meetforever/GRPO_CL huggingface dataset:
user: The longest common prefix of two words is the longest word that both words start with. For example, the longest common prefix of the words “identity” and “idealistic” is the word “ide”. A database contains $N$ words.

The algorithm to search for a query word $W$ in the database is primitive. It compares the word $W$ one by one with each word in the database. Two words are compared letter by letter until a letter in which they differ is found or until the end of one of the words is reached (it is then established either that the words are equal or that one is longer than the other). When the algorithm finds the word $W$ in the database, it terminates.

Analysing the algorithm shows that the number of steps needed to find a word $W$ is equal to the number of words $W$ is compared to, plus the sum of the lengths of the longest common prefixes of W and each of the words it was compared to.

Write a program that calculates the number of steps the algorithm uses to find each of the $Q$ query words.

-----Input-----
The first line contains an integer $N$ $(1 \leq N \leq 30000)$, the number of words in the database. Each of the following $N$ lines contains a single word from the database. The words are given in the order the algorithm compares them to a query word. All words in the database will be distinct. The following line contains an integer $Q$ $(1 \leq Q \leq 30000)$, the number of words searched for. Each of the following $Q$ lines contains a single query word.

All words in the input will be strings of less than $30$ lowercase letters of the English alphabet

-----Output-----
Output one integer per line for each query word, the number of steps the algorithm uses when searching for the word.

-----Examples-----
Sample Input:
5
hobotnica
robot
hobi
hobit
robi
4
robi
hobi
hobit
rakija
Sample Output:
12
10
16
7
user: You’ve intercepted encrypted communications between Martian diplomats. Since Martian diplomats are often spies, you decide to decrypt the messages. While the Martians have skilled rocket tech, they lag behind in number theory considerably, which compromises their encryption protocol.

Fortunately for you, spies friendly to you have reverse engineered the Martian protocol. It turns out that the Martians are using a shift-based cipher combined with a very long one-time pad. More specifically, the decryption procedure works as follows:

Step 1: Define the function $f(x) = (33x + 1) \mod 2^{20}$.


Further define $f^1(x) = f(x)$,  $f^2(x) = f(f(x))$,  $f^3(x) = f(f(f(x)))$, and so on.

Step 2: Create a $X$ by $X$ size grid, fill the upper left corner with $f^1(0)$, the next cell to the right with $f^2(0)$, $f^3(0)$ etc. Once the top row is filled, continue to the cell below the upper left cell, and fill with $f^{X+1}(0)$. Continue this process until all rows are filled.

Step 3: Sum all the values in every column, and take those values mod $2^{20}$.

Step 4: Concatenate the base-10 representations of the column sums together, to get a very long base-10 number. For instance, if you had column sums of 10 and 12 for the first and second column, the leftmost four digits of the resulting value would be 1012.

Step 5: Convert the result of step 4 from base $10$ to base $27$. This will yield the one-time pad the Martians used.

Step 6: For each letter $l$ of the intercepted message, shift the letter by the amount given by the corresponding digit of step 5, base $27$. “Shifting” means to add the digit at the corresponding position of the pad to the value of the letter in the encrypted message and then to compute its remainder modulo $27$. You may assume that both the encrypted and the decrypted message consist of only uppercase English characters ‘A’ through ‘Z’ and spaces, which are assigned values $0 \ldots 26$ (A = 0, B = 1, ... Z = 25, SPACE = 26). Thus, if the encrypted message has letter ‘D’ in position $3$, and the $3^{\text {rd}}$ base-$27$ digit of the pad is $25$, then the decrypted letter after shifting would be $3 + 25 = 1 \mod 27$ which is ‘B’.

Step 7: Output the decrypted message.

-----Input-----
The first line of the input contains two positive integers, $N$ ($1 \le N \le 10^6$), and $X$ ($1 \le X \le 2.5 \cdot 10^5$). It is guaranteed that the base $27$ result of step 5 will be longer or equal to the length of the intercepted message. The second line of the input contains a string consisting of uppercase letters and spaces of length $N$, the encrypted text.

-----Output-----
Output the decrypted text.

-----Examples-----
Sample Input:
14 4
JQ IRKEYFG EXQ
Sample Output:
THIS IS A TEST
user: Lukas is to hold a presentation on useful mathematical tricks. E.g., to take the square root of a number you just need to remove the first half of the number. To convince his audience he uses the well tested method of proof by example: $\sqrt {25} = 5$ and $\sqrt {5776} = 76$ so the method obviously works. To multiply a number by $X = 2.6$ all you have to do is move the first digit to the end of the number, $135\times 2.6 = 351$ and $270270\times 2.6 = 702702$. 

Lukas wants to demonstrate that this last method works for any $X$. To do this he will ask his audience for values of $X$ and then show them example multiplications for which the method works. Lukas has noticed that he can not just pick arbitrary numbers for his examples, so now he wants your help. Can you write a program that given $X$ gives a list of integers for which multiplying by $X$ is equivalent to moving the first digit to the end of the number? Lukas does not like very large numbers so do not list any numbers with more than 8 digits.

-----Input-----
The input is a single decimal number $X$ ($1\leq X < 1000$) with at most 4 digits after the decimal point.

-----Output-----
Output a list of all positive integers less than $10^8$ for which Lukas’ second trick works. Write the numbers in ascending order, one number per line. If the list is empty, output instead “No solution”.

-----Examples-----
Sample Input:
2.6
Sample Output:
135
270
135135
270270
user: The 1941 October Revolution Parade of November $7^{th}$, 1941, taking place in Moscow, Soviet Union, was a parade in honor of the October Revolution 24 years ealier. It was one of the most memorable parade because of the serious circumstance at that time: Soviet’s forces had constantly been dominated since the last 4 months, and Moscow was surrounded by Nazi under an extremely high pressure. Many soldiers joined that parade, and immediately rushed into the battle field after then. The winning against Nazi later pushed Hitler’s forces very far away from Moscow and completely destroyed his Barbarossa plan…

In order to ensure safety for the parade, Stalin gathered information about the positions of Nazi’s troops. He knew that Nazi’s troops can be depicted as $N$ points on the Cartesian plane. He was also aware of $S$ Soviet’s defending castles, which can be represented by $S$ points.

Stalin thought that one castle was in danger, if there exist a group of four Nazi’s troops, which forms a non-degenerate quadrilateral and the castle lies inside or on its border. Recall that a quadrilateral is non-degenerate iff no three of its vertices are collinear, and its edges do not intersect (with the exception that edges can intersect at vertices). Stalin wanted to know how many castles were in danger, so that he can send a suitable protection for them.

-----Input-----
 - The first line of the input contains one integer $N$ $(4 \leq N \leq 1000)$ - the number of Nazi’s tropps.
 - Each of the next $N$ lines contains two integers $x$ and $y$ $(0 \leq x, y \leq 10^6)$ representing one point where a Nazi’s troop took place.
 - The next line contains one integer $S$ $(1 \leq S \leq 1000)$ - the number of Soviet castles.
 - Each of the next $S$ lines contains two integers $x$ and $y$ $(0 \leq x, y \leq 10^6)$ representing position of one castle.

It is guaranteed that all given points are distinct.

-----Output-----
Write in one line the number castles which were in danger.




-----Sample Clarification-----
The $1^{st}$ sample corresponds to the following figure. Blue points represent Nazi troops’ locations, oranges points represent in-danger castles, green points represent non in-danger castles.

The $2^{nd}$ sample corresponds to the following figure. Note that the quadrilateral is degenerated, so no castle is in danger.

-----Examples-----
Sample Input:
4
0 1
3 7
4 5
6 5
9
1 4
1 6
2 3
2 5
3 5
3 6
4 8
5 4
6 3
Sample Output:
4
user: You have been hired at the Nano Wiring Efficient Route Company (NWERC) to help with the design of their new circuit boards. The circuits themselves have already been designed, and your task is to come up with a way to print them onto the blank boards that the company has bought. 

More specifically, each circuit design consists of a number of connection points with some connections between them such that the resulting graph is connected and does not have any cycles (i.e., the graph is a tree).

You are free to place the connection points anywhere on the circuit board and solder the connections between them so that no two connections intersect (except at the connection points). The boards you ordered are fairly large, so there is no danger of running out of space. You can solder so precisely that connections and connection points can be considered infinitesimal.

This would all be very easy, however your boss persists that each connection needs to be a straight line of length exactly $1\text { mm}$ (this is, so he says, to make sure the electrons do not have to travel around corners, which would be detrimental to the efficiency of the design).

You soon realise that battling with him will be unsuccessful. Your quickest way out of this is to etch a new design according to his specifications.

-----Input-----
The input consists of:
 - One line with one integer $n$ ($2 \le n \le 1000$), the number of connection points. The points are numbered from $1$ to $n$.
 - $n-1$ lines, each with two integers $a$ and $b$ ($1 \le a,b \le n$), describing a connection between $a$ and $b$.

It is guaranteed that these edges describe a valid tree.

-----Output-----
Output $n$ lines, the $i$th of which contains two real numbers $x_ i,y_ i$, the coordinates of point $i$. To make the production feasible, the following restrictions apply:
 - The distance between each pair of points should be at least $10^{-4}$.
 - The length of each edge should be $1$, up to an absolute error of at most $10^{-6}$.
 - Edges that are not incident to the same vertex should be at least a distance $10^{-6}$ apart.
 - The coordinates may not exceed an absolute value of $3000$.

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

-----Examples-----
Sample Input:
5
1 2
1 3
1 4
1 5
Sample Output:
0.0000000 0.0000000
1.0000000 0.0000000
-1.0000000 0.0000000
0.0000000 1.0000000
0.0000000 -1.0000000
user: Little Matej is solving an OOP (Object-oriented programming) laboratory exercise and he’s having trouble with solving one subtask.

He is given a set that contains $N$ words. He is also given $Q$ queries where each query is one pattern. A pattern consists of a single character “*” and lowercase letters of the English alphabet. For example, “*”, “kul*to”, “ana*”.

A pattern is said to cover a word if such an array of letters (which can be empty) exists that, when replacing the character “*”, the pattern and the word become completely identical. It is necessary to output how many words each pattern covers.

-----Input-----
The first line of input contains two integers $N$ and $Q$ ($1 \leq N, Q \leq 100000$). Each of the following $N$ lines contains a word that consists of lowercase letters of the English alphabet. Each of the following $Q$ lines contains a pattern for which you need to output how many words from the first set it covers. The total number of characters will be less than $4000000$.

-----Output-----
Output $Q$ lines, the $k$-th line containing the number of words that the $k$-th pattern covers.

-----Examples-----
Sample Input:
3 3
aaa
abc
aba
a*a
aaa*
*aaa
Sample Output:
2
1
1
user: Remember the busy boards for toddlers that have an array of holes into which to hammer pegs of various shapes? There’s a new, electronic version. The board consists of a 2D grid of pegs. Each peg on the board can be either up or down, but not both simultaneously. You can pick any peg that is currently up, and “hammer” it down. This will push that peg down, and also raise all of the other pegs in its row, and its column, regardless of their current state. You cannot “hammer” a peg that is down (well, maybe you can, but it will have no effect). Those poor kids will never get all the pegs down at one time!

This example shows what happens when the top right peg is “hammered.” ($\circ =$ up, $\bullet =$ down)

A substitute teacher wants to challenge her class. She uses the “Teacher Mode” to set up the board in a particular configuration, and then asks her students to see if they can get the board to a second configuration by hammering some (perhaps none) of the pegs.

That may be too tough of a problem for toddlers, but maybe you can handle it.

-----Input-----
Each test case will begin with a line with two space-separated integers $r$ and $c$ ($1\! \le \! r,c\! \le \! 1000$), which are the dimensions of the board.

Each of the next $r$ lines will have exactly $c$ characters, consisting only of capital ‘O’ (representing a peg that is up), capital ‘X’ (representing a peg that is down), and no spaces or other characters. This is the starting configuration.

Following this, each of the next $r$ lines will have exactly $c$ characters, consisting only of capital ‘O’ (representing a peg that is up), capital ‘X’ (representing a peg that is down), and no spaces or other characters. This is the target configuration.

-----Output-----
Output a single integer, $1$ if it is possible to reach the target configuration from the starting configuration, and $0$ if it is impossible.

-----Examples-----
Sample Input:
4 2
XO
OX
XO
OX
OX
OO
XO
OO
Sample Output:
1
user: I don’t know how you feel about your school time, but I become maudlin when I remember those days. One of our teachers told us at the final year that among all the educational institutions in life one misses his/her school days the most. And yes, I miss those days a lot.

Let me tell you that we had a grid board in our school and it was not as banal as it looks in the picture. The board was colorful and we also had different color chalks to use on it. Can you imagine how exciting it was for me when I first saw this board? In class break we used to draw on this board and play different games, few of them I can recall.

One of them was like this—firstly two players will mark some grid points. Then they will toss deciding who plays first. At each turn a player marks four points as $A$, $B$, $C$ and $D$ . Then join $(A, B)$, $(B, C)$, $(C, D)$ and $(D, A)$ to form a quadrilateral. Twice of the area of that quadrilateral is added to his score and the turn changes. (In case, if you are wondering why twice—it is just to ensure that the score is always integer). A player can not draw a quadrilateral if it was drawn before. However, you can use previously used points. For example, suppose there are $5$ points on the grid, $P$, $Q$, $R$, $S$ and $T$. First player can choose, $(A, B, C, D) = (P, Q, R, S)$, but then the second player can not choose $(A, B, C, D) = (R, S, P, Q)$ because both of them depict the same quadrilateral. If both of the players play optimally to maximize their own score I wonder what could be the sum of their scores.

So your task is to construe this game. You are given coordinates of $N$ distinct points, if two players play the above mentioned game optimally then what is the sum of their scores?

-----Input-----
The first line contains a positive integer $N$ ($N \leq 700$). Hence follows $N$ coordinates of the points $(x, y)$. In case you don’t know, I should say—I am not from your time, I was brought here by a few scientists from future. And in my time we use huge boards so the absolute value of the coordinates can be as large as $10^6$. Just to ensure that no one can draw a degenerate quadrilateral, no three points will be collinear.

-----Output-----
Output the sum of the scores. Since this score can be huge just print the answer modulo $1000003$.

-----Examples-----
Sample Input:
4
2 0
0 2
-2 0
0 -2
Sample Output:
16
user: Nick is a bird watcher and often visits the forum “CrowFinders” to discuss his hobby with like-minded people. CrowFinders has a voting system where users can upvote or downvote comments, which increases or decreases their score by $1$. This means that each comment can end up with any integer score (including negative scores). Once when Nick was browsing a heated discussion about the classification of jackdaws as crows, he found something very pleasing: a chain of comments that alternated between positive and negative scores. But a few days later, he found that the comment chain was no longer alternating. Now Nick wants to make it alternating again. 

A comment chain is alternating if the scores $s_1, s_2, \ldots , s_ n$ of the comments all are non-zero, and every pair of adjacent scores $s_ i$, $s_{i+1}$ have opposite signs. In particular, a single comment with a non-zero score or even a comment chain without any comment is an alternating comment chain.

There are two operations Nick can do to make the comment chain alternating:
 - Create a fake account and upvote/downvote some of the comments. This increases/decreases their respective scores by $1$. Each fake account can only upvote/downvote each comment at most once, but it can vote on any subset of the comments. It takes $c$ seconds to create an account and use it to vote (regardless of how many comments are upvoted/downvoted).
 - Report one specific comment to remove it from the chain. Thinking of convincing reasons for the report takes $r$ seconds. (Nick is an excellent arguer, so once the report is filed, the comment is guaranteed to be removed.)

Nick can apply these operations in any order, any number of times. How fast can he make the comment chain alternating?

For example, consider Sample Input 1 below, where the scores in the comment chain are $8, 8, 2, -2$, and it takes Nick $10$ seconds to create an account and $50$ seconds to file a report for one comment. In this case it is optimal to first create $3$ fake accounts and use them to upvote the fourth comment and downvote the third, followed by reporting the first comment. This results in the scores $8, -1, 1$, which is an alternating chain. The time used for this is $80$ seconds.

-----Input-----
The input consists of:
 - One line with three integers $n$, $c$, and $r$ ($1 \leq n \leq 5\cdot 10^5$, $1 \leq c,r \leq 10^9$), the number of comments in the chain, the time it takes to create a fake account and the time it takes to report one comment respectively.
 - One line with $n$ integers $s_1, \ldots , s_ n$ ($-10^9 \leq s_ i \leq 10^9$ for all $i$), the current score of each comment in the chain.

-----Output-----
Output the smallest time to make the comment chain alternating by applying the operations above.

-----Examples-----
Sample Input:
4 10 50
8 8 2 -2
Sample Output:
80
user: Gladstone Gander is walking through Duckburg and needs to get to his date with Daisy Duck as soon as possible. If he doesn’t get there in time, Donald might show up and take his place instead. 

Duckburg has recently started providing a very eco-friendly way of public transport: bikes. At many bike stations throughout the city, one can pick up a free bike, ride it to another bike station, and drop it there. This gives Gladstone two ways of transportion: on foot or by bike. Biking is faster, of course, but he must pick up and leave the bikes at the designated stations. Gladstone can walk or bike between any two points in a straight line.

Gladstone possesses a map of the (rectangular) center of Duckburg. His current position is on this map and so is the meeting point with Daisy. The map also contains the locations of all bike stations within the boundaries of the map.

There can be way more bike stations though, that are not within the boundaries of the map. Considering his luck, you can assume that the moment Gladstone walks (or bikes) off the map, he encounters a bike station if that suits him well. The bike stations not on the map can be located anywhere outside the map, they do not have to lie on integer coordinates.

That leaves Gladstone with the task of figuring out which route to take. Can you help him out? Given the map and his infinite amount of luck, what is the fastest time to his date with Daisy?

-----Input-----
The input consists of:
 - one line with two integers $v_{\text {walk}}$ and $v_{\text {bike}}$ ($1\le v_{\text {walk}}< v_{\text {bike}} \le 1000$), the speeds of walking and of biking;
 - one line with four integers $x_1, y_1, x_2$ and $y_2$ ($-10^6\le x_1< x_2\le 10^6$; $-10^6\le y_1< y_2\le 10^6$), the bounding coordinates of the map of the center of Duckburg;
 - one line with two integers $x_{\text {G}}$ and $y_{\text {G}}$, Gladstone’s position;
 - one line with two integers $x_{\text {D}}$ and $y_{\text {D}}$, Daisy’s position;
 - one line with one integer $n$ ($0\le n\le 1000$), the number of known bike stations;
 - $n$ lines with two integers $x_{\text {station}}$ and $y_{\text {station}}$ each, the coordinates of the known bike stations.

All coordinates are on the map of the center, i.e., $x_1\le x\le x_2$ and $y_1\le y\le y_2$.

-----Output-----
Output one line with the shortest possible time for Gladstone to get to Daisy. Your answer should have an absolute or relative error of at most $10^{-6}$.

-----Examples-----
Sample Input:
1 8
0 0 10 10
5 1
5 9
3
5 8
2 2
9 6
Sample Output:
3.000000000