meetforever/GRPO_CL huggingface dataset:
user: It’s Christmas time and JW’s $1$-dimensional shop is selling Christmas trees. However, the demand for trees is much higher than the number of trees available. Hence, JW has come up with a special strategy to help decide who gets what tree: a game of Musical Trees!

Musical Trees is much like the game Musical Chairs. There’s a set of trees lined up in a straight ($1$-dimensional) line. At first, everyone starts by wandering around the store while the music is playing. When the music stops, everyone runs to the nearest tree (the tree the smallest distance away) and whoever reaches a tree first gets to the claim that tree. Since people are lazy, they will only ever try to run to the closest tree to them, and hence multiple people may try to get the same tree. Note this means some trees may be unclaimed if they are closest to no one. Also, like in Musical Chairs, no tree can be claimed by more than one person.

The music has just stopped in Musical Trees and as everyone is running to the closest tree, you want to figure out the number of people who won’t get any tree.

-----Input-----
The first line consists the number of people $n$ ($1\le n\le 100$) and the number of trees $m$ ($1 \le m \le 100$). The next line contains $n$ integers $p_1,p_2,\ldots ,p_ n$, the positions of all the people when the music stops ($1 \le p_ i \le 1000$). The last line contains $m$ integers $t_1,t_2,\ldots ,t_ m$, the positions of all the trees ($1 \le t_ i \le 1000$). No two people or two trees will have the same position. Some people may try to cheat though, and will already be at the same position as a tree when the music stops. Note that if a person has more than one closest tree to them, they will always go for the one with the smallest $t_ i$.

-----Output-----
Output the number of people who won’t get a tree.

-----Examples-----
Sample Input 1:
2 3
1 4
2 4 5
Sample Output 1:
0

Sample Input 2:
3 2
1 5 10
4 6
Sample Output 2:
1
user: As a huge fan of the popular collectible card game Numinous Wilds: the Elven Reign Chronicles (NWERC), you have a large collection of cards which you carefully organise by their rarity. One day you notice that someone has touched your collection, and that some of the cards are now out of order. The most natural suspect, of course, is your little brother Billy, who was absolutely $100\% $ forbidden from playing with your cards. After a few minutes of interrogation Billy confesses that he indeed took a few consecutive cards from the middle of the stack, but he swears that he put them back in exactly the same order as they were. You suspect that Billy, being so young, may have simply mistakenly reversed the order of the cards that he took. Now you want to check your theory and decide if you can find the batch of cards that Billy took to play with. 

Is it possible to restore the order of the cards into non-decreasing order of their rarity by reversing just one contiguous batch of cards?

-----Input-----
The input consists of:
 - One line containing an integer $n$ ($1 \le n \le 10^6$), the number of cards in your collection.
 - One line containing $n$ integers $v_1, \ldots , v_ n$ ($1 \le v_{i} \le 10^9$ for all $i$), the current order of the cards’ rarity values.

-----Output-----
If the cards can be sorted by reversing exactly one contiguous subsequence of the list, then output the $1$-based start and end indices of such a subsequence. Otherwise, output “impossible”. If there are multiple valid solutions you may output any one of them.

-----Examples-----
Sample Input 1:
7
10 13 19 19 15 14 20
Sample Output 1:
3 6

Sample Input 2:
6
9 1 8 2 7 3
Sample Output 2:
impossible
user: Today you are doing your calculus homework, and you are tasked with finding a Lipschitz constant for a function f(x), which is defined for $N$ integer numbers $x$ and produces real values. Formally, the Lipschitz constant for a function f is the smallest real number $L$ such that for any $x$ and $y$ with f(x) and f(y) defined we have:\[ |f(x) - f(y)| \leq L \cdot |x - y|. \]

-----Input-----
The first line contains $N$ – the number of points for which f is defined. The next $N$ lines each contain an integer $x$ and a real number $z$, which mean that $f(x) = z$. Input satisfies the following constraints:
 - $2 \leq N \leq 200000$.
 - All $x$ and $z$ are in the range $-10^9 \leq x,z \leq 10^9$.
 - All $x$ in the input are distinct.

-----Output-----
Print one number – the Lipschitz constant. The result will be considered correct if it is within an absolute error of $10^{-4}$ from the jury’s answer.

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

Sample Input 2:
2
1 4
2 2
Sample Output 2:
2
user: Mario is making up silly games again instead of reading Dostoevsky for school. The rules of his newest game follow. First he chooses a random word from the book. Then he splits the word in two arbitrary places to get three separate words. After that he reverses the order of the letters in each of those three words (exchanges the first and last letters, the second and second last and so on).

Finally, he puts the three words back together in the same order in which they were before splitting. The goal of the game is to obtain the lexicographically smallest word possible. In other words, of all words that can be obtained by the above procedure, find one which would be earliest in a dictionary.

Write a program that plays Mario’s game perfectly.

-----Input-----
The first and only line of input contains Mario’s chosen word, a string of lowercase letters of the English alphabet with no spaces.

The input word will be between $3$ and $50$ characters long (inclusive).

-----Output-----
Output the best word on a single line.

-----Examples-----
Sample Input 1:
dcbagfekjih
Sample Output 1:
abcdefghijk

Sample Input 2:
mobitel
Sample Output 2:
bometil
user: Mirko and Slavko are playing a new game, “Trojke” (Triplets, in English). First they use a chalk to draw an $N \times N$ square grid on the road. Then they write letters into some of the squares. No letter is written more than once in the grid.

The game consists of trying to find three letters on a line as fast as possible. Three letters are considered to be on the same line if there is a line going through the centre of each of the three squares.

After a while it gets harder to find new triplets. Mirko and Slavko need a program that counts all the triplets, so that they know if the game is over or they need to search further.

-----Input-----
The first line contains an integer $N$ ($3 \le N \le 100$), the dimension of the grid.

Each of the $N$ following lines contains $N$ characters describing the grid – uppercase letters and the character ’.’ which marks an empty square.

-----Output-----
Output the number of triples on a single line.

-----Examples-----
Sample Input 1:
4
...D
..C.
.B..
A...
Sample Output 1:
4

Sample Input 2:
5
..T..
A....
.FE.R
....X
S....
Sample Output 2:
3
user: A polyomino is a polyform with the square as its base form. It is a connected shape formed as the union of one or more identical squares in distinct locations on the plane, taken from the regular square tiling, such that every square can be connected to every other square through a sequence of shared edges (i.e., shapes connected only through shared corners of squares are not permitted).

 The most well-known polyominos are the seven tetrominos made out of four squares (see figure), famous from the Tetris® game, and of course the single domino consisting of two squares from the game with the same name. Some polyomino can be obtained by gluing several copies of the same smaller polyomino translated (but not rotated or mirrored) to different locations in the plane. We call those polyomino powers.



-----Input-----
One line with two positive integers $h, w \leq 10$. Next follows an $h \times w$ matrix of characters ‘.’ or ‘X’, the ‘X’s describing a polyomino and ‘.’ space.

-----Output-----
A $k$-power with $2 \leq k \leq 5$ copies of a smaller polyomino: Output a $h\times w$ matrix on the same format as the input with the ‘X’s replaced by the numbers $1$ through $k$ in any order identifying the factor pieces. Furthermore, if multiple solutions exist, any will do. Otherwise, output “No solution” if no solution exists.

-----Examples-----
Sample Input 1:
3 7
.XXXXX.
.XX..X.
XXXX...
Sample Output 1:
No solution

Sample Input 2:
1 3
XXX
Sample Output 2:
123
user: In this economy, we all know how hard it is to get a job. Mirko, a recent college graduate, however, got lucky – he is now employed as a runeologist by the Language Institute of Croatia. His friend Slavko believes runeology isn’t a science and is hence angry at Mirko for believing the opposite. One foggy Christmas day, Mirko’s laptop broke. Since he isn’t great with computers, he gave it to Slavko to repair it. Slavko, feeling a little naughty, decided to mess up a particular file Mirko was working on.

This file contains a matrix of $R$ rows and $C$ columns. Each element of the matrix is a single letter. No two columns of the matrix are equal. To have some fun with pseudo-scientist Mirko, Slavko decided he will delete as many rows as possible from the top of the table, without breaking the no-equal-column rule.

-----Input-----
The first line of input contains two integers $R$ and $C$ ($2 \le R, C \le 1000$), the number of rows and the number of columns, respectively.

In each of the next $R$ lines there are $C$ small letters of the English alphabet. These $R \times C$ letters represent Mirko’s table (which does not have two equal columns).

-----Output-----
Output a single integer, the maximum number of rows which can be deleted from the top of the table so that no two columns are equal.

-----Examples-----
Sample Input 1:
2 6
dobarz
adatak
Sample Output 1:
0

Sample Input 2:
3 4
alfa
beta
zeta
Sample Output 2:
2
user: Match sticks can be used to form digital numbers. The arrangement of matches that forms each digit between ‘0’ and ‘9’ is illustrated in the figure.

You are given two sequences of digits $X$ and $Y$. There are matches that have been arranged to form the digits in $X$. Can you move exactly one match from them, so that the resulting matches form the other sequence $Y$?

-----Input-----
The input contains one line with two sequences of digits $X$ and $Y$. It is guaranteed that $X$ and $Y$ have the same length but are different sequences. Each sequence contains digits between ‘0’ and ‘9’ and has at least one and no more than $12$ digits. A sequence may contain leading zeros.

-----Output-----
Output “yes” if it is possible to move exactly one match to change $X$ into $Y$. Otherwise output “no”.

-----Examples-----
Sample Input 1:
60 58
Sample Output 1:
yes

Sample Input 2:
046 040
Sample Output 2:
yes
user: Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.



For example, given n = 3, a solution set is:


[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]

Answer: {"fn_name": "generateParenthesis", "inputs": [[3],[1]], "outputs": [["\"((()))\"","\"(()())\"","\"(())()\"","\"()(())\"","\"()()()\""], ["\"()\""]]}
user: Given a collection of intervals, merge all overlapping intervals.

Example 1:


Input: [[1,3],[2,6],[8,10],[15,18]]
Output: [[1,6],[8,10],[15,18]]
Explanation: Since intervals [1,3] and [2,6] overlaps, merge them into [1,6].


Example 2:


Input: [[1,4],[4,5]]
Output: [[1,5]]
Explanation: Intervals [1,4] and [4,5] are considerred overlapping.

Answer: {"fn_name": "merge", "inputs": [[[[1,3],[2,6],[8,10],[15,18]]], [[[1,4],[4,5]]]], "outputs": [[[1,6],[8,10],[15,18]], [[1,5]]]}
user: Given a collection of candidate numbers (candidates) and a target number (target), find all unique combinations in candidates where the candidate numbers sums to target.

Each number in candidates may only be used once in the combination.

Note:


       All numbers (including target) will be positive integers.
       The solution set must not contain duplicate combinations.


Example 1:


Input: candidates = [10,1,2,7,6,1,5], target = 8,
A solution set is:
[
  [1, 7],
  [1, 2, 5],
  [2, 6],
  [1, 1, 6]
]


Example 2:


Input: candidates = [2,5,2,1,2], target = 5,
A solution set is:
[
  [1,2,2],
  [5]
]

Answer: {"fn_name": "combinationSum2", "inputs": [[[[10,1,2,7,6,1,5]], [8]], [[[2,5,2,1,2]], [5]]], "outputs": [[[1,1,6],[1,2,5],[1,7],[2,6]], [[1,2,2],[5]]]}
user: Given a set of non-overlapping intervals, insert a new interval into the intervals (merge if necessary).

You may assume that the intervals were initially sorted according to their start times.

Example 1:


Input: intervals = [[1,3],[6,9]], newInterval = [2,5]
Output: [[1,5],[6,9]]


Example 2:


Input: intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]
Output: [[1,2],[3,10],[12,16]]
Explanation: Because the new interval [4,8] overlaps with [3,5],[6,7],[8,10].

Answer: {"fn_name": "insert", "inputs": [ [[[1,3],[6,9]], [2,5]], [[[1,2],[3,5],[6,7],[8,10],[12,16]], [4,8]] ], "outputs": [[[1,5],[6,9]], [[1,2],[3,10],[12,16]]]}
user: Given a string t, we will call it unbalanced if and only if the length of t is at least 2, and more than half of the letters in t are the same. For example, both voodoo and melee are unbalanced, while neither noon nor a is.
You are given a string s consisting of lowercase letters. Determine if there exists a (contiguous) substring of s that is unbalanced. If the answer is positive, show a position where such a substring occurs in s.

-----Constraints-----
 - 2 ≦ |s| ≦ 10^5
 - s consists of lowercase letters.

-----Partial Score-----
 - 200 points will be awarded for passing the test set satisfying 2 ≦ N ≦ 100.

-----Input-----
The input is given from Standard Input in the following format:
s

-----Output-----
If there exists no unbalanced substring of s, print -1 -1.
If there exists an unbalanced substring of s, let one such substring be s_a s_{a+1} ... s_{b} (1 ≦ a < b ≦ |s|), and print a b. If there exists more than one such substring, any of them will be accepted.

-----Sample Input-----
needed

-----Sample Output-----
2 5

The string s_2 s_3 s_4 s_5 = eede is unbalanced. There are also other unbalanced substrings. For example, the output 2 6 will also be accepted.
user: Ash like soup very much! So, on the Raksha Bandhan day, his sister gave him a soup maker as a gift. Soup maker in the ith hour will make volume  Vi liters of soup and pours it in a bowl.
Each hour, the Volume of soup in every bowl is reduced due to evaporation. More precisely, when the temperature on a given hour is Ti, the Volume of soup in every bowl will reduce its volume by Ti. If this would reduce the volume of soup to or below zero, Bowl gets empty. All bowls are independent of each other.
Note that the Volume of soup in every bowl made in an hour i already lose part of its volume at the same hour. In an extreme case, this may mean that there is no soup left in the bowl at the end of a particular hour.
You are given the initial volumes of soup in bowls and the temperature on each hour. Determine the total volume of soup evaporated in each hour.
Input
The first line contains a single integer N (1 ≤ N ≤ 10^5) — the number of hours.
The second line contains N integers V 1, V 2, …, V N (0 ≤ V i ≤ 10^9), where V i is the initial volume of soup made in an hour i.
The third line contains N integers T 1, T 2, …, T N (0 ≤ T i ≤ 10^9), where T i is the temperature in an hour i.
Output
Output a single line with N integers, where the i-th integer represents the total volume of soup melted in an hour i.
Examples
Input
3
10 10 5
5 7 2
Output
5 12 4
Input
5
30 25 20 15 10
9 10 12 4 13
Output
9 20 35 11 25
Note
In the first sample, In the first hour, 10 liters of soup is prepared, which evaporates to the size of 5 at the same hour. In the second hour, another 10 liters of soup is made. Since it is a bit warmer than the hour before, the first bowl gets empty while the second bowl shrinks to 3. At the end of the second hour, only one bowl with 3 liters soup is left. In the third hour, another bowl with less volume of soup is made, but as the temperature dropped too, both bowls survive till the end of the hour.
user: -----INOI 2017, Problem 2, Training-----
Ash and his Pokemon Pikachu are going on a journey.  Ash has planned his route
for the journey so that it passes through N cities, numbered 1, 2, …, N, and in this order.

When they set out, Pikachu has an initial strength of Sin as well as an experience
value (XV) of 0. As they travel they may increase his strength and experience value
in a manner to be described below.

In each city,  Ash can choose either to train Pikachu or let Pikachu battle the
Gym-leader (but not both).  The Gym-leader in ith city has experience E[i]. If
Pikachu enters a city i with strength S and decides to train, then this
increases his strength by the cube of the sum of the digits in his current
strength. For example, if he entered a city with a strength of 12, then
training will increase his strength to 12 + (1+2)3 = 39.  On the other hand,
if he enters city i with strength S and battles the Gym-leader, then this
increases his experience value XV by S*E[i].

Ash wants your help to find out the maximum XV that Pikachu can attain 
at the end of his journey.

-----Input-----
- The first line contains two space separated integers, N and Sin, which are the number of cities, and the initial strength, respectively.

- The second line contains N space separated integers, which correspond to E[1], E[2],..., E[N].

-----Output-----
- A single integer which is the maximum XV that Pikachu can attain.

-----Constraints-----
For all test cases you may assume that: 

- 1 ≤ N ≤ 5000
- 0 ≤ Sin ≤ 109
- 0 ≤ E[i] ≤ 104

Subtask 1: For 10% of the score,

- N ≤ 20 and Sin = 1

Subtask 2: For further 40% of the score,

- E[i] = k for all i
i.e. E[i] is some constant k, for all i

Subtask 3: For further 50% of the score,

- 
No further constraints.


-----Example-----
Input 1:
2 12
5 10

Output 1:
390

-----Explanation 1-----
Suppose Pikachu trains in the first city, his strength will increase to 39, because as explained above, 12 + (1+2)3 = 39. If he battles in the first city, his XV will increase by (12*5) = 60.

If Pikachu trains in the first city, and then battles in the second city, his XV will increase by 39*10 = 390. So, the final XV will be 0+390 = 390. You can check that you cannot do better than this. Hence the answer is 390.

Input 2:
4 1
100 1 6 2

Output 2:
120

-----Explanation 2-----
Pikachu battles in the first city, trains in the second and third, and then battles in the fourth city. So his strength going into each of the four cities is (1, 1, 2, 10). And so he gains 1*100 XV from the first city and 10*2 XV from the fourth city. This gets him a total of 120 XV, and you can verify that nothing better can be done.

Note:
You may download the problem statements PDF and test cases zipped files here: http://pd.codechef.com/com/inoi/problems.zip. Please feel free to use them during the contest. 
Password for the PDF and test cases zip files: DPtrumpsGreedy2017
user: You have just bought a new house, and it has a huge, beautiful lawn. A lawn that needs cutting. Several times. Every week. The whole summer. 

After pushing the lawnmower around the lawn during the hottest Saturday afternoon in history, you decided that there must be a better way. And then you saw the ads for the new robotic lawnmovers. But which one should you buy? They all have different cutting speeds, cutting times and recharge times, not to mention different prices!

According to the advertisement, a robotic lawnmover will spend all its time either cutting the lawn or recharging its battery. Starting from a full battery, it will cut the lawn at a given rate of $c$ square meters per minute for a cutting time of $t$ minutes, after which it has run out of battery. Once out of battery, it will immediately start recharging. After recharging for $r$ minutes the battery is full again and it immediately starts cutting.

You decide that in order for your lawn to look sufficiently prim and proper, the lawnmower that you buy must be powerful enough to cut your whole lawn at least once a week on average. Formally, if we start the mower fully charged at the beginning of the week and run it for exactly $T$ weeks, it needs to cut the whole lawn at least $T$ times, for all positive integers $T$. But apart from this, you have no specific requirements, so among the ones that satisfy this requirement, you will simply go for the cheapest option. For the purposes of cutting your lawn, you may make the simplifying assumption that a week is always exactly $10080$ minutes long.

-----Input-----
The first line of input contains two integers $\ell $ and $m$ ($1 \le \ell \le 10^6$, $1 \le m \le 100$), the size of your lawn in square meters, and the number of lawnmowers to consider, respectively.

Then follow $m$ lines, each containing a string $n$ and $4$ integers $p$, $c$, $t$, and $r$, separated by commas, describing a lawnmower as follows:
 - $n$ is the name of the lawnmower, a string of at most $60$ printable characters (ASCII $32$ to $126$) excluding ‘,’, neither starting nor ending with a space,
 - $1 \leq p \leq 100000$ is the price of the lawnmover,
 - $1 \leq c \leq 100$ is the cutting rate in square meters per minute,
 - $1 \leq t \leq 10080$ is the cutting time in minutes, and
 - $1 \leq r \leq 10080$ is the recharge time in minutes.

-----Output-----
Output the name of the cheapest lawnmower capable of cutting your whole yard at least once a week on average. If several lawnmovers share the same lowest price, output all of their names, in the same order they were given in the input. If there is no such mower, output “no such mower”.

-----Examples-----
Sample Input:
7000 4
Grass Slayer 2000,9999,10,120,120
Slow-Mowe,999,1,120,240
Eco-cut X2,5499,2,25,35
Mowepower,5499,3,25,35
Sample Output:
Eco-cut X2
Mowepower
user: The city of Xentopia has a well-connected railway network. The city has $N$ junctions numbered from $1$ to $N$. There are $M$ pairs of railway tracks that exist between the junctions. Trains can travel in both directions on each track. Each railway track is labelled either red, blue, or white in colour.

Tima, a tourist in the city, wants to travel from junction $S$ to junction $T$ in the minimum possible time. She has a map of the railway network that she can use to achieve this goal.

Tima, being rather eccentric, has an interesting constraint for her travel: She wants to travel via exactly $k_1$ red tracks, exactly $k_2$ blue tracks, and any number of white tracks, in any order. She is fine with using a railway track more than once.

Can you tell the minimum time Tima will take to go from $S$ to $T$, ensuring that her constraint is not violated?

-----Input-----
The first line contains four space-separated integers: $N$, ($1 \leq N \leq 450$); $M$, ($1 \leq M \leq 1100$); $k_1$; and $k_2$, ($0 \leq k_1, k_2 \leq 800$, $k_1 \cdot k_2 \leq 800$). Following are $M$ lines. Each line contains four space-separated integers: $U~ V~ X~ C$, denoting that a track exists between junction $U$ and junction $V$, ($1 \leq U, V \leq N$, $U \neq V$); the train covers this track in $X$ seconds, ($0 \leq X \leq 10^9$); and the track is labelled colour $C$, ($0 \leq C \leq 2$). A white track is denoted by $C=0$, a red track is denoted by $C=1$, and a blue track is denoted by $C=2$.

The last line contains two space-separated integers $S$, ($1 \leq S \leq N$), and $T$, ($1 \leq T \leq N$), the source and destination of Tima’s journey, respectively. Note: $S$ may be equal to $T$.

-----Output-----
Print a single integer denoting the total time Tima would take. If it is not possible for Tima to reach her destination using exactly $k_1$ red tracks, $k_2$ blue tracks, and any number of white tracks, output -1.

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