meetforever/GRPO_CL huggingface dataset:
user: Evenland used to be a normal country. Then Steven became ruler and now everything must be done as he wishes. For some odd reason he is obsessed with the number two. Everything must be even in his country, hence he even changed the name to Evenland. 

The other day, Steven was driving through his country when he noticed that, at some intersections, an odd number of roads meet. Naturally, some roads must now be destroyed in order to make the number of roads even at every intersection.

You are in charge of this project. You start wondering: in how many ways can this project be carried out? In other words, in how many ways can you select a set of roads to destroy so that all intersections become even? The resulting road network does not have to be connected, so for instance, one possible way is to destroy all roads.

-----Input-----
The first line of the input contains two integers $N$ and $M$, where $1\leq N, M\leq 100000$. $N$ denotes the number of intersections in Evenland and $M$ is the number of roads. $M$ lines follow, each contains two space separated integers $a$, $b$ indicating that there is a road between intersections $a$ and $b$. You may assume that $1\leq a, b\leq N$ and $a\not= b$. There might be more than one road connecting a pair of intersections.

-----Output-----
Output one line with one integer – the number of ways of making all intersections even. Since this number might be big, output the remainder modulo $1000000009$.

-----Examples-----
Sample Input:
4 5
1 2
1 3
1 4
2 3
2 4
Sample Output:
4
user: The airline company NCPC Airways has flights to and from $n$ cities, numbered from 1 to $n$, around the entire world. However, they only have $n - 1$ different flights (operating in both directions), so in order to travel between any two cities you might have to take several flights. In fact, since the management has made sure that it’s possible to travel between any pair of cities, there is exactly one set of flights a passenger have to take in order to travel between two cities (assuming you want to use the same airline).

Recently many of NCPC Airways frequent flyers have complained that they have had to change flights too often to get to their final destination. Since NCPC Airways doesn’t want to loose their customers to other airline companies, but still keep the nice property of their flights, they have decided to cancel one of their current flights and replace it with another flight. Help the company by writing a program which finds the best flight to cancel and the best new flight to add so that the maximum number of flight changes a passenger might have to make when travelling between any pair of cities in which NCPC Airways operates is minimized.

The input will be constructed so that it is always possible to improve the maximum number of flight changes needed.

-----Input-----
The first line in the input contains the integer $n$ ($4 \leq n \leq 2500$), the number of cities NCPC Airways operates in. Then follow $n - 1$ lines specifying the flights. Each flight is given as a pair of cities $a$ and $b$ ($1 \le a, b \le n$).

-----Output-----
The output should consist of three lines. The first line should contain an integer, the minimum number of flights needed to take when travelling between any pair of cities after changing one of the flights. The second line should contain two integers, specifying the two cities between which the flight should be canceled. The third line should contain two integers, specifying the two cities where a new flight should be added.

If there are more than one optimal solution, any one of them will be accepted.

-----Examples-----
Sample Input:
4
1 2
2 3
3 4
Sample Output:
2
3 4
2 4
user: In this problem you will be solving one of the most profound challenges of humans across the world since the beginning of time – how to make lots of money.

You are a middleman in the widget market. Your job is to buy widgets from widget producer companies and sell them to widget consumer companies. Each widget consumer company has an open request for one widget per day, until some end date, and a price at which it is willing to buy the widgets. On the other hand, each widget producer company has a start date at which it can start delivering widgets and a price at which it will deliver each widget.

Due to fair competition laws, you can sign a contract with only one producer company and only one consumer company. You will buy widgets from the producer company, one per day, starting on the day it can start delivering, and ending on the date specified by the consumer company. On each of those days you earn the difference between the producer’s selling price and the consumer’s buying price.

Your goal is to choose the consumer company and the producer company that will maximize your profits.

-----Input-----
The first line of input contains two integers $m$ and $n$ ($1 \leq m, n \leq 500000$) denoting the number of producer and consumer companies in the market, respectively. It is followed by $m$ lines, the $i^{\text {th}}$ of which contains two integers $p_ i$ and $d_ i$ ($1 \leq p_ i, d_ i \leq 10^9$), the price (in dollars) at which the $i^{\text {th}}$ producer sells one widget and the day on which the first widget will be available from this company. Then follow $n$ lines, the $j^{\text {th}}$ of which contains two integers $q_ j$ and $e_ j$ ($1 \leq q_ j, e_ j \leq 10^9$), the price (in dollars) at which the $j^{\text {th}}$ consumer is willing to buy widgets and the day immediately after the day on which the last widget has to be delivered to this company.

-----Output-----
Display the maximum total number of dollars you can earn. If there is no way to sign contracts that gives you any profit, display 0.

-----Examples-----
Sample Input:
2 2
1 3
2 1
3 5
7 2
Sample Output:
5
user: Oskar really loves onions. Unfortunately, the onions he loves belong to the local vegetable farmer, Lökas Tomatcek. Since Oskar is very cheap, he simply steals Lökas’ onions from the large, convex, onion field. For obvious reasons, Lökas does not approve of this. Rather than going to the police, however, Lökas wants to raise a high-energy laser fence around the onions to replace his wooden fence. 

As laser fences are rather expensive, Lökas can only afford to upgrade $K$ of the fence posts to laser fence posts. If a set of posts are upgraded, the lasers will protect all the onions lying strictly within the convex hull of the selected fence posts. This may not be all of the onions though. Lökas wonders which posts he should upgrade if he wants to protect as many of his $N$ onions as possible.

The original fence has the shape of a convex polygon with $M$ fence posts as vertices, and all the onions lie strictly within the fence.

-----Input-----
The first line of input consists of three space-separated integers $3 \le N \le 10000$, $3 \le M \le 400$ and $3 \le K \le 400$. These are the number of onions, the number of old fence posts, and the number of fence posts Lökas can upgrade.

Then follow $N$ lines with two space-separated integers $0 \le X_ i, Y_ i \le 10^9$ each. $(X_ i, Y_ i)$ gives the coordinate of the $i$-th onion.

Then follow $M$ lines with two space-separated integers $0 \le A_ i, B_ i \le 10^9$ each. $(A_ i, B_ i)$ gives the coordinate of the $i$-th fence post.

The fence posts will be given in clockwise order of the old fence. No three fence posts will lie on a line.

-----Output-----
Output should be a single integer; the maximum number of onions Lökas can protect.

-----Examples-----
Sample Input:
3 5 3
1 1
2 2
1 3
0 0
0 3
1 4
3 3
3 0
Sample Output:
2
user: Žofka is bending a copper wire. She starts with a straight wire placed on the table with the starting point glued to the middle of the table. She then repeatedly picks a point on the wire and bends the part starting at that point (away from the starting point) by $90$ degrees (either clockwise or counterclockwise). Throughout the process the starting point stays glued to the middle of the table.

The most important consideration is that she does not want the wire to touch itself as she bends it (that would summon the wire ghost). She needs your help. She has a list of points together with the direction at each point (clockwise or counterclockwise). She wants to know if bending the wire at the listed points in the given order would cause the wire ghost to appear at any time during the process.

-----Input-----
The first line contains two integers $L$ and $n$ where $L$ is the length of the wire and $n$ is the number of points. Each of the next $n$ lines contains a number from $\{ 0,\dots ,L\} $ (describing the point on the wire) followed by W (clockwise) or C (counter clockwise). You may assume $L\leq 100000000$ and $n\leq 1000$.

-----Output-----
The output consists of a single line consisting of the string GHOST if the wire would touch itself during the bending, and the string SAFE otherwise.

-----Examples-----
Sample Input:
4 3
3 C
2 C
1 C
Sample Output:
GHOST
user: Johan has a really boring job at the airport. It is his duty to make sure no bags collide when sliding onto the circular conveyor belt in the luggage pick-up zone. All pieces of luggage are loaded onto a straight conveyer belt which ends above the circular conveyor belt. Johan is then manually varying the speed of the straight conveyor so that no collisions occur. He would rather set a constant speed so that he can go to the fika room. There is a sensor at the start of the long conveyor belt so that he can get the positions of all pieces of luggage into his computer. Now all he needs is a program giving him the maximum speed that will avoid all collisions.

The circular conveyor belt moves at a constant speed of $1$ m/s. If a piece of luggage is dropped on the circular belt within one meter of the position of another piece of luggage they may collide, so this should be avoided. Some bags might be picked up on the first round, but you can not know in advance which will be left. The straight conveyor can be set to any speed between $0.1$ m/s and $10$ m/s.

-----Input-----
The first line of input contains two positive integers $N$ and $L$ ($1 \leq N \leq L \leq 1000$), where $N$ is the number of pieces of luggage and $L$ is the length of the circular conveyor belt in meters. The second line contains $N$ unique space-separated numbers $x_ i$ ($0 \leq x_ i \leq 1000$) with two digits after the decimal point, denoting luggage positions in meters.

-----Output-----
Output the maximum speed $v$ in m/s ($0.1 \leq v \leq 10$) that makes sure no collisions will occur, or “no fika” if there is no such speed. The answer is considered correct if it has an absolute error of at most $10^{-9}$.

You may assume that when an optimal $v$ exists, each speed in the interval $[v - 10^{-9}, v]$ will also be a valid speed.

-----Examples-----
Sample Input:
2 3
0.00 2.00
Sample Output:
2
user: Despite the unfortunate incident last summer, which resulted in ten little puppies, you have been tasked with taking care of your neighbors’ dogs again. Shadow and Lydia may be very cute mutts, but this year you have strict instructions to walk them one by one. However, you have other things to do during the summer than walking dogs! Like playing fetch and solving programming problems! It seems terribly inefficient to walk the dogs one at a time. 

Shadow and Lydia have a particular walk they each prefer and know by heart. If you just let them out, they will follow their favorite walk, eventually ending up in their respective doghouses. Problem solved!

Sadly, you realize that if you just let both dogs out at the same time and let them do their walks on their own, they might get too close to each other. If they get too close, they will leave their favorite walk to “have some fun’’ and you are not sure you can find good homes for any more puppies. To ensure this does not happen, you need to calculate the minimum distance between the dogs when they are out walking on their own.

Both dogs start at the same time and keep exactly the same pace. Immediately after a dog arrives at its doghouse it stays inside and goes to sleep, so we no longer need to worry about the distance to the other dog, even though the other dog may still walk for a while longer. Note that a dog is still awake at the exact moment of entering its house and falls asleep immediately after entering.

-----Input-----
The first line of input consists of an integer $n$ ($2 \le n \le 100000$), the number of points describing the walk of Shadow. The next $n$ lines contain $2$ integers each, giving the $x$ and $y$ coordinates of Shadow’s walk. Two consecutive points in the walk always differ in at least one coordinate. All coordinates are non-negative and at most $10000$. Similarly, the next line contains an integer $m$ ($2 \le m \le 100000$), the number of points describing the walk of Lydia. The next $m$ lines describe its walk in the same format as for Shadow.

-----Output-----
Output the minimum distance between the two dogs during their walks. The numbers should be accurate to an absolute or relative error of at most $10^{-4}$.

-----Examples-----
Sample Input:
2
0 0
10 0
2
30 0
15 0
Sample Output:
10
user: Per is repairing roads. The job is concentrated on roads with one lane in each direction. Thus, when Per closes down the lane in one direction, all traffic has to go through the other lane. This is done by allowing only one direction of travel at any time. Per is often assigned the task of directing the traffic through this lane.

No car drives before being given a “go” signal from Per, and all the cars drive through the maintained segment at the same speed. Because there is only one lane, cars in one direction must leave the segment before cars in the other direction can enter. For safety reasons, cars driving in the same direction have to keep a distance of at least $3$ seconds between each other.

For example, if cars A and B arrive at the west endpoint at second $10$, Per can let them go at earliest second $10$ and $13$ in the order they arrived. If it, in this example, takes $8$ seconds to pass and car C arrives at the east endpoint at second $17$, then car C has to wait $4$ seconds until Per lets it go at second $21$.

There is a problem of drivers getting irritated with Per; they think they have to stop for too long. Per has been logging how long they can bear to wait before they get irritated. One day, to be able to evaluate his work, Per noted down when the cars arrived at the two endpoints of the segment. Per’s question is the following: what is the least number of drivers that can be irritated? We assume that a driver gets irritated if the time between the moment he arrives at the maintained segment and the moment he is actually given the “go” exceeds his irritation time limit.

-----Input-----
The first line of the input contains two integers $t$ and $n$ ($4 \leq t \leq 180$ and $1\leq n\leq 250$), where $t$ is the time in seconds needed for a car to pass the segment under maintenance, and $n$ is the total number of cars arriving at the segment. The following $n$ lines describe the cars. The $i$-th line contains the description of the $i$-th car in the following format:
 - one character $d$, being W for cars arriving at the west endpoint of the segment, and E for the ones that arrive at the east endpoint; and
 - two integers $a$ and $r$ ($0 \leq a < 86400$ and $0 \leq r \leq 3600$), where $a$ denotes the arrival time in seconds after midnight, and $r$ denotes the time in seconds it takes for the driver to get irritated.

The cars arrive in the order specified in the input and they cannot overtake each other. In particular, a car whose driver is already irritated has to stay in the queue until eventually receiving the “go” and passing the maintained segment.

-----Output-----
Output one line with the least possible number of irritated drivers.

-----Examples-----
Sample Input:
8 3
W 10 0
W 10 3
E 17 4
Sample Output:
0
user: You may have heard of the lost city of Atlantis. As legend goes, Atlantis was a city of great wealth and power. Then the Gods became displeased with Atlantis and sank it into the ocean. What you may not have heard is the story of Demetrios, the only person in Atlantis with a ship at the time the city was pushed underwater.

Demetrios was an incredibly selfish man and thought of only one thing when he noticed the water level in the city rising: collecting the wealth of accessible gold in Atlantis and transporting it into his ship before the treasure was lost forever. Luckily for Demetrios, when the water level began rising, the many guards keeping safe the gold stores abandoned their posts to seek safety.

Demetrios knows the location of every gold store in Atlantis and how long it will take him to get to a particular store and back to his ship. He also knows the altitude at which each gold store resides, which determines when the store will be swallowed by the rising sea. The trouble is that he’s not sure he’ll have time to make it to every store before they become submerged. He now wonders the maximum number of stores he can visit prior to their respective submersion, if he picks his schedule optimally.

During the 2017 NCNA Regional, the following clarification was posted: “Important: The gold store must remain above water during the ENTIRE trip to and from the store.”

-----Input-----
The first line of input will contain the integer $n$, ($1 \leq n \leq 200000$), the number of gold stores in Atlantis. The next $n$ lines will contain two integers on each line, $t_ i$ and $h_ i$, ($1 \leq t_ i, h_ i \leq 10^9$), the round-trip time in seconds it will take Demetrios to visit store $i$ and return to his ship with the gold, and the feet above sea level of store $i$, respectively.

-----Output-----
Output the maximum number of gold stores Demetrios can visit such that each is visited prior to it becoming submerged. Assume sea level rises by one foot every second, starts at height $0$, and begins rising immediately.

-----Examples-----
Sample Input:
5
5 8
5 6
3 4
5 13
6 10
Sample Output:
3
user: Ylva loves bonbons, probably more than anything else on this planet. She loves them so much that she made a large plate of $R \cdot C$ bonbons for her fikaraster1.

Ylva has a large wooden tray which can fit $R$ rows of $C$ bonbons per row, that she will put the bonbons on. Her bonbons have three different fillings: Nutella Buttercream, Red Wine Chocolate Ganache, and Strawberry Whipped Cream. Since Ylva is a master chocolatier, she knows that presentation is $90\% $ of the execution. In particular, it looks very bad if two bonbons of the same color are adjacent to each other within a row or a column on the tray. We call an arrangement of bonbons where this is never the case a good arrangement.

Given the number of bonbons of each flavour, and the size of Ylva’s tray, can you help her find a good arrangement of the bonbons, or determine that no such arrangement exists?

-----Input-----
The first line of input contains the two space-separated integers $2 \le R, C \le 1000$. The next line contains three non-negative space-separated integers $a, b, c$ – the number of bonbons of the three flavours which Ylva has baked. It is guaranteed that $a + b + c = R \cdot C$. Both $R$ and $C$ will be even.

-----Output-----
If no good arrangement can be found, output impossible. Otherwise, output $R$ lines, each containing $C$ characters, representing a good arrangement. Each row should contain only characters A, B, C, depending on which flavour should be placed on a certain position. The number of A bonbons placed must be equal to $A$, and so on.

-----Examples-----
Sample Input:
4 4
10 3 3
Sample Output:
impossible
user: NVWLS, or “No Vowels” puzzles are popular among puzzle enthusiasts. For example, consider the following no-vowels message:

BTWNSBTLSHDNGNDTHBSNCFLGHTLSTHNNCFQLSN

which is inscribed on the famous “Kryptos” statue located at the CIA’s headquarters in Virginia. This message is derived from the following sentence by removing all vowels and spaces:

BETWEEN SUBTLE SHADING AND THE ABSENCE OF LIGHT
LIES THE NUANCE OF IQLUSION

Given a dictionary (a set of words that can be used to construct a sentence) and a message (which comes from a sentence which uses only those words, but with all vowels and spaces removed), reconstruct the original sentence using the dictionary words!

-----Input-----
The first line contains an integer $n$ denoting the number of words in the dictionary. The next $n$ lines each contain a dictionary word using one or more uppercase English letters. Each word contains at least one consonant.

For the purposes of this problem, the letters A, E, I, O, and U are vowels and all other letters are consonants.

The dictionary is followed by a single non-empty line of uppercase consonants representing the no-vowels message. It is guaranteed that the no-vowels message can be constructed in at least one way using only the dictionary words.

The total number of letters in all dictionary words is no greater than $100000$. The total number of letters in the no-vowels message does not exceed $300000$.

-----Output-----
Output a whitespace-separated sequence of dictionary words that yields the original no-vowels message when all spaces and vowels are removed. If there are multiple reconstructions, choose the one with the largest overall number of vowels. If there are still multiple reconstructions, you may output any one of them. No judge input will require your program to output more than $15000000$ characters.

-----Examples-----
Sample Input:
11
BETWEEN
SUBTLE
SHADING
AND
THE
ABSENCE
OF
LIGHT
LIES
NUANCE
IQLUSION
BTWNSBTLSHDNGNDTHBSNCFLGHTLSTHNNCFQLSN
Sample Output:
BETWEEN SUBTLE SHADING AND THE ABSENCE OF LIGHT LIES THE NUANCE OF IQLUSION
user: Casting spells is the least understood technique of dealing with real life. Actually, people find it quite hard to distinguish between real spells like “abrahellehhelleh” (used in the battles and taught at the mage universities) and screams like “rachelhellabracadabra” (used by uneducated witches for shouting at cats). Finally, the research conducted at the Unheard University showed how one can measure the power of a word (be it a real spell or a scream). It appeared that it is connected with the mages’ ability to pronounce words backwards. (Actually, some singers were burned at the stake for exactly the same ability, as it was perceived as demonic possession.) Namely, the power of a word is the length of the maximum subword of the form $ww^Rww^R$ (where $w$ is an arbitrary sequence of characters and $w^R$ is $w$ written backwards). If no such subword exists, then the power of the word is $0$. For example, the power of abrahellehhelleh is $12$ as it contains hellehhelleh and the power of rachelhellabracadabra is $0$. Note that the power of a word is always a multiple of $4$.

-----Input-----
The input is a single line containing a word of length $3 \cdot 10^5$, consisting of (large or small) letters of the English alphabet.

-----Output-----
You should output one integer $k$, the power of the word.

-----Examples-----
Sample Input:
abrahellehhelleh
Sample Output:
12