meetforever/GRPO_CL huggingface dataset:
user: Yan and Fen have just accepted jobs in TechValley California allowing them to pursue their childhood dream of renting the most expensive apartment in the area.

Yan and Fen have decided that the rent of an apartment denoted $R$ is a function of its square footage $x$ and the number of smartbulbs $y$ it has. The cost of $1$ square foot is given by $a$ and the cost of $1$ smartbulb is given by $b$ and thus we have,\begin{equation*} R = ax + by \end{equation*}

Fortunately for the pair, TechValley California has no shortage of expensive apartments for rent. Unfortunately, there are some specific constraints on the apartment and the contents of the apartment that Yan and Fen must follow. First the square footage of the apartment and the number of smart bulbs must both be greater than or equal to $1$.\begin{align*} x & \geq 1\\ y & \geq 1 \end{align*}

Secondly, the square footage of the apartment plus the number of smartbulbs cannot exceed a specific $m$, you may assume that $m$ will always be an even integer.\begin{equation*} x + y \leq m \end{equation*}

Lastly, since both Yan and Fen need lots of outlets in their apartment to support all their electronics they will only look at apartments that have exactly $2$ outlets for each square foot of the house in addition to one outlet for each smartbulb with minimum of $\sigma $ outlets. You may assume that $\sigma $ will always be an even integer.\begin{equation*} 2x + y \geq \sigma \end{equation*}

Find the maximum rent of an apartment $R$ subject to these constraints

-----Input-----
The input consists of a single test case with two lines. The test case starts with two integers $a$ and $b$ ($0 \leq a, b < 100$), the price per square foot and price per smart bulb respectively. The next line consists of two integers $m$ and $\sigma $ ($0 < m, \sigma \leq 10^8$ and $m, \sigma $ are both even) the square footage and smartbulbs maximum and the minimum number of outlets respectively.

-----Output-----
Output a single line with the maximum value of $R$. Note that $R$ is guaranteed to be an integer and the input will be supplied such that there will always be a solution.

-----Examples-----
Sample Input:
3 1
12 16
Sample Output:
34
user: Martin has invited everyone he knows to celebrate his 535th birthday, and a whopping $n$ people from all over the world have accepted the invitation.

When deciding the seating arrangement, Martin’s mother Margarethe have decided that all the guests should be seated with maximum awkwardness; this is to ensure that nobody has anything meaningful to discuss during dinner, and everyone would instead silently enjoy her rather tasty coriander soup (as the saying goes; “when the food is good, conversation dies”).

Margarethe knows that awkwardness is maximized if the guests are seated in a long row along a single table, in such a way that nobody sits next to someone speaking the same language as themselves. Better yet, she has defined the awkwardness level of a seating arrangement to be the minimum number of seats separating any two guests speaking the same language. If no two people speak the same language, the awkwardness level is defined to be $n$ (the number of guests). Two seats next to each other are said to be separated by $1$.

Given the languages spoken in a proposed seating arrangement, can you help Margarethe determine the awkwardness level?

-----Input-----
The first line contains an integer $n$ ($1 \leq n \leq 100000$) denoting the number of guests. On the second line follows $n$ integers, the $i$’th of which $x_ i$ ($0 \leq x_ i \leq 10^9$) indicating the language spoken by the guest seated at position $i$ in the proposed arrangement (each guest speaks exactly one language).

-----Output-----
A single integer, the awkwardness level of the proposed seating arrangement.

-----Examples-----
Sample Input:
4
1 2 3 1
Sample Output:
3
user: The English word “mile” derives from the Latin “mille passus”, meaning “a thousand paces”. A Roman mile was the distance a soldier would walk in $1000$ paces (a pace being two steps, one with each foot). 

Over time, the actual distance referred to as a “mile” has changed. The modern English mile is $5280$ (modern) feet. The Roman mile is believed to have been about $4854$ (modern) feet. Therefore a distance of $x$ English miles would correspond to $1000 \cdot \frac{5280}{4854}$ Roman paces.

Write a program to convert distances in English miles into Roman paces.

-----Input-----
Input will consist of a single line containing a single real number $0 \le X \le 1000$ denoting a distance in English miles. The number $X$ has at most $3$ digits of precision after the decimal point.

-----Output-----
Print an integer denoting the closest number of Roman paces equivalent to X. Your answer should be rounded to the closest integer (with an exact $.5$ decimal part rounded up).

-----Examples-----
Sample Input:
1.0
Sample Output:
1088
user: Of course you have all heard of the International Cheese Processing Company. Their machine for cutting a piece of cheese into slices of exactly the same thickness is a classic. Recently they produced a machine able to cut a spherical cheese (such as Edam) into slices – no, not all of the same thickness, but all of the same weight! But new challenges lie ahead: cutting Swiss cheese. 

Swiss cheese such as Emmentaler has holes in it, and the holes may have different sizes. A slice with holes contains less cheese and has a lower weight than a slice without holes. So here is the challenge: cut a cheese with holes in it into slices of equal weight.

By smart sonar techniques (the same techniques used to scan unborn babies and oil fields), it is possible to locate the holes in the cheese up to micrometer precision. For the present problem you may assume that the holes are perfect spheres.

Each uncut block has size $100 \times 100 \times 100$ where each dimension is measured in millimeters. Your task is to cut it into $s$ slices of equal weight. The slices will be $100$ mm wide and $100$ mm high, and your job is to determine the thickness of each slice.

-----Input-----
The first line of the input contains two integers $n$ and $s$, where $0 \leq n \leq 10000$ is the number of holes in the cheese, and $1 \le s \le 100$ is the number of slices to cut. The next $n$ lines each contain four positive integers $r$, $x$, $y$, and $z$ that describe a hole, where $r$ is the radius and $x$, $y$, and $z$ are the coordinates of the center, all in micrometers.

The cheese block occupies the points $(x,y,z)$ where $0 \le x,y,z \le 100000$, except for the points that are part of some hole. The cuts are made perpendicular to the $z$ axis.

You may assume that holes do not overlap but may touch, and that the holes are fully contained in the cheese but may touch its boundary.

-----Output-----
Display the $s$ slice thicknesses in millimeters, starting from the end of the cheese with $z=0$. Your output should have an absolute or relative error of at most $10^{-6}$.

-----Examples-----
Sample Input:
0 4
Sample Output:
25.000000000
25.000000000
25.000000000
25.000000000
user: Young Mirko threw matches all over the floor of his room.

His mom did not like that and ordered him to put all the matches in a box. Mirko soon noticed that not all of the matches on the floor fit in the box, so he decided to take the matches that don’t fit and throw them in the neighbour’s garbage, where his mom (hopefully) won’t find them.

Help Mirko determine which of the matches fit in the box his mom gave him. A match fits in the box if its entire length can lie on the bottom of the box. Mirko examines the matches one by one.

-----Input-----
The first line of input contains an integer $N$ ($1 \leq N \leq 50$), the number of matches on the floor, and two integers $W$ and $H$, the dimensions of the box ($1 \leq W \leq 100$, $1 \leq H \leq 100$).

Each of the following $N$ lines contains a single integer between $1$ and $1000$ (inclusive), the length of one match.

-----Output-----
For each match, in the order they were given in the input, output on a separate line “DA” if the match fits in the box or “NE” if it does not.

-----Examples-----
Sample Input:
5 3 4
3
4
5
6
7
Sample Output:
DA
DA
DA
NE
NE
user: You’d like to figure out whether a car was speeding while it was driving down a straight road. Unfortunately, you don’t have any radar guns or related instruments for measuring speed directly; all you have are photographs taken of the car at various checkpoints on the road at various times. Given when and where these photographs were taken, what is the fastest speed that you can prove the car must have been going at some point along the road?

-----Input-----
The first line of input contains an integer $n$ ($2 \le n \le 100$), which is the number of photographs taken.

Each of the following $n$ lines contains two space-separated integers $t$ ($0 \le t \le 10^4$) and

$d$ ($0 \le d \le 10^6$), where $t$ is the time of the photograph in hours, and $d$ is the distance along the road in miles. The first photograph is always taken at time $0$ with distance $0$, and both the times and distances strictly increase.

-----Output-----
Output a single integer, which is the greatest integral speed that you can be certain the car was going at some point in miles per hour.

-----Examples-----
Sample Input:
2
0 0
7 42
Sample Output:
6
user: You are teaching discrete math. You have done your best to teach your students about axioms and inference rules, proofs and theorems. Sometimes the students write beautiful proofs that Fermat would be proud of but sometimes, also like Fermat, their proofs are not quite right. You are getting a little tired of hunting through some of these so-called “proofs” for the magic tricks that let them prove $1 = 2$ and had the great idea to write a computer program to speed things up!

Because this is the first class in proof-based mathematics, you have started your students off with a simple proof system. All proof lines consist of a list of assumptions, an arrow, and a conclusion. If there are no assumptions, the conclusion is an axiom. A line of the proof is valid if and only if all assumptions were conclusions of previous lines. Sometimes the students derive a conclusion more than once just to be extra sure it is true, and that is perfectly all right!

-----Input-----
The first line of input consists of an integer $1 \le n \le 400000$, the number of lines in the “proof”. Then follow the $n$ lines of the “proof”. Each line has $0 \le a \le 5$ assumptions, followed by an arrow (the string “->”), followed by one conclusion. All assumptions and conclusions consist of $1 \le c \le 5$ uppercase alphabetic characters. The assumptions, arrow, and conclusion are all separated by single spaces.

-----Output-----
If every line is correct output “correct”. Otherwise, output the number of the first line with an error (line numbers start at $1$).

-----Examples-----
Sample Input:
3
-> ALICE
-> BOB
ALICE BOB -> CARL
Sample Output:
correct
user: The recent schoolboard elections were hotly contested: a proposal to swap school start times for elementary and high school students, a controversial new dress code proposal that bans athletic clothes in school, and a proposal to raise real-estate taxes to pay for a new football practice facility, and the list goes on and on. It is now hours after the polls have closed and a winner has yet to emerge! 

In their desperation, the election officials turn to you and ask you to write a program to count the vote!

-----Input-----
The input consists of a single test case, which is a list of votes cast. Each line in the input contains the name of a candidate for whom a vote was cast. A name may consist of multiple words, separated by spaces. Words contain letters or hyphens, but no other punctuation characters. There will be at least $2$ votes on the list. The list of votes ends with a single line containing the characters ***. This line should not be counted. There can be up to $100000$ valid votes.

-----Output-----
If a candidate obtained a simple or absolute majority of all votes cast (that is, more than any other candidate), output the name of this candidate! If no candidate obtained a simple majority, output: “Runoff!” (don’t forget to include the exclamation mark!)

-----Examples-----
Sample Input:
Penny Franklin
Marti Graham
Connie Froggatt
Joseph Ivers
Connie Froggatt
Penny Franklin
Connie Froggatt
Bruce Stanger
Connie Froggatt
Barbara Skinner
Barbara Skinner
***
Sample Output:
Connie Froggatt
user: Characters in Star Wars each speak a language, but they typically understand a lot more languages that they don’t or can’t speak. For example, Han Solo might speak in Galactic Basic and Chewbacca might respond in Shyriiwook; since they each understand the language spoken by the other, they can communicate just fine like this.

We’ll say two characters can converse if they can exchange messages in both directions. Even if they didn’t understand each other’s languages, two characters can still converse as long as there is a sequence of characters who could translate for them through a sequence of intermediate languages. For example, Jabba the Hutt and R2D2 might be able to converse with some help. Maybe when Jabba spoke in Huttese, Boba Fett could translate to Basic, which R2D2 understands. When R2D2 replies in Binary, maybe Luke could translate to Basic and then Bib Fortuna could translate back to Huttese for Jabba.

In Star Wars Episode IV, there’s a scene with a lot of different characters in a cantina, all speaking different languages. Some pairs of characters may not be able to converse (even if others in the cantina are willing to serve as translators). This can lead to all kinds of problems, fights, questions over who shot first, etc. You’re going to help by asking some of the patrons to leave. The cantina is a business, so you’d like to ask as few as possible to leave. You need to determine the size of the smallest set of characters $S$ such that if all the characters in $S$ leave, all pairs of remaining characters can converse.

For example, in the first sample input below, Chewbacca and Grakchawwaa can converse, but nobody else understands Shyriiwook, so they can’t converse with others in the bar. If they leave, everyone else can converse. In the second sample input, Fran and Ian can converse, as can Polly and Spencer, but no other pairs of characters can converse, so either everyone but Polly and Spencer must leave or everyone but Fran and Ian.

-----Input-----
Input starts with a positive integer, $1 \le N \le 100$, the number of characters in the cantina. This is followed by $N$ lines, each line describing a character. Each of these $N$ lines starts with the character’s name (which is distinct), then the language that character speaks, then a list of $0$ to $20$ additional languages the character understands but doesn’t speak. All characters understand the language they speak. All character and language names are sequences of $1$ to $15$ letters (a-z and A-Z), numbers, and hyphens. Character names and languages are separated by single spaces.

-----Output-----
Print a line of output giving the size of the smallest set of characters $S$ that should be asked to leave so that all remaining pairs of characters can converse.

-----Examples-----
Sample Input:
7
Jabba-the-Hutt Huttese
Bib-Fortuna Huttese Basic
Boba-Fett Basic Huttese
Chewbacca Shyriiwook Basic
Luke Basic Jawaese Binary
Grakchawwaa Shyriiwook Basic Jawaese
R2D2 Binary Basic
Sample Output:
2
user: As you didn’t show up to the yearly general meeting of the Nordic Club of Pin Collectors, you were unanimously elected to organize this years excursion to Pin City. You are free to choose from a number of weekends this autumn, and have to find a suitable hotel to stay at, preferably as cheap as possible. 

You have some constraints: The total cost of the trip must be within budget, of course. All participants must stay at the same hotel, to avoid last years catastrophe, where some members got lost in the city, never being seen again.

-----Input-----
The first line of input consists of four integers: $1 \leq N \leq 200$, the number of participants, $1 \leq B \leq 500000$, the budget, $1 \leq H \leq 18$, the number of hotels to consider, and $1 \leq W \leq 13$, the number of weeks you can choose between. Then follow two lines for each of the $H$ hotels. The first gives $1 \leq p \leq 10000$, the price for one person staying the weekend at the hotel. The second contains $W$ integers, $0 \leq a \leq 1000$, giving the number of available beds for each weekend at the hotel.

-----Output-----
Output the minimum cost of the stay for your group, or “stay home” if nothing can be found within the budget.

-----Examples-----
Sample Input:
3 1000 2 3
200
0 2 2
300
27 3 20
Sample Output:
900
user: The following are musical notes in “increasing order”:$A$, $A\sharp $, $B$, $C$, $C\sharp $, $D$, $D\sharp $, $E$, $F$, $F\sharp $, $G$, $G\sharp $

The difference between consecutive notes is a semitone, and the sequence wraps around so the note that is one semitone above $G\sharp $ is $A$. The difference between a tone is the same as two semitones. So the note that is one tone above $B$ is $C\sharp $. The note that is one tone above $G$ is $A$.

We do not worry about flats such as $C\flat $ nor do we worry about adding a $\sharp $ sign to $B$ and $E$ in this problem (they are aliases for notes that are already listed).

A major scale is defined by a note (such as $A$ or $C\sharp $) and all other notes following that one in an arithmetic progression:tone, tone, semitone, tone, tone, tone, semitone

The starting note appears in the name of the scale.

For example, the scale $A\sharp $-major consists of the following notes:$A\sharp $, $C$, $D$, $D\sharp $, $F$, $G$, $A$, $A\sharp $

(by convention, the first note is repeated at the end of the sequence).

Note that $A\sharp $-major is typically not considered a standard musical scale. It is identical in sound to $B\flat $, and proper notation of $A\sharp $-major would require the use of double-sharps. We ignore such issues in this problem and just use the $12$ notes given at the top of this problem.

Finally, in this problem a song is just a sequence of notes. Your job is to identify all major scales such that the song uses only notes in that scale.

-----Input-----
The first line of input is an integer $1\leq n \leq 100$ denoting the number of notes played in a song. The second line consists of a sequence of notes, separated by spaces.

-----Output-----
Output consists of a single line that lists all scales the song may be played in. Consecutive scales should be separated by a single space and the scales must appear in lexicographic order. If the song may not fit in any one of these scales, simply output a line containing the text none.

-----Examples-----
Sample Input:
10
C D F D C D F F F C 
Sample Output:
A# C D# F
user: Anders talks in the Swedish dialect of östgötska. Unfortunately, this makes it somewhat hard to get a programming job in the Swedish capital of Stockholm. The trendy Stockholm hipsters only accept applicants speaking the standard Swedish dialect, rikssvenska.

To increase his chances of passing interviews, he wishes to practice talking rikssvenska. To help him with this, he wants you to write a program that can determine whenever he accidentally reverts to speaking östgötska.

A simple way of determining if a sentence is written in östgötska is if at least $40\% $ of the words in the sentence contains the letter ä. For simplicity, this is encoded as the letter combination ae (meaning any appearance of the substring ae is to be regarded as an occurrence of the letter ä).

-----Input-----
The first and only line of input contains a sequence of space-separated words. Each word consists only of letters a-z. There are at most $100$ words, and each word contains at most $15$ letters a-z (meaning that the ae combination counts as two letters for this limit).

-----Output-----
Output “dae ae ju traeligt va” if the input sentence is in östgötska, otherwise output “haer talar vi rikssvenska”.

-----Examples-----
Sample Input:
dae ae ju traeligt va
Sample Output:
dae ae ju traeligt va
user: The big café chain Espresso Bucks is expanding to the country of Gridland. Since you are an expert on Gridland culture and geography, Espresso Bucks have hired you to decide where to put their coffee shops for maximum profit. Gridland consists of an $n$ by $m$ grid, where some cells are land, and some are water. At most one coffee shop can be built on each land cell. Nothing can be built on the water cells, but on the other hand, no one lives in the water. After a lot of long meetings with the Espresso Bucks people, you have come to the conclusion that there are only two constraints the placement of coffee shops has to satisfy: 
 - Each land cell must have a coffee shop directly on it, or adjacent to it.
 - No two coffee shops can be adjacent to each other.

Two cells are adjacent if one is immediately to the west, north, east, or south of the other. Find any placement of coffee shops that satisfies these constraints.

-----Input-----
The first line of input consists of two integers $n$ and $m$ ($1 \leq n,m \leq 100$). The following $n$ lines each contain a string of length $m$ consisting only of the characters ‘.’ (land) and ‘#’ (water). This is the map of gridland. It is guaranteed that the map contains at least one land cell.

-----Output-----
Output a copy of the map of gridland, where some of the land cells have been replaced with the letter ‘E’, meaning that a coffee shop was placed on the corresponding land cell. This placement should satisfy the constraints above. If there are many solutions, any one will be accepted.

-----Examples-----
Sample Input:
5 6
....#.
....#.
#.....
......
##...#
Sample Output:
E..E#.
..E.#E
#..E..
.E...E
##E.E#
user: You’ve been put in charge of an art exhibit from the famous minimalist sculptor J (even his name is minimalist!). J’s work involves the careful layout of vertically dispositioned orthogonal parallelpipeds in a set of tapering obelisks — in other words, he puts smaller boxes on top of larger boxes. His most recent triumph is called “2 by 3’s Decreasing,” in which he has various sets of six boxes arranged in two stacks of three boxes each. One such set is shown below:

J has sent you the art exhibit and it is your job to set up each of the six-box sets at various locations throughout the museum. But when the sculptures arrived at the museum, uncultured barbarians (i.e., delivery men) simply dropped each set of six boxes on the floor, not realizing the aesthetic appeal of their original layout. You need to reconstruct each set of two towers, but you have no idea which box goes on top of the other! All you know is the following: for each set of six, you have the heights of the two towers, and you know that in any tower the largest height box is always on the bottom and the smallest height box is on the top. Armed with this information, you hope to be able to figure out which boxes go together before tomorrow night’s grand opening gala.

-----Input-----
The input consists of eight positive integers. The first six represent the heights of the six boxes. These values will be given in no particular order and no two will be equal.

The last two values (which will never be the same) are the heights of the two towers.

All box heights will be $\leq 100$ and the sum of the box heights will equal the sum of the tower heights.

-----Output-----
Output the heights of the three boxes in the first tower (i.e., the tower specified by the first tower height in the input), then the heights of the three boxes in the second tower. Each set of boxes should be output in order of decreasing height. Each test case will have a unique answer.

-----Examples-----
Sample Input:
12 8 2 4 10 3 25 14
Sample Output:
12 10 3 8 4 2