vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
In many programming languages, the “plus” symbol (‘+’) has at least two standard meanings:
 - arithmetic addition
 - string concatenation

Inspired by the old adage, “Variety is the spice of life,” the designers of the Doubleplusgood (DPG) language (launched to great fanfare in 1984 by the Ministry of Truth Tables) decided that, in certain contexts, the meaning of the plus symbol would be decided dynamically and randomly at run time. In particular, for expressions consisting of alternating integers and plus symbols, every time the same program is executed, the meaning of each plus symbol is randomly chosen to be either addition or string concatenation. It follows that a single expression of this form can potentially evaluate to many different integers. For example, consider\[ 1+9+8+4 \]

For clarity, we’ll use $\boxplus $ to denote a plus symbol that the DPG runtime environment decides to interpret as string concatenation, which, it is important to note, has higher precedence than addition in DPG. Then $1+9+8+4$ can evaluate to $7$ distinct values:\begin{align*} 1\boxplus 9 \boxplus 8 \boxplus 4 & =1984\\ 1 \boxplus 9 \boxplus 8 + 4 & =198 + 4 =202\\ 1 \boxplus 9 + 8 \boxplus 4 & =19 + 84 =103\\ 1 \boxplus 9 + 8 + 4 & =19 + 8 + 4 =31\\ 1 + 9 \boxplus 8 \boxplus 4 & =1 + 984 =985\\ 1 + 9 \boxplus 8 + 4 & =1 + 98 + 4 =103\\ 1 + 9 + 8 \boxplus 4 & =1 + 9 + 84 =94\\ 1 + 9 + 8 + 4 & =22 \end{align*}

(Note that $103$ was formed in two different ways.) Given a sequence of alternating integers and plus symbols, your task is to determine the number of distinct integers to which the expression can evaluate.

-----Input-----
The input is a single line consisting of alternating positive integers and plus symbols. The line begins and ends with a positive integer, and is guaranteed to contain at least one plus symbol. The maximum number of digits in the input is $18$.

-----Output-----
Output the number of distinct integers to which the input expression can evaluate in DPG.

-----Examples-----
Sample Input 1:
1+9+8+4
Sample Output 1:
7

Sample Input 2:
1+2+3+4+5+6+7+8+9
Sample Output 2:
188

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

Write a function that takes a negative or positive integer, which represents the number of minutes before (-) or after (+) Sunday midnight, and returns the current day of the week and the current time in 24hr format ('hh:mm') as a string. 

```python
day_and_time(0)       should return 'Sunday 00:00'
day_and_time(-3)      should return 'Saturday 23:57'
day_and_time(45)      should return 'Sunday 00:45'
day_and_time(759)     should return 'Sunday 12:39'
day_and_time(1236)    should return 'Sunday 20:36'
day_and_time(1447)    should return 'Monday 00:07'
day_and_time(7832)    should return 'Friday 10:32'
day_and_time(18876)   should return 'Saturday 02:36'
day_and_time(259180)  should return 'Thursday 23:40' 
day_and_time(-349000) should return 'Tuesday 15:20'
```

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given an alphabet consisting of *n* letters, your task is to make a string of the maximum possible length so that the following conditions are satisfied: 
 -  the *i*-th letter occurs in the string no more than *a**i* times; -  the number of occurrences of each letter in the string must be distinct for all the letters that occurred in the string at least once.

Input Specification:
The first line of the input contains a single integer *n* (2<=<=≤<=<=*n*<=<=≤<=<=26) — the number of letters in the alphabet.

The next line contains *n* integers *a**i* (1<=≤<=*a**i*<=≤<=109) — *i*-th of these integers gives the limitation on the number of occurrences of the *i*-th character in the string.

Output Specification:
Print a single integer — the maximum length of the string that meets all the requirements.

Demo Input:
['3\n2 5 5\n', '3\n1 1 2\n']

Demo Output:
['11\n', '3\n']

Note:
For convenience let's consider an alphabet consisting of three letters: "a", "b", "c". In the first sample, some of the optimal strings are: "cccaabbccbb", "aabcbcbcbcb". In the second sample some of the optimal strings are: "acc", "cbc".

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given an array consisting of *n* non-negative integers *a*1,<=*a*2,<=...,<=*a**n*.

You are going to destroy integers in the array one by one. Thus, you are given the permutation of integers from 1 to *n* defining the order elements of the array are destroyed.

After each element is destroyed you have to find out the segment of the array, such that it contains no destroyed elements and the sum of its elements is maximum possible. The sum of elements in the empty segment is considered to be 0.

Input Specification:
The first line of the input contains a single integer *n* (1<=≤<=*n*<=≤<=100<=000) — the length of the array.

The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=109). 

The third line contains a permutation of integers from 1 to *n* — the order used to destroy elements.

Output Specification:
Print *n* lines. The *i*-th line should contain a single integer — the maximum possible sum of elements on the segment containing no destroyed elements, after first *i* operations are performed.

Demo Input:
['4\n1 3 2 5\n3 4 1 2\n', '5\n1 2 3 4 5\n4 2 3 5 1\n', '8\n5 5 4 4 6 6 5 5\n5 2 8 7 1 3 4 6\n']

Demo Output:
['5\n4\n3\n0\n', '6\n5\n5\n1\n0\n', '18\n16\n11\n8\n8\n6\n6\n0\n']

Note:
Consider the first sample: 
 1.  Third element is destroyed. Array is now 1 3  *  5. Segment with maximum sum 5 consists of one integer 5. 1.  Fourth element is destroyed. Array is now 1 3  *   * . Segment with maximum sum 4 consists of two integers 1 3. 1.  First element is destroyed. Array is now  *  3  *   * . Segment with maximum sum 3 consists of one integer 3. 1.  Last element is destroyed. At this moment there are no valid nonempty segments left in this array, so the answer is equal to 0.

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

**_Given_**   *a number* , **_Return_**  **_The Maximum number _**  *could be formed from the digits of the number given* . 
___
# Notes

* **_Only Natural numbers_** *passed to the function , numbers Contain digits [0:9] inclusive*

* **_Digit Duplications_** *could occur* , So also **_consider it when forming the Largest_**

____
# Input >> Output Examples:

```
maxNumber (213) ==> return (321)
```
## **_Explanation_**:

As `321` is **_The Maximum number _**  *could be formed from the digits of the number   **_213_*** . 
___

```
maxNumber (7389) ==> return (9873)
```
## **_Explanation_**:

As `9873` is **_The Maximum number _**  *could be formed from the digits of the number  **_7389_*** . 
___

```
maxNumber (63729) ==> return (97632)
```
## **_Explanation_**:

As `97632` is **_The Maximum number _**  *could be formed from the digits of the number  **_63729_*** . 
___

```
maxNumber (566797) ==> return (977665)
```
## **_Explanation_**:

As `977665` is **_The Maximum number _**  *could be formed from the digits of the number  **_566797_*** .

**_Note_** : **_Digit duplications are considered when forming the largest_** . 
___

```
maxNumber (17693284) ==> return (98764321)
```
## **_Explanation_**:
 
As `98764321` is **_The Maximum number _**  *could be formed from the digits of the number  **_17693284_*** .
___
___
___

# [Playing with Numbers Series](https://www.codewars.com/collections/playing-with-numbers)

# [Playing With Lists/Arrays Series](https://www.codewars.com/collections/playing-with-lists-slash-arrays)

# [For More Enjoyable Katas](http://www.codewars.com/users/MrZizoScream/authored)
___

## ALL translations are welcomed

## Enjoy Learning !!
# Zizou

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Paul Eigon recently got a new job at a famous company in town. They have all sorts of cool stuff at the office. Video games, a swimming pool, a sauna, and even a ping-pong table! Paul really loves his enjoyable new workplace.

Mr. Eigon plays a lot of ping-pong at work. While he is playing, he enjoys having a nice conversation with his opponent. Discussions are jolly fun to have, but they can also be a bit distracting, enough for Paul to sometimes completely forget whose turn it is to serve the ball the upcoming round!

Paul’s ping-pong games are played with simple rules. The game is played by two players. The game starts with one of the players serving the ball, and that player does so during the $N$ first rounds. After that, the other player serves the ball for $N$ rounds, and so on. Each round is won by exactly one of the players and a player gets one point for each won round (there can be no draws). When one of the players has reached a certain number of points, that player wins the game.

Paul is in desperate need of a new way to figure out which player should serve the ball the upcoming round, and he wants you to help him. You should write a program that given $N$ and the current score of the game prints out whose turn it is to serve the ball the upcoming round. His plan is to run your program on his secret high technology pocket computer, in order to impress his opponent. And by the way, Paul always serves the first ball (if that makes it easier for you).

-----Input-----
Input consists of three integers $N$, $P$ and $Q$ on a single line. $1 \leq N \leq 10^9$ denotes the number of serves a player will perform in a row before it is the other player’s turn to serve the ball. $0 \leq P \leq 10^9$ denotes Paul’s current score in the ongoing ping-pong game, and $0 \leq Q \leq 10^9$ denotes his opponent’s score.

-----Output-----
Output should consists of a single word on a single line. If it is Paul’s turn to serve the ball, your program should output paul. Otherwise, your program should output opponent.

-----Examples-----
Sample Input:
5 3 7
Sample Output:
paul

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
The Super Duper Secret Meeting of the Super Duper Secret Military Squad takes place in a Super Duper Secret Place. The place is an infinite plane with introduced Cartesian coordinate system. The meeting table is represented as a rectangle whose sides are parallel to the coordinate axes and whose vertexes are located at the integer points of the plane. At each integer point which belongs to the table perimeter there is a chair in which a general sits.

Some points on the plane contain radiators for the generals not to freeze in winter. Each radiator is characterized by the number *r**i* — the radius of the area this radiator can heat. That is, if the distance between some general and the given radiator is less than or equal to *r**i*, than the general feels comfortable and warm. Here distance is defined as Euclidean distance, so the distance between points (*x*1,<=*y*1) and (*x*2,<=*y*2) is 

Each general who is located outside the radiators' heating area can get sick. Thus, you should bring him a warm blanket. Your task is to count the number of warm blankets you should bring to the Super Duper Secret Place.

The generals who are already comfortable do not need a blanket. Also the generals never overheat, ever if they are located in the heating area of several radiators. The radiators can be located at any integer points on the plane, even inside the rectangle (under the table) or on the perimeter (directly under some general). Even in this case their radius does not change.

Input Specification:
The first input line contains coordinates of two opposite table corners *x**a*, *y**a*, *x**b*, *y**b* (*x**a*<=≠<=*x**b*,<=*y**a*<=≠<=*y**b*). The second line contains integer *n* — the number of radiators (1<=≤<=*n*<=≤<=103). Then *n* lines contain the heaters' coordinates as "*x**i* *y**i* *r**i*", the numbers are separated by spaces. All input data numbers are integers. The absolute value of all coordinates does not exceed 1000, 1<=≤<=*r**i*<=≤<=1000. Several radiators can be located at the same point.

Output Specification:
Print the only number — the number of blankets you should bring.

Demo Input:
['2 5 4 2\n3\n3 1 2\n5 3 1\n1 3 2\n', '5 2 6 3\n2\n6 2 2\n6 5 3\n']

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

Note:
In the first sample the generals are sitting at points: (2, 2), (2, 3), (2, 4), (2, 5), (3, 2), (3, 5), (4, 2), (4, 3), (4, 4), (4, 5). Among them, 4 generals are located outside the heating range. They are the generals at points: (2, 5), (3, 5), (4, 4), (4, 5).

In the second sample the generals are sitting at points: (5, 2), (5, 3), (6, 2), (6, 3). All of them are located inside the heating range.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Ksenia has a chessboard of size n × m. Each cell of the chessboard contains one of the characters: "<", ">", "^", "v", "#". The cells that contain character "#" are blocked. We know that all chessboard cells that touch the border are blocked.

Ksenia is playing with two pawns on this chessboard. Initially, she puts the pawns on the chessboard. One cell of the chessboard can contain two pawns if and only if the cell is blocked. In other cases two pawns can not stand in one cell. The game begins when Ksenia put pawns on the board. In one move, Ksenia moves each pawn to a side adjacent cell in the direction of arrows painted on the cell on which the corresponding pawn sits (if the pawn sits on "#", it does not move). Assume that Ksenia moves pawns simultaneously (see the second test case). 

Of course, Ksenia plays for points. How can one calculate the points per game? Very simply! Let's count how many movements the first pawn made and how many movements the second pawn made, sum these two numbers — it will be the resulting score of the game. 

Ksenia wonders: what is the maximum number of points she can earn (for that, she should place the pawns optimally well early in the game). Help her and find that number. 

Input

The first line contains two integers, n and m (1 ≤ n, m ≤ 2000) — the sizes of the board. Each of the following n lines contains m characters – the board's description. Each character is one of the characters: "<", ">", "^", "v", "#".

It is guaranteed that the border cells of the table are blocked cells (with character "#").

Output

If Ksenia can get infinitely many points, print -1. Otherwise, print the maximum number of points she can get.

Examples

Input

1 1
#


Output

0


Input

3 4
####
#&gt;^{}#
####


Output

3

Input

3 4
####
#&gt;&lt;#
####


Output

-1

Input

7 5
#####
##v##
##v##
#####
##^{}##
##^{}##
#####


Output

4

Input

7 5
#####
##v##
##v##
##&lt;##
##^{}##
##^{}##
#####

Output

5

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Takahashi wants to gain muscle, and decides to work out at AtCoder Gym.
The exercise machine at the gym has N buttons, and exactly one of the buttons is lighten up.
These buttons are numbered 1 through N.
When Button i is lighten up and you press it, the light is turned off, and then Button a_i will be lighten up. It is possible that i=a_i.
When Button i is not lighten up, nothing will happen by pressing it.
Initially, Button 1 is lighten up. Takahashi wants to quit pressing buttons when Button 2 is lighten up.
Determine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons.

-----Constraints-----
 - 2 ≤ N ≤ 10^5
 - 1 ≤ a_i ≤ N

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

-----Output-----
Print -1 if it is impossible to lighten up Button 2.
Otherwise, print the minimum number of times we need to press buttons in order to lighten up Button 2.

-----Sample Input-----
3
3
1
2

-----Sample Output-----
2

Press Button 1, then Button 3.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are an experienced Codeforces user. Today you found out that during your activity on Codeforces you have made y submissions, out of which x have been successful. Thus, your current success rate on Codeforces is equal to x / y.

Your favorite rational number in the [0;1] range is p / q. Now you wonder: what is the smallest number of submissions you have to make if you want your success rate to be p / q?


-----Input-----

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each of the next t lines contains four integers x, y, p and q (0 ≤ x ≤ y ≤ 10^9; 0 ≤ p ≤ q ≤ 10^9; y > 0; q > 0).

It is guaranteed that p / q is an irreducible fraction.

Hacks. For hacks, an additional constraint of t ≤ 5 must be met.


-----Output-----

For each test case, output a single integer equal to the smallest number of submissions you have to make if you want your success rate to be equal to your favorite rational number, or -1 if this is impossible to achieve.


-----Example-----
Input
4
3 10 1 2
7 14 3 8
20 70 2 7
5 6 1 1

Output
4
10
0
-1



-----Note-----

In the first example, you have to make 4 successful submissions. Your success rate will be equal to 7 / 14, or 1 / 2.

In the second example, you have to make 2 successful and 8 unsuccessful submissions. Your success rate will be equal to 9 / 24, or 3 / 8.

In the third example, there is no need to make any new submissions. Your success rate is already equal to 20 / 70, or 2 / 7.

In the fourth example, the only unsuccessful submission breaks your hopes of having the success rate equal to 1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There is an empty grid (all cells are colored white) of N rows and M columns.

Chef can fill each cell with either RED or GREEN color.  
Chef defines a *valid* path as a path of cells starting from (1,1) and ending at (N,M), where, Chef moves either right or down by 1 cell each time.

For a particular grid, Chef defines the *score* of the grid as the number of *valid* paths containing equal number of RED and GREEN cells.

Find the sum of *scores* of all possible colored grids containing N rows and M columns.  
Since the answer can be large, output it modulo 998244353.

------ Input Format ------ 

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of two integers N and M - denoting the dimensions of the grid.

------ Output Format ------ 

For each test case, output the sum of *scores* of all possible colored grids containing N rows and M columns, modulo 998244353.

------ Constraints ------ 

$1 ≤ T ≤ 1000$
$1 ≤ N, M ≤ 1000$

----- Sample Input 1 ------ 
3
1 1
1 2
2 3

----- Sample Output 1 ------ 
0
2
72

----- explanation 1 ------ 
Test case $1$: There are $2$ possible coloured grids of size $1 \times 1$. In the first grid, the one and only cell is colored RED. In the second grid, the one and only cell is colored GREEN. Neither of the grids have a *valid* path with equal number of red and green cells. Thus, score of each grid is $0$.

Test case $2$: There are $4$ possible coloured grids of the given dimension:

For grids $1$ and $4$, the scores are $0$ as there are no valid paths with equal red and green cells. Grids $2$ and $3$ have score $1$ each. The valid path with equal red and green cells is $(1,1) \rightarrow (1,2)$ in both the grids.

Thus, the sum of scores of all possible coloured grids is $2$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In a rainforest there are $n$ treehouses high in the forest canopy on different trees (numbered from $1$ to $n$). The $i$-th tree’s location is at $(x_ i, y_ i)$. The first $e$ of them in the list are close enough to neighboring open land around the rainforest so that transportation between all of them is easy by foot. Some treehouses may already be connected by direct straight cables through the air that can allow transport between them.

Residents want easy transportation between all the treehouses and the open land, by some combination of walking (between those near the open land), and using one or more cables between treehouses. This may require the addition of more cables. Since the cables are expensive, they would like to add the smallest possible length of cable.

The height of a cable up two trees can be set so cables can criss-cross other cables, and not allow any snags or crashes. It is not safe to try to switch between two criss-crossed cables in mid-air!

-----Input-----
The input will start with the three integers $n$ ($1 \le n \le 1000$), $e$ ($1 \le e \le n$), and $p$ ($0 \le p \le 1000$), where $p$ is the number of cables in place already.

Next come $n$ lines, each with two real numbers $x$ and $y$ ($|x|, |y| \le 10000$) giving the location of a treehouse. The $i$-th coordinate pair is for the treehouse with ID $i$. All coordinate pairs are unique. Real numbers are stated as integers or include one digit after a decimal point.

Next come $p$ lines, each with two integers $a$, $b$, where $1 \le a < b \le n$, giving the two treehouse ids of an existing cable between their trees. No ID pair will be repeated.

-----Output-----
The output is the minimum total length of new cable that achieves the connection goal, expressed with absolute or relative error less than $0.001$.

-----Examples-----
Sample Input 1:
3 1 0
0.0 0.0
2.0 0.0
1.0 2.0
Sample Output 1:
4.236067

Sample Input 2:
3 1 1
0.0 0.0
0.5 2.0
2.5 2.0
1 2
Sample Output 2:
2.000000

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Alex was programming while Valentina (his toddler daughter) got there and started asking many questions about the round brackets (or parenthesis) in the code. He explained her a bit and when she got it he gave her a task in order to finish his code on time.

For the purpose of this problem we consider only strings consisting of opening and closing round brackets, that is characters '(' and ')'.

The sequence of brackets is called correct if: 
 1.  it's empty; 1.  it's a correct sequence of brackets, enclosed in a pair of opening and closing brackets; 1.  it's a concatenation of two correct sequences of brackets. 
For example, the sequences "()()" and "((()))(())" are correct, while ")(()", "(((((" and "())" are not.

Alex took a piece of paper, wrote a string *s* consisting of brackets and asked Valentina to count the number of distinct non-empty substrings of *s* that are correct sequences of brackets. In other words, her task is to count the number of non-empty correct sequences of brackets that occur in a string *s* as a substring (don't mix up with subsequences).

When Valentina finished the task, Alex noticed he doesn't know the answer. Help him don't loose face in front of Valentina and solve the problem!

Input Specification:
The first line of the input contains an integer *n* (1<=≤<=*n*<=≤<=500<=000) — the length of the string *s*.

The second line contains a string *s* of length *n* consisting of only '(' and ')'.

Output Specification:
Print the number of distinct non-empty correct sequences that occur in *s* as substring.

Demo Input:
['10\n()()()()()\n', '7\n)(())()\n']

Demo Output:
['5\n', '3\n']

Note:
In the first sample, there are 5 distinct substrings we should count: "()", "()()", "()()()", "()()()()" and "()()()()()".

In the second sample, there are 3 distinct substrings we should count: "()", "(())" and "(())()".

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