meetforever/GRPO_CL huggingface dataset:
user: A group of friends has just played a round of miniature golf. Miniature golf courses consist of a number of holes. Each player takes a turn to play each hole by hitting a ball repeatedly until it drops into the hole. A player’s score on that hole is the number of times they hit the ball. To prevent incompetent players slowing down the game too much, there is also an upper limit $\ell $ (a positive integer) on the score: if a player has hit the ball $\ell $ times without the ball dropping into the hole, the score for that hole is recorded as $\ell $ and that player’s turn is over. The total score of each player is simply the sum of their scores on all the holes. Naturally, a lower score is considered better.

There is only one problem: none of the players can remember the value of the integer $\ell $. They decide that they will not apply any upper limit while playing, allowing each player to keep playing until the ball drops into the hole. After the game they intend to look up the value of $\ell $ and adjust the scores, replacing any score on a hole that is larger than $\ell $ with $\ell $.

The game has just finished, but the players have not yet looked up $\ell $. They wonder what their best possible ranks are. For this problem, the rank of a player is the number of players who achieved an equal or lower total score after the scores are adjusted with $\ell $. For example, if the adjusted scores of the players are $3$, $5$, $5$, $4$, and $3$, then their ranks are $2$, $5$, $5$, $3$ and $2$ respectively.

Given the scores of the players on each hole, determine the smallest possible rank for each player.

-----Input-----
The first line of input contains two integers $p$ and $h$, where $p$ ($2 \le p \le 500$) is the number of players and $h$ ($1 \le h \le 50$) is the number of holes. The next $p$ lines each contain $h$ positive integers. The $j^{\text {th}}$ number on the $i^{\text {th}}$ of these lines is the score for player $i$ on hole $j$, and does not exceed $10^9$.

-----Output-----
Output a line with the minimum possible rank for each player, in the same order as players are listed in the input.

-----Examples-----
Sample Input:
3 3
2 2 2
4 2 1
4 4 1
Sample Output:
1
2
2
user: The full-board residents of the famous but misnamed Adephagia School For Boys feel hard done by. Recent savings have seen dinnertime puddings cut back to a single biscuit while the masters finish their meals with fine raspberry jelly every night. Although the choice of custard cream or bourbon is not a bad one, the children hunger for the raspberry-filled delight and have planned a midnight raid.

A child must make it from their dorm, across the school to the kitchen without being seen by the patrolling masters. In any turn a child can stand still, or move to a horizontally or vertically neighbouring cell. Each turn the patrolling masters will move a step along their route. When they reach the end of their route, they will turn and continue to retrace their steps indefinitely. A child will be caught if the child and a master are on the same row or column with no blocked area between them.

If the child can make it to the fridge in the kitchen unseen, we recognise they can either make it back to their bed unseen or get caught fully of jelly and not care. See the first example, where the child can reach the fridge after $26$ turns, even though it gets spotted at that same time.

-----Input-----
 - One line consisting of two positive integers $r$ $c$ ($1 < r, c \leq 60$), the size of the school in rows and columns.
 - One line consisting of two pairs of bracketed positive integers, the row and column coordinates of the starting bed in the dormitory and the fridge in the kitchen respectively.
 - Another $r$ lines, each containing a string of $c$ characters with the following meaning:
 - ‘.’: Walkable area
 - ‘#’: Blocked area
 - One line consisting of a single integer $p$ ($1 \le p \le 200$) representing the number of patrolling masters.
 - Another $p$ lines, each a size-prefixed list of between $1$ and $7$ space-separated bracketed $(r, c)$ coordinates representing a contiguous path for the master to patrol.

All ‘special’ coordinates (locations of the bed, fridge, and masters) will be marked as walkable on the map.

-----Output-----
On a single line print the minimum number of turns for the child to reach the jelly. If the child cannot reach the jelly, output IMPOSSIBLE.

-----Examples-----
Sample Input:
5 5
(2 5) (5 3)
.....
.#.#.
.#.#.
....#
.#.##
1
6 (4 2) (4 3) (3 3) (2 3) (1 3) (1 2)
Sample Output:
26
user: You are a newly designed and created robot. As a robot, you are excellent at shooting lasers: your lasers always go perfectly straight, go infinitely far, and are infinitely thin. To test you, the scientist who made you set out a number of targets for you to hit with your laser beam. The targets (point-like objects) are set up in a large, open room.

Unfortunately, you are running low on battery. You only have enough charge left to fire two shots. The targets are transparent, so you might be able to shoot multiple targets with your laser beam. In fact, you are able to hit an infinite number of targets with a single shot, as long as they are on a straight line. In addition, you can move anywhere before and between the two shots. Can you figure out if it is possible to hit all targets with at most two shots from your laser beams?

-----Input-----
The first line contains an integer $N$, satisfying $1 \leq N \leq 100000$, the number of targets.

The following $N$ lines each contain two integers $X_ i$ and $Y_ i$, satisfying $-10^9 \leq X_ i,Y_ i \leq 10^9$. Each pair $(X_ i,Y_ i)$ specifies the coordinates of one of the $N$ targets. No two targets are placed at the same coordinates.

You may assume that height does not play a role in this problem.

-----Output-----
Output a single line containing a single word: “success” if it is possible to line up the two shots so that they hit all the targets, and “failure” if it is not.

-----Examples-----
Sample Input:
6
-1 0
0 0
1 0
-1 1
0 2
1 1
Sample Output:
failure
user: Although we imagine interplanetary probes to be very sophisticated pieces of technology, their information systems are quite archaic. You might assume that they have a certain amount of contiguous main memory and can store their data wherever is convenient, but unfortunately that is not the case. The probe’s main memory is organised in a number of FIFO (first-in-first-out) queues. In such a queue, data has to be taken out of the queue in the same order as it has been added to it.

A probe has multiple sensors and each sensor is linked to one of the queues. Whenever a sensor finishes recording, it appends the generated data to its queue. A sensor can write data to the queue only if the queue has enough space left to take all the data; if not, the data is lost.

In order to transfer data from the probe to Earth (in a process called downlinking), the path between the satellite and Earth must not be blocked by anything (e.g. a planet like Jupiter) and the antenna must be correctly positioned. During each downlink opportunity, data can be taken from multiple queues and transmitted back to Earth. The total amount of data that can be transmitted during a downlink opportunity depends on the length of the downlink opportunity and distance to Earth. Sensors do not collect data during downlink opportunities, since all electricity available is devoted to the transmitter.

The most important thing for scientists is not to lose any data recorded by sensors. In particular, all queues have to be empty after the last downlink opportunity. The scientists have asked you to write a program to determine whether all data can be transferred to Earth in a given time frame.

-----Input-----
 - one line containing three positive integers $n,q,s$ ($1\leq n,q \leq 30$, $1 \leq s \leq 100$), the number of downlink windows, FIFO queues, and sensors, respectively.
 - one line with $s$ integers $q_1 \ldots q_ s$ ($1 \leq q_ i \leq q$ for each $i$), determining for each sensor the queue it feeds its data into.
 - one line with $q$ integers $c_1 \ldots c_ q$ ($1 \leq c_ i \leq 10^6$ for each $i$), determining for each queue the size of the queue in megabytes.
 - $n$ lines, each describing one downlink window. Each contains $s + 1$ non-negative integers.
 - The first integer $d$ ($1 \leq d \leq 10^6$) states the number of megabytes that can be transferred to earth during the window.
 - The following $s$ numbers $a_1 \ldots a_ s$ ($0 \leq a_ i \leq 10^6$ for each $i$) describing the amount of data (in megabytes) generated by each of the sensors after the last but before this downlink window.

There will never be new data during a downlink window.

-----Output-----
Output “possible” if it is possible to transfer all data to Earth, and “impossible” otherwise.

-----Examples-----
Sample Input:
2 2 2
1 2
3 3
5 2 2
5 2 2
Sample Output:
possible
user: After attending the ProgNova contest, Peter walks out of the school to enjoy a weekend of shopping in Manhattan!

Peter has a shopping list with $m$ different items (numbered $1$ to $m$) he wants to purchase. There are $n$ shopping malls in Manhattan. Each shopping mall sells one of these $m$ items. (All the items Peter wants to buy are super rare and exclusive!) The $i$-th shopping mall is located at $(x_ i, y_ i)$ and sells only item $t_ i$.

Peter is planning for his shopping route. He starts from his school, which is located at $(0, 0)$. A move from $(x_1, y_1)$ to $(x_2, y_2)$ is said to be vertical if $|x_1 - x_2| < |y_1 - y_2|$. Otherwise, the move is horizontal. Peter always moves directly to a shopping mall or his school from his current position. He does not stop anywhere else. Peter may move to a same position multiple times. After buying all the items on the list, Peter will return to his school.

Peter hates to move vertically and wants to make as few vertical moves as possible. What is the minimum number of vertical moves Peter has to make so as to purchase all the $m$ items? Peter does not care about his total travel distance, or the number of horizontal moves he makes.

-----Input-----
The first line has two integer $n$ ($1 \leq n \leq 3\cdot 10^5$) and $m$ ($1 \leq m \leq 16$). Each of the next $n$ lines contains three integers. The $i$-th line has $x_ i$, $y_ i$ ($|x|, |y| \leq 10^9$) and $t_ i$ ($1 \leq t \leq m$). No two shopping malls share a same location and no shopping mall is located at $(0, 0)$. It is guaranteed that every of the $m$ items is sold by at least one shopping mall.

-----Output-----
Output the minimum number of vertical moves Peter has to make.

-----Examples-----
Sample Input:
3 2
1 1 2
1 2 1
-1 1 2
Sample Output:
0
user: You are given an integer $x$ of $n$ digits $a_1, a_2, \ldots, a_n$, which make up its decimal notation in order from left to right.

Also, you are given a positive integer $k < n$.

Let's call integer $b_1, b_2, \ldots, b_m$ beautiful if $b_i = b_{i+k}$ for each $i$, such that $1 \leq i \leq m - k$.

You need to find the smallest beautiful integer $y$, such that $y \geq x$. 


-----Input-----

The first line of input contains two integers $n, k$ ($2 \leq n \leq 200\,000, 1 \leq k < n$): the number of digits in $x$ and $k$.

The next line of input contains $n$ digits $a_1, a_2, \ldots, a_n$ ($a_1 \neq 0$, $0 \leq a_i \leq 9$): digits of $x$.


-----Output-----

In the first line print one integer $m$: the number of digits in $y$.

In the next line print $m$ digits $b_1, b_2, \ldots, b_m$ ($b_1 \neq 0$, $0 \leq b_i \leq 9$): digits of $y$.


-----Examples-----
Input
3 2
353

Output
3
353

Input
4 2
1234

Output
4
1313
user: Have you ever tried to explain to the coordinator, why it is eight hours to the contest and not a single problem has been prepared yet? Misha had. And this time he has a really strong excuse: he faced a space-time paradox! Space and time replaced each other.

The entire universe turned into an enormous clock face with three hands — hour, minute, and second. Time froze, and clocks now show the time h hours, m minutes, s seconds.

Last time Misha talked with the coordinator at t_1 o'clock, so now he stands on the number t_1 on the clock face. The contest should be ready by t_2 o'clock. In the terms of paradox it means that Misha has to go to number t_2 somehow. Note that he doesn't have to move forward only: in these circumstances time has no direction.

Clock hands are very long, and Misha cannot get round them. He also cannot step over as it leads to the collapse of space-time. That is, if hour clock points 12 and Misha stands at 11 then he cannot move to 1 along the top arc. He has to follow all the way round the clock center (of course, if there are no other hands on his way).

Given the hands' positions, t_1, and t_2, find if Misha can prepare the contest on time (or should we say on space?). That is, find if he can move from t_1 to t_2 by the clock face.


-----Input-----

Five integers h, m, s, t_1, t_2 (1 ≤ h ≤ 12, 0 ≤ m, s ≤ 59, 1 ≤ t_1, t_2 ≤ 12, t_1 ≠ t_2).

Misha's position and the target time do not coincide with the position of any hand.


-----Output-----

Print "YES" (quotes for clarity), if Misha can prepare the contest on time, and "NO" otherwise.

You can print each character either upper- or lowercase ("YeS" and "yes" are valid when the answer is "YES").


-----Examples-----
Input
12 30 45 3 11

Output
NO

Input
12 0 1 12 1

Output
YES

Input
3 47 0 4 9

Output
YES



-----Note-----

The three examples are shown on the pictures below from left to right. The starting position of Misha is shown with green, the ending position is shown with pink. Note that the positions of the hands on the pictures are not exact, but are close to the exact and the answer is the same. $\oplus 0 \theta$
user: THE SxPLAY & KIVΛ - 漂流 KIVΛ & Nikki Simmons - Perspectives

With a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space.

The space can be considered a 2D plane, with an infinite number of data nodes, indexed from $0$, with their coordinates defined as follows:  The coordinates of the $0$-th node is $(x_0, y_0)$  For $i > 0$, the coordinates of $i$-th node is $(a_x \cdot x_{i-1} + b_x, a_y \cdot y_{i-1} + b_y)$ 

Initially Aroma stands at the point $(x_s, y_s)$. She can stay in OS space for at most $t$ seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point $(x_s, y_s)$ to warp home.

While within the OS space, Aroma can do the following actions:  From the point $(x, y)$, Aroma can move to one of the following points: $(x-1, y)$, $(x+1, y)$, $(x, y-1)$ or $(x, y+1)$. This action requires $1$ second.  If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs $0$ seconds. Of course, each data node can be collected at most once. 

Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within $t$ seconds?


-----Input-----

The first line contains integers $x_0$, $y_0$, $a_x$, $a_y$, $b_x$, $b_y$ ($1 \leq x_0, y_0 \leq 10^{16}$, $2 \leq a_x, a_y \leq 100$, $0 \leq b_x, b_y \leq 10^{16}$), which define the coordinates of the data nodes.

The second line contains integers $x_s$, $y_s$, $t$ ($1 \leq x_s, y_s, t \leq 10^{16}$) – the initial Aroma's coordinates and the amount of time available.


-----Output-----

Print a single integer — the maximum number of data nodes Aroma can collect within $t$ seconds.


-----Examples-----
Input
1 1 2 3 1 0
2 4 20

Output
3
Input
1 1 2 3 1 0
15 27 26

Output
2
Input
1 1 2 3 1 0
2 2 1

Output
0


-----Note-----

In all three examples, the coordinates of the first $5$ data nodes are $(1, 1)$, $(3, 3)$, $(7, 9)$, $(15, 27)$ and $(31, 81)$ (remember that nodes are numbered from $0$).

In the first example, the optimal route to collect $3$ nodes is as follows:   Go to the coordinates $(3, 3)$ and collect the $1$-st node. This takes $|3 - 2| + |3 - 4| = 2$ seconds.  Go to the coordinates $(1, 1)$ and collect the $0$-th node. This takes $|1 - 3| + |1 - 3| = 4$ seconds.  Go to the coordinates $(7, 9)$ and collect the $2$-nd node. This takes $|7 - 1| + |9 - 1| = 14$ seconds. 

In the second example, the optimal route to collect $2$ nodes is as follows:   Collect the $3$-rd node. This requires no seconds.  Go to the coordinates $(7, 9)$ and collect the $2$-th node. This takes $|15 - 7| + |27 - 9| = 26$ seconds. 

In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.
user: Firecrackers scare Nian the monster, but they're wayyyyy too noisy! Maybe fireworks make a nice complement.

Little Tommy is watching a firework show. As circular shapes spread across the sky, a splendid view unfolds on the night of Lunar New Year's eve.

A wonder strikes Tommy. How many regions are formed by the circles on the sky? We consider the sky as a flat plane. A region is a connected part of the plane with positive area, whose bound consists of parts of bounds of the circles and is a curve or several curves without self-intersections, and that does not contain any curve other than its boundaries. Note that exactly one of the regions extends infinitely.


-----Input-----

The first line of input contains one integer n (1 ≤ n ≤ 3), denoting the number of circles.

The following n lines each contains three space-separated integers x, y and r ( - 10 ≤ x, y ≤ 10, 1 ≤ r ≤ 10), describing a circle whose center is (x, y) and the radius is r. No two circles have the same x, y and r at the same time.


-----Output-----

Print a single integer — the number of regions on the plane.


-----Examples-----
Input
3
0 0 1
2 0 1
4 0 1

Output
4

Input
3
0 0 2
3 0 2
6 0 2

Output
6

Input
3
0 0 2
2 0 2
1 1 2

Output
8



-----Note-----

For the first example, $000$ 

For the second example, [Image] 

For the third example, $\text{Q)}$
user: You are given two squares, one with sides parallel to the coordinate axes, and another one with sides at 45 degrees to the coordinate axes. Find whether the two squares intersect.

The interior of the square is considered to be part of the square, i.e. if one square is completely inside another, they intersect. If the two squares only share one common point, they are also considered to intersect.


-----Input-----

The input data consists of two lines, one for each square, both containing 4 pairs of integers. Each pair represents coordinates of one vertex of the square. Coordinates within each line are either in clockwise or counterclockwise order.

The first line contains the coordinates of the square with sides parallel to the coordinate axes, the second line contains the coordinates of the square at 45 degrees.

All the values are integer and between $-100$ and $100$.


-----Output-----

Print "Yes" if squares intersect, otherwise print "No".

You can print each letter in any case (upper or lower).


-----Examples-----
Input
0 0 6 0 6 6 0 6
1 3 3 5 5 3 3 1

Output
YES

Input
0 0 6 0 6 6 0 6
7 3 9 5 11 3 9 1

Output
NO

Input
6 0 6 6 0 6 0 0
7 4 4 7 7 10 10 7

Output
YES



-----Note-----

In the first example the second square lies entirely within the first square, so they do intersect.

In the second sample squares do not have any points in common.

Here are images corresponding to the samples: [Image]  [Image]  [Image]
user: Tokitsukaze and CSL are playing a little game of stones.

In the beginning, there are $n$ piles of stones, the $i$-th pile of which has $a_i$ stones. The two players take turns making moves. Tokitsukaze moves first. On each turn the player chooses a nonempty pile and removes exactly one stone from the pile. A player loses if all of the piles are empty before his turn, or if after removing the stone, two piles (possibly empty) contain the same number of stones. Supposing that both players play optimally, who will win the game?

Consider an example: $n=3$ and sizes of piles are $a_1=2$, $a_2=3$, $a_3=0$. It is impossible to choose the empty pile, so Tokitsukaze has two choices: the first and the second piles. If she chooses the first pile then the state will be $[1, 3, 0]$ and it is a good move. But if she chooses the second pile then the state will be $[2, 2, 0]$ and she immediately loses. So the only good move for her is to choose the first pile. 

Supposing that both players always take their best moves and never make mistakes, who will win the game?

Note that even if there are two piles with the same number of stones at the beginning, Tokitsukaze may still be able to make a valid first move. It is only necessary that there are no two piles with the same number of stones after she moves.


-----Input-----

The first line contains a single integer $n$ ($1 \le n \le 10^5$) — the number of piles.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_1, a_2, \ldots, a_n \le 10^9$), which mean the $i$-th pile has $a_i$ stones.


-----Output-----

Print "sjfnb" (without quotes) if Tokitsukaze will win, or "cslnb" (without quotes) if CSL will win. Note the output characters are case-sensitive.


-----Examples-----
Input
1
0

Output
cslnb

Input
2
1 0

Output
cslnb

Input
2
2 2

Output
sjfnb

Input
3
2 3 1

Output
sjfnb



-----Note-----

In the first example, Tokitsukaze cannot take any stone, so CSL will win.

In the second example, Tokitsukaze can only take a stone from the first pile, and then, even though they have no stone, these two piles will have the same number of stones, which implies CSL will win.

In the third example, Tokitsukaze will win. Here is one of the optimal ways:

  Firstly, Tokitsukaze can choose the first pile and take a stone from that pile.  Then, CSL can only choose the first pile, because if he chooses the second pile, he will lose immediately.  Finally, Tokitsukaze can choose the second pile, and then CSL will have no choice but to lose. 

In the fourth example, they only have one good choice at any time, so Tokitsukaze can make the game lasting as long as possible and finally win.