meetforever/GRPO_CL huggingface dataset:
user: The postal service is interested in cutting costs as an alternative to raising the postage rates. One way to do this is by minimizing the distance traveled when delivering mail from the post office to all the required locations and returning to the post office. It may be that all the mail to be delivered does not fit on the mail truck at once, in which case the distance traveled by the truck must include travel back to the post office to reload. For simplicity, we assume a one dimensional world with the post office at the origin, and delivery locations each identified by a single coordinate. As an example, suppose a postal truck can carry up to $100$ letters and that $50$ letters need to be delivered to location $-10$, that $175$ need to be delivered to location $10$, and $20$ delivered to location $25$. A maximally efficient plan would be:

Deliver the $50$ letters to location $-10$ (travel $2 \cdot 10$), the first $100$ letters to location $10$ (travel $2 \cdot 10$), the remaining $75$ letters to location $10$ while on the way to delivering the $20$ to location $25$ (travel $2 \cdot 25$). The total round-trip distance traveled is $90$.

-----Input-----
The first line contains two integers, $N$ and $K$, where $3 \leq N \leq 1000$ is the number of delivery addresses on the route, and $1 \leq K \leq 10000$ is the carrying capacity of the postal truck. Each of the following $N$ lines will contain two integers $x_ j$ and $t_ j$, the location of a delivery and the number of letters to deliver there, where $-1500 \leq x_1 < x_2 < \cdots < x_ N \leq 1500$ and $1 \leq t_ j \leq 800$ for all $j$. All delivery locations are nonzero (that is, none are at the post office).

-----Output-----
Output the minimum total travel distance needed to deliver all the letters and return to the post office.

-----Examples-----
Sample Input:
3 100
-10 50
10 175
25 20
Sample Output:
90
user: Trouble has come to the remote group of islands known as Insumulia. Due to an unfortunate combination of over-consumption, natural climate variations, and generally difficult conditions, the island of Incunabula has run out of trees. Because several other Insumulian islands depended on trees from Incunabula through trade, its collapse will have repercussions all over Insumulia. In this problem, we’ll simulate a (highly oversimplified) model of the situation to determine the effects of the collapse of Incunabula. 

We model the situation as follows. Each island has a threshold $T_ i$ on the amount of incoming goods (for simplicity we assume that there is only a single commodity of goods) it needs to receive per lunar cycle in order for the society of the island to sustain itself. If the amount of incoming goods drops below the threshold, society on the island will collapse and die out, and the island will no longer provide goods to other islands, thereby potentially causing them to collapse as well. Each island provides some amount of goods to a number of other islands. If an island collapses, we assume that goods that would have been delivered to that island is effectively lost; it does not get redistributed and delivered to other islands instead. Also, once an island dies out it is not repopulated (until possibly long after the ongoing collapses have finished).

Your job is to write a program to compute the number of islands that survive after the potential chain reaction of collapses that is caused by the collapse of Incunabula.

-----Input-----
The first line of input contains an integer $N$ ($1 \le N \le 100000$), the number of islands in Insumulia.

Then follow $N$ lines, describing each island. The $i$’th such description starts with two integers $T_ i$, $K_ i$, where $0 \le T_ i \le 50000$ is the amount of goods the $i$’th island needs to receive in order to survive, and $0 \le K_ i \le N-1$ is the number of other islands the $i$’th islands receives goods from. The remainder of the description of the $i$’th island is a list of $K_ i$ pairs of integers. The $j$’th such pair, $S_{ij}$, $V_{ij}$, indicates that island $i$ receives $V_{ij}$ units of goods from island $S_{ij}$ each lunar cycle. You may assume that the $S_{ij}$’s are distinct and between $1$ and $N$ (inclusive), and that none of them equals $i$. The values $V_{ij}$ satisfy $1 \le V_{ij} \le 1000$ and their sum is at least $T_ i$. The sum of all the $K_ i$’s for all the $N$ islands is at most $500000$.

Islands are numbered from $1$ to $N$, and Incunabula is island number $1$.

-----Output-----
Output a single integer, the number of islands surviving the collapses.

-----Examples-----
Sample Input:
4
0 0
25 3 1 10 3 10 4 10
10 1 2 10
10 1 2 10
Sample Output:
0
user: Last weekend you and your friends went to visit the local farmer’s market at the town square. As you were standing around in a circle talking, you couldn’t help overhearing two of your friends musing over what sounded like an interesting problem: They were considering the number of ways in which you could all shake hands, such that everyone in the circle simultaneously shaked hands with one other person, but where no arms crossed each other.

After a few seconds’ thought you decided to join your two friends, to share (with them) the solution to their problem. “If we are $2n$ persons”, you said, “pick any particular person, and let that person shake hands with somebody. That person will have to leave an even number of people on each side of the person with whom he/she shakes hands. Of the remaining $n-1$ pairs of people, he/she can leave zero on the right and $n-1$ pairs on the left, $1$ on the right and $n-2$ pairs on the left, and so on. The pairs remaining on the right and left can independently choose any of the possible non-crossing handshake patterns, so the count $C_ n$ for $n$ pairs of people is given by:\[ C_ n = C_{n-1}C_0 + C_{n-2}C_1 + \ldots + C_1C_{n-2} + C_0C_{n-1}, \]

which, together with the fact that $C_0=C_1=1$, is just the definition of the Catalan numbers.” By consulting your handy combinatorics book, you find out that there is a much more efficient formula for calculating $C_ n$, namely:\[ C_ n = \frac{\binom {2n}{n}}{n+1}. \]

After a collective groan from the group, your particularly cheeky friend Val called out “Well, since we are at the town square, why don’t you try to square your Catalan numbers!”. This was met with much rejoicing, while you started to think about how to square the Catalan sequence…

-----Task-----
Let $C_ n$ be the $n$th Catalan number as defined above. By regarding the sequence $(C_ n)_{n\geq 0}$ of Catalan numbers, we can define a sequence $(S_ n)_{n\geq 0}$, corresponding to “squaring the Catalan sequence”, by considering the Cauchy product, or discrete convolution, of $(C_ n)_{n\geq 0}$ with itself, i.e.,\[ S_ n = \sum _{k=0}^{n}C_ kC_{n-k}. \]

Your task is to write a program for calculating the number $S_ n$.1

-----Input-----
The input contains one line containing one non-negative integer: $n$, with $0 \leq n \leq 5000$.

-----Output-----
Output a line containing $S_ n$.

-----Examples-----
Sample Input:
0
Sample Output:
1
user: You are organising a king of the hill tournament, the Buenos Aires Paddleboarding Competition (BAPC), with $n$ participants. In a king of the hill tournament, one person starts as a “king” and is then challenged by another person, the winning person becomes the new king. This is repeated until all participants have challenged exactly once (except for the starting person). In a paddleboarding match, there are no draws. The person which ends up as king, wins the tournament. Since you are the organiser, you get to choose the starting person and the order in which they challenge the king.

Someone is offering you a substantial amount of money in case one of the participants, Henk, ends up winning the tournament. You happen to know, for any two participants $x$ and $y$, which of the two would win if they were to match during the tournament. Consequently, you choose to do the unethical: you will try to rig the game. Can you find a schedule that makes Henk win the tournament?

-----Input-----
 - The first line contains an integer $1 \leq n \leq 1000$, the number of participants. The participants are numbered $0, \dots , n-1$, where Henk is $0$.
 - Then $n$ lines follow, where each line has exactly $n$ characters (not counting the newline character). These lines represent the matrix with the information of who beats who, as follows. On line $i$ the $j$th character is (note that $0 \leq i, j < n$):
 - ’1’ if person $i$ will win against person $j$.
 - ’0’ if person $i$ will lose against person $j$.
 - ’X’ if $i = j$.

-----Output-----
Print a sequence of participants, such that the first person starts as king and the consequent participants challenge the king. If there is no way to rig the game such that Henk wins, print “impossible”.

-----Examples-----
Sample Input:
3
X10
0X1
10X
Sample Output:
1 2 0
user: You have recently made a grid traversing robot that can find its way from the top left corner of a grid to the bottom right corner. However, you had forgotten all your AI programming skills, so you only programmed your robot to go rightwards and downwards (that’s after all where the goal is). You have placed your robot on a grid with some obstacles, and you sit and observe. However, after a while you get tired of observing it getting stuck, and ask yourself “How many paths are there from the start position to the goal position?”, and “If there are none, could the robot have made it to the goal if it could walk upwards and leftwards?”

So you decide to write a program that, given a grid of size $n \times n$ with some obstacles marked on it where the robot cannot walk, counts the different ways the robot could go from the top left corner $s$ to the bottom right $t$, and if none, tests if it were possible if it could walk up and left as well. However, your program does not handle very large numbers, so the answer should be given modulo $2^{31} - 1$.

-----Input-----
On the first line is one integer, $1 \leq n \leq 1000$. Then follows $n$ lines, each with $n$ characters, where each character is one of ’.’ and ’#’, where ’.’ is to be interpreted as a walkable tile and ’#’ as a non-walkable tile. There will never be a wall at $s$, and there will never be a wall at $t$.

-----Output-----
Output one line with the number of different paths starting in $s$ and ending in $t$ (modulo $2^{31} - 1$) or THE GAME IS A LIE if you cannot go from $s$ to $t$ going only rightwards and downwards but you can if you are allowed to go left and up as well, or INCONCEIVABLE if there simply is no path from $s$ to $t$.

-----Examples-----
Sample Input:
5
.....
#..#.
#..#.
...#.
.....
Sample Output:
6
user: The University of Lagado is organising events for the upcoming Fresher’s week and has been told — much to the surprise of its staff — that some of the undergraduates may enjoy a beer tasting. While sourcing a wide variety of drinks for the students to taste, the university realised that in the interests of safety there should be a limit on the alcohol consumption of any student, enforced by a strict limit on the amount any individual is allowed to spend.

In common with many popular establishments, the drinks with varying strengths are served in varying amounts: Either a litre, a half litre or a third of a litre to limit possible intoxication. $1\% $ of a litre at $100\% $ strength equals one unit of alcohol.

The students are looking forward to the event, but in order to make the most of their money and still be bright-eyed and bushy tailed for the first week of morning lectures, they don’t wish to get too drunk. How can the students spend all their money and consume in full their self-imposed alcohol limit for the night?

-----Input-----
 - One line containing three numbers:
 - $m$ ($0.00 \le m \le 10.00$), the amount of money they can spend to two decimal places;
 - $u$ ($0.0 \le u \le 20.0$), the number of units they aim to drink to one decimal place;
 - $d$ ($1 \le d \le 8$), the number of different drinks available.
 - Another $d$ lines, each containing:
 - up to $20$ lowercase latin letters (the name of the drink);
 - an integer between $0$ and $100$ (its strength as a percentage);
 - its size (either ‘$1/1$’ for a litre, ‘$1/2$’ for a half or ‘$1/3$’ for a third);
 - a real number to two decimal places; its cost.

Name, strength, price and cost will be separated by spaces.

-----Output-----
If the students’ aims are possible, write one or more lines, each listing the name of the drink purchased followed by the positive integer count of how many drinks of that type were bought. If there are several solutions, output any.

Otherwise, output a single line containing the word IMPOSSIBLE.

-----Examples-----
Sample Input:
10.00 9.0 2
fire 2 1/1 4.00
water 10 1/2 2.00
Sample Output:
fire 2
water 1
user: Cady’s Chocolate Company just opened down the street! Cady’s chocolate is world famous, and her recipe is top secret. But the company is more renowned for the fact that they sell the chocolate in random quantities. Each box of chocolate may contain anywhere from $1$ to $100$ pieces.

Bob’s nephews, John and Sam, love Cady’s Chocolate, but Bob has a dilemma. John will get jealous of Sam if he gets more pieces of chocolate, and vice versa. Bob knows how many pieces of chocolate are in each box.

Write a program to help him determine if it is possible to split the boxes between John and Sam such that both get the same number of pieces of chocolate, and such that all boxes of chocolate are used.

-----Input-----
The input consists of a single test case. The first line contains an integer $n$ ($1 \le n \le 1000$), the number of boxes of chocolate Bob bought. The next line contains $n$ integers $a_ i$ representing the number of pieces of chocolate in the $i^{\text {th}}$ box ($1\le a_ i \le 100$).

-----Output-----
If it is possible for Bob to split the boxes such that John and Sam get the same number of pieces of chocolate, output YES. Otherwise, output NO.

-----Examples-----
Sample Input:
6
1 4 3 12 13 1
Sample Output:
YES
user: Two kingdoms had been at war for a long time, until the emperor intervened to bring an end to the conflict. The territory in question comprises an $M$ by $N$ rectangular grid. At the emperor’s insistence, the two kings have withdrawn their troops until no two opposing troops are in adjacent squares of the map (adjacent being horizontal or vertical – diagonal is not considered).

The emperor proposes to designate certain squares of the map as neutral territory. Neither king will be allowed to move troops into those squares, and the emperor’s own forces will patrol them to be sure that both kings observe these rules.

The emperor is frugal and does not want to commit more soldiers to this effort than absolutely necessary. His generals have marked each square of the map with the number of soldiers required to secure that square. What remains is to choose which of those squares should be patrolled.

Write a program to determine the minimum number of soldiers that the emperor will need to be deploy to guarantee that the troops of one kingdom cannot move, in one or more steps, into squares occupied by the troops of the second kingdom (moving horizontally or vertically) without encountering the emperor’s own soldiers.

-----Input-----
Input begins with a line containing $2$ integers, $w$ and $h$, denoting the width and height of the map, where $1 \leq w, h \leq 40$.

This is followed by $h$ lines. Each line contains $w$ characters, left justified. These characters will be ‘A’ or ‘B’, designating a position held by king A or king B, or a single numeric digit, designating a currently unoccupied position that can be secured by the use of that number of soldiers. For example, a ‘2’ would indicate that two soldiers must be deployed to that square to secure it against passage of other troops. A ‘0’ indicates terrain that is impassible – the emperor need not commit soldiers there because the kingdom troops cannot pass through that square.

No ‘A’ will be adjacent, horizontally or vertically, to any ‘B’.

There will be at least one ‘A’ and one ‘B’ in the input.

-----Output-----
Print a single line containing an integer denoting the minimum number of soldiers that the emperor must deploy to guarantee that there is no open path between any ‘A’ position and any ‘B’ position, using any combination of horizontal or vertical moves.

-----Examples-----
Sample Input:
8 5
A11111AA
AA7B111A
111BB111
11BBB111
11BBB11B
Sample Output:
13
user: Lucy is making her road bike ready for the season. All parts have been checked for wear and tear and washed clean and she is ready to put the beauty back together again. There is only one thing troubling her. During the winter she has been to several motivational talks by previous professional cyclists. They have all talked about the importance of correct cadence while cycling. The cadence is the frequency your feet are pedaling at when you are cycling. Lucy is now wondering if she should change her gears setup before she reassembles the bike and goes on her first ride for the year.

Bike gears typically consist of a set of different-sized gears on the crank (the thing connected to the pedals) and a set of different-sized gears on the back wheel. These are connected by the chain to drive the bike forward. Can you help her figure out if she can keep her current setup and still change to all gears without it affecting her cadence too much? Specifically she does not want her cadence to be increased by more than $P$% when changing to the next lighter gear. We assume that the bicycle will continue at the same speed immediately after the gear change.

-----Input-----
The first line of the input consists of three integers $N$, $M$ and $P$ representing the number of gears on the crank, the numbers of gears on the back wheel, and the maximum cadence change in percentage Lucy will tolerate when changing gears.

 Then follows a line with $N$ integers $C_ i$ each representing the number of teeth on each of the gears on the crank.

 Then follows a line with $M$ integers $D_ j$ each representing the number of teeth on each of the gears on the back wheel.



-----Output-----
Output a single line with the text Ride on! if Lucy can change through all the gears from heaviest to lightest in her current setup and Time to change gears! if she cannot.

-----Limits-----
 - $1 \leq N, M \leq 100$
 - $0 \leq P \leq 1000$
 - $3 \leq C, D \leq 100000$

-----Examples-----
Sample Input:
2 11 15
50 34
11 12 13 14 16 18 20 22 25 28 32
Sample Output:
Ride on!
user: When reading programming problems, one can often get some hints regarding the topic of the problem by skimming the problem statement for certain words. If, for example, the word “vertex” or “edge” appears, the problem is almost certainly a graph problem, while the words “words” or “letters” suggest that the problem is about strings.

Your task is to implement a simple program that attempts to classify a problem according to one of $N$ categories. Each category has an associated set of words, which, if they appear as words in a statement, suggest the problem belongs to this category. When classifying a statement, the program should suggest those categories which have the highest number of occurences of their associated words. Note that words that are part of other words do not count. For example, the word statement should not count as an occurance for the word ate.

In the above example, we suggested that the category graph may have the associated words vertex and edge and the category string could have the associated words words and letters. Then, if there were $3$ occurances each of the words vertex and edge, the number of matches for the category graph would be $6$. If the statement contained $14$ occurances of words and $4$ of letters, the number of matches for the category string would be $18$. Since there are more matches for the second category, the program should suggest it.

If there are multiple categories with the same number of matches, your program should suggest all of them.

-----Input-----
The first line of input contains the number of categories $1 \le N \le 10$.

The next $N$ lines each contain a description of a category. The description starts with the name of the category – a single word. Then, an integer $1 \le W \le 10$ follows – the number of words associated with this category. This is followed by those $W$ words, separated by spaces. No two words within a category are the same, and no two categories have the same name.

This is followed by a number of lines describing the statement of the problem. Each line contains a list of space-separated words.

Every word in the input will consist solely of at most $30$ lower-case letters a-z. The statement consists of between $1$ and $10000$ words.

-----Output-----
For each suggested category, output the name of the category on a single line, in lexicographical order.

-----Examples-----
Sample Input:
4
datastructure 3 query range sum
geometry 3 euclid range vertex
graph 3 query vertex hamiltonian
math 3 hamiltonian sum euclid
consider the hamiltonian graph where each vertex corresponds
to an linear equation we can solve these using the euclid
algorithm now you will receive a query corresponding to a
range of vertices your task is to compute the sum of the
minimum solution of those vertices
Sample Output:
datastructure
geometry
graph
math
user: In a game of American Football, there are several factors to take into consideration when detailing the rules of the game. The goal of the game is to move the football across the field into the endzone of the defending team through a series of plays, which form a drive. In each play, the attacking team may either gain or lose a number of yards, that is, their position on the field moves either towards or away from the defending team’s endzone.

In the simplified version of football that we consider, a team has four chances (in up to four plays) to advance the ball $10$ yards downfield; if they are successful, they will have achieved a “first down” and keep possession of the ball. If they achieve a first down, they have another up to four plays to continue their drive towards the defending team’s endzone. If they keep possession and reach the defending team’s endzone, they will have achieved a Touchdown. If they are pushed back into their own endzone, a Safety occurs and ends the drive. Otherwise the team loses possession of the ball and Nothing happens.

Sadly, the outcome of a drive has been lost, and all that remains is the yards gained or lost on each play! Your job is to determine whether a Touchdown, Safety, or Nothing occurred on the given drive.

For simplicity, we assume that the team starts the drive on their own $20$ yard line on a $100$ yard field (with $0$ being the team’s own endzone, and $100$ being the defending team’s endzone). This means that a touchdown is scored if at least $80$ yards are gained in total, relative to the starting position, and without losing possession due to failing to get a first down. Note that it is possible for a team to score a Touchdown without getting a first down. A safety occurs if the team is pushed back $20$ yards from their original starting position, which would place them in their own endzone. Nothing occurs if neither of these events occurs.

-----Input-----
The input starts of a line containing one integer $N$ ($1 \le N \le 15$), which is the number of plays that this given drive recorded. Following this line are $N$ integers representing the numbers of yards gained or lost on each particular play. Each given number is between $-100$ and $100$ yards (exclusive range) since that is the length of the football field.

-----Output-----
Output a single word, the result of the drive! If a touchdown is achieved, output “Touchdown”, if a safety is achieved, output “Safety”, else output “Nothing”. (Do not add a period at the end.) Once the outcome has been determined, your program should ignore any remaining yards listed in the drive.

-----Examples-----
Sample Input:
9
10 3 8 22 -4 16 8 3 14
Sample Output:
Touchdown