vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
You are given a garland consisting of $n$ lamps. States of the lamps are represented by the string $s$ of length $n$. The $i$-th character of the string $s_i$ equals '0' if the $i$-th lamp is turned off or '1' if the $i$-th lamp is turned on. You are also given a positive integer $k$.

In one move, you can choose one lamp and change its state (i.e. turn it on if it is turned off and vice versa).

The garland is called $k$-periodic if the distance between each pair of adjacent turned on lamps is exactly $k$. Consider the case $k=3$. Then garlands "00010010", "1001001", "00010" and "0" are good but garlands "00101001", "1000001" and "01001100" are not. Note that the garland is not cyclic, i.e. the first turned on lamp is not going after the last turned on lamp and vice versa.

Your task is to find the minimum number of moves you need to make to obtain $k$-periodic garland from the given one.

You have to answer $t$ independent test cases.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 25~ 000$) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains two integers $n$ and $k$ ($1 \le n \le 10^6; 1 \le k \le n$) — the length of $s$ and the required period. The second line of the test case contains the string $s$ consisting of $n$ characters '0' and '1'.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$ ($\sum n \le 10^6$).


-----Output-----

For each test case, print the answer — the minimum number of moves you need to make to obtain $k$-periodic garland from the given one.


-----Example-----
Input
6
9 2
010001010
9 3
111100000
7 4
1111111
10 3
1001110101
1 1
1
1 1
0

Output
1
2
5
4
0
0

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

Select 3 grid points from the closed rectangular section surrounded by points (0,0), (n-1,0), (0, m-1), (n-1, m-1) and make a triangle. make.
At this time, the absolute difference between the number of triangles containing the point (x1, y1) but not the point (x2, y2) and the number of triangles containing the point (x2, y2) but not the point (x1, y1) Find the value.
Those whose points are on the border are considered to be included in the triangle.
However, if the three points are aligned in a straight line, it is not considered to be a triangle.

Constraints

* 2 ≤ n, m ≤ 500
* 0 ≤ x1, x2 ≤ n-1
* 0 ≤ y1, y2 ≤ m-1
* (x1, y1) ≠ (x2, y2)

Input


n m x1 y1 x2 y2


All inputs are given as integers.
N, m, x1, y1, x2, y2 are given on one line, separated by blanks.

Output

Output the absolute value of the difference on one line.

Examples

Input

2 2 0 0 0 1


Output

0


Input

3 2 1 0 0 0


Output

3

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

The Pony Express was a mail service operating in the US in 1859-60.




It reduced the time for messages to travel between the Atlantic and Pacific coasts to about 10 days, before it was made obsolete by the [transcontinental telegraph](https://en.wikipedia.org/wiki/First_transcontinental_telegraph).

# How it worked

There were a number of *stations*, where:

* The rider switched to a fresh horse and carried on, or
* The mail bag was handed over to the next rider


# Kata Task

`stations` is a list/array of distances (miles) from one station to the next along the Pony Express route.

Implement the `riders` method/function, to return how many riders are necessary to get the mail from one end to the other.

**NOTE:** Each rider travels as far as he can, but never more than 100 miles.

---
*Good Luck.
DM.*

---

See also

* The Pony Express
* The Pony Express (missing rider)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
This is the time of Akbar and Birbal. One day , in the state there happened some riots and murders .Akbar found some N people guilty in this matter.He called Birbal to punish them .Birbal gave them a unique punishment .He ordered the first person(guilty) to dig all the N spaces indicated on the ground.Then he called the second person to dig all the even spaces on the ground(spaces in multiples of 2) ,and if the space is already digged then fill it by sand .Similarly ,he asked the third person to dig all the spaces in multiple of 3 and fill it if it is already digged...an so on. After the N persons have completed their punishments,Birbal asked the first person to tell the amount of spaces remained undigged .What is the answer of this person??

INPUT:
A single integer(T),denoting the number of test cases.
Then,following T lines will contain a single line containing integer N.

OUTPUT:
A integer for each test case denoting the answer of the person.

Constraints:
0<T ≤ 100
0<N<10^18

SAMPLE INPUT
1
2

SAMPLE OUTPUT
1

Explanation

In given sample Input,there are 2 persons. So first will come and dig the 1st and 2nd space.Then ,2nd person will come and as the 2nd space is already digged so he will fill 2nd space.Therefore,the number of undigged spaces is only 1 i.e. the required answer.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Innokentiy decides to change the password in the social net "Contact!", but he is too lazy to invent a new password by himself. That is why he needs your help. 

Innokentiy decides that new password should satisfy the following conditions:
 -  the length of the password must be equal to *n*, -  the password should consist only of lowercase Latin letters, -  the number of distinct symbols in the password must be equal to *k*, -  any two consecutive symbols in the password must be distinct. 
Your task is to help Innokentiy and to invent a new password which will satisfy all given conditions.

Input Specification:
The first line contains two positive integers *n* and *k* (2<=≤<=*n*<=≤<=100, 2<=≤<=*k*<=≤<=*min*(*n*,<=26)) — the length of the password and the number of distinct symbols in it. 

Pay attention that a desired new password always exists.

Output Specification:
Print any password which satisfies all conditions given by Innokentiy.

Demo Input:
['4 3\n', '6 6\n', '5 2\n']

Demo Output:
['java\n', 'python\n', 'phphp\n']

Note:
In the first test there is one of the appropriate new passwords — java, because its length is equal to 4 and 3 distinct lowercase letters a, j and v are used in it.

In the second test there is one of the appropriate new passwords — python, because its length is equal to 6 and it consists of 6 distinct lowercase letters.

In the third test there is one of the appropriate new passwords — phphp, because its length is equal to 5 and 2 distinct lowercase letters p and h are used in it.

Pay attention the condition that no two identical symbols are consecutive is correct for all appropriate passwords in tests.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Little Chris is bored during his physics lessons (too easy), so he has built a toy box to keep himself occupied. The box is special, since it has the ability to change gravity.

There are n columns of toy cubes in the box arranged in a line. The i-th column contains ai cubes. At first, the gravity in the box is pulling the cubes downwards. When Chris switches the gravity, it begins to pull all the cubes to the right side of the box. The figure shows the initial and final configurations of the cubes in the box: the cubes that have changed their position are highlighted with orange.

<image>

Given the initial configuration of the toy cubes in the box, find the amounts of cubes in each of the n columns after the gravity switch!

Input

The first line of input contains an integer n (1 ≤ n ≤ 100), the number of the columns in the box. The next line contains n space-separated integer numbers. The i-th number ai (1 ≤ ai ≤ 100) denotes the number of cubes in the i-th column.

Output

Output n integer numbers separated by spaces, where the i-th number is the amount of cubes in the i-th column after the gravity switch.

Examples

Input

4
3 2 1 2


Output

1 2 2 3 


Input

3
2 3 8


Output

2 3 8 

Note

The first example case is shown on the figure. The top cube of the first column falls to the top of the last column; the top cube of the second column falls to the top of the third column; the middle cube of the first column falls to the top of the second column.

In the second example case the gravity switch does not change the heights of the columns.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Recall the definition of the Fibonacci numbers:


f1 := 1

f2 := 2

fn := fn-1 + fn-2 (n>=3)

Given two numbers a and b, calculate how many Fibonacci numbers are in the range [a,b].


-----Input-----

The input contains several test cases. Each test case consists of two non-negative integer numbers a and b. Input is terminated by a=b=0. Otherwise, a<=b<=10^100. The numbers a and b are given with no superfluous leading zeros.

-----Output-----

For each test case output on a single line the number of Fibonacci numbers fi with a<=fi<=b.

-----Example-----
Input:

10 100
1234567890 9876543210
0 0

Output:

5
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Alice and Bob are playing Dots and Boxes. The game is played on an $N\times N$ square lattice of dots, and they alternate drawing a line segment between horizontally or vertically adjacent dots that haven’t been connected before. Every time a unit square is formed by four line segments, the player who put down the last segment scores one point for that square. The game ends when the square lattice has been completely filled with line segments, and whoever scored the most points wins.

Alice and Bob aren’t really in a competitive mood today, so they’ve just been playing for fun. Hence they aren’t following any specific game strategy, and, in particular, even if it’s possible to make a move that scores a point or is clearly superior in some way, they won’t necessarily make that move. But now they’ve been playing for a while and neither of them has scored a single point. If neither of them scores a point pretty soon, they may get bored. Given the current state of the game, how many moves could be made, in the worst case, before either Alice or Bob is guaranteed to have scored a point?

-----Input-----
Input starts with a line containing an integer $N$ ($2 \leq N \leq 80$), the size of the square lattice. Then follows an ASCII representation of the current state of the game, $2N-1$ rows high and $2N-1$ columns wide, listed in row-major order. There are cells of four types ($1 \leq i,j \leq N$):
 - Cell $(2i-1,2j-1)$ is ‘*’, representing dot $(i,j)$.
 - Cell $(2i,2j)$ is ‘.’, representing empty space.
 - Cell $(2i,2j-1)$ is ‘|’ if dots $(i,j)$ and $(i+1,j)$ have been connected by a line segment, and ‘.’ otherwise.
 - Cell $(2i-1,2j)$ is ‘-’ if dots $(i,j)$ and $(i,j+1)$ have been connected by a line segment, and ‘.’ otherwise.

It is guaranteed that no player has scored a point, meaning that no unit squares have been formed.

-----Output-----
Output the number of moves that can be made, in the worst case, before either Alice or Bob is guaranteed to have scored a point.

-----Examples-----
Sample Input 1:
3
*-*.*
|.|.|
*.*-*
|...|
*.*.*
Sample Output 1:
3

Sample Input 2:
2
*.*
...
*.*
Sample Output 2:
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The bear decided to store some raspberry for the winter. He cunningly found out the price for a barrel of honey in kilos of raspberry for each of the following n days. According to the bear's data, on the i-th (1 ≤ i ≤ n) day, the price for one barrel of honey is going to is x_{i} kilos of raspberry.

Unfortunately, the bear has neither a honey barrel, nor the raspberry. At the same time, the bear's got a friend who is ready to lend him a barrel of honey for exactly one day for c kilograms of raspberry. That's why the bear came up with a smart plan. He wants to choose some day d (1 ≤ d < n), lent a barrel of honey and immediately (on day d) sell it according to a daily exchange rate. The next day (d + 1) the bear wants to buy a new barrel of honey according to a daily exchange rate (as he's got some raspberry left from selling the previous barrel) and immediately (on day d + 1) give his friend the borrowed barrel of honey as well as c kilograms of raspberry for renting the barrel.

The bear wants to execute his plan at most once and then hibernate. What maximum number of kilograms of raspberry can he earn? Note that if at some point of the plan the bear runs out of the raspberry, then he won't execute such a plan.


-----Input-----

The first line contains two space-separated integers, n and c (2 ≤ n ≤ 100, 0 ≤ c ≤ 100), — the number of days and the number of kilos of raspberry that the bear should give for borrowing the barrel.

The second line contains n space-separated integers x_1, x_2, ..., x_{n} (0 ≤ x_{i} ≤ 100), the price of a honey barrel on day i.


-----Output-----

Print a single integer — the answer to the problem.


-----Examples-----
Input
5 1
5 10 7 3 20

Output
3

Input
6 2
100 1 10 40 10 40

Output
97

Input
3 0
1 2 3

Output
0



-----Note-----

In the first sample the bear will lend a honey barrel at day 3 and then sell it for 7. Then the bear will buy a barrel for 3 and return it to the friend. So, the profit is (7 - 3 - 1) = 3.

In the second sample bear will lend a honey barrel at day 1 and then sell it for 100. Then the bear buy the barrel for 1 at the day 2. So, the profit is (100 - 1 - 2) = 97.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We consider permutations of the numbers $1,..., N$ for some $N$. By permutation we mean a rearrangment of the number $1,...,N$. For example
24517638245176382 \quad 4 \quad 5 \quad 1 \quad 7 \quad 6 \quad 3 \quad 8
is a permutation of $1,2,...,8$. Of course,
12345678123456781 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7 \quad 8
is also a permutation of $1,2,...,8$.
We can "walk around" a permutation in a interesting way and here is how it is done for the permutation above:
Start at position $1$. At position $1$ we have $2$ and so we go to position $2$. Here we find $4$ and so we go to position $4$. Here we find $1$, which is a position that we have already visited. This completes the first part of our walk and we denote this walk by  ($1$ $2$ $4$ $1$). Such a walk is called a cycle. An interesting property of such walks, that you may take for granted, is that the position we revisit will always be the one we started from!
We continue our walk by jumping to first unvisited position, in this case position $3$ and continue in the same manner. This time we find $5$ at position $3$ and so we go to position $5$ and find $7$ and we go to position $7$ and find $3$ and thus we get the cycle ($3$ $5$ $7$ $3$). Next we start at position $6$ and get ($6$ $6$), and finally we start at position $8$ and get the cycle ($8$ $8$). We have exhausted all the positions. Our walk through this permutation consists of $4$ cycles.
One can carry out this walk through any permutation and obtain a set of cycles as the result. Your task is to print out the cycles that result from walking through a given permutation.

-----Input:-----
The first line of the input is a positive integer $N$ indicating the length of the permutation. The next line contains $N$ integers and is a permutation of $1,2,...,N$.

-----Output:-----
The first line of the output must contain a single integer $k$ denoting the number of cycles in the permutation. Line $2$ should describe the first cycle, line $3$ the second cycle and so on and line $k+1$ should describe the $k^{th}$ cycle.

-----Constraints:-----
- $1 \leq N \leq 1000$.

-----Sample input 1:-----
8
2 4 5 1 7 6 3 8

-----Sample output 1:-----
4
1 2 4 1
3 5 7 3
6 6
8 8 

-----Sample input 2:-----
8
1 2 3 4 5 6 7 8

-----Sample output 2:-----
8
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are N islands lining up from west to east, connected by N-1 bridges.
The i-th bridge connects the i-th island from the west and the (i+1)-th island from the west.
One day, disputes took place between some islands, and there were M requests from the inhabitants of the islands:
Request i: A dispute took place between the a_i-th island from the west and the b_i-th island from the west. Please make traveling between these islands with bridges impossible.
You decided to remove some bridges to meet all these M requests.
Find the minimum number of bridges that must be removed.

-----Constraints-----
 - All values in input are integers.
 - 2 \leq N \leq 10^5
 - 1 \leq M \leq 10^5
 - 1 \leq a_i < b_i \leq N
 - All pairs (a_i, b_i) are distinct.

-----Input-----
Input is given from Standard Input in the following format:
N M
a_1 b_1
a_2 b_2
:
a_M b_M

-----Output-----
Print the minimum number of bridges that must be removed.

-----Sample Input-----
5 2
1 4
2 5

-----Sample Output-----
1

The requests can be met by removing the bridge connecting the second and third islands from the west.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Magic The Gathering is a collectible card game that features wizards battling against each other with spells and creature summons. The game itself can be quite complicated to learn. In this series of katas, we'll be solving some of the situations that arise during gameplay. You won't need any prior knowledge of the game to solve these contrived problems, as I will provide you with enough information.

## Creatures

Each creature has a power and toughness. We will represent this in an array. [2, 3] means this creature has a power of 2 and a toughness of 3.

When two creatures square off, they each deal damage equal to their power to each other at the same time. If a creature takes on damage greater than or equal to their toughness, they die.

Examples:

- Creature 1 - [2, 3]
- Creature 2 - [3, 3]
- Creature 3 - [1, 4]
- Creature 4 - [4, 1]

If creature 1 battles creature 2, creature 1 dies, while 2 survives. If creature 3 battles creature 4, they both die, as 3 deals 1 damage to 4, but creature 4 only has a toughness of 1.

Write a function `battle(player1, player2)` that takes in 2 arrays of creatures. Each players' creatures battle each other in order (player1[0] battles the creature in player2[0]) and so on. If one list of creatures is longer than the other, those creatures are considered unblocked, and do not battle.

Your function should return an object (a hash in Ruby) with the keys player1 and player2 that contain the power and toughness of the surviving creatures.

Example:
```
Good luck with your battles!


Check out my other Magic The Gathering katas:


Magic The Gathering #1: Creatures
Magic The Gathering #2: Mana

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has a sequence $A_1, A_2, \ldots, A_N$. For a positive integer $M$, sequence $B$ is defined as $B = A*M$ that is, appending $A$ exactly $M$ times. For example, If $A = [1, 2]$ and $M = 3$, then $B = A*M = [1, 2, 1, 2, 1, 2]$
You have to help him to find out the minimum value of $M$ such that the length of the longest strictly increasing subsequence is maximum possible.

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output:-----
For each test case, print a single line containing one integer ― the minimum value of $M$.

-----Constraints-----
- $1 \le T \le 500$
- $1 \le N \le 2*10^5$
- $1 \le A_i \le 10^9$
- It's guaranteed that the total length of the sequence $A$ in one test file doesn't exceed $2*10^6$

-----Sample Input:-----
3
2
2 1
2
1 2
5
1 3 2 1 2

-----Sample Output:-----
2
1
2

-----Explanation:-----
In the first test case, Choosing $M = 2$ gives $B = [2, 1, 2, 1]$ which has a longest strictly increasing sequence of length $2$ which is the maximum possible.
In the second test case, Choosing $M = 1$ gives $B  = [1, 2]$ which has a longest strictly increasing sequence of length $2$ which is the maximum possible.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Petya has a polygon consisting of $n$ vertices. All sides of the Petya's polygon are parallel to the coordinate axes, and each two adjacent sides of the Petya's polygon are perpendicular. It is guaranteed that the polygon is simple, that is, it doesn't have self-intersections and self-touches. All internal area of the polygon (borders are not included) was painted in black color by Petya.

Also, Petya has a rectangular window, defined by its coordinates, through which he looks at the polygon. A rectangular window can not be moved. The sides of the rectangular window are parallel to the coordinate axes.

Determine the number of black connected areas of Petya's polygon, which can be seen through the rectangular window.

Input Specification:
The first line contain four integers $x_1, y_1, x_2, y_2$ ($x_1 &lt; x_2$, $y_2 &lt; y_1$) — the coordinates of top-left and bottom-right corners of the rectangular window. 

The second line contains a single integer $n$ ($4 \le n \le 15\,000$) — the number of vertices in Petya's polygon.

Each of the following $n$ lines contains two integers — the coordinates of vertices of the Petya's polygon in counterclockwise order. Guaranteed, that the given polygon satisfies the conditions described in the statement.

All coordinates of the rectangular window and all coordinates of the vertices of the polygon are non-negative and do not exceed $15\,000$.

Output Specification:
Print the number of black connected areas of Petya's polygon, which can be seen through the rectangular window.

Demo Input:
['5 7 16 3\n16\n0 0\n18 0\n18 6\n16 6\n16 1\n10 1\n10 4\n7 4\n7 2\n2 2\n2 6\n12 6\n12 12\n10 12\n10 8\n0 8\n']

Demo Output:
['2']

Note:
The example corresponds to the picture above.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given $S$, a set of integers, find the largest $d$ such that $a + b + c = d$ where $a, b, c$ and $d$ are distinct elements of $S$.

-----Input-----
The input starts with an integer $1 \le N \le 4000$, the number of elements in $S$. It is followed by $N$ lines containing the elements of $s$, one per line. Each element of $S$ is a distinct integer between $-536870912$ and $+536870911$, inclusive.

-----Output-----
Output a single line containing the maximum $d$ as described in the statement. If no such $d$ exists, output a single line containing no solution.

-----Examples-----
Sample Input:
5
2
3
5
7
12
Sample Output:
12

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: 000001

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
The input contains a single integer *a* (1<=≤<=*a*<=≤<=64).

Output a single integer.

Input Specification:
The input contains a single integer *a* (1<=≤<=*a*<=≤<=64).

Output Specification:
Output a single integer.

Demo Input:
['2\n', '4\n', '27\n', '42\n']

Demo Output:
['1\n', '2\n', '5\n', '6\n']

Note:
none

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