meetforever/GRPO_CL huggingface dataset:
user: Gunnar dislikes forces of nature and always comes up with innovative plans to decrease their influence over him. Even though his previous plan of a giant dome over Stockholm to protect from too much sunlight (as well as rain and snow) has not yet been realized, he is now focusing on preempting the possible effects climate change might have on the Baltic Sea, by the elegant solution of simply removing the Baltic from the equation. 

First, Gunnar wants to build a floodbank connecting Denmark and Norway to separate the Baltic from the Atlantic Ocean. The floodbank will also help protect Nordic countries from rising sea levels in the ocean. Next, Gunnar installs a device that can drain the Baltic from the seafloor. The device will drain as much water as needed to the Earth’s core where it will disappear forever (because that is how physics works, at least as far as Gunnar is concerned). However, depending on the placement of the device, the entire Baltic might not be completely drained – some pockets of water may remain.

To simplify the problem, Gunnar is approximating the map of the Baltic using a $2$-dimensional grid with $1$ meter squares. For each square on the grid, he computes the average altitude. Squares with negative altitude are covered by water, squares with non-negative altitude are dry. Altitude is given in meters above the sea level, so the sea level has altitude of exactly $0$. He disregards lakes and dry land below the sea level, as these would not change the estimate much anyway.

Water from a square on the grid can flow to any of its $8$ neighbours, even if the two squares only share a corner. The map is surrounded by dry land, so water never flows outside of the map. Water respects gravity, so it can only flow closer to the Earth’s core – either via the drainage device or to a neighbouring square with a lower water level.

Gunnar is more of an idea person than a programmer, so he has asked for your help to evaluate how much water would be drained for a given placement of the device.

-----Input-----
The first line contains two integers $h$ and $w$, $1 \leq h, w \leq 500$, denoting the height and width of the map.

Then follow $h$ lines, each containing $w$ integers. The first line represents the northernmost row of Gunnar’s map. Each integer represents the altitude of a square on the map grid. The altitude is given in meters and it is at least $-10^6$ and at most $10^6$.

The last line contains two integers $i$ and $j$, $1 \leq i \leq h, 1 \leq j \leq w$, indicating that the draining device is placed in the cell corresponding to the $j$’th column of the $i$’th row. You may assume that position $(i, j)$ has negative altitude (i.e., the draining device is not placed on land).

-----Output-----
Output one line with one integer – the total volume of sea water drained, in cubic meters.

-----Examples-----
Sample Input:
3 3
-5 2 -5
-1 -2 -1
5 4 -5
2 2
Sample Output:
10
user: Frida is a writer for Cosmopolitan who writes restaurant reviews. She enjoys it a lot, but it seems that, throughout the years, she has reviewed all the restaurants on Earth. It’s now time to move one level up; she is going to review the food served by the airlines, so that the readers can make better decisions on which flights to take.

Her boss gave her a list of flight connections that she needs to review for the upcoming issue of Cosmopolitan. She knows that they serve the same food in both directions of every flight, so she only needs to take it once. She realized that she will need to take some additional flights, because she can not make all reviews using only flights in the list from her boss. Therefore she did some quick research and made a list of additional flights which she might take. She will not review the food on these flights; they will only be used so that she can make all the reviews.

Frida’s goal is to make all the reviews while spending the least money on flight tickets. Her office is in Stockholm, so she starts and ends her journey there. Each flight is both ways between two cities and has a fixed price in both directions. You can assume that it is possible to make all the reviews using some of the additional flights.

For the purposes of this problem we ignore the price Frida has to pay for accommodation and we also ignore the departure and arrival times of flights by assuming that every flight is very often and reasonably short. We only focus on the total price of the flights.

-----Input-----
The first line contains $2$ space separated integers $N, R, (2\leq N\leq 13, 0\leq R\leq 78)$, where $N$ is the number of airports mentioned in the input and $R$ is the number of flights to review. The airports are numbered $1, \dots , N$ and Stockholm has number $1$.

The next $R$ lines describe the $R$ flights to review. Each line contains 3 space separated integers $a, b, c, (1\leq a, b\leq N, 1\leq c\leq 10000)$, where $a, b$ denote 2 distinct airports and $c$ is the cost of the flight in Swedish kronor in both directions. No pair of $2$ cities is listed twice.

The next line contains an integer $F$, $(0\leq F\leq 200)$, the number of additional flights available. The next $F$ lines contain descriptions of flights in the same format as above. There may be more flights between a pair of cities. You may assume that it is possible to make all the reviews using some of these additional flights.

-----Output-----
Output one line with one integer – the lowest total cost of flight tickets, such that Frida can make all the reviews and return back to Stockholm.

-----Examples-----
Sample Input:
5 3
1 2 1000
2 3 1000
4 5 500
2
1 4 300
3 5 300
Sample Output:
3100
user: According to Sheldon Cooper, the best number is $73$. In his own words, “The best number is $73$. $73$ is the $21$st prime number. Its mirror, $37$, is the $12$th, and its mirror, $21$, is the product of multiplying $7$ and $3$. In binary, $73$ is a palindrome: $1001001$, which backwards is $1001001$. Exactly the same.”

Prime numbers are boring stuff, and so are palindromes. On the other hand, the binary representation of $73$ is rather remarkable: it’s $1$ one followed by $2$ zeroes, followed by $1$ one, followed by $2$ zeros, followed by $1$ one. This is an interesting pattern that we can generalize: $N$ ones, followed by $M$ zeros, followed by $N$ ones, followed by $M$ zeros, etc, ending in either $N$ ones or $M$ zeroes. For $73$, $N$ is $1$, $M$ is $2$, and there are $5$ runs of equal symbols. With $N = 2$, $M = 1$ and $4$ runs, we would have the string $110110$, which is the binary representation of $54$.

Acknowledging Sheldon’s powerful insight, let us introduce the concept of a Sheldon number: a positive integer whose binary representation matches the pattern $ABABAB\ldots ABA$ or the pattern $ABABAB\ldots AB$, where all the occurrences of $A$ represent a string with $N$ occurrences of the bit $1$ and where all the occurrences of $B$ represent a string with $M$ occurrences of the bit $0$, with $N > 0$ and $M > 0$. Furthermore, in the representation, there must be at least one occurrence of the string $A$ (but the number of occurrences of the string $B$ may be zero).

Many important numbers are Sheldon numbers: $1755$, the year of the great Lisbon earthquake, $1984$, of Orwellian fame, and $2015$, the current year! Also, $21$, which Sheldon mentions, is a Sheldon number, and so is $42$, the answer given by the Deep Thought computer to the Great Question of Life, the Universe and Everything.

Clearly, there is an infinite number of Sheldon numbers, but are they more dense or less dense than prime numbers?

-----Task-----
Your task is to write a program that, given two positive integers, computes the number of Sheldon numbers that exist in the range defined by the given numbers.

-----Input-----
The input contains one line, with two space separated integer numbers, $X$ and $Y$.

-----Constraints-----

$0 \leq X \leq Y < 2^{63}$

-----Output-----
The output contains one line, with one number, representing the number of Sheldon numbers that are greater or equal to $X$ and less or equal to $Y$.

-----Sample Output Explanation-----
In the first sample, all numbers between $1$ and $10$ are Sheldon Numbers. In the second sample, $73$ is the only Sheldon number in the given range.

-----Examples-----
Sample Input:
1 10
Sample Output:
10
user: You are totally bored with nothing to do. You notice a pattern of spots on the wall in front of you and begin to dwell on them. There is no obvious pattern of symmetry. With time this becomes very grating, and you contemplate adding more spots to satisfy your quest for balance. For this exercise you are to resolve this situation with a computer program.

Given an array of spots with coordinates in the range from $-20000$ to $20000$, determine the fewest additional spots needed to generate a pattern with some symmetry. The symmetry can be around a point or across a line. If the symmetry is around a point, the point does not need to be a spot in the data, or even a point with integral coordinates. If the symmetry is across a line, the line may be at any angle. The coordinates of the additional spots may or may not be within the $-20000$ to $20000$ limits.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The first line of input will consist of a single integer $n$ ($1 \le n \le 1000$) indicating the number of spots. Each of the next $n$ lines will hold two space-separated integers $x$ and $y$ ($-20000 \le x,y \le 20000$), which are the coordinates of a spot. The locations of all spots are guaranteed to be unique.

-----Output-----
Output a single integer, indicating the smallest number of spots which need to be added so that all of the spots are symmetric about some point, or about some line.

-----Examples-----
Sample Input:
4
0 0
1000 0
0 1000
1000 1000
Sample Output:
0
user: Lukáš loves skiing. One morning, the sun was shining like no other sun had ever shone before, and he wanted to do something exciting. There had been a slight storm during the night, and the wind had cleared snow from certain parts of the mountain, making them icy and more dangerous to ski down. Lukáš was aware of this, but brave as he (mostly) is, he decided that he would climb his favourite mountain and go for some really exciting skiing. 

Lukáš starts at the top of the mountain, and wants to get to the bottom. There are $N$ small cabins scattered along the mountainside, numbered $0$ to $N-1$. He will always go from one cabin to another, along certain pistes. For each piste, which always connects exactly two cabins, he has calculated the probability of falling along that piste. The cabin numbered $0$ is located at the top, and the cabin numbered $N-1$ is located at the bottom of the mountain.

If Lukáš feels like it, he can take his skis off and walk down a piste instead. By doing this, it is guaranteed that he will not fall along this piste in the direction that he walks. But taking the skis off is not very brave…

Lukáš can only ski down the mountain, i.e. from a lower numbered cabin to a higher numbered one, but he can walk along any piste in any direction. It is guaranteed that Lukáš can walk from the top of the mountain to the bottom of it.

Your task is to help Lukáš predict his chances of getting down the hill without falling. For each number $k \in [0,N-1]$ you should calculate the maximum probability that Lukáš gets down the hill without falling, while walking along at most $k$ pistes, and assuming he choses his walking wisely.

-----Input-----
The first line contains two integers $1 \le N \le 300$ and $0 \le M \le \frac{N(N-1)}{2}$, the number of cabins and pistes respectively.

Then follow $M$ lines, each describing a piste with three numbers $0 \le a, b < N$ and $0 \le w \le 1$, where $a$ and $b$ are the numbers of the cabins the piste connects, and $w$ is the probability that Lukáš will fall while skiing down the piste.

-----Output-----
Output should consist of $N$ floating point numbers $p_ k$ ($k \in [0,N-1]$), each denoting the maximum probability that Lukáš didn’t fall when walking along at most $k$ pistes. If it is impossible to get down the hill by walking along at most $k$ pistes, then output $p_ k=-1$. Output them on a single line separated by spaces. Your answer is considered correct if the relative or absolute error is at most $10^{-9}$.

-----Examples-----
Sample Input:
2 1
0 1 0.5
Sample Output:
0.500000000 1.000000000
user: Two bicycle courier services have been competing in Metro City for many years, stealing customers back and forth from one another. Recently, they have come to realize that they would be better off if they could attract new customers instead. A problem is that, over time, each company’s customers have become so widely scattered across the city that some of their delivery times are unacceptably slow, leading to customer dissatisfaction and a poor reputation.

The companies would like to divide up their current customers so that each company could run ads saying “We guarantee delivery in no more than M minutes”, hoping to attract new customers. The streets of Metro City are laid out on a grid, with buildings at integer coordinates of the grid. The couriers must travel along those roads – they cannot cut through buildings. It takes one minute to travel one unit of distance in the $x$ or $y$ direction.

Divide up the current customer base to minimize the longest delivery time required by either company to have a courier travel from one customer of that company to any other customer of the same company.
 - A delivery is considered to have been completed when the courier reaches the $(x,y)$ address of the customer. No time is counted for wandering the hallways of the customer’s building.
 - It is acceptable that a courier traveling from one customer to another will pass by customers of the same or of the other company. No extra time delay is accrued for riding past a customer.
 - If it should happen that one company winds up with only a single customer, that company puts someone on site to deliver messages within that one building. This is considered a zero delivery time.

-----Input-----
Input starts with one line containing an integer $N$, the number of customers to be divided up, where $2 < N \leq 1000$.

This is followed by $N$ lines, each containing a pair of integers $x$ and $y$ denoting the position of one customer, where $0 \leq x, y \leq 1000$.

-----Output-----
Print a single line containing the longest delivery time required by the two companies (i.e., the maximum of the two longest delivery times offered by each company separately).

-----Examples-----
Sample Input:
6
1 1
4 1
1 5
10 10
10 8
7 10
Sample Output:
7
user: - Percent sign sand dollar sign! And colon semicolon, too!

 - You Asterisk-mouth! – Sam & Max: Hit the Road 

When typing SMS messages on a mobile phone, each of the ten digit buttons represent several alphabetic characters. On my phone (an ancient Ericsson T65, in case anyone was wondering), I have the following mapping (1 is used for space, and 0 for some common non-alphabetic symbols):

2 $\rightarrow $ ABC

3 $\rightarrow $ DEF

4 $\rightarrow $ GHI

5 $\rightarrow $ JKL

6 $\rightarrow $ MNO

7 $\rightarrow $ PQRS

8 $\rightarrow $ TUV

9 $\rightarrow $ WXYZ

As you’ve probably experienced, this makes the typing quite cumbersome. The phones usually try to compensate this by making use of a dictionary – basically, the idea is that there will typically be relatively few actual words having the same button combination. The way this works is that when you have typed a certain digit sequence, you can cycle through the words in the dictionary that map to this digit sequence using the “up” and “down” buttons. Pressing “up” gives you the next word, and pressing “down” gives you the previous word. Words are ordered by how common they are, most common words first and least common words last. This wraps, so that pressing “up” at the last word gives you the first word and similarly for “down”. Initially after having pressed a digit sequence, you will get the first (most common) word that maps to this sequence.

This usually works quite well, but if you’re trying to type a word that does not exist in the dictionary, you have to write it by separating it into several parts, where each part is a word in the dictionary. In order to start writing a new part, you have to press the “right” button on the keypad.

Obviously, the number of keys needed to type a word depends on how (and if) we divide it into parts. Now, I would like to know how to type a word (that may or may not be from the dictionary) using as few key presses as possible (it’s not that I’m lazy, I just want to decrease the wear and tear of my keypad).

-----Input-----
The input begins with an integer $1 \le N \le 200000$ giving the size of the dictionary, followed by $N$ lines, giving the words of the dictionary from most common to least common. Words consist solely of lower case ’a’-’z’ and are at most 10 characters long.

Then follows an integer $1 \le Q \le 1000$ giving the number of words to type. This is followed by $Q$ lines, each containing a nonempty word to type. It will always be possible to type the given words using the given dictionary. The total length of all $Q$ words to type will be at most $500000$.

-----Output-----
For each query, output a line containing any optimal keypress solution in the following format.
 - For pressing any of the digits 2-9, simply output that digit.
 - For pressing right, output ’R’.
 - For pressing up or down $x > 0$ times, output “U($x$)” or “D($x$)”, respectively.

Note that the minimum number of keypresses may be very big: it can exceed $2^{32}$.

-----Examples-----
Sample Input:
1
echo
1
echoecho
Sample Output:
3246R3246
user: At $3147.3$ meters high, Fansipan is the tallest mountain in the Indochina peninsula. To promote tourism, $n$ stations were built on the mountain, numbered from $1$ to $n$.

Two companies, Mobi and Vina are in charge of operating cable cars connecting the stations. Each of the two companies have $k$ cable cars. The $i$-th cable car of Mobi connects two stations $MS_ i$ and $ME_ i$. The $i$-th cable car of Vina connects two stations $VS_ i$ and $VE_ i$.

Two stations are called connected by a company, iff we can go from one station to the other by using cable cars only of that company. To achieve peaceful cooperation, the two companies agreed with the following conditions:
 - For every valid $i$, $MS_ i < ME_ i$ and $VS_ i < VE_ i$.
 - All $MS_ i$ are unique, all $ME_ i$ are unique.
 - All $VS_ i$ are unique, all $VE_ i$ are unique.
 - For any $i \ne j$, if $MS_ i < MS_ j$, then $ME_ i < ME_ j$.
 - For any $i \ne j$, if $VS_ i < VS_ j$, then $VE_ i < VE_ j$.
 - No pair of stations is connected by both companies. In other words, for every pair of stations $i$ and $j$, if $i$ and $j$ are connected by Mobi, they should not be connected by Vina, and vice versa.

Given $n$ and $k$, your task is to check whether it is possible for Mobi and Vina to each operates $k$ cable cars, satisfying all the above conditions.

-----Input-----
The input contains two integers $n$ and $k$, separated by a single space $(1 \le k < n \le 100)$.

-----Output-----
For each test case, if it is not possible to satisfy all the conditions, print ‘NO’. Otherwise, print ‘YES’, followed by $2 \cdot k$ lines. In the first $k$ lines, the $i$-th line contains two integers $MS_ i$ and $ME_ i$. In the last $k$ lines, the $i$-th line contains two integers $VS_ i$ and $VE_ i$.

-----Examples-----
Sample Input:
3 1
Sample Output:
YES
1 2
1 3
user: Night clubs aren’t what they used to be. Our benevolent state has decided that, for health and safety reasons, every club must now meet a minimum lighting standard. They have moved to verify standards by dividing each club up into $1\text { m}^2$ cells and measuring the light levels on the floor with probes in the centre of each cell.

Club owners aren’t happy about this; they will comply with the letter of the law, but don’t want to spend a penny more than they have to on electricity. Instead of upgrading their lighting, they will fence off the offending parts of the club to deal with later.

You will be given a grid representing a map of the lights in a club. Each cell of the grid ($r, c$) will have a light directly above its centre with a bulb of strength $s$, ($0 \le s \le 9$).

The ceiling is flat—its height is constant. Each light will affect every other cell, increasing the light level at distance $(x,y,z)$ by:\[ \frac{s}{x^2+y^2+z^2} \]

Building a section of transparent fencing between any two cells usually costs £11. However, if the cells on both sides meet the minimum lighting standard, the price per length of fencing rises steeply to £43, as builders find it hard to work under the pulsating night club lights and demand extra compensation.

Of course, building a fence along the outside of the clubbing area would not do, as that could block fire exits and cause a whole other kind of hazard.

How much will you have to spend on fencing out the dark spots?

-----Input-----
 - One line containing an integer $B$ ($0 < B \le 9$), the minimum required light level.
 - One line containing an integer $H$ ($0 < H \le 5$), the height of the ceiling in the club.
 - One line containing two integers $R$ and $C$ ($0 < R,C \le 30$), the length and width of the club.
 - $R$ further lines, each containing a string of $C$ digits, representing the strength of lights at each cell of the club.

It is guaranteed that the $2(R+C)-4$ cells along the borders of the club are sufficiently lit.

-----Output-----
 - One line containing one integer: the total number of pounds that must be spent on fencing.

-----Examples-----
Sample Input:
9
1
6 6
333333
300003
300003
300003
300003
333333
Sample Output:
176
user: Per is obsessed with factorials. He likes to calculate them, estimate them, read about them, draw them, dream about them and fight about them. He even has the value of $12!=479001600$ tattooed on his back.

He noticed a long time ago that factorials have many trailing zeroes and also wrote a program to calculate the number of trailing zeroes. For example $12!$ ends with 600, so it has 2 trailing zeroes. Now he wants to make one step further, look at the 3 digits right before the trailing zeroes. In the case of $12!$, the last 3 digits before the trailing zeroes are $016$.

-----Task-----
Given an integer $n$, find the last 3 digits before the trailing zeroes in $n!$. If there are fewer then 3 such digits, find all of them.

-----Input-----
The input contains one line with one integer $n$ ($1\leq n\leq 10000000$).

-----Output-----
Output one line with the 3 digits before trailing zeroes of $n!$. If there are fewer than 3 such digits, output all of them.

-----Examples-----
Sample Input:
5
Sample Output:
12