meetforever/GRPO_CL huggingface dataset:
user: In ACM-ICPC contests, there are usually three people in a team. For each person in the team, you know their scores in three skills - hard work, intelligence and persistence.
You want to check whether it is possible to order these people (assign them numbers from 1 to 3) in such a way that for each 1 ≤ i ≤ 2, i+1-th person is stricly better than the i-th person.
A person x is said to be better than another person y if x doesn't score less than y in any of the skills and scores more than y in at least one skill.
Determine whether such an ordering exists.

-----Input-----
The first line fo the input contains an integer T denoting the number of test cases.
Each test consists of three lines. Each of these lines contains three space separated integers s1, s2 and s3 denoting the scores of one member of the team in each of the three skills, in the given order.

-----Output-----
For each test case, output a single line containing "yes" if such an ordering exists or "no" if doesn't exist (without quotes).

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ s1, s2, s3 ≤ 100

-----Example-----
Input
3
1 2 3
2 3 4
2 3 5
1 2 3
2 3 4
2 3 4
5 6 5
1 2 3
2 3 4

Output
yes
no
yes

-----Explanation-----
Test Case 1: We can order them as (3, 2, 1). Person 3 is better than Person 2 because his scores in the first two skills are not lesser than Person 2's. And in skill 3, Person 3 scores higher. Similarly, Person 2 is better than Person 1. He scores more than Person 1 in every skill, in fact.
user: Chef had an interesting dream last night. He dreamed of a new revolutionary chicken recipe. When he woke up today he tried very hard to reconstruct the ingredient list. But, he could only remember certain ingredients. To simplify the problem, the ingredient list can be represented by a string of lowercase characters 'a' - 'z'.
Chef can recall some characters of the ingredient list, all the others, he has forgotten. However, he is quite sure that the ingredient list was a palindrome.
You are given the ingredient list Chef dreamed last night. The forgotten characters are represented by a question mark ('?'). Count the number of ways Chef can replace the forgotten characters with characters 'a' - 'z' in such a way that resulting ingredient list is a palindrome.

-----Input-----
The first line of input contains a single integer T, the number of test cases. T lines follow, each containing a single non-empty string - the ingredient list as recalled by Chef. Whatever letters he couldn't recall are represented by a '?'.

-----Output-----
For each test case, output a single line containing the number of valid ways the ingredient list could be completed. Since the answers can be very large, output each answer modulo 10,000,009.

-----Example-----
Input:
5
?
??
ab?
a?c
aba

Output:
26
26
1
0
1

-----Constraints-----

1 ≤ T ≤ 20

1 ≤ sum of length of all input strings ≤ 1,000,000

Each input string contains only lowercase roman letters ('a' - 'z') or question marks.
user: In the 2-D world of Flatland, the Circles were having their sports day and wanted to end it with a nice formation. So, they called upon Mr. Sphere from Spaceland for help. Mr Sphere decides to arrange the Circles in square formations. He starts with $N$ Circles and forms the largest possible square using these Circles. He then takes the remaining Circles and repeats the procedure. A square of side $S$ requires $S^2$ Circles to create.
Find the number of squares he will be able to form at the end of the process.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single integer $N$.

-----Output:-----
For each testcase, output a single integer denoting the number of squares.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 1000$

-----Sample Input:-----
2

85

114          

-----Sample Output:-----
2

4

-----EXPLANATION:-----
Test case 1 : Mr Sphere forms a square of side 9 using 81 Circles and then forms a square of side 2 using the remaining 4.
user: There is a city with $N$ numbered $0 - N-1$ shops. A market is a place where we can reach from one shop to another using some road. There are $M$ roads in this city connecting each connecting any two shops. 
Find the number of markets in the city.
NOTE:  A market having only one shop is also a valid market.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- First line of Each Test Case is $N, M$, denoting the number of shops and the number of roads respectively.
- Next M lines consist of two integers $A$ and $B$ denoting that there exists a road between Shop A and Shop B

-----Output:-----
For each testcase, output the number of markets.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N,M \leq 10^3$
- $0 \leq A,B < N$

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

-----Sample Output:-----
2
user: Chef Jessie has a lot of recipes with her (N). She often remembered the starting few characters of the recipe and forgot the rest. As all the great chefs do, Jessie also numbered the recipes depending on the priority. So, given the list of recipes along with their priorities answer Jessie’s queries.
Jessie’s queries are as follows:

She gives you the first few characters of a recipe; you have to print the complete recipe with the highest priority.
Note:

Every recipe has a unique priority

-----Input-----

First line contains an integer N - the number of recipes.

Followed by N strings Si along with an integer each Vi.
Si stands for the recipe and Vi for the priority.

It is followed by an integer Q - the number of queries.

Followed by Q strings Qi.

Each string Si, Qi contain only lowercase Latin alphabets ('a' - 'z') and '-'.

-----Output-----
Q – lines, each contain the answer for each of the query.

If for a query no recipe matches print "NO". (Without quotes)
Constraints:
0 <= N <= 1000

0 <= Q <= 1000

-10^9 <= Vi <= 10^9

1 <= |Si| <= 1000 (length of Si)

1 <= |Qi| <= 1000 (length of Qi)

-----Example-----
Input:
4
flour-with-eggs 100
chicken-ham -10
flour-without-eggs 200
fish-with-pepper 1100
6
f
flour-with
flour-with-
c
fl
chik

Output:
fish-with-pepper
flour-without-eggs
flour-with-eggs
chicken-ham
flour-without-eggs
NO
user: -----Problem Statement-----
Sereja has a sequence of n integers a[1], a[2], ..., a[n]. Sereja can do following transformation of the array:

- create a new sequence of n integers b[1], b[2], ..., b[n]in this way:    (1 ≤ i ≤ n)

- Replace the sequence a by b, i.e., a[i] = b[i] for all i in [1, n] 

Sereja decided to use his transformation k times. Then he computed the value of      , where r — the sequence obtained after k transformations of sequence a, as described above.

Sereja lost sequence a, but he was left with the numbers q(r) and k. Now Sereja is interested in the question : what is the number of the sequences of the integers с[1], с[2], ..., с[n], such that 1 ≤ c[i] ≤ m and q(d) = q(r), where d — the sequence obtained after k transformations of sequence c, as described above.

-----Input-----
The first lines contains a single integer T, denoting the number of test cases. Each  test case consist of four integers : n, m, q(r), k.

-----Output-----
In a single line print the remainder of division the answer of the problem on number 10^9 + 7.

-----Constraints-----

- 1 ≤ T ≤ 10000
- 1 ≤ n, m, q(r), k ≤ 10^9

-----Example-----
Input:
3
1 1 1 1
2 2 1 1
2 3 1 1

Output:
0
2
4
user: Chef and his friends are playing the game AMONG US. They all have chosen their names as numbers. There are N people in Chef’s group including him, and each swears that he is not the imposter. However, it turns out there were N+1 people in the game. Now all that Chef needs to know is the name of the imposter, which is a number. Also remember that numbers can be duplicate. Can you help out Chef in finding the imposter?
Input : 
First line contains the value of N. Second line contains the N numbers that Chef’s friends used as their names. Third line contains the N+1 numbers that people in the game have used as their names.
Output : 
Print the extra number in new line.
Constraints : 
1 ≤ Numbers used as names ≤ 1,000
1 ≤ N ≤ 1,000,000
Sample Input : 
3
4 2 5
4 2 3 5
Sample Output : 
3
user: Autobots are instructed by Optimus Prime to mobilize in the form of a rectangular shape with each Autobot on each vertex of the rectangle region on a -”deployment area” (which may consist of one or more regions). This is done so as to take care of the inner rectangular area called “region”. However the rule states-“no two regions may overlap”.  You have been asked to remove some regions from the “deployment area” so the remaining regions do not obscure each other. To keep the disturbance to the minimum level, you should remove the minimum number of regions to achieve this goal. You may not remove a region and place it in another position; all regions you leave in “deployment area” must be in their original position.
When you examined the “deployment area”, you noticed something very nice. Every region was placed on the deployment area by placing each autobot in the four corners. This was done in a very courteous manner since each autobot is guarding only the region it is holding. 
The reason Optimus Prime wants your help because you are good at taking down a single region without disturbing the rest, even if that region is obscured by many others.


-----Input-----
The first line consists of a single integer T indicating the number of test cases (about 25).
Each test case consists begins with a single integer n indicating the number of regions. The next n lines consist of 4 integers x0, x1, y0, and y1 satisfying x0 < x1 and y0 < y1. This means the region covers all points (x,y) satisfying x0 <= x <= x1 and y0 <= y <= y1.
As stated before hand, no corner of any region will intersect any other region anywhere. That is, if (x,y) is a corner point of one region and another region is described by x0, x1, y0, and y1, then we do not have x0 <= x <= x1 and y0 <= y <= y1.
Bounds: 1 <= n <= 100 and each integer in a region description fits in a signed 32 bit integer.

-----Output-----
The output for each test case is a single line containing a single integer that is the maximum number of regions that can be left on the wall such that no two regions share a common point in the deployment area.

-----Example-----
Input:
1
4
0 4 0 4
1 3 1 2
2 3 1 3
3 4 1 3
Output:
2
user: Write a program, which takes an integer N and if the number is less than 10 then display "Thanks for helping Chef!" otherwise print "-1".

-----Input-----

The first line contains an integer T, total number of testcases. Then follow T lines, each line contains an integer N. 

-----Output-----
For each test case, output the given string or -1 depending on conditions, in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000
- -20 ≤ N ≤ 20

-----Example-----
Input
3 
1
12
-5
Output
Thanks for helping Chef!
-1
Thanks for helping Chef!
user: Today is the planned day tor Thik and Ayvak's wedding. Kark is infatuated with Ayvak. He offers to play a game with Thik. Whosoever wins, will get to marry Ayvak. Ayvak, who values games of chance over all the other things in life, agrees to this.

Kark sets up an N by M grid (N rows, M columns), labelled from left to right and top to bottom consecutively with numbers from 1 to M*N, with 1 at the top left corner and M*N at the bottom right corner. For example, a labelled 3 by 6 grid looks as follows:

Kark has already painted K unit squares of the grid with a heart each. Next, Thik randomly picks a rectangle with sides on the grid lines, and having a positive area, with each valid rectangle having an equal probability of being chosen. Three distinct possibilities for Thik's rectangle in the 3 by 6 grid are shown below: 

The nine different rectangles in a 2 by 2 grid are shown below:


If Thik's rectangle contains at least half of the hearts, Thik gets to marry Ayvak. Otherwise, Kark will marry Ayvak. Kark wants to know whether or not he has an advantage here, so he wants to know the expected value of the number of hearts a randomly chosen rectangle will cover. I'm sure that you have a good heart, so please, cover this job for him. 

-----Input-----
The first line of input contains one integer T, the number of test cases.
For each test case, the first line contains 3 space-separated integers N, M, K, as described in the problem statement. The next line contains K space-separated integers, each a single number from 1 to M*N, representing a square that is painted with a heart. It is guaranteed that all K integers are distinct.

-----Output-----
Output T lines, each containing a single real number, containing the expected number of hearts that a randomly chosen rectangle will contain. The answer will be considered correct if its relative or absolute error does not exceed 10-6.

-----Constraints-----
- 1 ≤ T ≤ 5  
- 1 ≤ N, M ≤ 107  
- 1 ≤ K ≤ 105 
- Each of the K integers representing a heart are between 1 and N*M, inclusive. All K integers are distinct. 

-----Subtasks-----Subtask 1 (15 points) : 

- 1 ≤ N, M ≤ 10
- 1 ≤ K ≤ N * M  
Subtask 2 (85 points) : no additional constraints 


-----Example-----
Input:
1
2 2 2
1 2

Output:
0.8888888888888888

-----Explanation-----
There are a total of 9 possible rectangles Thik could draw, shown in the figure above, and grid squares 1 and 2 are painted with a heart. The top row of possible selections (shown in the figure) contain 1, 0, 1, 2, and 2 hearts (from left to right), and the bottom row of possible selections (in the figure) contain 1, 0, 1, and 0 hearts. Therefore, 3/9 of the time 0 hearts are contained in the rectangle, 4/9 of the times 1 heart is contained in the rectangle, and 2/9 of the time 2 hearts are contained in the rectangle. The expected value is then 0 * 3/9 + 1 * 4/9 + 2 * 2/9 = 8/9.
user: Recently, chef Ciel often hears about lucky numbers.

Everybody knows that lucky numbers are positive integers
whose decimal representation contains only the lucky digits 4 and 7.
For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Ciel decides to make Ciel numbers.
As you know, Ciel likes the digit 8 very much.
And then, Ciel likes the digits 5 and 3.
So Ciel defines Ciel numbers as the positive integers k such that d(k, 8) ≥ d(k, 5) ≥ d(k, 3) and d(k, i) = 0 for all i = 0, 1, 2, 4, 6, 7, 9,
where d(k, i) denotes the number of the digit i in the decimal representation of the integer k.
For example, the first few Ciel numbers are 8, 58, 85, 88, 358, 385, 538, 583, 588, 835, 853, 858, 885, 888, ....

Ciel's restaurant has N menus.
And Ciel want to know how many menus have Ciel numbers as their price.
Your task is to find it.

-----Input-----

The first line contains an integer N.
Then N lines follow.
Each line has the name Si of the menu and its price Pi separated by a single space.

-----Output-----

Print the number of menus whose prices are one of Ciel numbers.

-----Constraints-----

1 ≤ N ≤ 1000

1 ≤ |Si| ≤ 100, where |Si| denotes the length of Si

Each letter of Si is either an alphabetical letter or a digit or a single quotation mark or a space.

1 ≤ Pi < 1000000 (106)
Pi contains no leading zeros.

-----Sample Input-----
6
milk 58
Ciel's Drink 80
The curry 2nd edition 888888
rice omelet 85855
unagi 1
The first    and last letters can be a space    358

-----Sample Output-----
3

-----Output details-----

58 and 888888 and 358 are Ciel numbers.
80 and 85855 and 1 are not Ciel numbers.

-----Notes-----

Different operating systems have different ways of representing a newline; do not assume one particular way will be used.
user: Abhi and his friends (Shanky,Anku and Pandey) love to play with strings. Abhi invented a simple game. He will give a string S to his friends. Shanky and Anku will play the game while Pandey is just a spectator. Shanky will traverse the string from beginning (left to right) while Anku will traverse from last (right to left). Both have to find the first character they encounter during their traversal,that appears only once in the entire string. Winner will be one whose character is alphabetically more superior(has higher ASCII value). When it is not possible to decide the winner by comparing their characters, Pandey will be the winner.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.

Each test case contains a string S having only lowercase alphabets ( a..z ).

-----Output-----
For each test case, output a single line containing "SHANKY" if Shanky is the winner or "ANKU" if Anku is the winner or "PANDEY" if the winner is Pandey. Output your answer without quotes.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 < |S| ≤ 10^5

-----Example-----
Input:
3
google
breakraekb
aman

Output:
SHANKY
PANDEY
ANKU

-----Explanation-----
Example case 2. Both Shanky and Anku can not find any such character. Hence it is not possible to decide the winner between these two. So Pandey is the winner.
user: Chef is an advocate for Go Green Initiative. Today he had n trees planted in a row outside his his restaurant. Today, the height of i-th tree is hi feet. The trees grow at a rate of mi feet per day.
Chef knows that trees will look beautiful if they form a zig-zag sequence. The trees will be said to be in Zig-zag sequence if the heights of tree first increases or decreases, then alternates between decreasing/increasing respectively. Formally, the trees will be said to in Zig-zag sequence if one of the following two conditions holds.

- h1 < h2 > h3 < h4 and so on..
- h1 >  h2 < h3 > h4 and so on..

Chef wants to know intervals of time when the heights of the trees will form a zig-zag sequence.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer n, denoting the number of trees.
The ith of following N lines contains two space separated integers hi and mi, denoting the initial height and the growth speed for ith tree.

-----Output-----
For each test case, output an integer Q - the amount of the periods of consecutive moments of time, when the trees for a zig-zag sequence.
On the following Q lines, output the intervals of time when the trees' heights form a zig-zag sequence. For each intervals, output its' smallest and the largest instants of time. If the range is infinite, output Inf as the right bound.
The test cases are designed in such a way that the total output won't exceed 2 MB.

-----Constraints-----

- 1 ≤ T ≤ 105
- 1 ≤ n ≤ 10
- Subtask 1 (23 points): 0 ≤ hi, mi ≤ 10
- Subtask 2 (77 points): 0 ≤ hi, mi ≤ 109
- 1 ≤ sum of n over a test cases in a single test file ≤ 5 × 105

-----Example-----
Input:3
3
0 1
2 2
0 3
2
2 1
1 2
3
1 1
2 2
3 3

Output:1
0 1
2
0 0
2 Inf
0

-----Explanation-----
Example case 1. In the first case 0 2 0 is already a zig-zag sequence, but on the 2nd second it will become 2 6 6 and will never turn back into zig-zag
user: In Snakeland, there are some snakes and mongooses. They are lined up in a row. The information about how exactly they are lined up it is provided to you by a string of length n. If the i-th character of this string is 's', then it means that there is a snake at the i-th position, whereas the character 'm' denotes a mongoose.
You might have heard about the age-old rivalry between hares and tortoises, but in Snakeland, the rivalry between snakes and mongooses is much more famous. The snakes and the mongooses want to hold a final poll in which the ultimate winner of this age-old battle will be decided. If the snakes get more votes than the mongooses, they will be the ultimate winners. Similarly, if the mongooses get more votes than snakes, they will be the ultimate winners. Obviously, each animal is loyal to their species, i.e. each snake will vote for the snakes to be the ultimate champions and each mongoose for the mongooses.

Tomorrow's the election day. Before the elections, the mongooses decided to cheat. They planned that each mongoose will eat at most one of its neighbor snakes. Two animals are said to be neighbors of each other if they are consecutive to each other in the row. After this, the elections will be held. The mongooses planned in such a way that the number of snakes eaten is maximized. Can you find out who will win the final poll? Output "snakes", "mongooses" or "tie" correspondingly.

-----Input-----
First line of the input contains an integer T denoting the number of test cases. The description of T test cases follow.
The only line of each test case contains a string consisting of characters 's' and 'm'. 

-----Output-----
For each test case output a single line containing "snakes", "mongooses" or "tie" correspondingly (without quotes).

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ |s| ≤ 100

-----Example-----
Input
4
sm
ssm
sms
ssmmmssss

Output
mongooses
tie
tie
snakes

-----Explanation-----
Example 1. The mongoose will eat the snake. Only the mongoose will be left. So, on the election day, there is one mongoose and zero snakes. So mongooses will win.
Example 2. The mongoose will eat the snake at position 2 (1-based indexing). One mongoose and one snake will be left. Hence, there will be a tie.
Example 3. The mongoose can eat either the snake to its left or to the right. But, it can eat only one of them. Afterwards, there will be a single snake and mongoose. So, it will result in a tie. 
Example 4. The mongooses can eat at max two snakes. For example, s*mmm*sss, where * denotes the snakes that were eaten by mongooses. After this, we have four snakes and three mongooses. So, the snakes win.
user: Every great chef knows that lucky numbers are positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.  

Our chef has recently returned from the Lucky country. He observed that every restaurant in the Lucky country had a lucky number as its name. 
He believes that having a lucky number as a restaurant name can indeed turn out to be very lucky.  

Our chef believes that it is possible to make a lucky number having N digits even luckier. Any number following the rules below is called Lucky lucky number -  

1. The number contains only digits 4 and 7. 

2. Count of digit 4 in the number should be divisible by 7. 

3. Count of digit 7 in the number should be divisible by 4. 

Help our chef to compute the count of digit 4 in the smallest Lucky lucky number having N digits. 

-----Input-----

First line contains T, number of test cases. Each of the next T lines contains a number N, the number of digits in the Lucky lucky number to be formed. 

1<=T<=1000 

1<=N<=1000000000 (10^9) 

-----Output-----

If it is not possible to form a Lucky lucky number having N digits, output -1.
Otherwise, output the count of digit 4 in the smallest Lucky lucky number having N digits.

-----Example-----
Input:
5
7
4
11
1
15

Output:
7
0
7
-1
7

Explanation
For the last test case, N = 15, the smallest lucky lucky number is
444444477777777. The count of digit 4 is 7.