vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Biologists have discovered a strange DNA molecule, best described as a sequence of $N$ characters from the set $\{ A, B\} $. An unlikely sequence of mutations has resulted in a DNA strand consisting only of $A$’s. Biologists found that very odd, so they began studying the mutations in greater detail.

They discovered two types of mutations. One type results in changing any single character of the sequence ($A \rightarrow B$ or $B \rightarrow A$). The second type changes a whole prefix of the sequence, specifically replacing all characters in positions from $1$ to $K$ (for some $K$ between $1$ and $N$, inclusive) with the other character ($A$ with $B$, $B$ with $A$).

Compute the least possible number of mutations that could convert the starting molecule to its end state (containing only $A$ characters). Mutations can occur in any order.

-----Input-----
The first line of input contains the positive integer $N$ ($1 \le N \le 1000000$), the length of the molecule. The second line of input contains a string with $N$ characters, with each character being either $A$ or $B$. This string represents the starting state of the molecule.

-----Output-----
The first and only line of output must contain the required minimum number of mutations.

-----Examples-----
Sample Input 1:
4
ABBA
Sample Output 1:
2

Sample Input 2:
5
BBABB
Sample Output 2:
2

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Alice received a cake for her birthday! Her cake can be described by a convex polygon with $n$ vertices. No three vertices are collinear.

Alice will now choose exactly $k$ random vertices ($k{\ge }3$) from her cake and cut a piece, the shape of which is the convex polygon defined by those vertices. Compute the expected area of this piece of cake.

-----Input-----
Each test case will begin with a line with two space-separated integers $n$ and $k$ ($3\! \le \! k\! \le \! n\! \le \! 2500$), where $n$ is the number of vertices of the cake, and $k$ is the number of vertices of the piece that Alice cuts.

Each of the next $n$ lines will contain two space-separated real numbers $x$ and $y$ ($-10.0{\le }x,y{\le }10.0$), where $(x,y)$ is a vertex of the cake. The vertices will be listed in clockwise order. No three vertices will be collinear. All real numbers have at most $6$ digits after the decimal point.

-----Output-----
Output a single real number, which is the expected area of the piece of cake that Alice cuts out. Your answer will be accepted if it is within an absolute error of $10^{-6}$.

-----Examples-----
Sample Input 1:
4 3
0 0
1 1
2 1
1 0
Sample Output 1:
0.50000000

Sample Input 2:
5 5
0 4
4 2
4 1
3 -1
-2 4
Sample Output 2:
12.50000000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are attempting to climb up the roof to fix some leaks, and have to go buy a ladder. The ladder needs to reach to the top of the wall, which is $h$ centimeters high, and in order to be steady enough for you to climb it, the ladder can be at an angle of at most $v$ degrees from the ground. How long does the ladder have to be?

-----Input-----
The input consists of a single line containing two integers $h$ and $v$, with meanings as described above. You may assume that $1 \le h \le 10000$ and that $1 \le v \le 89$.

-----Output-----
Write a single line containing the minimum possible length of the ladder in centimeters, rounded up to the nearest integer.

-----Examples-----
Sample Input:
500 70
Sample Output:
533

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a hexagonal grid with $n$ rows, where $n$ is an odd integer. The rows are numbered $1$ to $n$ from top to bottom. The odd-numbered rows have exactly $n$ hexagons, and the even-numbered rows have exactly $n-1$ hexagons. Let’s denote the $j$-th hexagon in the $i$-th row by $(i, j)$.

For example, the below figure shows a hexagonal grid with $n = 3$.

Let’s assign an integer between $-1$ and $6$ to each hexagon. Let’s $a_{i, j}$ be the integer assigned to the hexagon $(i, j)$. The following figure shows one example assignment:

Let’s color some edges of some hexagons. A coloring is valid iff it satisfies the following conditions:
 - For every pair of valid indices $i$ and $j$, either $a_{i, j} = -1$, or $a_{i, j}$ is equal to the number of colored edges of the hexagon $(i, j)$.
 - The colored edges form one or more loops. Each loop must not self-intersect. Two different loops must not share any vertices or edges.

The following figure shows a valid coloring:

The following two figures show two invalid colorings. The one on the left does not satisfy the $1$st condition, and the one on the right does not satisfy the $2$nd condition.

How many valid colorings are there?

-----Input-----
The first line of the input contains a single integer $n$ ($n$ is an odd integer between $1$ and $7$). The next $n$ lines contain the numbers $a_{i, j}$ $(-1 \le a_{i, j} \le 6)$. The $i$-th line contains exactly $n$ integers if $i$ is odd, and $n-1$ integers otherwise.

-----Output-----
Print a single integer — the number of valid colorings.

-----Explanation of the sample input-----
The first sample was shown in the above figures.

The second example is shown below:

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

Sample Input 2:
7
-1 4 5 1 0 -1 -1
-1 3 2 0 0 1
-1 4 -1 1 0 -1 -1
1 3 4 2 2 4
0 2 3 -1 4 4 2
-1 4 4 3 3 2
1 -1 -1 -1 4 2 -1
Sample Output 2:
1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Ho ho! So you think you know integers, do you? Well then, young wizard, tell us what the Nth digit of the [Champernowne constant](https://en.wikipedia.org/wiki/Champernowne_constant) is!

The constant proceeds like this: `0.12345678910111213141516...`

I hope you see the pattern!

Conjure a function that will accept an integer, `n`, and return the (one-indexed) `n`th digit of Champernowne's constant. Can you get it to run in _constant_ time?

For example:

`n = 1` should return `0` (the very first digit)

`n = 2` should return `1` (we ignore the period character since it's not a digit!)

`n = 20` should return `4` (that's the `4` in the number `14`, 20th in sequence)

For any invalid values, such as `0` and below, or non-integers, return... `NaN`!

I hope (for your sake) that you've been practicing your mathemagical spells, because a naïve solution will _not_ be fast enough to compete in this championship!

Invoke with _precision_, and be wary of rounding errors in the realms of enormity!

May the best integer win!

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef Two and Chef Ten are playing a game with a number $X$. In one turn, they can multiply $X$ by $2$. The goal of the game is to make $X$ divisible by $10$.
Help the Chefs find the smallest number of turns necessary to win the game (it may be possible to win in zero turns) or determine that it is impossible.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single integer denoting the initial value of $X$. 

-----Output-----
For each test case, print a single line containing one integer — the minimum required number of turns or $-1$ if there is no way to win the game.

-----Constraints-----
- $1 \le T \le 1000$
- $0 \le X \le 10^9$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
3
10
25
1

-----Example Output-----
0
1
-1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are N infants registered in AtCoder, numbered 1 to N, and 2\times 10^5 kindergartens, numbered 1 to 2\times 10^5.
Infant i has a rating of A_i and initially belongs to Kindergarten B_i.
From now on, Q transfers will happen.
After the j-th transfer, Infant C_j will belong to Kindergarten D_j.
Here, we define the evenness as follows. For each kindergarten with one or more infants registered in AtCoder, let us find the highest rating of an infant in the kindergarten. The evenness is then defined as the lowest among those ratings.
For each of the Q transfers, find the evenness just after the transfer.

-----Constraints-----
 - 1 \leq N,Q \leq 2 \times 10^5
 - 1 \leq A_i \leq 10^9
 - 1 \leq C_j \leq N
 - 1 \leq B_i,D_j \leq 2 \times 10^5
 - All values in input are integers.
 - In the j-th transfer, Infant C_j changes the kindergarten it belongs to.

-----Input-----
Input is given from Standard Input in the following format:
N Q
A_1 B_1
A_2 B_2
:
A_N B_N
C_1 D_1
C_2 D_2
:
C_Q D_Q

-----Output-----
Print Q lines.
The j-th line should contain the evenness just after the j-th transfer.

-----Sample Input-----
6 3
8 1
6 2
9 3
1 1
2 2
1 3
4 3
2 1
1 2

-----Sample Output-----
6
2
6

Initially, Infant 1, 4 belongs to Kindergarten 1, Infant 2, 5 belongs to Kindergarten 2, and Infant 3, 6 belongs to Kindergarten 3.
After the 1-st transfer that makes Infant 4 belong to Kindergarten 3, Infant 1 belongs to Kindergarten 1, Infant 2, 5 belong to Kindergarten 2, and Infant 3, 4, 6 belong to Kindergarten 3. The highest ratings of an infant in Kindergarten 1, 2, 3 are 8, 6, 9, respectively. The lowest among them is 6, so the 1-st line in the output should contain 6.
After the 2-nd transfer that makes Infant 2 belong to Kindergarten 1, Infant 1, 2 belong to Kindergarten 1, Infant 5 belongs to Kindergarten 2, and Infant 3, 4, 6 belong to Kindergarten 3. The highest ratings of an infant in Kindergarten 1, 2, 3 are 8, 2, 9, respectively. The lowest among them is 2, so the 2-nd line in the output should contain 2.
After the 3-rd transfer that makes Infant 1 belong to Kindergarten 2, Infant 2 belongs to Kindergarten 1, Infant 1, 5 belong to Kindergarten 2, and Infant 3, 4, 6 belong to Kindergarten 3. The highest ratings of an infant in Kindergarten 1, 2, 3 are 6, 8, 9, respectively. The lowest among them is 6, so the 3-rd line in the output should contain 6.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Xenia the vigorous detective faced n (n ≥ 2) foreign spies lined up in a row. We'll consider the spies numbered from 1 to n from left to right. 

Spy s has an important note. He has to pass the note to spy f. Xenia interrogates the spies in several steps. During one step the spy keeping the important note can pass the note to one of his neighbours in the row. In other words, if this spy's number is x, he can pass the note to another spy, either x - 1 or x + 1 (if x = 1 or x = n, then the spy has only one neighbour). Also during a step the spy can keep a note and not pass it to anyone.

But nothing is that easy. During m steps Xenia watches some spies attentively. Specifically, during step t_{i} (steps are numbered from 1) Xenia watches spies numbers l_{i}, l_{i} + 1, l_{i} + 2, ..., r_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n). Of course, if during some step a spy is watched, he can't do anything: neither give the note nor take it from some other spy. Otherwise, Xenia reveals the spies' cunning plot. Nevertheless, if the spy at the current step keeps the note, Xenia sees nothing suspicious even if she watches him.

You've got s and f. Also, you have the steps during which Xenia watches spies and which spies she is going to watch during each step. Find the best way the spies should act in order to pass the note from spy s to spy f as quickly as possible (in the minimum number of steps).


-----Input-----

The first line contains four integers n, m, s and f (1 ≤ n, m ≤ 10^5; 1 ≤ s, f ≤ n; s ≠ f; n ≥ 2). Each of the following m lines contains three integers t_{i}, l_{i}, r_{i} (1 ≤ t_{i} ≤ 10^9, 1 ≤ l_{i} ≤ r_{i} ≤ n). It is guaranteed that t_1 < t_2 < t_3 < ... < t_{m}.


-----Output-----

Print k characters in a line: the i-th character in the line must represent the spies' actions on step i. If on step i the spy with the note must pass the note to the spy with a lesser number, the i-th character should equal "L". If on step i the spy with the note must pass it to the spy with a larger number, the i-th character must equal "R". If the spy must keep the note at the i-th step, the i-th character must equal "X".

As a result of applying the printed sequence of actions spy s must pass the note to spy f. The number of printed characters k must be as small as possible. Xenia must not catch the spies passing the note.

If there are miltiple optimal solutions, you can print any of them. It is guaranteed that the answer exists.


-----Examples-----
Input
3 5 1 3
1 1 2
2 2 3
3 3 3
4 1 1
10 1 3

Output
XXRR

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
On a planet called RUIZ LAND, which is ruled by the queen, Erika Ruiz. Each person on that planet has a strength value (strength value >0).
That planet has a special rule made by the queen that a boy and a girl will form a couple if their Hate value is a prime number where $Hate$ is given by the formula:-
Hate = (boy's strength value)  XOR (girl's strength value )
You are given $N$ numbers denoting the strength value of $N$ girls, and each of the $N$ girls has to form a couple with a boy such that sum of $Hate$ value of all the $N$ couples will be minimum.
You need to print the strength value of each boy, Where the boy at index $i$ will form a couple with the girl at index $i$, where $1 \leq i \leq N$.
Assume that you can always find at least one boy having that strength for each girl.

-----Input:-----
- First line will contain $N$, the number of Girls. 
- Next line contains $N$ numbers separated by space denoting strength value for each girl.

-----Output:-----
Print the required $N$ numbers denoting strength of boys.

-----Constraints-----
- $1 \leq N \leq 100000$
- $1 \leq A_i \leq 10^9$ , (where $1 \leq i \leq N$) and $A_i$ denotes strength of i'th girl.

-----Sample Input:-----
2
10 16

-----Sample Output:-----
8 18

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

Given the sequence a_1, a_2, .., a_N.

In the query, answer the number of terms whose value is l or more and r or less.

input


N Q
a_1 a_2 ... a_N
l_1 r_1
l_2 r_2
::
l_q r_q


output


ans_1
ans_2
::
ans_q


On line i, output the answer to the i-th query, that is, the number of j such as l_i \ leq a_j \ leq r_i.

Constraint

* 1 \ leq N, Q \ leq 10 ^ 5
* 1 \ leq a_i \ leq 10 ^ 9
* 1 \ leq l_i \ leq r_i \ leq 10 ^ 9



Input example


6 3
8 6 9 1 2 1
2 8
1 7
3 5


Output example


3
Four
0






Example

Input

6 3
8 6 9 1 2 1
2 8
1 7
3 5


Output

3
4
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has an array A = (A1, A2, ..., AN), which has N integers in it initially. Chef found that for i ≥ 1, if Ai > 0, Ai+1 > 0, and Ai+2 exists, then he can decrease both Ai, and Ai+1 by one and increase Ai+2 by one. If Ai+2 doesn't exist, but Ai > 0, and Ai+1 > 0, then he can decrease both Ai, and Ai+1 (which will be the currently last two elements of the array) by one and add a new element at the end, whose value is 1.
Now Chef wants to know the number of different arrays that he can make from A using this operation as many times as he wishes. Help him find this, and because the answer could be very large, he is fine with you reporting the answer modulo 109+7.
Two arrays are same if they have the same number of elements and if each corresponding element is the same. For example arrays (2,1,1) and (1,1,2) are different. 

-----Input-----
- The first line of the input contains a single integer T denoting the number of test cases.
- The first line contains a single integer N denoting the initial number of elements in A.
- The second line contains N space-separated integers: A1, A2, ... , AN. 

-----Output-----
For each test case, output answer modulo 109+7 in a single line. 

-----Constraints-----
- 1 ≤ T ≤ 5
- 1 ≤ N ≤ 50
- 0 ≤ Ai ≤ 50

-----Subtasks-----
- Subtask 1 (20 points) : 1 ≤ N ≤ 8, 0 ≤ Ai ≤ 4
- Subtask 2 (80 points) : Original constraints

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

Output:
9
4
9

-----Explanation-----
Example case 1.
We'll list the various single steps that you can take (ie. in one single usage of the operation):
- (2, 3, 1) → (2, 2, 0, 1)
- (2, 2, 0, 1) → (1, 1, 1, 1)
- (1, 1, 1, 1) → (1, 1, 0, 0, 1)
- (1, 1, 0, 0, 1) → (0, 0, 1, 0, 1)
- (1, 1, 1, 1) → (1, 0, 0, 2)
- (1, 1, 1, 1) → (0, 0, 2, 1)
- (2, 3, 1) → (1, 2, 2)
- (1, 2, 2) → (0, 1, 3)

So all the arrays you can possibly get are: 
(2, 3, 1), (2, 2, 0, 1), (1, 1, 1, 1), (1, 1, 0, 0, 1), (0, 0, 1, 0, 1), (1, 0, 0, 2), (0, 0, 2, 1), (1, 2, 2), and (0, 1, 3)
Since there are 9 different arrays that you can reach, the answer is 9.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Consider the following expansion:
```Haskell
solve("3(ab)") = "ababab" -- "ab" repeats 3 times
solve("2(a3(b))" = "abbbabbb" -- "a3(b)" == "abbb" repeats twice.
```

Given a string, return the expansion of that string. 

Input will consist of only lowercase letters and numbers (1 to 9) in valid parenthesis. There will be no letters or numbers after the last closing parenthesis.

More examples in test cases. 

Good luck!

Please also try [Simple time difference](https://www.codewars.com/kata/5b76a34ff71e5de9db0000f2)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Polycarpus has a sequence, consisting of n non-negative integers: a_1, a_2, ..., a_{n}.

Let's define function f(l, r) (l, r are integer, 1 ≤ l ≤ r ≤ n) for sequence a as an operation of bitwise OR of all the sequence elements with indexes from l to r. Formally: f(l, r) = a_{l} | a_{l} + 1 | ...  | a_{r}. 

Polycarpus took a piece of paper and wrote out the values of function f(l, r) for all l, r (l, r are integer, 1 ≤ l ≤ r ≤ n). Now he wants to know, how many distinct values he's got in the end. 

Help Polycarpus, count the number of distinct values of function f(l, r) for the given sequence a.

Expression x | y means applying the operation of bitwise OR to numbers x and y. This operation exists in all modern programming languages, for example, in language C++ and Java it is marked as "|", in Pascal — as "or".


-----Input-----

The first line contains integer n (1 ≤ n ≤ 10^5) — the number of elements of sequence a. The second line contains n space-separated integers a_1, a_2, ..., a_{n} (0 ≤ a_{i} ≤ 10^6) — the elements of sequence a.


-----Output-----

Print a single integer — the number of distinct values of function f(l, r) for the given sequence a.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.


-----Examples-----
Input
3
1 2 0

Output
4
Input
10
1 2 3 4 5 6 1 2 9 10

Output
11


-----Note-----

In the first test case Polycarpus will have 6 numbers written on the paper: f(1, 1) = 1, f(1, 2) = 3, f(1, 3) = 3, f(2, 2) = 2, f(2, 3) = 2, f(3, 3) = 0. There are exactly 4 distinct numbers among them: 0, 1, 2, 3.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
A string is called palindrome if it reads the same from left to right and from right to left. For example "kazak", "oo", "r" and "mikhailrubinchikkihcniburliahkim" are palindroms, but strings "abb" and "ij" are not.

You are given string *s* consisting of lowercase Latin letters. At once you can choose any position in the string and change letter in that position to any other lowercase letter. So after each changing the length of the string doesn't change. At first you can change some letters in *s*. Then you can permute the order of letters as you want. Permutation doesn't count as changes. 

You should obtain palindrome with the minimal number of changes. If there are several ways to do that you should get the lexicographically (alphabetically) smallest palindrome. So firstly you should minimize the number of changes and then minimize the palindrome lexicographically.

Input Specification:
The only line contains string *s* (1<=≤<=|*s*|<=≤<=2·105) consisting of only lowercase Latin letters.

Output Specification:
Print the lexicographically smallest palindrome that can be obtained with the minimal number of changes.

Demo Input:
['aabc\n', 'aabcd\n']

Demo Output:
['abba\n', 'abcba\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
“The Drinking Musicians”, a widely known and popular folk group, are coming to your town. The musicians are known not only by their playing skills, but also their rough character. They never arrive on time, don’t know which town they’re in, and frequently have trouble finding the stage.

Additionally, during the concert, each of the musicians at one point takes a break. If three or more of them are on a break at the same time, they start stirring trouble in town and the rest of the group start panicking and playing the wrong chords.

The concert will be $T$ minutes long, during which each of the $N$ members will take a break. The length of the break is known for each member.

Help the organizer of the concert by writing a program that determines how to schedule the breaks of the members so that, at any given moment, at most two are absent from the stage. All breaks must be entirely during the concert.

-----Input-----
The first line of input contains the integers $T$ and $N$ ($1 \le T \le 5000$, $1 \le N \le 500$), the length of the concert in minutes and the number of musicians in the group.

The next line contains $N$ integers (each between $1$ and $T$ inclusive) separated by single spaces, the length of the break in minutes for each member.

Note: The input data will be such that a solution, although not necessarily unique, will always exist.

-----Output-----
For each musician output one integer, the number of minutes the musician will spend on stage before going on the break. Output the musicians in the same order they were given in the input.

-----Examples-----
Sample Input:
8 3
4 4 4
Sample Output:
0 2 4

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Xenia lives in a city that has *n* houses built along the main ringroad. The ringroad houses are numbered 1 through *n* in the clockwise order. The ringroad traffic is one way and also is clockwise.

Xenia has recently moved into the ringroad house number 1. As a result, she's got *m* things to do. In order to complete the *i*-th task, she needs to be in the house number *a**i* and complete all tasks with numbers less than *i*. Initially, Xenia is in the house number 1, find the minimum time she needs to complete all her tasks if moving from a house to a neighboring one along the ringroad takes one unit of time.

Input Specification:
The first line contains two integers *n* and *m* (2<=≤<=*n*<=≤<=105,<=1<=≤<=*m*<=≤<=105). The second line contains *m* integers *a*1,<=*a*2,<=...,<=*a**m* (1<=≤<=*a**i*<=≤<=*n*). Note that Xenia can have multiple consecutive tasks in one house.

Output Specification:
Print a single integer — the time Xenia needs to complete all tasks.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Demo Input:
['4 3\n3 2 3\n', '4 3\n2 3 3\n']

Demo Output:
['6\n', '2\n']

Note:
In the first test example the sequence of Xenia's moves along the ringroad looks as follows: 1 → 2 → 3 → 4 → 1 → 2 → 3. This is optimal sequence. So, she needs 6 time units.

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