meetforever/GRPO_CL huggingface dataset:
user: Mirko has just installed a brand new drawing program. The program supports $K$ different colours, denoted by integers from 1 to $K$. All drawing is performed on a canvas with dimensions $N\times N$. In the beginning, all cells are white (denoted by 1).

The upper left cell of the canvas has coordinates $(0, 0)$. The first coordinate, $x$, increases iterating over rows, and the second, $y$, increases iterating over columns.

Mirko’s favourite pastime is drawing rectangular checkerboard patterns using the command PAINT c x1 y1 x2 y2, where $c$ denotes the chosen colour, and $(x1, y1)$ and $(x2, y2)$ are coordinates of the upper left and lower right cells, respectively, of the rectangle being painted.

The upper left cell of the rectangle will be painted in the chosen colour, while the rest are determined by the checkerboard pattern. Cells that are not painted over by the chosen colour will retain their previous colour. For example, a white canvas painted over by a red checkerboard pattern will look like this:

Mirko has recently discovered two additional commands. He can save his painting at any time using the creatively named command SAVE, and load it again later using the command LOAD x, where $x$ is a positive integer representing the ordinal number of the save.

Unfortunately, the program has crashed and Mirko’s painting is lost forever. Luckily, Mirko has saved a log of all used commands. Can you help Mirko by reconstructing the lost painting?

-----Input-----
The first line of input contains three positive integers, $N$ ($1 \leq N \leq 1000$), $K$ ($2 \leq K \leq 100000$), and $M$ ($1 \leq M \leq 100000$, $M$ is the number of commands).

Each of the following $M$ lines contains one of the three described commands. The input will not contain any illegal commands.

-----Output-----
Output $N$ lines, each containing N integers representing the colours of cells in the corresponding row of the painting.

-----Examples-----
Sample Input 1:
4 3 2
PAINT 2 0 0 3 3
PAINT 3 0 3 3 3
Sample Output 1:
2 1 2 3
1 2 1 2
2 1 2 3
1 2 1 2

Sample Input 2:
3 3 4
PAINT 3 0 0 1 1
SAVE
PAINT 2 1 1 2 2
LOAD 1
Sample Output 2:
3 1 1
1 3 1
1 1 1
user: All of you are probably very familiar with the problem of finding the longest monotone subsequence. You probably think you know all about it. In order to convince us, solve the problem “opposite” to finding the longest monotone subsequence.

For given $N$ and $K$, find a sequence that consists of numbers from $1$ to $N$ such that each of the numbers in it appears exactly once and the length of its longest monotone subsequence (ascending or descending) is exactly $K$.

-----Input-----
The first line of input contains the integers $N$ and $K$ ($1 \leq K \leq N \leq 10^6$), the length of the sequence and the required length of the longest monotone subsequence.

-----Output-----
If the required sequence doesn’t exist, output $-1$ in the first and only line.

If the required sequence exists, output the required sequence of $N$ numbers in the first and only line. Separate the numbers with a single space.

The required sequence (if it exists) is not necessarily unique, so you can output any valid sequence.

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

Sample Input 2:
5 1
Sample Output 2:
-1
user: $N$ points are placed in the coordinate plane.

Write a program which calculates in how many ways a right triangle can be formed by three of the given points. A right triangle is one in which one of the angles is $90$ degrees.

-----Input-----
The first line of input contains an integer $N$ ($3 \le N \le 1500$), the number of points.

Each of the following $N$ lines contains the coordinates of one point, two integers separated by a space. The coordinates will be between $-10^9$ and $10^9$.

No two points will be located at the same coordinates.

-----Output-----
Output the number of right triangles.

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

Sample Input 2:
4
5 0
2 6
8 6
5 7
Sample Output 2:
0
user: -----Input-----
The first line of input contains a line contains a line with four non-negative integers, $2 \le n \le 250$, $0 \le m \le 5000$, $0 \le s \le n-1$ and $0 \le t \le n-1$, separated by single spaces, where $n$ is the numbers of nodes in the graph, $m$ is the number of edges, $s$ is the source and $t$ is the sink ($s \ne t$). Nodes are numbered from $0$ to $n-1$. Then follow $m$ lines, each line consisting of four (space-separated) integers $u$, $v$, $c$ and $w$ indicating that there is an edge from $u$ to $v$ in the graph with capacity $1 \le c \le 10000$ and cost $1 \le w \le 1000$.

-----Output-----
Output a single line containing two integers; the size $F$ of a maximum flow from node $s$ to node $t$, and the cost of a mimimum cost flow of size $F$. You may assume that $F < 2^{31}$.

-----Examples-----
Sample Input 1:
4 4 0 3
0 1 4 10
1 2 2 10
0 2 4 30
2 3 4 10
Sample Output 1:
4 140

Sample Input 2:
2 1 0 1
0 1 1000 100
Sample Output 2:
1000 100000
user: The International Corporation for Protection and Control (ICPC) develops efficient technology for, well, protection and control. Naturally, they are keen to have their own headquarters protected and controlled. Viewed from above, the headquarters building has the shape of a convex polygon. There are several suitable places around it where cameras can be installed to monitor the building. Each camera covers a certain range of the polygon sides (building walls), depending on its position. ICPC wants to minimize the number of cameras needed to cover the whole building.

-----Input-----
The input consists of a single test case. Its first line contains two integers $n$ and $k$ ($3 \le n \le 10^6$ and $1 \le k \le 10^6$), where $n$ is the number of walls and $k$ is the number of possible places for installing cameras. Each of the remaining $k$ lines contains two integers $a_ i$ and $b_ i$ ($1 \le a_ i, b_ i \le n$). These integers specify which walls a camera at the $i^{th}$ place would cover. If $a_ i \le b_ i$ then the camera covers each wall $j$ such that $a_ i \le j \le b_ i$. If $a_ i > b_ i$ then the camera covers each wall $j$ such that $a_ i \le j \le n$ or $1 \le j \le b_ i$.

-----Output-----
Display the minimal number of cameras that suffice to cover each wall of the building. The ranges covered by two cameras may overlap. If the building cannot be covered, display impossible instead.

-----Examples-----
Sample Input 1:
100 7
1 50
50 70
70 90
90 40
20 60
60 80
80 20
Sample Output 1:
3

Sample Input 2:
8 2
8 3
5 7
Sample Output 2:
impossible
user: A factorial $n!$ of a positive integer $n$ is defined as the product of all positive integers smaller than or equal to $n$. For example,\[ 21! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot 21 = 51090942171709440000. \]

It is straightforward to calculate the factorial of a small integer, and you have probably done it many times before. In this problem, however, your task is reversed. You are given the value of $n!$ and you have to find the value of $n$.

-----Input-----
The input contains the factorial $n!$ of a positive integer $n$. The number of digits of $n!$ is at most $10^{6}$.

-----Output-----
Output the value of $n$.

-----Examples-----
Sample Input 1:
120
Sample Output 1:
5

Sample Input 2:
51090942171709440000
Sample Output 2:
21
user: You have $N$ objects, each with $M$ copies. How many ways are there to take exactly $K$ of them?

-----Input-----
The first line of input contains three integers, $N$, $M$ and $K$ respectively, subjected to $1 \leq N, M, K \leq 10^5$.

-----Output-----
Output the number of ways. As the number of ways could be large, output them modulo $10^6 + 7$.

-----Examples-----
Sample Input 1:
10 1 2
Sample Output 1:
45

Sample Input 2:
3 3 3
Sample Output 2:
10
user: The citizens of Fictitia have had enough! The city keeps getting bigger and bigger, and all the more boring. Fictitia consists of horizontal and vertical streets only. The distance between each pair of neighboring parallel streets is always the same; we take this as the unit distance. Surely some variation could not hurt? 

In order to draw more support and make their unhappiness known to the municipality, a group of citizens has agreed to gather at an intersection of the city to protest. The question is: which intersection? Since there is not much difference between them, the idea was raised to select an intersection $(x^*,y^*)$ that minimizes the total distance everyone has to travel. Since everyone lives close to an intersection, the individual distance travelled by someone who lives at $(x,y)$ is given by $|x-x^*|+|y-y^*|$.

However, this could present a problem for the people who live far away, since they might have trouble getting there in time. Therefore it was decided that the intersection should be at most a certain distance $d$ away from everyone. Given that restriction, can you help them identify an intersection that minimizes the total distance everyone has to travel?

-----Input-----
The input consists of:
 - one line with one integer $n$ ($2 \leq n \leq 100000$), the number of citizens;
 - $n$ lines each with two integers $x$ and $y$ ($0 \leq x,y \leq 10^9$), the coordinates of each citizen’s house;
 - one line with one integer $d$ ($0 \leq d \leq 2 \cdot 10^9$), the maximum distance that each citizen should have to travel.

It is possible for multiple citizens to live at the same intersection.

-----Output-----
Output one line with a single integer: the smallest possible total distance that all citizens need to travel. If there is no intersection that everyone lives within a distance $d$ of, output “impossible” instead.

-----Examples-----
Sample Input 1:
5
3 1
4 1
5 9
2 6
5 3
10
Sample Output 1:
18

Sample Input 2:
5
3 1
4 1
5 9
2 6
5 3
5
Sample Output 2:
20
user: Fourth Great and Bountiful Human Empire is developing a transconduit tunnel network connecting all it’s planets. The Empire consists of $N$ planets, represented as points in the 3D space. The cost of forming a transconduit tunnel between planets $A$ and $B$ is:\[ \operatorname {TunnelCost}(A,B) = \min \{ |x_ A - x_ B |, |y_ A -y_ B |, |z_ A -z_ B | \} \]

where $(x_ A, y_ A, z_ A)$ are the 3D coordinates of planet $A$, and $(x_ B, y_ B, z_ B)$ are coordinates of planet $B$. The Empire needs to build exactly $N - 1$ tunnels in order to fully connect all planets, either by direct links or by chain of links. You need to come up with the lowest possible cost of successfully completing this project.

-----Input-----
The first line of input contains one integer $N$ ($1 \le N \le 100000$), the number of planets.

The next $N$ lines contain exactly $3$ integers each. All integers are between $-10^9$ and $10^9$ inclusive. Each line contains the $x$, $y$, and $z$ coordinate of one planet (in order).

No two planets will occupy the exact same point in space.

-----Output-----
The first and only line of output should contain the minimal cost of forming the network of tunnels.

-----Examples-----
Sample Input 1:
2
1 5 10
7 8 2
Sample Output 1:
3

Sample Input 2:
3
-1 -1 -1
5 5 5
10 10 10
Sample Output 2:
11
user: Your competitors are in possession of a mysterious apparatus which gives them an advantage over you. The apparatus has $n$ on/off switches and $n$ lights. We believe that each of the switches is connected to exactly one of the lights, and vice versa, but we don’t know which switch is connected to which light.

Your spy satellites have taken several different photographs of the apparatus showing different configurations of the switches and lights. Are these photos sufficient to narrow down the number of possible wirings of the mysterious apparatus so that you will be able to build a replica of the mysterious apparatus?

-----Input-----
The first line of input consists of two integers $n$ and $m$, where $1 \le n \le 1000$ is the number of switches/lights on the apparatus, and $0 \le m \le 1000$ is the number of photos you have of the apparatus. The next lines describe the photos. Each photo is described by two lines, each containing a binary string of length $n$. The $i$’th position in the first line indicates whether the $i$’th switch is on (1) or off (0), and the $i$’th position in the second line indicates whether the $i$’th light is on (1) or off (0).

-----Output-----
Write a single line of output giving the number of different wirings of the apparatus that are consistent with all the photographs. As this number may be huge, we only ask that you compute it modulo 1000003.

-----Examples-----
Sample Input 1:
3 1
110
011
Sample Output 1:
2

Sample Input 2:
4 2
1000
1000
0000
0010
Sample Output 2:
0
user: Young Mirko has been buying voodoo dolls lately. Considering that he is very interested in the cheapest purchase possible, he has been tracking the prices of voodoo dolls each day. His price list consists of doll prices in the last $N$ days, where doll price $a_ i$ represents the price of a doll $i$ days ago.

Mirko thinks he has noticed a connection between the average doll price in a sequence of consecutive days and the price on the following day. He wants to test his hunch and is puzzled by a very interesting question: “For a given $P$, how many different consecutive subsequences in the last $N$ days are there, when the average doll price was greater than or equal to $P$?”

Two consecutive subsequences are considered different if their beginnings or ends are different.

-----Input-----
The first line of input contains the integer $N$, the sequence length ($1 \leq N \leq 1000000$). The second line of input contains $N$ prices $a_ i$ ($0 \leq a_ i \leq 1000000000$). The third line of input contains an integer $P$. ($0 \leq P \leq 1000000000$).

-----Output-----
The first and only line of output must contain the answer to Mirko’s question for a given $P$.

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

Sample Input 2:
3
1 3 2
2
Sample Output 2:
5
user: Your fancy debugger will not help you in this matter. There are many ways in which code can produce different behavior between debug and release builds, and when this happens, one may have to resort to more primitive forms of debugging. 

So you and your printf are now on your own in the search for a line of code that causes the release build to crash. Still you are lucky: adding printf statements to this program affects neither the bug (it still crashes at the same original code line) nor the execution time (at least not notably). So even the naive approach of putting a printf statement before each line, running the program until it crashes, and checking the last printed line, would work.

However, it takes some time to add each printf statement to the code, and the program may have a lot of lines. So perhaps a better plan would involve putting a printf statement in the middle of the program, letting it run, seeing whether it crashes before the added line, and then continuing the search in either the first or second half of the code.

But then again, running the program may take a lot of time, so the most time-efficient strategy might be something in between. Write a program that computes the minimum worst-case time to find the crashing line (no matter where it is), assuming you choose an optimal strategy for placing your printf statements.

We’re releasing the new version in five hours, so this issue is escalated and needs to be fixed ASAP.

-----Input-----
The input consists of one line with three integers:
 - $n$ ($1 \le n \le 10^6$), the number of code lines;
 - $r$ ($1 \le r \le 10^9$), the amount of time it takes to compile and run the program until it crashes;
 - $p$ ($1 \le p \le 10^9$), the time it takes to add a single printf line.

You have already run the program once and therefore already know that it does crash somewhere.

-----Output-----
Output the worst-case time to find the crashing line when using an optimal strategy.

-----Examples-----
Sample Input 1:
1 100 20
Sample Output 1:
0

Sample Input 2:
10 10 1
Sample Output 2:
19
user: You just graduated from programming school and nailed a Python programming job. The first day at work you realize that you have inherited a mess. The spaghetti design pattern was chosen by the previous maintainer, who recently fled the country. You try to make sense of the code, but immediately discover that different files depend cyclically on each other. Testing the code, in fact running the code, has not yet been attempted. 

As you sit down and think, you decide that the first thing to do is to eliminate the cycles in the dependency graph. So you start by finding a shortest dependency cycle.

-----Input-----
The first line of input contains a number $n$, $1 \le n \le 500$, the number of files. Then follows one line with $n$ distinct names of files. Each name is a string with at least $1$ and at most $8$ lower case letters ‘a’ to ‘z’. Then follow $n$ sections, one section per file name, in the order they were given on the second line. Each section starts with one line containing the name of the file and an integer $k$, followed by $k$ lines, each starting with “import”.

Each “import” line is a comma-space separated line of dependencies. No file imports the same file more than once, and every file imported is listed in the second line of the input. Comma-space separated means that every line will start with “import”, then have a list of file names separated by “, ” (see sample inputs for examples). Each import statement is followed by at least one file name.

-----Output-----
If the code base has no cyclic dependencies, output “SHIP IT”. Otherwise, output a line containing the names of files in a shortest cycle, in the order of the cycle (i.e., the $i$th file listed must import the $(i+1)$st file listed, and the last file listed must import the first). If there are many shortest cycles, any one will be accepted.

-----Examples-----
Sample Input 1:
4
a b c d
a 1
import d, b, c
b 2
import d
import c
c 1
import c
d 0
Sample Output 1:
c

Sample Input 2:
5
classa classb myfilec execd libe
classa 2
import classb
import myfilec, libe
classb 1
import execd
myfilec 1
import libe
execd 1
import libe
libe 0
Sample Output 2:
SHIP IT
user: A student called Slon is very mischievous in school. He is always bored in class and he is always making a mess. The teacher wanted to calm him down and “tame” him, so he has given him a difficult mathematical problem.

The teacher gives Slon an arithmetic expression $A$, the integer $P$ and $M$. Slon has to answer the following question: “What is the minimal non-negative value of variable x in expression $A$ so that the remainder of dividing $A$ with $M$ is equal to $P$?”. The solution will always exist.

Additionally, it will hold that, if we apply the laws of distribution on expression $A$, variable $x$ will not multiply variable $x$ (formally, the expression is a polynomial of the first degree in variable $x$).

Examples of valid expressions: $5 + x \cdot (3 + 2)$, $x + 3 \cdot x + 4 \cdot (5 + 3 \cdot (2 + x - 2 \cdot x))$.

Examples of invalid expressions: $5 \cdot (3 + x \cdot (3 + x))$, $x \cdot (x + x \cdot (1 + x))$.

-----Input-----
The first line of input contains the expression $A$ ($1 \leq \lvert A\rvert \leq 100000$). The second line of input contains two integers $P$ ($0 \leq P \leq M - 1$) and $M$ ($1 \leq M \leq 1000000$). The arithmetic expression $A$ will only consists of characters +, -, *, (, ), x and digits from 0 to 9. The brackets will always be paired, the operators +, - and * will always be applied to exactly two values (there will not be an expression $(-5)$ or $(4+-5)$) and all multiplications will be explicit (there will not be an expression $4(5)$ or $2(x)$).

-----Output-----
The first and only line of output must contain the minimal non-negative value of variable $x$.

-----Examples-----
Sample Input 1:
5+3+x
9 10
Sample Output 1:
1

Sample Input 2:
20+3+x
0 5
Sample Output 2:
2
user: Images by John Fowler, Carol Highsmith, and Richard Woodland

You have decided to spend a day of your trip to Rapid City taking photographs of the South Dakota Badlands, which are renowned for their spectacular and unusual land formations. You are an amateur photographer, yet very particular about lighting conditions.

After some careful research, you have located a beautiful location in the Badlands, surrounded by picturesque landscapes. You have determined a variety of features that you wish to photograph from this location. For each feature you have identified the earliest and latest time of day at which the position of the sun is ideal. However, it will take quite a bit of time to take each photograph, given the need to reposition the tripod and camera and your general perfectionism. So you are wondering if it will be possible to successfully take photographs of all these features in one day.

-----Input-----
The first line of the input contains two integers $n$ ($1 \leq n \leq 10^4$) and $t$ ($1 \leq t \leq 10^5$), where $n$ is the number of desired photographs and $t$ is the time you spend to take each photograph. Following that are $n$ additional lines, each describing the available time period for one of the photographs. Each such line contains two nonnegative integers $a$ and $b$, where $a$ is the earliest time that you may begin working on that photograph, and $b$ is the time by which the photograph must be completed, with $a + t \leq b \leq 10^9$.

-----Output-----
Display yes if it is possible to take all $n$ photographs, and no otherwise.

-----Examples-----
Sample Input 1:
2 10
0 15
5 20
Sample Output 1:
yes

Sample Input 2:
2 10
1 15
0 20
Sample Output 2:
no
user: Sarah is cycling to work. On her way there, she encounters the same traffic light every day. Before she reaches the lights, she alternates between using social media on her mobile device and glancing at the traffic lights, observing if they are green, yellow or red at that time. From experience, she knows that the lights have a fixed green-yellow-red cycle, and how long each stage lasts. So if the light goes from red to green at time $T$, she knows it will stay green until (but not including) $T+T_ g$, then go yellow until (but not including) $T+T_ g+T_ y$ and finally stay red until (but not including) $T+T_ g+T_ y+T_ r$, at which point it will turn green again. However, she does not know $T$, the time at which the traffic light cycle starts. Based on her observations, she can deduce what values of $T$ are (im)possible. Assuming that all possible values of $T$ that are consistent with her observations are equally likely, can you compute the probability that the lights will be green at a certain time?

-----Input-----
 - The first line contains three positive integers $T_ g$ $T_ y$ $T_ r$, corresponding to the duration (in seconds) for which the lights stay green, yellow, and red ($0 < T_ g,T_ y,T_ r \leq 10^8$).
 - The second line contains a single positive integer $n$, the number of times Sarah looked at the lights ($3 \leq n < 1000$).
 - Each of the next $n$ lines contains one integer $0\leq t \leq 10^9$ followed by a color $c$: the time (in seconds) of the observation and color of the lights at that moment. The times of the observations are given in strictly increasing order. Sarah did see the lights being each color (green, yellow, and red) at least once.
 - The last line contains an integer $ 0 \leq t_ q \leq 10^9$ and a color $c_ q$. These specify the question asked: What is the probability of the lights being color $c_ q$ at time $t_ q$?

-----Output-----
 - $0 \leq p \leq 1$, the probability of the lights being color $c_ q$ at time $t_ q$. Your answer is considered correct if it has absolute or relative error of at most $10^{-3}$.

-----Examples-----
Sample Input 1:
4 4 4
3
2 green
18 yellow
34 red
5 green
Sample Output 1:
0.25

Sample Input 2:
4 4 4
4
2 green
6 yellow
10 red
14 green
4 red
Sample Output 2:
0