vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Omkar is building a waterslide in his water park, and he needs your help to ensure that he does it as efficiently as possible.

Omkar currently has $n$ supports arranged in a line, the $i$-th of which has height $a_i$. Omkar wants to build his waterslide from the right to the left, so his supports must be nondecreasing in height in order to support the waterslide. In $1$ operation, Omkar can do the following: take any contiguous subsegment of supports which is nondecreasing by heights and add $1$ to each of their heights. 

Help Omkar find the minimum number of operations he needs to perform to make his supports able to support his waterslide!

An array $b$ is a subsegment of an array $c$ if $b$ can be obtained from $c$ by deletion of several (possibly zero or all) elements from the beginning and several (possibly zero or all) elements from the end.

An array $b_1, b_2, \dots, b_n$ is called nondecreasing if $b_i\le b_{i+1}$ for every $i$ from $1$ to $n-1$.


-----Input-----

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 100$). Description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the number of supports Omkar has.

The second line of each test case contains $n$ integers $a_{1},a_{2},...,a_{n}$ $(0 \leq a_{i} \leq 10^9)$ — the heights of the supports.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.


-----Output-----

For each test case, output a single integer — the minimum number of operations Omkar needs to perform to make his supports able to support his waterslide.


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

Output
3
2
0



-----Note-----

The subarray with which Omkar performs the operation is bolded.

In the first test case:

First operation:

$[5, 3, \textbf{2}, 5] \to [5, 3, \textbf{3}, 5]$

Second operation:

$[5, \textbf{3}, \textbf{3}, 5] \to [5, \textbf{4}, \textbf{4}, 5]$

Third operation:

$[5, \textbf{4}, \textbf{4}, 5] \to [5, \textbf{5}, \textbf{5}, 5]$

In the third test case, the array is already nondecreasing, so Omkar does $0$ operations.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Consider an array of numeric strings where each string is a positive number with anywhere from $\mbox{I}$ to $10^{6}$ digits. Sort the array's elements in non-decreasing, or ascending order of their integer values and return the sorted array.

Example 

$unsorted=[\text{'1'},\text{'200'},\text{'150'},\text{'3'}]$  

Return the array ['1', '3', '150', '200']. 

Function Description  

Complete the bigSorting function in the editor below.  

bigSorting has the following parameter(s):  

string unsorted[n]: an unsorted array of integers as strings  

Returns  

string[n]:  the array sorted in numerical order  

Input Format

The first line contains an integer, $n$, the number of strings in $un sorted$. 

Each of the $n$ subsequent lines contains an integer string, ${un sorted}[i]$.

Constraints

$1\leq n\leq2\times10^5$
Each string is guaranteed to represent a positive integer.
There will be no leading zeros.
The total number of digits across all strings in $un sorted$ is between $\mbox{I}$ and $10^{6}$ (inclusive).

Sample Input 0
6
31415926535897932384626433832795
1
3
10
3
5

Sample Output 0
1
3
3
5
10
31415926535897932384626433832795

Explanation 0

The initial array of strings is $unsorted=[31415926535879338846464383795,1,3,10,3,5]$. When we order each string by the real-world integer value it represents, we get: $1\leq3\leq3\leq5\leq10\leq31415926535897932384626433832795$

We then print each value on a new line, from smallest to largest.

Sample Input 1
8
1
2
100
12303479849857341718340192371
3084193741082937
3084193741082938
111
200

Sample Output 1
1
2
100
111
200
3084193741082937
3084193741082938
12303479849857341718340192371

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In Kingdom of Byteland,there are N jewellery shops that connected by road such that there is zero or more bidirectional way to go from one shop to another.
Each shops has Jewellery of certain type.

Jewellery in Byteland has special property : if 'x' type jewellery is combined with 'y' type jewellery then it gets converted to (x xor y) type jewellery. 

Cost of jewellery of type 'n' : n (in decimal representation)
Don SRK decided to rob the Kingdom of jewellery shops.He starts to rob from any shop and Rob as many shops as possible such that it maximizes the cost of jewellery he possesses. 

Input:

The first line of input consists  an integer n (1 ≤ n ≤ 100)followed by  n x n matrix A 

if A[i][j] = 'Y' then there is road from i to j , otherwise 'N' no road between them.

Next Line contains n integers => type[i] : representing type of jewellery in ith shop .(0 ≤ type[i] ≤ 1023)

Output:

Print an integer indicating Maximum cost of jewellery Robbed by Don.

SAMPLE INPUT
5
NYYYY
YNNNN
YNNNN
YNNNN
YNNNN
0 4 8 32 512

SAMPLE OUTPUT
556

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Furik and Rubik take part in a relay race. The race will be set up on a large square with the side of *n* meters. The given square is split into *n*<=×<=*n* cells (represented as unit squares), each cell has some number.

At the beginning of the race Furik stands in a cell with coordinates (1,<=1), and Rubik stands in a cell with coordinates (*n*,<=*n*). Right after the start Furik runs towards Rubik, besides, if Furik stands at a cell with coordinates (*i*,<=*j*), then he can move to cell (*i*<=+<=1,<=*j*) or (*i*,<=*j*<=+<=1). After Furik reaches Rubik, Rubik starts running from cell with coordinates (*n*,<=*n*) to cell with coordinates (1,<=1). If Rubik stands in cell (*i*,<=*j*), then he can move to cell (*i*<=-<=1,<=*j*) or (*i*,<=*j*<=-<=1). Neither Furik, nor Rubik are allowed to go beyond the boundaries of the field; if a player goes beyond the boundaries, he will be disqualified. 

To win the race, Furik and Rubik must earn as many points as possible. The number of points is the sum of numbers from the cells Furik and Rubik visited. Each cell counts only once in the sum.

Print the maximum number of points Furik and Rubik can earn on the relay race.

Input Specification:
The first line contains a single integer (1<=≤<=*n*<=≤<=300). The next *n* lines contain *n* integers each: the *j*-th number on the *i*-th line *a**i*,<=*j* (<=-<=1000<=≤<=*a**i*,<=*j*<=≤<=1000) is the number written in the cell with coordinates (*i*,<=*j*).

Output Specification:
On a single line print a single number — the answer to the problem.

Demo Input:
['1\n5\n', '2\n11 14\n16 12\n', '3\n25 16 25\n12 18 19\n11 13 8\n']

Demo Output:
['5\n', '53\n', '136\n']

Note:
Comments to the second sample: The profitable path for Furik is: (1, 1), (1, 2), (2, 2), and for Rubik: (2, 2), (2, 1), (1, 1). 

Comments to the third sample: The optimal path for Furik is: (1, 1), (1, 2), (1, 3), (2, 3), (3, 3), and for Rubik: (3, 3), (3, 2), (2, 2), (2, 1), (1, 1). The figure to the sample:

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Mirko has found an old chessboard and a set of pieces in his attic. Unfortunately, the set contains only white pieces, and apparently an incorrect number of them. A set of pieces should contain:
 - One king
 - One queen
 - Two rooks
 - Two bishops
 - Two knights
 - Eight pawns

Mirko would like to know how many pieces of each type he should add or remove to make a valid set.

-----Input-----
The input consists of $6$ integers on a single line, each between $0$ and $10$ (inclusive). The numbers are, in order, the numbers of kings, queens, rooks, bishops, knights and pawns in the set Mirko found.

-----Output-----
Output should consist of $6$ integers on a single line; the number of pieces of each type Mirko should add or remove. If a number is positive, Mirko needs to add that many pieces. If a number is negative, Mirko needs to remove pieces.

-----Examples-----
Sample Input:
0 1 2 2 2 7
Sample Output:
1 0 0 0 0 1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given an array A of N positive integers. 

In one operation, you can do the following:
Choose an index i (1 ≤ i ≤ N), and change the value of A_{i} to either (A_{i})^2 or \lfloor \sqrt{A_{i}} \rfloor.

Find the minimum number of operations required, such that, for the final array A:
A is sorted in non-decreasing order;
A_{N} ≤ 10^{18}.

NOTE: The elements of the array might not fit in a 32-bit integer.

------ 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 lines of input:
- The first line of each test case contains N - the size of the array.
- The next line contains N integers, A_{1}, A_{2}, A_{3}, \ldots, A_{N} - the elements of the array.

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

For each test case, output on a new line, the minimum number of operations required.

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

$1 ≤ T ≤ 1000$
$1 ≤ N ≤ 10^{5}$
$1 ≤ A_{i} ≤ 10^{18}$
- The sum of $N$ over all test cases won't exceed $10^{5}$.

----- Sample Input 1 ------ 
3
4
1 3 9 9
4
1 9 3 9
3
4 2 1

----- Sample Output 1 ------ 
0
1
3

----- explanation 1 ------ 
Test case $1$: The array is already sorted, no operation is required.

Test case $2$: Using one operation, we can change $A_{2}$ to $\lfloor \sqrt{A_{2}}\rfloor = 3$. The final array is $A = [1, 3, 3, 9]$ which is sorted in non-decreasing order.

Test case $3$: We make the following operations:
- Change $A_{2}$ to $\lfloor \sqrt{A_{2}}\rfloor = 1$.
- Change $A_{1}$ to $\lfloor \sqrt{A_{1}}\rfloor = 2$.
- Change $A_{1}$ to $\lfloor \sqrt{A_{1}}\rfloor = 1$.

The final array is $A = [1, 1, 1]$ which is sorted in non-decreasing order.

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

In this problem, a straight line passing through a certain point X and a certain point Y in the three-dimensional space is written as a straight line XY.

A cone and a point P inside the cone are given in three-dimensional space. Let point Q be the intersection of a straight line passing through point P and perpendicular to the bottom of the cone and the bottom of the cone. At this time, the center of the bottom surface of the cone is O, and the intersection of the straight line OQ and the circumference of the bottom surface of the cone is point A and point B from the side closer to point Q (however, point O and point Q are the same point). In the case of, let points A and B be the intersections of any straight line passing through point O and the circumference of the bottom of the cone.) Also, in a plane that includes the bottom surface of the cone, let points C and D be the intersections of the straight line that passes through point O and intersects the straight line AB perpendicularly with the circumference of the bottom surface of the cone (however, points C and D). Can be replaced).


The figure below is a view of the bottom surface of the cone as seen from the direction of the apex of the cone.

View of the bottom of the cone as seen from the apex of the cone


Let the intersection of the straight line AP and the cone of the straight line BP (in the case of the straight line AP, the intersection that is not the point A. The same applies to the straight line BP) be the point A'and the point B', and pass through the points A'and B'. Cut the cone at the plane S parallel to the straight line CD. At this time, output the volume of the figure including the vertices after cutting and the volume of the other figure separated by blanks.

Input

X coordinate y coordinate z coordinate of the apex of the cone
X coordinate y coordinate z coordinate of the center of the base of the cone Radius of the base of the cone
X coordinate y coordinate z coordinate of point P

Each value on each row is given separated by spaces.

Constraint

All input values ​​are integers, the absolute value of which is less than or equal to 1000.
The height of the cone and the radius of its base are greater than or equal to 1, and the distance between point P and the cone is greater than or equal to 10-5.

Output

Output the volume of the figure including the vertices after cutting and the volume of the other figure separated by blanks.
However, it must not contain an error greater than 10-5.

Sample Input 1


0 0 10
0 0 0 4
0 0 1


Sample Output 1


91.769438 75.782170


Sample Input 2


0 0 10
0 0 0 4
1 1 1


Sample Output 2


84.050413 83.501195


Sample Input 3


0 0 0
8 9 10 5
1 1 1


Sample Output 3


0.071663 409.709196






Example

Input

0 0 10
0 0 0 4
0 0 1


Output

91.769438 75.782170

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
It is often heard that the apple doesn’t fall far from the tree. But is that really so?

The National Statistics Department has tracked the falling of apples in a fruit garden for $G$ consecutive years. The fruit garden can be represented as a matrix with dimensions $R \times S$. Each field of the matrix can contain more than one apple tree.

Interestingly enough, each year there was exactly one apple fall, so the Department decided to write down $G$ pairs of numbers $(r_ i, s_ i)$ that denote the row and column of the location where the apple fell during the $i$-th year. Moreover, by next year, a new tree grew at that location.

Your task is to determine the squared distance between the nearest tree and the apple that fell, measured in unit fields of the matrix (we assume it is that tree from which the apple fell).

The distance between fields $(r_1, s_1)$ and $(r_2, s_2)$ in the matrix are calculated as\begin{equation*} d((r_1, s_1),(r_2, s_2)) = \sqrt {(r_1-r_2)^2 + (s_1-s_2)^2} \end{equation*}

-----Input-----
The first line of input contains two integers, $R$ and $S$ ($1 \leq R, S \leq 500$), the number of rows and columns of the matrix.

Each of the following $R$ lines contains $S$ characters ’x’ or ’.’. The character ’.’ denotes an empty field, and the character ’x’ denotes a field with at least one tree.

The fruit garden will initially contain at least one tree.

After that, an integer $G$ ($1 \leq G \leq 10^5$) follows, the number of years the fruit garden has been under observation.

Each of the following $G$ lines describes the falls of the apples. Each line contains a pair of space-separated integers $r_ i$, $s_ i$ that denote the row and column of the location where the apple fell in the $i$-th year ($1 \leq r_ i \leq R$, $1 \leq s_ i \leq S$).

-----Output-----
Output $G$ numbers, the required squared distances from the task, each in its own line.

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

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Iahub is a big fan of tourists. He wants to become a tourist himself, so he planned a trip. There are n destinations on a straight road that Iahub wants to visit. Iahub starts the excursion from kilometer 0. The n destinations are described by a non-negative integers sequence a_1, a_2, ..., a_{n}. The number a_{k} represents that the kth destination is at distance a_{k} kilometers from the starting point. No two destinations are located in the same place. 

Iahub wants to visit each destination only once. Note that, crossing through a destination is not considered visiting, unless Iahub explicitly wants to visit it at that point. Also, after Iahub visits his last destination, he doesn't come back to kilometer 0, as he stops his trip at the last destination. 

The distance between destination located at kilometer x and next destination, located at kilometer y, is |x - y| kilometers. We call a "route" an order of visiting the destinations. Iahub can visit destinations in any order he wants, as long as he visits all n destinations and he doesn't visit a destination more than once. 

Iahub starts writing out on a paper all possible routes and for each of them, he notes the total distance he would walk. He's interested in the average number of kilometers he would walk by choosing a route. As he got bored of writing out all the routes, he asks you to help him.


-----Input-----

The first line contains integer n (2 ≤ n ≤ 10^5). Next line contains n distinct integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^7).


-----Output-----

Output two integers — the numerator and denominator of a fraction which is equal to the wanted average number. The fraction must be irreducible.


-----Examples-----
Input
3
2 3 5

Output
22 3


-----Note-----

Consider 6 possible routes:  [2, 3, 5]: total distance traveled: |2 – 0| + |3 – 2| + |5 – 3| = 5;  [2, 5, 3]: |2 – 0| + |5 – 2| + |3 – 5| = 7;  [3, 2, 5]: |3 – 0| + |2 – 3| + |5 – 2| = 7;  [3, 5, 2]: |3 – 0| + |5 – 3| + |2 – 5| = 8;  [5, 2, 3]: |5 – 0| + |2 – 5| + |3 – 2| = 9;  [5, 3, 2]: |5 – 0| + |3 – 5| + |2 – 3| = 8. 

The average travel distance is $\frac{1}{6} \cdot(5 + 7 + 7 + 8 + 9 + 8)$ = $\frac{44}{6}$ = $\frac{22}{3}$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In English, we have a concept called root, which can be followed by some other words to form another longer word - let's call this word successor. For example, the root an, followed by other, which can form another word another.




Now, given a dictionary consisting of many roots and a sentence. You need to replace all the successor in the sentence with the root forming it. If a successor has many roots can form it, replace it with the root with the shortest length.



You need to output the sentence after the replacement.



Example 1:

Input: dict = ["cat", "bat", "rat"]
sentence = "the cattle was rattled by the battery"
Output: "the cat was rat by the bat"




Note:

The input will only have lower-case letters.
 1 
 1 
 1 
 1

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

Some numbers are more important to get right during data entry than others: a common example is product codes.

To reduce the possibility of mistakes, product codes can be crafted in such a way that simple errors are detected. This is done by calculating a single-digit value based on the product number, and then appending that digit to the product number to arrive at the product code.

When the product code is checked, the check digit value is stripped off and recalculated. If the supplied value does not match the recalculated value, the product code is rejected.

A simple scheme for generating self-check digits, described here, is called Modulus 11 Self-Check.

## Calculation method

Each digit in the product number is assigned a multiplication factor. The factors are assigned ***from right to left***, starting at `2` and counting up. For numbers longer than six digits, the factors restart at `2` after `7` is reached. The product of each digit and its factor is calculated, and the products summed. For example:

```python
digit     :  1    6    7    7    0    3    6    2    5
factor    :  4    3    2    7    6    5    4    3    2
           ---  ---  ---  ---  ---  ---  ---  ---  ---
             4 + 18 + 14 + 49 +  0 + 15 + 24 +  6 + 10 = 140
```

Then the sum of the products is divided by the prime number `11`. The remainder is inspected, and:

* if the remainder is `0`, the check digit is also `0`
* if the remainder is `1`, the check digit is replaced by an uppercase `X`
* for all others, the remainder is subtracted from `11`

The result is the **check digit**.

## Your task

Your task is to implement this algorithm and return the input number with the correct check digit appended.

## Examples

```python
input: "036532"

product sum = 2*2 + 3*3 + 5*4 + 6*5 + 3*6 + 0*7 = 81
remainder   = 81 mod 11 = 4
check digit = 11 - 4 = 7

output: "0365327"
```

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given two arithmetic progressions: *a*1*k*<=+<=*b*1 and *a*2*l*<=+<=*b*2. Find the number of integers *x* such that *L*<=≤<=*x*<=≤<=*R* and *x*<==<=*a*1*k*'<=+<=*b*1<==<=*a*2*l*'<=+<=*b*2, for some integers *k*',<=*l*'<=≥<=0.

Input Specification:
The only line contains six integers *a*1,<=*b*1,<=*a*2,<=*b*2,<=*L*,<=*R* (0<=&lt;<=*a*1,<=*a*2<=≤<=2·109,<=<=-<=2·109<=≤<=*b*1,<=*b*2,<=*L*,<=*R*<=≤<=2·109,<=*L*<=≤<=*R*).

Output Specification:
Print the desired number of integers *x*.

Demo Input:
['2 0 3 3 5 21\n', '2 4 3 0 6 17\n']

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

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
This problem is given in two editions, which differ exclusively in the constraints on the number $n$.

You are given an array of integers $a[1], a[2], \dots, a[n].$ A block is a sequence of contiguous (consecutive) elements $a[l], a[l+1], \dots, a[r]$ ($1 \le l \le r \le n$). Thus, a block is defined by a pair of indices $(l, r)$.

Find a set of blocks $(l_1, r_1), (l_2, r_2), \dots, (l_k, r_k)$ such that:  They do not intersect (i.e. they are disjoint). Formally, for each pair of blocks $(l_i, r_i)$ and $(l_j, r_j$) where $i \neq j$ either $r_i < l_j$ or $r_j < l_i$.  For each block the sum of its elements is the same. Formally, $$a[l_1]+a[l_1+1]+\dots+a[r_1]=a[l_2]+a[l_2+1]+\dots+a[r_2]=$$ $$\dots =$$ $$a[l_k]+a[l_k+1]+\dots+a[r_k].$$  The number of the blocks in the set is maximum. Formally, there does not exist a set of blocks $(l_1', r_1'), (l_2', r_2'), \dots, (l_{k'}', r_{k'}')$ satisfying the above two requirements with $k' > k$.  $\left. \begin{array}{|l|l|l|l|l|l|} \hline 4 & {1} & {2} & {2} & {1} & {5} & {3} \\ \hline \end{array} \right.$ The picture corresponds to the first example. Blue boxes illustrate blocks. 

Write a program to find such a set of blocks.


-----Input-----

The first line contains integer $n$ ($1 \le n \le 1500$) — the length of the given array. The second line contains the sequence of elements $a[1], a[2], \dots, a[n]$ ($-10^5 \le a_i \le 10^5$).


-----Output-----

In the first line print the integer $k$ ($1 \le k \le n$). The following $k$ lines should contain blocks, one per line. In each line print a pair of indices $l_i, r_i$ ($1 \le l_i \le r_i \le n$) — the bounds of the $i$-th block. You can print blocks in any order. If there are multiple answers, print any of them.


-----Examples-----
Input
7
4 1 2 2 1 5 3

Output
3
7 7
2 3
4 5

Input
11
-5 -4 -3 -2 -1 0 1 2 3 4 5

Output
2
3 4
1 1

Input
4
1 1 1 1

Output
4
4 4
1 1
2 2
3 3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Artem has an array of n positive integers. Artem decided to play with it. The game consists of n moves. Each move goes like this. Artem chooses some element of the array and removes it. For that, he gets min(a, b) points, where a and b are numbers that were adjacent with the removed number. If the number doesn't have an adjacent number to the left or right, Artem doesn't get any points. 

After the element is removed, the two parts of the array glue together resulting in the new array that Artem continues playing with. Borya wondered what maximum total number of points Artem can get as he plays this game.


-----Input-----

The first line contains a single integer n (1 ≤ n ≤ 5·10^5) — the number of elements in the array. The next line contains n integers a_{i} (1 ≤ a_{i} ≤ 10^6) — the values of the array elements.


-----Output-----

In a single line print a single integer — the maximum number of points Artem can get.


-----Examples-----
Input
5
3 1 5 2 6

Output
11

Input
5
1 2 3 4 5

Output
6

Input
5
1 100 101 100 1

Output
102

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