vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
A student of z-school found a kind of sorting called z-sort. The array a with n elements are z-sorted if two conditions hold:

  a_{i} ≥ a_{i} - 1 for all even i,  a_{i} ≤ a_{i} - 1 for all odd i > 1. 

For example the arrays [1,2,1,2] and [1,1,1,1] are z-sorted while the array [1,2,3,4] isn’t z-sorted.

Can you make the array z-sorted?


-----Input-----

The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of elements in the array a.

The second line contains n integers a_{i} (1 ≤ a_{i} ≤ 10^9) — the elements of the array a.


-----Output-----

If it's possible to make the array a z-sorted print n space separated integers a_{i} — the elements after z-sort. Otherwise print the only word "Impossible".


-----Examples-----
Input
4
1 2 2 1

Output
1 2 1 2

Input
5
1 3 2 2 5

Output
1 5 2 3 2

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a linked list of strings having n nodes check to see whether the combined string formed is palindrome or not. 
Input:
You have to complete the method which takes one argument: the head of the linked list . You should not read any input from stdin/console.. There are multiple test cases. For each test case, this method will be called individually.
Output:
Your function should return True if the combined string is pallindrome else it should return False.
User Task:
The task is to complete the function compute() which returns true or false.
Constraints:
1 <=T<= 10^{3}
1 <=n<= 10^{3}
Example:
Input :
2
5
a bc d dcb a
4
a bc d ba
Output :
True
False
Explanation:
case 1 : as String "abcddcba" is palindrome the function should return true
case 2 : as String "abcdba" is not palindrome the function should return false

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We’re working on a new super-computer, built to unleash the hidden computing powers of all eight dimensions of reality. The secret to utilizing more dimensions turns out to be to use counting registers of different sizes. In particular, we have eight registers, counting cyclically modulo the different primes $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$. A size $p$ register stores a value between $0$ and $p-1$ (inclusive). 

The only operation available is an “increment” operation. When it is performed, the size $2$ register is increased by $1$. If this increment causes overflow (i.e., if the old value was $1$) the value is reset to $0$, and the size $3$ is incremented. If this causes overflow the size $3$ register is reset to $0$ and the size $5$ register is incremented, and so on. If this goes all the way to the last register and the size $19$ register overflows, the computer blows up.

In order not to destroy the computer in testing, we need to build a program to check the safety of doing increment operations before we perform them. Given the current state of the registers, you need to compute how many more operations can safely be performed before the computer blows up.

-----Input-----
The input consists of a single line containing eight integers $v_2$, $v_3$, $v_5$, $v_7$, $v_{11}$, $v_{13}$, $v_{17}$, $v_{19}$ indicating the current values of the registers. The value of the size $p$ register is always between $0$ and $p-1$ (inclusive).

-----Output-----
Ouput a single line containing an integer $N$, the number of additional operations that can be performed without the computer blowing up.

-----Examples-----
Sample Input 1:
0 0 4 6 10 12 16 18
Sample Output 1:
5

Sample Input 2:
1 2 4 6 10 12 16 18
Sample Output 2:
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Two bicycle courier services have been competing in Metro City for many years, stealing customers back and forth from one another. Recently, they have come to realize that they would be better off if they could attract new customers instead. A problem is that, over time, each company’s customers have become so widely scattered across the city that some of their delivery times are unacceptably slow, leading to customer dissatisfaction and a poor reputation.

The companies would like to divide up their current customers so that each company could run ads saying “We guarantee delivery in no more than M minutes”, hoping to attract new customers. The streets of Metro City are laid out on a grid, with buildings at integer coordinates of the grid. The couriers must travel along those roads – they cannot cut through buildings. It takes one minute to travel one unit of distance in the $x$ or $y$ direction.

Divide up the current customer base to minimize the longest delivery time required by either company to have a courier travel from one customer of that company to any other customer of the same company.
 - A delivery is considered to have been completed when the courier reaches the $(x,y)$ address of the customer. No time is counted for wandering the hallways of the customer’s building.
 - It is acceptable that a courier traveling from one customer to another will pass by customers of the same or of the other company. No extra time delay is accrued for riding past a customer.
 - If it should happen that one company winds up with only a single customer, that company puts someone on site to deliver messages within that one building. This is considered a zero delivery time.

-----Input-----
Input starts with one line containing an integer $N$, the number of customers to be divided up, where $2 < N \leq 1000$.

This is followed by $N$ lines, each containing a pair of integers $x$ and $y$ denoting the position of one customer, where $0 \leq x, y \leq 1000$.

-----Output-----
Print a single line containing the longest delivery time required by the two companies (i.e., the maximum of the two longest delivery times offered by each company separately).

-----Examples-----
Sample Input:
6
1 1
4 1
1 5
10 10
10 8
7 10
Sample Output:
7

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
On vacations n pupils decided to go on excursion and gather all together. They need to overcome the path with the length l meters. Each of the pupils will go with the speed equal to v_1. To get to the excursion quickly, it was decided to rent a bus, which has seats for k people (it means that it can't fit more than k people at the same time) and the speed equal to v_2. In order to avoid seasick, each of the pupils want to get into the bus no more than once.

Determine the minimum time required for all n pupils to reach the place of excursion. Consider that the embarkation and disembarkation of passengers, as well as the reversal of the bus, take place immediately and this time can be neglected. 


-----Input-----

The first line of the input contains five positive integers n, l, v_1, v_2 and k (1 ≤ n ≤ 10 000, 1 ≤ l ≤ 10^9, 1 ≤ v_1 < v_2 ≤ 10^9, 1 ≤ k ≤ n) — the number of pupils, the distance from meeting to the place of excursion, the speed of each pupil, the speed of bus and the number of seats in the bus. 


-----Output-----

Print the real number — the minimum time in which all pupils can reach the place of excursion. Your answer will be considered correct if its absolute or relative error won't exceed 10^{ - 6}.


-----Examples-----
Input
5 10 1 2 5

Output
5.0000000000

Input
3 6 1 2 1

Output
4.7142857143



-----Note-----

In the first sample we should immediately put all five pupils to the bus. The speed of the bus equals 2 and the distance is equal to 10, so the pupils will reach the place of excursion in time 10 / 2 = 5.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper.
At least how many sheets of paper does he need?

-----Constraints-----
 - N is an integer.
 - 1 \leq N \leq 100

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

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

-----Sample Input-----
5

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

By printing the 1-st, 2-nd pages on the 1-st sheet, 3-rd and 4-th pages on the 2-nd sheet, and 5-th page on the 3-rd sheet, we can print all the data on 3 sheets of paper.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Let f(x) represent the number of set bits (i.e. bit = 1) in the binary representation of non-negative integer x.
For e.g. f(3) = 2, since 3 is represented as '11' in binary.

Xenny's friend Xynazog gave him the following task:

Given two non-negative integers A and B, find the sum of f(x) for all x in range [A, B] (A and B inclusive).

Xenny being bad at counting, needs your help to solve this task.
Input Format:

First line contains an integer T - the no. of testcases.

T lines follow.

Each line contains two space-separated integers - A and B.

Output Format:

Output an integer - the answer to each testcase on a newline.

Constraints:

1 ≤ T ≤ 10^5

1 ≤ A, B ≤ 10^9

SAMPLE INPUT
1
1 3

SAMPLE OUTPUT
4

Explanation

1 => '01'
2 => '10'
3 => '11'

Total Set Bits = 4

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

Time Limit: 2 seconds

Memory Limit: 64 megabytes

Problem Description:
Ever since Kalevitch, a famous Berland abstractionist, heard of fractals, he made them the main topic of his canvases. Every morning the artist takes a piece of graph paper and starts with making a model of his future canvas. He takes a square as big as *n*<=×<=*n* squares and paints some of them black. Then he takes a clean square piece of paper and paints the fractal using the following algorithm: 

Step 1. The paper is divided into *n*2 identical squares and some of them are painted black according to the model.

Step 2. Every square that remains white is divided into *n*2 smaller squares and some of them are painted black according to the model.

Every following step repeats step 2.

Unfortunately, this tiresome work demands too much time from the painting genius. Kalevitch has been dreaming of making the process automatic to move to making 3D or even 4D fractals.

Input Specification:
The first line contains integers *n* and *k* (2<=≤<=*n*<=≤<=3, 1<=≤<=*k*<=≤<=5), where *k* is the amount of steps of the algorithm. Each of the following *n* lines contains *n* symbols that determine the model. Symbol «.» stands for a white square, whereas «*» stands for a black one. It is guaranteed that the model has at least one white square.

Output Specification:
Output a matrix *n**k*<=×<=*n**k* which is what a picture should look like after *k* steps of the algorithm.

Demo Input:
['2 3\n.*\n..\n', '3 2\n.*.\n***\n.*.\n']

Demo Output:
['.*******\n..******\n.*.*****\n....****\n.***.***\n..**..**\n.*.*.*.*\n........\n', '.*.***.*.\n*********\n.*.***.*.\n*********\n*********\n*********\n.*.***.*.\n*********\n.*.***.*.\n']

Note:
none

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

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Problem Description:
In a Berland's zoo there is an enclosure with camels. It is known that camels like to spit. Bob watched these interesting animals for the whole day and registered in his notepad where each animal spitted. Now he wants to know if in the zoo there are two camels, which spitted at each other. Help him to solve this task.

The trajectory of a camel's spit is an arc, i.e. if the camel in position *x* spits *d* meters right, he can hit only the camel in position *x*<=+<=*d*, if such a camel exists.

Input Specification:
The first line contains integer *n* (1<=≤<=*n*<=≤<=100) — the amount of camels in the zoo. Each of the following *n* lines contains two integers *x**i* and *d**i* (<=-<=104<=≤<=*x**i*<=≤<=104,<=1<=≤<=|*d**i*|<=≤<=2·104) — records in Bob's notepad. *x**i* is a position of the *i*-th camel, and *d**i* is a distance at which the *i*-th camel spitted. Positive values of *d**i* correspond to the spits right, negative values correspond to the spits left. No two camels may stand in the same position.

Output Specification:
If there are two camels, which spitted at each other, output YES. Otherwise, output NO.

Demo Input:
['2\n0 1\n1 -1\n', '3\n0 1\n1 1\n2 -2\n', '5\n2 -10\n3 10\n0 5\n5 -5\n10 1\n']

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

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Consider an array $a$ of length $n$ with elements numbered from $1$ to $n$. It is possible to remove the $i$-th element of $a$ if $gcd(a_i, i) = 1$, where $gcd$ denotes the greatest common divisor. After an element is removed, the elements to the right are shifted to the left by one position.

An array $b$ with $n$ integers such that $1 \le b_i \le n - i + 1$ is a removal sequence for the array $a$ if it is possible to remove all elements of $a$, if you remove the $b_1$-th element, then the $b_2$-th, ..., then the $b_n$-th element. For example, let $a = [42, 314]$:

$[1, 1]$ is a removal sequence: when you remove the $1$-st element of the array, the condition $gcd(42, 1) = 1$ holds, and the array becomes $[314]$; when you remove the $1$-st element again, the condition $gcd(314, 1) = 1$ holds, and the array becomes empty.

$[2, 1]$ is not a removal sequence: when you try to remove the $2$-nd element, the condition $gcd(314, 2) = 1$ is false.

An array is ambiguous if it has at least two removal sequences. For example, the array $[1, 2, 5]$ is ambiguous: it has removal sequences $[3, 1, 1]$ and $[1, 2, 1]$. The array $[42, 314]$ is not ambiguous: the only removal sequence it has is $[1, 1]$.

You are given two integers $n$ and $m$. You have to calculate the number of ambiguous arrays $a$ such that the length of $a$ is from $1$ to $n$ and each $a_i$ is an integer from $1$ to $m$.


-----Input-----

The only line of the input contains two integers $n$ and $m$ ($2 \le n \le 3 \cdot 10^5$; $1 \le m \le 10^{12}$).


-----Output-----

Print one integer — the number of ambiguous arrays $a$ such that the length of $a$ is from $1$ to $n$ and each $a_i$ is an integer from $1$ to $m$. Since the answer can be very large, print it modulo $998244353$.


-----Examples-----

Input
2 3
Output
6
Input
4 2
Output
26
Input
4 6
Output
1494
Input
1337 424242424242
Output
119112628


-----Note-----

None

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The management of the software company JunkCode has recently found, much to their surprise and disappointment, that productivity has gone down since they implemented their enhanced set of coding guidelines. The idea was that all developers should make sure that every code change they push to the master branch of their software repository strictly follows the coding guidelines. After all, one of the developers, Perikles, has been doing this since long before these regulations became effective so how hard could it be? 

Rather than investing a lot of time figuring out why this degradation in productivity occurred, the line manager suggests that they loosen their requirement: developers can push code that weakly violates the guidelines as long as they run cleanup phases on the code from time to time to make sure the repository is tidy.

She suggests a metric where the “dirtiness” of a developer’s code is the sum of the pushes that violate the guidelines – so-called dirty pushes – made by that developer, each weighted by the number of days since it was pushed. The number of days since a dirty push is a step function that increases by one each midnight following the push. Hence, if a developer has made dirty pushes on days $1$, $2$, and $5$, the dirtiness on day $6$ is $5+4+1=10$. She suggests that a cleanup phase, completely fixing all violations of the coding guidelines, must be completed before the dirtiness reaches $20$. One of the developers, Petra, senses that this rule must be obeyed not only because it is a company policy. Breaking it will also result in awkward meetings with a lot of concerned managers who all want to know why she cannot be more like Perikles? Still, she wants to run the cleanup phase as seldomly as possible, and always postpones it until it is absolutely necessary. A cleanup phase is always run at the end of the day and fixes every dirty push done up to and including that day. Since all developers are shuffled to new projects at the start of each year, no dirtiness should be left after midnight at the end of new year’s eve.

-----Input-----
The first line of input contains an integer $n$ ($1 \leq n \leq 365$), the number of dirty pushes made by Petra during a year. The second line contains $n$ integers $d_1, d_2, \ldots , d_ n$ ($1 \leq d_ i \leq 365$ for each $1 \le i \le n$) giving the days when Petra made dirty pushes. You can assume that $d_ i < d_ j$ for $i < j$.

-----Output-----
Output the total number of cleanup phases needed for Petra to keep the dirtiness strictly below $20$ at all times.

-----Examples-----
Sample Input:
5
1 45 65 84 346
Sample Output:
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In the city of Saint Petersburg, a day lasts for $2^{100}$ minutes. From the main station of Saint Petersburg, a train departs after $1$ minute, $4$ minutes, $16$ minutes, and so on; in other words, the train departs at time $4^k$ for each integer $k \geq 0$. Team BowWow has arrived at the station at the time $s$ and it is trying to count how many trains have they missed; in other words, the number of trains that have departed strictly before time $s$. For example if $s = 20$, then they missed trains which have departed at $1$, $4$ and $16$. As you are the only one who knows the time, help them!

Note that the number $s$ will be given you in a binary representation without leading zeroes.


-----Input-----

The first line contains a single binary number $s$ ($0 \leq s < 2^{100}$) without leading zeroes.


-----Output-----

Output a single number — the number of trains which have departed strictly before the time $s$.


-----Examples-----
Input
100000000

Output
4

Input
101

Output
2

Input
10100

Output
3



-----Note-----

In the first example $100000000_2 = 256_{10}$, missed trains have departed at $1$, $4$, $16$ and $64$.

In the second example $101_2 = 5_{10}$, trains have departed at $1$ and $4$.

The third example is explained in the statements.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Free Ice Cream

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
After their adventure with the magic mirror Kay and Gerda have returned home and sometimes give free ice cream to kids in the summer.

At the start of the day they have *x* ice cream packs. Since the ice cream is free, people start standing in the queue before Kay and Gerda's house even in the night. Each person in the queue wants either to take several ice cream packs for himself and his friends or to give several ice cream packs to Kay and Gerda (carriers that bring ice cream have to stand in the same queue).

If a carrier with *d* ice cream packs comes to the house, then Kay and Gerda take all his packs. If a child who wants to take *d* ice cream packs comes to the house, then Kay and Gerda will give him *d* packs if they have enough ice cream, otherwise the child will get no ice cream at all and will leave in distress.

Kay wants to find the amount of ice cream they will have after all people will leave from the queue, and Gerda wants to find the number of distressed kids.

Input Specification:
The first line contains two space-separated integers *n* and *x* (1<=≤<=*n*<=≤<=1000, 0<=≤<=*x*<=≤<=109).

Each of the next *n* lines contains a character '+' or '-', and an integer *d**i*, separated by a space (1<=≤<=*d**i*<=≤<=109). Record "+ *d**i*" in *i*-th line means that a carrier with *d**i* ice cream packs occupies *i*-th place from the start of the queue, and record "- *d**i*" means that a child who wants to take *d**i* packs stands in *i*-th place.

Output Specification:
Print two space-separated integers — number of ice cream packs left after all operations, and number of kids that left the house in distress.

Demo Input:
['5 7\n+ 5\n- 10\n- 20\n+ 40\n- 20\n', '5 17\n- 16\n- 2\n- 98\n+ 100\n- 98\n']

Demo Output:
['22 1\n', '3 2\n']

Note:
Consider the first sample.
 1.  Initially Kay and Gerda have 7 packs of ice cream. 1.  Carrier brings 5 more, so now they have 12 packs. 1.  A kid asks for 10 packs and receives them. There are only 2 packs remaining. 1.  Another kid asks for 20 packs. Kay and Gerda do not have them, so the kid goes away distressed. 1.  Carrier bring 40 packs, now Kay and Gerda have 42 packs. 1.  Kid asks for 20 packs and receives them. There are 22 packs remaining.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
One day Polycarp decided to rewatch his absolute favourite episode of well-known TV series "Tufurama". He was pretty surprised when he got results only for season 7 episode 3 with his search query of "Watch Tufurama season 3 episode 7 online full hd free". This got Polycarp confused — what if he decides to rewatch the entire series someday and won't be able to find the right episodes to watch? Polycarp now wants to count the number of times he will be forced to search for an episode using some different method.

TV series have n seasons (numbered 1 through n), the i-th season has a_{i} episodes (numbered 1 through a_{i}). Polycarp thinks that if for some pair of integers x and y (x < y) exist both season x episode y and season y episode x then one of these search queries will include the wrong results. Help Polycarp to calculate the number of such pairs!


-----Input-----

The first line contains one integer n (1  ≤ n  ≤  2·10^5) — the number of seasons.

The second line contains n integers separated by space a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9) — number of episodes in each season.


-----Output-----

Print one integer — the number of pairs x and y (x < y) such that there exist both season x episode y and season y episode x.


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

Output
0

Input
3
8 12 7

Output
3

Input
3
3 2 1

Output
2



-----Note-----

Possible pairs in the second example:  x = 1, y = 2 (season 1 episode 2 [Image] season 2 episode 1);  x = 2, y = 3 (season 2 episode 3 [Image] season 3 episode 2);  x = 1, y = 3 (season 1 episode 3 [Image] season 3 episode 1). 

In the third example:  x = 1, y = 2 (season 1 episode 2 [Image] season 2 episode 1);  x = 1, y = 3 (season 1 episode 3 [Image] season 3 episode 1).

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