meetforever/GRPO_CL huggingface dataset:
user: Tim is an absolutely obsessive soda drinker, he simply cannot get enough. Most annoyingly though, he almost never has any money, so his only obvious legal way to obtain more soda is to take the money he gets when he recycles empty soda bottles to buy new ones. In addition to the empty bottles resulting from his own consumption he sometimes find empty bottles in the street. One day he was extra thirsty, so he actually drank sodas until he couldn’t afford a new one.

-----Input-----
Three non-negative integers $e,f,c$, where $e<1000$ equals the number of empty soda bottles in Tim’s possession at the start of the day, $f<1000$ the number of empty soda bottles found during the day, and $2 \le c<2000$ the number of empty bottles required to buy a new soda.

-----Output-----
How many sodas did Tim drink on his extra thirsty day?

-----Examples-----
Sample Input:
9 0 3
Sample Output:
4
user: Slavko is learning about different numeral systems. Slavko is not the brightest when it comes to math, so he is starting out converting binary numerals to octal. The algorithm Slavko uses is this:
 - Pad the binary numeral with zeros on the left until the number of digits is divisible by three.
 - Group adjacent binary digits into groups of $3$ digits.
 - Replace each group of binary digits with the corresponding octal digit (as in Table 1).

000

0

001

1

010

2

011

3

100

4

101

5

110

6

111

7Table 1: Binary to octal 

Write a program that converts a binary numeral to octal so that Slavko can verify his results.

-----Input-----
The input contains a binary numeral. The number of digits will be less than $100$, and the first digit will be $1$.

-----Output-----
Output the number in octal.

-----Examples-----
Sample Input:
1010
Sample Output:
12
user: A nice part of the Roman Catholic Mass is the rite of peace when people shake hands with their neighbours and say “peace be with you”. Mirko has found a way to turn this ritual into his own favor. Inside the church, there are $R$ rows of benches where each row can hold a capacity of $S$ people. We can imagine the seating order as a matrix sized $R \times S$ where each element represents either a person or an empty seating space. Let us assume that each person shakes hands with their neighbours. That means that the neighbours are located in one of the eight neighbouring elements (if such element exists):


A seating order of the people inside the church has been given before Mirko enters. Mirko is, of course, late for the morning Mass and will sit in an empty space so that he shakes hands with as many people as he can. If there are no empty seats left, Mirko will simply give up on the idea and go to the evening Mass instead. We can assume that nobody enters the church after Mirko.

Calculate the total number of handshakes given during the morning Mass.

-----Input-----
The first line of input contains positive integers $R$ and $S$ ($1 \leq R, S \leq 50$) as stated in the text. Each of the following $R$ lines contains $S$ characters. These $R \times S$ characters represent the seating order. The character “.” (dot) represents an empty place and the character “o” (lowercase letter o) represents a person.

-----Output-----
The first and only line of output should contain the required number of handshakes.

-----Examples-----
Sample Input:
2 3
..o
o..
Sample Output:
2
user: Mirko has $N$ items (labeled with numbers from $1$ to $N$) and $L$ drawers (labeled with numbers from $1$ to $L$). All items are currently scattered throughout his room, so he decided to clean them up. Each drawer can contain one item, and in order to make it easier for Mirko to find them later, he has determined in advance exactly two drawers ($A_ i$ and $B_ i$) for each item $i$.

Mirko stores the items in order from $1$ to $N$ using the first rule he can apply:
 - If the drawer $A_ i$ is empty, he stores the item $i$ in that drawer.
 - If the drawer $B_ i$ is empty, he stores the item $i$ in that drawer.
 - Try to move the item from $A_ i$ to its other drawer; if that one’s filled too, try moving that item to its other drawer, and so on until you either succeed or get back to a previously seen drawer. In case of success, store the item $i$ in the drawer $A_ i$. In case of failure, continue to next rule.
 - Try moving the item from $B_ i$ to its other drawer; if that one’s filled too, try moving that item to its other drawer, and so on until you either succeed or get back to a previously seen drawer. In case of success, store the item $i$ in the drawer $B_ i$. In case of failure, continue to next rule.
 - Give up and throw away the item $i$.

For given pairs of drawers for each item, determine which items will be stored and which will be thrown away.

-----Input-----
The first line of input consists of two integers, $N$ and $L$ ($1 \leq N, L \leq 300000$), the number of items and the number of drawers.

Each of the following $N$ lines contains two integers: $A_ i$ and $B_ i$ ($1 \leq A_ i, B_ i \leq L$), the pair of drawers corresponding to item $i$. The numbers $A_ i$ and $B_ i$ will be different.

-----Output-----
For each item, respectively, output where it ends up. In case the item is stored successfully, output “LADICA” (without quotes, Croatian word for drawer). In case the item is thrown away, output “SMECE” (without quotes, Croatian word for trash).

-----Examples-----
Sample Input:
5 3
1 2
1 3
1 2
1 3
1 2
Sample Output:
LADICA
LADICA
LADICA
SMECE
SMECE
user: Jimmy and his friends were all standing in a lineup for ice cream when a huge gust blew them all around. The friends want to keep things fair and make sure everyone gets their ice cream in the order they started with. The friends do not remember the order, but each of them remember exactly how many people were between them and Jimmy. Jimmy is always the first person in line. Can you help him and his friends remember the order?

-----Input-----
The first line contains a single integer $n$ ($1 \leq n \leq 100$), the number of people in the line.

The second line contains $n-1$ space separated integers, where $d_ i$ ($0 \leq d_ i \leq n-2$) is the number of people between the $(i+1)^\textrm {th}$ person and Jimmy.

Jimmy is always first in the lineup.

-----Output-----
Print a single line with $n$ integers, the people in the order of the original lineup. It is guaranteed that there is always a unique solution.

-----Examples-----
Sample Input:
2
0
Sample Output:
1 2
user: It was time for the 7th Nordic Cinema Popcorn Convention, and this year the manager Ian had a brilliant idea. In addition to the traditional film program, there would be a surprise room where a small group of people could stream a random movie from a large collection, while enjoying popcorn and martinis. 

However, it turned out that some people were extremely disappointed, because they got to see movies like Ghosts of Mars, which instead caused them to tear out their hair in despair and horror.

To avoid this problem for the next convention, Ian has come up with a solution, but he needs your help to implement it. When the group enters the surprise room, they will type in a list of movies in a computer. This is the so-called horror list, which consists of bad movies that no one in the group would ever like to see. Of course, this list varies from group to group.

You also have access to the database Awesome Comparison of Movies which tells you which movies are directly similar to which. You can assume that movies that are similar to bad movies will be almost as bad. More specificly, we define the Horror index as follows:\[ HI = \left\{ \begin{array}{ll} 0 & \textrm{if movie is on horror list. This overrides the other definitions.} \\ Q+1 & \textrm{if the worst directly similar movie has $HI = Q$} \\ +\infty & \textrm{if not similar at all to a horrible movie} \end{array} \right. \]

-----Input-----
The first line of input contains three positive integers $N$, $H$, $L$ ($1 \leq H < N \leq 1000,0 \leq L \leq 10000$), where $N$ is the number of movies (represented by IDs, ranging from $0$ to $N-1$), $H$ is the number of movies on the horror list and $L$ is the number of similarities in the database.

The second line contains $H$ unique space-separated integers $x_ i$ ($0 \leq x_ i <N$) denoting the ID of the movies on the horror list.

The following $L$ lines contains two space-separated integers $a_ i,b_ i$ ($0 \leq a_ i < b_ i < N$), denoting that movie with ID $a_ i$ is similar to movie with ID $b_ i$ (and vice versa).

-----Output-----
Output the ID of the movie in the collection with the highest Horror Index. In case of a tie, output the movie with the lowest ID.

-----Examples-----
Sample Input:
6 3 5
0 5 2
0 1
1 2
4 5
3 5
0 2
Sample Output:
1
user: Iceland is famous for its geothermal activity, which supplies the country with much of its electricity and heating. It is also a source of pleasure, in the form of hot springs. 

Kalle is visiting one of Iceland’s famous hot springs. It contains $n$ pools of water, where the $i$th one has temperature $t_ i$. Although staying in one of the warmer pools for a long time sure is relaxing, Kalle is on a very tight schedule and just wants a quick dip in each of the pools. As you may know, the nicest thing about hot baths is the contrast between hot and cold. Therefore, to get the most out of his stay, Kalle wants to find an ordering of the pools so that the difference in temperature between subsequent pools is increasing.

Given a sequence of pool temperatures $t_1, t_2, \dots , t_ n$, rearrange them into a new sequence $t’_1, t’_2, \dots , t’_ n$ such that for all $2 \leq i \leq n-1$ it holds that\[ |t’_{i-1} - t’_ i| \leq |t’_ i - t’_{i+1}|. \]

-----Input-----
The input consists of:
 - One line with an integer $n$ ($2 \le n \leq 10^5$), the number of pools.
 - One line with $n$ integers $t_1, \ldots , t_ n$ ($-10^5\leq t_ i \leq 10^5$ for each $i$), the temperatures in each of the $n$ pools.

-----Output-----
Output a rearrangement of the sequence satisfying the given requirement. If no solution exists, output “impossible”. If there are multiple valid solutions, you may output any one of them.

-----Examples-----
Sample Input:
3
1 3 4
Sample Output:
4 3 1
user: Anthony recently started watching YouTube videos with the title “$X$ but every time $Y$ happens it speeds up by $Z$”. He likes watching these videos because it saves time, but he wonders how much time he actually saves by watching these videos (instead of the originals).

You may assume that the new video $X’$ is exactly the same as the original video $X$, except certain segments of the new video play faster. Each time event $Y$ happens, $X’$ speeds up by $p$%. Suppose event $Y$ happens $n$ times in $X’$, and it happens at timestamps $t_1, t_2, \ldots , t_ n$ (in seconds). That means the segment $[0, t_1)$ is playing at original speed, the segment $[t_1, t_2)$ is playing at $(100+p)$% speed, the segment $[t_2, t_3)$ is playing at $(100+2p)$% speed, and so on. Also, $X’$ is $k$ seconds long.

Can you help Anthony compute the original length of the video?

-----Input-----
The first line of the input contains three integers $n, p, k$. It is guaranteed that $1\leq n\leq 5000$, $0\leq p\leq 100$, and $n\leq k\leq 20000$.

The next line of the input contains $n$ integers $t_ i$, denoting the timestamp of the event $Y$. It is guaranteed that the timestamps are given in chronological order, and that $1\leq t_ i\leq k$.

-----Output-----
A single number $T$ denoting the length of the original video in seconds. Your answer is considered correct if its absolute or relative error is at most $10^{-6}$.

-----Examples-----
Sample Input:
2 20 15
3 10
Sample Output:
18.400
user: Anyone knows that the best place to learn the art of espionage is at the Manhattan Academy of Private Spies (MAPS). Scattered across Manhattan are a number of safe houses, which are used by MAPS when conducting drills. During a drill, each spy-in-training is required to travel from their current location to the nearest safe house. If there are multiple safe houses that are nearest to their current location, then it does not matter which safe house that spy chooses to travel to. Each safe house is large enough to accommodate any number of spies.

Manhattan is modeled as a grid of city blocks. Initially (before any drill), each block may contain a single safe house or a single spy, but not both. The distance between two city blocks is measured using Manhattan distance, also known as taxicab distance. Formally, the Manhattan distance between two locations is the sum of the absolute value of their vertical difference and the absolute value of their horizontal difference.

What is the maximum Manhattan distance that any spy has to travel to reach the nearest safe house?

-----Input-----
The first line of input contains an integer, $N$, where $2\leq N\leq 100$, denoting the width and height of the grid. Each of the next $N$ lines contain $N$ characters, with each character denoting a city block. A spy is represented by an ‘S’ character, a safe house is represented by an ‘H’ character, and the remaining city blocks in the grid are represented by ‘.’ (period) characters. There is at least one spy and at least one safe house.

-----Output-----
Output an integer indicating the maximum Manhattan distance that any spy has to travel in order to reach the nearest safe house.

-----Examples-----
Sample Input:
5
....H
.....
S....
....H
.....
Sample Output:
5
user: As you know, a kayaking competition is going on as we speak. Unfortunately strong winds have damaged a few kayaks, and the race starts in 5 minutes!. Fortunately, some teams have brought reserve kayaks. Since kayaks are bulky and hard to carry, teams are willing to lend kayaks to opposing teams if and only if they are starting immediately next to them. For example, team with the starting number 4 will lend its reserve kayak only to teams 3 and 5. Of course if some team did bring a reserve and its kayak was damaged, they will use it themselves and not lend it to anyone.

You as the organizer now need to know, what is the minimal number of teams that cannot start the race, not even in borrowed kayaks.

-----Input-----
The first line of input contains three integers $N$, $(2 \le N \le 10)$, total number of teams, $S$, $(2 \le S \le N)$, number of teams with damaged kayaks and $R$, $(1 \le R \le N)$, number of teams with reserve kayaks.

The second line contains exactly $S$ numbers, the starting numbers of teams with damaged kayaks. The second line will not contain duplicates.

The third line contains exactly $R$ numbers, the starting numbers of teams with reserve kayaks. The third line will not contain duplicates.

-----Output-----
The first and only line of output should contain the smallest number of teams that cannot start the competition.

-----Examples-----
Sample Input:
5 2 3
2 4
1 3 5
Sample Output:
0
user: George has bought a pizza. George loves cheese. George thinks the pizza does not have enough cheese. George gets angry.

George’s pizza is round, and has a radius of $R$ cm. The outermost $C$ cm is crust, and does not have cheese. What percent of George’s pizza has cheese?

-----Input-----
The input consists of a single line with two space separated integers, $R$ and $C$.

-----Output-----
Output the percentage of the pizza that has cheese. Your answer must have an absolute or relative error of at most $10^{-6}$.

-----Limits-----
 - $1 \leq C \leq R \leq 100$

-----Examples-----
Sample Input:
1 1
Sample Output:
0.000000000
user: Frosh commencing their studies at Waterloo have diverse interests, as evidenced by their desire to take various combinations of courses from among those available.

University administrators are uncomfortable with this situation, and therefore wish to offer a conformity prize to frosh who choose one of the most popular combinations of courses. How many frosh will win the prize?

-----Input-----
The input begins with an integer $1 \leq n \leq 10000$, the number of frosh. For each frosh, a line follows containing the course numbers of five distinct courses selected by the frosh. Each course number is an integer between $100$ and $499$.

-----Output-----
The popularity of a combination is the number of frosh selecting exactly the same combination of courses. A combination of courses is considered most popular if no other combination has higher popularity. Output a single line giving the total number of students taking some combination of courses that is most popular.

-----Examples-----
Sample Input:
3
100 101 102 103 488
100 200 300 101 102
103 102 101 488 100
Sample Output:
2
user: A famous story about the mathematicians G.H. Hardy and Srinivasa Ramanujan goes as follows (as told by Hardy):  I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxicab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. “No”, he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways.” 

It is from this story the taxicab numbers got their name. The $n$’th taxicab numbers is defined to be the smallest number that can be expressed as a sum of two positive cube numbers in $n$ distinct ways.

It turns out that these numbers grows rather quickly. This makes them very hard to compute, which is not very fun. A variation of the concept is to consider what we will call the bus numbers – all the numbers which can expressed as the sum of two positive cube numbers in at least $2$ distinct ways. Note that according to this definition, all taxicab numbers (except the first) are also bus numbers.

Your task is to write a program that generates bus numbers; in particular, the largest bus number that is at most equal to some limit $m$.

-----Input-----
The input consists of:
 - one line with an integer $m$ ($1 \le m \le 400000$), the upper bound of the bus number.

-----Output-----
Output the largest bus number $x$ which does not exceed $m$. If there is no such number, output none.

-----Examples-----
Sample Input:
1730
Sample Output:
1729
user: You are playing the following simple game with a friend:
 - The first player picks a positive integer $X$.
 - The second player gives a list of $k$ positive integers $Y_1, \ldots , Y_ k$ such that $(Y_1+1)(Y_2+1) \cdots (Y_ k+1) = X$, and gets $k$ points.

Write a program that plays the second player.

-----Input-----
The input consists of a single integer $X$ satisfying $10^3 \le X \le 10^9$, giving the number picked by the first player.

-----Output-----
Write a single integer $k$, giving the number of points obtained by the second player, assuming she plays as good as possible.

-----Examples-----
Sample Input:
65536
Sample Output:
16
user: You are given a two dimensional chess board of size $N \times N$ ($1$-based indexing). Some of the cells on this board are ‘.’ denoting an empty cell. Some of the cells on this board are ‘#’ denoting a blocked cell, which you are not allowed to visit. Exactly one of the cells on this board is ‘K’ denoting the initial position of the knight.

A knight at position $(r, c)$ can move to any of the valid positions in set $S$ = $\{ (r + 2, c + 1)$, $(r + 2, c - 1)$, $(r - 2, c + 1)$, $(r - 2, c - 1)$, $(r + 1, c + 2)$, $(r + 1, c - 2)$, $(r - 1, c + 2)$, $(r - 1, c - 2)\} $. Here valid position means that the resulting $(r’, c’)$ should be within the bounds of the chess grid, i.e. $1 \leq r’ \leq N$ and $1 \leq c’ \leq N$.

The question is you have to determine the minimum number of steps required for the Knight to reach cell $(1, 1)$ avoiding cells with ‘#’ in the path.

Note - There will be exactly one ‘K’ in the grid and cell $(1, 1)$ will NOT be a ‘#’.

-----Input-----
The first line contains an integer $N$ ($1 \le N \le 10^2$) denoting the dimension of the chess board. Each of the next $N$ lines contains a string denoting the $i^{th}$ row. The length of these strings will be $N$.

-----Output-----
Print the value of minimum number of steps. However, if $(1, 1)$ is not reachable, print ‘-$1$’ (without the quotes).

-----Examples-----
Sample Input:
4
....
....
....
...K
Sample Output:
2
user: Going to a contest such as NWERC is not all fun and games, there are also some worldly matters to tend to. One of these is to book hotel rooms in time, before all the rooms in town are booked. 

In this problem, you should write a program to search for available rooms in a given hotel. The hotel has $r$ rooms, numbered from $1$ to $r$, and you will be given a list describing which of these rooms are already booked.

-----Input-----
The input consists of:
 - one line with two integers $r$ and $n$ ($1\leq r \leq 100$, $0 \leq n \le r$), the number of rooms in the hotel and the number of rooms that are already booked, respectively;
 - $n$ lines, each with an integer between $1$ and $r$ (inclusive), a room number that is already booked;

All $n$ room numbers of the already booked rooms are distinct.

-----Output-----
If there are available rooms, output the room number of any such room. Otherwise, output “too late”.

-----Examples-----
Sample Input:
100 5
42
3
2
99
1
Sample Output:
23
user: A large field has a dog and a gopher. The dog wants to eat the gopher, while the gopher wants to run to safety through one of several gopher holes dug in the surface of the field.

Neither the dog nor the gopher is a math major; however, neither is entirely stupid. The gopher decides on a particular gopher hole and heads for that hole in a straight line at a fixed speed. The dog, which is very good at reading body language, anticipates which hole the gopher has chosen, and heads at double the speed of the gopher to the hole, where it intends to gobble up the gopher. If the dog reaches the hole first, the gopher gets gobbled; otherwise, the gopher escapes.

You have been retained by the gopher to select a hole through which it can escape, if such a hole exists.

-----Input-----
The first line of input contains four real numbers: the $(x,y)$ coordinates of the gopher followed by the $(x,y)$ coordinates of the dog. Subsequent lines of input each contain two real numbers: the $(x,y)$ coordinates of a gopher hole. All coordinates are in metres, with exactly three digits after the decimal point.

There are not more than $1000$ gopher holes and all coordinates are between $-10000$ and $+10000$.

-----Output-----
Your output should consist of a single line. If the gopher can escape the line should read “The gopher can escape through the hole at ($x$,$y$).” identifying the appropriate hole.

Otherwise the output line should read “The gopher cannot escape.” If the gopher may escape through more than one hole, any one will do. If the gopher and dog reach the hole at the same time, the gopher escapes successfully.

-----Examples-----
Sample Input:
1.000 1.000 2.000 2.000
1.500 1.500
Sample Output:
The gopher cannot escape.