vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Martha is interviewing at Subway. One of the rounds of the interview requires her to cut a bread of size $l\times b$ into smaller identical pieces such that each piece is a square having maximum possible side length with no left over piece of bread.

Input Format

The first line contains an integer $\mathbf{T}$. $\mathbf{T}$ lines follow. Each line contains two space separated integers $\boldsymbol{l}$ and $\boldsymbol{b}$ which denote length and breadth of the bread. 

Constraints

$1\leq T\leq1000$
$1\leq l,b\leq1000$

Output Format

$\mathbf{T}$ lines, each containing an integer that denotes the number of squares of maximum size, when the bread is cut as per the given condition.

Sample Input 0
2
2 2
6 9

Sample Output 0
1
6

Explanation 0

The 1^{st} testcase has a bread whose original dimensions are $2\times2$, the bread is uncut and is a square. Hence the answer is 1. 

The 2^{nd} testcase has a bread of size $6\times9$. We can cut it into 54 squares of size $1\times1$, 6 of size $3\times3$. For other sizes we will have leftovers. Hence, the number of squares of maximum size that can be cut is 6.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We will define the median of a sequence b of length M, as follows:
 - Let b' be the sequence obtained by sorting b in non-decreasing order. Then, the value of the (M / 2 + 1)-th element of b' is the median of b. Here, / is integer division, rounding down.
For example, the median of (10, 30, 20) is 20; the median of (10, 30, 20, 40) is 30; the median of (10, 10, 10, 20, 30) is 10.
Snuke comes up with the following problem.
You are given a sequence a of length N.
For each pair (l, r) (1 \leq l \leq r \leq N), let m_{l, r} be the median of the contiguous subsequence (a_l, a_{l + 1}, ..., a_r) of a.
We will list m_{l, r} for all pairs (l, r) to create a new sequence m.
Find the median of m.

-----Constraints-----
 - 1 \leq N \leq 10^5
 - a_i is an integer.
 - 1 \leq a_i \leq 10^9

-----Input-----
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N

-----Output-----
Print the median of m.

-----Sample Input-----
3
10 30 20

-----Sample Output-----
30

The median of each contiguous subsequence of a is as follows:
 - The median of (10) is 10.
 - The median of (30) is 30.
 - The median of (20) is 20.
 - The median of (10, 30) is 30.
 - The median of (30, 20) is 30.
 - The median of (10, 30, 20) is 20.
Thus, m = (10, 30, 20, 30, 30, 20) and the median of m is 30.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.

Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding *n* cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).

The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints. 

A color hint goes like that: a player names some color and points at all the cards of this color. 

Similarly goes the value hint. A player names some value and points at all the cards that contain the value.

Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.

Input Specification:
The first line contains integer *n* (1<=≤<=*n*<=≤<=100) — the number of Borya's cards. The next line contains the descriptions of *n* cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.

Output Specification:
Print a single integer — the minimum number of hints that the other players should make.

Demo Input:
['2\nG3 G3\n', '4\nG4 R4 R3 B3\n', '5\nB1 Y1 W1 G1 R1\n']

Demo Output:
['0\n', '2\n', '4\n']

Note:
In the first sample Borya already knows for each card that it is a green three.

In the second sample we can show all fours and all red cards.

In the third sample you need to make hints about any four colors.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
As a Swede, you hold a deep love for the traditional Thursday lunch of pea soup and pancakes. You love it so much, in fact, that you will eat it any meal it is available. You find yourself looking at the menus for all your favorite restaurants every day to see if this combination is available, and realized you can do this more easily with a program. Given a list of restaurant menus, decide where to eat. 

-----Input-----
The first line of input contains a number $n$ ($1 \le n \le 10$), the number of restaurants. Then follow the $n$ restaurant menus. Each menu starts with a line containing a number $k$ ($1 \le k \le 10$), the number of menu items for the day. The remainder of the menu consists of $k + 1$ lines, each containing a nonempty string of at most $100$ characters. The first of these lines is the restaurant name, and the rest are menu items. Strings consist only of lower case letters ‘a’-‘z’ and spaces, and they always start and end with a letter. All restaurant names are unique.

-----Output-----
Output a single line. If at least one restaurant has both “pea soup” and “pancakes” as menu items, output the name of the first of those restaurants, by the order in which the restaurants appear in the input. Otherwise, output “Anywhere is fine I guess”.

-----Examples-----
Sample Input:
2
2
q
potatoes
salad
3
nymble
pancakes
pea soup
punsch
Sample Output:
nymble

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an absolute path for a file (Unix-style), simplify it.

For example,
path = "/home/", => "/home"
path = "/a/./b/../../c/", => "/c"

Corner Cases:


       Did you consider the case where path = "/../"?
       In this case, you should return "/".
       Another corner case is the path might contain multiple slashes '/' together, such as "/home//foo/".
       In this case, you should ignore redundant slashes and return "/home/foo".

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

There are four warriors, they need to go through a dark tunnel. Tunnel is very narrow, every time only can let two warriors through, and there are lot of dangerous traps. Fortunately, they have a lamp that can illuminate the tunnel to avoid being trapped by the trap.

In order to pass this tunnel, they need five steps:

1. Two people go through the tunnel with the lamp
2. And then one people come back with the lamp
3. And then two people go through the tunnel with the lamp
4. And then one people come back with the lamp
5. And then two people go through the tunnel with the lamp
 
Each warrior has his own walking speed, we need to calculate the shortest time they have to cross the tunnel.
 
For example:
 
Four warriors is `a,b,c,d`. Their speed are `[3,4,5,6]`. It means they need 3 minutes, 4 minutes, 5 minutes and 6 minutes to cross the tunnel. The shortest crossing time should be 21 minutes, the method is as follows:
 
```
a and b go through the tunnel  ---> Spend 4 minutes
(Time spent should be calculated by the person who is slow)
a come back                    ---> Spend 3 minutes
a and c go through the tunnel  ---> Spend 5 minutes
a come back                    ---> Spend 3 minutes
a and d go through the tunnel  ---> Spend 6 minutes
```
Do you have any other better way?
 
## Task
Complete function `shortestTime()` that accepts 1 argument: `speed` that are the spent time of four warriors. Returns the shortest time that all warriors go through the tunnel.
 
**Note: The method in example above is not always the best way.**

## Example

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Rhezo calls a number good if the number is divisible by all numbers from 1 to 9. His father also likes good numbers, and has promised him to buy 1 chocolate per every good number he tells him. He doesn't want to make the task simple for Rhezo, therefore he gives him 2 strings T and P.

He tells Rhezo to find the number of ways to select one or more occurrences of P in T, so that the product of starting positions of all those occurrences is a good number. Rhezo likes chocolates and is not so good at programming. Help him. As the answer could be large, output the answer modulo 10^9+7.

Input:

First line contains the string P. Second line contains the string T.

Output:

Help Rhezo to find the number of ways to select one or more occurrences of P in T, so that the product of starting positions of all those occurrences is a good number.

Constraints:

Length of S, T ≤ 10^4

SAMPLE INPUT
a
aaaaaaa

SAMPLE OUTPUT
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given two strings s1 and s2, we want to visualize how different the two strings are.
We will only take into account the *lowercase* letters (a to z).
First let us count the frequency of each *lowercase* letters in s1 and s2.

`s1 = "A aaaa bb c"`

`s2 = "& aaa bbb c d"`

`s1 has 4 'a', 2 'b', 1 'c'`

`s2 has 3 'a', 3 'b', 1 'c', 1 'd'`

So the maximum for 'a' in s1 and s2 is 4 from s1; the maximum for 'b' is 3 from s2.
In the following we will not consider letters when the maximum of their occurrences
is less than or equal to 1.

We can resume the differences between s1 and s2 in the following string:
`"1:aaaa/2:bbb"`
where `1` in `1:aaaa` stands for string s1 and `aaaa` because the maximum for `a` is 4.
In the same manner `2:bbb` stands for string s2 and `bbb` because the maximum for `b` is 3.

The task is to produce a string in which each *lowercase* letters of s1 or s2 appears as many times as
its maximum if this maximum is *strictly greater than 1*; these letters will be prefixed by the 
number of the string where they appear with their maximum value and `:`. 
If the maximum is in s1 as well as in s2 the prefix is `=:`.

In the result, substrings (a substring is for example 2:nnnnn or 1:hhh; it contains the prefix) will be in decreasing order of their length and when they have the same length sorted in ascending lexicographic order (letters and digits - more precisely sorted by codepoint); the different groups will be separated by '/'. See examples and "Example Tests".

Hopefully other examples can make this clearer.

```
s1 = "my&friend&Paul has heavy hats! &"
s2 = "my friend John has many many friends &"
mix(s1, s2) --> "2:nnnnn/1:aaaa/1:hhh/2:mmm/2:yyy/2:dd/2:ff/2:ii/2:rr/=:ee/=:ss"

s1 = "mmmmm m nnnnn y&friend&Paul has heavy hats! &"
s2 = "my frie n d Joh n has ma n y ma n y frie n ds n&"
mix(s1, s2) --> "1:mmmmmm/=:nnnnnn/1:aaaa/1:hhh/2:yyy/2:dd/2:ff/2:ii/2:rr/=:ee/=:ss"

s1="Are the kids at home? aaaaa fffff"
s2="Yes they are here! aaaaa fffff"
mix(s1, s2) --> "=:aaaaaa/2:eeeee/=:fffff/1:tt/2:rr/=:hh"
```
# Note for Swift, R, PowerShell
The prefix `=:` is replaced by `E:`
``` 
s1 = "mmmmm m nnnnn y&friend&Paul has heavy hats! &"
s2 = "my frie n d Joh n has ma n y ma n y frie n ds n&"
mix(s1, s2) --> "1:mmmmmm/E:nnnnnn/1:aaaa/1:hhh/2:yyy/2:dd/2:ff/2:ii/2:rr/E:ee/E:ss"
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Consider the following well known rules:

- A number is divisible by 3 if the sum of its digits is divisible by 3. Let's call '3' a "1-sum" prime
- For 37, we take numbers in groups of threes from the right and check if the sum of these groups is divisible by 37. 
  Example: 37 * 123456787 = 4567901119 => 4 + 567 + 901 + 119 = 1591 = 37 * 43. Let's call this a "3-sum" prime because we use groups of 3.
- For 41, we take numbers in groups of fives from the right and check if the sum of these groups is divisible by 41. This is a "5-sum" prime.
- Other examples: 239 is a "7-sum" prime (groups of 7), while 199 is a "99-sum" prime (groups of 99).

Let's look at another type of prime:
- For 11, we need to add all digits by alternating their signs from the right. 
  Example: 11 * 123456 = 1358016 => 6-1+0-8+5-3+1 = 0, which is divible by 11. Let's call this a "1-altsum" prime
- For 7, we need to group the digits into threes from the right and add all groups by alternating their signs.
  Example: 7 * 1234567891234 = 8641975238638 => 638 - 238 + 975 - 641 + 8 = 742/7 = 106. 
- 7 is a "3-altsum" prime because we use groups of threes. 47 is a "23-altsum" (groups of 23), while 73 is a "4-altsum" prime (groups of 4).


You will be given a prime number `p` and your task is to find the smallest positive integer `n` such that `p’s` divisibility testing is `n-sum` or `n-altsum`.

For example:
```
solve(3) = "1-sum"
solve(7) = "3-altsum"
```
Primes will not exceed `50,000,000`. More examples in test cases. 

You can get some insight from [Fermat's little theorem](https://en.wikipedia.org/wiki/Fermat%27s_little_theorem). 

Good luck!

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
- Input: Integer `n`
- Output: String

Example:

`a(4)` prints as
```
   A   
  A A  
 A A A 
A     A
```

`a(8)` prints as
```
       A       
      A A      
     A   A     
    A     A    
   A A A A A   
  A         A  
 A           A 
A             A
```

`a(12)` prints as
```
           A           
          A A          
         A   A         
        A     A        
       A       A       
      A         A      
     A A A A A A A     
    A             A    
   A               A   
  A                 A  
 A                   A 
A                     A
```
Note:

- Each line's length is `2n - 1`
- Each line should be concatenate by line break `"\n"`
- If `n` is less than `4`, it should return `""`
- If `n` is odd, `a(n) = a(n - 1)`, eg `a(5) == a(4); a(9) == a(8)`

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

You are asked to build a compressor for Boolean expressions that transforms expressions to the shortest form keeping their meaning.

The grammar of the Boolean expressions has terminals `0` `1` `a` `b` `c` `d` `-` `^` `*` `(` `)`, start symbol <E> and the following production rule:

> <E>  ::=  `0`  |  `1`  |  `a`  |  `b`  |  `c`  |  `d`  |  `-`<E>  |  `(`<E>`^`<E>`)`  |  `(`<E>`*`<E>`)`

Letters `a`, `b`, `c` and `d` represent Boolean variables that have values of either `0` or `1`. Operators are evaluated as shown in the Table below. In other words, `-` means negation (NOT), `^` means exclusive disjunction (XOR), and `*` means logical conjunction (AND).

Table: Evaluations of operators
<image>

Write a program that calculates the length of the shortest expression that evaluates equal to the given expression with whatever values of the four variables.

For example, `0`, that is the first expression in the sample input, cannot be shortened further. Therefore the shortest length for this expression is 1.

For another example, `(a*(1*b))`, the second in the sample input, always evaluates equal to `(a*b)` and `(b*a)`, which are the shortest. The output for this expression, thus, should be `5`.

Input

The input consists of multiple datasets. A dataset consists of one line, containing an expression conforming to the grammar described above. The length of the expression is less than or equal to 16 characters.

The end of the input is indicated by a line containing one `.` (period). The number of datasets in the input is at most 200.

Output

For each dataset, output a single line containing an integer which is the length of the shortest expression that has the same value as the given expression for all combinations of values in the variables.

Sample Input


0
(a*(1*b))
(1^a)
(-(-a*-b)*a)
(a^(b^(c^d)))
.


Output for the Sample Input


1
5
2
1
13






Example

Input

0
(a*(1*b))
(1^a)
(-(-a*-b)*a)
(a^(b^(c^d)))
.


Output

1
5
2
1
13

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Kang the Penguin has forgotten some letters of his password, help him figure them out!

Of course, Kang knows that something as important as a password should be easy to remember, but it also cannot be too short. Thus, he knows that he originally decided to generate his password in the following manner. First, he starts with some non-empty string $S$, consisting of lowercase letters only. Then, he chooses $26$ non-empty strings $T_ a, T_ b, \dots , T_ z$, each consisting of at least two lowercase English letters. He defines a function $f$, which converts each character $i$ to its corresponding string $T_ i$ and concatenates the results. For example, if $T_ a$ was “abc” and $T_ b$ was “cba”, applying $f$ to “aba” would result in the string “abccbaabc”.

Now, he applies $f$ repeatedly to $S$, applying it $K$ times in total. The final result is his password $P = f^K (S)$.

While he remembers most of his password, he has forgotten $M$ of the letters. The $i^\textrm {th}$ letter that he has forgotten is in position $m_ i$ in the string $P$. It is guaranteed that each $m_ i$ will be less than or equal to the final length of the password $|P|$. Help Kang to figure out what the forgotten letters are!

-----Input-----
The $1^\textrm {st}$ line of the input contains a single lowercase string $S$, where $1 \leq |S| \leq 1000000$.

The $2^\textrm {nd}$ line of the input contains $13$ strings $T_ a, T_ b, \dots , T_ m$, separated by spaces, where $2 \leq |T_ a|, |T_ b|, \dots , |T_ m| \leq 50$.

The $3^\textrm {rd}$ line of the input contains $13$ strings $T_ n, T_ o, \dots , T_ z$, separated by spaces, where $2 \leq |T_ n|, |T_ o|, \dots , |T_ z| \leq 50$.

The strings $T_ a, T_ b, \dots , T_ z$ each contains only lowercase English characters (a–z).

The $4^\textrm {th}$ line of the input contains a single integer $K$, where $1 \leq K \leq 10^{15}$.

The $5^\textrm {th}$ line of the input contains a single integer $M$, where $1 \leq M \leq 1000$.

The $6^\textrm {th}$ line of the input contains $M$ integers, the $i^\textrm {th}$ of which is the integer $m_ i$, where $1 \leq m_ i \leq \min (|f^K(S)|,10^{15})$.

-----Output-----
Output $M$ lines, each containing a single lowercase character. The $i^\textrm {th}$ line of the output should contain the letter in the $m_ i^\textrm {th}$ position of the password $P$.

-----Examples-----
Sample Input:
abca
bc cd da dd ee ff gg hh ii jj kk ll mm
nn oo pp qq rr ss tt uu vv ww xx yy zz
1
2
1 8
Sample Output:
b
c

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In 1978 AD the great Sir Isaac Newton, whilst proving that $\mathcal{P}$ is a strict superset of $\mathcal{NP}$, defined the Beta Alpha Pi Zeta function $f$ as follows over any sequence of positive integers $a_1, \dots , a_ n$. Given integers $1\leq i\leq j\leq n$, we define $f(i, j)$ as $\gcd (a_ i, a_{i+1}, \dots , a_{j-1}, a_ j)$. 

About a century later Lothar Collatz applied this function to the sequence $1, 1, 1, \dots , 1$, and observed that $f$ always equalled $1$. Based on this, he conjectured that $f$ is always a constant function, no matter what the sequence $a_ i$ is. This conjecture, now widely known as the Collatz Conjecture, is one of the major open problems in botanical studies. (The Strong Collatz Conjecture claims that however many values $f$ takes on, the real part is always $\frac{1}{2}$.)

You, a budding young cultural anthropologist, have decided to disprove this conjecture. Given a sequence $a_ i$, calculate how many different values $f$ takes on.

-----Input-----
The input consists of two lines.
 - A single integer $1 \leq n \leq 5 \cdot 10^5$, the length of the sequence.
 - The sequence of integers $a_1, a_2, \dots , a_ n$. It is given that $1 \leq a_ i \leq 10^{18}$.

-----Output-----
Output a single line containing a single integer, the number of distinct values $f$ takes on over the given sequence.

-----Examples-----
Sample Input:
4
9 6 2 4
Sample Output:
6

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A festival will be held in a town's main street. There are n sections in the main street. The sections are numbered 1 through n from left to right. The distance between each adjacent sections is 1.

In the festival m fireworks will be launched. The i-th (1 ≤ i ≤ m) launching is on time t_{i} at section a_{i}. If you are at section x (1 ≤ x ≤ n) at the time of i-th launching, you'll gain happiness value b_{i} - |a_{i} - x| (note that the happiness value might be a negative value).

You can move up to d length units in a unit time interval, but it's prohibited to go out of the main street. Also you can be in an arbitrary section at initial time moment (time equals to 1), and want to maximize the sum of happiness that can be gained from watching fireworks. Find the maximum total happiness.

Note that two or more fireworks can be launched at the same time.


-----Input-----

The first line contains three integers n, m, d (1 ≤ n ≤ 150000; 1 ≤ m ≤ 300; 1 ≤ d ≤ n).

Each of the next m lines contains integers a_{i}, b_{i}, t_{i} (1 ≤ a_{i} ≤ n; 1 ≤ b_{i} ≤ 10^9; 1 ≤ t_{i} ≤ 10^9). The i-th line contains description of the i-th launching.

It is guaranteed that the condition t_{i} ≤ t_{i} + 1 (1 ≤ i < m) will be satisfied.


-----Output-----

Print a single integer — the maximum sum of happiness that you can gain from watching all the fireworks.

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


-----Examples-----
Input
50 3 1
49 1 1
26 1 4
6 1 10

Output
-31

Input
10 2 1
1 1000 4
9 1000 4

Output
1992

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a string $S$. Find the number of ways to choose an unordered pair of non-overlapping non-empty substrings of this string (let's denote them by $s_1$ and $s_2$ in such a way that $s_2$ starts after $s_1$ ends) such that their concatenation $s_1 + s_2$ is a palindrome.
Two pairs $(s_1, s_2)$ and $(s_1', s_2')$ are different if $s_1$ is chosen at a different position from $s_1'$ or $s_2$ is chosen at a different position from $s_2'$.

-----Input-----
The first and only line of the input contains a single string $S$.

-----Output-----
Print a single line containing one integer — the number of ways to choose a valid pair of substrings.

-----Constraints-----
- $1 \le |S| \le 1,000$
- $S$ contains only lowercase English letters

-----Subtasks-----
Subtask #1 (25 points): $|S| \le 100$
Subtask #2 (75 points): original constraints

-----Example Input-----
abba

-----Example Output-----
7

-----Explanation-----
The following pairs of substrings can be chosen: ("a", "a"), ("a", "ba"), ("a", "bba"), ("ab", "a"), ("ab", "ba"), ("abb", "a"), ("b", "b").

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