meetforever/GRPO_CL huggingface dataset:
user: The current programming club president, Norbit, gives speeches at the weekly club meetings. Casual viewers are underwhelmed with the quality of Norbit’s elocution. Specifically, Norbit often hesitates during his speeches with interjections like “umm.”

You, however, are no casual viewer–you are a computer scientist! You have noticed strange patterns in Norbit’s speech. Norbit’s interjections, when arranged together, form a binary code! By substituting $1$’s and $0$’s for u’s and m’s, respectively, you produce 7-bit binary ASCII codes that spell out secret messages.

For example, the letter ‘a’ has an ASCII code of $97$, which translates to a binary value of $1100001$ and an umm code of “uummmmu”. An umm code can be split up in the speech. For example, an encoding of ‘a’ could be stretched across three utterances: “uum”, “mmm”, “u” (possibly with other non-umm code words occurring between them).

Now that you have discovered Norbit’s secret, you go back through transcripts of his previous speeches to decode his cleverly concealed messages.

-----Input-----
There is one line of input of length $S$ ($20 \le S \le 500000$), which ends with a single newline. Before the newline, the input may contain any characters in the ASCII range $32$ – $126$ (that is, space (‘ ’) through tilde (‘~’)).

Let’s define a “word” as a space-delimited sequence of characters. If a word does not contain any letters or digits except lowercase u’s and/or m’s, then it is part of the umm-coded message. If a word contains digits or letters other than lowercase u and m, then it is not part of the umm-coded message (even if it does contain u or m). Note that a word that is part of the umm-coded message may contain punctuation (which is defined as anything other than letters, digits, or space). Naturally, you should only consider the u and m characters (and not punctuation) when decoding the umm-coded message. Let $M$ be the length of the entire umm-coded message (counting only its u and m characters). It is guaranteed that $M \ge 7$ and $M$ is evenly divisible by $7$.

-----Output-----
Print the de-umm-coded message. Note that for this problem, the judging is case-sensitive. It is guaranteed that each character that should be output is in the same ASCII range as the input.

-----Examples-----
Sample Input:
uu Friends m Romans ummuuummmuuuuumm countrymen mmuummmuu
Sample Output:
icpc
user: Today the Intergalactic Council of Pebble Coins (ICPC) conducted an intergalactic auction of the Neutronium Chaos Pebble Coin (NCPC). This coin, which was forged in the Ancient Coin Machine (ACM), is rumored to be the key to ruling the universe. 

Due to the extremely competitive nature of the auction, as well as the odd mechanics of the intergalactic currency used (far too advanced for mere mortals to understand), the auction was conducted with the following rules:
 - only one participant was allowed to make a bid at a time,
 - each participant was only allowed to make one bid, and
 - a participant making a bid had to bid at least twice the amount of the highest bid at the time.

The first participant making a bid was allowed to make a bid of any positive amount.

After the auction there were a lot of sore losers – understandably, having just lost their chance at world domination. To make the losers feel a little better and prevent possible rioting, the ICPC has decided to hold a lottery for the participants. The winners of the lottery are determined as follows. The ICPC picks a random number $s$. A group of participants is called winning if the sum of their bets from the auction is equal to $s$. A participant wins the lottery and receives a prize – a shiny Pebble Coin – if they belong to any winning group of participants.

Given the names of the participants, the bets that they made, and the random number $s$ chosen by the ICPC, help them determine which participants won the lottery.

-----Input-----
The first line of input contains two integers $n$ and $s$, where $1 \le n \le 1000$ is the number of participants, and $1 \le s < 10^{1000}$ is the random number chosen by the ICPC.

Then follow $n$ lines describing the participants. Each line contains a string $t$ and an integer $b$, where $t$ is the name of a participant, and $1 \le b < 10^{1000}$ is the amount of his bet. The name of each participant is unique and consists of between $1$ and $20$ letters from the English alphabet.

-----Output-----
Output an integer $k$ denoting the number of participants that won the lottery. Then output $k$ lines containing the names of the participants that won the lottery, one per line, in any order.

-----Examples-----
Sample Input:
5 63
Vader 3
Voldemort 7
BorgQueen 20
Terminator 40
Megatron 101
Sample Output:
3
BorgQueen
Terminator
Vader
user: Two great friends, Eddie John and Kris Cross, are attending the Brackets Are Perfection Conference. They wholeheartedly agree with the main message of the conference and they are delighted with all the new things they learn about brackets.

One of these things is a bracket sequence. If you want to do a computation with $+$ and $\times $, you usually write it like so:\[ (2 \times (2 + 1 + 0 + 1) \times 1) + 3 + 2. \]

The brackets are only used to group multiplications and additions together. This means that you can remove all the operators, as long as you remember that addition is used for numbers outside any parentheses! A bracket sequence can then be shortened to\[ (\; 2 \; ( \; 2 \; 1 \; 0 \; 1 \; ) \; 1 \; ) \; 3 \; 2. \]

That is much better, because it saves on writing all those operators. Reading bracket sequences is easy, too. Suppose you have the following bracket sequence\[ 5 \; 2 \; (\; 3 \; 1 \; (\; 2 \; 2 \; ) \; ( \; 3 \; 3 \; ) \; 1 \; ). \]

You start with addition, so this is the same as the following:\[ 5 + 2 + (\; 3 \; 1 \; (\; 2 \; 2 \; ) \; ( \; 3 \; 3 \; ) \; 1 \; ). \]

You know the parentheses group a multiplication, so this is equal to\[ 5 + 2 + (3 \times 1 \times (\; 2 \; 2 \; ) \times ( \; 3 \; 3 \; ) \times 1). \]

Then there is another level of parentheses: that groups an operation within a multiplication, so the operation must be addition.\[ 5 + 2 + (3 \times 1 \times (2 + 2 ) \times (3 + 3) \times 1 ) = 5 + 2 + (3 \times 1 \times 4 \times 6 \times 1) = 5+2 + 72 = 79. \]

Since bracket sequences are so much easier than normal expressions with operators, it should be easy to evaluate some big ones. We will even allow you to write a program to do it for you.

Note that $(\; )$ is not a valid bracket sequence, nor a subsequence of any valid bracket sequence.

-----Input-----
 - One line containing a single integer $1\leq n\leq 3\cdot 10^5$.
 - One line consisting of $n$ tokens, each being either (, ), or an integer $0\leq x < 10^9+7$. It is guaranteed that the tokens form a bracket sequence.

-----Output-----
Output the value of the given bracket sequence. Since this may be very large, you should print it modulo $10^9+7$.

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

Sample Input 2:
8
( 2 ( 2 1 ) ) 3
Sample Output 2:
9

Sample Input 3:
4
( 12 3 )
Sample Output 3:
36

Sample Input 4:
6
( 2 ) ( 3 )
Sample Output 4:
5

Sample Input 5:
6
( ( 2 3 ) )
Sample Output 5:
5
user: “Sabotage!” exclaimed J.R. Diddly, president and founder of Diddly Widgets Inc. 

“Vandalism, perhaps. Nothing’s actually been damaged.” responded Robert Lackey, the chief accountant.

Both were staring up at the large counter suspended above the factory floor, a counter that had faithfully recorded the number of widgets that had come off the assembly line since the factory was opened. But someone had changed the number being displayed so that it formed...

“It’s a palindrome.” said Lackey. “It reads the same forwards as backwards.”

“What I don’t understand,” said Diddly, “is why our security guards didn’t catch the vandals during their regular sweeps. It must have taken them hours to click forward to this new number, one step at a time.”

“No.” replied Lackey. “Although we only advance the rightmost digit each time a new widget is built, it’s possible to spin any of the digits. With a little planning, this might have taken only a few seconds.”

-----Description-----
Consider a digital counter consisting of $k$ wheels, each showing a digit from 0 to 9. Each wheel is mounted so that it can advance to the next digit in a single step, e.g., from 3 to 4, or from 8 to 9.

It is also possible to advance from digit 9 to digit 0. However, when this happens, the wheel on its immediate left will also advance to the next digit automatically. This can have a cascade effect on multiple wheels to the left, but they all happen in a single step.

Given the current setting of the counter, find the smallest number of steps until one can reach a palindrome. The palindrome must respect leading zeros, e.g., 0011 is not a palindrome.

For example, for input 610, it takes four steps. This can be done by incrementing the 6 wheel four times, resulting in 010.

-----Input-----
Input will consist of single line containing an integer of $1$ to $40$ digits. The number of digits in the input is the number of wheels on the counter. Numbers may contain leading zeros.

-----Output-----
Print a single line of output containing one integer, the minimum number of wheel advances required to produce a palindrome.

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

Sample Input 2:
009990001
Sample Output 2:
3

Sample Input 3:
29998
Sample Output 3:
5

Sample Input 4:
610
Sample Output 4:
4

Sample Input 5:
981
Sample Output 5:
2
user: To address the impending STEM shortage early on, your local elementary school decided to teach graph theory to its kindergarten students! To tap into their age-specific skills, the students are asked to color the vertices of a graph with colors of their own choosing. There is one constraint, however: they cannot use the same color for two vertices if those vertices are connected by an edge. Furthermore, they are asked to use as few different colors as possible. The illustration shows a few examples of student work. 

There is one problem, as you can imagine: there is no money to train teachers to grade these students’ submissions! Thus, your task is to write a program that computes the sample solutions for the graphs given on each work sheet!

-----Input-----
The input consists of a description of a single graph. The first line contains a number $N$ ($2 \le N \le 11$), the number of vertices in the graph. Vertices are numbered $0 \ldots N-1$. The following $N$ lines contain one or more numbers each. The $i^{th}$ line contains a list of vertex numbers ${ v_ j }$, denoting edges from $v_ i$ to each $v_ j$ in the list. You may assume that the graph is connected (there is a path between any two pairs of vertices).

-----Output-----
Output the minimum number of colors required to color all vertices of the graph such that no vertices that share an edge are colored using the same color!

The sample input corresponds to the graphs shown on the illustration.

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

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

Sample Input 3:
6
1 3
0 2 4
1 5
0 4
1 3 5
2 4
Sample Output 3:
2

Sample Input 4:
4
1 2 3
0 2 3
0 1 3
0 1 2
Sample Output 4:
4
user: You need to hire some people to paint a fence. The fence is composed of $10000$ contiguous sections, numbered from $1$ to $10000$.

You get some offers from painters to help paint the fence. Each painter offers to paint a contiguous subset of fence sections in a particular color. You need to accept a set of the offers, such that:
 - Each section of the fence is painted.
 - At most 3 colors are used to paint the fence.

If it is possible to satisfy these two requirements, find the minimum number of offers that you must accept.

-----Input-----
The first line of input contains an integer $N$, the number of offers. Then follow $N$ lines, one for each offer, each containing “$C$ $A$ $B$” where $C$ is the color, which is an uppercase string of up to 10 letters, $A$ is the first section and $B$ is the last section to be painted. $1 \leq A \leq B \leq 10000$.

You may assume that $1 \leq N \leq 300$.

-----Output-----
Output one line containing the number of offers that need to be accepted, or “IMPOSSIBLE” if there is no acceptable set of offers.

-----Examples-----
Sample Input 1:
2
BLUE 1 5000
RED 5001 10000
Sample Output 1:
2

Sample Input 2:
3
BLUE 1 6000
RED 2000 8000
WHITE 7000 10000
Sample Output 2:
3

Sample Input 3:
4
BLUE 1 3000
RED 2000 5000
ORANGE 4000 8000
GREEN 7000 10000
Sample Output 3:
IMPOSSIBLE

Sample Input 4:
2
BLUE 1 4000
RED 4002 10000
Sample Output 4:
IMPOSSIBLE
user: Spotting patterns in seemingly random strings is a problem with many applications. E.g., in our efforts to understand the genome we investigate the structure of DNA strings. In data compression we are interested in finding repetitions, so the data can be represented more efficiently with pointers. Another plausible example arises from the area of artificial intelligence, as how to interpret information given to you in a language you do not know. The natural thing to do in order to decode the information message would be to look for repetitions in it. So if the SETI project (the Search for Extra Terrestrial Intelligence) ever get a signal in the H21-spectra, we need to know how to decompose it.

One way of capturing the redundancy of a string is to find its factoring. If two or more identical substrings $A$ follow each other in a string $S$, we can represent this aprt of $S$ as the substring $A$, enclosed by parentheses, raised to the power of the number of repetitions. E.g., the string $DOODOO$ can be factored as $(DOO)^2$, but also as $(D(O)^2)^2$. Naturally, the latter factoring is considered better since it cannot be factored any further. We say that a factoring is irreducible if it does not contain any consecutive repetition of a substring. A string may have several irreducible factorings, as seen by the example string $POPPOP$. It can be factored as $(POP)^2$, as well as $PO(P)^2OP$. The first factoring has a shorter representation and motivates the following definition. The weigh of a factoring equals the number of characters in it, excluding the parentheses and the exponents. Thus the weight of $(POP)^2$ is $3$, whereas $PO(P)^2OP$ has weight $5$. A maximal facotring is a factoring with the smallest possible weight. It should be clear that a maximal factoring is always an irreducible one, but there may still be several maximal factorings. E.g., the string $ABABA$ has two maximal factorings $(AB)^2A$ and $A(BA)^2$.

-----Input-----
The input consists of a single line, containing a string of at least one, but at most $200$ characters from the capital alphabet A-Z.

-----Output-----
Output the weight of a maximal factoring of the input string.

-----Examples-----
Sample Input 1:
PRATTATTATTIC
Sample Output 1:
6

Sample Input 2:
GGGGGGGGG
Sample Output 2:
1

Sample Input 3:
PRIME
Sample Output 3:
5

Sample Input 4:
BABBABABBABBA
Sample Output 4:
6
user: To store DNA sequences your company has developed a LongLongString class that can store strings with up to ten billion characters. The class supports two basic operations: 
 - Ins($p$, $c$): Insert the character $c$ at position $p$.
 - Del($p$): Delete the character at position $p$.

A DNA editing program is written as a series of Ins and Del operations. Your job is to write a program that compare two DNA editing programs and determine if they are identical, i.e., when applied to any sufficiently long string, whether the end result is the same.

For example:
 - Del(1) Del(2) and Del(3) Del(1) are identical.
 - Del(2) Del(1) and Del(1) Del(2) are different.
 - An empty sequence and Ins(1, $X$) Del(1) are identical.
 - Ins(14, $B$) Ins(14, $A$) and Ins(14, $A$) Ins(15, $B$) are identical.
 - Ins(14, $A$) Ins(15, $B$) and Ins(14, $B$) Ins(15, $A$) are different.

-----Input-----
Input will consist of the descriptions of two DNA editing programs.

Each program will consist of some number of operations (between $0$ and $2000$). Each operation will be given on its own line. The first character of the line will be D for a Del operation, I for an Ins operation, or E marking the end of the program.

A Del operation will have the D character, followed by a space, and then a single integer between $1$ and $10^{10}$, indicating the character position to delete. All characters after this deleted character will be shifted one position lower.

An Ins operation will have the I character, followed by a space, and then a single integer between $1$ and $10^{10}$, indicating the location to insert the new character; all pre-existing characters with this index and higher will be shifted one position higher. Following this integer will be another space and then an uppercase alphabetic character that is the character to insert.

-----Output-----
If the two programs are identical, print “0” on a single line (without quotation marks). Otherwise, print “1” on a single line (without quotation marks).

-----Examples-----
Sample Input 1:
D 1
D 2
E
D 3
D 1
E
Sample Output 1:
0

Sample Input 2:
D 2
D 1
E
D 1
D 2
E
Sample Output 2:
1

Sample Input 3:
I 1 X
D 1
E
E
Sample Output 3:
0

Sample Input 4:
I 14 B
I 14 A
E
I 14 A
I 15 B
E
Sample Output 4:
0
user: Trapped at home in quarantine, Johan tries to keep madness at bay and fend off isolation by playing Critter Junction, a social simulation video game. One of the main aspects of the game is collecting and harvesting various types of resources, in order to gain Bling, the currency of the game. Johan specializes in running the fruit% category of the game, in which the goal is to obtain the maximum amount of Bling in $40$ days using only fruits and no other resources. 

Each fruit can be sold for $100$ Bling, or planted to become a fruit tree (but not both). Every three days, starting on the third day after it was planted, a fruit tree yields three new fruits.

There are also some more exotic fruits that can be bought from the neighboring village. Once per day, the player can travel to the neighboring village and pay $400$ Bling to buy a single exotic fruit which you can then plant or sell already on the same day. Analogously to normal fruits, these exotic fruits can be planted into exotic fruit trees which yield three exotic fruits every three days. Each exotic fruit can be sold for $500$ Bling.

Any number of fruits/exotic fruits can be harvested, sold and planted during a day (subject to availability of course, e.g. it is not possible to sell more fruits than you actually have), but at most a single exotic fruit can be bought. These activities can be done in any order, so it is for instance possible within the same day to first harvest a few fruits (exotic or not), then sell those fruits for Bling, then use that Bling to buy an exotic fruit, and then either plant or sell that exotic fruit.

Given the current state of Johan’s fruit farm, what is the maximum amount of Bling he can achieve in the remaining time?

-----Input-----
The input consists of a single line containing six integers $d$, $b$, $f$, $t_0$, $t_1$ and $t_2$ ($1 \le d \le 40$, $0 \le b \le 500$, and $0 \le f, t_0, t_1, t_2 \le 100$), where:
 - $d$ is the number of remaining days Johan has
 - $b$ is the current amount of Bling Johan has.
 - $f$ is the current number of fruits Johan has.
 - $t_ i$ is the number of fruit trees Johan has that will yield crop $i$ days from today (for $0 \le i \le 2$).

Johan currently does not have any exotic fruits or exotic fruit trees.

-----Output-----
Output a single integer: the maximum amount of Bling Johan can have after playing $d$ days.

-----Examples-----
Sample Input 1:
4 0 1 0 0 0
Sample Output 1:
300

Sample Input 2:
5 0 1 0 1 0
Sample Output 2:
1900

Sample Input 3:
6 0 1 1 0 0
Sample Output 3:
2300

Sample Input 4:
10 399 0 0 0 0
Sample Output 4:
399
user: The online retailer Amagoogsoftbook currently offers $N$ different so-called “home assistants”, which it wants to recommend to its customers. For this recommendation, they wish to rank all the assistants. The quality of this ranking is not very important – multiple assistants may even be assigned the same rank – but they wish to maximize the number of distinct ranks assigned, to lessen the decision fatigue of their customers.

To ensure that the ranking is not completely arbitrary, they have collected for each assistant $i$ two measurements $a_ i$ and $b_ i$ – the quality of the jokes the assistant can tell and how nice are the compliments the assistant is able to give (clearly these are the two most important aspects). These measurements are of course somewhat subjective, so we wish to ignore small differences in them. However, if for two given assistants $i$ and $j$ we have that $a_ i + K < a_ j$ or $b_ i + K < b_ j$, the ranking of assistant $j$ must be the same or higher than the ranking of assistant $i$. This rule may force two products to be given the same ranking, for example if an assistant $i$ gives much better puns than assistant $j$, while assistant $j$ gives the superior self-esteem boosts.

What is the maximum number of distinct ranks, taken over all possible rankings?

-----Input-----
The first line contains the integers $1 \le N \le 100000$ and $0 \le K \le 10^9$ – the number of assistants and the measurement difference limit as described in the statement. The next line contains the $N$ integers $a_1, a_2, \dots , a_ N$. The next line contains the $N$ integers $b_1, b_2, \dots , b_ N$.

All measurements are between $0$ and $10^9$.

-----Output-----
Output a single integer: the maximum number of distinct ranks.

-----Examples-----
Sample Input 1:
2 10
1 12
1 13
Sample Output 1:
2

Sample Input 2:
2 10
1 5
1 12
Sample Output 2:
2

Sample Input 3:
2 10
1 5
1 4
Sample Output 3:
2

Sample Input 4:
2 10
1 5
4 1
Sample Output 4:
2
user: A properly designed room is, as we all know, well-lit.

In keeping with the teachings of Feng Shui, you have placed a number of lamps around a newly-designed room at strategic places to give it a friendlier air.

Some of the lights project positive energy, and the rest give out only negative energy. Luckily, your neighbourhood guru knows all about this, and will gladly help you to keep the delicate energy balance…For a small fee.

The balancing line of a particular lighting arrangement is the shortest continuous closed circuit dividing energy sources into two parts, those inside the line and those outside the line, such that the sum of energies inside and outside is equal—cancelling out any negative effects.

What is the length of this line?

-----Input-----
 - A line with one positive integer, $N$ ($2 \le N \le 12$), the number of lamps.
 - $N$ more lines, each containing three space-separated integers $x_{i}$ and $y_{i}$ ($1 \leq x_{i}, y_{i} \leq 99$) giving the coordinates of the $i$-th lamp expressed in centimetres from the corner of the room, and $e_ i$ ($-2000 \le e_ i \le 2000$), the energy contribution of this lamp. A lamp placed at ($x, y$) has a square footprint that fits inside the square with opposite corners ($x-1, y-1$) and ($x+1, y+1$) with a tiny amount of space to spare.

It is guaranteed that no two lamps will have overlapping footprints.

-----Output-----
Write one real number: the length of the shortest continuous line dividing the positive and negative energy sources in the room. Your answer should be correct up to an absolute or relative precision of $10^{-6}$.

If no such line exists, output IMPOSSIBLE instead.

-----Examples-----
Sample Input 1:
4
10 10 5
10 20 5
20 10 5
20 20 5
Sample Output 1:
28

Sample Input 2:
4
10 10 5
10 20 1
20 10 12
20 20 8
Sample Output 2:
36.2842712475

Sample Input 3:
6
1 1 15
5 1 100
9 1 56
1 5 1
5 5 33
9 5 3
Sample Output 3:
28.970562748

Sample Input 4:
8
4 4 1
4 6 1
4 8 1
6 6 14
8 4 1
8 6 1
8 8 1
99 6 -8
Sample Output 4:
32