meetforever/GRPO_CL huggingface dataset:
user: Sarah and Patricia are young, very gifted sisters. Ever since they learned arithmetic in preschool, they have been bothering their mother Marguerite day and night to practice their calculations. Marguerite bought the two girls an arithmetic practice book, which has $n$ pages and a positive integer on each page. Those integers can be used for practicing arithmetic calculations. Marguerite hopes that the book can keep the two girls busy for a while so that she can work on her other chores.

Sarah and Patricia need to know whether their calculated answers are right, but Marguerite does not have the time to check their work. She therefore comes up with the clever idea of adversarial toddler training. Marguerite knows that Sarah is good at addition and Patricia is talented in multiplication. So she first chooses a range of consecutive book pages (at least two), and then asks Sarah to calculate the sum of the integers on these pages, and asks Patricia to calculate the product of these integers. If she chooses the pages carefully, then the two girls’ answers would be the same, and she can simply let Sarah and Patricia compare their answers!

As Sarah and Patricia do not want to practice on the same range multiple times, Marguerite wants to know in how many different ways she can select a range of pages for her toddler training (and when to buy a new practice book).

-----Input-----
The input has a single integer $n$ ($2 \leq n \leq 2 \cdot 10^5$) on the first line. The second line has $n$ positive integers giving the numbers in the arithmetic practice book ordered by the pages. None of these integers are larger than $10^9$.

-----Output-----
Output a single integer, the number of ways for Marguerite to choose a range of at least two consecutive pages so that Sarah’s answer matches Patricia’s.

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

Sample Input 2:
8
1 2 4 1 1 2 5 1
Sample Output 2:
4
user: It’s exam time in Mirko’s village. Everyone wants to pass the exam with as little effort as possible, which is not easy. Mirko realized that it would be best for him to find someone who knows more than him and learn from them. Everyone followed and now everyone is looking for someone to learn from. We can model how well a student is prepared for the exam with two integers, $A$ and $B.$ The number $A$ represents how well a student understands the subject, while the number $B$ is proportional to the quantity of their knowledge.

As the head of the village, Mirko decided that a student will ask another student for help only if that student has both numbers greater than or equal to the first student’s numbers (no student will ask someone who doesn’t understand the subject as well as themselves or who knows less). Additionally, students will try to minimize the difference in knowledge quantity (so that students don’t bother those that are way better). If this choice is not unique, they will try to minimize the difference in understanding.

Mirko’s village has recently become a very popular suburb and new students keep moving in (in time for the exam). With Mirko’s strict rules, they get confused about Mirko’s rules and don’t know where to go). They decided to ask a programmer from a neighbouring village for help.

-----Input-----
The first line of input contains an integer $N$ $(1 \le N \le 200000)$, the number of queries and arrivals in the village. Each of the following $N$ lines contains either:
 - "D $A$ $B$", a student has moved in whose knowledge is $A$ and $B$
 - "P $i$", the $i$-th student to move in wants to know whom to ask for help

The numbers $A$ and $B$ are between 1 and $2\cdot 10^9$. No two students have both numbers equal.

-----Output-----
For each query ("P $i$" line), output which student the $i$-th student should ask for help. The students are numbered in the order they moved into the village (starting from 1). If a student cannot be helped, output "NE".

-----Examples-----
Sample Input 1:
6
D 3 1
D 2 2
D 1 3
P 1
P 2
P 3
Sample Output 1:
NE
NE
NE

Sample Input 2:
6
D 8 8
D 2 4
D 5 6
P 2
D 6 2
P 4
Sample Output 2:
3
1
user: In a fishing contest, the participants fish in a lake, represented as a 2D grid of dimension $r \times c$. Each integer point in the grid contains fish. 

At point $(x, y)$, fish first appear at second $t_{x, y}$ and disappear just before time $t_{x, y} + k$ seconds. Outside of this time, no fish can be caught at this position. It takes no time to catch all the fish at a point, and all points contain the same amount of fish. Furthermore, moving to the point immediately north, west, south or east from the point you are currently at takes exactly $1$ second (though you are not required to move).

Assume that you start at some position $(x_0, y_0)$ at second $1$, and can catch fish until (and including) second $l$. From how many points in the lake can you catch fish, if you travel optimally on the lake?

-----Input-----
The input consists of:
 - one line with the integers $r$, $c$, $k$ and $l$ ($1 \le r, c \le 100$, $1 \le k \le 5$, $1 \le l \le 10^5$), the dimensions of the lake, the number of seconds fish stays at a point, and the number of seconds you can catch fish.
 - one line with the integers $x_0$ and $y_0$ ($0 \le x_0 < r$, $0 \le y_0 < c$), your original position.
 - $r$ lines, the $x$’th of which contains $c$ integers $t_{x, 0}, \dots , t_{x, c - 1}$ (each between $1$ and $l$, inclusive), the times at which fish appears on points in the $x$’th row.

-----Output-----
Output the maximum number of points you could catch fish from.

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

Sample Input 2:
2 3 5 6
1 1
1 1 6
1 2 2
Sample Output 2:
5
user: An artist who wanted to create an installation where his works appeared to be floating in midair has cast a large cube of clear acrylic to serve as a base. Unfortunately, during the casting, some small flecks of dirt got into the mix, and now appear as a cluster of pinpoint flaws in the otherwise clear cube.

He wants to drill out the portion of the cube containing the flaws so that he can plug the removed volume with new, clear acrylic. He would prefer to do this in one drilling step. For stability’s sake, the drill must enter the cube only once, perpendicular to one of its faces. The cube’s faces are parallel to the coordinate axes.

Given the $(x,y,z)$ positions of the flaws, and treating the size of the flaws as negligible, what is the smallest diameter drill bit that can be used to remove the flaws in one operation??

-----Input-----
The first line of input contains an integer $N$ denoting the number of flaws. $3 \leq N \leq 5000$

This is followed by $N$ lines of input, each containing three real numbers in the range $-1000.0\ldots 1000.0$, denoting the $(x,y,z)$ coordinates of a single flaw. Each number contains at most $6$ digits following a decimal point. The decimal point may be omitted if all succeeding digits are zero.

-----Output-----
Print the diameter of the smallest drill bit that would remove all the flaws.

The answer is considered correct if the absolute or relative error is less than $10^{-4}$

-----Examples-----
Sample Input 1:
3
1.0 0.0 1.4
-1.0 0.0 -1.4
0.0 1.0 -0.2
Sample Output 1:
2.0000000000

Sample Input 2:
5
1.4 1.0 0.0
-0.4 -1.0 0.0
-0.1 -0.25 -0.5
-1.2 0.0 0.9
0.2 0.5 0.5
Sample Output 2:
2.0000000000
user: Božo is a strange little boy. Every day he tires his friends with strange questions. Today’s question is: how many integers in the interval $[A, B]$ are there such that the sum of their digits is $S$, and which is the smallest such number?

Write a program that answers Božo’s question so that he can get some sleep.

-----Input-----
The input contains three integers $A$, $B$ and $S$ ($1 \le A \le B < 10^{15}$, $1 \le S \le 135$).

-----Output-----
The first line should contain the number of integers in the interval with the digit sum equal to $S$.

The second line should contain the smallest such integer.

The input data will guarantee that the first number is at least $1$.

-----Examples-----
Sample Input 1:
1 9 5
Sample Output 1:
1
5

Sample Input 2:
1 100 10
Sample Output 2:
9
19
user: It is the first day of school at Liking University, or “Lku” for short. Lku administration is very strict with attendance, especially on the first day. In order to verify everyone’s attendance, the Lku’s principal has made an attendance list. He then asked to all students to stand in line to his office in order to mark everyone’s attendance.

The principal would go through the list, top-down and inspect if the person in front of him was the one currently on top the list. This inspection takes exactly one second. If it was, then the principal would strike the name from the list. Regardless of whether the student’s name would match or not with the one on top the list, the student in front of the queue would be asked to go somewhere somewhere else in the line. This implies going to an arbitrary position in the line, e.g. going to the back, somewhere in the middle or the front (continue standing on the same spot). The student can decide which position he or she wants to go to.

The list itself was written hastily and had several flaws – some students could be left out from it and some students’ names could appear on the list more than once. Knowing the contents of the list and the position of each student within the initial line, what is the minimal time that it can take for every name to be stricken from the attendance list if the students choose their new positions in the queue optimally?

-----Input-----
The first line of input contains two integers $N$ and $M$ $(1 \leq N, M \leq 3 \cdot 10^5)$ – the total number of students in the line and the number of names on the list respectively.

The second line contains $M$ integers $a_1, a_2, \dots , a_ M$ $(1 \leq a_ i \leq N)$ – the names of students as they appear in the list (top-down).

The third line contains $N$ integers $b_1, b_2, \dots , b_ N$ $(1 \leq b_ i \leq N)$ – the initial order of the students as they appear in line, where $b_ i$ is the name of $i$:th student in the line ($b_1$ is the name of the first student in the line).

The students are numbered between $1$ and $N$.

-----Output-----
The output consists of two lines:
 - The first line of output is $K$ – the minimal number of inspections that the principal needs to do.
 - The second line of the output consists of $K$ integers. For every inspection, output a number for which position in the line the student has to go back to after the inspection.

If there are multiple solutions which result in minimal number of inspections, then output any of them.

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

Sample Input 2:
4 5
4 1 2 4 4
4 3 2 1
Sample Output 2:
7
4 4 2 4 4 1 4
user: Donald is playing a game of cards against his cousin Gladstone. Each round proceeds as follows:
 - Donald chooses an (integer) amount of coins and both of the cousins puts that many coins in the pot.
 - The cards are dealt.
 - The game is played.
 - The player who won gets all the coins in the pot.

This continues until either $n$ rounds have been played, or until one of the players have run out of coins.

Unfortunately, Gladstone is quite possibly the luckiest person alive. As his luck would let him win every single round, the cousins’ game would surely lead to a quick economic demise for Donald. To balance the situation, Donald has hired his nephews to distract Gladstone a few times, by giving him a prank phone call between steps 2 and 3 above. Every round in which Gladstone is distracted, Donald is able to look at Gladstone’s cards and can with this extra knowledge and some card swapping be certain to win the round.

But things are still not easy for Donald. Gladstone will not be distracted during every round, and Donald has no way of knowing in advance during which rounds Gladstone will be distracted, which effectively means that Gladstone’s luck will take its course and do its best to cheat Donald out of his hard-earned coins. Is it still possible for Donald to come out richer from this experience, by being careful in how he chooses his bets?

Note that in step 2, Donald can never bet more coins than he has, or more coins than Gladstone has.

-----Input-----
The input consists of four integers $d$, $g$, $n$, and $k$, where $1 \le d, g \le 1000$ are the amounts of coins Donald and Gladstone initially have, $1 \le n \le 50$ is the number of rounds they will play, and $0 \le k \le n$ is the number of rounds during which Gladstone will be distracted.

-----Output-----
Write a single line containing an integer $M$ giving the maximum amount of coins Donald can be certain to have at the end of the game.

-----Examples-----
Sample Input 1:
2 10 3 2
Sample Output 1:
4

Sample Input 2:
10 10 5 0
Sample Output 2:
10
user: Zvonko is playing with digits again, even though his mother has warned him that he is doing too much math and should go outside to play with his friends.

In his latest game, Zvonko looks for multiples of an integer $X$, composed only of certain digits. A multiple of $X$ is any number divisible by $X$.

In order to ruin Zvonko’s fun, his mother decided to get a program that solves the problem. Write a program that calculates how many multiples of $X$ are between $A$ and $B$ (inclusive), such that, when written in decimal, they contain only certain allowed digits.

-----Input-----
The first line of input contains three integers $X$, $A$ and $B$ ($1 \le X < 10^{11}$ , $1 \le A \le B < 10^{11}$). The second line contains the allowed digits. The digits will be given with no spaces, sorted in increasing order and without duplicates. There will be at least one allowed digit.

-----Output-----
Output the number of multiples Zvonko can make on a single line.

-----Examples-----
Sample Input 1:
2 1 20
0123456789
Sample Output 1:
10

Sample Input 2:
6 100 9294
23689
Sample Output 2:
111
user: Many pharmacies in the United States fill prescriptions strictly on a first-come, first-served basis, even preferring prescriptions submitted electronically from a remote site to prescriptions dropped off by waiting customers in the store. This frequently leads to situations where customers have to wait for prescriptions because pharmacy technicians are busy filling prescriptions that may not be picked up until much later anyway.

This problem asks you to investigate the effect of an “in-store customers first” policy. Under this policy, technicians fill prescriptions in the order in which they are dropped off, but they will not start filling remote prescriptions as long as there are in-store prescriptions to be filled.

Write a program that computes the average completion time for in-store and remote customers under this policy!

-----Input-----
The input consists of a single test case. The first line contains two integers $n$ ($0 < n \le 100000$) and $t$ ($0 < T \le 10$), where $n$ denotes the number of prescriptions and $T$ the number of technicians working at the pharmacy. This is followed by $n$ lines, one line per prescription.

Each line consists of one integer $d$ ($0 < d \le 10^9$), which is the time (in seconds) when the prescription was dropped off, followed by a single character ‘R’ or ‘S’ for a remote or in-store prescription, followed by a single integer $k$ ($0 < k \le 500$) describing the number of seconds it takes a technician to fill this prescription. Prescriptions are listed in increasing order of drop-off time, but multiple prescriptions may be dropped off at the same time, in which case preference should be given to any in-store prescriptions, regardless of the order in which they appear in the input. If two prescriptions of the same type are dropped off at the same time, the prescription needing the shorter fill time must be filled first, again regardless of the order in which they appear in the input.

Once a technician starts working on a prescription, they will finish filling it, even if an in-store prescription is dropped off while they are working. Each prescription requires one pharmacy technician to fill it, and each technician can work on only one prescription at a time. The technicians work until all prescriptions are filled. You should ignore the time it would take for technicians to decide which prescription to fill next, so a technician who finishes a prescription can start working immediately on the next prescription.

-----Output-----
Output two numbers $o$ and $r$, denoting the average completion time for in-store and remote prescriptions, respectively. A prescription’s completion time is defined as the time difference between when a prescription was dropped off and when it was filled. If there were no in-store or remote prescriptions in the input, output $0$ for $o$ or $r$ instead. Your answer is considered correct if it is within a relative or absolute error of $10^{-6}$.

-----Examples-----
Sample Input 1:
5 3
1 R 4
2 R 2
3 R 2
4 S 2
5 S 1
Sample Output 1:
1.500000 2.666667

Sample Input 2:
5 2
1 R 4
2 R 2
3 R 2
4 S 2
5 S 1
Sample Output 2:
1.500000 3.666667
user: While debugging a program Mirko noticed that a bug in the program may be linked with the existence of so called square killers in the program memory. The program memory is a matrix composed of $R$ rows and $C$ columns consisting only of zeroes and ones. A square killer is a square submatrix in memory, consisting of more than one character, that, when rotated $180$ degrees looks exactly the same. For example, the following matrix contains $3$ square killers:

101010      ....10      ......      101...
111001      ....01      ...00.      111...
101001      ......      ...00.      101...

memory      killer      killer      killer

Mirko is wondering if there is a connection between the size of the largest square killer and the bug in the program. Help Mirko by writing a program that, given the layout of the memory, outputs the size of the largest square killer. The size of the square killer is the number of rows (or columns) that the killer consists of. In the example above the killer sizes are $2$, $2$ and $3$, respectively.

-----Input-----
The first will contain two integers, $R$ and $C$, smaller than or equal to $300$. The next $R$ lines will each contain $C$ characters (‘0’ or ‘1’) with no spaces.

-----Output-----
Output the size of the largest killer on a single line, or output $-1$ if there are no square killers.

-----Examples-----
Sample Input 1:
3 6
101010
111001
101001
Sample Output 1:
3

Sample Input 2:
4 5
10010
01010
10101
01001
Sample Output 2:
3
user: Lifeguards have a very important job. They prevent people from drowning and allow millions of people every year to experience the joys of water. You are one of these lifeguards, and you take your job very seriously. If regulations were up to you, everyone would have to wear life vests when in the water, which is why you are part of the Buoyancy Activists Promoting Change. As a result of your persistent lobbying, the pool at which you are a lifeguard has decided to hire a second lifeguard. You are very happy with the increased security at your local swimming pool.

You get along quite well with the new lifeguard, but you discover you have not prepared his arrival properly; on the first day of working together you have some trouble figuring out who is supposed to watch which swimmers. This is completely unacceptable and could lead to casualties! You immediately start working on this problem: following the mantra “shared responsibility is no responsibility”, you try to divide the people in the swimming pool into two groups as follows: any swimmer is the responsibility of the lifeguard closest to this swimmer. Thus, knowing the exact positions of all swimmers, you and your coworker both find a position such that both of you are responsible for the exact same number of swimmers. Furthermore, you want at most one swimmer for whom the distance to you and your coworker is equal. This swimmer counts for both lifeguards.

As you and your coworker are amazing sprinters, you do not care for the actual distance between you and the swimmers, only that the swimmers are divided nicely into two equally sized groups.

-----Input-----
 - The first line contains an integer $2\leq n \leq 10^5$, the number of swimmers.
 - Each of the next $n$ lines contains two integers $-10^9\leq x\leq 10^9$ and $-10^9\leq y\leq 10^9$, the position of the swimmer.

-----Output-----
Print two lines, both containing integers $x$ and $y$ with $-10^{18}\leq x,y\leq 10^{18}$, the locations of you and your coworker.

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

-----Examples-----
Sample Input 1:
5
0 0
0 1
1 0
0 -1
-1 0
Sample Output 1:
-3 -1
3 1

Sample Input 2:
4
2 4
6 -1
3 5
-1 -1
Sample Output 2:
3 4
3 -1
user: It is the time for the Holidays, which means it’s time for the annual Holiday Cookie Throwing contest where cookies are thrown against a wall. Cookies are really simple polygons that rotate clockwise while in flight.

Due to many years of advanced research and precise throwing equipment, these cookies can fly under idealized conditions: their center of mass follows an ideal parabola ($g = 9.81 \frac{m}{s^2}$), and their angular velocity stays constant.

Given a cookie’s shape, initial angle and speed as well as its angular velocity, compute which of the cookie’s corners hits the wall first, and when!

-----Input-----
The input consists of a single test case. The first line contains $5$ numbers: an integer $n$ ($3 \le n \le 20$) denoting the number of vertices of the cookie polygon, a real number $\omega $ ($0 \le \omega \le 10$), the angular velocity in $\text {rad}/s$ in clockwise direction, a real number $v_0$ ($1 \le v_0 \le 10$), the initial velocity of the cookie in $\frac{m}{s}$, an integer $\theta $ ($0 \le \theta \le 80$), the initial angle of the cookie’s trajectory, given in degrees measured counter-clockwise relative to the $(1, 0)$ unit vector, a real number $w$ ($20 \le w \le 500$), denoting the $x$-coordinate of the wall towards which the cookie is moving. You may assume that there are no other objects in space aside from the cookie, and that the wall is of infinite height (e.g., from $-\infty \ldots \infty $).

This is followed by $n$ lines, one for each vertex. Each line contains two real numbers $x_ i$ and $y_ i$ ($|x_ i| < 20, |y_ i| < 20$) denoting the initial position of a cookie’s corner. Corners are numbered $1 \ldots n$. The cookie polygon’s vertices are given in counter-clockwise order. The polygon is simple (e.g., not self-intersecting) and has a non-zero area.

All real numbers are given with no more than $6$ decimal digits after the period.

-----Output-----
Output two numbers $i$ and $T_ i$, denoting the index $i$ ($1 \le i \le n$) of the corner that hits the wall first and the time $T_ i$ in seconds when that happens. The index corresponds to the order in the input. $T_ i$ must be given with an absolute error of less than $10^{-3}$! You may assume that no two vertices hit the wall within $10^{-2}$ seconds of each other, and that the first vertex to hit the wall would pierce it for at least $10^{-3}$ seconds.

-----Examples-----
Sample Input 1:
3 6 5 45 20
0 0
2 0
1 1.5
Sample Output 1:
2 5.086781

Sample Input 2:
3 0.25 2 45 20
0 0
2 0
1 1.5
Sample Output 2:
1 12.715255