meetforever/GRPO_CL huggingface dataset:
user: Most of you have played card games (and if you haven’t, why not???) in which the deck of cards is randomized by shuffling it one or more times.

A perfect shuffle  is a type of shuffle where the initial deck is divided exactly in half, and the two halves are perfectly interleaved. For example, a deck consisting of eight cards ABCDEFGH (where A is the top card of the deck) would be divided into two halves ABCD and EFGH and then interleaved to get AEBFCGDH. Note that in this shuffle the original top card (A) stays on top — this type of perfect shuffle is called an out-shuffle. An equally valid perfect shuffle would start with the first card from the second half and result in EAFBGCHD — this is known as an in-shuffle.

While normal shuffling does a good job at randomizing a deck, perfect shuffles result in only a small number of possible orderings. For example, if we perform multiple out-shuffles on the deck above, we obtain the following: ABCDEFGH $\rightarrow $ AEBFCGDH $\rightarrow $ ACEGBDFH $\rightarrow $ ABCDEFGH $\rightarrow \cdots $

So after 3 out-shuffles, the deck is returned to its original state. A similar thing happens if we perform multiple in-shuffles on an 8-card deck, though in this case it would take 6 shuffles before we get back to where we started. With a standard 52 card deck, only 8 out-shuffles are needed before the deck is returned to its original order (talented magicians can make use of this result in many of their tricks). These shuffles can also be used on decks with an odd number of cards, but we have to be a little careful: for out-shuffles, the first half of the deck must have 1 more card than the second half; for in-shuffles, it’s the exact opposite. For example, an out-shuffle on the deck ABCDE results in ADBEC, while an in-shuffle results in CADBE.

For this problem you will be given the size of a deck and must determine how many in- or out-shuffles it takes to return the deck to its pre-shuffled order.

-----Input-----
The input consists of one line containing a positive integer $n \leq 1000$ (the size of the deck) followed by either the word in or out, indicating whether you should perform in-shuffles or out-shuffles.

-----Output-----
For each test case, output the case number followed by the number of in- or out-shuffles required to return the deck to its original order.

-----Examples-----
Sample Input 1:
8 out
Sample Output 1:
3

Sample Input 2:
8 in
Sample Output 2:
6

Sample Input 3:
52 out
Sample Output 3:
8
user: While breaking ground for the Obama Presidential Center, which will be located just a few blocks from campus in Jackson Park, archeologists from the Oriental Institute have made an astounding discovery: a new set of scrolls from the ancient and certainly not made-up Apaxian civilization!

It seems that the Apaxian civilization, which the Oriental Institute is starting to suspect may have been way too concerned with string manipulation, provided a way for young Apaxians to extend their name using the name of one of their parents. The basic principle was to take an Apaxian name $Y$, add ex, and then the name $P$ of one of the parents. For example, if $Y$ is menolaxios and $P$ is mox, the extended name is $\texttt{menolaxios}+\texttt{ex}+\texttt{mox}=\texttt{menolaxiosexmox}$

However, there were a few exceptions to this rule:
 - If $Y$ ends with e, then the extended name is $Y+\texttt{x}+P$
 - If $Y$ ends with any other vowel (a,i,o, or u), we remove that final vowel from $Y$, and then extend $Y$ with $\texttt{ex}+P$
 - If $Y$ already ends with ex, then the extended name is simply $Y+P$.

As usual, the Oriental Institute has asked us to help them apply the power of computation to generating these extended names.

-----Input-----
The input contains two strings separated by a single space: $Y$ and $P$, as defined above. Each string contains only lowercase English letters, and is at least $2$ characters long and at most $10$ characters long.

-----Output-----
The output is a single string containing the extended name, as defined above.

-----Examples-----
Sample Input 1:
menolaxios mox
Sample Output 1:
menolaxiosexmox

Sample Input 2:
alemaxe maxos
Sample Output 2:
alemaxexmaxos

Sample Input 3:
pamoli toxes
Sample Output 3:
pamolextoxes
user: You are an eccentric billionaire with an affinity for sending stuff to Mars. In an ideal world you would send stuff to Mars all the time, but your engineers tell you that it is most efficient to do it when Earth and Mars are somewhat close to each other. 

Your engineers have calculated that optimal launch windows occur once every 26 months, and that one of them occurs in April 2018. They also tell you that they will not have any Big Finished Rockets by then, so you will have to wait for a later launch window.

Since your rocket scientists apparently can not be bothered to tell you about the optimal launch windows before it is too late, you have to keep track of that yourself. Write a program that determines if there is an optimal launch window in any given year.

-----Input-----
The only line of input contains an integer $y$ ($2018 \le y \le 10000$), the year you are interested in.

-----Output-----
Output “yes” if there is an optimal launch window in the year $y$, otherwise output “no”.

-----Examples-----
Sample Input 1:
2018
Sample Output 1:
yes

Sample Input 2:
2019
Sample Output 2:
no

Sample Input 3:
2020
Sample Output 3:
yes
user: A bored technician whose job requires inspecting each of $10$ equipment stations on a regular basis has tried to inject a little variety into his days by creating a deck of cards, each card bearing a number in the range $1..10$. From this deck he randomly deals out $K$ cards at the start of the day, and uses the numbers on these to determine which stations and in what order he will visit them on that day. (He has decided that it is OK to visit the same station more than once in the same day.)

As time goes by, he adds cards for the number of stations where he finds problems, so that he will visit them more often, so the number of cards bearing each digit may vary considerably.

One day he deals out his cards, and notices that they have come out in strictly ascending order. He starts to wonder just how likely such an ordering would be.

Find the number of ways to deal the cards that form a strictly ascending sequence. (“Strictly ascending” in this problem means that, for example $[2, 4, 5]$ would be accepted but $[3, 1, 2]$ and $[2, 2, 4]$ would not.)

-----Input-----
The first line of input contains $10$ non-negative integers $n_ i$, each denoting the number of cards bearing the number $i$. The sum of these $10$ numbers is in the range $1\ldots 1000$.

This is followed by a line containing an integer $K$, $1 \leq K \leq 10$, denoting the number of cards to be dealt.

-----Output-----
Print a single line containing an integer denoting the number of ways to deal $K$ cards from that deck that would form a strictly ascending sequence.

-----Examples-----
Sample Input 1:
4 0 0 0 4 0 0 0 0 4
3
Sample Output 1:
64

Sample Input 2:
4 0 0 0 4 0 0 0 0 4
4
Sample Output 2:
0

Sample Input 3:
10 10 10 20 0 10 10 10 10 10
4
Sample Output 3:
1820000
user: Define a $k$-periodic string as follows:

A string $s$ is $k$-periodic if the length of the string $|s|$ is a multiple of $k$, and if you chop the string up into $|s|/k$ substrings of length $k$, then each of those substrings (except the first) is the same as the previous substring, but with its last character moved to the front.

For example, the following string is $3$-periodic:abccabbcaabc

The above string can break up into substrings abc, cab, bca, and abc, and each substring (except the first) is a right-rotation of the previous substring (abc -> cab -> bca -> abc)

Given a string, determine the smallest k for which the string is k-periodic.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The single line of input contains a string $s$ ($1 \le |s| \le 100$) consisting only of lowercase letters.

-----Output-----
Output the integer $k$, which is the smallest $k$ for which the input string is $k$-periodic.

-----Examples-----
Sample Input 1:
aaaaaaaa
Sample Output 1:
1

Sample Input 2:
abbaabbaabba
Sample Output 2:
2

Sample Input 3:
abcdef
Sample Output 3:
6
user: Driving through the Irish countryside, one frequently sees enigmatic small grey stones sitting by the wayside, spaced about a kilometre and a half apart. As it turns out, these stones once had a purpose: they were milestones, intended to demarcate this venerable unit of measurement.

Being so old and, crucially, collectible by magpies and larger scamps alike, not all of these stones have remained.

Passing by some more of these tattered markers at a constant but unknown speed, you may still be able to gain some information from their placements. For example, since you started counting you have passed exactly $M$ remaining stones; how fast could you have been driving?

-----Input-----
 - One line containing two positive integers, $M$ and $N$ ($ 2 \leq M \leq N \leq 10^3 $): the number of consecutive stones you noticed and the total number of stones along the road respectively.
 - One line containing $M$ distinct non-negative integers $T_{1..M}$ in ascending order—the times at which you passed stones in hours ($ 0 \leq T_ i \leq 10^{15} $).
 - One line containing $N$ distinct non-negative integers $X_{1..N}$ in ascending order—the distances along the road of each milestone ($ 0 \leq X_ i \leq 10^{15} $) in miles.

-----Output-----
Output two lines:
 - First, the number of distinct possible speeds at which the car could have been travelling.
 - Second, a space-separated list of all of the possible distances between the first milestone you saw and the second milestone you saw, in increasing order.

-----Examples-----
Sample Input 1:
4 12
1 2 4 5
6 8 12 18 26 28 30 34 36 37 39 40
Sample Output 1:
2
1 2

Sample Input 2:
5 10
1 2 3 4 5
0 1 2 3 4 5 6 7 8 9
Sample Output 2:
1
1

Sample Input 3:
3 6
1 2 4
11 12 15 19 24 30
Sample Output 3:
0
user: In the United States of America, telephone numbers within an area code consist of seven digits: the prefix number is the first three digits and the line number is the last four digits. Traditionally, the $555$ prefix number has been used to provide directory information and assistance as in the following examples:
 - 555-1212
 - 555-9876
 - 555-5000
 - 555-7777

Telephone company switching hardware would detect the $555$ prefix and route the call to a directory information operator. Nowadays, telephone switching is done digitally and somewhere along the line a computer decides where to route calls.

For this problem, write a program that determines if a supplied seven-digit telephone number should be routed to the directory information operator, that is, the prefix number is $555$.

-----Input-----
The single line of input contains a single integer $n$ ($1000000 \le n \le 9999999$), which is a telephone number.

-----Output-----
Output a single integer, which is $1$ if the number should be routed to the directory information operator, or $0$ if the number should not be routed to the directory information operator.

-----Examples-----
Sample Input 1:
5551212
Sample Output 1:
1

Sample Input 2:
5519876
Sample Output 2:
0

Sample Input 3:
5055555
Sample Output 3:
0
user: Yraglac has been a bit bored with Calgary lately and decided to move to the United States. After arriving in the strange land, he discovered that the people there use a temperature scale known as Fahrenheit. Celsius and Fahrenheit are related by the following equation:\[ \left[ ^\circ F \right] = \frac95 \left[ ^\circ C \right] + 32 \]

It is your job to help Yraglac convert Fahrenheit to Celsius. When it comes to temperatures, however, Yraglac is a bit particular. Given a temperature expressed as a fraction in Fahrenheit, he wants to know the exact value in Celsius, expressed as a fraction in lowest terms.

-----Input-----
The input consists of a single test case representing a fractional number in Fahrenheit. It will be in the form $a/b$ or $-a/b$ where $a$ and $b$ are integers such that $0 \leq a, b \leq 1000000$ and $b \neq 0$. Note that the input is not guaranteed to be a fraction in lowest terms. You should consider temperatures below absolute zero to be valid.

-----Output-----
Output a single line with the exact result of converting the temperature to Celsius, expressed as a fraction in lowest terms (that is, $\gcd (a,b) = 1$).

-----Examples-----
Sample Input 1:
32/1
Sample Output 1:
0/1

Sample Input 2:
33/1
Sample Output 2:
5/9

Sample Input 3:
-40/1
Sample Output 3:
-40/1
user: In the past century, a new style of music composition has emerged. Unlike more traditional methods based on keys and chords, the technique known as dodecaphony focuses on using all twelve notes equally. As a quick reminder, the twelve notes, in ascending order are,\[ C, C\sharp , D, D\sharp , E, F, F\sharp , G, G\sharp , A, A\sharp , B \]

The sequence then wraps around so that the next note after $B$ is $C$ and so on. For this problem, we’ll ignore equivalent notations that use flats, double sharps, or double flats.

Each successive note above is considered one semitone away from the next. Now in our simplified version of dodecaphony, a melody is a permutation of the previous melody by one of three relations.

First, we have transposition, where each note has been shifted up by $n$ semitones. A retrograde is when the notes have their order reversed. Finally we have inversion about the first note of the melody. With inversions, the first note doesn’t change, but the rest of the notes are inverted such that the the interval (number of semitones) between that note and the first note is negated.

For example, if $F$ is our first note, and we want to invert an $A\sharp $, which is $5$ semitones higher, the inverted note would be a $C$, which is $5$ semitones lower. Note that the first note in an inverted melody is always just the first note of the original melody.

Given two melodies, can you tell what relation the second has to the first?

-----Input-----
The first line contains a single integer $2 \leq l \leq 50$, the number of notes in each melody.

The next two lines each contain $l$ space separated notes. It is guaranteed that each note will be one of the twelve listed above.

-----Output-----
Output on a single line “Transposition” if the second melody is a transposition of the first, “Retrograde” if the second melody is the first melody reversed, “Inversion” if the second melody is an inversion of the first melody, else “Nonsense” if it is none of the other cases.

If the second melody satisfies more than one relation, output the first valid relation in the order of “Transposition”, then “Retrograde”, then “Inversion”.

-----Examples-----
Sample Input 1:
3
C E G
D F# A
Sample Output 1:
Transposition

Sample Input 2:
7
C C G G A A G
C C F F D# D# F
Sample Output 2:
Inversion

Sample Input 3:
7
A B C D E F G
G F E D C B A
Sample Output 3:
Retrograde
user: Nimions speak a funny form of language.

Whichever word they are trying to say, from which ever language, it doesn’t quite come out the same. There are several rules for converting words, from any language, to nimionese.

For any word:
 - All nimion words start with ‘hard’ consonants (b, c, d, g, k, n, p, t) so you must replace each first letter with the nearest one (choose the option nearest to ‘A’ if there is a tie).
 - “Each” becomes “Dach”.
 - Any hard consonant in subsequent syllables after the first one is remarkably better if it is replaced with the same consonant as the one at the start of the word.
 - “Hip-po” becomes “Gip-go”.
 - No word ends in a hard consonant. You must add an ‘ah’, ‘oh’ or ‘uh’ at the end, whichever is nearest, rounding toward ‘A’ in the case of a tie, to the last hard consonant in the word.
 - “Dog” becomes “Dogah”
 - “Hip” becomes “Gipoh”.

-----Input-----
The only line of input contains a sentence of between $1$ and $50$ words and up to $10^4$ symbols, including single whitespace characters (‘ ’) between words and the dashes (‘-’) between each syllable.

Apart from dashes, the sentence will contain solely lower-and-upper-case Latin letters—and only the first letters of words can be upper-case.

-----Output-----
Write to standard output the same sentence from the input, translated to nimionese. Remove any dashes before printing.

It is guaranteed that the output will fit within $5 \cdot 10^4$ characters.

-----Examples-----
Sample Input 1:
I love ba-na-na
Sample Output 1:
Gah kove bababa

Sample Input 2:
Cat-a-pil-lar
Sample Output 2:
Catacillar

Sample Input 3:
Co-ding is the best
Sample Output 3:
Cociccah gs the bestuh
user: Fidget spinners are so 2017; this year’s rage are fidget cubes. A fidget cube is a cube with unit side lengths, which you hold in your hand and fidget with. Kids these days, right? 

You work in the planning department for a company that creates and ships fidget cubes. Having done some market analysis, you found that your customers want to receive shipments of exactly $V$ fidget cubes.

This means you have to design a container that will hold exactly $V$ fidget cubes. Since fidget cubes are very fragile, you cannot have any empty space in your container. If there is empty space, they might move around, bump into each other and get damaged. Because of this, you decide to ship the fidget cubes in a rectangular cardboard box.

The cost of a cardboard box is proportional to its surface area, costing exactly one unit of money per square unit of surface area. Of course you want to spend as little money as possible. Subject to the above constraints, how much money do you have to spend on a box for $V$ fidget cubes?

-----Input-----
The input contains a single integer, $1 \leq V \leq 10^6$, the number of fidget cubes for which you need to build a box.

-----Output-----
Print the cost of the cheapest rectangular box as specified in the statement.

-----Examples-----
Sample Input 1:
1
Sample Output 1:
6

Sample Input 2:
4
Sample Output 2:
16

Sample Input 3:
3
Sample Output 3:
14
user: After the festive opening of your new store, the Boutique store for Alternative Paramedicine and Cwakhsahlvereigh, to your disappointment you find out that you are not making as many sales as you had hoped. To remedy this, you decide to run a special offer: you will mark some subset of the $n$ items for sale in your store as participating in the offer, and if people buy exactly two of these items, and the cost of these items is strictly more than $X$ euros, you will give them a free complimentary unicorn horn!

Since you recently found out all your unicorn horns are really narwhal tusks, you decide to rig the offer by picking the participating items in such a way that no one can earn a horn anyway.

To make sure no one becomes suspicious, you want to mark as many items as possible as participating in the offer.

-----Input-----
 - On the first line are two integers, $1 \leq n \leq 10^5$, the number of items for sale in your store, and $1\leq X \leq 10^9$, the minimum cost specified in the statement.
 - On the second line are $n$ positive integers, each at most $10^9$. These are the prices of the items in the store.

-----Output-----
Print the maximum number of items you can mark as part of your special offer, without anyone actually being able to receive a horn.

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

Sample Input 2:
5 10
4 8 1 9 7
Sample Output 2:
2

Sample Input 3:
4 10
1 3 1 7
Sample Output 3:
4
user: The Nordic Company of Passing Carriages is losing money at an alarming rate because most of their trains are empty. However, on some lines the passengers are complaining that they cannot fit in the cars and have to wait for the next train!

The authorities want to fix this situation. They asked their station masters to write down, for a given train, how many people left the train at their station, how many went in, and how many had to wait. Then they hired your company of highly paid consultants to assign properly sized trains to their routes.

You just received the measurements for a train, but before feeding them to your optimisation algorithm you remembered that they were collected on a snowy day, so any sensible station master would have preferred to stay inside their cabin and make up the numbers instead of going outside and counting.

Verify your hunch by checking whether the input is inconsistent, i.e., at every time the number of people in the train did not exceed the capacity nor was below $0$ and no passenger waited in vain (i.e., waited on the station when there was room in the train). The train should start and finish the journey empty, in particular passengers should not wait for the train at the last station.

-----Input-----
The first line contains two integers $C$ and $n$ ($1 \leq C \leq 10^9$, $2 \leq n \leq 100$), the total capacity and the number of stations the train stops in. The next $n$ lines contain three integers each, the number of people that left the train, entered the train, and had to stay at a station. Lines are given in the same order as the train visits each station. All integers are between $0$ and $10^9$ inclusive.

-----Output-----
One line containing one word: possible if the measurements are consistent, impossible otherwise.

-----Examples-----
Sample Input 1:
1 2
0 1 1
1 0 0
Sample Output 1:
possible

Sample Input 2:
1 2
1 0 0
0 1 0
Sample Output 2:
impossible

Sample Input 3:
1 2
0 1 0
1 0 1
Sample Output 3:
impossible
user: Recently your town has been infested by swindlers who convince unknowing tourists to play a simple dice game with them for money. The game works as follows: given is an $n$-sided die, whose sides have $1, 2, \ldots , n$ pips, and a positive integer $k$. You then roll the die, and then have to make a choice. Option $1$ is to stop rolling. Option $2$ is to reroll the die, with the limitation that the die can only be rolled $k$ times in total. Your score is the number of pips showing on your final roll.

Obviously the swindlers are better at this game than the tourists are. You, proud supporter of the Battle Against Probabilistic Catastrophes, decide to fight this problem not by banning the swindlers but by arming the tourists with information.

You create pamphlets on which tourists can find the maximum expected score for many values of $n$ and $k$. You are sure that the swindlers will soon stop their swindling if the tourists are better prepared than they are!

The layout of the flyers is done, and you have distribution channels set up. All that is left to do is to calculate the numbers to put on the pamphlet.

Given the number of sides of the die and the number of times you are allowed to roll, calculate the expected (that is, average) score when the game is played optimally.

-----Input-----
 - A single line with two integers $1\leq n\leq 100$, the number of sides of the die, and $1\leq k\leq 100$, the number of times the die may be rolled.

-----Output-----
Output the expected score when playing optimally. Your answer should have an absolute or relative error of at most $10^{-7}$.

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

Sample Input 2:
2 3
Sample Output 2:
1.875

Sample Input 3:
6 2
Sample Output 3:
4.25