meetforever/GRPO_CL huggingface dataset:
user: Last year, some of the judges tried to travel to NWERC’10 by train. This turned into a big disaster: on the way there, a fire in a control room caused huge delays, while on the return trip, trains in Bremen were delayed due to a terrorist threat in Hamburg. Of course, these huge delays caused other delays in the train schedule, so the big question was which trains to take: would it be better to take this slow regional train now, or wait for that intercity train, which has a big chance of being delayed?

This year, the judges have planned ahead and carefully analyzed the train schedule. They even kept track of how often trains were delayed and by how much. Now that they have all this information, they want to travel as quickly possible, minimizing the expected duration of the journey. Can you help them?

For each train connection, the judges know exactly what its scheduled departure time and duration are, as well as the probability that its arrival at the destination will be delayed. You may assume that the probabilities of delays are independent and that the judges can adapt their itinerary as they go, depending on any delays which they might already have incurred. Trains always depart on time, but may arrive late and the judges do not know whether a train’s arrival will be delayed until they have boarded it. It takes judges no time to switch trains, so they can take a connecting train that departs at the same time as they arrive at a place.

The judges can choose the time of their initial departure as they wish and they want to minimize the expected duration1 of their total trip.

-----Input-----
 - one line with the judges’ place of origin and destination, these are different.
 - one line with an integer $n$ ($1 \leq n \leq 1000$): the number of train connections.
 - $n$ lines, each describing a train connection:
 - the origin and destination of this connection, these are different.
 - an integer $m$ ($0\leq m\leq 59$), the departure time in minutes after each full hour.
 - an integer $t$ ($1\leq t\leq 300$), the standard journey time (assuming no delays).
 - an integer $p$ ($0\leq p\leq 100$), the probability of delays as a percentage.
 - an integer $d$ ($1\leq d\leq 120$), the maximum delay in minutes.

All place names are given as strings of upper and lower case alphabetical characters, of length at most 20. If a train is delayed, then the length of the delay will be a whole number of minutes, and will be uniformly distributed in the range $[1,d]$.

-----Output-----
Output a floating point number: the minimum expected duration of the total trip in minutes. This number should be accurate up to $10^{-6}$ relative or absolute precision. Output IMPOSSIBLE instead if the destination is not reachable.

-----Examples-----
Sample Input 1:
Hamburg Bremen
3
Hamburg Bremen 15 68 10 5
Hamburg Bremen 46 55 50 60
Bremen Frankfurt 14 226 10 120
Sample Output 1:
68.3

Sample Input 2:
Amsterdam Rotterdam
1
Amsterdam Utrecht 10 22 5 10
Sample Output 2:
IMPOSSIBLE
user: Alice and Bob are playing Dots and Boxes. The game is played on an $N\times N$ square lattice of dots, and they alternate drawing a line segment between horizontally or vertically adjacent dots that haven’t been connected before. Every time a unit square is formed by four line segments, the player who put down the last segment scores one point for that square. The game ends when the square lattice has been completely filled with line segments, and whoever scored the most points wins.

Alice and Bob aren’t really in a competitive mood today, so they’ve just been playing for fun. Hence they aren’t following any specific game strategy, and, in particular, even if it’s possible to make a move that scores a point or is clearly superior in some way, they won’t necessarily make that move. But now they’ve been playing for a while and neither of them has scored a single point. If neither of them scores a point pretty soon, they may get bored. Given the current state of the game, how many moves could be made, in the worst case, before either Alice or Bob is guaranteed to have scored a point?

-----Input-----
Input starts with a line containing an integer $N$ ($2 \leq N \leq 80$), the size of the square lattice. Then follows an ASCII representation of the current state of the game, $2N-1$ rows high and $2N-1$ columns wide, listed in row-major order. There are cells of four types ($1 \leq i,j \leq N$):
 - Cell $(2i-1,2j-1)$ is ‘*’, representing dot $(i,j)$.
 - Cell $(2i,2j)$ is ‘.’, representing empty space.
 - Cell $(2i,2j-1)$ is ‘|’ if dots $(i,j)$ and $(i+1,j)$ have been connected by a line segment, and ‘.’ otherwise.
 - Cell $(2i-1,2j)$ is ‘-’ if dots $(i,j)$ and $(i,j+1)$ have been connected by a line segment, and ‘.’ otherwise.

It is guaranteed that no player has scored a point, meaning that no unit squares have been formed.

-----Output-----
Output the number of moves that can be made, in the worst case, before either Alice or Bob is guaranteed to have scored a point.

-----Examples-----
Sample Input 1:
3
*-*.*
|.|.|
*.*-*
|...|
*.*.*
Sample Output 1:
3

Sample Input 2:
2
*.*
...
*.*
Sample Output 2:
4
user: In the country of Elecuador, a very strange voting system is used. When it is time for the election, each one of the $n$ citizens will arrive in some order to the voting station. There are only two parties to vote for, conveniently named $1$ and $2$. When arriving to the voting station, a person will vote for one of the parties, unless they are a teller. The tellers do not vote, instead they count how many votes each of the two parties has at the time the teller arrives, and if one of the parties has more votes than the other then that party receives one point (if the two parties have the same number of votes, neither of them receives a point). The party with the most points at the end wins. If both parties end up with the same number of points, chaos ensues.

As the president of Elecuador representing party $1$, you are worried that the coming election will be the end of your reign. Fortunately, you have a plan to stop this from happening. Being the president, you know who everyone in the country will vote for, who the tellers are, and in what order everyone will arrive to the voting station. By making the right phone calls, you can also affect when the tellers arrive. In one move, it is possible to swap a teller with an adjacent person in the list of arrivals to the voting station. Note that it is not possible to swap two adjacent non-tellers. What is the minimum number of swaps necessary to ensure that party $1$ wins?

-----Input-----
The input starts with a line containing an integer $n$ $n$ ($1 \le n \le 5000$), the number of citizens in Elecuador. Then follows a line containing a string $s$ of length $n$, consisting of the characters $0$, $1$, and $2$. This string represents the citizens in the order they arrive to the voting station. If the $i$’th character $s_ i$ is $1$ or $2$, it means that the $i$’th citizen will vote for party $1$ or $2$, respectively. If $s_ i$ is $0$, it means that the $i$’th citizen is a teller.

-----Output-----
If it is possible to ensure victory, output one integer, the minimum number of swaps necessary. Otherwise, output “impossible”.

-----Examples-----
Sample Input 1:
8
12210020
Sample Output 1:
4

Sample Input 2:
4
1111
Sample Output 2:
impossible
user: Buffalo Bill wishes to cross a $1000 \times 1000$ square field. A number of snakes are on the field at various positions, and each snake can strike a particular distance in any direction. Can Bill make the trip without being bitten?

Assume that the southwest corner of the field is at $(0,0)$ and the northwest corner at $(0,1000)$. Bill must enter the field somewhere between the southwest and northwest corner and must leave somewhere between the southeast and northeast corners.

-----Input-----
The input consists of a line containing $0 \le n \le 1000$, the number of snakes. A line follows for each snake, containing three integers: the $(x,y)$ location of the snake ($0 \le x, y \le 1000$) and its strike distance $1 \le d \le 1000$. The snake will bite anything that passes strictly closer than this distance from its location.

-----Output-----
If Bill can complete the trip, give coordinates with exactly two decimal digits at which he may enter and leave the field. Use the format shown in the sample input. If Bill may enter and leave at several places, give the most northerly. If there is no such pair of positions, print “Bill will be bitten.”

-----Examples-----
Sample Input 1:
3
500 500 499
0 0 999
1000 1000 200
Sample Output 1:
Bill enters at (0.00, 1000.00) and leaves at (1000.00, 800.00).

Sample Input 2:
4
250 250 300
750 250 300
250 750 300
750 750 300
Sample Output 2:
Bill will be bitten.
user: Sweet Apple Acres has been infested by evil fruit-hungry bats! The Apple family has called for Twilight Sparkle’s help to get rid of them.

Twilight needs to use a powerful spell to eliminate the threat the bats pose. Poring through the volumes of magic books, she found an ancient spell by the legendary Star Swirl the Bearded that, if executed, can increase her power enough to drive the bats out.

This spell has $M$ steps, which must be performed in order. Each step is either:
 - a + step, which adds $1$ to the power of the caster, or
 - a x step, which multiplies the power of the caster by $2$.

Twilight starts with power $1$.

Unfortunately, since Twilight is not very strong, the power that she can actually discharge is limited by her strength $S$. If she has power $p$, the amount of power she can discharge is equal to the remainder after dividing $p$ by $2^S$.

It is therefore clear that the amount of power she has is not necessarily equal to the amount of power she can actually discharge. She wants to maximize the amount of power she can discharge; to this end, she realized that she can transform some—possibly none, possibly all—of the steps in the spell into no-op o steps, which do not affect her power.

Which steps should she turn into no-op steps to maximize the amount of power she can discharge?

-----Input-----
The first line of input contains two integers, $M$ ($1 \leq M \leq 10^6$) and $S$ ($1 \leq S \leq 10^9$), the number of steps in the spells and Twilight’s strength.

The second line of input contains a string of $M$ characters. In particular, the $i^\text {th}$ of these characters is either + or x, the type of the $i^\text {th}$ step.

-----Output-----
Output on a line by itself the same string with some—possibly none, possibly all—of the characters replaced with o, representing a way of replacing some steps with no-ops that maximizes the amount of power she can discharge.

If there are multiple correct answers, you can output any of them.

-----Examples-----
Sample Input 1:
8 3
++xx+x++
Sample Output 1:
++xx+o++

Sample Input 2:
8 3
xxxxxxxx
Sample Output 2:
xxoooooo
user: Better Documents Inc. is contemplating the next generation of word processors. Now, nearly every word processor includes a Spell Checker. BDI, however, is looking forward to replacing that with a true Typo Checker. We’ve all been caught, after relying on a spell checker, by typing mistakes (“typos”) that just happen to wind up as a correctly spelled word, just not the word we intended. BDI hopes to use AI to determine when a word’s context suggests that it is out of place and probably should have been a different, but similarly spelled, word.

As a first step in this process, they want to see how common such similar words really are in ordinary text. Write a program to read in paragraphs of text and to produce a list of similarly spelled words occurring in that text.

For the purpose of this program, a word is any maximal string of non-whitespace characters containing at least one alphabetic character. Whitespace can be either blanks or line terminators (“\r” or “\n”). The core of a word is what you have left after removing any non-alphabetic characters and replacing any upper-case alphabetic characters to their lower-case equivalents.

Two words are considered to be similarly spelled if the core of one word can be converted to the core of the other word by a single application of any one of the following transformations:
 - Delete a single character.
 - Insert a single alphabetic character.
 - Replace a single character by a different alphabetic character.
 - Transpose (exchange) any two adjacent characters.

-----Input-----
Input consists of $1$ to $100$ lines of text, followed by an end of input marker in the form of a line containing only the string “***”.

Each line of text will contain $0$ to $80$ ASCII characters (not counting line terminators).

-----Output-----
For each word core in the text that has one or more similarly spelled words, print a line consisting of
 - That word core
 - A colon (“:”) followed by a blank
 - A list of all similarly spelled word cores (with no duplicates and not containing the core to the left of the colons), in alphabetic order, separated by single spaces.

The lines printed should be in alphabetic order of the word cores to the left of the colon.

If there are no similarly spelled words in the input, print a single line containing the string “***”.

-----Examples-----
Sample Input 1:
Lost is Close to Lose

"Better Documents Inc. wants to add Typo Checking in to the
next generation of word processors," he said.
***
Sample Output 1:
close: lose
he: the
in: inc is
inc: in
is: in
lose: close lost
lost: lose
the: he

Sample Input 2:
The fox said, "When?"
"Not till 12 o'clock", replied the hen.
"That clock is stopped, it will never strike.", he said.
***
Sample Output 2:
clock: oclock
he: hen the
hen: he when
is: it
it: is
oclock: clock
the: he
till: will
when: hen
will: till
user: The most common technique for shuffling a deck of cards is called the Riffle or Dovetail shuffle. The deck is split into two stacks, which are then interleaved with each other. The deck can be split anywhere, and the two stacks can be interleaved in any way.

For example, consider a deck with 10 unique cards:

1 2 3 4 5 6 7 8 9 10

Split them somewhere

1 2 3 4 5 6       7 8 9 10  

And interleave them in some way:

1 2    7   3   8 9    4 5   10   6  

Do it again. Split them somewhere:

1 2 7        3 8 9 4 5 10 6  

And interleave them in some way:

3 8    1   9 4 5    2 7   10 6  

This is one possible ordering after $2$ shuffles. Suppose there are $n$ unique cards, and that they start out perfectly ordered: $1, 2, 3, ..., n$. Given an ordering of the deck, what is the smallest number of shuffles that could possibly put the deck in that order?

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will begin with a single integer $n$ ($1 \le n \le 1000000$) indicating the number of cards in the deck. On the next line will be $n$ unique integers $c$ ($1 \le c \le n$), with a single space between them, indicating an ordering of the $n$ cards. The values $c$ are guaranteed to be a permutation of the numbers $1 \ldots n$.

-----Output-----
Output a single line with a single integer indicating the minimum number of shuffles that could possibly put the deck in the given order.

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

Sample Input 2:
10
3 8 1 9 4 5 2 7 10 6
Sample Output 2:
2
user: Every (positive) rational number can be expressed as a ratio of two (positive) integers. However, in decimal form, rational numbers often have an infinitely repeating pattern, e.g., $1/7 = 0.142857142857142857$... A convenient way of writing this repeating pattern is to put a bar over the first occurrence of the repeating part, so $1/7$ would be written:\[ 0.\overline{142857}. \]

Given a rational number consisting of a series of digits, followed by a decimal point, followed by more digits, and then a number indicating how many of the rightmost digits repeat (i.e., the number of digits under the bar), your task is to find the ratio of two integers, in the most reduced form, that represent the same rational number. For example, for the input “$0.142857$ $6$” you should find $1/7$.

-----Input-----
The input will be a single line with two numbers separated by one space. The first number will consist of $1$ to $3$ digits ($0$–$9$), followed by a decimal point, followed by $1$ to $11$ digits ($0$–$9$), representing the decimal form of the number, possibly with leading zeros. The second number will be a positive integer indicating how many of the rightmost digits of the preceding number repeat. The first number will always be greater than $0$. The second number will never be less than $1$ nor larger than the number of digits to the right of the decimal point.

-----Output-----
Print the corresponding fraction in its most reduced form, that is, the fraction with the smallest possible integer values in the numerator and denominator.

-----Examples-----
Sample Input 1:
0.142857 6
Sample Output 1:
1/7

Sample Input 2:
1.6 1
Sample Output 2:
5/3
user: A $10 \times 10 \times 10$ three-dimensional grid of tightly packed cubic atomic energy cells aboard the starship Fiugtuwf is reporting failures on several of its cells. The ship’s engineer must set up enclosures that will contain all of the cells that are reported to be failing, in order to avoid a meltdown. It is imperative that the enclosures be finished in the shortest amount of time, even if that requires some healthy cells to be enclosed along with the defective ones. The enclosures are formed by square panels which fit perfectly between adjacent cells, or can be placed along the sides of the cells on the edges of the grid. Each panel is exactly the size and shape of a face of one of the cubic cells. For full containment, each enclosure must be completely closed. Given the coordinates of each defective cell, report the minimum number of panels required to contain the problem.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will start with a line with a single integer $n$ ($0 \le n \le 1000$) indicating the number of defective cells. Each of the next $n$ lines will hold an $(x,y,z)$ coordinate ($0 \le x,y,z \le 9$) indicating the location in the grid of a defective cell. All of the coordinates in a test case will be unique.

-----Output-----
Output a single line with a single integer, indicating the minimum number of panels required to contain the defective cells.

-----Examples-----
Sample Input 1:
1
0 0 0
Sample Output 1:
6

Sample Input 2:
2
0 0 0
0 0 1
Sample Output 2:
10
user: You are given a hexagonal grid with $n$ rows, where $n$ is an odd integer. The rows are numbered $1$ to $n$ from top to bottom. The odd-numbered rows have exactly $n$ hexagons, and the even-numbered rows have exactly $n-1$ hexagons. Let’s denote the $j$-th hexagon in the $i$-th row by $(i, j)$.

For example, the below figure shows a hexagonal grid with $n = 3$.

Let’s assign an integer between $-1$ and $6$ to each hexagon. Let’s $a_{i, j}$ be the integer assigned to the hexagon $(i, j)$. The following figure shows one example assignment:

Let’s color some edges of some hexagons. A coloring is valid iff it satisfies the following conditions:
 - For every pair of valid indices $i$ and $j$, either $a_{i, j} = -1$, or $a_{i, j}$ is equal to the number of colored edges of the hexagon $(i, j)$.
 - The colored edges form one or more loops. Each loop must not self-intersect. Two different loops must not share any vertices or edges.

The following figure shows a valid coloring:

The following two figures show two invalid colorings. The one on the left does not satisfy the $1$st condition, and the one on the right does not satisfy the $2$nd condition.

How many valid colorings are there?

-----Input-----
The first line of the input contains a single integer $n$ ($n$ is an odd integer between $1$ and $7$). The next $n$ lines contain the numbers $a_{i, j}$ $(-1 \le a_{i, j} \le 6)$. The $i$-th line contains exactly $n$ integers if $i$ is odd, and $n-1$ integers otherwise.

-----Output-----
Print a single integer — the number of valid colorings.

-----Explanation of the sample input-----
The first sample was shown in the above figures.

The second example is shown below:

-----Examples-----
Sample Input 1:
3
-1 2 -1
2 2
1 -1 1
Sample Output 1:
1

Sample Input 2:
7
-1 4 5 1 0 -1 -1
-1 3 2 0 0 1
-1 4 -1 1 0 -1 -1
1 3 4 2 2 4
0 2 3 -1 4 4 2
-1 4 4 3 3 2
1 -1 -1 -1 4 2 -1
Sample Output 2:
1
user: As you might know, the memory in current computers consists of a sequence of bits and each of these bits can be in two possible states. Megan’s company has now developed a great new memory unit where every bit has three possible states. This would all be great, if it wasn’t for Megan’s boss. The boss wants her to write a program for this memory unit for integer operations, but instead of using ternary base (i.e., base 3), Megan’s boss decided that the bits should be interpreted as a binary number, with the exception that the digit 2 is allowed as well. 

For example, $201$ in this strange representation is $2\cdot 2^2+0\cdot 2^1+ 1\cdot 2^0=9$. Some numbers are shorter in this representation, but for other numbers it doesn’t help at all – for instance, $15$ is $1111$ in binary and this is the only way of writing it in the new representation as well.

It seems that there is nothing else that Megan can do to convince her boss. Since she likes math, she started wondering about different representations of the same number. For example 9 has three representations: $201, 121$ and $1001$. Can you help her figure out how many representations a given number has?

-----Input-----
The first and only line of the input contains a string consisting of ’0’ and ’1’. The string represents a non-negative integer $N$ in binary. The leftmost bit is the most significant one. The number of bits will be at least $1$ and at most $10000$.

-----Output-----
Output a line giving the number of different binary representations of $N$ that also use $2$ as a digit. Since this number might be big, output the remainder modulo $1000000009$.

-----Examples-----
Sample Input 1:
1001
Sample Output 1:
3

Sample Input 2:
1111
Sample Output 2:
1
user: In the USA, a type of dance called square dance is very popular. Four dancing pairs stand as to form a square. A caller then gives a series of moves that the dancers should perform, moving around on the floor.

American wizards, however, find square dancing a bit simplistic. Instead, they have come up with a kind of dance called circle dancing. In the dance, $N$ wizards stand in a circle numbered $1$ through $N$ clockwise. A caller then gives a series of moves that the dancers should perform, moving around on the floor. Each such move has the following form. Every wizard is given a number $p_ i$. They then all teleport simultaneously $p_ i$ positions clockwise or counterclockwise in the ring. For example, given the number 1 they should move to one of the two places immediately adjacent to their current position.

After a move is performed, no two wizards may occupy the same position. This means a certain amount of coordination is required when teleporting. Can you tell the wizards how they should teleport in order to not collide with each other?

-----Input-----
The first line of input contains a single integer $N$ ($1 \le N \le 300000$), the number of wizards. The next line contains the $N$ integers $p_1, p_2, \dots , p_ N$ ($0 \le p_ i < N$). The wizards are numbered $1, 2, \dots , N$ clockwise in the circle.

-----Output-----
Output a string with $N$ characters. The $i$’th character should be L if the $i$’th wizard should teleport clockwise, and R if he should teleport counterclockwise. If there are multiple valid solutions, output the lexicographically smallest one. If there is no valid solution, output no dance.

-----Examples-----
Sample Input 1:
3
1 1 1
Sample Output 1:
LLL

Sample Input 2:
5
1 2 2 1 2
Sample Output 2:
LLRLR