meetforever/GRPO_CL huggingface dataset:
user: There’s a new art installation in town, and it inspires you…to play a childish game. The art installation consists of a floor with an $n\! \times \! n$ matrix of square tiles. Each tile holds a single number from $1$ to $k$. You want to play hopscotch on it. You want to start on some tile numbered $1$, then hop to some tile numbered $2$, then $3$, and so on, until you reach some tile numbered $k$. You are a good hopper, so you can hop any required distance. You visit exactly one tile of each number from $1$ to $k$.

What’s the shortest possible total distance over a complete game of Hopscotch? Use the Manhattan distance: the distance between the tile at $(x_1,y_1)$ and the tile at $(x_2,y_2)$ is $|x_1-x_2| + |y_1-y_2|$.

-----Input-----
The first line of input contains two space-separated integers $n$ ($1 \le n \le 50$) and $k$ ($1 \le k \le n^2$), where the art installation consists of an $n\! \times \! n$ matrix with tiles having numbers from $1$ to $k$.

Each of the next $n$ lines contains $n$ space-separated integers $x$ ($1 \le x \le k$). This is the art installation.

-----Output-----
Output a single integer, which is the total length of the shortest path starting from some $1$ tile and ending at some $k$ tile, or $-1$ if it isn’t possible.

-----Examples-----
Sample Input:
10 5
5 1 3 4 2 4 2 1 2 1
4 5 3 4 1 5 3 1 1 4
4 2 4 1 5 4 5 2 4 1
5 2 1 5 5 3 5 2 3 2
5 5 2 3 2 3 1 5 5 5
3 4 2 4 2 2 4 4 2 3
1 5 1 1 2 5 4 1 5 3
2 2 4 1 2 5 1 4 3 5
5 3 2 1 4 3 5 2 3 1
3 4 2 5 2 5 3 4 4 2
Sample Output:
5
user: “A watched pot never boils”, as the saying goes. Chef Edward has been cooking for ages, and empirically the saying seems to be true in his kitchen – he has yet to see a pot actually start boiling. His wife Gunilla is a bit suspicious of Edward’s claim though. She knows how he often loses focus after a little while, and thinks that it is very likely Edward gets tired of watching after about the same period of time starting when he puts it on the stove.

Being scientifically minded, Gunilla quickly designed an experiment which could help Edward gain more insight into the boiling of pots. Every time during the last week when Edward boiled a pot of water, he wrote down the intervals of time when he was not watching the pot. Now, he has a large log of these intervals, and wonders whether Gunilla is right (i.e. it may be the case Edward just happened to watch away every time the pot started boiling), or if his hypothesis is correct.

Given this data, is it possible that the pot actually starts boiling after the same amount of time, every time?

-----Input-----
The first line of the input contains an integer $1 \le N \le 1000$, the number of times Edward boiled water in the last week. Then, $N$ descriptions of a boiling follow. Each description contains two numbers $0 \le a \le b \le 1000$. This means that Edward looked away during seconds $[a, b]$ (i.e. from the start of second $a$, to the end of second $b$), and that Edward first saw the pot boiling once he looked back.

-----Output-----
If it is impossible that all the pots actually started boiling at the same point in time, output edward is right. Otherwise, output gunilla has a point.

-----Examples-----
Sample Input:
2
1 7
5 5
Sample Output:
gunilla has a point
user: The other day Bjarki was playing one of his many video games, $\sim $s. In $\sim $s you build a house, start a family, and slowly, but surely, gain riches and fame. One particular day in the game there was a $30$ year anniversary party and Bjarki’s characters invited all their friends.

During the party people started chatting. Due to the way $\sim $s is programmed once people start chatting they can’t stop. So as time goes on people get added to conversations but they never leave them. Steadily, groups of people chatting start to form and a person from one group can’t join another without the groups merging.

Bjarki is starting to get bored watching this process so he starts counting the size of the groups. But every person is so small on the screen it’s actually easier for him to notice the speechbubble form, which indicate a merger of groups. Bjarki gives you two different types of queries. One indicates a speechbubble and the other means Bjarki wants to know the size of a particular group chat.

-----Input-----
The first line of the input contains two integers $1 \leq n, q \leq 10^6$, $n$ denoting the total amount of guests at the party and $q$ denoting the amount of queries. Then $q$ lines follow, the $i$-th of which contains either contains ‘t’ and two integers $1 \leq a, b \leq n$ or ‘s’ and one integer $1 \leq a \leq n$. If the line begins with ‘t’ it indicates that the groups guest $a$ and guest $b$ belong to merge and if the line begins with ‘s’ you should print the size of the group guest $a$ belongs to.

-----Output-----
The output should contain one line containing one integer for each query of the ‘s’ type indicating the size of the specified group.

-----Examples-----
Sample Input:
10 11
t 1 10
t 1 2
t 1 3
s 1
s 2
s 3
s 4
t 5 6
s 5
s 6
s 10
Sample Output:
4
4
4
1
2
2
4
user: Over the years, Grandpa Bernie has traveled all over the world. He doesn’t travel that much anymore, but he loves to tell his grandchildren stories from all these trips. He’ll tell them the story from when he went to Israel for the first time, or when he went to Greece for the third time.

His memory works in a funny way. He can easily remember his $k$:th trip to a particular country, but he’ll have a hard time remembering in which year he went on that trip. Given a list of all the trips Grandpa Bernie went on, can you answer a number of queries asking in which year he went on his $k$:th trip to a particular country?

-----Input-----
The input consists of:
 - one line with one integer $n$ ($1 \leq n \leq 10^5$), the number of trips Grandpa Bernie went on;
 - $n$ lines each containing the name $s$ ($1 \leq |s| \leq 20$) of a country and an integer $y$ ($1 \leq y \leq 10^6$) representing a trip to country $s$ that Grandpa Bernie went on in year $y$;
 - one line with one integer $q$ ($1 \leq q \leq 10^5$), the number of queries;
 - $q$ lines each containing the name $s$ of a country and an integer $k$ representing a query for the $k$:th time Grandpa Bernie went to country $s$.

Each country name only consists of letters from the English alphabet. It is also guaranteed that, for each query asking for the $k$:th trip to country $s$, $k$ is at least $1$ and no greater than the number of times Grandpa Bernie went to country $s$. In particular, it is guaranteed that Grandpa Bernie has visited country $s$ at least once.

-----Output-----
For each query for the $k$:th trip Grandpa Bernie went to a country $s$, output a single line containing the year in which Grandpa Bernie went on that trip.

-----Examples-----
Sample Input:
4
Iceland 2016
Sweden 2015
Iceland 1982
Norway 1999
3
Sweden 1
Iceland 1
Iceland 2
Sample Output:
2015
1982
2016
user: Leo has started a job in a travel agency. His first task is to organize a summer trip to an exotic overseas city. During the summer season, events of various types take place in the city: sports matches, concerts, beach parties, and many others. At any given time, there is exactly one event taking place. Events of any particular type may take place more than once during the season. The itinerary of events that Leo offers to his clients cannot be chosen arbitrarily; the company requires them to form a so-called “good itinerary.” A good itinerary is a consecutive sequence of at least two events in the summer season, where the first and last events are of different types, and they are both unique among all event types during the sequence. For example, if the first event in a good itinerary is a beach party, none of the other events during the itinerary can also be a beach party. There are no other restrictions on the event types in the sequence of a good itinerary.

Before he starts organizing the trip, Leo wants to know the total number of good itineraries that are possible given a calendar of events that will take place over the summer season.

-----Input-----
The input consists of one line with a string describing the sequence of event types in the summer season. All characters are lowercase English letters (’a’ – ’z’), with different letters represent different types of events. Character $i$ of the string encodes the $i$th event of the summer. There are no blanks or spaces in the string.

The length of the input string is at least $2$ and at most $100000$ characters.

-----Output-----
Print the number of good itineraries that exist for the given summer season.

-----Examples-----
Sample Input:
abbcccddddeeeee
Sample Output:
10
user: Engineers have taken over the university’s English department! As part of their plan to dominate the university, they have employed you to write their nefarious software. Their goal is to eliminate all duplicated words from all texts in the English department, because, as they say, “duplicated words are duplicated work” and “duplicated work wastes money.” Actually, what they would really say is “duplicated words are . work” and “. . wastes money”. This is what your program should do – remove all duplicate words and replace them with a period.

-----Input-----
Input is a textbook with at most $2000$ lines. Each line contains up to $100$ characters. Punctuation does not appear (it has already been removed by another programmer); words are made up of up to $20$ lower and uppercase characters (a–z). There are at most $20000$ total words in the input. Each pair of adjacent words is separated by a single space. Case does not matter when comparing words for duplicates (i.e. ‘Book’ and ‘book’ and ‘bOoK’ should be considered the same word). Input ends at end of file.

-----Output-----
Print each word the first time it appears, but thereafter if that word appears again print a period.

-----Examples-----
Sample Input:
Engineering will save the world from inefficiency
Inefficiency is a blight on the world and its
humanity
Sample Output:
Engineering will save the world from inefficiency
. is a blight on . . and its
humanity
user: It’s time for the annual 3-SAT competition, where the contestants compete to answer as many instances of 3-SAT as possible within the time limit. 3-SAT is a classic NP-complete problem, where you are given a boolean formula in conjunctive normal form, in which we have a set of clauses each consisting of exactly three literals. Each literal refer either positively or negatively to a variable, which can be assigned a value of either True or False. The question is whether there exists an assignment to the variables such that every clause evaluates to True. No clause will contain duplicates of a literal (however it is possible that a clause contain both $\neg x_ i$ and $x_ i$). An example of a 3-SAT instance is shown below (from sample input 1):\[ (\neg x_1 \vee x_2 \vee x_3) \wedge (\neg x_1 \vee \neg x_2 \vee x_3) \wedge (x_1 \vee \neg x_2 \vee x_3) \wedge (x_1 \vee \neg x_2 \vee \neg x_3) \wedge (x_1 \vee x_2 \vee \neg x_3) \]Øyvind is a judge in the competition, responsible for verifying the quality of problem instances crafted by the other judges before the contest starts. Øyvind hates 3-SAT instances with less than eight clauses – as these are always satisfiable they provide no real challenge for the contestants. Therefore, he will deem such problem instances to be unsatisfactory. Whenever Øyvind encounters an instance with eight or more clauses he knows that it is a real challenge to figure out whether this instance is satisfiable or not – and therefore he will judge these problem instances to be satisfactory. Given an instance of 3-SAT, can you help find Øyvind’s judgement? 

-----Input-----
The input is a single instance of the 3-SAT problem. The first line is two space-separated integers: $m$ ($1 \leq m \leq 20$), the number of clauses and $n$ ($3 \leq n \leq 20$), the number of variables. Then $m$ clauses follow, one clause per line. Each clause consists of 3 distinct space-separated integers in the range $[-n, n] \setminus \{ 0\} $. For each clause, the three values correspond to the three literals in the clause. If the literal is negative, that means that the clause is satisfied if the corresponding variable is set to False, and if it is positive the clause is satisfied if the variable is set to True.

-----Output-----
Print “satisfactory” on a single line if Øyvind finds the 3-SAT instance to be satisfactory, and “unsatisfactory” otherwise.

-----Examples-----
Sample Input:
5 3
-1 2 3
-1 -2 3
1 -2 3
1 -2 -3
1 2 -3
Sample Output:
unsatisfactory
user: Black Friday is the Friday following Thanksgiving Day in the United States (the fourth Thursday of November). Since the early 2000s, it has been regarded as the beginning of the Christmas shopping season in the US, and most major retailers open very early and offer promotional sales. (Source: Wikipedia)

You work in the IT support division of an electronics store. This year, in an attempt to prevent overcrowding, the management has decided to limit the number of people entering the store. They divide the people at the entrance into groups of size $n$ and process them as follows: all $n$ participants roll a die, and report the outcomes $a_1, a_2, \ldots , a_ n$. To prevent cheating, instead of selecting the one with the highest outcome, the rule is to select the participant with the highest unique outcome. Everybody not selected has to move to the back of the queue. If there is no winner, the experiment is repeated.

For example, if there are three players and the outcomes are 6, 6 and 5, then the third player wins, because the first and second player lose even though their outcomes are higher, since they both have the same outcome. If instead the third player also rolls 6, then nobody wins.

They asked you to write a program for selecting the winner.

-----Input-----
The first line of the input contains one integer $n$, $1 \leq n \leq 100$, the group size. The second line contains $n$ integers $a_1, a_2, \ldots , a_ n$ ($1 \leq a_ i \leq 6$ for all $1 \leq i \leq n$): the outcome of each participant’s die roll.

-----Output-----
Output the index of the participant that has the highest unique outcome, or “none” (without the quotes) if nobody has a unique outcome.

-----Examples-----
Sample Input:
8
1 1 1 5 3 4 6 6
Sample Output:
4
user: After an unsuccessful attempt at claiming power peacefully, Borko has decided to tear down Mirko’s village hall, which was built for him out of cardboard by his loyal servants.

For this he will use Mirko’s microprocessor (which was stolen from him by Borko’s friend Zvonko), a bucket of water and a bag of sodium. He will enter the time of the “explosion” into the microprocessor, and it will drop the sodium in the water after the time is up.

Borko knows the current time and when he wants the explosion. He is not very fond of arithmetic and Zvonko is currently playing with marbles in his back yard so he can’t help him.

Write a program that calculates the time to the explosion (this is the time Borko will enter into the microprocessor). The time Borko wants is at least one second and at most 24 hours.

-----Input-----
The first line of input contains the current time in hh:mm:ss format (hours, minutes, seconds). The hours will be between $0$ and $23$ (inclusive) and the minutes and seconds between $0$ and $59$. The second line contains the time of the explosion in the same format.

-----Output-----
Output the desired time on a single line, in the same format as the times in the input.

-----Examples-----
Sample Input:
20:00:00
04:00:00
Sample Output:
08:00:00
user: Your friend Nick needs your help with a hard problem that he came across in real life. Nick has a loo roll of length $\ell $ centimetres in his bathroom. Every time he visits the toilet, he uses exactly $n$ centimetres of loo roll. When the roll runs out, Nick always goes to the store and buys a new one of length $\ell $ directly afterwards. However, sometimes the roll runs out even though Nick still needs a non-zero amount of paper. Let us call such an event a crisis. 

Nick has a clever way of preventing crises from happening: he uses a backup roll. The backup roll is another roll of length $\ell $ that is hidden somewhere in the bathroom, and when the regular roll runs out even though Nick still needs more paper, he will take that amount from the backup roll. Then he will replace the regular roll directly after the visit.

As you can imagine, this makes crises much less frequent. But still, the backup roll will also slowly run out, and eventually a crisis might still happen. So to generalize this, Nick wants to use several layers of backup rolls. First he will take paper from roll number $1$ (the regular roll), if it runs out he will take from roll number $2$, then if roll $2$ runs out from roll number $3$, and so on all the way up to roll number $k$. After each visit, all the rolls that have run out will be replaced. Nick managed to prove that if he picks a large enough number $k$, he can actually make it so that crises never happen! Your task is to find the smallest such number $k$.

-----Input-----
The input consists of a single line containing the two integers $\ell $ and $n$ ($1 \leq n \leq \ell \leq 10^{10}$).

-----Output-----
Output the smallest integer $k$ such that crises will never happen when using $k$ layers of rolls (including the regular roll).

-----Examples-----
Sample Input:
31 6
Sample Output:
4
user: Euler’s number (you may know it better as just $e$) has a special place in mathematics. You may have encountered $e$ in calculus or economics (for computing compound interest), or perhaps as the base of the natural logarithm, $\ln {x}$, on your calculator.

While $e$ can be calculated as a limit, there is a good approximation that can be made using discrete mathematics. The formula for $e$ is:\begin{align*} e & = \displaystyle \sum _{i=0}^n\dfrac {1}{i!}\\ & = \dfrac {1}{0!} +\dfrac {1}{1!} +\dfrac {1}{2!}+\dfrac {1}{3!}+\dfrac {1}{4!} + \cdots \\ \end{align*}

Note that $0! = 1$. Now as $n$ approaches $\infty $, the series converges to $e$. When $n$ is any positive constant, the formula serves as an approximation of the actual value of $e$. (For example, at $n=10$ the approximation is already accurate to $7$ decimals.)

You will be given a single input, a value of $n$, and your job is to compute the approximation of $e$ for that value of $n$.

-----Input-----
A single integer $n$, ranging from $0$ to $10000$.

-----Output-----
A single real number – the approximation of $e$ computed by the formula with the given $n$. All output must be accurate to an absolute or relative error of at most $10^{-12}$.

-----Examples-----
Sample Input:
3
Sample Output:
2.6666666666666665
user: Paul Eigon recently got a new job at a famous company in town. They have all sorts of cool stuff at the office. Video games, a swimming pool, a sauna, and even a ping-pong table! Paul really loves his enjoyable new workplace.

Mr. Eigon plays a lot of ping-pong at work. While he is playing, he enjoys having a nice conversation with his opponent. Discussions are jolly fun to have, but they can also be a bit distracting, enough for Paul to sometimes completely forget whose turn it is to serve the ball the upcoming round!

Paul’s ping-pong games are played with simple rules. The game is played by two players. The game starts with one of the players serving the ball, and that player does so during the $N$ first rounds. After that, the other player serves the ball for $N$ rounds, and so on. Each round is won by exactly one of the players and a player gets one point for each won round (there can be no draws). When one of the players has reached a certain number of points, that player wins the game.

Paul is in desperate need of a new way to figure out which player should serve the ball the upcoming round, and he wants you to help him. You should write a program that given $N$ and the current score of the game prints out whose turn it is to serve the ball the upcoming round. His plan is to run your program on his secret high technology pocket computer, in order to impress his opponent. And by the way, Paul always serves the first ball (if that makes it easier for you).

-----Input-----
Input consists of three integers $N$, $P$ and $Q$ on a single line. $1 \leq N \leq 10^9$ denotes the number of serves a player will perform in a row before it is the other player’s turn to serve the ball. $0 \leq P \leq 10^9$ denotes Paul’s current score in the ongoing ping-pong game, and $0 \leq Q \leq 10^9$ denotes his opponent’s score.

-----Output-----
Output should consists of a single word on a single line. If it is Paul’s turn to serve the ball, your program should output paul. Otherwise, your program should output opponent.

-----Examples-----
Sample Input:
5 3 7
Sample Output:
paul
user: Thrilled about his new valid set of pieces, Mirko rushed over to Slavko’s, to find that Slavko too found a set of chess pieces in his attic. Slavko’s set, miraculously, contains only black pieces. But since neither of them can play chess, they settled on smashing one another senseless with their chessboards.

While Slavko is warming up with a series of stretches, Mirko decided to sabotage Slavko’s chessboard. An expert in carving wood, he decided to cut Slavko’s chessboard so that it shatters into as many pieces as possible when Slavko attempts to hit Mirko.

Mirko can only make horizontal and vertical cuts (parallel to the sides to the board), edge to edge, and has time to make at most $N$ cuts.

-----Input-----
The first line of input contains an integer $N$ ($1 \le N \le 10^9$), the number of cuts Mirko can make.

-----Output-----
Output the largest number of pieces Slavko’s chessboard can crash into.

-----Examples-----
Sample Input:
1
Sample Output:
2
user: Your favourite social media website is changing their policy on login password validation: a slight error when logging in is now acceptable! In particular, assuming the password you chose when creating the account is $S$, a password $P$ entered while logging in will be accepted if any of the following conditions are met:
 - $P$ and $S$ are identical;
 - $S$ can be formed from $P$ by prepending a single digit (0–9);
 - $S$ can be formed from $P$ by appending a single digit;
 - $S$ is equal to $P$ after reversing the case of all letters in $P$.

To reverse the case of a string, replace all uppercase letters with their equivalent lowercase letters, and all lowercase letters with their equivalent uppercase letters, while leaving all other characters the same. For example, the case-reversal of pa55WORD is PA55word.

Any other attempted password $P$ will be rejected. So for example, if $S$ is c0deninja5, then c0deninja will be accepted, but not C0deninja5 or c0deninja51.

Write a program which, given alphanumeric strings $S$ and $P$, determines whether $P$ should be accepted.

-----Input-----
The first line of the input is the string $S$, the stored password, and the second line of input is the password $P$ that a user has entered while attempting to log in. Each string consists of only digits 0–9, lowercase letters a–z, and uppercase letters A–Z. The strings won’t contain spaces or any other extraneous characters, and will each contain at least one and at most $101$ characters.

-----Output-----
Print Yes if $P$ should be accepted according to the above rules, and No otherwise.

-----Examples-----
Sample Input:
123
123a
Sample Output:
No