meetforever/GRPO_CL huggingface dataset:
user: Nested quotations are great not only for writing literature with a complex narrative structure, but also in programming languages. While it may seem necessary to use different quotation marks at different nesting levels for clarity, there is an alternative. We can display various nesting levels using $k$-quotations, which are defined as follows.

A $1$-quotation is a string that begins with a quote character, ends with another quote character and contains no quote characters in-between. These are just the usual (unnested) quotations. For example, 'this is a string' is a $1$-quotation.

For $k > 1$, a $k$-quotation is a string that begins with $k$ quote characters, ends with another $k$ quote characters and contains a nested string in-between. The nested string is a non-empty sequence of $(k-1)$-quotations, which may be preceded, separated, and/or succeeded by any number of non-quote characters. For example, ''All 'work' and no 'play''' is a $2$-quotation.

Given a description of a string, you must determine its maximum possible nesting level.

-----Input-----
The input consists of two lines. The first line contains an integer $n$ ($1 \le n \le 100$). The second line contains $n$ integers $a_1, a_2, \ldots , a_ n$ ($1 \le a_ i \le 100$), which describe a string as follows. The string starts with $a_1$ quote characters, which are followed by a positive number of non-quote characters, which are followed by $a_2$ quote characters, which are followed by a positive number of non-quote characters, and so on, until the string ends with $a_ n$ quote characters.

-----Output-----
Display the largest number $k$ such that a string described by the input is a $k$-quotation. If there is no such $k$, display no quotation instead.

-----Examples-----
Sample Input 1:
5
2 1 1 1 3
Sample Output 1:
2

Sample Input 2:
1
22
Sample Output 2:
4
user: Even though she saw Zvonko steal Mirko’s microprocessor in the second task, Mirko’s sister Ivana did not tell Mirko because she likes Zvonko. She suggested to him that they go see a movie together so that she would “forget” about the incident.

Zvonko does not care much for girls because they take away precious time he usually spends practicing his math-fu. He suggested that the two of them play a game and, if Ivana wins, they will go see a movie together. Ivana agreed, being good at jump rope and she sometimes even kicks a football around with her two brothers.

Zvonko laid $N$ positive integers in a circle on the floor and explained the rules:
 - The first player takes any number.
 - The second player takes either of the two numbers adjacent to the one the first player took.
 - The next player takes a number adjacent to any of the numbers taken so far, and so on until they run out of numbers. The player to take more odd numbers (not divisible by 2) wins.

Zvonko plays optimally; he always looks for a strategy that leads to certain victory or a draw. Zvonko does not know how well Ivana plays. Being a true cavalier, he let Ivana have the first move. But Ivana only cares about sitting next to Zvonko in front of the big screen so she seeks help playing.

Write a program that finds how many different first moves Ivana can make, so that she has a chance of winning afterwards.

-----Input-----
The first line of input contains an integer $N$ $(1 \leq N \leq 100)$, how many numbers there are in the circle. The second line contains $N$ integers separated by single spaces. All numbers will be between $1$ and $1000$ (inclusive). No two numbers will be the same.

-----Output-----
Output the desired number on a single line.

-----Examples-----
Sample Input 1:
3
3 1 5
Sample Output 1:
3

Sample Input 2:
4
1 2 3 4
Sample Output 2:
2
user: Apostrophes and double quotes tend to get badly encoded by systems, causing them to print back things like &#x27; or \". As a QA tester, Nova has seen lots of these issues. Today, she overheard that the Tweeper messaging app may have an issue with these symbols as well, and may encode them in strange ways. This was interesting, so she has written a Tweep to see if this is the case. Based on this Tweep, can you find out if Tweeper has an encoding issue, and if so, what the symbols are encoded into?

-----Input-----
The input is two strings separated by a line. The first string $I$ represents the input characters that was sent in, and the second string $O$ is how Tweeper presents the string. To avoid encoding troubles, apostrophes and double quotes have been replaced with + and -, respectively.

-----Output-----
The output should have $n$ lines of output, one for each possible encoding + and - may have. Each line must have two strings $a^{+}_ i$ and $a^{-}_ i$, representing what a + and a - can be encoded as, respectively.

If the string is empty, print instead <empty>, and if the string can be anything, print <any>. If there are multiple answers, you can output them in any order.

If there is no valid answer, write corrupted instead.

-----Limits-----
 - $1 \leq |I|, |O| \leq 280$
 - $I$ and $O$ contain only the lowercase letters a-z, 0-9, + and -

-----Examples-----
Sample Input 1:
a+b-c
a-b+d-c
Sample Output 1:
- +d-

Sample Input 2:
knuth-morris-pratt
knuthmorrispratt
Sample Output 2:
<any> <empty>
user: Having recently been hired by Netwerc Industries as a network engineer, your first task is to assess their large and dated office network. After mapping out the entire network, which consists of network switches and cables between them, you get a hunch that, not only are some of the switches redundant, some of them are not used at all! Before presenting this to your boss, you decide to make a program to test your claims. 

The data you have gathered consists of the map of the network, as well as the length of each cable. While you do not know the exact time it takes to send a network packet across each cable, you know that it can be calculated as $\ell / v + c$, where
 - $\ell $ is the length of the cable,
 - $v$ is the propagation speed of the cable, and
 - $c$ is the overhead of transmitting the packet on and off the cable.

You have not been able to measure $v$ and $c$. The only thing you know about them is that they are real numbers satisfying $v > 0$ and $c \ge 0$, and that they are the same for all cables. You also know that when a network packet is being transmitted from one switch to another, the network routing algorithms will ensure that the packet takes an optimal path—a path that minimises the total transit time.

Given the map of the network and the length of each cable, determine which switches could never possibly be part of an optimal path when transmitting a network packet from switch $1$ to switch $n$, no matter what the values of $v$ and $c$ are.

-----Input-----
The input consists of:
 - One line with two integers $n$, $m$ ($2 \leq n \leq 2000$, $1 \leq m \leq 10^4$), the number of switches and the number of cables in the network. The switches are numbered from $1$ to $n$.
 - $m$ lines, each with three integers $a$, $b$ and $\ell $ ($1 \leq a, b \leq n$, $1\leq \ell \leq 10^9$), representing a network cable of length $\ell $ connecting switches $a$ and $b$.

There is at most one cable connecting a given pair of switches, and no cable connects a switch to itself. It is guaranteed that there exists a path between every pair of switches.

-----Output-----
First output a line with an integer $k$, the number of switches that could never possibly be part of an optimal path when a packet is transmitted from switch $1$ to switch $n$. Then output a line with $k$ integers, the indices of the $k$ unused switches, in increasing order.

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

Sample Input 2:
5 6
1 2 2
2 3 2
3 5 2
1 4 3
4 5 3
1 5 6
Sample Output 2:
0
user: A long time ago in a galaxy far, far away$\ldots $ there was a cinematic universe with countless sequels, prequels, and everything in-between. You have always been confused of the ordering of the Star Wars movies. First they created the plot order movies $4$, $5$ and $6$. Then movie $1$, $2$ and $3$. Now they are creating side plot movies that fit in between old movies. 

We actually have two orderings of Star Wars movies: creation order and plot order. You’d like to be able to translate between these orderings. Both orderings start at $1$. If a movie is created and inserted at plot index $i$ the plot index of every movie with a plot index $j$ where $i \leq j$ is increased by $1$.

-----Input-----
The first line of the input contains a single number $Q$, where $1 < Q \leq 600000$.

Then follows $Q$ lines with a query on each.

A query has the following form $q x$, where $q$ is either $1$ or $2$, and $x$ is a positive integer. If $q$ is $1$ it means that we created a movie that currently is number $x$ in plot order. For $q=2$ we would like to know what the creation index is of the movie that currently has the plot index $x$.

If the number of movies so far is denoted with $n$, it is guaranteed that if $q=1$, $1 \leq x \leq n+1$ and if $q=2$, $1 \leq x \leq n$.

-----Output-----
For each query with $q=2$ output a line with a single number, the creation index of the movie with plot index $x$.

-----Sample Explanation-----
Sample Input $1$ corresponds to the $6$ original Star Wars movies. First three movies were created in order, then three more were created that has plot indices prior to the three created first. Then we inspect the creation order of all the movies in plot order. The $1$st, $2$nd and $3$rd movies in plot order are the $4$th, $5$th and $6$th movies created. The $4$th, $5$th and $6$th movies in plot order are the $1$st, $2$nd and $3$rd movies created.

-----Examples-----
Sample Input 1:
12
1 1
1 2
1 3
1 1
1 2
1 3
2 1
2 2
2 3
2 4
2 5
2 6
Sample Output 1:
4
5
6
1
2
3

Sample Input 2:
6
1 1
1 2
1 3
2 1
2 2
2 3
Sample Output 2:
1
2
3
user: Peter has lined up hay bales. Some hay bales contain parasites and he wants to move the infected hay bales to the back of the sequence, to minimize the chance that the parasites spread. To sort the haybales, he repeatedly takes out any three consecutive hay bales and puts them back in sorted order. Your task is to calculate the minimum number of operations Peter has to execute to sort the sequence.

-----Input-----
The input contains a single string $s$ ($3 \leq |s| \leq 500$), the sequence of hay bales. Each character of $s$ is either ‘C’ (for a clean hay bale) or ‘P’ (for an infected one).

-----Output-----
The output must contain one integer, the minimum number of steps Peter has to execute.

-----Examples-----
Sample Input 1:
CPCC
Sample Output 1:
1

Sample Input 2:
PPPPCCCC
Sample Output 2:
8
user: —“I’m stopping by Žnidaršić’s house, you play the piano, Perica.”

 —“Ok, dad, I will!”

And so, Perica began playing the piano. His piano consists of $N$ keys. Each key has a value written on it, $a_ i$. When Perica plays the piano, he presses exactly $K$ different keys at the same time. The piano is a bit strange because, after pressing $K$ keys at the same time, it will play only the key with the largest value. Perica is going to play each combination of $K$ keys on the piano and he wants to know the sum of values of the keys that will be played.

Help Perica determine the remainder of that number modulo $1000000007$.

-----Input-----
The first line of input contains two integers $N$ and $K$ ($1 \leq N \leq 100000$, $1 \leq K \leq 50$). The following line of input contains $N$ integers $a_ i$ ($0 \leq a_ i \leq 10^9$).

-----Output-----
The first and only line of output must contain the required number from the task.

-----Examples-----
Sample Input 1:
5 3
2 4 2 3 4
Sample Output 1:
39

Sample Input 2:
5 1
1 0 1 1 1
Sample Output 2:
4
user: Archeologists recently found the remains of Greco-Roman architecture. The location can be modeled as a grid of $R \cdot C$ square cells. For each of the cells, archeologists have determined if some building was there or if the cell has always been empty.

After examining the artifacts in detail, they concluded that the location contains two buildings from different periods in time, and that the floor plans of both buildings are of square shape.

Because the buildings were from different periods in time, it is possible that their floor plans overlap. Determine the possible location and size (length of the side of the square occupied by the floor plan) for each building.

-----Input-----
The first line contains two integers $R$ ($1 \le R \le 100$) and $C$ ($1 \le C \le 100$), the size of the location.

Each of the next $R$ lines contains a string of $C$ characters ‘.’ (dot) or ‘x’ (lowercase letter). The character ‘.’ means that nothing was found in that cell, while ‘x’ indicates that there was a building there.

-----Output-----
For each of the two buildings, output on a single line the row and column of its upper left corner, and the size (side length) of the building.

Note: the test data will be such that a solution always exists, although it may not be unique. If there is more than one solution, any one will be accepted.

-----Examples-----
Sample Input 1:
3 3
xx.
xxx
...
Sample Output 1:
1 1 2
2 3 1

Sample Input 2:
4 6
xx....
xx.xxx
...xxx
...xxx
Sample Output 2:
1 1 2
2 4 3
user: Alice and Bob are travelling in Italy. They are travelling by car and unfortunately they took a wrong turn. Now they are stuck in the city centre of Pisa. (You may know that you need an allowance to drive in the city centre, so they are at risk of getting a fine.) As they were not fully prepared for this, they have a map, but no GPS. The map lists all intersections. At each intersection you can go either left or right (you cannot go straight or take a U-turn, as many streets are one-way).

Of course, they paid attention when entering Pisa and tried to follow on the map. Unfortunately, Alice thinks they are at intersection $A$, while Bob believes they are now at intersection $B$. You can imagine this is quite a stressful situation. Instead of figuring out how to get out of Pisa, they want to know who is right first. On the map it is indicated from which intersections you can see the leaning tower of Pisa. So they believe they can conduct an experiment: drive a bit and take the same actions on the map starting from $A$ and $B$. They can trace the route they drive on the map for both of their starting points. As soon as the tower of Pisa should be visible for one of them but not for the other, they can look out of the window to see who is right. You may assume exactly one of them is right.

-----Input-----
 - The first line of the input has three space-separated integers. The first integer, $2 \leq n \leq 10^5$ is the number of intersections. The next two integers are $0 \leq A, B < n$, the intersections that Alice and Bob respectively think they are currently at. In particular $A \neq B$.
 - Then follow $n$ lines. The $i$’th of these lines ($0\leq i<n$) has three space-separated integers: $l_ i$ $r_ i$$t_ i$. If you are at intersection $i$ and take a left turn, you arrive at $l_ i$, while a right turn brings you to $r_ i$. The number $t_ i = 1$ if you can see the leaning tower of Pisa from intersection $i$. Otherwise $t_ i = 0$.

-----Output-----
Print the minimal number of turns it takes to show either person correct. If no experiment can tell whether Alice or Bob is correct, print “indistinguishable”.

-----Examples-----
Sample Input 1:
3 1 2
1 2 1
0 2 0
0 1 0
Sample Output 1:
indistinguishable

Sample Input 2:
2 0 1
1 1 1
0 0 0
Sample Output 2:
0
user: Consider an $n \times m$ matrix of ones and zeros. For example, this $4 \times 4$:$\begin{matrix} 1 & 1 & 1 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 1 & 1 & 0 \end{matrix}$

We can compute even parity for each row, and each column. In this case, the row parities are $[0, 1, 1, 0]$ and the column parities are $[1, 0, 0, 1]$ (the parity is $1$ if there is an odd number of $1$s in the row or column, $0$ if the number of $1$s is even). Note that the top row is row $1$, the bottom row is row $n$, the leftmost column is column $1$, and the rightmost column is column $m$.

Suppose we lost the original matrix, and only have the row and column parities. Can we recover the original matrix? Unfortunately, we cannot uniquely recover the original matrix, but with some constraints, we can uniquely recover a matrix that fits the bill. Firstly, the recovered matrix must contain as many $1$’s as possible. Secondly, of all possible recovered matrices with the most $1$’s, use the one which has the smallest binary value when you start with row $1$, concatenate row $2$ to the end of row $1$, then append row $3$, row $4$, and so on.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will consist of exactly two lines. The first line will contain a string $R$ ($1 \le |R| \le 50$), consisting only of the characters $0$ and $1$. These are the row parities, in order. The second line will contain a string $C$ ($1 \le |C| \le 50$), consisting only of the characters $0$ and $1$. These are the column parities, in order.

-----Output-----
If it is possible to recover the original matrix with the given constraints, then output the matrix as $|R|$ lines of exactly $|C|$ characters, consisting only of $0$’s and $1$’s. If it is not possible to recover the original matrix, output $-1$.

-----Examples-----
Sample Input 1:
0110
1001
Sample Output 1:
1111
0111
1110
1111

Sample Input 2:
0
1
Sample Output 2:
-1
user: “Increase my killing power, eh?” – Homer Simpson

You are probably familiar with the binary representation of integers, i.e. writing a nonnegative integer $n$ as $\sum _{i=0}^k a_ i \cdot 2^i$, where each $a_ i$ is either $0$ or $1$. In this problem, we consider a so called signed binary representation, in which we still write $n$ as $\sum _{i=0}^{k} a_ i \cdot 2^i$, but allow $a_ i$ to take on the values $-1$, $0$ and $1$. For instance, $n=13$ can be represented as\[ (1, 0, 0, -1, -1) = 2^4 - 2^1 - 2^0. \]

The binary representation of a number is unique, but obviously, the signed binary representation is not. In certain applications (e.g. in cryptography), one seeks to write a number $n$ in signed binary representation with as few non-zero digits as possible. For example, we consider the representation $(1, 0, 0, -1)$ to be a better representation of $n = 7$ than $(1, 1, 1)$. Your task is to write a program which will find such a minimal representation.

-----Input-----
The input consists of a single line containing a positive integer $n < 2^{100000}$ written in binary, without leading zeros.

-----Output-----
For each line of input, output one line containing the signed binary representation of $n$ that has the minimal number of non-zero digits, using the characters ‘-’ for $-1$, ‘0’ for $0$ and ‘+’ for $+1$. The number should be written without leading zeros. If there are several minimal representations, output the one that is lexicographically smallest (by the ASCII ordering, in which $‘\texttt{+}‘ < ‘\texttt{-}‘ < ‘\texttt{0}‘$).

-----Examples-----
Sample Input 1:
10000
Sample Output 1:
+0000

Sample Input 2:
1111
Sample Output 2:
+000-
user: Greg Brandon Sr. is working at a shipping company in Redmond that specializes in shipping Chromium. Redmond contains $n$ intersections and $m$ two-way roads that directly connect two intersections (Redmond can be modelled as a graph with $n$ vertices and $m$ edges). It is always possible to travel from any intersection to any other intersection via the roads.

The shipping company has two warehouses and $s$ employees. The warehouses and employees are currently located at some of the intersections in Redmond. Greg needs to make $t$ deliveries to his clients who are also located at some of the intersections in Redmond. For each delivery, one of his employees will travel to either warehouse to pick up the item to deliver, then travel to the corresponding client. Each warehouse always contains an infinite amount of each item. Greg would like to minimize the total distance travelled by his employees (he does not care about the return trip). Each employee may make at most one delivery.

-----Input-----
The first line of input contains four space-separated integers $n$, $m$, $s$, and $t$ ($2\le n\le 10^5$, $n-1\le m\le 2\cdot 10^5$, and $1\le t\le s\le 10^5$), denoting the number of intersections, the number of roads, the number of employees, and the number of deliveries respectively.

The second line of input contains two space-separated integers $a$ and $b$ ($1\le a, b\le n$), denoting the locations of the two warehouses. The warehouses could be at the same intersection.

The third line of input contains $s$ space-separated integers $x_ i$ ($1\le x_ i\le n$), denoting the locations of the $s$ employees. The $x_ i$’s are not necessarily distinct.

The fourth line of input contains $t$ space-separated integers $y_ i$ ($1\le y_ i\le n$), denoting the locations of the clients for the $t$ deliveries. The $y_ i$’s are not necessarily distinct.

Each of the next $m$ lines of input contains three space-separated integers $u$, $v$, and $d$ ($1\le u, v\le n$, $u\neq v$, and $1\le d\le 10^8$), denoting a road of distance $d$ connecting intersections $u$ and $v$. It is always possible to travel from one intersection to all other intersections.

-----Output-----
The only line of output should contain a single integer denoting the minimum total distance.

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

Sample Input 2:
2 1 1 1
2 2
1
1
1 2 1
Sample Output 2:
2
user: Luka is bored in chemistry class yet again. This time, he’s playing with intelligent bacteria. He has arranged his $K$ bacteria on a rectangular board divided in $N$ rows, labelled with numbers from $1$ to $N$ starting from the top, and $M$ columns, labelled with numbers from $1$ to $M$ starting from the left.

Each bacterium begins its adventure in a certain cell, facing one of the four neighbouring cells, and carries out the following actions every second:
 - Reads the number $X$ dedicated to that bacterium in the current cell.
 - Turns $90$ degrees clockwise, $X$ times.
 - If it is facing a cell outside the board, it turns $180$ degrees.
 - Finally, it moves to the cell that it is facing.

Luka has placed a trap in one cell. The trap will activate and kill the bacteria as soon as they all step on that cell in the same second.

Since Luka only has two hours of chemistry class today, help him determine how long the game will last, in seconds.

-----Input-----
The first line of input contains the positive integers $N$ ($3 \leq N \leq 50$), $M$ ($3 \leq M \leq 50$), and $K$ ($1 \leq K \leq 5$).

The second line of input contains the positive integers $X$ and $Y$, the row and column where Luka has placed the trap.

The remainder of the input consists of bacteria descriptions, for each bacterium $i$ from $1$ to $K$:
 - two positive integers $X_ i$, $Y_ i$ – the row and column of the starting cell of bacterium $i$, and the character $C_ i$ representing the starting direction that the bacterium is facing ($U$ – up, $R$ – right, $D$ – down, $L$ – left).
 - $N$ by $M$ matrix of digits between $0$ and $9$, inclusive; the digit in row $x$ and column $y$ represents the number in cell $(x, y)$ dedicated to bacterium $i$.

-----Output-----
The first and only line of output must contain the total duration of Luka’s game, in seconds. If the game will never end, output -1.

-----Examples-----
Sample Input 1:
3 3 1
2 2
1 1 R
010
000
000
Sample Output 1:
2

Sample Input 2:
3 4 2
2 2
3 4 R
2327
6009
2112
3 2 R
1310
2101
1301
Sample Output 2:
7