meetforever/GRPO_CL huggingface dataset:
user: Pasijans, patience, or solitaire is the name for a group of single player card games. One new such game, so new it has no name, is played with cards sporting random integers as values. The game starts by shuffling all cards and distributing them in $N$ sequences, not necessarily of equal length.

During each turn, the player can remove the first card in any sequence and place it at the end of the “Solution sequence”. The card that was second in the selected sequence now becomes the first and the turn ends. Of course once the card is in the “Solution sequence” it cannot be removed, replaced or altered in any way. So don’t even try.

The game ends when all cards are in the “Solution sequence”. The object of the game is to construct the best possible “Solution sequence”. One sequence is better than the other if for the first cards they differ, lets call them $X$ and $Y$, the value on the card $X$ is smaller than the value on the card $Y$.

Write a program that finds the best possible “Solution sequence”.

-----Input-----
The first line contains one integer $N$ ($1 \leq N \leq 1000$), the number of starting sequences.

The next $N$ lines contain descriptions of input sequences. Each line starts with an integer $L$ ($1 \leq L \leq 1000$), the length of the sequence. It is followed by $L$ positive integers, each at most $100000000$.

-----Output-----
One line containing $\sum L$ numbers, the best possible “Solution sequence” obtainable.

-----Examples-----
Sample Input 1:
3
1 2
1 100
1 1
Sample Output 1:
1 2 100

Sample Input 2:
2
5 10 20 30 40 50
2 28 27
Sample Output 2:
10 20 28 27 30 40 50
user: Black Vienna is a puzzle game where players try to deduce the secret identities of the three spies. There are $26$ suspects, represented by cards with a single letter from ‘A’ to ‘Z’. Suspect cards are shuffled and three are secretly set aside; these form the Black Vienna circle. The remaining $23$ cards are distributed between the two players. Note that players will necessarily get a different number of cards; one player may even get all $23$ cards while the other gets none.

The objective of the puzzle is to deduce which of the suspects are in the Black Vienna circle using player’s replies to investigations; each investigation consists of a pair of suspects and the player’s reply is the number of those suspects that are in his/her hand. Using several investigations it is possible to narrow which suspects can be in the Black Vienna circle (i.e., those that are not in any of the player’s hands).

-----Task-----
Write a program that reads a sequence of investigation replies and counts the number of admissible solutions, i.e. possible sets of three suspects representing the members of the Black Vienna circle. Note that it is possible that the player’s replies are inconsistent and therefore that the puzzle has no solution.

-----Input-----
The input consists of a line with the number $N$ of investigations followed by $N$ lines; each line consists of a sequence of two distinct letters (from ‘A’ to ‘Z’), a player number ($1$ or $2$) and a reply (an integer from $0$ to $2$).

-----Constraints-----
$0 \leq N \leq 50$ Number of investigations.

-----Output-----
The output is the number of distinct admissible solutions, i.e. sets of three members of the Black Vienna circle.

-----Examples-----
Sample Input 1:
0
Sample Output 1:
2600

Sample Input 2:
3
AB 1 1
AC 2 1
BC 2 1
Sample Output 2:
506
user: A bracket sequence consisting of ‘(’ and ‘)’ is defined to be valid as follows: 
 - An empty sequence is valid.
 - If $X$ is a valid bracket sequence, then $(X)$ is a valid bracket sequence.
 - If $X$ and $Y$ are valid bracket sequences, then the concatenation of $X$ and $Y$, $Z=XY$, is a valid bracket sequence.

For example, “(())”, “()()”, and “(()())()” are all valid bracket sequences, while “(” and “())” are invalid bracket sequences.

You get a bracket sequence from the professor of length $n$. However, it might not be valid at the moment. The professor asks you to check if it is possible to make the sequence valid by performing at most one segment inversion operation. That is, you may choose two 1-based indices $l$ and $r$ ($1~ \leq ~ l~ \leq ~ r~ \leq ~ n$) and invert each bracket with an index in the closed interval $[l,r]$. After the inversion, a left bracket ‘(’ becomes a right bracket ‘)’, and a right bracket ‘)’ becomes a left bracket ‘(’.

You can make “())(” valid by inverting the segment $[3,4]$. You can make “()))” valid by inverting the segment $[3,3]$, or alternatively by inverting the segment $[2,2]$. However, there does not exist a segment you can invert to make “)))(” valid.

-----Input-----
The input consists of one line containing between $1$ and $5000$ brackets.

-----Output-----
Output “possible” if you can make the bracket sequence valid by performing at most one segment inversion, or “impossible” otherwise.

-----Examples-----
Sample Input 1:
()))
Sample Output 1:
possible

Sample Input 2:
)))(
Sample Output 2:
impossible
user: In the free-market, ruthlessly capitalist world of train fares, only one thing matters: incentives.

Train companies are incentivised with bonuses for high throughput, successful journeys, and customer satisfaction. Conversely, the companies are disincentivised from failure via mandatory refunds for customers delayed by $30$ minutes or more.

Being a ruthless capitalist yourself, you have decided to take advantage of this generous delay compensation provision.

The refund is awarded provided that no matter the combination of trains you had taken (provided they followed the same route of stations as planned), you would still be unable to reach your destination in strictly less time than $30$ minutes (or $1800$ seconds), of the time you would have arrived assuming your booked journey was exactly on time.

Armed with your printout of the day’s delays, and the original timetable, you must ask yourself only one question: what is the earliest time you can book a train for from station $1$, in order to earn this restitutive reward?

-----Input-----
 - One line containing two integers: $N$ ($1 \le N \le 100$), the number of stations, and $M$ ($1 \le M \le 10^5$), the number of scheduled trains.
 - The next $M$ lines each contain 4 integers:
 - $X$, the starting station ($1 \le X \le N-1$),
 - $S$ and $T$ ($0 \le S \le T < 86400$), the planned departure and arrival times in seconds,
 - and $L$ ($0 \le L < 86400$), the duration by which the train’s departure and arrival times are delayed.

Stations are numbered from $1$ to $N$ in the order you will visit them. Each train goes between stations $X$ and $X+1$. It is possible to change between trains instantanesouly.

-----Output-----
 - One line containing one integer: the start time of the earliest train journey you could book in order to earn your compensation, or impossible if no such journey is possible.

-----Examples-----
Sample Input 1:
2 3
1 1800 9000 1800
1 2000 9200 1600
1 2200 9400 1400
Sample Output 1:
1800

Sample Input 2:
2 2
1 1800 3600 1800
1 1900 3600 1600
Sample Output 2:
impossible
user: In a tournament with $m$ teams, each team consisting of $n$ players, construct a playing schedule so that each player is paired up against all players in all teams except their own. That is, each player should play $(m-1) \cdot n$ games. 

The playing schedule should be divided into rounds. A player can play at most one game per round. If a player does not play a game in a round, that player is said to have a bye in that round.

Your task is to write a program that constructs a playing schedule so that no player has a bye in more than $1$ round. In other words, the total number of rounds in the playing schedule should be no more than $(m-1) \cdot n + 1$.

The order of the rounds and games, and who is home and away in a game, does not matter.

-----Input-----
The input consists of a single line with two integers $n$ and $m$ ($1 \le n \le 25$, $2 \le m \le 25$, $n \cdot m \le 100$), the number of players in a team and the total number of teams, respectively.

-----Output-----
Output one line per round in the playing schedule. Each line should contain a space separated list of games. A game is in the format “<player>-<player>”. The players in the first team are denoted as $\texttt{A}1, \texttt{A}2, ..., \texttt{A}n$; the second team $\texttt{B}1, \texttt{B}2, \ldots \texttt{B}n$ and so on.

-----Examples-----
Sample Input 1:
3 2
Sample Output 1:
A1-B2 B1-A2 A3-B3
A2-B3 B2-A3 A1-B1
A3-B1 B3-A1 A2-B2

Sample Input 2:
2 3
Sample Output 2:
A1-B1 A2-C2 B2-C1
A1-C1 A2-B1 B2-C2
A1-B2 A2-C1 B1-C2
A1-C2 A2-B2 B1-C1
user: Mirko has bought an apartment and wants to invite to dinner as many people as possible to celebrate with him. For this he needs a large rectangular wooden table for which he will sit down with his guests. The number of people a table can accommodate is equal to its perimeter (the sum of the lengths of all four sides). Mirko wants to buy a table such that it fits in his apartment and that as many people as possible can sit down with him for dinner. The table must be placed so that its edges are parallel to the edges of the apartment.

Given the layout of the apartment, find the number of people Mirko can invite to dinner.

-----Input-----
The first line contains two integers $R$ and $C$ ($1 \leq R, S \leq 1000$), the dimensions of the apartment. Each of the following $R$ rows contains exactly $S$ characters (without spaces), whether a square is free (‘.’) or blocked (‘X’).

Mirko can put his table only in free squares.

-----Output-----
Output the number of guests Mirko can invite to dinner after he buys his table on a single line.

-----Examples-----
Sample Input 1:
2 2
..
..
Sample Output 1:
7

Sample Input 2:
4 4
X.XX
X..X
..X.
..XX
Sample Output 2:
9
user: Consider an infinite chessboard and a special knight whose move types can change given power-ups. The knight is trying to reach square $(0, 0)$.

Some of the squares of the infinite chessboard have tarot cards on them. If the knight lands on some position $(r, c)$ on the infinite chessboard with a tarot card on it, then the knight has the option of buying that card at that position. Each tarot card will have a price, and will have two integer values written on it. The tarot card with values $a$ and $b$ written on it allow the knight to make relative jumps:$(-a, -b)\qquad (a, -b)\qquad (-a, b)\qquad (a, b)\qquad (b, a)\qquad (-b, a)\qquad (b, -a)\qquad (-b, -a)$

The knight retains all cards he purchases and can make relative moves from any of the cards he owns any number of times. The knight must only pay when obtaining cards and can perform jumps at no additional cost. For example, if he buys a card with $3$ and $2$ and another card with $8$ and $4$, he may jump by $(-2, 3)$, and from there jump by $(8, 4)$, and later jump by $(-3, 2)$. Of course, he cannot make a jump $(a,b)$ until after he arrives at a square with a tarot card with $a$ and $b$ on it, and purchases that card.

Given positions of the tarot cards on the board and their prices, find the least amount that the knight must pay to reach square $(0, 0)$.

-----Input-----
Each test case will begin with a line containing a single integer $n$ ($1\! \le \! n\! \le \! 1000$), which is the number of tarot cards on the chessboard.

Each of the next $n$ lines contains a description of a tarot card in five space-separated integers:$r$ $c$ $a$ $b$ $p$

($-10^9\! \le \! r, c\! \le \! 10^9, 1\! \le \! a, b, p\! \le \! 10^9$), where $(r,c)$ is the location of the tarot card, $a$ and $b$ are the offset values, and $p$ is the price of the card.

The first tarot card is the initial position of the knight. Multiple tarot cards may exist at the same location. The knight must have a tarot card to move.

-----Output-----
Output a single integer, which is the minimum cost for the knight to reach the goal at $(0,0)$. Output $-1$ if it is not possible to reach the goal.

-----Examples-----
Sample Input 1:
2
3 3 2 2 100
1 1 1 1 500
Sample Output 1:
600

Sample Input 2:
2
2 0 2 1 100
6 0 8 1 1
Sample Output 2:
100
user: Mr. Krabs is a hardcore cryptocurrency and blockchain technology enthusiast. In a recent conference, he heard about a new cryptocurrency called ByteConn333ct, which promises a very high rate of return. He wants to invest in this cryptocurrency, but its unique conversion rate to Canadian dollars makes him a bit apprehensive.

Several steps are need to compute the value of $B$ ByteConn333ct dollars (guaranteed to be an integer) in Canadian dollars. First, treat $B$ as a string consisting of only digits. Next, define a subset $S$ of characters from $B$ “valid” iff the characters in $S$ can be concatenated together in some way to form a number with no leading zeros that is also divisible by $3$. Finally, the converted value in Canadian dollars is the number of “valid” subsets modulo $10^9 + 7$.

Since Mr. Krabs is already so rich from his successful fast food restaurant business, he has decided to dump all of his life’s saving into investing ByteConn333ct. Mr. Krabs can’t wait to find out what amazing returns he will get, so he has hire you to compute the value of $S$ ByteConn333ct dollars in Canadian dollars so that he celebrate in advance this amazing investment he has made.

-----Input-----
The first line of the input contains a single integer $1\leq N\leq 200000$. The second line of the input contains a single $N$-digit non-negative integer $S$ without leading zeros.

-----Output-----
Output the value of $S$ByteConn333ct dollars in Canadian dollars (i.e. the number of valid subsets of $S$ modulo $10^9 + 7$).

-----Examples-----
Sample Input 1:
3
361
Sample Output 1:
3

Sample Input 2:
2
11
Sample Output 2:
0
user: Tony is going on a road trip. Because gas is so expensive, Tony wants to carefully choose the gas stations he refuels at to save as much money as possible.

For simplicity, assume Tony is driving on a straight road from left to right. There are $n$ gas stations along the road, where each gas station is uniquely identified by its distance to the right of the origin (Tony’s initial position). The cost per gallon of gas may be different at different gas stations. Finally, one gallon of gas allows Tony’s car to travel one kilometer.

When Tony reaches a gas station, he may refuel his car to any amount, as long as the total amount of fuel in his car doesn’t exceed the car’s fuel tank capacity $g$.

Assuming Tony has a full tank initially, what is the minimum cost to travel to the rightmost gas station?

-----Input-----
The first line of the input contains two integers $n$ and $g$. It is guaranteed that $1\leq n, g\leq 200000$.

The next $n$ lines contains two integers each. The first integer $d_ i$ is the distance of the gas station to the right of the origin (in kilometers). The second integer $c_ i$ is the cost per gallon of gas. It is guaranteed that $1\leq d_ i\leq 4\cdot 10^{10}$, $1\leq c_ i\leq 10^9$, and that no two gas stations are located at the same point.

-----Output-----
If it is possible for Tony to complete his trip without running out of gas, print a single integer $C$, the minimum cost to complete the trip. Otherwise, print “cancel road trip” (without quotes).

-----Examples-----
Sample Input 1:
3 10
2 100
1 10
11 5
Sample Output 1:
10

Sample Input 2:
3 10
2 100
1 10
13 5
Sample Output 2:
cancel road trip
user: The grand museum has just announced a large exhibit on jewelry from around the world. In the hopes of his potential future prosperity, the world-renowned thief and master criminal Edward Terrenando has decided to attempt the magnum opus of his career in thievery.

Edward is hoping to purloin a large number of jewels from the exhibit at the grand museum. But alas! He must be careful with which jewels to appropriate in order to maximize the total value of jewels stolen.

Edward has $k$ knapsacks of size $1$, $2$, $3$, up to $k$, and would like to know for each the maximum sum of values of jewels that can be stolen. This way he can properly weigh risk vs. reward when choosing how many jewels to steal. A knapsack of size $s$ can hold items if the sum of sizes of those items is less than or equal to $s$. If you can figure out the best total value of jewels for each size of knapsack, you can help Edward pull off the heist of the century!

-----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 will consist of two space-separated integers $n$ and $k$, where $n$ ($1 \le n \le 1000000$) is the number of jewels in the exhibit, and $k$ ($1 \le k \le 100000$) is the maximum size of knapsack available to Edward. The next $n$ lines each will describe a jewel. Each line will consist of two space-separated integers $s$ and $v$, where $s$ ($1 \le s \le 300$) is the size of the jewel, and $v$ ($1 \le v \le 10^9$) is its value. Each jewel can only be taken once per knapsack, but each knapsack is an independent problem.

-----Output-----
Output $k$ integers separated by whitespace. The first integer should be the maximum value of jewels that will fit in a knapsack of size $1$. The second should be the maximum value of jewels in a knapsack of size $2$, and so on.

-----Examples-----
Sample Input 1:
4 9
2 8
1 1
3 4
5 100
Sample Output 1:
1 8 9 9 100 101 108 109 109

Sample Input 2:
5 7
2 2
3 8
2 7
2 4
3 8
Sample Output 2:
0 7 8 11 15 16 19
user: Liam (angryneeson52) is playing his favorite tower defense game! This game involves destroying minions of his opponent while defending his own villages.

Liam’s favorite attack is an Area of Effect attack. The Area of Effect attack is a perfect circle. Liam simply picks a center and a radius for the attack and every minion in or on that circle gets destroyed! Minions are small enough to be considered points.

The game isn’t as simple as just destroying all minions. Liam must also avoid hitting his villages with his attacks. The attack may touch the walls of a village but must not enter the village. Villages are also perfect circles.

His attack also has a limit on its maximum radius. The attack can be reduced in radius but cannot go above the maximum.

Determine the maximum number of minions Liam can destroy in a single attack without damaging any of his own villages.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each input begins with a line with 3 space-separated integers, $n\ m\ r$, where:
 - $n$ ($1\le n \le 10$) is the number of Liam’s villages
 - $m$ ($1 \le m \le 2000$) is the number of opposing minions
 - $r$ ($1 \le r \le 20000$) is the maximum radius of Liam’s Area of Effect attack

The next $n$ lines will each contain 3 space-separated integers $vx\ vy\ vr$ which represent the location ($-20000\le vx, vy \le 20000$) and radius ($1\le vr \le 20000$) of one of Liam’s villages. No two villages will intersect or overlap.

The next $m$ lines will each contain 2 space-separated integers $mx\ my$ which represent the location ($-20000 \le mx, my \le 20000$) of one of the enemy minions. No two minions will occupy the same point, and no enemy minion will be inside any of Liam’s villages.

-----Output-----
Output a single integer representing the maximum number of enemy minions that Liam can destroy with a single attack.

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

Sample Input 2:
1 5 3
0 0 1
3 3
-3 3
3 -3
3 0
0 3
Sample Output 2:
3
user: We say that a sequence of $2K$ elements is interesting if neither the sum of the first $K$ elements, nor the sum of the last $K$ elements, is greater than $S$. A sequence $A$ of length $N$ is given. For every element, output the length of the longest interesting subsequence starting with that element.

-----Input-----
The first line contains integers $N$ and $S$ ($2 \leq N \leq 100000$, $1 \leq S \leq 2 \cdot 10^9$ ).

The following $N$ lines contain the sequence $A$, one integer per line. The integers are non-negative and their sum does not exceed $2\cdot 10^9$.

-----Output-----
Output $N$ lines. The $i$-th line must contain one integer, the length of the longest interesting subsequence starting with the i-th element. If an interesting subsequence at that position doesn’t exist, output 0 (zero).

-----Examples-----
Sample Input 1:
5 10000
1
1
1
1
1
Sample Output 1:
4
4
2
2
0

Sample Input 2:
5 9
1
1
10
1
9
Sample Output 2:
2
0
0
2
0
user: Having solved a tedious assignment, Mirko decided to play a game with his good friend Slavko.

They have written a sequence of $N$ letters on a piece of paper. Each one of them is trying to put together a word using letters from the sequence. They alternate taking turns consisting of removing a single letter from the sequence and appending it to the end of their word. Mirko has the first turn. The game ends when no letters are remaining in the sequence.

We define a word to be more beautiful than another word if it comes first alphabetically. The player who has the more beautiful word at the end of the game wins. If both players have equal words, they both lose.

Mirko is a much better player than Slavko, so he has decided to make it easier for Slavko by always selecting the rightmost remaining letter in the sequence. Knowing this, Slavko wants to find out if it is possible for him to win and which is the most beautiful word he can end the game with.

-----Input-----
The first line of input contains an even positive integer $N$ ($2 \le N \le 100 000$).

The second line of input contains $N$ characters, the starting letter sequence. All characters are lower case letters from the English alphabet.

-----Output-----
The first line of output must contain “DA” if it is possible for Slavko to win, and “NE” otherwise.

The second line of output must contain the most beautiful word that Slavko can have at the end of the game.

-----Examples-----
Sample Input 1:
2
ne
Sample Output 1:
NE
n

Sample Input 2:
4
kava
Sample Output 2:
DA
ak
user: An airline company offers flights out of $n$ airports. The flight time between any given pair of airports is known, but may differ on direction due to things like wind or geography. Upon landing at a given airport, a plane must be inspected before it can be flown again. This inspection time is dependent on the airport at which the inspection is taking place.

Given a set of $m$ flights that the airline company must realize, determine the minimum number of planes that the company needs to purchase. The airline may add unscheduled flights to move the airplanes around if that would reduce the total number of planes needed.

-----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 $n$ and $m$ ($2 \le n, m \le 500$). The next line contains $n$ space-separated nonnegative integers less than or equal to $10^6$, where the $i^{\text {th}}$ integer denotes the amount of time (in minutes) that an inspection takes at airport $i$.

Each of the next $n$ lines contains $n$ space-separated nonnegative integers less than or equal to $10^6$. On the $i^{\text {th}}$ line, The $j^{\text {th}}$ integer indicates the amount of time it takes to fly from airport $i$ to airport $j$. It takes no time to fly from an airport to itself. Note that the flight time from airport $i$ to $j$ is not necessarily the same as the flight time from airport $j$ to $i$.

The next $m$ lines contain three space-separated integers, $s$, $f$, and $t$, ($1 \le s, f \le n$, $s \ne f$, $1 \le t \le 10^6)$ indicating that a flight must start at airport $s$, end at airport $f$, and fly out from airport $s$ at exactly time $t$ heading directly to airport $f$.

-----Output-----
Output a single positive integer indicating the minimum number of planes the airline company must purchase in order to realize the $m$ requested flights.

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

Sample Input 2:
2 2
1 1
0 1
1 0
1 2 1
2 1 3
Sample Output 2:
1