vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Note that this is an easier version of the problem fancy

Oskar really loves onions. Unfortunately, the onions he loves belong to the local vegetable farmer, Lökas Tomatcek. Since Oskar is very cheap, he simply steals Lökas’ onions from the large, convex, onion field. For obvious reasons, Lökas does not approve of this. Rather than going to the police, however, Lökas wants to raise a high-energy laser fence around the onions to replace his wooden fence.

As laser fences are rather expensive, Lökas can only afford to upgrade $K$ of the fence posts to laser fence posts. If a set of posts are upgraded, the lasers will protect all the onions lying strictly within the convex hull of the selected fence posts. This may not be all of the onions though. Lökas wonders which posts he should upgrade if he wants to protect as many of his $N$ onions as possible.

The original fence has the shape of a convex polygon with $M$ fence posts as vertices, and all the onions lie strictly within the fence.

-----Input-----
The first line of input consists of three space-separated integers $3 \le N \le 1000$, $3 \le M \le 100$ and $3 \le K \le 100$. These are the number of onions, the number of old fence posts, and the number of fence posts Lökas can upgrade.

Then follow $N$ lines with two space-separated integers $0 \le X_ i, Y_ i \le 10^9$ each. $(X_ i, Y_ i)$ gives the coordinate of the $i$-th onion.

Then follow $M$ lines with two space-separated integers $0 \le A_ i, B_ i \le 10^9$ each. $(A_ i, B_ i)$ gives the coordinate of the $i$-th fence post.

The fence posts will be given in clockwise order of the old fence. No three fence posts will lie on a line.

-----Output-----
Output should be a single integer; the maximum number of onions Lökas can protect.

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

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In the year 2120 there is a vast subway network under all of Lund, consisting of $N$ stations and $M$ tunnels. Each tunnel connects two stations and the stations are numbered $1$, $\ldots $, $N$.

Erik has had enough of Skånetrafiken’s terrible route planning software and plans to build his own. To do this, he needs to know the length of each of the tunnels, but the subway map is incomplete in this regard. By looking out the window, Erik has noticed that some tunnels have special cables running alongside them, probably for providing power to the stations. The cables connect the stations so that every station is connected to the central station (the station numbered $1$). Knowing how greedy Skånetrafiken is, he is certain that the cables are placed so that the total length of cable is minimized.

Erik knows the precise length of some tunnels, and which tunnels contain cables. Using this information he wants to find the minimum possible length for each tunnel with unknown length. Unfortunately, Erik’s algorithm isn’t efficient enough to process the enormous size of Lund’s subway network. Can you help him by implementing a more efficient algorithm?

-----Input-----
The first line of input contains two integers $N$ and $M$, where $2 \leq N \leq 10^5$ and $N - 1 \leq M \leq 2 \cdot 10^5$, the number of stations and the number of tunnels, respectively. Each of the next $M$ lines contains the values $a_ i$, $b_ i$, $l_ i$ and $c_ i$. The integers $a_ i$ and $b_ i$, with $1 \leq a_ i, b_ i \leq N$ and $a_ i\neq b_ i$, denote the two stations connected by the $i$th tunnel. The value $l_ i$ is either an integer satisfying $1 \leq l_ i \leq 10^9$, the length of the $i$th tunnel if it is known, or a question mark “?”. Finally, $c_ i$ is $1$ if the $i$th tunnel contains a cable, and $0$ if not.

It is guaranteed that there is at most one tunnel connecting the same pair of stations, and that it is possible to travel between any pair of stations using the subway. It is also guaranteed that there exists a path between any station and station number $1$ using only tunnels where $c_ i = 1$.

-----Output-----
For each tunnel with $l_ i=\texttt{?}$, output one line with a single integer, the minimum possible length for that tunnel. Tunnel lengths should be output in the same order as the tunnels are listed in the input.

-----Sample Description-----
In the first sample case, the minimal distance for the unknown tunnel (between stations $3$ and $1$) is $5$. This is because, if the length were less than $5$, it would be more efficient for Skånetrafiken to run cables through the second and third tunnels.

-----Examples-----
Sample Input:
3 3
1 2 5 1
2 3 3 1
3 1 ? 0
Sample Output:
5

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Petya loves tickets very much. As we know, each ticket has a number that is a positive integer. Its length equals *n* (*n* is always even). Petya calls a ticket lucky if the ticket's number is a lucky number and the sum of digits in the first half (the sum of the first *n*<=/<=2 digits) equals the sum of digits in the second half (the sum of the last *n*<=/<=2 digits). Check if the given ticket is lucky.

Input Specification:
The first line contains an even integer *n* (2<=≤<=*n*<=≤<=50) — the length of the ticket number that needs to be checked. The second line contains an integer whose length equals exactly *n* — the ticket number. The number may contain leading zeros.

Output Specification:
On the first line print "YES" if the given ticket number is lucky. Otherwise, print "NO" (without the quotes).

Demo Input:
['2\n47\n', '4\n4738\n', '4\n4774\n']

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

Note:
In the first sample the sum of digits in the first half does not equal the sum of digits in the second half (4 ≠ 7).

In the second sample the ticket number is not the lucky number.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A new agent called Killjoy invented a virus COVID-2069 that infects accounts on Codeforces. Each account has a rating, described by an integer (it can possibly be negative or very large).

Killjoy's account is already infected and has a rating equal to $x$. Its rating is constant. There are $n$ accounts except hers, numbered from $1$ to $n$. The $i$-th account's initial rating is $a_i$. Any infected account (initially the only infected account is Killjoy's) instantly infects any uninfected account if their ratings are equal. This can happen at the beginning (before any rating changes) and after each contest. If an account is infected, it can not be healed.

Contests are regularly held on Codeforces. In each contest, any of these $n$ accounts (including infected ones) can participate. Killjoy can't participate. After each contest ratings are changed this way: each participant's rating is changed by an integer, but the sum of all changes must be equal to zero. New ratings can be any integer.

Find out the minimal number of contests needed to infect all accounts. You can choose which accounts will participate in each contest and how the ratings will change.

It can be proven that all accounts can be infected in some finite number of contests.


-----Input-----

The first line contains a single integer $t$ $(1 \le t \le 100)$ — the number of test cases. The next $2t$ lines contain the descriptions of all test cases.

The first line of each test case contains two integers $n$ and $x$ ($2 \le n \le 10^3$, $-4000 \le x \le 4000$) — the number of accounts on Codeforces and the rating of Killjoy's account.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ $(-4000 \le a_i \le 4000)$ — the ratings of other accounts.


-----Output-----

For each test case output the minimal number of contests needed to infect all accounts.


-----Example-----
Input
3
2 69
68 70
6 4
4 4 4 4 4 4
9 38
-21 83 50 -59 -77 15 -71 -78 20

Output
1
0
2



-----Note-----

In the first test case it's possible to make all ratings equal to $69$. First account's rating will increase by $1$, and second account's rating will decrease by $1$, so the sum of all changes will be equal to zero.

In the second test case all accounts will be instantly infected, because all ratings (including Killjoy's account's rating) are equal to $4$.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Jzzhu is the president of country A. There are *n* cities numbered from 1 to *n* in his country. City 1 is the capital of A. Also there are *m* roads connecting the cities. One can go from city *u**i* to *v**i* (and vise versa) using the *i*-th road, the length of this road is *x**i*. Finally, there are *k* train routes in the country. One can use the *i*-th train route to go from capital of the country to city *s**i* (and vise versa), the length of this route is *y**i*.

Jzzhu doesn't want to waste the money of the country, so he is going to close some of the train routes. Please tell Jzzhu the maximum number of the train routes which can be closed under the following condition: the length of the shortest path from every city to the capital mustn't change.

Input Specification:
The first line contains three integers *n*,<=*m*,<=*k* (2<=≤<=*n*<=≤<=105; 1<=≤<=*m*<=≤<=3·105; 1<=≤<=*k*<=≤<=105).

Each of the next *m* lines contains three integers *u**i*,<=*v**i*,<=*x**i* (1<=≤<=*u**i*,<=*v**i*<=≤<=*n*; *u**i*<=≠<=*v**i*; 1<=≤<=*x**i*<=≤<=109).

Each of the next *k* lines contains two integers *s**i* and *y**i* (2<=≤<=*s**i*<=≤<=*n*; 1<=≤<=*y**i*<=≤<=109).

It is guaranteed that there is at least one way from every city to the capital. Note, that there can be multiple roads between two cities. Also, there can be multiple routes going to the same city from the capital.

Output Specification:
Output a single integer representing the maximum number of the train routes which can be closed.

Demo Input:
['5 5 3\n1 2 1\n2 3 2\n1 3 3\n3 4 4\n1 5 5\n3 5\n4 5\n5 5\n', '2 2 3\n1 2 2\n2 1 3\n2 1\n2 2\n2 3\n']

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

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You will be given an integer a and a string s consisting of lowercase English letters as input.
Write a program that prints s if a is not less than 3200 and prints red if a is less than 3200.

-----Constraints-----
 - 2800 \leq a < 5000
 - s is a string of length between 1 and 10 (inclusive).
 - Each character of s is a lowercase English letter.

-----Input-----
Input is given from Standard Input in the following format:
a
s

-----Output-----
If a is not less than 3200, print s; if a is less than 3200, print red.

-----Sample Input-----
3200
pink

-----Sample Output-----
pink

a = 3200 is not less than 3200, so we print s = pink.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Given an integer $x$. Your task is to find out how many positive integers $n$ ($1 \leq n \leq x$) satisfy $$n \cdot a^n \equiv b \quad (\textrm{mod}\;p),$$ where $a, b, p$ are all known constants.

Input Specification:
The only line contains four integers $a,b,p,x$ ($2 \leq p \leq 10^6+3$, $1 \leq a,b &lt; p$, $1 \leq x \leq 10^{12}$). It is guaranteed that $p$ is a prime.

Output Specification:
Print a single integer: the number of possible answers $n$.

Demo Input:
['2 3 5 8\n', '4 6 7 13\n', '233 233 10007 1\n']

Demo Output:
['2\n', '1\n', '1\n']

Note:
In the first sample, we can see that $n=2$ and $n=8$ are possible answers.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a permutation of integers from 1 to n. Exactly once you apply the following operation to this permutation: pick a random segment and shuffle its elements. Formally:  Pick a random segment (continuous subsequence) from l to r. All $\frac{n(n + 1)}{2}$ segments are equiprobable.  Let k = r - l + 1, i.e. the length of the chosen segment. Pick a random permutation of integers from 1 to k, p_1, p_2, ..., p_{k}. All k! permutation are equiprobable.  This permutation is applied to elements of the chosen segment, i.e. permutation a_1, a_2, ..., a_{l} - 1, a_{l}, a_{l} + 1, ..., a_{r} - 1, a_{r}, a_{r} + 1, ..., a_{n} is transformed to a_1, a_2, ..., a_{l} - 1, a_{l} - 1 + p_1, a_{l} - 1 + p_2, ..., a_{l} - 1 + p_{k} - 1, a_{l} - 1 + p_{k}, a_{r} + 1, ..., a_{n}. 

Inversion if a pair of elements (not necessary neighbouring) with the wrong relative order. In other words, the number of inversion is equal to the number of pairs (i, j) such that i < j and a_{i} > a_{j}. Find the expected number of inversions after we apply exactly one operation mentioned above.


-----Input-----

The first line contains a single integer n (1 ≤ n ≤ 100 000) — the length of the permutation.

The second line contains n distinct integers from 1 to n — elements of the permutation.


-----Output-----

Print one real value — the expected number of inversions. Your answer will be considered correct if its absolute or relative error does not exceed 10^{ - 9}. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if $\frac{|a - b|}{\operatorname{max}(1, b)} \leq 10^{-9}$.


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

Output
1.916666666666666666666666666667

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Sonali and Priyanka are friends. Both are fascinated about "PokemonGo". One day Sonali give an Array to Priyanka and asks her to convert the Array into "Pokedex".
A "Pokedex" is an Array  such that all distinct elements in the Array occurs the same number of times in it.
For example, A={1,1,2,2} is a "Pokedex" because both the numbers (1 and 2) occurs the same number of times.
Whereas B={1,2,1,2,3} is NOT a "Pokedex" because the distinct elements (1,2,3) does not occurs the same number of time.
Priyanka gives the Array to her bff Harshit and asks him to remove some elements from the Array, Such that the new Array results in a "Pokedex".
Harshit wants to know from you if it's possible to be done with less then or equals to one removal.

Input Format:
First line contains a integer T that represents the total no. of test cases.
Each test case follows with a integer N the size of the array.
Next line contains N space separated integers.

Output Format:
For each testcase, print "YES" if there is a possibility to make the array a "Pokedex", Else print "NO".

Constraints:
1 ≤ t ≤ 10
1 ≤ n ≤ 10^5
1 ≤ Array element ≤10^7

SAMPLE INPUT
2
6
1 2 3 3 2 1
6
1 2 2 1 3 4

SAMPLE OUTPUT
YES
NO

Explanation

In the first test case (1,2,3) occurs the same number of times so its already a Pokedex.
In second case we would need more then one removals to form a Pokedex.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In this Kata, you will count the number of times the first string occurs in the second. 

```Haskell
solve("zaz","zazapulz") = 4 because they are ZAZapulz, ZAzapulZ, ZazApulZ, zaZApulZ
```

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.
## Task

You will receive a string consisting of lowercase letters, uppercase letters and digits as input. Your task is to return this string as blocks separated by dashes (`"-"`). The elements of a block should be sorted with respect to the hierarchy listed below, and each block cannot contain multiple instances of the same character. Elements should be put into the first suitable block.

The hierarchy is:
1. lowercase letters (`a - z`), in alphabetical order
2. uppercase letters (`A - Z`), in alphabetical order
3. digits (`0 - 9`), in ascending order

## Examples

* `"21AxBz" -> "xzAB12"` - since input does not contain repeating characters, you only need 1 block
* `"abacad" -> "abcd-a-a"` - character "a" repeats 3 times, thus 3 blocks are needed
* `"" -> ""` - an empty input should result in an empty output
* `"hbh420sUUW222IWOxndjn93cdop69NICEep832" -> "bcdehjnopsxCEINOUW0234689-dhnpIUW239-2-2-2"` - a more sophisticated example

Good luck!

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Recently Luba learned about a special kind of numbers that she calls beautiful numbers. The number is called beautiful iff its binary representation consists of *k*<=+<=1 consecutive ones, and then *k* consecutive zeroes.

Some examples of beautiful numbers: 
 -  12 (110); -  1102 (610); -  11110002 (12010); -  1111100002 (49610). 
More formally, the number is beautiful iff there exists some positive integer *k* such that the number is equal to (2*k*<=-<=1)<=*<=(2*k*<=-<=1).

Luba has got an integer number *n*, and she wants to find its greatest beautiful divisor. Help her to find it!

Input Specification:
The only line of input contains one number *n* (1<=≤<=*n*<=≤<=105) — the number Luba has got.

Output Specification:
Output one number — the greatest beautiful divisor of Luba's number. It is obvious that the answer always exists.

Demo Input:
['3\n', '992\n']

Demo Output:
['1\n', '496\n']

Note:
none

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
In a very ancient country the following game was popular. Two people play the game. Initially first player writes a string *s*1, consisting of exactly nine digits and representing a number that does not exceed *a*. After that second player looks at *s*1 and writes a string *s*2, consisting of exactly nine digits and representing a number that does not exceed *b*. Here *a* and *b* are some given constants, *s*1 and *s*2 are chosen by the players. The strings are allowed to contain leading zeroes.

If a number obtained by the concatenation (joining together) of strings *s*1 and *s*2 is divisible by *mod*, then the second player wins. Otherwise the first player wins. You are given numbers *a*, *b*, *mod*. Your task is to determine who wins if both players play in the optimal manner. If the first player wins, you are also required to find the lexicographically minimum winning move.

Input Specification:
The first line contains three integers *a*, *b*, *mod* (0<=≤<=*a*,<=*b*<=≤<=109, 1<=≤<=*mod*<=≤<=107).

Output Specification:
If the first player wins, print "1" and the lexicographically minimum string *s*1 he has to write to win. If the second player wins, print the single number "2".

Demo Input:
['1 10 7\n', '4 0 9\n']

Demo Output:
['2\n', '1 000000001\n']

Note:
The lexical comparison of strings is performed by the &lt; operator in modern programming languages. String *x* is lexicographically less than string *y* if exists such *i* (1 ≤ *i* ≤ 9), that *x*<sub class="lower-index">*i*</sub> &lt; *y*<sub class="lower-index">*i*</sub>, and for any *j* (1 ≤ *j* &lt; *i*) *x*<sub class="lower-index">*j*</sub> = *y*<sub class="lower-index">*j*</sub>. These strings always have length 9.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
The heat during the last few days has been really intense. Scientists from all over the Berland study how the temperatures and weather change, and they claim that this summer is abnormally hot. But any scientific claim sounds a lot more reasonable if there are some numbers involved, so they have decided to actually calculate some value which would represent how high the temperatures are.

Mathematicians of Berland State University came up with a special heat intensity value. This value is calculated as follows:

Suppose we want to analyze the segment of $n$ consecutive days. We have measured the temperatures during these $n$ days; the temperature during $i$-th day equals $a_i$.

We denote the average temperature of a segment of some consecutive days as the arithmetic mean of the temperature measures during this segment of days. So, if we want to analyze the average temperature from day $x$ to day $y$, we calculate it as $\frac{\sum \limits_{i = x}^{y} a_i}{y - x + 1}$ (note that division is performed without any rounding). The heat intensity value is the maximum of average temperatures over all segments of not less than $k$ consecutive days. For example, if analyzing the measures $[3, 4, 1, 2]$ and $k = 3$, we are interested in segments $[3, 4, 1]$, $[4, 1, 2]$ and $[3, 4, 1, 2]$ (we want to find the maximum value of average temperature over these segments).

You have been hired by Berland State University to write a program that would compute the heat intensity value of a given period of days. Are you up to this task?

Input Specification:
The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 5000$) — the number of days in the given period, and the minimum number of days in a segment we consider when calculating heat intensity value, respectively.

The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($1 \le a_i \le 5000$) — the temperature measures during given $n$ days.

Output Specification:
Print one real number — the heat intensity value, i. e., the maximum of average temperatures over all segments of not less than $k$ consecutive days.

Your answer will be considered correct if the following condition holds: $|res - res_0| &lt; 10^{-6}$, where $res$ is your answer, and $res_0$ is the answer given by the jury's solution.

Demo Input:
['4 3\n3 4 1 2\n']

Demo Output:
['2.666666666666667\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Let X be the set of all integers between 0 and n-1. Suppose we have a collection S1, S2, ..., Sm of subsets of X. Say an atom A is a subset of X such that for each Si we have either A is a subset of Si or A and Si do not have any common elements.

Your task is to find a collection A1, ..., Ak of atoms such that every item in X is in some Ai and no two Ai, Aj with i ≠ j share a common item. Surely such a collection exists as we could create a single set {x} for each x in X. A more interesting question is to minimize k, the number of atoms.

-----Input-----

The first line contains a single positive integer t ≤ 30 indicating the number of test cases. Each test case begins with two integers n,m where n is the size of X and m is the number of sets Si. Then m lines follow where the i'th such line begins with an integer vi between 1 and n (inclusive) indicating the size of Si. Following this are vi distinct integers between 0 and n-1 that describe the contents of Si.

You are guaranteed that 1 ≤ n ≤ 100 and 1 ≤ m ≤ 
30. Furthermore, each number between 0 and n-1 will appear in at least one set Si.

-----Output-----

For each test case you are to output a single integer indicating the minimum number of atoms that X can be partitioned into to satisfy the constraints.

-----Example-----
Input:
2
5 2
3 0 1 2
3 2 3 4
4 3
2 0 1
2 1 2
2 2 3

Output:
3
4

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