vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Alice is visiting New York City. To make the trip fun, Alice will take photos of the city skyline and give the set of photos as a present to Bob. However, she wants to find the set of photos with maximum beauty and she needs your help.

There are $n$ buildings in the city, the $i$-th of them has positive height $h_i$. All $n$ building heights in the city are different. In addition, each building has a beauty value $b_i$. Note that beauty can be positive or negative, as there are ugly buildings in the city too.

A set of photos consists of one or more photos of the buildings in the skyline. Each photo includes one or more buildings in the skyline that form a contiguous segment of indices. Each building needs to be in exactly one photo. This means that if a building does not appear in any photo, or if a building appears in more than one photo, the set of pictures is not valid.

The beauty of a photo is equivalent to the beauty $b_i$ of the shortest building in it. The total beauty of a set of photos is the sum of the beauty of all photos in it. Help Alice to find the maximum beauty a valid set of photos can have.


-----Input-----

The first line contains an integer $n$ ($1 \le n \le 3 \cdot 10^5$), the number of buildings on the skyline.

The second line contains $n$ distinct integers $h_1, h_2, \ldots, h_n$ ($1 \le h_i \le n$). The $i$-th number represents the height of building $i$.

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($-10^9 \le b_i \le 10^9$). The $i$-th number represents the beauty of building $i$.


-----Output-----

Print one number representing the maximum beauty Alice can achieve for a valid set of photos of the skyline.


-----Examples-----

Input
5
1 2 3 5 4
1 5 3 2 4
Output
15
Input
5
1 4 3 2 5
-3 4 -10 2 7
Output
10
Input
2
2 1
-2 -3
Output
-3
Input
10
4 7 3 2 5 1 9 10 6 8
-4 40 -46 -8 -16 4 -10 41 12 3
Output
96


-----Note-----

In the first example, Alice can achieve maximum beauty by taking five photos, each one containing one building.

In the second example, Alice can achieve a maximum beauty of $10$ by taking four pictures: three just containing one building, on buildings $1$, $2$ and $5$, each photo with beauty $-3$, $4$ and $7$ respectively, and another photo containing building $3$ and $4$, with beauty $2$.

In the third example, Alice will just take one picture of the whole city.

In the fourth example, Alice can take the following pictures to achieve maximum beauty: photos with just one building on buildings $1$, $2$, $8$, $9$, and $10$, and a single photo of buildings $3$, $4$, $5$, $6$, and $7$.

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

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Problem Description:
A chessboard *n*<=×<=*m* in size is given. During the zero minute we repaint all the black squares to the 0 color. During the *i*-th minute we repaint to the *i* color the initially black squares that have exactly four corner-adjacent squares painted *i*<=-<=1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly *x* times.

The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.

Input Specification:
The first line contains integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=5000). The second line contains integer *x* (1<=≤<=*x*<=≤<=109).

Output Specification:
Print how many squares will be painted exactly *x* times.

Demo Input:
['3 3\n1\n', '3 3\n2\n', '1 1\n1\n']

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

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef loves research! Now he is looking for subarray of maximal length with non-zero product.
Chef has an array A with N elements: A1, A2, ..., AN. 

Subarray Aij of array A is elements from index i to index j: Ai, Ai+1, ..., Aj. 
Product of subarray Aij is product of all its elements (from ith to jth). 

-----Input-----
- First line contains sinlge integer N denoting the number of elements.
- Second line contains N space-separated integers A1, A2, ..., AN denoting the elements of array. 

-----Output-----
- In a single line print single integer - the maximal length of subarray with non-zero product. 

-----Constraints-----
- 1 ≤ N ≤ 100000
- 0 ≤ Ai ≤ 10000

-----Example-----
Input:
6
1 0 2 3 0 4

Output:
2

Input:
1
0

Output:
0

Input:
3
1 0 1

Output:
1

-----Explanation-----
For the first sample subarray is: {2, 3}. 
For the second sample there are no subbarays with non-zero product. 
For the third sample subbarays is {1}, (the first element, or the third one).

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Dio Brando has set  a goal for himself of becoming the richest and the most powerful being on earth.To achieve his goals he will do anything using either manipulation,seduction or plain violence.
Only one guy stands between his goal of conquering earth ,named Jotaro Kujo aka JoJo .Now Dio has a stand (visual manifestation of life energy  i.e, special power )  “Za Warudo” ,which can stop time itself but needs to chant few words to activate the time stopping ability of the stand.There is a code hidden inside the words and if you can decipher the code then Dio loses his power.
In order to stop Dio ,Jotaro asks your help to decipher the code since he can’t do so while fighting Dio at the same time.
You will be given a string as input and you have to find the shortest substring which contains all the characters of itself and then make a number based on the alphabetical ordering of the characters.
For example : “bbbacdaddb”
shortest substring will be “bacd” and based on the alphabetical ordering
the answer is 2134

-----NOTE:-----
A substring is a contiguous subsegment of a string. For example, "acab" is a substring of "abacaba" (it starts in position 3 and ends in position 6), but "aa" or "d" aren't substrings of this string. So the substring of the string s from position l to position r is

S[l;r]=SlSl+1…Sr.

-----Input :-----
The first line contains $T$,number of test cases.
The second line contains a string $S$.

-----Output:-----
For each test cases ,output the number you can get from the shortest string 

-----Constraints:-----
$1 \leq t \leq 100$
$1 \leq |S| \leq 10^6$

-----Test Cases:-----

-----Sample Input:-----
6

abcdfgh

urdrdrav

jojojojoj

bbbbaaa

cddfsccs

tttttttttttt   

-----Sample Output:-----
1234678

2118418418122

1015

21

46193

20

-----Explanation:-----
Test case 1: abcdfgh is the shortest substring containing all char of itself and the number is 1234678

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?


-----Input-----

The first line of the input contains two integers s and x (2 ≤ s ≤ 10^12, 0 ≤ x ≤ 10^12), the sum and bitwise xor of the pair of positive integers, respectively.


-----Output-----

Print a single integer, the number of solutions to the given conditions. If no solutions exist, print 0.


-----Examples-----
Input
9 5

Output
4

Input
3 3

Output
2

Input
5 2

Output
0



-----Note-----

In the first sample, we have the following solutions: (2, 7), (3, 6), (6, 3), (7, 2).

In the second sample, the only solutions are (1, 2) and (2, 1).

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given an array A = [1, 2, 3, ..., n]:     

How many sequences ($S_{1}$) can you get after exact k adjacent swaps on A? 

How many sequences ($S_{2}$) can you get after at most k swaps on A?  

An adjacent swap can be made between two elements of the Array A, A[i] and A[i+1] or A[i] and A[i-1]. 

A swap otherwise can be between any two elements of the array A[i] and A[j] ∀ 1 ≤ i, j ≤ N, i ≠ j.

Input Format

First and only line contains n and k separated by space.    

Constraints

1 ≤ n ≤ 2500 

1 ≤ k ≤ 2500      

Output Format

Output $S_{1}$ % MOD and $S_{2} $% MOD in one line, where MOD = 1000000007.    

Sample Input
3 2

Sample Output
3 6

Explanation
Original array: [1, 2, 3]
1. After 2 adjacent swaps:
We can get [1, 2, 3], [2, 3, 1], [3, 1, 2] ==> S1 == 3

2. After at most 2 swaps:
1) After 0 swap: [1, 2, 3]
2) After 1 swap: [2, 1, 3], [3, 2, 1], [1, 3, 2].
3) After 2 swaps: [1, 2, 3], [2, 3, 1], [3, 1, 2]
==> S2 == 6

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Yes! You’ve finally been chosen to participate in the "Great Geek Game-show 3000". This is the moment you’ve been waiting for, ever since you puzzled out how to maximise your chances of winning. You will finally be rich, and able to buy all the algorithm books you want! Of course you will have to share the winnings with the other contestants, but since your algorithm is vastly superior to the randomness of all the other numb-skulls you are certain you will be able to keep most of the prize money for yourself, in exchange for telling them how you can all maximise your chances of winning. 

The rules of the game are the following: There is a stage with $N$ boxes, each containing the name of one of the $N$ contestants, and such that each contestant has their name in exactly one box. The contestants enter the stage one at a time, and each one is allowed to peek inside $K$ of the boxes. If they find their own name inside one of these boxes they can get off the stage, and the game continues with the next contestant. If all contestants find their own name, everyone wins. But if one contestant fails to find theirs, everyone loses. After the game has begun, no communication between the contestants is allowed. However you are all allowed to agree upon a strategy before the game begins, and this is where you explain to all the others that the algorithm of everyone choosing $K$ boxes at random is a very bad one, since it gives a chance of winning only equal to $\left(\frac{K}{N}\right)^N$. Instead you suggest the following algorithm:

Assign to each player and each box a unique number in the range $1, \dots , N$. Then each player starts with opening the box with the same number as themselves. The next box the player opens is the box whose number is found inside the first box, then the box whose number is found inside the second box, and so on. The process goes on until the player has opened $K$ boxes, or found their own number.

Now to bring home your point of how superior your algorithm is, you will need to calculate the exact odds of winning if all the contestants follow your directions. Unfortunately, this is the only thing you haven’t figured out yet

-----Input-----
One line with the following integers:

$1 \leq N \leq 10000000$ – the number of contestants.

$1 \leq K \leq N$ – the number of boxes each contestant may check.

-----Output-----
The chances you have of winning if everyone follows your algorithm. The answer should be accurate to an absolute or relative error of at most $10^{-6}$.

-----Examples-----
Sample Input 1:
4 2
Sample Output 1:
0.416667

Sample Input 2:
6 5
Sample Output 2:
0.833333

Sample Input 3:
137 42
Sample Output 3:
0.029351

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Hit n nails one by one at the coordinates P1 (x1, y1), P2 (x2, y2), P3 (x3, y3), ..., Pn (xn, yn) on the flat plate, and put them on the rubber band ring. Surround it with a single rubber band so that all the nails fit inside. At this time, the rubber bands must not intersect.

Create a program that reads the coordinates of the nails and outputs the number of nails that are not in contact with the rubber band when the nail is surrounded by the rubber band as described above. The rubber band shall expand and contract sufficiently. You may not hit more than one nail at the same coordinates. In addition, it is assumed that the nails covered with rubber bands are connected by a straight line, and that no more than three nails are lined up on the straight line. For example, there can be no input as shown in Figure 1. As shown in Figure 2, it is possible for nails without rubber bands to line up in a straight line.

<image> | <image>
--- | ---
Figure 1 | Figure 2



However, each coordinate value is a real number between -1000.0 and 1000.0. Also, n is an integer between 3 and 100.

Hint

Below is a diagram for the second sample input.

<image>
---



Input

Given multiple datasets. Each dataset is given in the following format:


n
x1, y1
x2, y2
...
...
xn, yn


When n is 0, it indicates the end of input. The number of datasets does not exceed 50.

Output

For each dataset, output the number of nails that are not in contact with the rubber. For example, if there is an input representing the four nails shown in Fig. 3, it will be surrounded as shown in Fig. 4, so the number of nails that are not in contact with the rubber band is one.

<image> | <image>
--- | ---
Figure 3 | Figure 4


Example

Input

4
1.0,0.0
0.0,1.0
2.0,1.0
1.0,2.0
9
-509.94,892.63
567.62,639.99
-859.32,-64.84
-445.99,383.69
667.54,430.49
551.12,828.21
-940.2,-877.2
-361.62,-970
-125.42,-178.48
0


Output

0
3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Preparing for Merge Sort

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Ivan has an array consisting of *n* different integers. He decided to reorder all elements in increasing order. Ivan loves merge sort so he decided to represent his array with one or several increasing sequences which he then plans to merge into one sorted array.

Ivan represent his array with increasing sequences with help of the following algorithm.

While there is at least one unused number in array Ivan repeats the following procedure:
 -  iterate through array from the left to the right; -  Ivan only looks at unused numbers on current iteration; -  if current number is the first unused number on this iteration or this number is greater than previous unused number on current iteration, then Ivan marks the number as used and writes it down. 
For example, if Ivan's array looks like [1, 3, 2, 5, 4] then he will perform two iterations. On first iteration Ivan will use and write numbers [1, 3, 5], and on second one — [2, 4].

Write a program which helps Ivan and finds representation of the given array with one or several increasing sequences in accordance with algorithm described above.

Input Specification:
The first line contains a single integer *n* (1<=≤<=*n*<=≤<=2·105) — the number of elements in Ivan's array.

The second line contains a sequence consisting of distinct integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=109) — Ivan's array.

Output Specification:
Print representation of the given array in the form of one or more increasing sequences in accordance with the algorithm described above. Each sequence must be printed on a new line.

Demo Input:
['5\n1 3 2 5 4\n', '4\n4 3 2 1\n', '4\n10 30 50 101\n']

Demo Output:
['1 3 5 \n2 4 \n', '4 \n3 \n2 \n1 \n', '10 30 50 101 \n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.

Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.

In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).

He may perform the following operation arbitrarily many times:

* Put an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x,y) \rightarrow (x+D,y) \rightarrow (x+D,y+D) \rightarrow (x,y+D) \rightarrow (x,y) in this order. Each of the four corners of the square must be on a lattice point.



Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.

Find the minimum scatteredness after he performs arbitrarily many operations.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq D \leq 1000
* 0 \leq x_i, y_i \leq 10^9
* Given coordinates are pairwise distinct
* All numbers given in input are integers

Input

Input is given from Standard Input in the following format:


N D
x_1 y_1
:
x_N y_N


Output

Print the answer.

Examples

Input

3 1
0 0
1 0
2 0


Output

1


Input

19 2
1 3
2 3
0 1
1 1
2 1
3 1
4 4
5 4
6 4
7 4
8 4
8 3
8 2
8 1
8 0
7 0
6 0
5 0
4 0


Output

4


Input

8 3
0 0
0 3
3 0
3 3
2 2
2 5
5 2
5 5


Output

4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chandu and Kundu are bored of dramatic games around. As they are very good friends and scholars they decided to discover a new game.  
In total they had N number of marbles with value inscribed on each of them from 1 to N. 
Chandu being from royal family has a treasure box. He emptied the box for the game to proceed.   

The game rule involved following operations : 
- Operation C : Chandu places a marble in the box. Each different marble can move inside the box only once. 
- Operation K : Kundu removes last entered marble from the box and notes down it's value on a chart.   

They were deciding further rules when a third person Mr. Chirp comes as a spoiler of the game.
Chirp gives them a number N which is the maximum value inscribed among all marbles, and a sequence P. P can possibly be empty. In that case, in input an empty line would be there.   

Also, he added following restriction : 
- Kundu can perform operation K to take out a marble M only when all the marbles from values 1 to M-1 have went in the box before.    

Mr. Chirp kept on chirping and told Chandu and Kundu to generate the sequence of C's and K's for the chart to get filled by pattern P. 
Now, you have to help these kids before they jump out of their window in frustration.

Input Format : 
First line contains a number N. Next line contains a pattern P(possibly empty). 
Read till end of file.Note: Maximum input cases in a file doesn't exceed 2*10^4.

Output Format :
For each case output on a separate line the minimum length pattern of C's and K's. Print -1 if it's not possible to generate the pattern using the given operations.   

Constraints : 
1 ≤ N ≤ 10^5 
0 ≤ len(P) ≤ 100
1 ≤ P[i] ≤ N

SAMPLE INPUT
41
6 11 8

SAMPLE OUTPUT
CCCCCCKCCCCCKKKK

Explanation

For getting 6 on chart first we need six C Operations for 1,2,3,4,5 and 6 followed by one K operation for getting 6 out. Afterwards for 11 we perform five C operations for 7,8,9,10,11 followed by one K operation. And finally, for 8 we need four K operations for 10, 9, 8 respectively.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Hasan loves playing games and has recently discovered a game called TopScore. In this soccer-like game there are $p$ players doing penalty shoot-outs. Winner is the one who scores the most. In case of ties, one of the top-scorers will be declared as the winner randomly with equal probability.

They have just finished the game and now are waiting for the result. But there's a tiny problem! The judges have lost the paper of scores! Fortunately they have calculated sum of the scores before they get lost and also for some of the players they have remembered a lower bound on how much they scored. However, the information about the bounds is private, so Hasan only got to know his bound.

According to the available data, he knows that his score is at least $r$ and sum of the scores is $s$.

Thus the final state of the game can be represented in form of sequence of $p$ integers $a_1, a_2, \dots, a_p$ ($0 \le a_i$) — player's scores. Hasan is player number $1$, so $a_1 \ge r$. Also $a_1 + a_2 + \dots + a_p = s$. Two states are considered different if there exists some position $i$ such that the value of $a_i$ differs in these states. 

Once again, Hasan doesn't know the exact scores (he doesn't know his exact score as well). So he considers each of the final states to be equally probable to achieve.

Help Hasan find the probability of him winning.

It can be shown that it is in the form of $\frac{P}{Q}$ where $P$ and $Q$ are non-negative integers and $Q \ne 0$, $P \le Q$. Report the value of $P \cdot Q^{-1} \pmod {998244353}$.


-----Input-----

The only line contains three integers $p$, $s$ and $r$ ($1 \le p \le 100$, $0 \le r \le s \le 5000$) — the number of players, the sum of scores of all players and Hasan's score, respectively.


-----Output-----

Print a single integer — the probability of Hasan winning.

It can be shown that it is in the form of $\frac{P}{Q}$ where $P$ and $Q$ are non-negative integers and $Q \ne 0$, $P \le Q$. Report the value of $P \cdot Q^{-1} \pmod {998244353}$.


-----Examples-----
Input
2 6 3

Output
124780545

Input
5 20 11

Output
1

Input
10 30 10

Output
85932500



-----Note-----

In the first example Hasan can score $3$, $4$, $5$ or $6$ goals. If he scores $4$ goals or more than he scores strictly more than his only opponent. If he scores $3$ then his opponent also scores $3$ and Hasan has a probability of $\frac 1 2$ to win the game. Thus, overall he has the probability of $\frac 7 8$ to win.

In the second example even Hasan's lower bound on goal implies him scoring more than any of his opponents. Thus, the resulting probability is $1$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Way Too Long Words

Time Limit: 1 seconds

Memory Limit: 256 megabytes

Problem Description:
Sometimes some words like "localization" or "internationalization" are so long that writing them many times in one text is quite tiresome.

Let's consider a word too long, if its length is strictly more than 10 characters. All too long words should be replaced with a special abbreviation.

This abbreviation is made like this: we write down the first and the last letter of a word and between them we write the number of letters between the first and the last letters. That number is in decimal system and doesn't contain any leading zeroes.

Thus, "localization" will be spelt as "l10n", and "internationalization» will be spelt as "i18n".

You are suggested to automatize the process of changing the words with abbreviations. At that all too long words should be replaced by the abbreviation and the words that are not too long should not undergo any changes.

Input Specification:
The first line contains an integer *n* (1<=≤<=*n*<=≤<=100). Each of the following *n* lines contains one word. All the words consist of lowercase Latin letters and possess the lengths of from 1 to 100 characters.

Output Specification:
Print *n* lines. The *i*-th line should contain the result of replacing of the *i*-th word from the input data.

Demo Input:
['4\nword\nlocalization\ninternationalization\npneumonoultramicroscopicsilicovolcanoconiosis\n']

Demo Output:
['word\nl10n\ni18n\np43s\n']

Note:
none

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