meetforever/GRPO_CL huggingface dataset:
user: Gunnar and Emma play a lot of board games at home, so they own many dice that are not normal $6$-sided dice. For example they own a die that has $10$ sides with numbers $47, 48, \ldots , 56$ on it.

There has been a big storm in Stockholm, so Gunnar and Emma have been stuck at home without electricity for a couple of hours. They have finished playing all the games they have, so they came up with a new one. Each player has 2 dice which he or she rolls. The player with a bigger sum wins. If both sums are the same, the game ends in a tie.

-----Task-----
Given the description of Gunnar’s and Emma’s dice, which player has higher chances of winning?

All of their dice have the following property: each die contains numbers $a, a+1, \dots , b$, where $a$ and $b$ are the lowest and highest numbers respectively on the die. Each number appears exactly on one side, so the die has $b-a+1$ sides.

-----Input-----
The first line contains four integers $a_1, b_1, a_2, b_2$ that describe Gunnar’s dice. Die number $i$ contains numbers $a_ i, a_ i + 1, \dots , b_ i$ on its sides. You may assume that $1\le a_ i \le b_ i \le 100$. You can further assume that each die has at least four sides, so $a_ i + 3\le b_ i$.

The second line contains the description of Emma’s dice in the same format.

-----Output-----
Output the name of the player that has higher probability of winning. Output “Tie” if both players have same probability of winning.

-----Examples-----
Sample Input 1:
1 4 1 4
1 6 1 6
Sample Output 1:
Emma

Sample Input 2:
1 8 1 8
1 10 2 5
Sample Output 2:
Tie
user: Arild just turned $1$ year old, and is currently learning how to count. His favorite thing to count is how many mouthfuls he has in a meal: every time he gets a bite, he will count it by saying the number out loud. 

Unfortunately, talking while having a mouthful sometimes causes Arild to mumble incomprehensibly, making it hard to know how far he has counted. Sometimes you even suspect he loses his count! You decide to write a program to determine whether Arild’s counting makes sense or not.

-----Input-----
The first line of input contains an integer $n$ ($1 \le n \le 1000$), the number of bites Arild receives. Then second line contains $n$ space-separated words spoken by Arild, the $i$’th of which is either a non-negative integer $a_ i$ ($0 \le a_ i \le 10000$) or the string “mumble”.

-----Output-----
If Arild’s counting might make sense, print the string “makes sense”. Otherwise, print the string “something is fishy”.

-----Examples-----
Sample Input 1:
5
1 2 3 mumble 5
Sample Output 1:
makes sense

Sample Input 2:
8
1 2 3 mumble mumble 7 mumble 8
Sample Output 2:
something is fishy
user: While mostly known for the programs she wrote for Charles Babbage’s Analytic Engine, Augusta Ada King-Noel, Countess of Lovelace, described how the method of finite differences could be used to solve all types of problems involving number sequences and series. These techniques were implemented in Babbage’s Difference Engine.

The algorithm: If we compute the difference between consecutive values in a numeric sequence, we will obtain a new sequence which is related to the derivative of the function implied by the original sequence. For sequences generated from first-order polynomials (linear functions) the successive differences will be a list of identical values, (i.e., a constant difference). For second-order polynomial functions the lists of differences will be a new sequence whose values change linearly. In turn, the list of differences of the values in this generated list (i.e., the finite differences of the list of differences) will be constant, and so on for higher-order polynomials. In general the $n^{\text {th}}$ row of differences will be constant for an $n^{\text {th}}$ degree polynomial.

For example, the first-order polynomial $3x + 3$ produces the sequence below at $x=0,1,2,3,4$, and the first differences are shown on the following line.

3     6     9    12    15   3     3     3     3

As another example, the polynomial $x^2$, if evaluated at inputs $x=3, 5, 7, 9,$ produces the sequence below.

9    25    49    81
  16    24    32 8     8

Furthermore, if we consider a minimum-order polynomial that produces the original sequence, its value at the next regularly spaced input can be predicted by extending the difference table.

-----Input-----
The input consists of a value $n$, designating the number of polynomial evaluations given with $2 \leq n \leq 10$, follwed by $n$ values $v_1, v_2, \ldots , v_{n}$ which represent the value of a polynomial when evaluated at $n$ regularly spaced input values. Each $v_ j$ will satisfy $-2000000 \leq v_ j \leq 2000000$ and at least two of those values will differ from each other.

-----Output-----
Output two integer values $d$ and $v_{n+1}$, separated by a space. The value $d$ must be the degree of a minimal-degree polynomial producing the original sequence, and $v_{n+1}$ must be the value of the polynomial if evaluated at the next regularly spaced input value.

-----Examples-----
Sample Input 1:
5 3 6 9 12 15
Sample Output 1:
1 18

Sample Input 2:
4 9 25 49 81
Sample Output 2:
2 121
user: The “eight queens puzzle” is a classic puzzle where you have to place eight queens on a chess board in such a way that no queen can attack another queen. Remember that, in chess, queens can move in any direction (horizontal, vertical, and diagonal), which means the eight queens would have to be laid out in such a way that no two queens are on the same row, column, or diagonal.

This puzzle actually has multiple solutions. The following is one possible solution:

Finding the solutions to the “eight queens puzzle” is actually an interesting computational problem. However, that’s not the problem you will be solving here. Instead, you will be solving a much simpler problem: given a proposed solution to the puzzle, you must verify whether it is a valid solution (i.e., whether no queen can attack another queen).

When referring to specific squares on the board, we will assume that the bottom-left square is the $(0,0)$ square, and that the $x$ coordinate increases as you move right, and the $y$ coordinate increases as you move up.

In other words, something like this:

Furthermore, we will consider the more general “$N$-queens puzzle”, where the chessboard can have $N\times N$ squares, and there will be $N$ queens on the board. For example, this would be a correct solution to the 4-queens puzzle:

And this would be an incorrect solution to the 4-queens puzzle:

Notice how the queen in (2,2) can attack the queen in (0,2) and the queen in (2,3).

-----Input-----
The input begins with a line containing a single integer: the value of $N$ ($0 < N \le 5000$). This is followed by $N$ lines, each containing the position of a queen as two integers: $x$ and $y$ (separated by a single space), where $0 \le x, y < N$.

-----Output-----
The output contains either CORRECT if the positions of the queens is a solution to the $N$-queens puzzle, and INCORRECT otherwise.

Note that the sample data presented below corresponds to the three boards shows earlier.

-----Examples-----
Sample Input 1:
8
1 5
6 2
3 1
5 0
4 6
0 3
2 7
7 4
Sample Output 1:
CORRECT

Sample Input 2:
4
2 3
1 0
0 2
3 1
Sample Output 2:
CORRECT
user: Young jedi Ivan has infiltrated in The Death Star and his task is to destroy it. In order to destroy The Death Star, he needs an array of non-negative integers $a_ i$ of length $N$ that represents the code for initiating the self-destruction of The Death Star. Ivan doesn’t have the array, but he has a piece of paper with requirements for that array, given to him by his good old friend Darth Vader.

On the paper, a square matrix of the size $N$ is written down. In that matrix $m$ in the $i$-th row and $j$-th column there is a number that is equal to bitwise and between numbers $a_ i$ and $a_ j$. Unfortunately, a lightsaber has destroyed all the fields on the matrix’s main diagonal and Ivan cannot read what is on these fields. Help Ivan to reconstruct an array for the self-destruction of The Death Star that meets the requirements of the matrix.

The solution doesn’t need to be unique, but will always exist.

-----Input-----
The first line of input contains the integer $N$ ($1 \leq N \leq 1000$), size of the matrix. Each of the following $N$ lines contains $N$ numbers $m_{ij}$ ($0 \leq m_{ij} \leq 10^9$), the elements of the matrix.

-----Output-----
The first and only line of output must contain any array of $N$ non-negative integers at most $10^9$ that meet the requirements from the task.

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

Sample Input 2:
5
0 0 1 1 1
0 0 2 0 2
1 2 0 1 3
1 0 1 0 1
1 2 3 1 0
Sample Output 2:
1 2 3 1 11
user: Write a program that, given a date in $2009$, determines the day of week on that date.

-----Input-----
The first line contains two positive integers $D$ (day) and $M$ (month) separated by a space. The numbers will be a valid date in $2009$.

-----Output-----
Output the day of the week on day $D$ of month $M$ in $2009$. The output should be one of the words “Monday”, “Tuesday”, “Wednesday”, “Thursday”, “Friday”, “Saturday” or “Sunday”.

-----Examples-----
Sample Input 1:
1 1
Sample Output 1:
Thursday

Sample Input 2:
17 1
Sample Output 2:
Saturday
user: The impossible has happened. Bear G. has fallen into his own trap. Lured by a delicious box of Domaćica, without even thinking, he rushed and fell into his trap. In order to get out of the trap, he must solve the following task with your help. You are given three integers $L$, $D$ and $X$.
 - determine the minimal integer $N$ such that $L \leq N \leq D$ and the sum of its digits is $X$
 - determine the maximal integer $M$ such that $L \leq M \leq D$ and the sum of its digits is $X$

Bear will be able to escape from the trap if he correctly determines numbers $N$ and $M$. The numbers $N$ and $M$ will always exist.

-----Input-----
The first line of input contains the integer $L$ ($1 \leq L \leq 10000$), the number from the task. The second line of input contains the integer $D$ ($1 \leq D \leq 10000$, $L \leq D$), the number from the task. The third line of input contains the integer $X$ ($1 \leq X \leq 36$), the number from the task.

-----Output-----
The first line of output must contain the integer $N$ from the task. The second line of output must contain the integer $M$ from the task.

-----Examples-----
Sample Input 1:
1
100
4
Sample Output 1:
4
40

Sample Input 2:
100
500
12
Sample Output 2:
129
480
user: Ante bought a piece of land. The land contains N apple trees, but his piece is triangular and it is not easy for him to determine which apple trees belong to him.

Your program will be given the coordinates of the vertices of the triangle forming Ante’s piece, and the coordinates of all apple trees. Determine the area of land belonging to Ante, and the number of trees belonging to him. We consider apple trees on the very border of his piece to belong to him.

The area of a triangle with vertices $(x_ A, y_ A), (x_ B, y_ B)$ and $(x_ C, y_ C)$ is given by the following formula:\[ \frac{|x_ A(y_ B - y_ C) + x_ B(y_ C - y_ A) + x_ C(y_ A - y_ B)|}{2} \]

-----Input-----
The first three lines contain the coordinates of the vertices of the triangle.

The following line contains the integer $N$ $(1 \le N \le 100)$, the number of apple trees.

Each of the following $N$ lines contains the coordinates of one apple tree.

All coordinate are pairs of positive integers less than 1000, separated by a space.

-----Output-----
Output the area of land belonging to Ante on the first line, with exactly one digit after the decimal point.

Output the number of trees belonging to Ante on the second line.

-----Examples-----
Sample Input 1:
1 1
5 1
3 3
4
3 1
3 2
3 3
3 4
Sample Output 1:
4.0
3

Sample Input 2:
3 2
5 4
1 6
3
2 4
3 5
4 3
Sample Output 2:
6.0
3
user: Along with some friends you formed the Band of Atonal Percussionists and Cellists. You have been playing for some years together, but you feel unsatisfied with the current level of play. Doing research into some interesting new styles, you are gripped by the intricate details of the world of jazz.

While of course you cannot apply all the new things you have learned immediately, you want to start with improvising some nice new rhythmic figures in the music your band plays. You will play a rhythm where every bar has $n$ beats in it, but then you split up every beat into $m$ notes. In total, you will have $nm$ notes per bar.

Everyone in the band knows that there is no room for squares in jazz. So the number of notes in a bar should be squarefree. That is, there is no number $k > 1$ such that $k^2$ divides the number of notes in a bar.

The percussionist has already suggested a number of beats per bar $n$; now it is up to you to find a number of notes per beat that does not leave any room for squares.

In the second sample we have $n=30$ and $m=7$. This works because $2\leq m < n$ and $m\cdot n = 210$ has no divisor $k^2$ for any $k>1$.

-----Input-----
 - The input is a single squarefree integer $3\leq n\leq 10^5$.

-----Output-----
 - Output an integer $2 \leq m < n$ such that $m \cdot n$ is still squarefree.

If there are multiple possible solutions, you may output any one of them.

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

Sample Input 2:
30
Sample Output 2:
7
user: Mirko and Slavko are USKOK agents tracking the movements of an unnamed corrupt government official. Anonymous sources have tipped them about his upcoming escape attempt. They now know he plans to use his diplomatic liaisons to try and hitch a ride on a CIA blimp leaving from Severin na Kupi blimp port.

It is common knowledge that all CIA blimps have the string “FBI” somewhere in their registration codes. They obtained a list of all blimps scheduled for the designated day. There are exactly 5 blimps on the list. Write a program that will point out all CIA blimps.

-----Input-----
There are exactly $5$ rows of input, each row representing one blimp registration code from the list. A registration code is a sequence of at most $11$ uppercase letters of the English alphabet, digits ‘0’ to ‘9’, or dashes ‘-’.

-----Output-----
The first and only line of output must contain a space separated list of integers, sorted in increasing order, indicating the corresponding input rows containing registrations of CIA blimps.

If there are no CIA blimps, output the string “HE GOT AWAY!”.

-----Examples-----
Sample Input 1:
N-FBI1
9A-USKOK
I-NTERPOL
G-MI6
RF-KGB1
Sample Output 1:
1

Sample Input 2:
N321-CIA
F3-B12I
F-BI-12
OVO-JE-CIA
KRIJUMCAR1
Sample Output 2:
HE GOT AWAY!
user: A company makes triangle-shaped ornaments for the upcoming holidays. Each ornament is tied at one of its corners to a rod using a string of unknown length. Multiple of these ornaments may be attached to the same rod. These ornaments should be able to swing (rotate around the axis formed by the string) without interfering with each other. 

Write a program that computes the minimum required length for the rod, given a list of triangles!

-----Input-----
The input consists of a single test case. The first line contains one integer $N$ ($0 < N \le 100$), denoting the number of triangles. The next $N$ lines each contain three integers $A, B, C$ denoting the lengths of the three sides of each triangle. The triangle will hang from the corner between sides $A$ and $B$. You are guaranteed that $A, B, C$ form a triangle that has an area that is strictly greater than zero.

-----Output-----
Output the required length $L$ such that all triangles can be hung from the rod, no matter how long or short each triangle’s string is. No triangle should swing beyond the rod’s ends. You may ignore the thickness of each ornament, the width of the string and you may assume that the string is attached exactly to the triangle’s end point.

Your answer should be accurate to within an absolute or relative error of $10^{-4}$.

-----Examples-----
Sample Input 1:
2
3 3 3
4 4 5
Sample Output 1:
8.0

Sample Input 2:
2
3 3 3
4 5 4
Sample Output 2:
6.843530573929037
user: We’re all familiar with harshad numbers. For this problem, you will ... what’s that? You aren’t familiar with harshad numbers? They’re also known as Niven numbers – does that ring a bell?? Anything???

Well, it’s a simple enough concept. A harshad number is a number which is evenly divisible by the sum of its digits. For example, $24$ is a harshad number: the sum of its digits is $2+4=6$ and $24$ is divisible by $6$. $156$ is also a harshad number, since $1+5+6=12$ and $156 = (12)(13$). $157$ is NOT a harshad number since it is not divisible by $1+5+7=13$.

OK, let’s start over.

We’re all familiar with harshad numbers. For this problem, you will be given a number $n$ and must find the smallest harshad number $\geq n$.

-----Input-----
Input consists of a single line containing a positive integer $n \leq 1000000000$.

-----Output-----
Display the smallest harshad number greater than or equal to $n$.

-----Examples-----
Sample Input 1:
24
Sample Output 1:
24

Sample Input 2:
25
Sample Output 2:
27
user: In many programming languages, the “plus” symbol (‘+’) has at least two standard meanings:
 - arithmetic addition
 - string concatenation

Inspired by the old adage, “Variety is the spice of life,” the designers of the Doubleplusgood (DPG) language (launched to great fanfare in 1984 by the Ministry of Truth Tables) decided that, in certain contexts, the meaning of the plus symbol would be decided dynamically and randomly at run time. In particular, for expressions consisting of alternating integers and plus symbols, every time the same program is executed, the meaning of each plus symbol is randomly chosen to be either addition or string concatenation. It follows that a single expression of this form can potentially evaluate to many different integers. For example, consider\[ 1+9+8+4 \]

For clarity, we’ll use $\boxplus $ to denote a plus symbol that the DPG runtime environment decides to interpret as string concatenation, which, it is important to note, has higher precedence than addition in DPG. Then $1+9+8+4$ can evaluate to $7$ distinct values:\begin{align*} 1\boxplus 9 \boxplus 8 \boxplus 4 & =1984\\ 1 \boxplus 9 \boxplus 8 + 4 & =198 + 4 =202\\ 1 \boxplus 9 + 8 \boxplus 4 & =19 + 84 =103\\ 1 \boxplus 9 + 8 + 4 & =19 + 8 + 4 =31\\ 1 + 9 \boxplus 8 \boxplus 4 & =1 + 984 =985\\ 1 + 9 \boxplus 8 + 4 & =1 + 98 + 4 =103\\ 1 + 9 + 8 \boxplus 4 & =1 + 9 + 84 =94\\ 1 + 9 + 8 + 4 & =22 \end{align*}

(Note that $103$ was formed in two different ways.) Given a sequence of alternating integers and plus symbols, your task is to determine the number of distinct integers to which the expression can evaluate.

-----Input-----
The input is a single line consisting of alternating positive integers and plus symbols. The line begins and ends with a positive integer, and is guaranteed to contain at least one plus symbol. The maximum number of digits in the input is $18$.

-----Output-----
Output the number of distinct integers to which the input expression can evaluate in DPG.

-----Examples-----
Sample Input 1:
1+9+8+4
Sample Output 1:
7

Sample Input 2:
1+2+3+4+5+6+7+8+9
Sample Output 2:
188
user: Graphical calculators have become popular among high school students. They allow functions to be plotted on screen with minimal efforts by the students. These calculators generally do not possess very fast processors. In this problem, you are asked to implement a method to speed up the plotting of a polynomial.

Given a polynomial $p(x) = a_ n x^n + ... + a_1 x + a_0$ of degree $n$, we wish to plot this polynomial at the $m$ integer points $x = 0, 1, \ldots , m-1$. A straightforward evaluation at these points requires $mn$ multiplications and $mn$ additions.

One way to speed up the computation is to make use of results computed previously. For example, if $p(x) = a_1 x + a_0$ and $p(i)$ has already been computed, then $p(i+1) = p(i) + a_1$. Thus, each successive value of $p(x)$ can be computed with one addition each.

In general, we can compute $p(i+1)$ from $p(i)$ with $n$ additions, after the appropriate initialization has been done. If we initialize the constants $C_0$, $C_1$, $\ldots $, $C_ n$ appropriately, one can compute $p(i)$ using the following pseudocode:

  p(0) = C_0; t_1 = C_1; ... t_n = C_n;
  for i from 1 to m-1 do p(i)    = p(i-1)  + t_1; t_1     = t_1     + t_2; t_2     = t_2     + t_3; : : t_(n-1) = t_(n-1) + t_n;
  end

For example, if $p(x) = a_1 x + a_0$, we can initialize $C_0 = a_0$ and $C_1 = a_1$.

Your task is to compute the constants $C_0, C_1, \ldots , C_ n$ for the above pseudocode to give the correct values for $p(i)$ at $i = 0, \ldots , m-1$.

-----Input-----
The input consists of one case specified on a single line. The first integer is $n$, where $1 \leq n \leq 6$. This is followed by $n+1$ integer coefficients $a_ n, \ldots , a_1, a_0$. You may assume that $|a_ i| \leq 50$ for all $i$, and $a_ n \neq 0$.

-----Output-----
Print the integers $C_0$, $C_1$, …, $C_ n$, separated by spaces.

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

Sample Input 2:
2 2 -4 5
Sample Output 2:
5 -2 4
user: Mirko is a great code breaker. He knows any cipher in the world can be broken by frequency analysis. He has completely the wrong idea what frequency analysis is, however.

He intercepted an enemy message. The message consists of $N$ numbers, smaller than or equal to $C$. Mirko belives freqency analysis consists of sorting this sequence so that more frequent numbers appear before less frequent ones.

Formally, the sequence must be sorted so that given any two numbers $X$ and $Y$, $X$ appears before $Y$ if the number of times $X$ appears in the original sequence is larger than the number of time $Y$ does. If the number of appearances is equal, the number whose value appears sooner in the input should appear sooner in the sorted sequence.

Help Mirko by creating a “frequency sorter”.

-----Input-----
First line of input contains two integers, $N$ ($1 \le N \le 1000$), the length of the message, and $C$ ($1 \le C \le 1000000000$), the number from the task description above.

The next line contains $N$ positive integers smaller than or equal to $C$, the message itself.

-----Output-----
The first and only line of output should contain $N$ numbers, the sorted sequence.

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

Sample Input 2:
9 3
1 3 3 3 2 2 2 1 1
Sample Output 2:
1 1 1 3 3 3 2 2 2
user: The impact factor of a scientific journal is a measure reflecting the average number of citations to articles published in science journals. For this task we are using a simplified formula for calculating the impact factor:\[ \frac{\text {Total count of citations received by articles published in the journal}}{\text {Total number of articles published}} \]

Rounding is always performed upwards. For example the impact factor of the “Journal for ore research and time wasting” that published $38$ articles cited $894$ times is $894 / 38 = 23.53$ rounding up to $24$.

You are the editor of one scientific journal. You know how many articles you are going to publish and the owners are pushing you to reach a specific impact factor. You are wondering how many scientists you will have to bribe to cite your articles to meet the owners demands. Since money is tight you want to bribe the minimal amount of scientists. Each bribed scientist buys you a single citation.

-----Input-----
First and only line of input will contain $2$ integers, $A$ ($1 \leq A \leq 100$), the number of articles you plan to publish and $I$ ($1 \leq I \leq 100$), the impact factor the owners require.

-----Output-----
The first and only line of output should contain one integer, the minimal number of scientists you need to bribe.

-----Examples-----
Sample Input 1:
38 24
Sample Output 1:
875

Sample Input 2:
1 100
Sample Output 2:
100