meetforever/GRPO_CL huggingface dataset:
user: You live in Grid City, which is composed of integer-numbered streets which run east-west (parallel to the $x$-axis) and integer-numbered avenues which run north-south (parallel to the $y$-axis). The streets and avenues have infinite length, and there is a street for every integer $y$-coordinate and an avenue for every $x$-coordinate. All intersections are labelled by their integer coordinates: for example, avenue $7$ and street $-3$ intersect at $(7,-3)$.

You drive a special electric car which uses up one unit of electrical charge moving between adjacent intersections: that is, moving either north or south to the next street, or moving east or west to the next avenue). Until your battery runs out, at each intersection, your car can turn left, turn right, go straight through, or make a U-turn. You may visit the same intersection multiple times on the same trip.

Suppose you know your starting intersection, your destination intersection and the number of units of electrical charge in your battery. Determine whether you can travel from the starting intersection to the destination intersection using the charge available to you in such a way that your battery is empty when you reach your destination.

-----Input-----
The input consists of three lines. The first line contains $a$ followed by $b$, indicating the starting coordinate $(a, b)$ ($-1000 \le a \le 1000$; $-1000 \le b \le 1000$).

The second line contains $c$ followed by $d$, indicating the destination coordinate $(c, d)$ ($-1000 \le c \le 1000$; $-1000 \le d \le 1000$).

The third line contains an integer $t$ ($0 \le t \le 10000$) indicating the initial number of units of electrical charge of your battery.

-----Output-----
Output Y if it is possible to move from the starting coordinate to the destination coordinate using exactly $t$ units of electrical charge. Otherwise output N.

-----Examples-----
Sample Input:
3 4
3 3
3
Sample Output:
Y
user: Consider a grid consisting of $N$ rows and $M$ columns, where each cell is either air, stone, or water. Each second, the water spreads in the following fashion:
 - If a water cell is directly above an air cell then the air cell turns into water in the next second.
 - If a water cell is directly above a stone cell then any air cells directly left or right of the water cell turn into water in the next second.

After some number of seconds, the water will have stopped spreading. Show how the grid looks when that happens. You can assume that all cells outside of the grid behave as air cells; for instance, if a water cell is at the bottommost row then its water will not spread to the sides.

-----Input-----
The first line consists of two integers $N$ and $M$ ($2 \leq N,M \leq 50$), the number of rows and columns in the grid.

Each of the following $N$ lines contains a string $S$ of length $M$. The string $S$ represents one of the rows in the grid. It consists of the symbols “.” (air), “#” (stone), and “V” (water).

-----Output-----
Print $N$ lines, each consisting of a string of length $M$, describing the grid as it looks when the water has stopped spreading.

-----Examples-----
Sample Input:
5 7
...V...
.......
.......
...#...
..###..
Sample Output:
...V...
...V...
..VVV..
.VV#VV.
.V###V.
user: Yi has moved to Sweden and now goes to school here. The first years of schooling she got in China, and the curricula do not match completely in the two countries. Yi likes mathematics, but now... The teacher explains the algorithm for subtraction on the board, and Yi is bored. Maybe it is possible to perform the same calculations on the numbers corresponding to the reversed binary representations of the numbers on the board? Yi dreams away and starts constructing a program that reverses the binary representation, in her mind. As soon as the lecture ends, she will go home and write it on her computer.

-----Task-----
Your task will be to write a program for reversing numbers in binary. For instance, the binary representation of 13 is 1101, and reversing it gives 1011, which corresponds to number 11.

-----Input-----
The input contains a single line with an integer $N$, $1 \leq N \leq 1\; 000\; 000\; 000$.

-----Output-----
Output one line with one integer, the number we get by reversing the binary representation of $N$.

-----Examples-----
Sample Input:
13
Sample Output:
11
user: Thore is a fashionable man. Every time he meets up with his programming team, he wears his hot pink team hoodie over a salmon colored shirt with shirt buttons in a dashing rose or pink shade. Of course, he can’t show up to two training sessions with the same buttons on his shirt, that would cause unbearable ridicule. If he can’t find buttons for this perfect color combination, he will come up with some poor excuse for not showing up. He has a box full of different colored buttons in labeled packages. Unfortunately, Thore is color blind, so his helpful daughter has labeled each package with the color of the buttons. Her writing is terrible though, she mixes uppercase and lowercase arbitrarily and has no spacing between words, so Thore needs your help to decipher the names on the labels and select buttons with either “pink” or “rose” somewhere in the name, ignoring case. 

-----Input-----
Input starts with an integer $1 \leq N \leq 1000$, the number of button packages in the box. The following $N$ lines each has a color name, one for each package. The names consist of up to 30 characters of letters A - Z, a - z.

-----Output-----
Print one integer, the number of training sessions Thore can attend. If he can’t attend any session because there are no pink buttons, output his standard excuse “I must watch Star Wars with my daughter”.

-----Examples-----
Sample Input:
12
pink
tequilaSunrose
mExicanPInK
Coquelicot
turqrose
roSee
JETblack
pink
babypink
pInKpinkPinK
PInkrose
lazerlemon
Sample Output:
9
user: You will be given three integers $A$, $B$ and $C$. The numbers will not be given in that exact order, but we do know that $A$ is less than $B$ and $B$ less than $C$. In order to make for a more pleasant viewing, we want to rearrange them in a given order.

-----Input-----
The first line contains the three positive integers $A$, $B$ and $C$, not necessarily in that order. The three numbers will be less than or equal to $100$.

The second line contains three uppercase letters ’A’, ’B’ and ’C’ (with no spaces between them) representing the desired order.

-----Output-----
Output $A$, $B$ and $C$ in the desired order on a single line, separated by single spaces.

-----Examples-----
Sample Input:
1 5 3
ABC
Sample Output:
1 3 5
user: Consider a positive integer $x$. Multiply its nonzero digits and you get another integer $y$. Repeating this process, you eventually arrive at a single digit between $1$ and $9$. Write a program that reads $x$ and outputs the resulting digit.

-----Input-----
An integer $x$ with $10 \leq x \leq 1000$.

-----Output-----
Print a digit between $1$ and $9$, the result of repeatedly multiplying the nonzero digits of $x$ as described above.

-----Explanation of Sample Inputs-----
In Sample Input $1$, we have $x = 808$. Multiplying $8$ and $8$, we arrive at $64$. Then we get $6 \cdot 4 = 24$, and finally $2 \cdot 4 = 8$, which is the sample output.

In Sample Input $2$, there is only a single nonzero digit, $2$. The product of all digits in a set containing only a single element is the digit itself. Thus the answer is $2$.

-----Examples-----
Sample Input:
808
Sample Output:
8
user: You are mapping a faraway planet using a satellite. The planet’s surface can be modeled as a grid. The satellite has captured an image of the surface. Each grid square is either land (denoted as ‘L’), water (denoted as ‘W’), or covered by clouds (denoted as ‘C’). Clouds mean that the surface could either be land or water; you cannot tell.

An island is a region of land where every grid cell in the island is connected to every other by some path, and every leg of the path only goes up, down, left or right.

Given an image, determine the minimum number of islands that is consistent with the given image.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The first line of input contains two integers, $r$ and $c$ ($1 \le r, c \le 50$), which are the number of rows and the number of columns of the image. The next $r$ lines will each contain exactly $c$ characters, consisting only of ‘L’ (representing Land), ‘W’ (representing Water), and ‘C’ (representing Clouds).

-----Output-----
Output a single integer, which is the minimum number of islands possible.

-----Examples-----
Sample Input:
4 5
CCCCC
CCCCC
CCCCC
CCCCC
Sample Output:
0
user: Young Mirko is a smart, but mischievous boy who often wanders around parks looking for new ideas. This time he’s come across pensioners playing the card game Belote. They’ve invited him to help them determine the total number of points in a game.

Each card can be uniquely determined by its number and suit. A set of four cards is called a hand. At the beginning of a game one suit that “trumps” any other is chosen, and it is called the dominant suit. The number of points in a game is equal to the sum of values of each card from each hand in the game. Mirko has noticed that the pensioners have played $N$ hands and that suit $B$ was the dominant suit.

The value of each card depends on its number and whether its suit is dominant, and is given in Table 1.

Number

Value 

Dominant

Not dominant

A

$11$

$11$

K

$4$

$4$

Q

$3$

$3$

J

$20$

$2$

T

$10$

$10$

9

$14$

$0$

8

$0$

$0$

7

$0$

$0$Table 1: Scores 

Write a programme that will determine and output the number of points in the game.

-----Input-----
The first line contains the number of hands $N$ ($1 \leq N \leq 100$) and the value of suit $B$ (S, H, D, C) from the task. Each of the following $4N$ lines contains the description of a card (the first character is the number of the $i$-th card (A, K, Q, J, T, 9, 8, 7), and the second is the suit (S, H, D, C)).

-----Output-----
The first and only line of output must contain the number of points from the task.

-----Examples-----
Sample Input:
2 S
TH
9C
KS
QS
JS
TD
AD
JH
Sample Output:
60
user: Oh no! Joanna just spilled some syrup on her keyboard and now some of the keys are sticky. This causes her considerable frustration, as every time she presses one of the sticky keys, the corresponding character gets entered twice on her computer. 

This could not have happened at a more inconvenient time; it is the start of the contest and she was just about to type in the solution to the first problem! Joanna does not have time to remove and clean every key on her keyboard, so she wonders if there is a way to quickly identify the sticky keys. Starting to panic, she quickly types some text on her keyboard and stares at the resulting text displayed on her screen.

Given the line of text that Joanna typed on her keyboard and the resulting text displayed on her screen, help her determine which keys must be sticky.

-----Input-----
The input consists of:
 - One line containing a string $s$ ($1 \leq \mathrm{length}(s) \leq 1000$), the text that Joanna typed on her keyboard.
 - One line containing a string $t$ ($1 \leq \mathrm{length}(t) \leq 1000$), the text displayed on Joanna’s screen as a result.

Both $s$ and $t$ consist only of lower-case letters (‘a’–‘z’) and spaces (‘ ’), and start and end with a letter.

It is guaranteed that $t$ is the result of doubling each character in $s$ that corresponds to a sticky key. At least one character in $s$ corresponds to a sticky key (i.e. $s \neq t$).

-----Output-----
Output all characters (letters and space) corresponding to keys that must be sticky, in any order.

-----Examples-----
Sample Input:
this is very annoying
thiss iss veery annoying
Sample Output:
se
user: Having discolored his white socks in a rather beige shade (as seen on the picture), Luktas Svettocek realised he can’t just throw all his laundry into one machine and expect it to retain its original colors. However, he is also too lazy to do his laundry in several rounds. He would much rather buy more laundry machines!

Each of Luktas’ socks have a color $D_ i$ which has a number between $0$ and $10^9$ assigned to it. After some experimentation, he found that he could wash any socks with a maximum absolute color difference of $K$ in the same machine without any discoloring. The color difference of two socks $i$ and $j$ is $|D_ i - D_ j|$.

Luktas now needs to know how many washing machines he needs to wash his $S$ socks, given that each machine can take at most $C$ socks a time.

-----Input-----
The first line consists of three integers $1 \le S, C \le 10^5$ and $0 \le K \le 10^9$, the number of socks, the capacity of a laundry machine and the maximum color difference, respectively. Then follow one line with $S$ integers; these are the color values $D_ i$ of every sock.

-----Output-----
Output a single integer; the number of machines Luktas needs to wash all his socks.

-----Examples-----
Sample Input:
5 3 0
0 0 1 1 2
Sample Output:
3
user: The factorial of $N$, written as $N!$, is defined as the product of all the integers from $1$ to $N$. For example, $3! = 1 \times 2 \times 3 = 6$.

This number can be very large, so instead of computing the entire product, just compute the last digit of $N!$ (when $N!$ is written in base $10$).

-----Input-----
The first line of input contains a positive integer $1 \leq T \leq 10$, the number of test cases. Each of the next $T$ lines contains a single positive integer $N$. $N$ is at most $10$.

-----Output-----
For each value of $N$, print the last digit of $N!$.

-----Examples-----
Sample Input:
3
1
2
3
Sample Output:
1
2
6
user: After acquiring a new integer and showing it off to other couples at a cocktail party, Alice and Bob headed home for a good night of sleep. As their integer was quite large, they were forced to carry it together. Then, on the Boole Boulevard, right by the Bayes Bay, disaster struck. History does not tell us which of our two protagonists stumbled first, but stumble they did, and their integer shattered into $n$ positive integral pieces on the pavement in front of them.

The couple’s marriage, already under financial stress due to the expensive integer acquisition, did not survive this event, and Bob and Alice resolved to separate. Thus the question was raised on how to split the remnants of their integer. Bob and Alice decided to play a game with the remaining $n$ pieces: the two would repeatedly choose pieces in alternating turns until none were left.

Bob and Alice, both very materialistic, seek to acquire the largest possible sum of integers possible. Compute the value of the integers each of them ends up with. Assume both players play optimally. Since A comes before B in the alphabet, Alice moves first.

-----Input-----
The input consists of two lines.
 - A single integer $1 \leq n \leq 15$, the number of pieces.
 - The values of the pieces $a_0, a_1, \dots , a_{n-1}$, space-separated. It is given that $1 \leq a_ i \leq 100$.

-----Output-----
Output a single line containing two integers, the combined value of Alice’s pieces, and the combined value of Bob’s pieces.

-----Examples-----
Sample Input:
3
3 1 2
Sample Output:
4 2
user: Once upon a time in a land of yore, there was a troll who lived ’neath one of the land’s many stone bridges. This troll was quite a mischievous troll, for you see, it had a habit of accusing anyone crossing the bridge of having stolen the troll’s property (which was a somewhat curious accusation given that the troll had no property), the punishment of which was to be eaten alive. Unfortunately for the troll, eventually the king got wind of its questionable business model, and sent out the valiant knights of the High Tavern to go, shall we say, Queen of Hearts, on the troll. 

Apprehensive of its imminent decapitation, the troll fled, and did not have the decency to even leave a forwarding address. Being a troll, it was clear that the troll was hiding under some other stone bridge than the one it had used for its shady business practice, but which? The knights decided to split up in groups and go search. Since a group needed to be able to avoid being eaten once the troll was found, each group had to consist of at least a certain number of knights. Each group of knights could search under one stone bridge per day (and travelling between bridges was done at lightning speed, thanks to the knights’ renowned iTravel™ technology). While clever enough to flee from its hunting ground, the troll is not bright enough to keep moving between different bridges: once the hunt starts, the troll stays in the same place. How many days would it take until the troll would surely have been found?

-----Input-----
The input consists of a single line containing three integers $b$, $k$ and $g$, where $2 \le b \le 1000$ is the number of stone bridges in the land, $1 \le k \le 100$ is the number of knights, and $1 \le g \le k$ is the number of knights needed in each group.

-----Output-----
Output a line containing a single integer $d$, the number of days until the troll is sure to have met its destiny.

-----Examples-----
Sample Input:
5 2 1
Sample Output:
2
user: An interesting theory in mathematics is that there is a sequence generator that, given any positive integer as the starting point, always ends with the number $1$. Although this theory has never been proven, the conjecture is known as the Collatz Conjecture (named after Lothar Collatz, who posed the idea in 1937). Given an integer, $n\geqslant 1$, this conjecture pertains to the sequence $h(n)$, which we recursively define as follows:
 - If $n=1$, the sequence is composed of a single integer: $1$
 - If $n$ is even, the sequence is composed of $n$ followed by sequence $h(n/2)$
 - If $n$ is odd, the sequence is composed of $n$ followed by sequence $h(3\cdot n + 1)$

For example, the following are the sequences for the numbers $5$ and $7$:

$h(5) = (5, 16, 8, 4, 2, 1)$

$h(7) = (7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1)$

The $h(n)$ sequence is commonly known as the hailstone sequence, because of its nature of going up and down like a hailstone in a cloud before eventually falling to Earth. In this problem, you will calculate the sum of all the values in a hailstone sequence. Using the sequences above, the sum of $h(5)$ is $36$ and the sum of $h(7)$ is $288$.

Your solution must use a RECURSIVE function,

 based on the recursive definition of $h(n)$ presented above.

On the exam, any other type of solution will receive zero points!

EVEN IF KATTIS JUDGES IT AS CORRECT!

Note: You are allowed to add up the numbers iteratively, as long as the $h(n)$ sequence is computed recursively.

-----Input-----
The input contains a single positive integer, $n$ ($0 < n \leqslant 2^{32}-1$).

-----Output-----
The output contains a single integer: the sum of all the values in $h(n)$. You may assume that this sum will fit in an unsigned 64-bit integer.

-----Examples-----
Sample Input:
5
Sample Output:
36
user: Linda is giving an exam. When the exam is over, Linda will redistribute the exams among the students for a peer review, so they may grade each other’s answers and assign preliminary scores.

The students are split up in several rooms of varying sizes. Linda has devised the following scheme for redistributing the exams:
 - Linda visits the first room, picks up all exams written there, and places them in a pile.
 - In each subsequent room Linda takes exams from the top of her pile and randomly distributes them to the students in the room. She then picks up all exams written in that room and adds them to the bottom of her pile.
 - After having visited each room exactly once, Linda returns to the first room, and distributes the remaining exams from her pile there.

Naturally, it is imperative that no student receives their own exam to review, and that Linda does not run out of exams in her pile while doing the redistribution (i.e., that when entering a room after the first one, Linda’s pile contains at least as many exams as there are students in the room). Whether or not this is the case depends on the order in which the rooms are visited. We say that an ordering of the rooms is safe if Linda will not run out of exams in her pile when visiting rooms in that order, and that there is no chance that any student receives their own exam to review.

Can you find a safe order in which to visit the rooms (or determine that no safe order exists)?

-----Input-----
The input consists of:
 - one line containing an integer $n$ ($2 \le n \le 30$), the number of rooms.
 - one line containing $n$ integers $s_1, \ldots , s_ n$ ($1 \le s_ i \le 100$ for each $i$), where $s_ i$ is the number of students in room $i$.

-----Output-----
If it is impossible to redistribute the exams safely, output “impossible”. Otherwise, output a safe order in which to visit the rooms. If there are multiple safe orders, you may give any of them.

-----Examples-----
Sample Input:
4
2 3 3 1
Sample Output:
2 3 4 1
user: Boating season is over for this year, and Theseus has parked his boat on land. Of course, the boat looks nothing like it did as of the beginning of the season; it never does. You see, Theseus is constantly looking for ways to improve his boat.

At every day of the boating season, Theseus bought exactly one type of item at his local supply store, and replaced the existing part on his boat with it. Now, as the season has ended, Theseus wonders what day he replaced all the parts from the previous season.

-----Input-----
The first line of the input consists of two space-separated integers $P$ and $N$, representing the number of parts the boat consists of, and the number of days in the boating season respectively.

 Then follows $N$ lines, each line has a single word $w_ i$, the type of boat part that Theseus bought on day $i$.

-----Output-----
Output the day Theseus ended up replacing the last existing part from the previous season, or paradox avoided if Theseus never ended up replacing all the different parts.

-----Limits-----
 - $1 \leq P \leq N \leq 1000$.
 - Each word $w_ i$ will consist only of the letters a–z and _ (underscore).
 - Each word $w_ i$ will be between $1$ and $20$ characters long.
 - The number of distinct $w_ i$s will be at most $P$.

-----Examples-----
Sample Input:
3 5
left_oar
right_oar
left_oar
hull
right_oar
Sample Output:
4
user: Mirko needs to choose four points in the plane so that they form a rectangle with sides parallel to the axes. He has already chosen three points and is confident that he hasn’t made a mistake, but is having trouble locating the last point. Help him.

-----Input-----
Each of the three points already chosen will be given on a separate line. All coordinates will be integers between $1$ and $1000$.

-----Output-----
Output the coordinates of the fourth vertex of the rectangle.

-----Examples-----
Sample Input:
5 5
5 7
7 5
Sample Output:
7 7