vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Given a positive floating point number N, the task is to find the smallest integer k, such that when we multiply k with N, we get a natural number.
 
Example 1:
Input: N = "30.25"
Output: 4
Explanation: 30.25 * 4 = 321, there is no 
number less than 4 which can convert 30.25
into natural number.
Example 2:
Input: N = "5.5"
Output: 2
Explanation: 5.5 * 2 = 11, there is no number
less than 2 which can convert 5.5 into 
natural number.
 
Your Task:
You don' need to read or print anything. Your task is to complete the function findMinMultiple() which takes N as input parameter in string format and returns the minimum k such that when we multiply it with N we get a natural number.
 
Expected Time Complexity:O(c) where c is constant
Expected Space Compelxity: O(1)
 
Constraints:
1 <= N <= 1000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Polycarp has a cat and his cat is a real gourmet! Dependent on a day of the week he eats certain type of food:  on Mondays, Thursdays and Sundays he eats fish food;  on Tuesdays and Saturdays he eats rabbit stew;  on other days of week he eats chicken stake. 

Polycarp plans to go on a trip and already packed his backpack. His backpack contains:  $a$ daily rations of fish food;  $b$ daily rations of rabbit stew;  $c$ daily rations of chicken stakes. 

Polycarp has to choose such day of the week to start his trip that his cat can eat without additional food purchases as long as possible. Print the maximum number of days the cat can eat in a trip without additional food purchases, if Polycarp chooses the day of the week to start his trip optimally.


-----Input-----

The first line of the input contains three positive integers $a$, $b$ and $c$ ($1 \le a, b, c \le 7\cdot10^8$) — the number of daily rations of fish food, rabbit stew and chicken stakes in Polycarps backpack correspondingly.


-----Output-----

Print the maximum number of days the cat can eat in a trip without additional food purchases, if Polycarp chooses the day of the week to start his trip optimally.


-----Examples-----
Input
2 1 1

Output
4

Input
3 2 2

Output
7

Input
1 100 1

Output
3

Input
30 20 10

Output
39



-----Note-----

In the first example the best day for start of the trip is Sunday. In this case, during Sunday and Monday the cat will eat fish food, during Tuesday — rabbit stew and during Wednesday — chicken stake. So, after four days of the trip all food will be eaten.

In the second example Polycarp can start his trip in any day of the week. In any case there are food supplies only for one week in Polycarps backpack.

In the third example Polycarp can start his trip in any day, excluding Wednesday, Saturday and Sunday. In this case, the cat will eat three different dishes in three days. Nevertheless that after three days of a trip there will be $99$ portions of rabbit stew in a backpack, can cannot eat anything in fourth day of a trip.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Create a program that rotates the pattern of 8 characters x 8 lines clockwise by 90 degrees, 180 degrees, and 270 degrees and outputs it.



Input

A pattern consisting of 8 characters x 8 lines is given. Characters consist of alphanumeric characters, half-width pound'#', and asterisk'*'.

Output

Output the rotated pattern in the following format.


90 (fixed half-width numbers)
Pattern rotated 90 degrees
180 (fixed half-width numbers)
180 degree rotated pattern
270 (fixed half-width numbers)
Pattern rotated 270 degrees


Examples

Input

#*******
#*******
#*******
#*******
#*******
#*******
#*******
########


Output

90
########
#*******
#*******
#*******
#*******
#*******
#*******
#*******
180
########
*******#
*******#
*******#
*******#
*******#
*******#
*******#
270
*******#
*******#
*******#
*******#
*******#
*******#
*******#
########


Input

*******
*******
*******
*******
*******
*******
*******


Output

90

*******
*******
*******
*******
*******
*******
*******
180

*******#
*******#
*******#
*******#
*******#
*******#
*******#
270
*******#
*******#
*******#
*******#
*******#
*******#
*******#

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Despite his bad reputation, Captain Flint is a friendly person (at least, friendly to animals). Now Captain Flint is searching worthy sailors to join his new crew (solely for peaceful purposes). A sailor is considered as worthy if he can solve Flint's task.

Recently, out of blue Captain Flint has been interested in math and even defined a new class of integers. Let's define a positive integer $x$ as nearly prime if it can be represented as $p \cdot q$, where $1 < p < q$ and $p$ and $q$ are prime numbers. For example, integers $6$ and $10$ are nearly primes (since $2 \cdot 3 = 6$ and $2 \cdot 5 = 10$), but integers $1$, $3$, $4$, $16$, $17$ or $44$ are not.

Captain Flint guessed an integer $n$ and asked you: can you represent it as the sum of $4$ different positive integers where at least $3$ of them should be nearly prime.

Uncle Bogdan easily solved the task and joined the crew. Can you do the same?


-----Input-----

The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases.

Next $t$ lines contain test cases — one per line. The first and only line of each test case contains the single integer $n$ $(1 \le n \le 2 \cdot 10^5)$ — the number Flint guessed.


-----Output-----

For each test case print:   YES and $4$ different positive integers such that at least $3$ of them are nearly prime and their sum is equal to $n$ (if there are multiple answers print any of them);  NO if there is no way to represent $n$ as the sum of $4$ different positive integers where at least $3$ of them are nearly prime.  You can print each character of YES or NO in any case.


-----Example-----
Input
7
7
23
31
36
44
100
258

Output
NO
NO
YES
14 10 6 1
YES
5 6 10 15
YES
6 7 10 21
YES
2 10 33 55
YES
10 21 221 6


-----Note-----

In the first and second test cases, it can be proven that there are no four different positive integers such that at least three of them are nearly prime.

In the third test case, $n=31=2 \cdot 7 + 2 \cdot 5 + 2 \cdot 3 + 1$: integers $14$, $10$, $6$ are nearly prime.

In the fourth test case, $n=36=5 + 2 \cdot 3 + 2 \cdot 5 + 3 \cdot 5$: integers $6$, $10$, $15$ are nearly prime.

In the fifth test case, $n=44=2 \cdot 3 + 7 + 2 \cdot 5 + 3 \cdot 7$: integers $6$, $10$, $21$ are nearly prime.

In the sixth test case, $n=100=2 + 2 \cdot 5 + 3 \cdot 11 + 5 \cdot 11$: integers $10$, $33$, $55$ are nearly prime.

In the seventh test case, $n=258=2 \cdot 5 + 3 \cdot 7 + 13 \cdot 17 + 2 \cdot 3$: integers $10$, $21$, $221$, $6$ are nearly prime.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The stardate is 1977 and the science and art of detecting Death Stars is in its infancy. Princess Heidi has received information about the stars in the nearby solar system from the Rebel spies and now, to help her identify the exact location of the Death Star, she needs to know whether this information is correct. 

Two rebel spies have provided her with the maps of the solar system. Each map is an N × N grid, where each cell is either occupied by a star or empty. To see whether the information is correct, Heidi needs to know whether the two maps are of the same solar system, or if possibly one of the spies is actually an Empire double agent, feeding her false information.

Unfortunately, spies may have accidentally rotated a map by 90, 180, or 270 degrees, or flipped it along the vertical or the horizontal axis, before delivering it to Heidi. If Heidi can rotate or flip the maps so that two of them become identical, then those maps are of the same solar system. Otherwise, there are traitors in the Rebel ranks! Help Heidi find out.


-----Input-----

The first line of the input contains one number N (1 ≤ N ≤ 10) – the dimension of each map. Next N lines each contain N characters, depicting the first map: 'X' indicates a star, while 'O' indicates an empty quadrant of space. Next N lines each contain N characters, depicting the second map in the same format.


-----Output-----

The only line of output should contain the word Yes if the maps are identical, or No if it is impossible to match them by performing rotations and translations.


-----Examples-----
Input
4
XOOO
XXOO
OOOO
XXXX
XOOO
XOOO
XOXO
XOXX

Output
Yes

Input
2
XX
OO
XO
OX

Output
No



-----Note-----

In the first test, you can match the first map to the second map by first flipping the first map along the vertical axis, and then by rotating it 90 degrees clockwise.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Happy traveller [Part 1]

There is a play grid NxN; Always square! 

   0  1  2  3
0 [o, o, o, X]
1 [o, o, o, o]
2 [o, o, o, o]
3 [o, o, o, o]


You start from a random point. I mean, you are given the coordinates of your start position in format (row, col). 

And your TASK is to define the number of unique paths to reach position X (always in the top right corner).


From any point you can go only UP or RIGHT.


Implement a function count_paths(N, (row, col)) which returns int; 
Assume input params are always valid.


Example:

count_paths(1, (0, 0))
grid 1x1:

[X]
 You are already in the target point, so return 0


count_paths(2, (1, 0))
grid 2x2:

[o, X]
[@, o]
 You are at point @; you can move UP-RIGHT or RIGHT-UP, and there are 2 possible unique paths here

count_paths(2, (1, 1))
grid 2x2:

[o, X]
[o, @]
 You are at point @; you can move only UP, so there is 1 possible unique path here

count_paths(3, (1, 0))
grid 3x3:

[o, o, X]
[@, o, o]
[o, o, o]
 You are at point @; you can move UP-RIGHT-RIGHT or RIGHT-UP-RIGHT, or RIGHT-RIGHT-UP, and there are 3 possible unique paths here


I think it's pretty clear =)

btw. you can use preloaded Grid class, which constructs 2d array for you. It's very very basic and simple. You can use numpy instead or any other way to produce the correct answer =)
 grid = Grid(2, 2, 0) 
samegrid = Grid.square(2) will give you a grid[2][2], which you can print easily to console. 

print(grid)


[0, 0]
[0, 0]


Enjoy!

You can continue adventures:
Happy traveller [Part 2]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a number N, find the first N Fibonacci numbers. The first two number of the series are 1 and 1.
Example 1:
Input:
N = 5
Output: 1 1 2 3 5
Example 2:
Input:
N = 7
Output: 1 1 2 3 5 8 13
Your Task:
Your task is to complete printFibb() which takes single argument N and returns a list of first N Fibonacci numbers.
Expected Time Complexity: O(N).
Expected Auxiliary Space: O(N).
Note: This space is used to store and return the answer for printing purpose.
Constraints:
1<= N <=84

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Write a function that takes a positive integer n, sums all the cubed values from 1 to n, and returns that sum.

Assume that the input n will always be a positive integer.

Examples:

```python
sum_cubes(2)
> 9 
# sum of the cubes of 1 and 2 is 1 + 8
```

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Since you are the best Wraith King, Nizhniy Magazin «Mir» at the centre of Vinnytsia is offering you a discount.

You are given an array *a* of length *n* and an integer *c*. 

The value of some array *b* of length *k* is the sum of its elements except for the  smallest. For example, the value of the array [3,<=1,<=6,<=5,<=2] with *c*<==<=2 is 3<=+<=6<=+<=5<==<=14.

Among all possible partitions of *a* into contiguous subarrays output the smallest possible sum of the values of these subarrays.

Input Specification:
The first line contains integers *n* and *c* (1<=≤<=*n*,<=*c*<=≤<=100<=000).

The second line contains *n* integers *a**i* (1<=≤<=*a**i*<=≤<=109) — elements of *a*.

Output Specification:
Output a single integer  — the smallest possible sum of values of these subarrays of some partition of *a*.

Demo Input:
['3 5\n1 2 3\n', '12 10\n1 1 10 10 10 10 10 10 9 10 10 10\n', '7 2\n2 3 6 4 5 7 1\n', '8 4\n1 3 4 5 5 3 4 1\n']

Demo Output:
['6\n', '92\n', '17\n', '23\n']

Note:
In the first example any partition yields 6 as the sum.

In the second example one of the optimal partitions is [1, 1], [10, 10, 10, 10, 10, 10, 9, 10, 10, 10] with the values 2 and 90 respectively.

In the third example one of the optimal partitions is [2, 3], [6, 4, 5, 7], [1] with the values 3, 13 and 1 respectively.

In the fourth example one of the optimal partitions is [1], [3, 4, 5, 5, 3, 4], [1] with the values 1, 21 and 1 respectively.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Each of you probably has your personal experience of riding public transportation and buying tickets. After a person buys a ticket (which traditionally has an even number of digits), he usually checks whether the ticket is lucky. Let us remind you that a ticket is lucky if the sum of digits in its first half matches the sum of digits in its second half.

But of course, not every ticket can be lucky. Far from it! Moreover, sometimes one look at a ticket can be enough to say right away that the ticket is not lucky. So, let's consider the following unluckiness criterion that can definitely determine an unlucky ticket. We'll say that a ticket is definitely unlucky if each digit from the first half corresponds to some digit from the second half so that each digit from the first half is strictly less than the corresponding digit from the second one or each digit from the first half is strictly more than the corresponding digit from the second one. Each digit should be used exactly once in the comparisons. In other words, there is such bijective correspondence between the digits of the first and the second half of the ticket, that either each digit of the first half turns out strictly less than the corresponding digit of the second half or each digit of the first half turns out strictly more than the corresponding digit from the second half.

For example, ticket 2421 meets the following unluckiness criterion and will not be considered lucky (the sought correspondence is 2<=&gt;<=1 and 4<=&gt;<=2), ticket 0135 also meets the criterion (the sought correspondence is 0<=&lt;<=3 and 1<=&lt;<=5), and ticket 3754 does not meet the criterion. 

You have a ticket in your hands, it contains 2*n* digits. Your task is to check whether it meets the unluckiness criterion.

Input Specification:
The first line contains an integer *n* (1<=≤<=*n*<=≤<=100). The second line contains a string that consists of 2*n* digits and defines your ticket.

Output Specification:
In the first line print "YES" if the ticket meets the unluckiness criterion. Otherwise, print "NO" (without the quotes).

Demo Input:
['2\n2421\n', '2\n0135\n', '2\n3754\n']

Demo Output:
['YES\n', 'YES\n', 'NO\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are $N$ villages numbered $1$ to $N$. The villages are connected through bi-directional paths in between them. The whole network is in the form of a tree. 
Each village has only $1$ fighter but they help each other in times of crisis by sending their fighter to the village in danger through paths along the villages. Defeating a fighter will mean conquering his village. In particular, If village $X$ is under attack, all villages having a path to $X$ will send their fighters for help. 
Naruto wants to conquer all the villages. But he cannot take on so many fighters at the same time so he plans to use  a secret technique with which he can destroy  any $1$ village (along with paths connected to it) in the blink of an eye.  However, it can be used only once. He realized that if he destroys any village, say $X$, the maximum number of fighters he has to fight at once reduces to $W$. He wants $W$ to be as small as possible. Help him find the optimal $X$.
In case of multiple answers, choose the smallest value of $X$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- First Line contains $N$.
- Next $N - 1$ lines contain $U, V$, denoting a path between village $U$ and $V$. 

-----Output:-----
- For each Test case, print in a new line, optimal $X$ and corresponding value of $W$.

-----Constraints-----
- $1 \leq T \leq 10$
- $3 \leq N \leq 10^5$
- $1 \leq U, V \leq N$ 
- $U != V$ 

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

-----Sample Output:-----
1 2
2 1

-----EXPLANATION:-----
Sample 1:  By destroying village $1$,  The fighters Naruto will be fighting at the same time will be from villages $[2, 4]$ and $[3, 5]$.  For this $W$ = $2$. No other choice can give lesser $W$. Hence $1$ is optimal choice.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# Task
Your task is to find the sum for the range `0 ... m` for all powers from `0 ... n.

# Example

 For `m = 2, n = 3`, the result should be `20`
 
 `0^0+1^0+2^0 + 0^1+1^1+2^1 + 0^2+1^2+2^2 + 0^3+1^3+2^3 = 20`
 
 Note, that no output ever exceeds 2e9.

# Input/Output


 - `[input]` integer m

  `0 <= m <= 50000`


 - `[input]` integer `n`

  `0 <= n <= 9`


 - `[output]` an integer(double in C#)

  The sum value.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You own and manage an office building. One of the tenants, a regional paper supply company, is complaining about the lack of security offered by the CrapTacular$^{\text {TM}}$ doors you installed in the building. A potential attacker could easily pick the locks on these doors to gain access to any room of the building. This is frankly unacceptable as there are reams upon reams of priceless paper stored inside the office.

To appease your tenant, you offer to replace one existing door with a new high-security door that will stop any attacker. To get the most benefit from the new door, it should protect the maximum possible number of rooms in the building. That is, you need to find which existing door to replace with a secure door such that the maximum number of rooms can only be reached from outside the building through the new door.

The building contains $0<N<100000$ rooms which are connected by $0<M<100000$ doors. Rooms are uniquely named by the integers in the range $[0,N)$. To figure out where to install the secure door, you have a floor plan of the building. The floor plan somehow represents all of the floors in one (possibly non-planar) graph. The only way to pass from one room to another, or the outside, is by using a door. All rooms can be reached, directly or via other rooms, from all other rooms and from the outside of the building.

-----Input-----
Input contains several lines of integers separated by spaces. The first line contains the number $N$, then $M$. The following $M$ lines describe each door with two numbers $-1 \le u < N$ and $-1 \le v < N$, $u \ne v$. The numbers $u$ and $v$ represent the rooms connected by the door. A door connects to the outside if $u$ or $v$ is $-1$. No door has $u = v$.

-----Output-----
The maximum number of rooms that can be protected with a single high-security door.

-----Sample Explanation-----
The image below illustrates the building described in Sample Input 2:





Here, double-headed arrows indicate doors. For example, the arrow between room $0$ and $1$ shows that there is a door there. The other arrow connecting room $0$ leads to the outside of the building. We could totally secure room $5$ by replacing the door between room $1$ and $5$, but this is not the optimal solution. The best solution for this input is to replace the door between room $1$ and $2$, since room $2$, $3$, and $4$ can only be reached from the outside of the building by passing through that door. The answer is thus $3$ because at most $3$ rooms can be secured.

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

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Alice and Bob created a new game while at the beach this summer. All they need is a set of numbered playing cards. They start by creating $P$ piles with all cards face-up and select a non-negative number $K$. After that, they take turns like this:
 - A player starts by selecting one of the piles.
 - Then, he removes from $0$ up to $K$ cards from the top of that pile, leaving at least one card in the pile.
 - Next, he looks at the card left at the top of the pile and must remove a number of cards equal to its value (from the top of the same pile).

Whoever doesn’t have more cards to remove, or whoever is forced to remove more cards than those available on a pile, loses the game.In the figure, you can see an example with two piles and $K = 1$. The player to move might: 
 - Select the first pile and $0$ cards to remove, being forced to remove $1$ card from the top next.
 - Select the second pile and $0$ cards to remove, having to remove $1$ card from the top next.
 - Select the second pile and $1$ card to remove, having to remove $2$ cards from the top next.

Alice has realized that Bob is very good at this game and will always win if he has the chance. Luckily, this time Alice is first to play. Is Alice able to win this game?

-----Task-----
Given the description of the piles with all the cards and the maximum number of cards they can start to remove, your goal is to find out whether Alice can win the game if she is the first to play.

-----Input-----
The first line contains $2$ space separated integers, $P$, the number of piles, and $K$, the maximum number of cards they can start to remove on their turn. The next $P$ lines start with an integer $N$, indicating the number of cards on a pile. $N$ space separated integers follow, representing the cards on that pile from the bottom to the top.

-----Constraints-----

$1 \leq P \leq 100$

Number of piles.

$1 \leq K \leq 10$

Maximum number of cards a player can start to remove.

$1 \leq c \leq 10$

Number on each card.

$1 \leq N \leq 1000$

Size of each pile.

-----Output-----
A single string, stating “Alice can win.” or “Bob will win.”, as appropriate.

-----Sample Output Explanation-----
In the first sample, the piles are the same, so Bob will always be able to mirror whatever move Alice makes.

In the second sample, Alice can start by removing $0$ cards from the second pile and then $1$ card from its top. Two legal moves will be possible next, Bob will make one and Alice the other.

-----Examples-----
Sample Input 1:
4 1
4 1 1 1 1
6 2 1 2 1 2 1
4 1 1 1 1
6 2 1 2 1 2 1
Sample Output 1:
Bob will win.

Sample Input 2:
2 1
1 1
3 1 2 1
Sample Output 2:
Alice can win.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array nums[] of n elements and a number k. Your task is to count the number of integers from 1 to k which are divisible by atleast one of the elements of nums[].
 
Example 1:
Input: nums = {2, 3}, k = 10
Output: 7
Explanation: The numbers from 1 to 10
which are divisible by either 2 or 3
are - 2, 3, 4, 6, 8, 9, 10
Example 2:
Input: nums = {2}, k = 5
Output: 2
Explanation: The numbers which are divisble 
by 2 from 1 to 5 are 2 and 4.
 
Your Task:
You don't have to read or print anyhting. Your task is to complete the function Count() which takes nums and k as input parameter and returns count of integers from 1 to k which are divisible by atleast one of the element of nums[].
 
Expected Time Compelxity: O(n * 2^{n} * log(k))
Expected Space Complexity: O(1)
 
Constraints:
1 <= n <= 12
1 <= k <= 10^{18}
1 <= nums[i] <= 20

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