meetforever/GRPO_CL huggingface dataset:
user: The Production Manager of a dance company has been tasked with determining the cost for the seasonal dance recital. Because of their exceptional skills, many dancers will perform in more than one routine, but this presents a problem; each dance routine incorporates a unique costume, so between routines, dancers must report backstage to a Wardrobe Specialist, who can change the dancer’s costume in time to begin their next scheduled routine.

A Wardrobe Specialist does a normal change on a dancer when the dancer performs in two routines that are not consecutive, but when a dancer is required to perform in two consecutive routines, a quick change is necessary. A Wardrobe Specialist charges a flat rate per recital that covers all normal changes, but charges an exorbitant amount for each quick change. The Production Manager is responsible for keeping the show under budget, and has hired you to write a program to report the minimum number of quick changes needed for a given recital, given that the order of the dance routines could be changed.

To describe the cast of dancers that are to perform during a recital, each dancer is assigned an identifying uppercase letter. (Fortunately, there are never more than 26 dancers, so characters from A to Z suffice.) To describe a full recital, a list of individual routines is given, with a string of characters defining which dancers appear in a routine. For example, consider the following recital description:

    ABC ABEF DEF ABCDE FGH

The above list describes a recital with 5 dance routines, including a total of 8 individual performers (dancers A through H). The first routine listed includes dancers {A, B, and C}. The second routine includes dancers {A, B, E, and F}. Notice that if these first two routines are performed in the above order, dancers A and B will require a quick change between the routines. In fact, if these five routines are scheduled in the order given above, a total of six quick changes are required. However, the schedule can be rearranged as follows:

    ABEF DEF ABC FGH ABCDE

In this case, only two quick changes are required (those for E and F between the first two dances).

-----Input-----
The first line contains a single integer $R$, with $2 \leq R \leq 10$, that indicates the number of routines in the recital. Following that will be $R$ additional lines, each describing the dancers for one routine in the form of a nonempty string of up to 26 non-repeating, lexicographically sorted uppercase alphabetic characters identifying the dancers who perform in that routine. Although a dancer’s letter will not appear more than once in a single routine, that dancer may appear in many different routines, and it may be that two or more routines have the identical set of dancers.

-----Output-----
Output a single integer designating the minimum number of quick changes required for the recital.

-----Examples-----
Sample Input 1:
5
ABC
ABEF
DEF
ABCDE
FGH
Sample Output 1:
2

Sample Input 2:
6
BDE
FGH
DEF
ABC
BDE
ABEF
Sample Output 2:
3
user: The hit new RPG mobile game Curveknights was recently released and Yraglac has been absolutely obsessed with it. Yraglac has been trying to farm materials for hours on end so he can promote his units but has suddenly realized that he has forgotten about an integral system that might speed this up: the crafting system!

Some higher tier materials can be crafted by combining lower tier ones. Yraglac has a list of materials that he needs, but would also like to know how many lower tier materials he would need if he wanted to take advantage of the crafting recipes. As it turns out, some of those lower tier materials might also be craftable with even lower tier materials and so on. Yraglac would like to know the numbers for each of these.

For example, suppose Yraglac needed $3$ Sugar Boxes. Crafting one of these requires $2$ Sugar Packs, $1$ Iron Chunk, and $1$ Magnesium Ore. You can also craft $1$ Iron Chunk using $3$ Iron Ores. Then Yraglac’s total list of materials would be $3$ Sugar Boxes, $6$ Sugar Packs, $3$ Iron Chunks, $3$ Magnesium Ore, and $9$ Iron Ores.

Given how many of each material Yraglac wants, can you find out how many of each Yraglac would need to craft them?

-----Inputs-----
The first line contains two space separated $2 \leq N \leq 50$, the number of materials and $N-1 \leq M \leq \frac{N(N-1)}{2}$, the number of crafting dependencies.

The second line contains $N$ space seperated integers describing the amount of each material Yraglac wants. The $a_ i$-th integer specifies the amount of the $i$-th material Yraglac wants where $0 \leq a_ i \leq 3$.

Each of the following $M$ lines contains three space seperated integers: $0 \leq u, v < N$, and $1 \leq w \leq 3$ indicating there is a recipe that takes $w$ quantities of material $u$ to produce one material $v$. It is guaranteed that each $u, v$ pair will be unique, and that there will never be any cycles in the crafting recipes.

-----Outputs-----
On a single line output the amount of materials Yraglac needs.

-----Examples-----
Sample Input 1:
5 4
0 0 0 0 3
0 1 3
1 4 1
2 4 1
3 4 2
Sample Output 1:
9 3 3 6 3

Sample Input 2:
6 5
0 0 0 0 0 3
0 3 3
1 4 3
2 5 1
3 5 1
4 5 1
Sample Output 2:
9 9 3 3 3 3
user: Emma and Marcos are two friends who love horror films. This year, and possibly the years hereafter, they want to watch as many films together as possible. Unfortunately, they do not exactly have the same taste in films. So, inevitably, every now and then either Emma or Marcos has to watch a film she or he dislikes. When neither of them likes a film, they will not watch it. To make things fair they thought of the following rule: They can not watch two films in a row which are disliked by the same person. In other words, if one of them does not like the current film, then they are reassured they will like the next one. They open the TV guide and mark their preferred films. They only receive one channel which shows one film per day. Luckily, the TV guide has already been determined for the next $1$ million days.

Can you determine the maximal number of films they can watch in a fair way?

-----Input-----
The input consists of two lines, one for each person. Each of these lines is of the following form:
 - One integer $0 \leq k \leq 1000000$ for the number of films this person likes;
 - followed by $k$ integers indicating all days (numbered by $0, \dots , 999999$) with a film this person likes.

-----Output-----
Output a single line containing a single integer, the maximal number of films they can watch together in a fair way.

-----Examples-----
Sample Input 1:
1 40
2 37 42
Sample Output 1:
3

Sample Input 2:
1 1
3 1 3 2
Sample Output 2:
2
user: It’s the slow crawl of rush hour. At any point of time, each vehicle is either stopped or is moving at the extremely slow speed of $1$ meter per second. Lately, vehicles come equipped with a simple “black box” that record all changes in a vehicle’s speed. In this problem, speeds change instantaneously. 

The road is modelled as the real line (units in meters). So a car is identified with its position on the line. Also, cars are $4.4$ meters long.

Given initial positions of two cars that are driving along the real line in the positive direction and a transcript of their speed changes, did these cars ever collide? While such a collision would be very slow speed (a “bumper tap”), any collision could result in erroneous readings from the black box in the future so the portions of the transcripts after a collision might not make sense.

-----Input-----
There is only one test case. The first line contains two integers $0 \leq X_1, X_2 \leq 10^6$ indicating the initial positions of the rears of the two vehicles in meters. You are guaranteed either $X_1 + 5 \leq X_2$ or $X_2 + 5 \leq X_1$. Initially (at time $0$), the two cars are stopped.

The second line begins with a number $0 \leq N_1 \leq 10^5$ indicating the number of times the speed of the first car changed. The rest of the line contains $N_1$ integers $0 < T_1 < T_2 < \ldots < T_{n_1} \leq 10^6$ indicating the times (in seconds) the first vehicle changed speeds. So at time $T_1$ it begins driving at $1$ m/s, at time $T_2$ it stops, at time $T_3$ it begins driving at $1$ m/s, and so on.

The last line begins with a number $0 \leq N_2 \leq 10^5$ and is followed by $N_2$ integers $0 < T’_1 < T’_2 < \ldots < T’_{n_2} \leq 10^6$ that describe the times the second vehicle starts and stops.

-----Output-----
If the vehicles collide, output the message bumper tap at time $S$ on a single line where $S$ is the number of seconds from time $0$ that the vehicles first collide, rounded up to the nearest second. If the vehicles do not collide, output the message safe and sound on a single line.

-----Examples-----
Sample Input 1:
0 5
3 1 4 5
3 1 4 6
Sample Output 1:
bumper tap at time 6

Sample Input 2:
10 0
2 1 2
1 1
Sample Output 2:
bumper tap at time 8
user: The technology behind the fridge has changed little over the years. Even so, many of the original owners of the Fred W. Wolf domestic refrigerator of 1913 would be amazed by the size and features of the modern appliances. However, since the 1960s one thing has been common for all fridge owners around the world: fridge magnets.

An effective, albeit lazy, way to keep a small child entertained is to supply them with a set of magnetic numbers and a large magnetic surface, such as said fridge, to provide the playing field upon which to apply these digits.

Far from a time-wasting exercise, this provides valuable training in the mathematical field of counting: moving the digits around to form “1”, “2”, and so on up to such heights as “10”, “11”, “12”, and even beyond.

The possibilities are endless! ...Or at least, they would be, if the supply of digits was not limited. Given the full list of what numbers we are in possession of, what is the smallest positive number that cannot be made using each of digits at most once?

-----Input-----
 - One string of at most $1000$ digits, containing the available digits in no particular order.

-----Output-----
 - One line containing one positive integer: the smallest natural number that it is not possible to assemble from the supplied digits.

-----Examples-----
Sample Input 1:
7129045863
Sample Output 1:
11

Sample Input 2:
55
Sample Output 2:
1
user: Years have passed since Bash dropped out of university to become a Pokenom trainer. The adventure was full of difficulties and hardship, but Bash overcame all obstacles and became the best Pokenom trainer, like no one ever was!

Today Bash is celebrating his $13$th anniversary of dropping out of university and becoming a Pokenom trainer.

For the celebration party, Bash decided to prepare cakes for his $N$ Pokenoms. Bash’s Pokenoms are numbered from $1$ to $N$, inclusive. There are $N$ different cakes. The $i$-th Pokenom wants to eat the $i$-th cake.

The cakes are made using some ingredients. Each ingredient is uniquely marked by a prime number between $1$ and $N$, inclusive.

The recipe of the $X$-th cake contains $k$ grams of ingredient $p$ iff $p^{k}$ divides $X$, and $p^{k+1}$ does not. In other words, let the prime factorization of $X$ be $X = p_{1}^{k_{1}} \times p_{2}^{k_{2}} \times \cdots \times p_{m}^{k_{m}}$, the recipe of the $X$-th cake contains $k_{1}$ grams of ingredient $p_{1}$, $k_{2}$ grams of ingredient $p_{2}$, …, $k_{m}$ grams of ingredient $p_{m}$.

Bash goes to a supermarket to buy ingredients. There, Bash realizes that the ingredients are very expensive. If Bash buys $k$ grams of ingredient $q$, Bash’s happiness decreases by $k^{2} \times C_{q}$.

If the $i$-th Pokenom sees that Bash buys enough ingredient for the $i$-th cake, the Pokenom’s happiness increases by $V_{i}$.

Please help Bash buy ingredients so that the total happiness of Bash and his $N$ Pokenoms is maximized!

Note that the $i$-th Pokenom just needs to see that Bash has enough ingredients for the $i$-th cake. So even if the amount of ingredients Bash buys is enough to make either the $x$-th cake or the $y$-th cake, but not both, the total happiness still increases by $V_{x} + V_{y}$.

For example, consider $N = 100$ and Bash buys $2$ grams of ingredient $2$, $1$ gram of ingredient $3$ and $1$ gram of ingredient $5$: Bash’s happiness decreases by $4 \times C_{2} + 1 \times C_{3} + 1 \times C_{5}$. Bash has enough ingredients for cakes $1..6, 10, 12, 15, 20, 30,$ and $60$. So the happiness of the Pokenoms increases by\[ V_{1} + V_{2} + \cdots + V_{6} + V_{10} + V_{12} + V_{15} + V_{20} + V_{30} + V_{60}. \]

-----Input-----
 - The first line contains one integer $N$ $(1 \leq N \leq 10^{4})$.
 - The second line contains $N$ integers $V_{1}, V_{2}, \ldots V_{N}$$(0 \leq V_{i} \leq 10^{4})$.
 - The third line contains $N$ integers $C_{1}, C_{2}, \ldots , C_{N}$$(0 \leq C_{i} \leq 10^{4})$. It is guaranteed that $C_{i} = 0$ if $i$ is not a prime.

-----Output-----
Print a single integer $B$ — the maximum total happiness of Bash and his Pokenoms.

-----Examples-----
Sample Input 1:
10
1 2 3 40 5 6 7 8 9 10
0 2 3 0 5 0 7 0 0 0
Sample Output 1:
51

Sample Input 2:
1
2207
0
Sample Output 2:
2207
user: Little Marin spent all his day generating test data for COCI. He simply couldn’t make it work, so he had a nervous breakdown and can’t even see clearly anymore. Every time he blinks while reading, the letters in a word get mixed up so that the letters from the second half of the word (the shorter half, if the length is an odd number) “jump in” between the letters from the first half in the following way:
 - the last letter “jumps in” between the first and the second letter
 - the penultimate letter “jumps in” between the second and the third letter
 - the $k$-th letter from the end “jumps in” between the $k$-th and the $(k+1)$-th letter from the beginning

For example, the word “abcdef” would become “afbecd” after blinking.

If Marin blinks again, the same thing happens. After two blinks, the word “abcdef” becomes “adfcbe”.

Marin has decided to write a program to help him determine what’s exactly written on the screen. Unfortunately, after a day’s work, he’s simply too tired and he needs your help. You are given $X$, the number of blinks, and the word Marin sees on the screen. Write a program to solve the mystery for Marin and determine what was actually the word before he blinked $X$ times.

-----Input-----
The first line of input contains a positive integer $X$ ($1 \leq X \leq 1000000000$), the number of times Marin blinked. The second line of input contains the word from the screen, its length being from the interval $[3,1000]$. The word will consist only from small letters of English alphabet.

-----Output-----
The first and only line of output must contain the original word, before Marin blinked $X$ times.

-----Examples-----
Sample Input 1:
4
acefdb
Sample Output 1:
abcdef

Sample Input 2:
1000
aaaaaa
Sample Output 2:
aaaaaa
user: Using roman numerals the numbers $1, 2, 3, 4, 5, 6, 7, 8, 9$ are written as ‘I’, ‘II’, ‘III’, ‘IV’, ‘V’, ‘VI’, ‘VII’, ‘VIII’, ‘IX’. The numbers $10, 20, 30, 40, 50, 60, 70, 80, 90$ are written as ‘X’, ‘XX’, ‘XXX’, ‘XL’, ‘L’, ‘LX’, ‘LXX’, ‘LXXX’, ‘XC’. Any number smaller than $100$ can be written by converting tens and ones separately and concatenating the results. So, for example, the number $48$ would be written as XLVIII, XL for $40$ and VIII for $8$. Given a number written in roman numerals, rearrange its characters so that you create the smallest possible number, written in roman numerals.

-----Input-----
The first and only line of input contains one integer $B$ ($1 \leq B < 100 $), written using roman numerals.

-----Output-----
The first and only line of output should contain a rearrangement of input characters so that it represents the smallest possible number, written in roman numerals.

-----Examples-----
Sample Input 1:
VII
Sample Output 1:
VII

Sample Input 2:
VI
Sample Output 2:
IV
user: Your family has been blessed with chocolate! A huge piece of chocolate has been given to you and your sister to share. However, as you gobbled up the large majority last time, your parents have invented a game to keep things fair (and to keep you occupied while they hide all the other chocolate). To keep things interesting, they have given you a rectangular piece of chocolate, which consists of little squares of both dark chocolate and white chocolate in a chessboard pattern. While you and your sister both love dark chocolate, you hate white chocolate! So, both you and your sister want as much dark chocolate as possible, while simultaneously obtaining as little white chocolate as possible. Every dark piece of chocolate you obtain gives you $1$ meaningless unit of happiness, while a white piece lowers your happiness by $1$ meaningless unit (and the same holds for your sister). Now, while you love your sister very much, there is always heavy competition between siblings, so your goal is to maximize the difference of your obtained happiness and her obtained happiness (while she tries to do the opposite, obviously). 

The game works as follows. Your parents place a $p \times q$-rectangle of the aforementioned mixed chocolate on a table. You are situated on the west side of the table and your sister on the south side. The side of length $p$ is parallel to the north-south line, while the side of length $q$ is parallel to the east-west line. Furthermore, the north-west square is made of dark chocolate. Then, starting with yourself, you take turns breaking off blocks of chocolate (which you can keep). You can break off any positive number of entire columns from the west side, while your sister breaks off any positive number of entire rows from the south side. You repeat this process until no more chocolate is left. Your sister is very smart and will always play the game perfectly.

A game might proceed like this, for example: you and your sister start with a $3\times 4$-rectangle. You decide to break off $2$ columns, obtaining $3$ dark and $3$ white chocolate squares, netting a happiness of zero. Your sister then breaks off $1$ row, obtaining $1$ dark and $1$ white squares as well, so no happiness for her either. You then take a single column, which nets you nothing again, after which your sister decides to break off one row, which nets her $1$ happiness! You then take the last piece, which makes you lose a unit of happiness, so your total score is $-1 - 1 = -2$. See the figure. (Note: the strategies used here might not be optimal.)

-----Input-----
Given are two positive integers $p$ and $q$, both at most $100$, the height and width of the chocolate rectangle.

-----Output-----
Output the largest possible difference (in your favour) between your net happiness and your sister’s net happiness.

-----Examples-----
Sample Input 1:
1 2
Sample Output 1:
2

Sample Input 2:
2 2
Sample Output 2:
0
user: The annual student team competition in table tennis of students enrolled in University of Zagreb takes place next Saturday! Each team consists of $K$ students. The excited students, $N$ of them, are waiting in queue to register.

Krešo works at the registration desk. He doesn’t really feel like doing his job so he decided not to allow students to choose a team. He decided that the first team will consist of the first $K$ students standing in queue, the second team the following $K$ students, the third one the following $K$ students and so on…($N$ will be divisible by $K$ so nobody is left hanging.)

Ante has estimated the skill of each player with an integer. He would like to have the $K$ strongest players in the first team, the following $K$ strongest in the second team and so on…

Krešo has just taken a break and Ante decided to shift the students standing in queue so that he achieves his goal. The way he shifts them is that he tells a student to step out of the queue and go back in queue after another student or to go to the front of the queue. It takes him one minute to do this.

It’s possible that Krešo is going to return from his break any moment so Ante needs to achieve his goal as soon as possible. Help Ante determine the minimal number of minutes necessary for him to achieve his goal.

-----Input-----
The first line of input contains the integers $N$ and $K$ ($1 \leq K \leq N \leq 100000)$. The integer $N$ is going to divisible by $K$.

The second line contains $N$ space separated integers $v_ i$ ($1 \leq v_ i \leq 10^9$), the $i$-th number denotes the skill of the $i$-th player standing in queue – lower value means higher skill.

All contestants are going to have distinct levels of skill.

-----Output-----
The first and only line of output must contain the minimal required number of minutes.

-----Examples-----
Sample Input 1:
4 1
9 12 5 13
Sample Output 1:
1

Sample Input 2:
6 2
16 2 1 7 5 10
Sample Output 2:
1
user: Friday is the highlight of Børge and Åse’s life. They can meet up with their buddies in the ITU Friday bar and discuss anything they want: the weather, sports, favourite editors, politics, religion, and gossip about celebrities. Life can be good.

Unfortunately, they don’t know which day of the week it is! They’ve woken up in a strange apartment, phones missing, and with little memory of the recent past. Which day is it? Which year is it even?

After some searching, they establish today’s date, because the calendar on the wall displays it. Also, Åse has found the remains of an old newspaper from 1 January in her handbag, which has that weekday printed on the front page.

Help Børge and Åse figure out if today is Friday.

-----Input-----
On the first line, today’s date. The date consists of two parts, separated by space. The first part is in an integer (the day of the month) $d$, with $1\leq d\leq 31$. The second part is the name of the month, abbreviated as JAN, FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT, NOV, or DEC.

On the second line, the name of the day on 1 January of the current year, abbreviated as MON, TUE, WED, THU, FRI, SAT, SUN.

-----Output-----
Output a single line: The four letters TGIF, abbreviating “Thank God it’s Friday” if today is certainly Friday. The two words not sure if today might be Friday, depending on if this year has a 29th of February. The emoticon :( if today is certainly not Friday.

-----Examples-----
Sample Input 1:
10 OCT
MON
Sample Output 1:
:(

Sample Input 2:
2 JAN
THU
Sample Output 2:
TGIF
user: Lea runs into a lot of words in her life. A lot of them she finds unpleasant. To compensate for that she started making up pleasant words. Lea makes up new words by writing a nice looking string of characters on a piece of paper. She than erases a few of the most nasty looking characters and replaces them with underscores ‘_’. After that she tries to replace the underscores with more acceptable characters trying to form a pleasant word.

Lea considers words pleasant if they do not contain $3$ sequential vowels, $3$ sequential consonants and contain at least one letter ‘L’.

In Croatian, the vowels are the letters A, E, I, O, and U only. All other lettters are consonants.

-----Input-----
The first and only line of input contains a string of characters, at most $100$. The string contains only of uppercase English letters and ‘_’ characters. There will be at most $10$ ‘_’ characters.

-----Output-----
The first and only line of output should cotain a single integer – the total number of pleasant words that can be formed by substituting underscores with uppercase letters of the English alphabet.

-----Examples-----
Sample Input 1:
L_V
Sample Output 1:
5

Sample Input 2:
V__K
Sample Output 2:
10