meetforever/GRPO_CL huggingface dataset:
user: Purple rain falls in the magic kingdom of Linearland which is a straight, thin peninsula. 

On close observation however, Prof. Nelson Rogers finds that actually it is a mix of Red and Blue drops.

In his zeal, he records the location and color of the raindrops in different locations along the peninsula. Looking at the data, Professor Rogers wants to know which part of Linearland had the “least” purple rain.

After some thought, he decides to model this problem as follows. Divide the peninsula into $n$ sections and number them West to East from $1$ to $n$. Then, describe the raindrops as a sequence of R and B, depending on whether the rainfall in each section is primarily red or blue. Finally, find a subsequence of where the difference between the number of R and the number of B is maximized.

-----Input-----
The input consists of a single line containing a string of $n$ characters ($1 \le n \le 10^5$), describing the color of the raindrops in sections $1$ to $n$.

It is guaranteed that the string consists of uppercase ASCII letters ‘R’ and ‘B’ only.

-----Output-----
Print, on a single line, two space-separated integers that describe the starting and ending positions of the part of Linearland that had the least purple rain.

If there are multiple possible answers, print the one that has the Westernmost (smallest-numbered) starting section. If there are multiple answers with the same Westernmost starting section, print the one with the Westernmost ending section.

-----Examples-----
Sample Input:
BBRRBRRBRB
Sample Output:
3 7
user: According to Wikipedia, to hear something “through the grapevine” is to learn of something informally and unofficially by means of gossip or rumor. In this problem, you are tasked with determining how many people will hear about a particular rumor “through the grapevine” after a certain number of days.

Rumors are always started by a single person. On any given day, a person who knows the rumor can spread it by telling the people that they know. Upon hearing of the rumor, that person must wait until the following day before they can begin to spread it themselves. Furthermore, some people are skeptical and will only spread the rumor once they’ve heard it from a number of distinct sources. However once a person has heard the rumor from enough people, they will always try to spread the rumor to as many people as possible.

-----Input-----
The first line will contain three integers: $0 < n \leq 100000$, $0 < m \leq 100000$, and $0 \leq d \leq 10000$, where $n$ is the number of people, $m$ is the number of connections, and $d$ is the number of days that elapse.

The next $n$ lines will each consist of a unique string $s$ and an integer $0 \leq t \leq 1000$ where $s$ is the name of a person and $t$ is their level of skepticism. In other words, person $s$ must hear the rumor from $t$ distinct other people before $s$ will begin spreading the rumor.

This is followed by $m$ lines each consisting of two strings $u$ and $v$ which indicates that person $u$ and person $v$ know each other. Each of these lines represents a unique pair of persons.

The final line will contain a single string $r$, the name of the person that the rumor originates from. Note that $r$ is the only person with skepticism $t = 0$. All strings are between $1$ and $20$ characters long and consists only of English lowercase or uppercase letters and digits.

-----Output-----
Output a single integer: the number of people (not including person $r$) that have heard the rumor after $d$ days.

-----Examples-----
Sample Input:
3 2 1
Alice 0
Bob 1
Carol 1
Alice Bob
Bob Carol
Alice
Sample Output:
1
user: The local zoo has acquired a large open garden in which animals may freely move as in their natural habitats and entertain visitors with their usual shenanigans.

The most popular animals are monkeys. With their climbing and jumping and other skills, they delight old and young visitors alike.

One species of monkey has specialized in climbing tall trees and picking off coconuts. Another species has specialized in breaking them open.

There are $N$ monkeys of the first type (numbered 1 through $N$) and $M$ monkeys of the second type (numbered 1 through $M$).

Monkey $k$ of the first type takes $A_ k$ seconds to find a good spot on the tree, after which it picks off its first coconut. After that the monkey produces a new coconut every $B_ k$ seconds.

Monkey $k$ of the second type takes $C_ k$ seconds to find a good tool for opening the coconuts, after which it opens its first coconut. After that the monkey opens another coconut every $D_ k$ seconds.

Unfortunately, the second type of monkey is extremely aggressive so the two types may not be in the garden at the same time. Therefore, zoo keepers will chase away the first type of monkeys as soon as they have picked off all the coconuts. Similarly, if monkeys of the same type stay too long after opening all the coconuts, fights will ensue. Because of that, zoo keepers will send them away as soon as they have opened all the coconuts.

The zoo keepers first arrive immediately after all coconuts have been picked, and again immediately after the monkeys open them all. The time needed for monkeys to enter or leave the garden is also negligibly small.

Tomislav especially likes the second type of monkey, but can never guess when to arrive in order to see them. Help him calculate the time when the second type arrives if he knows the total time that monkeys spent in the garden, but does not know the number of coconuts in the garden.

-----Input-----
The first line contains the integer $T$ $(1 \leq T \leq 1000000000)$, the total time that monkeys spent in the garden, in seconds.

The next line contains the integer $N$ $(1 \leq N \leq 100)$, the number of monkeys of the first type. Each of the following $N$ lines contains two integers $A_ k$ and $B_ k$ $(1 \leq A_ k, B_ k \leq 1000000000)$, how fast monkey $k$ of the first type is.

The next line contains the integer $M$ $(1 \leq M \leq 100)$, the number of monkeys of the second type. Each of the following $M$ lines contains two integers $C_ k$ and $D_ k$ $(1 \leq C_ k, D_ k \leq 1000000000)$, how fast monkey $k$ of the second type is.

-----Output-----
Output the number of seconds between the arrival of the first type of monkeys and the arrival of the second type.

-----Examples-----
Sample Input:
12
1
3 1
1
5 1
Sample Output:
5
user: Simone is learning to trade crypto currencies. Right now, she is looking into a new currency called CryptoKattis. A CryptoKattis can be used to improve your Kattis ranklist score without having to solve problems.

Simone, unlike most competitive programmers, is very perceptive of competition trends. She has lately noticed many coders talking about a new online judge called Doggo, and suspect that using the Kattis judge will soon fall out of fashion. This, of course, will cause the CryptoKattis to rapidly fall in value once demand fades.

To take advantage of this, Simone has performed very careful market research. This has allowed her to estimate the price of a CryptoKattis in dollars during the next $N$ days. She intends to use this data to perform a short sell. This means she will at some day borrow $100$ CryptoKattis from a bank, immediately selling the currency. At some other day, she must purchase the same amount of CryptoKattis to repay her loan. For every day between (and including) these two days, she must pay $K$ dollars in interest. What is the maximum profit Simone can make by carefully choosing when to borrow and repay the $100$ CryptoKattis?

-----Input-----
The first line of the input contains two integers $1 \le N \le 100000$ and $1 \le K \le 100$. $N$ is the number of days you know the CryptoKattis price of, and $K$ is the cost in dollars of borrowing CryptoKattis per day.

The next line contains $N$ integers separated by spaces. These are the CryptoKattis prices during the $N$ days. Each CryptoKattis price is between $1$ and $100000$ dollars.

-----Output-----
Output a single decimal number; the maximum profit you can make performing a short sell. If you cannot make a profit no matter what short sell you make, output $0$.

-----Examples-----
Sample Input:
5 10
1000 980 960 940 10
Sample Output:
98950
user: Lily is fascinated by numbers. She believes the whole world revolves around them, and that everything is connected by numbers. Her friends, Alice, Bob, Charlie and Diane, are not convinced. But she gives them an example:  Alice lives in house number 25 on her street, but that is exactly Bob’s age. Bob is born on June 4th, and Charlie was his parents’ fourth child. Finally, Diane has five fingers on her left hand, which happens to be the same as the number of toes that Bob has on his right foot! 

This shows that her friends are all connected—either directly or indirectly—by numbers. But she still has to convince her family as well as her coworkers.

Given a group of $n$ individuals, and a set of numbers that describe each individual, help Lily come up with a proof that shows that everyone in this group is either directly or indirectly connected by numbers, or determine that this is not possible.

-----Input-----
The input consists of:
 - One line with an integer $n$ ($2 \leq n \leq 2\cdot 10^5$), the number of individuals in the group. The individuals are numbered from $1$ to $n$.
 - $n$ lines, describing the individuals in the group.

The $i$th such line starts with an integer $m_ i$ ($1 \leq m_ i \leq 2\cdot 10^5$), the number of numbers that describe individual $i$.

The remainder of the line has $m_ i$ distinct integers $d_{i,1},\ldots ,d_{i,m_ i}$ ($1 \leq d_{i,j} \leq 10^9$ for each $j$), the set of numbers that describe individual $i$.

It is guaranteed that the sum over all $m_ i$ is at most $2\cdot 10^5$.

-----Output-----
Output a proof in the form of $n-1$ lines, each of which contains three integers $p$, $q$ and $r$, where $p$ and $q$ are distinct individuals that are both described by the number $r$. Using only these relations, it must be possible to show that any pair of individuals in the group are connected either directly or indirectly.

If no such proof exists, output “impossible”. If there are multiple proofs, you may output any one of them.

-----Examples-----
Sample Input:
6
2 17 10
1 5
2 10 22
3 17 22 9
2 17 8
3 9 22 16
Sample Output:
impossible
user: A land far, far away has N Members of Parliament (MP). They had a turbulent and passionate debate on the law on amendments to the law on a new referendum on referendums. From Monday to Friday, all MPs joyfully came to work and argued all day.

A diligent news reporter photographed MPs at their workplace in the heat of the argument every working day of the week. What she captured on the photos are pairs of MPs fighting and scowling at each other. The five photographs have been forwarded to you for thorough analysis.

It is a fact that each MP belongs to one of the two political parties. Let’s denote them with letters A and B. Your task is to estimate which MP belongs to which party, so that the following holds for your estimation: each MP argued with at most two distinct members of their own party.

-----Input-----
The first line of input contains an integer $N$ ($2 \leq N \leq 200000$), the number of MPs. MPs are denoted with numbers from $1$ to $N$.

The following five lines describe the photographs taken from Monday to Friday. Each of the five lines contains the list of pairs of MPs that are arguing on the photograph that day (scowling at each other). Stated first is the number of pairs $P$ ($1 \leq P \leq N/2$), followed by $P$ pairs in the form “$K$ $L$”, where $K$ and $L$ are labels of MPs scowling at each other. Before each pair there is a double space.

Of course, each MP is stated at most once per line, and no MP ever argues with herself.

-----Output-----
The first and only line of output must contain an array consisting of only characters A and B, so that the $K$-th character denotes the party of $K$-th MP in a division that satisfies the given conditions.

Since the solution isn’t going to be unique, output any.

-----Examples-----
Sample Input:
7
2  1 2  7 3
2  1 3  7 4
2  1 4  7 5
2  1 5  7 6
2  1 6  7 2
Sample Output:
ABBBBBA
user: Last winter, an avalanche swept away all the ski lifts from the ski resort Valen. Instead of rebuilding the lifts like they were before, the plan is to do it in a more optimized way, and you are responsible for this. 

The only thing remaining from the old lift system are $n$ pylons situated at integer coordinates in the plane. You would like to put lifts in the form of line segments between some of these pylons. The line segments must satisfy the following constraints:
 - A line segment can only go between pylons $(x_1, y_1)$ and $(x_2, y_2)$ if $|y_1-y_2| = 1$.
 - There are two types of pylons, one-way and two-way pylons. The one-way pylons can be connected to at most one other pylon, and the two-way pylons can be connected to at most two other pylons. However, if a two-way pylon $i$ is connected to two other pylons, then they must be on opposite sides of $i$ in the $y$-direction. In other words, the two pylons connected to $i$ must have different $y$-coordinates.
 - Two line segments may not intersect (except that the two line segments incident on a two-way pylon may touch at their endpoints).

What is the maximum number of ski lifts (line segments) you can place under these constraints?

-----Input-----
The first line contains one integer $n$ ($1 \leq n \leq 10^5$). Each of the following $n$ lines contains three integers $x$, $y$, and $a$, the coordinates and type of a pylon ($0 \leq x,y \leq 10^5$; $a=1$ for a one-way pylon and $a=2$ for a two-way pylon). All the pylons are situated at different coordinates.

-----Output-----
Output the maximum number of ski lift line segments that can be placed.

-----Examples-----
Sample Input:
8
1 0 1
3 0 2
0 1 1
2 1 2
4 1 2
1 2 2
2 3 1
4 3 1
Sample Output:
4
user: For the grand opening of the algorithmic games in NlogNsglow, a row of tower blocks is set to be demolished in a grand demonstration of renewal. Originally the plan was to accomplish this with controlled explosions, one for each tower block, but time constraints now require a hastier solution.

To help you remove the blocks more rapidly you have been given the use of a Universal Kinetic / Incandescent Energy Particle Cannon (UKIEPC). On a single charge, this cutting-edge contraption can remove either all of the floors in a single tower block, or all the $x$-th floors in all the blocks simultaneously, for user’s choice of the floor number $x$. In the latter case, the blocks that are less than $x$ floors high are left untouched, while for blocks having more than $x$ floors, all the floors above the removed $x$-th one fall down by one level.

-----Task-----
Given the number of floors of all towers, output the minimum number of charges needed to eliminate all floors of all blocks.

-----Input-----
The first line of input contains the number of blocks $n$, where $2 \leq n \leq 100000$. The second line contains $n$ consecutive block heights $h_ i$ for $i=1,2,\ldots ,n$, where $1 \leq h_ i \leq 1000000$.

-----Output-----
Output one line containing one integer: the minimum number of charges needed to tear down all the blocks.

-----Examples-----
Sample Input:
6
2 1 8 8 2 3
Sample Output:
5
user: A tennis match involves three people: two players and an umpire. Each of these has to come from a different country. There are $N$ countries, and the $i$th country has $a_ i$ tennis players and $b_ i$ umpires. (Nobody can be both a player and an umpire.) How many different tennis matches are possible? Two tennis matches are different if the sets of involved people are different.

-----Input-----
The first line contains an integer $N$, where $3 \leq N \leq 10^5$. The following $N$ lines each contain two integers $a_ i$ and $b_ i$ with $0 \leq a_ i, b_ i \leq 10^6$. You can assume $\sum _{i=1}^N a_ i \leq 10^6$ and $\sum _{i=1}^N b_ i \leq 10^6$.

-----Output-----
A single integer, the number of possible different tennis matches.

-----Explanation of Sample 1-----
Assume the players from the first country are called $A_1$ and $A_2$, the players from the second country are called $B_1$ and $B_2$, and the umpire from the third country is called $C$. Then there are $4$ matches where $C$ is the umpire: $\{ A_1, B_1, C\} $, $\{ A_1, B_2, C\} $, $\{ A_2, B_1, C\} $, and $\{ A_2, B_2, C\} $. Similarly, there are $8$ matches with the other umpires. In total, there are $12$ possible different matches.

-----Examples-----
Sample Input:
3
2 1
2 1
2 1
Sample Output:
12
user: Alice, Bob, and Clara are eating at a new restaurant today. They’re having trouble deciding what to order, so Alice proposes that they each pick some items from the menu, and then they will order the items that everyone picked. The menu has $m$ items, and Alice, Bob, and Clara will order $a$, $b$, and $c$ items respectively. Is it possible for them to pick some items such that no item is picked by everyone?

-----Input-----
The input contains a single line with four integers, $m$, $a$, $b$, $c$, where $1\leq m\leq 100,000$, and $1\leq a, b, c\leq m$.

-----Output-----
If it’s possible for Alice, Bob, and Clara to pick some item such that no item on the menu is picked by everyone, print “possible” (without quotes). Otherwise, print “impossible”.

-----Examples-----
Sample Input:
6 2 2 2
Sample Output:
possible
user: Quido plans to send a New Year greeting to his friend Hugo. He has recently acquired access to an advanced high-precision plotter and he is planning to print the greeting card on the plotter.

Here’s how the plotter operates. In step one, the plotter plots an intricate pattern of $n$ dots on the paper. In step two, the picture in the greeting emerges when the plotter connects by a straight segment each pair of dots that are exactly $2018$ length units apart.

The plotter uses a special holographic ink, which has a limited supply. Quido wants to know the number of all plotted segments in the picture to be sure that there is enough ink to complete the job.

-----Input-----
The first line of input contains a positive integer $n$ specifying the number of plotted points. The following $n$ lines each contain a pair of space-separated integer coordinates indicating one plotted point. Each coordinate is non-negative and less than $2^{31}$. There are at most $10^{5}$ points, all of them are distinct.

In this problem, all coordinates and distances are expressed in plotter length units, the length of the unit in the x-direction and in the y-direction is the same.

-----Output-----
The output contains a single integer equal to the number of pairs of points which are exactly $2018$ length units apart.

-----Examples-----
Sample Input:
4
20180000 20180000
20180000 20182018
20182018 20180000
20182018 20182018
Sample Output:
4
user: Jimmy is performing in ByteLand today! Anthony the Ant is a huge fan of Jimmy’s music, so he can’t wait to get to the concert.

ByteLand consists of of $N$ intersections and $M$ roads. Every road is bidirectional and connects two distinct intersections. Anthony is currently on intersection $s$ and the concert is being held at intersection $t$. Anthony must get to the concert in $T$ seconds and he can travel at $1$ meter/second.

Unfortunately for Anthony, he has a huge fear of spiders and ByteLand is full of spiders. Spiders reside at certain intersections in ByteLand. Anthony will choose a path from $s$ to $t$ that maximizes $D$, the minimum distance between any intersection on the path and any spider, such that the path can be travelled in no more than $T$ seconds.

-----Input-----
The first line contains three integers $N$ ($2\leq N\leq 100000$), $M$ ($1\leq M\leq \min (200000, n(n-1)/2)$), and $T$ ($1\leq T\leq 10^9$).

Each of the next $M$ lines specify the roads. A road is described by three integers $u, v$ ($0\leq u, v\leq N-1$ and $u\neq v$) and $d$ ($1\leq d\leq 10000$), which means that a $d$ meters long road connects intersections $u$ and $v$. It is guaranteed that at most one road connect any two intersections, and that there exists a path between any two intersections.

The next line contains $s, t$ ($0\leq s, t\leq N-1$ and $s\neq t$, representing Anthony’s current location and the location of the concert. You may assume Anthony can always travel from $s$ to $t$ in no more than $T$ seconds.

The last line contains a integer $1\leq K\leq N$, denoting the number of intersections occupied by spiders, followed by $K$ integers $0\leq a_ i\leq N-1$ denoting the intersections with spiders.

-----Output-----
Print the maximum $D$ (as defined earlier) for the path Anthony takes.

-----Examples-----
Sample Input:
4 4 3000
0 1 1
1 3 1
2 0 2018
2 3 42
0 3
1 1
Sample Output:
1
user: Pia is getting ready for her flight to the NWERC 2018 in Eindhoven. As she is packing her hard drive, she remembers the airline’s ridiculous weight restrictions, which may pose a problem. You see, the hard drive is essentially a string of ones and zeros, and its weight depends on the number of “bit changes” in it: for any two adjacent bits storing two different values, the hard drive gets slightly heavier, so Pia cannot just store arbitrary information on it.

To make matters worse, the drive is so old that some bits are already broken and will always store zeros. The first bit will never be broken, but the last bit will always be.

Pia decides to treat this situation as a challenge: she is now trying to modify the information on the hard drive so that it has exactly the maximum number of bit changes permitted by the airline. However, the broken bits make this harder than expected, so she needs your help.

Find a bit pattern which can be stored on the hard drive and has exactly the desired number of bit changes.

-----Input-----
The input consists of:
 - One line with three integers $n$, $c$, and $b$ ($2 \leq n \leq 5\cdot 10^5$, $1 \leq c, b \le n-1$), the size of the hard drive in bits, the desired amount of bit changes, and the number of broken bits. The positions on the hard drive are numbered from $1$ to $n$.
 - One line with $b$ integers $z_1, \ldots , z_ b$ ($2 \leq z_1 < z_2 < \ldots < z_ b = n$), the positions of the broken bits on the hard drive.

-----Output-----
Output a bit string of length $n$, representing Pia’s hard drive and containing exactly $c$ bit changes. If there are multiple valid solutions, you may output any one of them. It is guaranteed that at least one solution exists.

-----Examples-----
Sample Input:
5 2 3
2 3 5
Sample Output:
00010