vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
We have an integer N.
Print an integer x between N and 10^{13} (inclusive) such that, for every integer y between 2 and N (inclusive), the remainder when x is divided by y is 1.
Under the constraints of this problem, there is always at least one such integer x.

-----Constraints-----
 - All values in input are integers.
 - 2 \leq N \leq 30

-----Input-----
Input is given from Standard Input in the following format:
N

-----Output-----
Print an integer x between N and 10^{13} (inclusive) such that, for every integer y between 2 and N (inclusive), the remainder when x is divided by y is 1.
If there are multiple such integers, any of them will be accepted.

-----Sample Input-----
3

-----Sample Output-----
7

The remainder when 7 is divided by 2 is 1, and the remainder when 7 is divided by 3 is 1, too.
7 is an integer between 3 and 10^{13}, so this is a desirable output.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The new Formula 1 season is about to begin and Chef has got the chance to work with the Formula 1 technical team.  
Recently, the pre-season testing ended and the technical team found out that their timing system for qualifying was a little bit buggy. So, they asked Chef to fix it before the season begins.  
His task is to write a program to find the starting lineup of the race by taking the timings of the drivers in qualifying.
(If you don’t know the rules that make the starting grid in Formula 1, consider that the driver with the least time will start at the front). 
Note: 
- Two or more drivers can have the same name.  
- Every driver will have a distinct time.  

-----Input:-----
- The first line of the input consists of a single integer $T$ denoting the number of test cases.  
- First line of each test case consists of a single integer $N$ denoting the number of drivers to set a time.  
- The following $2*N$ lines consists of the driver’s name $S$ in one line and its timing details  $X$ (in milliseconds) in the next line.  

-----Output:-----
- For each test case output the starting lineup of the race i.e., name of each driver in the order they will start the race. Print each name in a new line.  

-----Constraints-----
- 1 <= $T$ <= 10  
- 1 <= $N$ <= 105 
- 1 <= $|S|$ <= 20  
- 1 <= $X$ <= 109 

-----Subtasks-----
Subtask #1 (20 points): 
- 1 <= $N$ <= 100  
Subtask #2 (80 points): 
- Original Constraints  

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

3

Hamilton

75000

Vettel

76000

Bottas

75500

2

Leclerc

666666

Verstappen

666777  

-----Sample Output:-----
Hamilton

Bottas

Vettel

Leclerc

Verstappen  

-----EXPLANATION:-----
The drivers with the least time are ahead in the lineup.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
## Task:
You have to write a function `pattern` which returns the following Pattern (See Pattern & Examples) upto `n` number of rows. 

* Note: `Returning` the pattern is not the same as `Printing` the pattern.

### Rules/Note:
* If `n < 1` then it should return "" i.e. empty string.
* There are `no whitespaces` in the pattern.

### Pattern:

    (n)(n-1)(n-2)...4321
    (n)(n-1)(n-2)...432
    (n)(n-1)(n-2)...43
    (n)(n-1)(n-2)...4
    ...............
    ..............
    (n)(n-1)(n-2)
    (n)(n-1)
    (n)
    
### Examples:

* pattern(4):

      4321
      432
      43
      4
    
* pattern(11):

      1110987654321
      111098765432
      11109876543
      1110987654
      111098765
      11109876
      1110987
      111098
      11109
      1110
      11


~~~if-not:cfml
* Hint: Use \n in string to jump to next line
~~~
~~~if:cfml
* Hint: Use chr(10) in string to jump to next line
~~~

[List of all my katas]("http://www.codewars.com/users/curious_db97/authored")

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Sagheer is walking in the street when he comes to an intersection of two roads. Each road can be represented as two parts where each part has 3 lanes getting into the intersection (one for each direction) and 3 lanes getting out of the intersection, so we have 4 parts in total. Each part has 4 lights, one for each lane getting into the intersection (l — left, s — straight, r — right) and a light p for a pedestrian crossing.  [Image] 

An accident is possible if a car can hit a pedestrian. This can happen if the light of a pedestrian crossing of some part and the light of a lane that can get to or from that same part are green at the same time.

Now, Sagheer is monitoring the configuration of the traffic lights. Your task is to help him detect whether an accident is possible.


-----Input-----

The input consists of four lines with each line describing a road part given in a counter-clockwise order.

Each line contains four integers l, s, r, p — for the left, straight, right and pedestrian lights, respectively. The possible values are 0 for red light and 1 for green light.


-----Output-----

On a single line, print "YES" if an accident is possible, and "NO" otherwise.


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

Output
YES

Input
0 1 1 0
1 0 1 0
1 1 0 0
0 0 0 1

Output
NO

Input
1 0 0 0
0 0 0 1
0 0 0 0
1 0 1 0

Output
NO



-----Note-----

In the first example, some accidents are possible because cars of part 1 can hit pedestrians of parts 1 and 4. Also, cars of parts 2 and 3 can hit pedestrians of part 4.

In the second example, no car can pass the pedestrian crossing of part 4 which is the only green pedestrian light. So, no accident can occur.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Accounting

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Problem Description:
A long time ago in some far country lived king Copa. After the recent king's reform, he got so large powers that started to keep the books by himself.

The total income *A* of his kingdom during 0-th year is known, as well as the total income *B* during *n*-th year (these numbers can be negative — it means that there was a loss in the correspondent year). 

King wants to show financial stability. To do this, he needs to find common coefficient *X* — the coefficient of income growth during one year. This coefficient should satisfy the equation:

Surely, the king is not going to do this job by himself, and demands you to find such number *X*.

It is necessary to point out that the fractional numbers are not used in kingdom's economy. That's why all input numbers as well as coefficient *X* must be integers. The number *X* may be zero or negative.

Input Specification:
The input contains three integers *A*, *B*, *n* (|*A*|,<=|*B*|<=≤<=1000, 1<=≤<=*n*<=≤<=10).

Output Specification:
Output the required integer coefficient *X*, or «No solution», if such a coefficient does not exist or it is fractional. If there are several possible solutions, output any of them.

Demo Input:
['2 18 2\n', '-1 8 3\n', '0 0 10\n', '1 16 5\n']

Demo Output:
['3', '-2', '5', 'No solution']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Create a function which accepts one arbitrary string as an argument, and return a string of length 26.

The objective is to set each of the 26 characters of the output string to either `'1'` or `'0'` based on the fact whether the Nth letter of the alphabet is present in the input (independent of its case).

So if an `'a'` or an `'A'` appears anywhere in the input string (any number of times), set the first character of the output string to `'1'`, otherwise to `'0'`. if `'b'` or `'B'` appears in the string, set the second character to `'1'`, and so on for the rest of the alphabet.

For instance:

```
"a   **&  cZ"  =>  "10100000000000000000000001"
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.

Determine if he is correct.  

-----Constraints-----
 - c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive).

-----Input-----
Input is given from Standard Input in the following format:
c_{1,1} c_{1,2} c_{1,3}
c_{2,1} c_{2,2} c_{2,3}
c_{3,1} c_{3,2} c_{3,3}

-----Output-----
If Takahashi's statement is correct, print Yes; otherwise, print No.

-----Sample Input-----
1 0 1
2 1 2
1 0 1

-----Sample Output-----
Yes

Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef likes all arrays equally. But he likes some arrays more equally than others. In particular, he loves Rainbow Arrays. 
An array is Rainbow if it has the following structure:
- First a1 elements equal 1. 
- Next a2 elements equal 2. 
- Next a3 elements equal 3. 
- Next a4 elements equal 4. 
- Next a5 elements equal 5. 
- Next a6 elements equal 6. 
- Next a7 elements equal 7. 
- Next a6 elements equal 6. 
- Next a5 elements equal 5. 
- Next a4 elements equal 4. 
- Next a3 elements equal 3. 
- Next a2 elements equal 2. 
- Next a1 elements equal 1. 
- ai can be any non-zero positive integer.
- There are no other elements in array. 

Help Chef in finding out if the given array is a Rainbow Array or not. 

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases.
- The first line of each test case contains an integer N, denoting the number of elements in the given array. 
- The second line contains N space-separated integers A1, A2, ..., AN denoting the elements of array. 

-----Output-----
- For each test case, output a line containing "yes" or "no" (without quotes) corresponding to the case if the array is rainbow array or not. 

-----Constraints-----
- 1 ≤ T ≤ 100
- 7 ≤ N ≤ 100
- 1 ≤ Ai ≤ 10

-----Subtasks-----
- Subtask 1 (100 points) : Original constraints

-----Example-----
Input
3
19
1 2 3 4 4 5 6 6 6 7 6 6 6 5 4 4 3 2 1
14
1 2 3 4 5 6 7 6 5 4 3 2 1 1
13
1 2 3 4 5 6 8 6 5 4 3 2 1

Output
yes
no
no

-----Explanation-----
The first example satisfies all the conditions. 
The second example has 1 element of value 1 at the beginning and 2 elements of value 1 at the end. 
The third one has no elements with value 7 after elements with value 6.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Up the hill

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Hiking club "Up the hill" just returned from a walk. Now they are trying to remember which hills they've just walked through.

It is known that there were *N* stops, all on different integer heights between 1 and *N* kilometers (inclusive) above the sea level. On the first day they've traveled from the first stop to the second stop, on the second day they've traveled from the second to the third and so on, and on the last day they've traveled from the stop *N*<=-<=1 to the stop *N* and successfully finished their expedition.

They are trying to find out which heights were their stops located at. They have an entry in a travel journal specifying how many days did they travel up the hill, and how many days did they walk down the hill.

Help them by suggesting some possible stop heights satisfying numbers from the travel journal.

Input Specification:
In the first line there is an integer non-negative number *A* denoting the number of days of climbing up the hill. Second line contains an integer non-negative number *B* — the number of days of walking down the hill (*A*<=+<=*B*<=+<=1<==<=*N*, 1<=≤<=*N*<=≤<=100<=000).

Output Specification:
Output *N* space-separated distinct integers from 1 to *N* inclusive, denoting possible heights of the stops in order of visiting.

Demo Input:
['0\n1\n', '2\n1']

Demo Output:
['2 1 \n', '1 3 4 2']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Fafa and the Gates

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Two neighboring kingdoms decided to build a wall between them with some gates to enable the citizens to go from one kingdom to another. Each time a citizen passes through a gate, he has to pay one silver coin.

The world can be represented by the first quadrant of a plane and the wall is built along the identity line (i.e. the line with the equation *x*<==<=*y*). Any point below the wall belongs to the first kingdom while any point above the wall belongs to the second kingdom. There is a gate at any integer point on the line (i.e. at points (0,<=0), (1,<=1), (2,<=2), ...). The wall and the gates do not belong to any of the kingdoms. 

Fafa is at the gate at position (0,<=0) and he wants to walk around in the two kingdoms. He knows the sequence *S* of moves he will do. This sequence is a string where each character represents a move. The two possible moves Fafa will do are 'U' (move one step up, from (*x*,<=*y*) to (*x*,<=*y*<=+<=1)) and 'R' (move one step right, from (*x*,<=*y*) to (*x*<=+<=1,<=*y*)). 

Fafa wants to know the number of silver coins he needs to pay to walk around the two kingdoms following the sequence *S*. Note that if Fafa visits a gate without moving from one kingdom to another, he pays no silver coins. Also assume that he doesn't pay at the gate at point (0,<=0), i. e. he is initially on the side he needs.

Input Specification:
The first line of the input contains single integer *n* (1<=≤<=*n*<=≤<=105) — the number of moves in the walking sequence.

The second line contains a string *S* of length *n* consisting of the characters 'U' and 'R' describing the required moves. Fafa will follow the sequence *S* in order from left to right.

Output Specification:
On a single line, print one integer representing the number of silver coins Fafa needs to pay at the gates to follow the sequence *S*.

Demo Input:
['1\nU\n', '6\nRURUUR\n', '7\nURRRUUU\n']

Demo Output:
['0\n', '1\n', '2\n']

Note:
The figure below describes the third sample. The red arrows represent the sequence of moves Fafa will follow. The green gates represent the gates at which Fafa have to pay silver coins.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Rushitote went to a programming contest to distribute apples and oranges to the contestants.   
He has N apples and M oranges, which need to be divided equally amongst the contestants. Find the maximum possible number of contestants such that:
Every contestant gets an equal number of apples; and
Every contestant gets an equal number of oranges.

Note that every fruit with Rushitote *must* be distributed, there cannot be any left over.

For example, 2 apples and 4 oranges can be distributed equally to two contestants, where each one receives 1 apple and 2 oranges.  
However, 2 apples and 5 oranges can only be distributed equally to one contestant.

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- The first and only line of each test case contains two space-separated integers N and M — the number of apples and oranges, respectively.

------ Output Format ------ 

For each test case, output on a new line the answer: the maximum number of contestants such that everyone receives an equal number of apples and an equal number of oranges.

------ Constraints ------ 

$1 ≤ T ≤ 1000$
$1 ≤ N , M ≤ 10^{9}$

----- Sample Input 1 ------ 
3
1 5
2 4
4 6
----- Sample Output 1 ------ 
1
2
2
----- explanation 1 ------ 
Test case $1$: There's only one apple, so distributing to more than one person is impossible.

Test case $2$: As explained in the statement, $2$ people can each receive $1$ apple and $2$ oranges.

Test case $3$: $2$ people can each receive $2$ apples and $3$ oranges. It's not possible to distribute equally to more than two people.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
One of the perhaps most important factors in deciding the winning team of a football match is the amount of cheers the teams get from their supporters. The Sportify football team is about to meet their worst opponent, Spoilify. As the manager of Sportify’s cheerleading squad, you have to decide on a cheerleading tactic which will ensure you the win.

At your disposal you have $n$ cheerleaders. Each cheerleader has energy to cheer for a total of $t$ minutes of the 90 minute long game (the cheerleaders do not recover energy during the short half-time intermission). For each cheerleader you have to decide when in the game they should cheer. The cheerleading schedule for a match is divided into one minute intervals, and during each interval each cheerleader either cheers or does not cheer during the entire interval.

If a team gets more cheers than the other team for 5 consecutive minutes of the game, that team will score a goal. The 5 minute count is then reset, so if a team gets more cheers than the other team for, say, 17 consecutive minutes, that team will score three goals. The 5 minute interval can not run over the half time intermission, e.g., getting more cheers than the other team from the 43’rd minute to the 49’th minute is not sufficient to score a goal.

As an additional ace up your sleeve, you have spied on the Spoilify cheerleading team and know what their strategy for the game is. Based on this information, what is the best result that can be obtained?

-----Input-----
The first line of input consists of three integers $0 \le n \le 20$, $1 \le t \le 90$, and $0 \le m \le 1000$. The meanings of $n$ and $t$ are described above, and $m$ gives the number of time intervals that the Spoilify cheearleading team is active. Next follow $m$ lines, each consisting of two integers $a$ and $b$, $0 \le a < b \le 90$, indicating that a cheerleader from Spoilify is cheering from time $a$ to time $b$ of the match. These intervals may overlap or even be equal, meaning that several cheerleaders are active simultaneously.

-----Output-----
Output two integers $A$ and $B$ where $A$ is the number of goals scored by the Sportify team and $B$ is the number of goals scored by the Spoilify team, assuming you use an optimal cheerleading tactic. If there are many possible results, you should first attempt to maximize the score difference $A-B$, and if there are still many possible results, maximize your score $A$.

-----Examples-----
Sample Input:
1 31 2
20 60
50 90
Sample Output:
4 3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has decided to start home delivery from his restaurant. He hopes that he will get a lot of orders for delivery, however there is a concern. He doesn't have enough work forces for all the deliveries.  For this he has came up with an idea - he will group together all those orders which have to be delivered in nearby areas. 

In particular, he has identified certain bidirectional roads which he calls as fast roads. They are short and usually traffic free, so the fast travel is possible along these roads. His plan is that he will send orders to locations A and B together if and only if it is possible to travel between A and B using only fast roads. Your task is, given the configuration of fast roads, identify which orders are to be sent together.

-----Input-----
First line of input contains an integer T, the number of test cases. Then T test cases follow. First line of each test case contains two space separated integers N and M, denoting number of locations and the number of fast roads. Then M lines follow each containing two space separated integers A and B, denoting that there is a fast road between locations A and B. Assume that locations are indexed by numbers from 0 to N-1. 

Next line contains an integer Q denoting the number of queries. Each of the next Q lines contain two integers X and Y. For each query you have to find out if orders meant for locations X and Y are to be sent together or not.

Note that there might be multiple fast roads between same pair of locations, also there might be a fast road that links a location to itself.

-----Output-----
For each test case print Q lines - one for each query. Output "YO" if the orders are to be 
delivered together and "NO" otherwise (quotes for clarity).

-----Constraints-----
1 ≤ T ≤ 100
1 ≤ N ≤ 100
1 ≤ M ≤ 1000
0 ≤ A, B, X, Y ≤ N-1
1 ≤ Q ≤ 3000

-----Example-----
Input:
1
4 2
0 1
1 2
3
0 2
0 3
2 1

Output:
YO
NO
YO

-----Warning!-----
There are large input and output files in this problem. Make sure you use fast enough I/O methods.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Little Timmy is exceptionally good at math tables, so his maths teacher decided to make things a bit more interesting. His teacher takes two numbers A and B and merges the tables of A and B in sorted order (ascending order), removing the duplicates and thus creates supertable of A and B and asks Little Timmy the Nth number in the supertable.
Given A, B and N, calculate the Nth number in the supertable of A and B.

Input
First line contains number of test cases T . Each test case contains three integers A , B and N .

Output
For each test case print the N^th number of the supertable.

Constraints:
1 ≤ T ≤ 300000
1 ≤ A, B ≤ 1000
1 ≤ N ≤ 1000000000

SAMPLE INPUT
4
3 5 2
3 5 3
2 3 4
2 3 6

SAMPLE OUTPUT
5
6
6
9

Explanation

Test Case #1:

A=3, B= 5
Table of A = 3 , 6 , 9 , 12 ,15 ,18  and so on
Table of B =5 , 10 , 15 , 20  and so on 
After Merging : 3, 5, 6,  9 ,10 , 12 ,15 ,15, 18, 20   and so on
Remove Duplicates : 3 , 5 , 6, 9 , 10 , 12 , 15 , 18 , 20  and so on
For N= 2 , 2nd element of the supertable is 5 .

Test Case #2:

For N=3 , 3rd element of the supertable is 6.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.