vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Music Macro Language (MML) is a language for textual representation of musical scores. Although there are various dialects of MML, all of them provide a set of commands to describe scores, such as commands for notes, rests, octaves, volumes, and so forth.

In this problem, we focus on rests, i.e. intervals of silence. Each rest command consists of a command specifier ‘R’ followed by a duration specifier. Each duration specifier is basically one of the following numbers: ‘1’, ‘2’, ‘4’, ‘8’, ‘16’, ‘32’, and ‘64’, where ‘1’ denotes a whole (1), ‘2’ a half (1/2), ‘4’ a quarter (1/4), ‘8’ an eighth (1/8), and so on. This number is called the base duration, and optionally followed by one or more dots. The first dot adds the duration by the half of the base duration. For example, ‘4.’ denotes the duration of ‘4’ (a quarter) plus ‘8’ (an eighth, i.e. the half of a quarter), or simply 1.5 times as long as ‘4’. In other words, ‘R4.’ is equivalent to ‘R4R8’. In case with two or more dots, each extra dot extends the duration by the half of the previous one. Thus ‘4..’ denotes the duration of ‘4’ plus ‘8’ plus ‘16’, ‘4...’ denotes the duration of ‘4’ plus ‘8’ plus ‘16’ plus ‘32’, and so on. The duration extended by dots cannot be shorter than ‘64’. For exapmle, neither ‘64.’ nor ‘16...’ will be accepted since both of the last dots indicate the half of ‘64’ (i.e. the duration of 1/128).

In this problem, you are required to write a program that finds the shortest expressions equivalent to given sequences of rest commands.



Input

The input consists of multiple datasets. The first line of the input contains the number of datasets N. Then, N datasets follow, each containing a sequence of valid rest commands in one line. You may assume that no sequence contains more than 100,000 characters.

Output

For each dataset, your program should output the shortest expression in one line. If there are multiple expressions of the shortest length, output the lexicographically smallest one.

Example

Input

3
R2R2
R1R2R4R8R16R32R64
R1R4R16


Output

R1
R1......
R16R1R4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Every year the professor selects the top two students from his class and takes them on a fun filled field trip, this year Ali and Zafar were selected.
The professor took them to a place where there was a never-ending queue of solid metal cubes. The professor could see $n$ cubes at a time. On the day before, he had painted the first $n$ cubes from the left with various colours.
Ali was allowed to choose any painted cube to initially stand on (say $X$). Zafar was asked to stand on the last painted cube (the $n^{th}$ cube) with the professor.
The two students were given an activity each:
- Ali had to shout out the colour of the cube he is standing on.
- Zafar had to paint the adjacent cube on the right of him with that colour.
Both Ali and Zafar had to take one step to the right each time they performed their activity.
The Professor jumped along with Zafar, and never left his side. Throughout the activity he was looking leftwards keeping an eye on Ali. They were given a gold star and were allowed to go home when all the cubes that the professor could see at the time were painted with the same color.
Ali wanted to choose a position furthest from the professor and also wanted the gold star.
Can you help Ali to choose this position $X$?
The cubes are numbered from 1 starting from the first painted cube.
The colours are represented as integers.

-----Input:-----
- The first line contains one integer n, the number of cubes initially painted.
- The second line contains n space-separated integers: $a_1$, $a_2$, $\dots$, $a_n$, the colours the professor chose for the first $n$ cubes.

-----Output:-----
Print a single line containing one integer $X$, the position Ali should initially stand on.

-----Constraints-----
- $1 \leq n \leq 10^{6}$
- $0 \leq a_i \leq 999$

-----Sample Input 1:-----
4

3 3 8 8   

-----Sample Output 1:-----
3

-----Sample Input 2:-----
4

2 8 7 3

-----Sample Output 2:-----
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a positive integer n, generate a square matrix filled with elements from 1 to n2 in spiral order.

Example:


Input: 3
Output:
[
 [ 1, 2, 3 ],
 [ 8, 9, 4 ],
 [ 7, 6, 5 ]
]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
=====Function Descriptions=====
any()
This expression returns True if any element of the iterable is true. If the iterable is empty, it will return False.

Code
>>> any([1>0,1==0,1<0])
True
>>> any([1<0,2<1,3<2])
False

all()
This expression returns True if all of the elements of the iterable are true. If the iterable is empty, it will return True.

Code
>>> all(['a'<'b','b'<'c'])
True
>>> all(['a'<'b','c'<'b'])
False

=====Problem Statement=====
You are given a space separated list of integers. If all the integers are positive, then you need to check if any integer is a palindromic integer.

=====Input Format=====
The first line contains an integer N. N is the total number of integers in the list. The second line contains the space separated list of N integers.

=====Constraints=====
0<N<100

=====Output Format=====
Print True if all the conditions of the problem statement are satisfied. Otherwise, print False.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Monocarp is playing a computer game once again. He is a wizard apprentice, who only knows a single spell. Luckily, this spell can damage the monsters.

The level he's currently on contains $n$ monsters. The $i$-th of them appears $k_i$ seconds after the start of the level and has $h_i$ health points. As an additional constraint, $h_i \le k_i$ for all $1 \le i \le n$. All $k_i$ are different.

Monocarp can cast the spell at moments which are positive integer amounts of second after the start of the level: $1, 2, 3, \dots$ The damage of the spell is calculated as follows. If he didn't cast the spell at the previous second, the damage is $1$. Otherwise, let the damage at the previous second be $x$. Then he can choose the damage to be either $x + 1$ or $1$. A spell uses mana: casting a spell with damage $x$ uses $x$ mana. Mana doesn't regenerate.

To kill the $i$-th monster, Monocarp has to cast a spell with damage at least $h_i$ at the exact moment the monster appears, which is $k_i$.

Note that Monocarp can cast the spell even when there is no monster at the current second.

The mana amount required to cast the spells is the sum of mana usages for all cast spells. Calculate the least amount of mana required for Monocarp to kill all monsters.

It can be shown that it's always possible to kill all monsters under the constraints of the problem.


-----Input-----

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.

The first line of the testcase contains a single integer $n$ ($1 \le n \le 100$) — the number of monsters in the level.

The second line of the testcase contains $n$ integers $k_1 < k_2 < \dots < k_n$ ($1 \le k_i \le 10^9$) — the number of second from the start the $i$-th monster appears at. All $k_i$ are different, $k_i$ are provided in the increasing order.

The third line of the testcase contains $n$ integers $h_1, h_2, \dots, h_n$ ($1 \le h_i \le k_i \le 10^9$) — the health of the $i$-th monster.

The sum of $n$ over all testcases doesn't exceed $10^4$.


-----Output-----

For each testcase, print a single integer — the least amount of mana required for Monocarp to kill all monsters.


-----Examples-----

Input
3
1
6
4
2
4 5
2 2
3
5 7 9
2 1 2
Output
10
6
7


-----Note-----

In the first testcase of the example, Monocarp can cast spells $3, 4, 5$ and $6$ seconds from the start with damages $1, 2, 3$ and $4$, respectively. The damage dealt at $6$ seconds is $4$, which is indeed greater than or equal to the health of the monster that appears.

In the second testcase of the example, Monocarp can cast spells $3, 4$ and $5$ seconds from the start with damages $1, 2$ and $3$, respectively.

In the third testcase of the example, Monocarp can cast spells $4, 5, 7, 8$ and $9$ seconds from the start with damages $1, 2, 1, 1$ and $2$, respectively.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Let *D*(*x*) be the number of positive divisors of a positive integer *x*. For example, *D*(2)<==<=2 (2 is divisible by 1 and 2), *D*(6)<==<=4 (6 is divisible by 1, 2, 3 and 6).

You are given an array *a* of *n* integers. You have to process two types of queries:
 1.  REPLACE *l* *r* — for every  replace *a**i* with *D*(*a**i*); 1.  SUM *l* *r* — calculate . 
Print the answer for each SUM query.

Input Specification:
The first line contains two integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=3·105) — the number of elements in the array and the number of queries to process, respectively.

The second line contains *n* integers *a*1, *a*2, ..., *a**n* (1<=≤<=*a**i*<=≤<=106) — the elements of the array.

Then *m* lines follow, each containing 3 integers *t**i*, *l**i*, *r**i* denoting *i*-th query. If *t**i*<==<=1, then *i*-th query is REPLACE *l**i* *r**i*, otherwise it's SUM *l**i* *r**i* (1<=≤<=*t**i*<=≤<=2, 1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*).

There is at least one SUM query.

Output Specification:
For each SUM query print the answer to it.

Demo Input:
['7 6\n6 4 1 10 3 2 4\n2 1 7\n2 4 5\n1 3 5\n2 4 4\n1 5 7\n2 1 7\n']

Demo Output:
['30\n13\n4\n22\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Consider the palindromic prime numbers(Numbers which are palindrome as well as prime).Let p be the product of non zero digits of a nth palindromic prime number.Let product of digits of a palindromic prime is multiplied by a number m to generate number q(q=p*m).Your task is simple; you have to find number of divisors of q.

INPUT:

First Line contains number of test cases t.
Second line contains two space separated numbers n and m.

OUTPUT:

Output each test case in new line number of divisors of q.

CONSTRAINTS:

t ≤ 10000
n ≤ 113
1 ≤ m ≤ 100

SAMPLE INPUT
1
2 1

SAMPLE OUTPUT
2

Explanation

2nd palindromic prime is 3 value of m is 1 so value of q is 3.Numbers of divisors of 3 is 2(1 and 3)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# Task
Imagine `n` horizontal lines and `m` vertical lines.

Some of these lines intersect, creating rectangles.

How many rectangles are there?

# Examples

For `n=2, m=2,` the result should be `1`.

there is only one 1x1 rectangle.

For `n=2, m=3`, the result should be `3`.

there are two 1x1 rectangles and one 1x2 rectangle. So `2 + 1 = 3`.

For n=3, m=3, the result should be `9`.

there are four 1x1 rectangles, two 1x2 rectangles, two 2x1 rectangles and one 2x2 rectangle. So `4 + 2 + 2 + 1 = 9`.



# Input & Output


- `[input]` integer `n`

Number of horizontal lines.

Constraints: `0 <= n <= 100`


- `[input]` integer `m`

Number of vertical lines.

Constraints: `0 <= m <= 100`


- `[output]` an integer

Number of rectangles.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The "Russian Peasant Method" is an old algorithm used by Russian peasants (and before them ancient Egyptians) to perform multiplication.  Consider that X and Y are two numbers.  X can be any number but Y must be a positive integer. To multiply X and Y:

1. Let the product = 0
2. If Y is odd, then the product = product + X
3. X = X + X
4. Y = integer part of Y / 2 
5. if Y is nonzero, repeat from step 2; otherwise the algorithm terminates and returns the product.

For example:

Let X = 10

Let Y = 5

X: 10 20 40 80

Y: 5  2  1  0

product = 10 + 40 = 50

Note: usage of multiplication is of course forbidden...

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

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Problem Description:
Anfisa the monkey learns to type. She is yet unfamiliar with the "space" key and can only type in lower-case Latin letters. Having typed for a fairly long line, Anfisa understood that it would be great to divide what she has written into *k* lines not shorter than *a* and not longer than *b*, for the text to resemble human speech more. Help Anfisa.

Input Specification:
The first line contains three integers *k*, *a* and *b* (1<=≤<=*k*<=≤<=200, 1<=≤<=*a*<=≤<=*b*<=≤<=200). The second line contains a sequence of lowercase Latin letters — the text typed by Anfisa. It is guaranteed that the given line is not empty and its length does not exceed 200 symbols.

Output Specification:
Print *k* lines, each of which contains no less than *a* and no more than *b* symbols — Anfisa's text divided into lines. It is not allowed to perform any changes in the text, such as: deleting or adding symbols, changing their order, etc. If the solution is not unique, print any of them. If there is no solution, print "No solution" (without quotes).

Demo Input:
['3 2 5\nabrakadabra\n', '4 1 2\nabrakadabra\n']

Demo Output:
['ab\nrakad\nabra\n', 'No solution\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You're familiar with [list slicing](https://docs.python.org/3/library/functions.html#slice) in Python and know, for example, that:

```python
>>> ages = [12, 14, 63, 72, 55, 24]
>>> ages[2:4]
[63, 72]
>>> ages[2:]
[63, 72, 55, 24]
>>> ages[:3]
[12, 14, 63]
```

write a function `inverse_slice()` that takes three arguments: a list `items`, an integer `a` and an integer `b`. The function should return a new list with the slice specified by `items[a:b]` _excluded_. For example:

```python
>>>inverse_slice([12, 14, 63, 72, 55, 24], 2, 4)
[12, 14, 55, 24]
```

The input will always be a valid list, `a` and `b` will always be different integers equal to or greater than zero, but they _may_ be zero or be larger than the length of the list.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:
 - f(b,n) = n, when n < b
 - f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b
Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b,
and n \ {\rm mod} \ b denotes the remainder of n divided by b.
Less formally, f(b,n) is equal to the sum of the digits of n written in base b.
For example, the following hold:
 - f(10,\,87654)=8+7+6+5+4=30
 - f(100,\,87654)=8+76+54=138
You are given integers n and s.
Determine if there exists an integer b (b \geq 2) such that f(b,n)=s.
If the answer is positive, also find the smallest such b.

-----Constraints-----
 - 1 \leq n \leq 10^{11}
 - 1 \leq s \leq 10^{11}
 - n,\,s are integers.

-----Input-----
The input is given from Standard Input in the following format:
n
s

-----Output-----
If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b.
If such b does not exist, print -1 instead.

-----Sample Input-----
87654
30

-----Sample Output-----
10


Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A no is said to be  k-Almost Prime Number if it  has exactly k prime factors (not necessary distinct). Your task is to complete the function printKAlmostPrimes which takes two argument k and N and prints the  first N numbers that are k prime. 
Input:
The first line of input is the no of test cases . Then T test cases follow . Each test case contains two integers k and N .
Output:
For each test case output will be N space separated first N numbers that are k prime numbers.
Constraints:
1<=T<=100
1<=k<=10
1<=N<=50
Example(To be used only for expected output):
Input
1
2 5
Output
4 6 9 10 14
Explanation
In above test case
4 has two prime factors, 2 x 2
6 has two prime factors, 2 x 3
Similarly, 9(3 x 3), 10(2 x 5) and 14(2 x 7)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
After solving some Graph Theory related problems KBG challenged Sameer to solve the following problem.

There is an undirected graph consisting of N vertices numbered from 1 to N.

For every pair of vertices u and v (u \neq v) in the graph, there is a undirected weighted edge between u and v if and only if u divides v, with weight \frac{v}{u}. Note that such a graph will not have self loops or multiple edges.

You must answer Q queries. In each query you are given two vertices u and v. You must find the minimum distance from vertex u to vertex v.

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

- The first line contains a single integer T — the number of test cases. Then the test cases follow.
- The first line of each test case contains two integers N and Q — the number of vertices and the number of queries.
- The next Q lines contain two space-separated integers u and v — vertices corresponding to the query.

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

For each test case, print Q lines — the answers to the Q queries.

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

$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$ 
$1 ≤ Q ≤ 10^{5}$
$1 ≤ u , v ≤ N$
- The sum of $N$ over all test cases does not exceed $10^{5}$.
- The sum of $Q$ over all test cases does not exceed $10^{5}$.

------ subtasks ------ 

Subtask 1 (100 points): Original Constraints.

----- Sample Input 1 ------ 
1
6 2
3 6
2 3

----- Sample Output 1 ------ 
2
5

----- explanation 1 ------ 
Test case 1: Given $N = 6$ and $2$ queries..
- In the first query, $u = 3$ and $v = 6$. So there is an edge from $6$ to $3$ with weight $2$. we can use that path and minimum cost will be $2$.

- In the second query, $u = 2$ and $v = 3$. So there is an edge from $2$ to $1$ with weight $2$ and from $3$ to $1$ with weight $3$. we can use that path $(2 \rightarrow 1 \rightarrow 3)$ and minimum cost will be $5$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
As I was cleaning up the warehouse, I found an old document that describes how to get to the treasures of my ancestors. The following was written in this ancient document.


1. First, stand 1m east of the well on the outskirts of the town and turn straight toward the well.
2. Turn clockwise 90 degrees, go straight for 1m, and turn straight toward the well.
3. Turn clockwise 90 degrees, go straight for 1m, and turn straight toward the well.
Four.                   〃
Five.                   〃
6::


From the second line onward, exactly the same thing was written. You wanted to find the treasure, but found it awkward. Unlike in the past, the building is in the way, and you can't see the well even if you go straight in the direction of the well, or you can't go straight even if you try to go straight for 1m. In addition, this ancient document has nearly 1000 lines, and it takes a considerable amount of time and physical strength to work according to the ancient document. Fortunately, however, you can take advantage of your computer.

Enter the number of lines n written in the old document and create a program that outputs the location of the treasure. However, n is a positive integer between 2 and 1,000.



input

Given multiple datasets. For each dataset, one integer n, which represents the number of lines in the old document, is given on each line.

The input ends with -1. The number of datasets does not exceed 50.

output

Assuming that there is a treasure at the position x (m) to the east and y (m) to the north from the well on the outskirts of the town, output each data set in the following format.


x
y


The output is a real number and may contain an error of 0.01 or less.

Example

Input

3
6
-1


Output

0.29
1.71
-2.31
0.80

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We have a string S consisting of uppercase English letters. Additionally, an integer N will be given.
Shift each character of S by N in alphabetical order (see below), and print the resulting string.
We assume that A follows Z. For example, shifting A by 2 results in C (A \to B \to C), and shifting Y by 3 results in B (Y \to Z \to A \to B).

-----Constraints-----
 - 0 \leq N \leq 26
 - 1 \leq |S| \leq 10^4
 - S consists of uppercase English letters.

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

-----Output-----
Print the string resulting from shifting each character of S by N in alphabetical order.

-----Sample Input-----
2
ABCXYZ

-----Sample Output-----
CDEZAB

Note that A follows Z.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We have a long seat of width X centimeters.
There are many people who wants to sit here. A person sitting on the seat will always occupy an interval of length Y centimeters.
We would like to seat as many people as possible, but they are all very shy, and there must be a gap of length at least Z centimeters between two people, and between the end of the seat and a person.
At most how many people can sit on the seat?

-----Constraints-----
 - All input values are integers.
 - 1 \leq X, Y, Z \leq 10^5
 - Y+2Z \leq X

-----Input-----
Input is given from Standard Input in the following format:
X Y Z

-----Output-----
Print the answer.

-----Sample Input-----
13 3 1

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

There is just enough room for three, as shown below:
Figure

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given is a string S. Replace every character in S with x and print the result.

-----Constraints-----
 - S is a string consisting of lowercase English letters.
 - The length of S is between 1 and 100 (inclusive).

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

-----Output-----
Replace every character in S with x and print the result.

-----Sample Input-----
sardine

-----Sample Output-----
xxxxxxx

Replacing every character in S with x results in xxxxxxx.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# Task
 Pero has been into robotics recently, so he decided to make a robot that checks whether a deck of poker cards is complete.

 He’s already done a fair share of work - he wrote a programme that recognizes the suits of the cards. For simplicity’s sake, we can assume that all cards have a suit and a number.

 The suit of the card is one of the characters `"P", "K", "H", "T"`, and the number of the card is an integer between `1` and `13`. The robot labels each card in the format `TXY` where `T` is the suit and `XY` is the number. If the card’s number consists of one digit, then X = 0. For example, the card of suit `"P"` and number `9` is labelled `"P09"`.

 A complete deck has `52` cards in total. For each of the four suits there is exactly one card with a number between `1` and `13`.

 The robot has read the labels of all the cards in the deck and combined them into the string `s`.
 
 Your task is to help Pero finish the robot by writing a program that reads the string made out of card labels and returns the number of cards that are missing for each suit.

 If there are two same cards in the deck, return array with `[-1, -1, -1, -1]` instead.

# Input/Output


 - `[input]` string `s`

  A correct string of card labels. 0 ≤ |S| ≤ 1000


 - `[output]` an integer array

  Array of four elements, representing the number of missing card of suits `"P", "K", "H", and "T"` respectively. If there are two same cards in the deck, return `[-1, -1, -1, -1]` instead.


# Example

 For `s = "P01K02H03H04"`, the output should be `[12, 12, 11, 13]`.
 
 `1` card from `"P"` suit, `1` card from `"K"` suit, `2` cards from `"H"` suit, no card from `"T"` suit.
 
 For `s = "H02H10P11H02"`, the output should be `[-1, -1, -1, -1]`.
 
 There are two same cards `"H02"` in the string `s`.

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