
sequence was 1 2 or 2 1. The debug sequence tells us that the first number was
|
| 67 |
+
smaller than the second so we know the sequence was 1 2. The checksum is 994.
|
| 68 |
+
|
| 69 |
+
In the second example, N is 2 and the debug sequence is `2`. This time the
|
| 70 |
+
original sequence is 2 1.
|
| 71 |
+
|
| 72 |
+
In the third example, N is 4 and the debug sequence is `12212`. The original
|
| 73 |
+
sequence is 2 4 3 1.
|
| 74 |
+
|
2012/round1/recover_the_sequence.out
ADDED
|
@@ -0,0 +1,40 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 994
|
| 2 |
+
Case #2: 1024
|
| 3 |
+
Case #3: 987041
|
| 4 |
+
Case #4: 570316
|
| 5 |
+
Case #5: 940812
|
| 6 |
+
Case #6: 523359
|
| 7 |
+
Case #7: 477535
|
| 8 |
+
Case #8: 934263
|
| 9 |
+
Case #9: 770156
|
| 10 |
+
Case #10: 487200
|
| 11 |
+
Case #11: 984393
|
| 12 |
+
Case #12: 106718
|
| 13 |
+
Case #13: 811951
|
| 14 |
+
Case #14: 569818
|
| 15 |
+
Case #15: 709190
|
| 16 |
+
Case #16: 273515
|
| 17 |
+
Case #17: 849698
|
| 18 |
+
Case #18: 568298
|
| 19 |
+
Case #19: 185674
|
| 20 |
+
Case #20: 378672
|
| 21 |
+
Case #21: 802415
|
| 22 |
+
Case #22: 284922
|
| 23 |
+
Case #23: 523225
|
| 24 |
+
Case #24: 567769
|
| 25 |
+
Case #25: 636508
|
| 26 |
+
Case #26: 449921
|
| 27 |
+
Case #27: 923660
|
| 28 |
+
Case #28: 900872
|
| 29 |
+
Case #29: 194939
|
| 30 |
+
Case #30: 313933
|
| 31 |
+
Case #31: 219766
|
| 32 |
+
Case #32: 864609
|
| 33 |
+
Case #33: 21064
|
| 34 |
+
Case #34: 280883
|
| 35 |
+
Case #35: 658792
|
| 36 |
+
Case #36: 225962
|
| 37 |
+
Case #37: 789644
|
| 38 |
+
Case #38: 816281
|
| 39 |
+
Case #39: 613647
|
| 40 |
+
Case #40: 162643
|
2012/round1/squished_status.html
ADDED
|
@@ -0,0 +1,22 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
<p>Some engineers got tired of dealing with all the different ways of encoding status messages, so they decided to invent their own. In their new scheme, an encoded status message consists of a sequence of integers representing the characters in the message, separated by spaces. Each integer is between 1 and <strong>M</strong>, inclusive. The integers do not have leading zeroes. Unfortunately they decided to compress the encoded status messages by removing all the spaces!
|
| 2 |
+
</p>
|
| 3 |
+
<p>
|
| 4 |
+
Your task is to figure out how many different encoded status messages a given compressed status message could have originally been. Because this number can be very large, you should return the answer modulo 4207849484 (0xfaceb00c in hex).
|
| 5 |
+
</p>
|
| 6 |
+
<p>
|
| 7 |
+
For example, if the compressed status message is "12" it might have originally been "1 2", or it might have originally been "12". The compressed status messages are between 1 and 1000 characters long, inclusive. Due to database corruption, a compressed status may contain sequences of digits that could not result from removing the spaces in an encoded status message.
|
| 8 |
+
</p>
|
| 9 |
+
<h3>Input</h3>
|
| 10 |
+
<p>
|
| 11 |
+
The input begins with a single integer, <strong>N</strong>, the number of compressed status messages you must analyze. This will be followed by <strong>N</strong> compressed status messages, each consisting of an integer <strong>M</strong>, the highest character code for that database, then the compressed status message, which will be a string of digits each in the range '0' to '9', inclusive. All tokens in the input will be separated by some whitespace.
|
| 12 |
+
</p>
|
| 13 |
+
<h3>Output</h3>
|
| 14 |
+
<p>
|
| 15 |
+
For each of the test cases numbered in order from 1 to <strong>N</strong>, output "Case #<strong>i</strong>: " followed by a single integer containing the number of different encoded status messages that could be represented by the corresponding compressed sequence modulo 4207849484. If none are possible, output a 0.
|
| 16 |
+
</p>
|
| 17 |
+
<h3>Constraints</h3>
|
| 18 |
+
<p>
|
| 19 |
+
5 ≤ <strong>N</strong> ≤ 25<br/>
|
| 20 |
+
2 ≤ <strong>M</strong> ≤ 255<br/>
|
| 21 |
+
1 ≤ length of encoded status ≤ 1000
|
| 22 |
+
</p>
|
2012/round1/squished_status.in
ADDED
|
@@ -0,0 +1,44 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
39
|
| 2 |
+
12
|
| 3 |
+
12
|
| 4 |
+
255
|
| 5 |
+
219
|
| 6 |
+
30
|
| 7 |
+
1234321
|
| 8 |
+
2
|
| 9 |
+
101
|
| 10 |
+
70 8675309
|
| 11 |
+
56 070999427563706517458243835585840290099051637074025394195594348586510834073090163948736588183957349602833959886681418618106557443908727133367714791349473784783516431847035942668366755350157283760764531248617211483790180304621672055750617302943116131142903069883759519683748609377968256054437899455604836182222294525031294343713833201869042441444846948174771572377238024369781
|
| 12 |
+
185 489437731668051889380494808019998308605322017238185334
|
| 13 |
+
171 0087894675463649
|
| 14 |
+
175 33261754228351577578476525209779523127988179898466814632178091966058732629419096182580147726136461252536159859524910309245482518510505400224632364198859663324442131165491882159875547854981497794081342777200378592265262155658847609559210120775240641876041334241839722160083429540405974129979019249434170766042056362227975365345975347996046245948796399196770147994465983195413064659360096554725677890698596977258412582128147198281435385157843685997656109714879412014816286117391379038777327721869676082363453428964553414522582206337809654803310865854542820645495167089958357370335148408859823985527100656590244938554098917907444254926202944319101970754422155318990081301125652572165950553705741636948079747710140051073020357141045775814824559298927842929023036895195372463299081602885132125136042633005801172450983103013385560426338
|
| 15 |
+
36 47535259024547208982019240866549128223533497184879808355855834278389362293644101374873794784103627966059977206730315221676055275048105254086231825161183825398378241999021760601119976227358281353338615988290370298568412785903703509442264
|
| 16 |
+
203 687737220877470653784446097316072785470
|
| 17 |
+
113 51304587103122063086234867477045723173180547403247145600300063966119431864569659559335776509576195196593245332640561449734900616851975700264874390248030968166
|
| 18 |
+
206 448062369945695105287978047551780633933470173673381071374141684019805955017087536053718898917395302000087903383816560700874774939832281360760911551985292789432111705459321334755294477723140443502005380072257563972493947809649578402865552045222601282789930994492309469352141654770147698835946064815324585555522877368846404626788009261501975204754546844243717958911872956808794759039606795872610542253998760234801819677617489625864819272219684204522313232690092941926218256616690572691607530627540612798710546329112670031169508720597503651412508929468129545146310784328053092871340403641805483642889649081298732122033800925634814498445704989125336724435475323195250510991702765430307806236903626071365562848810666101442405095082913070741350043764590108123272413025874645910344552082757964848163999535616317954203928421315693835330208399766051964651633665123178313806434629994308647682571165130773523173316492602519138190346
|
| 19 |
+
65 1876770264484195462373867075504289953849589913192143959493706119994453644071550093082492880383797477491586448128262806265749453109591037917448951185219315245647751499988944695031480940961675592872609377955465767010356210472779712879459920877915616417323912577285316301998836348539369087459603916941305730245213
|
| 20 |
+
197 99549789825776366897151574826765450
|
| 21 |
+
40 9188174
|
| 22 |
+
180 71135853797525154801574664429928955385969111492458546393108368
|
| 23 |
+
163 830372735507449871809731465
|
| 24 |
+
134 2406258858721918774208848120315517208323779940599828715494389738665554681038314446893101871003518703575496336511449627393919132748479928913340144555418397315103310973766058610954180421686012930554663239422912710632257959476189261669997676809989671567278292632886370402049069985046878555076392720791616383499884307075233764956906527854413716114792441649375534077153257152101247222135886802040538230547674927916381416649052144975585897241738727151911864406075
|
| 25 |
+
173 30112824594327595526379236283733863054755720634395622456658473382016537089827468578466186440548412571221610515303525092317381280436948960142601743842389999840805575879010781899131467875
|
| 26 |
+
190 1486139411639384409848749958784650368455059410476755670372360119439112197939878529158062954308851
|
| 27 |
+
159 34547389644611849324902048638970235
|
| 28 |
+
92 87425153970967993390831896675153851510854781083794529288118964576857047283178102891855976962574675710971584027
|
| 29 |
+
90 4657792635807324354837720297526378517183982130663318441767993667273162151581154568833078842147657012720840483968446450279932334516
|
| 30 |
+
167 7097501306639266460334251854124701398441264526401775944932032561851537066954595173614023494661949988333225311
|
| 31 |
+
25 646522
|
| 32 |
+
119 63155576629807163707985640922769106772917396795739548570858093440561312802733843811003
|
| 33 |
+
210 85878750696889017446575830667629960421673460475788331401992664560464795536162396046534097613201747910328526207118280591048874750330716122398307043580519193336856577563682207032364946147148694229628149394147905227355778765319414508752275911061103515923770789
|
| 34 |
+
144 403420455286144733012394352796117676232438993658729712221550931250841303194844906324788136156913626810108948602023083594977223986502041169240216642530162552975968233385427485675131472718018964836808453936722129133940950121976774689537233792725857619706585846714131638551181612253217
|
| 35 |
+
140 14081739843975501051165157925935539505458771396682117602623690411292162645875639965745417670827042186680858848536653039548367352690174908952912337675176219645613802479750293944671739084427422387764770357943062
|
| 36 |
+
190 9529102074196543040963325
|
| 37 |
+
157 36138325509814056284116360672
|
| 38 |
+
220 857671336285619706286505259778502070
|
| 39 |
+
205 52266698626452
|
| 40 |
+
204 335498212
|
| 41 |
+
111 2636907296373399885646047517304031318176238406483770114869777782538642745151012568233889125626174631927487710326357830166987670817345199561837513121049890870755907
|
| 42 |
+
116 972759570129420701017343026504780735238724865028026190998930433648895154524191409145141283939575313912329760551461452376912991044578
|
| 43 |
+
224 2487323315219036305119522514586914514992258092515923847091331536327563425076754497614583159414480884501649219370710323252847898226085122496517560821297108819714616754255018516844563766341
|
| 44 |
+
120 874308165313353435924811434341778738339969013714566776179652
|
2012/round1/squished_status.md
ADDED
|
@@ -0,0 +1,40 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Some engineers got tired of dealing with all the different ways of encoding
|
| 2 |
+
status messages, so they decided to invent their own. In their new scheme, an
|
| 3 |
+
encoded status message consists of a sequence of integers representing the
|
| 4 |
+
characters in the message, separated by spaces. Each integer is between 1 and
|
| 5 |
+
**M**, inclusive. The integers do not have leading zeroes. Unfortunately they
|
| 6 |
+
decided to compress the encoded status messages by removing all the spaces!
|
| 7 |
+
|
| 8 |
+
Your task is to figure out how many different encoded status messages a given
|
| 9 |
+
compressed status message could have originally been. Because this number can
|
| 10 |
+
be very large, you should return the answer modulo 4207849484 (0xfaceb00c in
|
| 11 |
+
hex).
|
| 12 |
+
|
| 13 |
+
For example, if the compressed status message is "12" it might have originally
|
| 14 |
+
been "1 2", or it might have originally been "12". The compressed status
|
| 15 |
+
messages are between 1 and 1000 characters long, inclusive. Due to database
|
| 16 |
+
corruption, a compressed status may contain sequences of digits that could not
|
| 17 |
+
result from removing the spaces in an encoded status message.
|
| 18 |
+
|
| 19 |
+
### Input
|
| 20 |
+
|
| 21 |
+
The input begins with a single integer, **N**, the number of compressed status
|
| 22 |
+
messages you must analyze. This will be followed by **N** compressed status
|
| 23 |
+
messages, each consisting of an integer **M**, the highest character code for
|
| 24 |
+
that database, then the compressed status message, which will be a string of
|
| 25 |
+
digits each in the range '0' to '9', inclusive. All tokens in the input will
|
| 26 |
+
be separated by some whitespace.
|
| 27 |
+
|
| 28 |
+
### Output
|
| 29 |
+
|
| 30 |
+
For each of the test cases numbered in order from 1 to **N**, output "Case
|
| 31 |
+
#**i**: " followed by a single integer containing the number of different
|
| 32 |
+
encoded status messages that could be represented by the corresponding
|
| 33 |
+
compressed sequence modulo 4207849484. If none are possible, output a 0.
|
| 34 |
+
|
| 35 |
+
### Constraints
|
| 36 |
+
|
| 37 |
+
5 ≤ **N** ≤ 25
|
| 38 |
+
2 ≤ **M** ≤ 255
|
| 39 |
+
1 ≤ length of encoded status ≤ 1000
|
| 40 |
+
|
2012/round1/squished_status.out
ADDED
|
@@ -0,0 +1,39 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 2
|
| 2 |
+
Case #2: 4
|
| 3 |
+
Case #3: 6
|
| 4 |
+
Case #4: 0
|
| 5 |
+
Case #5: 2
|
| 6 |
+
Case #6: 0
|
| 7 |
+
Case #7: 34654464
|
| 8 |
+
Case #8: 0
|
| 9 |
+
Case #9: 0
|
| 10 |
+
Case #10: 0
|
| 11 |
+
Case #11: 371280
|
| 12 |
+
Case #12: 0
|
| 13 |
+
Case #13: 0
|
| 14 |
+
Case #14: 0
|
| 15 |
+
Case #15: 7651419
|
| 16 |
+
Case #16: 4
|
| 17 |
+
Case #17: 2173147248
|
| 18 |
+
Case #18: 6552
|
| 19 |
+
Case #19: 2229146040
|
| 20 |
+
Case #20: 1263721604
|
| 21 |
+
Case #21: 3478186852
|
| 22 |
+
Case #22: 499590
|
| 23 |
+
Case #23: 1051059688
|
| 24 |
+
Case #24: 2351149120
|
| 25 |
+
Case #25: 61689176
|
| 26 |
+
Case #26: 2
|
| 27 |
+
Case #27: 384124832
|
| 28 |
+
Case #28: 3480803032
|
| 29 |
+
Case #29: 1591622528
|
| 30 |
+
Case #30: 2555632640
|
| 31 |
+
Case #31: 1365
|
| 32 |
+
Case #32: 37800
|
| 33 |
+
Case #33: 121275
|
| 34 |
+
Case #34: 610
|
| 35 |
+
Case #35: 55
|
| 36 |
+
Case #36: 2725167472
|
| 37 |
+
Case #37: 2694707812
|
| 38 |
+
Case #38: 192415212
|
| 39 |
+
Case #39: 452999512
|
2012/round2/monopoly.html
ADDED
|
@@ -0,0 +1,34 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
<p>In a certain business sector there are currently N small companies, each having just a single employee. These employees are numbered 1 through N.</p>
|
| 2 |
+
|
| 3 |
+
<p>The business sector is about to be transformed into a monopoly. This will happen through a series of mergers, until there is only one company. A single merger involves two companies. In a merger, the president of one company becomes the direct report of the president of the other company, preserving the rest of the hierarchies of both companies.</p>
|
| 4 |
+
|
| 5 |
+
<p>You will be given the descriptions of all mergers. Depending on how they are performed (which of the two presidents involved becomes the president of the new company), the hierarchy can of the final company can take different shapes. We want the hierarchy of the final company to be as shallow as possible. The task is to find the smallest possible number of levels in the final hierarchy.</p>
|
| 6 |
+
|
| 7 |
+
<p>There is also a limit D on the number of direct reports any employee can have. Because of this limit, there may be only one way to accomplish a certain merger, or it might even be impossible. However, there will always be some way to accomplish all the mergers.</p>
|
| 8 |
+
|
| 9 |
+
<h3>Input</h3>
|
| 10 |
+
|
| 11 |
+
<p>The first line contains the number of test cases T.</p>
|
| 12 |
+
|
| 13 |
+
<p>Each test case starts with a blank line. The next line contains two integers, N and D.</p>
|
| 14 |
+
|
| 15 |
+
<p>Each of the following N-1 lines describes a single merger, with two integers between 1 and N. These are the employees whose companies are merging. The two employees will never already be part of the same company.</p>
|
| 16 |
+
|
| 17 |
+
<p>The mergers must be performed in the order in which they are given.</p>
|
| 18 |
+
|
| 19 |
+
<h3>Constraints</h3>
|
| 20 |
+
<p>
|
| 21 |
+
5 ≤ T ≤ 20<br/>
|
| 22 |
+
2 ≤ N ≤ 30,000<br/>
|
| 23 |
+
1 ≤ D ≤ 5,000<br/>
|
| 24 |
+
The input test cases will be such that it is possible to accomplish all mergers.<br/>
|
| 25 |
+
</p>
|
| 26 |
+
|
| 27 |
+
<h3>Output</h3>
|
| 28 |
+
|
| 29 |
+
<p>For each of the test cases numbered in order from 1 to T, output "Case #i: " followed by a single integer, the smallest number of levels in the final hierarchy.</p>
|
| 30 |
+
|
| 31 |
+
<h3>Examples</h3>
|
| 32 |
+
|
| 33 |
+
<p>In the first example, we have N=3 and D=2. The first merger happens between the companies of employees 1 and 2. In the resulting company we can have employee 1 as the president with 2 as his report, or vice versa. Next this company merges with the company of employee 3. If we have employee 3 become the president, the hierarchy will be a chain 3-1-2 or 3-2-1. If 1 or 2 become the president, that president will have the other two employees as direct reports. This last hierarchy has two levels.</p>
|
| 34 |
+
|
2012/round2/monopoly.in
ADDED
|
The diff for this file is too large to render.
See raw diff
|
|
|
2012/round2/monopoly.md
ADDED
|
@@ -0,0 +1,58 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
In a certain business sector there are currently N small companies, each
|
| 2 |
+
having just a single employee. These employees are numbered 1 through N.
|
| 3 |
+
|
| 4 |
+
The business sector is about to be transformed into a monopoly. This will
|
| 5 |
+
happen through a series of mergers, until there is only one company. A single
|
| 6 |
+
merger involves two companies. In a merger, the president of one company
|
| 7 |
+
becomes the direct report of the president of the other company, preserving
|
| 8 |
+
the rest of the hierarchies of both companies.
|
| 9 |
+
|
| 10 |
+
You will be given the descriptions of all mergers. Depending on how they are
|
| 11 |
+
performed (which of the two presidents involved becomes the president of the
|
| 12 |
+
new company), the hierarchy can of the final company can take different
|
| 13 |
+
shapes. We want the hierarchy of the final company to be as shallow as
|
| 14 |
+
possible. The task is to find the smallest possible number of levels in the
|
| 15 |
+
final hierarchy.
|
| 16 |
+
|
| 17 |
+
There is also a limit D on the number of direct reports any employee can have.
|
| 18 |
+
Because of this limit, there may be only one way to accomplish a certain
|
| 19 |
+
merger, or it might even be impossible. However, there will always be some way
|
| 20 |
+
to accomplish all the mergers.
|
| 21 |
+
|
| 22 |
+
### Input
|
| 23 |
+
|
| 24 |
+
The first line contains the number of test cases T.
|
| 25 |
+
|
| 26 |
+
Each test case starts with a blank line. The next line contains two integers,
|
| 27 |
+
N and D.
|
| 28 |
+
|
| 29 |
+
Each of the following N-1 lines describes a single merger, with two integers
|
| 30 |
+
between 1 and N. These are the employees whose companies are merging. The two
|
| 31 |
+
employees will never already be part of the same company.
|
| 32 |
+
|
| 33 |
+
The mergers must be performed in the order in which they are given.
|
| 34 |
+
|
| 35 |
+
### Constraints
|
| 36 |
+
|
| 37 |
+
5 ≤ T ≤ 20
|
| 38 |
+
2 ≤ N ≤ 30,000
|
| 39 |
+
1 ≤ D ≤ 5,000
|
| 40 |
+
The input test cases will be such that it is possible to accomplish all
|
| 41 |
+
mergers.
|
| 42 |
+
|
| 43 |
+
### Output
|
| 44 |
+
|
| 45 |
+
For each of the test cases numbered in order from 1 to T, output "Case #i: "
|
| 46 |
+
followed by a single integer, the smallest number of levels in the final
|
| 47 |
+
hierarchy.
|
| 48 |
+
|
| 49 |
+
### Examples
|
| 50 |
+
|
| 51 |
+
In the first example, we have N=3 and D=2. The first merger happens between
|
| 52 |
+
the companies of employees 1 and 2. In the resulting company we can have
|
| 53 |
+
employee 1 as the president with 2 as his report, or vice versa. Next this
|
| 54 |
+
company merges with the company of employee 3. If we have employee 3 become
|
| 55 |
+
the president, the hierarchy will be a chain 3-1-2 or 3-2-1. If 1 or 2 become
|
| 56 |
+
the president, that president will have the other two employees as direct
|
| 57 |
+
reports. This last hierarchy has two levels.
|
| 58 |
+
|
2012/round2/monopoly.out
ADDED
|
@@ -0,0 +1,20 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 2
|
| 2 |
+
Case #2: 3
|
| 3 |
+
Case #3: 3
|
| 4 |
+
Case #4: 3
|
| 5 |
+
Case #5: 4
|
| 6 |
+
Case #6: 2
|
| 7 |
+
Case #7: 501
|
| 8 |
+
Case #8: 8
|
| 9 |
+
Case #9: 7
|
| 10 |
+
Case #10: 7
|
| 11 |
+
Case #11: 6
|
| 12 |
+
Case #12: 19
|
| 13 |
+
Case #13: 16
|
| 14 |
+
Case #14: 13
|
| 15 |
+
Case #15: 35
|
| 16 |
+
Case #16: 45
|
| 17 |
+
Case #17: 22
|
| 18 |
+
Case #18: 15
|
| 19 |
+
Case #19: 8
|
| 20 |
+
Case #20: 1244
|
2012/round2/road_removal.html
ADDED
|
@@ -0,0 +1,24 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
<p>You are given a network with <b>N</b> cities and <b>M</b> bidirectional roads connecting these cities. The first <b>K</b> cities are important. You need to remove the minimum number of roads such that in the remaining network there are no cycles that contain important cities. A cycle is a sequence of at least three different cities such that each pair of neighboring cities are connected by a road and the first and the last city in the sequence are also connected by a road.</p>
|
| 2 |
+
|
| 3 |
+
<h2>Input</h2>
|
| 4 |
+
<p>The first line contains the number of test cases <strong>T</strong>.</p>
|
| 5 |
+
|
| 6 |
+
<p>Each case begins with a line containing integers <strong>N</strong>, <strong>M</strong> and <strong>K</strong>, which represent the number of cities, the number of roads and the number of important cities, respectively. The cities are numbered from <strong>0</strong> to <strong>N-1</strong>, and the important cities are numbered from <strong>0</strong> to <strong>K-1</strong>. The following <strong>M</strong> lines contain two integers <strong>a[i]</strong> and <strong>b[i]</strong>, <strong>0</strong> ≤ <strong>i</strong> < <strong>M</strong>, that represent two different cities connected by a road.</p>
|
| 7 |
+
|
| 8 |
+
<p>It is guaranteed that <strong>0</strong> ≤ <strong>a[i]</strong>, <strong>b[i]</strong> < <strong>N</strong> and <strong>a[i]</strong> ≠ <strong>b[i]</strong>. There will be at most one road between two cities.</p>
|
| 9 |
+
|
| 10 |
+
<h2>Output</h2>
|
| 11 |
+
<p>For each of the test cases numbered in order from <strong>1</strong> to <strong>T</strong>, output "Case #i: " followed by a single integer, the minimum number of roads that need to be removed such that there are no cycles that contain an important city.</p>
|
| 12 |
+
|
| 13 |
+
<h2>Constraints</h2>
|
| 14 |
+
<p>
|
| 15 |
+
1 ≤ <strong>T</strong> ≤ 20<br/>
|
| 16 |
+
1 ≤ <strong>N</strong> ≤ 10,000<br/>
|
| 17 |
+
1 ≤ <strong>M</strong> ≤ 50,000<br/>
|
| 18 |
+
1 ≤ <strong>K</strong> ≤ <strong>N</strong></p>
|
| 19 |
+
|
| 20 |
+
|
| 21 |
+
<h3>Example</h3>
|
| 22 |
+
|
| 23 |
+
<p>In the first example, we have <strong>N</strong>=5 cities that are connected by <strong>M</strong>=7 roads and the cities <strong>0</strong> and <strong>1</strong> are important. We can remove two roads connecting (<strong>0</strong>, <strong>1</strong>) and (<strong>1</strong>, <strong>2</strong>) and the remaining network will not contain cycles with important cities. Note that in the remaining network there is a cycle that contains only non-important cities, and that there are also multiple ways to remove two roads and satisfy all conditions. One cannot remove only one road and destroy all cycles that contain important cities.</p>
|
| 24 |
+
|
2012/round2/road_removal.in
ADDED
|
The diff for this file is too large to render.
See raw diff
|
|
|
2012/round2/road_removal.md
ADDED
|
@@ -0,0 +1,45 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
You are given a network with **N** cities and **M** bidirectional roads
|
| 2 |
+
connecting these cities. The first **K** cities are important. You need to
|
| 3 |
+
remove the minimum number of roads such that in the remaining network there
|
| 4 |
+
are no cycles that contain important cities. A cycle is a sequence of at least
|
| 5 |
+
three different cities such that each pair of neighboring cities are connected
|
| 6 |
+
by a road and the first and the last city in the sequence are also connected
|
| 7 |
+
by a road.
|
| 8 |
+
|
| 9 |
+
## Input
|
| 10 |
+
|
| 11 |
+
The first line contains the number of test cases **T**.
|
| 12 |
+
|
| 13 |
+
Each case begins with a line containing integers **N**, **M** and **K**, which
|
| 14 |
+
represent the number of cities, the number of roads and the number of
|
| 15 |
+
important cities, respectively. The cities are numbered from **0** to **N-1**,
|
| 16 |
+
and the important cities are numbered from **0** to **K-1**. The following
|
| 17 |
+
**M** lines contain two integers **a[i]** and **b[i]**, **0** ≤ **i** < **M**,
|
| 18 |
+
that represent two different cities connected by a road.
|
| 19 |
+
|
| 20 |
+
It is guaranteed that **0** ≤ **a[i]**, **b[i]** < **N** and **a[i]** ≠
|
| 21 |
+
**b[i]**. There will be at most one road between two cities.
|
| 22 |
+
|
| 23 |
+
## Output
|
| 24 |
+
|
| 25 |
+
For each of the test cases numbered in order from **1** to **T**, output "Case
|
| 26 |
+
#i: " followed by a single integer, the minimum number of roads that need to
|
| 27 |
+
be removed such that there are no cycles that contain an important city.
|
| 28 |
+
|
| 29 |
+
## Constraints
|
| 30 |
+
|
| 31 |
+
1 ≤ **T** ≤ 20
|
| 32 |
+
1 ≤ **N** ≤ 10,000
|
| 33 |
+
1 ≤ **M** ≤ 50,000
|
| 34 |
+
1 ≤ **K** ≤ **N**
|
| 35 |
+
|
| 36 |
+
### Example
|
| 37 |
+
|
| 38 |
+
In the first example, we have **N**=5 cities that are connected by **M**=7
|
| 39 |
+
roads and the cities **0** and **1** are important. We can remove two roads
|
| 40 |
+
connecting (**0**, **1**) and (**1**, **2**) and the remaining network will
|
| 41 |
+
not contain cycles with important cities. Note that in the remaining network
|
| 42 |
+
there is a cycle that contains only non-important cities, and that there are
|
| 43 |
+
also multiple ways to remove two roads and satisfy all conditions. One cannot
|
| 44 |
+
remove only one road and destroy all cycles that contain important cities.
|
| 45 |
+
|
2012/round2/road_removal.out
ADDED
|
@@ -0,0 +1,20 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
Case #1: 2
|
| 2 |
+
Case #2: 4
|
| 3 |
+
Case #3: 72
|
| 4 |
+
Case #4: 33
|
| 5 |
+
Case #5: 361
|
| 6 |
+
Case #6: 398
|
| 7 |
+
Case #7: 4851
|
| 8 |
+
Case #8: 1176
|
| 9 |
+
Case #9: 511
|
| 10 |
+
Case #10: 1014
|
| 11 |
+
Case #11: 1114
|
| 12 |
+
Case #12: 286
|
| 13 |
+
Case #13: 0
|
| 14 |
+
Case #14: 1070
|
| 15 |
+
Case #15: 731
|
| 16 |
+
Case #16: 22
|
| 17 |
+
Case #17: 3135
|
| 18 |
+
Case #18: 13995
|
| 19 |
+
Case #19: 4569
|
| 20 |
+
Case #20: 190
|
2012/round2/sequence_slicing.html
ADDED
|
@@ -0,0 +1,39 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
| 1 |
+
<p>Let <b>S</b> be a sequence of <b>N</b> natural numbers. We can define an infinite sequence <b>MS</b> in the following way:
|
| 2 |
+
<b>MS</b>[k] = <b>S</b>[k mod <b>N</b>] + <b>N</b> * floor(k / <b>N</b>).
|
| 3 |
+
Where k is a zero based index. </p>
|
| 4 |
+
<p>For example if the sequence <b>S</b> is {2, 1, 3} then <b>MS</b> would be {2, 1, 3, 5, 4, 6, 8, 7, 9, 11, 10, 12...}</p>
|
| 5 |
+
|
| 6 |
+
<p>Now consider a subsequence of <b>MS</b> generated by picking two random indices <b>a</b>, <b>b</b> from the range [<b>0</b>..<b>R</b>] inclusive, and taking all the elements between them, that is:
|
| 7 |
+
<b>MS</b>[min(<b>a</b>, <b>b</b>)..max(<b>a</b>, <b>b</b>)].
|
| 8 |
+
<p>If we use the same <b>MS</b> as in the example above and <b>a</b> = 2, <b>b</b> = 5 then our subsequence would be {3, 5, 4, 6}.
|
| 9 |
+
</p>
|
| 10 |
+
<p>Your task is to calculate the probability that the selected subsequence has at least <b>K</b> distinct elements. <b>a</b> and <b>b</b> are selected independently and with a uniform distribution. The result should be printed as a fraction. See the "Output" section for clarification.
|
| 11 |
+
|
| 12 |
+
<h3>Input</h3>
|
| 13 |
+
<p>The first line of the input file contains an integer <b>T</b>. This is followed by <b>T</b> test cases, each of which has two lines.</p>
|
| 14 |
+
<p>The first line of each test case contains three integers separated by spaces, <b>N</b>, <b>K</b>, and <b>R</b>.<br/>
|
| 15 |
+
|
| 16 |
+
<p>The second line contains <b>N</b> space separated integers, <b>S</b>[0] through <b>S</b>[<b>N</b>-1].</p>
|
| 17 |
+
|
| 18 |
+
<h3>Constraints</h3>
|
| 19 |
+
<p>1 ≤ <b>T</b> ≤ 20<br/>
|
| 20 |
+
1 ≤ <b>N</b> ≤ 2,000<br/>
|
| 21 |
+
1 ≤ <b>K</b> ≤ <b>R</b> ≤ 1,000,000,000<br/>
|
| 22 |
+
1 ≤ <b>S</b>[i] ≤ 100,000</p>
|
| 23 |
+
|
| 24 |
+
<h3>Output</h3>
|
| 25 |
+
<p>
|
| 26 |
+
For each of the test cases numbered in order from 1 to <strong>T</strong>, output "Case #<b>i</b>: " followed by the probability that the selected subsequence of <b>MS</b> has at least <b>K</b> distinct elements. The probability should be expressed as a fraction <b>p</b>/<b>q</b>, where <b>p</b> and <b>q</b> represent the numerator and denominator respectively and are relatively prime (that is they share no common positive divisors except 1).
|
| 27 |
+
</p>
|
| 28 |
+
|
| 29 |
+
<p>If the probability is 0 or 1 output 0/1 or 1/1 respectively.</p>
|
| 30 |
+
|
| 31 |
+
<h3>Examples</h3>
|
| 32 |
+
<p>In the first example there are 36 different subsequences to consider. 6 of them have only a single number, and the remaining 30 have at least 2 different numbers, so the answer is 5/6.
|
| 33 |
+
</p>
|
| 34 |
+
<p>
|
| 35 |
+
The second example is similar, but now the sequence looks like {2, 1, 5, 5, 4, 8}. There are 8 subsequences with less than 2 distinct numbers: the six single number subsequences plus (a=2, b=3) and (a=3, b=2) which both result in {5,5}. That gives a probability of (36 - 8) / 36 = 7/9.
|
| 36 |
+
</p>
|
| 37 |
+
<p>
|
| 38 |
+
The third example uses the same sequence as the second example, but now we want to have subsequences with at least 4 different numbers. All pairs of indices that have this property are: (0,4), (0, 5), (1, 5), (4, 0), (5, 0), and (5, 1). Six out of thirty six results in a probability of 1/6.
|
| 39 |
+
</p>
|
2012/round2/sequence_slicing.in
ADDED
|
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|
2012/round2/sequence_slicing.md
ADDED
|
@@ -0,0 +1,64 @@
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|
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|
|
|
|
|
|
|
|
| 1 |
+
Let **S** be a sequence of **N** natural numbers. We can define an infinite
|
| 2 |
+
sequence **MS** in the following way: **MS**[k] = **S**[k mod **N**] + **N** *
|
| 3 |
+
floor(k / **N**). Where k is a zero based index.
|
| 4 |
+
|
| 5 |
+
For example if the sequence **S** is {2, 1, 3} then **MS** would be {2, 1, 3,
|
| 6 |
+
5, 4, 6, 8, 7, 9, 11, 10, 12...}
|
| 7 |
+
|
| 8 |
+
Now consider a subsequence of **MS** generated by picking two random indices
|
| 9 |
+
**a**, **b** from the range [**0**..**R**] inclusive, and taking all the
|
| 10 |
+
elements between them, that is: **MS**[min(**a**, **b**)..max(**a**, **b**)].
|
| 11 |
+
|
| 12 |
+
If we use the same **MS** as in the example above and **a** = 2, **b** = 5
|
| 13 |
+
then our subsequence would be {3, 5, 4, 6}.
|
| 14 |
+
|
| 15 |
+
Your task is to calculate the probability that the selected subsequence has at
|
| 16 |
+
least **K** distinct elements. **a** and **b** are selected independently and
|
| 17 |
+
with a uniform distribution. The result should be printed as a fraction. See
|
| 18 |
+
the "Output" section for clarification.
|
| 19 |
+
|
| 20 |
+
### Input
|
| 21 |
+
|
| 22 |
+
The first line of the input file contains an integer **T**. This is followed
|
| 23 |
+
by **T** test cases, each of which has two lines.
|
| 24 |
+
|
| 25 |
+
The first line of each test case contains three integers separated by spaces,
|
| 26 |
+
**N**, **K**, and **R**.
|
| 27 |
+
|
| 28 |
+
The second line contains **N** space separated integers, **S**[0] through
|
| 29 |
+
**S**[**N**-1].
|
| 30 |
+
|
| 31 |
+
### Constraints
|
| 32 |
+
|
| 33 |
+
1 ≤ **T** ≤ 20
|
| 34 |
+
1 ≤ **N** ≤ 2,000
|
| 35 |
+
1 ≤ **K** ≤ **R** ≤ 1,000,000,000
|
| 36 |
+
1 ≤ **S**[i] ≤ 100,000
|
| 37 |
+
|
| 38 |
+
### Output
|
| 39 |
+
|
| 40 |
+
For each of the test cases numbered in order from 1 to **T**, output "Case
|
| 41 |
+
#**i**: " followed by the probability that the selected subsequence of **MS**
|
| 42 |
+
has at least **K** distinct elements. The probability should be expressed as a
|
| 43 |
+
fraction **p**/**q**, where **p** and **q** represent the numerator and
|
| 44 |
+
denominator respectively and are relatively prime (that is they share no
|
| 45 |
+
common positive divisors except 1).
|
| 46 |
+
|
| 47 |
+
If the probability is 0 or 1 output 0/1 or 1/1 respectively.
|
| 48 |
+
|
| 49 |
+
### Examples
|
| 50 |
+
|
| 51 |
+
In the first example there are 36 different subsequences to consider. 6 of
|
| 52 |
+
them have only a single number, and the remaining 30 have at least 2 different
|
| 53 |
+
numbers, so the answer is 5/6.
|
| 54 |
+
|
| 55 |
+
The second example is similar, but now the sequence looks like {2, 1, 5, 5, 4,
|
| 56 |
+
8}. There are 8 subsequences with less than 2 distinct numbers: the six single
|
| 57 |
+
number subsequences plus (a=2, b=3) and (a=3, b=2) which both result in {5,5}.
|
| 58 |
+
That gives a probability of (36 - 8) / 36 = 7/9.
|
| 59 |
+
|
| 60 |
+
The third example uses the same sequence as the second example, but now we
|
| 61 |
+
want to have subsequences with at least 4 different numbers. All pairs of
|
| 62 |
+
indices that have this property are: (0,4), (0, 5), (1, 5), (4, 0), (5, 0),
|
| 63 |
+
and (5, 1). Six out of thirty six results in a probability of 1/6.
|
| 64 |
+
|
2012/round2/sequence_slicing.out
ADDED
|
@@ -0,0 +1,34 @@
|
|
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|
|
|
|
|
|
| 1 |
+
Case #1: 5/6
|
| 2 |
+
Case #2: 7/9
|
| 3 |
+
Case #3: 1/6
|
| 4 |
+
Case #4: 0/1
|
| 5 |
+
Case #5: 998005995006/1000002000001
|
| 6 |
+
Case #6: 2692922/5841889
|
| 7 |
+
Case #7: 69911/315844
|
| 8 |
+
Case #8: 11382034/14250625
|
| 9 |
+
Case #9: 23677986/24611521
|
| 10 |
+
Case #10: 233678/3876961
|
| 11 |
+
Case #11: 1/1
|
| 12 |
+
Case #12: 10566737/27602450
|
| 13 |
+
Case #13: 894152/6171605
|
| 14 |
+
Case #14: 631400/4531323
|
| 15 |
+
Case #15: 2727724/54272689
|
| 16 |
+
Case #16: 51911/46967432
|
| 17 |
+
Case #17: 2084441/4456321
|
| 18 |
+
Case #18: 13044037/18060050
|
| 19 |
+
Case #19: 0/1
|
| 20 |
+
Case #20: 1/1
|
| 21 |
+
Case #21: 7406024/21669025
|
| 22 |
+
Case #22: 335222/1575025
|
| 23 |
+
Case #23: 4188535/6780816
|
| 24 |
+
Case #24: 172484/1565001
|
| 25 |
+
Case #25: 62267074/95942025
|
| 26 |
+
Case #26: 10535999529895110/85209558285138169
|
| 27 |
+
Case #27: 568783218408907/8314358527108732
|
| 28 |
+
Case #28: 0/1
|
| 29 |
+
Case #29: 416515005307519/7653652276052250
|
| 30 |
+
Case #30: 1844737452390571/1890800074855561
|
| 31 |
+
Case #31: 35334298477125432/35624192971900729
|
| 32 |
+
Case #32: 98894340234057202/100064691043101225
|
| 33 |
+
Case #33: 778741908690941/859699982029952
|
| 34 |
+
Case #34: 6/1000000002000000001
|
2012/round3/divisor_function_optimization.html
ADDED
|
@@ -0,0 +1,19 @@
|
|
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|
|
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|
|
|
|
|
|
|
|
| 1 |
+
<p> Let <b>d(N)</b> be the number of positive divisors of positive integer <b>N</b>.
|
| 2 |
+
Consider the infinite sequence <b>x(n) = d(n)<sup>a</sup> / n<sup>b</sup>, n = 1, 2, 3, …</b>
|
| 3 |
+
where <b>a</b> and <b>b</b> are fixed positive integers.
|
| 4 |
+
It can be shown that this sequence tends to zero. Hence it attains its maximum. Denote it by <b>p/q</b> where <b>p</b> and <b>q</b> are co-prime positive integers. Your task is for given <b>a</b> and <b>b</b> find <b>p</b> and <b>q</b> modulo <b>M = 10<sup>9</sup>+7</b>. But to keep input and output small you will be given tuples <b>(b1; b2; a1; a2; c)</b> and need to calculate the sum of <b>(p mod M)</b> for all pairs <b>(a; b)</b> such that <b>b1 ≤ b ≤ b2</b>, <b>a1 ≤ a ≤ a2</b> and <b> a ≤ c*b</b>, and the same sum for <b>q</b>-values. </p>
|
| 5 |
+
|
| 6 |
+
<h3>Input</h3>
|
| 7 |
+
<p>The first line contains a positive integer <b>T</b>, the number of test cases. <b>T</b> test cases follow. The only line of each test case contains five space separated positive integers <b>b1, b2, a1, a2</b> and <b>c</b>.</p>
|
| 8 |
+
|
| 9 |
+
<h3>Output</h3>
|
| 10 |
+
<p>For each of the test cases numbered in order from <b>1</b> to <b>T</b>, output "Case #i: " followed by a space separated pair of integers: the sum of <b>(p mod M)</b> for all pairs <b>(a; b)</b> mentioned above and the sum of <b>(q mod M)</b> for all such pairs. Note that you need to find the sum of residues not the residue of sum (see testcase 3 as a reference).</p>
|
| 11 |
+
|
| 12 |
+
<h3>Constraints</h3>
|
| 13 |
+
<p>
|
| 14 |
+
1 ≤ <b>T</b> ≤ 20<br/>
|
| 15 |
+
1 ≤ <b>b1</b> ≤ <b>b2</b> ≤ 10,000<br/>
|
| 16 |
+
1 ≤ <b>a1</b> ≤ <b>a2</b> ≤ 250,000<br/>
|
| 17 |
+
1 ≤ <b>c</b> ≤ 25<br/>
|
| 18 |
+
in each testcase the total number of pairs <b>(a; b)</b> for which the answer should be calculated does not exceed 100,000<br/></p>
|
| 19 |
+
|