vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Title: Xor-MST

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given a complete undirected graph with *n* vertices. A number *a**i* is assigned to each vertex, and the weight of an edge between vertices *i* and *j* is equal to *a**i*<=*xor*<=*a**j*.

Calculate the weight of the minimum spanning tree in this graph.

Input Specification:
The first line contains *n* (1<=≤<=*n*<=≤<=200000) — the number of vertices in the graph.

The second line contains *n* integers *a*1, *a*2, ..., *a**n* (0<=≤<=*a**i*<=&lt;<=230) — the numbers assigned to the vertices.

Output Specification:
Print one number — the weight of the minimum spanning tree in the graph.

Demo Input:
['5\n1 2 3 4 5\n', '4\n1 2 3 4\n']

Demo Output:
['8\n', '8\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Divisors of 42 are : 1, 2, 3, 6, 7, 14, 21, 42.
These divisors squared are: 1, 4, 9, 36, 49, 196, 441, 1764.
The sum of the squared divisors is 2500 which is 50 * 50, a square!

Given two integers m, n (1 <= m <= n) we want to find all integers 
between m and n whose sum of squared divisors is itself a square.
42 is such a number.

The result will be an array of arrays or of tuples (in C an array of Pair) or a string, each subarray having two elements,
first the number whose squared divisors is a square and then the sum
of the squared divisors.

#Examples:
```
list_squared(1, 250) --> [[1, 1], [42, 2500], [246, 84100]]
list_squared(42, 250) --> [[42, 2500], [246, 84100]]
```

The form of the examples may change according to the language, see `Example Tests:` for more details.

**Note**

In Fortran - as in any other language - the returned string is not permitted to contain any redundant trailing whitespace: you can use dynamically allocated character strings.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We guessed some integer number $x$. You are given a list of almost all its divisors. Almost all means that there are all divisors except $1$ and $x$ in the list.

Your task is to find the minimum possible integer $x$ that can be the guessed number, or say that the input data is contradictory and it is impossible to find such number.

You have to answer $t$ independent queries.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 25$) — the number of queries. Then $t$ queries follow.

The first line of the query contains one integer $n$ ($1 \le n \le 300$) — the number of divisors in the list.

The second line of the query contains $n$ integers $d_1, d_2, \dots, d_n$ ($2 \le d_i \le 10^6$), where $d_i$ is the $i$-th divisor of the guessed number. It is guaranteed that all values $d_i$ are distinct.


-----Output-----

For each query print the answer to it.

If the input data in the query is contradictory and it is impossible to find such number $x$ that the given list of divisors is the list of almost all its divisors, print -1. Otherwise print the minimum possible $x$.


-----Example-----
Input
2
8
8 2 12 6 4 24 16 3
1
2

Output
48
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Background
----------
In another dimension, there exist two immortal brothers: Solomon and Goromon. As sworn loyal subjects to the time elemental, Chronixus, both Solomon and Goromon were granted the power to create temporal folds. By sliding through these temporal folds, one can gain entry to parallel dimensions where time moves relatively faster or slower.

Goromon grew dissatisfied and one day betrayed Chronixus by stealing the Temporal Crystal, an artifact used to maintain the time continuum. Chronixus summoned Solomon and gave him the task of tracking down Goromon and retrieving the Temporal Crystal.

Using a map given to Solomon by Chronixus, you must find Goromon's precise location.

Mission Details
---------------
The map is represented as a 2D array. See the example below:

```python
map_example = [[1,3,5],[2,0,10],[-3,1,4],[4,2,4],[1,1,5],[-3,0,12],[2,1,12],[-2,2,6]]
```
Here are what the values of each subarray represent:
- **Time Dilation:** With each additional layer of time dilation entered, time slows by a factor of `2`. At layer `0`, time passes normally. At layer `1`, time passes at half the rate of layer `0`. At layer `2`, time passes at half the rate of layer `1`, and therefore one quarter the rate of layer `0`.
- **Directions** are as follow: `0 = North, 1 = East, 2 = South, 3 = West`
- **Distance Traveled:** This represents the distance traveled relative to the current time dilation layer. See below:

```
The following are equivalent distances (all equal a Standard Distance of 100):
Layer: 0, Distance: 100
Layer: 1, Distance: 50
Layer: 2, Distance: 25
```
For the `mapExample` above:
```
mapExample[0] -> [1,3,5]
1 represents the level shift of time dilation
3 represents the direction
5 represents the distance traveled relative to the current time dilation layer

Solomon's new location becomes [-10,0]

mapExample[1] -> [2,0,10]
At this point, Solomon has shifted 2 layers deeper.
He is now at time dilation layer 3.
Solomon moves North a Standard Distance of 80.
Solomon's new location becomes [-10,80]

mapExample[2] -> [-3,1,4]
At this point, Solomon has shifted out 3 layers.
He is now at time dilation layer 0.
Solomon moves East a Standard Distance of 4.
Solomon's new location becomes [-6,80]
```
Your function should return Goromon's `[x,y]` coordinates.

For `mapExample`, the correct output is `[346,40]`.

Additional Technical Details
----------------------------
- Inputs are always valid.
- Solomon begins his quest at time dilation level `0`, at `[x,y]` coordinates `[0,0]`.
- Time dilation level at any point will always be `0` or greater.
- Standard Distance is the distance at time dilation level `0`.
- For given distance `d` for each value in the array: `d >= 0`.
- Do not mutate the input

**Note from the author:** I made up this story for the purpose of this kata. Any similarities to any fictitious persons or events are purely coincidental.

If you enjoyed this kata, be sure to check out [my other katas](https://www.codewars.com/users/docgunthrop/authored).

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given positive integers A and B.
If A is a divisor of B, print A + B; otherwise, print B - A.

-----Constraints-----
 - All values in input are integers.
 - 1 \leq A \leq B \leq 20

-----Input-----
Input is given from Standard Input in the following format:
A B

-----Output-----
If A is a divisor of B, print A + B; otherwise, print B - A.

-----Sample Input-----
4 12

-----Sample Output-----
16

As 4 is a divisor of 12, 4 + 12 = 16 should be printed.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Two players are playing a game with a set of $K$ six-sided dice. One player calls out a number in the range $K\ldots 6K$ and the other tries to roll that number. After the first roll, the player is allowed to pick up any number ($0\ldots K$) of dice and re-roll them.

Given the number of dice, the target number the player wants to roll, and the set of numbers the player obtained on the first roll, what number of dice should the player pick up to maximize their chances of getting the target number on the second roll?

-----Input-----
Input begins with a line containing $2$ integers, $K$, the number of dice, and $T$, the target number. The bounds are $2 \leq K \leq 24$ and $K \leq T \leq 6K$.

The next line contains $K$ integers, indicating the numbers that were rolled on each of the dice on the first roll. All will be integers in the range $1\ldots 6$.

-----Output-----
Print a single line containing an integer denoting the number of dice that the roller should pick up and re-roll in order to maximize the chances of getting an overall sum of $T$. (The roller will be able to choose which dice to pick up, but you are only asked to print the number of dice, not which ones.)

If there are more than one numbers of dice that can be picked up to achieve the same probability of getting to $T$, print the smallest such value.

-----Examples-----
Sample Input 1:
3 9
5 4 1
Sample Output 1:
1

Sample Input 2:
4 13
2 2 2 2
Sample Output 2:
3

Sample Input 3:
18 90
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
Sample Output 3:
12

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

 Find the longest successive exclamation marks and question marks combination in the string. A successive exclamation marks and question marks combination must contains two part: a substring of "!" and a substring "?", they are adjacent. 
 
 If more than one result are found, return the one which at left side; If no such a combination found, return `""`.

# Examples

```
find("!!") === ""
find("!??") === "!??"
find("!?!!") === "?!!"
find("!!???!????") === "!!???"
find("!!???!?????") === "!?????"
find("!????!!!?") === "????!!!" 
find("!?!!??!!!?") === "??!!!"
```

# Note
Please don't post issue about difficulty or duplicate. Because:
>[That's unfair on the kata creator. This is a valid kata and introduces new people to javascript some regex or loops, depending on how they tackle this problem.  --matt c](https://www.codewars.com/kata/remove-exclamation-marks/discuss#57fabb625c9910c73000024e)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are a person who is always fond of eating candies. Your friend gave you a candy of length N, to eat during the break period of your school.

You start eating this candy from one of the ends. But as it is not your candy, your friend told you to eat exactly K unit length of candy during each bite. You will stop eating if the candy's length becomes 0. This means that you have eaten the entire candy. 

If at some point of time, the candy's length is positive, but less than K, you *cannot* take a bite thereafter.

Can you eat the complete candy? If yes, print the number bites it will take, else print -1.

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

- First line will contain T, number of testcases. Then the testcases follow.
- Each testcase contains of two spaced integers N, K.

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

For each testcase, print the minimum number of bites you need to eat the complete candy. Print -1 if it is
not possible to do so.

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

$1 ≤ T ≤ 10^{5}$
$0 ≤ N ≤ 10^{6}$
$1 ≤ K ≤ 10^{6}$

----- Sample Input 1 ------ 
3
3 1
3 2
0 3

----- Sample Output 1 ------ 
3
-1
0

----- explanation 1 ------ 
Test case 1:
When you eat your first bite of length $1$, the length of the candy will become $2$. After the second bite, the candy's length will be $1$ and finally after the third bite, candy's length will be $0$, and hence you eat the entire candy!

Test case 2:
After the first bite, candy's length will become $1$. You cannot go for the second bite as candy's length is positive and less than $2$.

Test case 3: 
Candy's length is already $0$, hence it can be said that you have eaten the entire candy!

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Codeforces user' handle color depends on his rating — it is red if his rating is greater or equal to 2400; it is orange if his rating is less than 2400 but greater or equal to 2200, etc. Each time participant takes part in a rated contest, his rating is changed depending on his performance.

Anton wants the color of his handle to become red. He considers his performance in the rated contest to be good if he outscored some participant, whose handle was colored red before the contest and his rating has increased after it.

Anton has written a program that analyses contest results and determines whether he performed good or not. Are you able to do the same?


-----Input-----

The first line of the input contains a single integer n (1 ≤ n ≤ 100) — the number of participants Anton has outscored in this contest .

The next n lines describe participants results: the i-th of them consists of a participant handle name_{i} and two integers before_{i} and after_{i} ( - 4000 ≤ before_{i}, after_{i} ≤ 4000) — participant's rating before and after the contest, respectively. Each handle is a non-empty string, consisting of no more than 10 characters, which might be lowercase and uppercase English letters, digits, characters «_» and «-» characters.

It is guaranteed that all handles are distinct.


-----Output-----

Print «YES» (quotes for clarity), if Anton has performed good in the contest and «NO» (quotes for clarity) otherwise.


-----Examples-----
Input
3
Burunduk1 2526 2537
BudAlNik 2084 2214
subscriber 2833 2749

Output
YES
Input
3
Applejack 2400 2400
Fluttershy 2390 2431
Pinkie_Pie -2500 -2450

Output
NO


-----Note-----

In the first sample, Anton has outscored user with handle Burunduk1, whose handle was colored red before the contest and his rating has increased after the contest.

In the second sample, Applejack's rating has not increased after the contest, while both Fluttershy's and Pinkie_Pie's handles were not colored red before the contest.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Create a function xMasTree(height) that returns a christmas tree of the correct height. The height is passed through to the function and the function should return a list containing each line of the tree. 
```
xMasTree(5) should return : ['____#____', '___###___', '__#####__', '_#######_', '#########', '____#____', '____#____']
xMasTree(3) should return : ['__#__', '_###_', '#####', '__#__', '__#__']
```
The final idea is for the tree to look like this if you decide to print each element of the list: 
``` 
xMasTree(5) will result in:
____#____              1
___###___              2
__#####__              3
_#######_              4
#########       -----> 5 - Height of Tree
____#____        1      
____#____        2 - Trunk/Stem of Tree

xMasTree(3) will result in:
__#__                  1
_###_                  2
#####          ----->  3 - Height of Tree
__#__           1
__#__           2 - Trunk/Stem of Tree
```
Pad with underscores i.e _ so each line is the same length. The last line forming the tree having only hashtags, no spaces. Also remember the trunk/stem of the tree.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Yet another Armageddon is coming! This time the culprit is the Julya tribe calendar. 

The beavers in this tribe knew math very well. Smart Beaver, an archaeologist, got a sacred plate with a magic integer on it. The translation from Old Beaverish is as follows: 

"May the Great Beaver bless you! May your chacres open and may your third eye never turn blind from beholding the Truth! Take the magic number, subtract a digit from it (the digit must occur in the number) and get a new magic number. Repeat this operation until a magic number equals zero. The Earth will stand on Three Beavers for the time, equal to the number of subtractions you perform!"

Distinct subtraction sequences can obviously get you different number of operations. But the Smart Beaver is ready to face the worst and is asking you to count the minimum number of operations he needs to reduce the magic number to zero.


-----Input-----

The single line contains the magic integer n, 0 ≤ n.

  to get 20 points, you need to solve the problem with constraints: n ≤ 10^6 (subproblem C1);  to get 40 points, you need to solve the problem with constraints: n ≤ 10^12 (subproblems C1+C2);  to get 100 points, you need to solve the problem with constraints: n ≤ 10^18 (subproblems C1+C2+C3). 


-----Output-----

Print a single integer — the minimum number of subtractions that turns the magic number to a zero.


-----Examples-----
Input
24

Output
5


-----Note-----

In the first test sample the minimum number of operations can be reached by the following sequence of subtractions: 

 24 → 20 → 18 → 10 → 9 → 0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Two of the nodes of a Binary Search Tree (BST) are swapped. Fix (or correct) the BST by swapping them back. Do not change the structure of the tree.
Note: It is guaranteed that the given input will form BST, except for 2 nodes that will be wrong.
 
Example 1:
Input:
       10
     /    \
    5      8
   / \
  2   20
Output: 1
Explanation:
 
Example 2:
Input:
         11
       /    \
      3      17
       \    /
        4  10
Output: 1 
Explanation: 
By swapping nodes 11 and 10, the BST 
can be fixed.
Your Task:
You don't need to take any input. Just complete the function correctBst() that takes root node as parameter. The function should return the root of corrected BST. BST will then be checked by driver code and 0 or 1 will be printed.
Expected Time Complexity: O(Number of nodes)
Expected Auxiliary Space: O(logN), N = number of nodes
 
Constraints:
1 <= Number of nodes <= 10^5

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You can not just take the file and send it. When Polycarp trying to send a file in the social network "Codehorses", he encountered an unexpected problem. If the name of the file contains three or more "x" (lowercase Latin letters "x") in a row, the system considers that the file content does not correspond to the social network topic. In this case, the file is not sent and an error message is displayed.

Determine the minimum number of characters to remove from the file name so after that the name does not contain "xxx" as a substring. Print 0 if the file name does not initially contain a forbidden substring "xxx".

You can delete characters in arbitrary positions (not necessarily consecutive). If you delete a character, then the length of a string is reduced by $1$. For example, if you delete the character in the position $2$ from the string "exxxii", then the resulting string is "exxii".


-----Input-----

The first line contains integer $n$ $(3 \le n \le 100)$ — the length of the file name.

The second line contains a string of length $n$ consisting of lowercase Latin letters only — the file name.


-----Output-----

Print the minimum number of characters to remove from the file name so after that the name does not contain "xxx" as a substring. If initially the file name dost not contain a forbidden substring "xxx", print 0.


-----Examples-----
Input
6
xxxiii

Output
1

Input
5
xxoxx

Output
0

Input
10
xxxxxxxxxx

Output
8



-----Note-----

In the first example Polycarp tried to send a file with name contains number $33$, written in Roman numerals. But he can not just send the file, because it name contains three letters "x" in a row. To send the file he needs to remove any one of this letters.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Polycarp takes part in a math show. He is given n tasks, each consists of k subtasks, numbered 1 through k. It takes him t_{j} minutes to solve the j-th subtask of any task. Thus, time required to solve a subtask depends only on its index, but not on the task itself. Polycarp can solve subtasks in any order.

By solving subtask of arbitrary problem he earns one point. Thus, the number of points for task is equal to the number of solved subtasks in it. Moreover, if Polycarp completely solves the task (solves all k of its subtasks), he recieves one extra point. Thus, total number of points he recieves for the complete solution of the task is k + 1.

Polycarp has M minutes of time. What is the maximum number of points he can earn?


-----Input-----

The first line contains three integer numbers n, k and M (1 ≤ n ≤ 45, 1 ≤ k ≤ 45, 0 ≤ M ≤ 2·10^9).

The second line contains k integer numbers, values t_{j} (1 ≤ t_{j} ≤ 1000000), where t_{j} is the time in minutes required to solve j-th subtask of any task.


-----Output-----

Print the maximum amount of points Polycarp can earn in M minutes.


-----Examples-----
Input
3 4 11
1 2 3 4

Output
6

Input
5 5 10
1 2 4 8 16

Output
7



-----Note-----

In the first example Polycarp can complete the first task and spend 1 + 2 + 3 + 4 = 10 minutes. He also has the time to solve one subtask of the second task in one minute.

In the second example Polycarp can solve the first subtask of all five tasks and spend 5·1 = 5 minutes. Also he can solve the second subtasks of two tasks and spend 2·2 = 4 minutes. Thus, he earns 5 + 2 = 7 points in total.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A number is simply made up of digits.  
The number 1256 is made up of the digits 1, 2, 5, and 6.  
For 1256 there are 24 distinct permutations of the digits:  
1256, 1265, 1625, 1652, 1562, 1526, 2156, 2165, 2615, 2651, 2561, 2516,   
5126, 5162, 5216, 5261, 5621, 5612, 6125, 6152, 6251, 6215, 6521, 6512.
  
Your goal is to write a program that takes a number, n, and returns the average value of all distinct permutations of the digits in n.  Your answer should be rounded to the nearest integer. For the example above the return value would be 3889. * 
  
  n will never be negative
  
A few examples:
```python
permutation_average(2)
return 2

permutation_average(25)
>>> 25 + 52 = 77
>>> 77 / 2 = 38.5
return 39 *

permutation_average(20)
>>> 20 + 02 = 22
>>> 22 / 2 = 11
return 11

permutation_average(737)
>>> 737 + 377 + 773 = 1887
>>> 1887 / 3 = 629
return 629

```

Note: Your program should be able to handle numbers up to 6 digits long
~~~if:python
\* Python version 3 and above uses Banker Rounding so the expected values for those tests would be 3888 and 38 respectively
~~~
~~~if-not:python
\* ignore these marks, they're for Python only
~~~

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Define a $k$-periodic string as follows:

A string $s$ is $k$-periodic if the length of the string $|s|$ is a multiple of $k$, and if you chop the string up into $|s|/k$ substrings of length $k$, then each of those substrings (except the first) is the same as the previous substring, but with its last character moved to the front.

For example, the following string is $3$-periodic:abccabbcaabc

The above string can break up into substrings abc, cab, bca, and abc, and each substring (except the first) is a right-rotation of the previous substring (abc -> cab -> bca -> abc)

Given a string, determine the smallest k for which the string is k-periodic.

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The single line of input contains a string $s$ ($1 \le |s| \le 100$) consisting only of lowercase letters.

-----Output-----
Output the integer $k$, which is the smallest $k$ for which the input string is $k$-periodic.

-----Examples-----
Sample Input 1:
aaaaaaaa
Sample Output 1:
1

Sample Input 2:
abbaabbaabba
Sample Output 2:
2

Sample Input 3:
abcdef
Sample Output 3:
6

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