vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Bizon the Champion isn't just attentive, he also is very hardworking.

Bizon the Champion decided to paint his old fence his favorite color, orange. The fence is represented as n vertical planks, put in a row. Adjacent planks have no gap between them. The planks are numbered from the left to the right starting from one, the i-th plank has the width of 1 meter and the height of a_{i} meters.

Bizon the Champion bought a brush in the shop, the brush's width is 1 meter. He can make vertical and horizontal strokes with the brush. During a stroke the brush's full surface must touch the fence at all the time (see the samples for the better understanding). What minimum number of strokes should Bizon the Champion do to fully paint the fence? Note that you are allowed to paint the same area of the fence multiple times.


-----Input-----

The first line contains integer n (1 ≤ n ≤ 5000) — the number of fence planks. The second line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9).


-----Output-----

Print a single integer — the minimum number of strokes needed to paint the whole fence.


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

Output
3

Input
2
2 2

Output
2

Input
1
5

Output
1



-----Note-----

In the first sample you need to paint the fence in three strokes with the brush: the first stroke goes on height 1 horizontally along all the planks. The second stroke goes on height 2 horizontally and paints the first and second planks and the third stroke (it can be horizontal and vertical) finishes painting the fourth plank.

In the second sample you can paint the fence with two strokes, either two horizontal or two vertical strokes.

In the third sample there is only one plank that can be painted using a single vertical stroke.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Mihai has an $8 \times 8$ chessboard whose rows are numbered from $1$ to $8$ from top to bottom and whose columns are numbered from $1$ to $8$ from left to right.

Mihai has placed exactly one bishop on the chessboard. The bishop is not placed on the edges of the board. (In other words, the row and column of the bishop are between $2$ and $7$, inclusive.)

The bishop attacks in all directions diagonally, and there is no limit to the distance which the bishop can attack. Note that the cell on which the bishop is placed is also considered attacked.

An example of a bishop on a chessboard. The squares it attacks are marked in red.

Mihai has marked all squares the bishop attacks, but forgot where the bishop was! Help Mihai find the position of the bishop.


-----Input-----

The first line of the input contains a single integer $t$ ($1 \leq t \leq 36$) — the number of test cases. The description of test cases follows. There is an empty line before each test case.

Each test case consists of $8$ lines, each containing $8$ characters. Each of these characters is either '#' or '.', denoting a square under attack and a square not under attack, respectively.


-----Output-----

For each test case, output two integers $r$ and $c$ ($2 \leq r, c \leq 7$) — the row and column of the bishop.

The input is generated in such a way that there is always exactly one possible location of the bishop that is not on the edge of the board.


-----Examples-----

Input
3
.....#..
#...#...
.#.#....
..#.....
.#.#....
#...#...
.....#..
......#.
#.#.....
.#......
#.#.....
...#....
....#...
.....#..
......#.
.......#
.#.....#
..#...#.
...#.#..
....#...
...#.#..
..#...#.
.#.....#
#.......
Output
4 3
2 2
4 5


-----Note-----

The first test case is pictured in the statement. Since the bishop lies in the intersection row $4$ and column $3$, the correct output is 4 3.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Vasya is studying number theory. He has denoted a function f(a, b) such that:  f(a, 0) = 0;  f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b. 

Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.


-----Input-----

The first line contains two integer numbers x and y (1 ≤ x, y ≤ 10^12).


-----Output-----

Print f(x, y).


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

Output
3

Input
6 3

Output
1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
As we all know Barney's job is "PLEASE" and he has not much to do at work. That's why he started playing "cups and key". In this game there are three identical cups arranged in a line from left to right. Initially key to Barney's heart is under the middle cup. $\left. \begin{array}{l}{\text{Rey}} \\{\text{to my}} \\{\text{heart}} \end{array} \right.$ 

Then at one turn Barney swaps the cup in the middle with any of other two cups randomly (he choses each with equal probability), so the chosen cup becomes the middle one. Game lasts n turns and Barney independently choses a cup to swap with the middle one within each turn, and the key always remains in the cup it was at the start.

After n-th turn Barney asks a girl to guess which cup contains the key. The girl points to the middle one but Barney was distracted while making turns and doesn't know if the key is under the middle cup. That's why he asked you to tell him the probability that girl guessed right.

Number n of game turns can be extremely large, that's why Barney did not give it to you. Instead he gave you an array a_1, a_2, ..., a_{k} such that  $n = \prod_{i = 1}^{k} a_{i}$ 

in other words, n is multiplication of all elements of the given array.

Because of precision difficulties, Barney asked you to tell him the answer as an irreducible fraction. In other words you need to find it as a fraction p / q such that $\operatorname{gcd}(p, q) = 1$, where $gcd$ is the greatest common divisor. Since p and q can be extremely large, you only need to find the remainders of dividing each of them by 10^9 + 7.

Please note that we want $gcd$ of p and q to be 1, not $gcd$ of their remainders after dividing by 10^9 + 7.


-----Input-----

The first line of input contains a single integer k (1 ≤ k ≤ 10^5) — the number of elements in array Barney gave you.

The second line contains k integers a_1, a_2, ..., a_{k} (1 ≤ a_{i} ≤ 10^18) — the elements of the array.


-----Output-----

In the only line of output print a single string x / y where x is the remainder of dividing p by 10^9 + 7 and y is the remainder of dividing q by 10^9 + 7.


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

Output
1/2

Input
3
1 1 1

Output
0/1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We say that a binary string (a string containing only characters '0' and '1') is pure if it does not contain either of the strings "0101" or "1010" as a subsequence.
Recall that string T is a subsequence of string S if we can delete some of the letters of S (possibly none) such that the resulting string will become T.
You are given a binary string $S$ with length $N$. We want to make this string pure by deleting some (possibly zero) characters from it. What is the minimum number of characters we have to delete?

-----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 and only line of each test case contains a single string $S$ with length $N$.

-----Output-----
For each test case, print a single line containing one integer — the minimum number of characters we have to delete from $S$.

-----Constraints-----
- $1 \le T \le 40$
- $1 \le N \le 1,000$
- $S$ contains only characters '0' and '1'

-----Example Input-----
4
010111101
1011100001011101
0110
111111

-----Example Output-----
2
3
0
0

-----Explanation-----
Example case 1: We can delete the first and third character of our string. There is no way to make the string pure by deleting only one character.
Example case 3: The given string is already pure, so the answer is zero.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Nearly each project of the F company has a whole team of developers working on it. They often are in different rooms of the office in different cities and even countries. To keep in touch and track the results of the project, the F company conducts shared online meetings in a Spyke chat.

One day the director of the F company got hold of the records of a part of an online meeting of one successful team. The director watched the record and wanted to talk to the team leader. But how can he tell who the leader is? The director logically supposed that the leader is the person who is present at any conversation during a chat meeting. In other words, if at some moment of time at least one person is present on the meeting, then the leader is present on the meeting.

You are the assistant director. Given the 'user logged on'/'user logged off' messages of the meeting in the chronological order, help the director determine who can be the leader. Note that the director has the record of only a continuous part of the meeting (probably, it's not the whole meeting).


-----Input-----

The first line contains integers n and m (1 ≤ n, m ≤ 10^5) — the number of team participants and the number of messages. Each of the next m lines contains a message in the format:  '+ id': the record means that the person with number id (1 ≤ id ≤ n) has logged on to the meeting.  '- id': the record means that the person with number id (1 ≤ id ≤ n) has logged off from the meeting. 

Assume that all the people of the team are numbered from 1 to n and the messages are given in the chronological order. It is guaranteed that the given sequence is the correct record of a continuous part of the meeting. It is guaranteed that no two log on/log off events occurred simultaneously.


-----Output-----

In the first line print integer k (0 ≤ k ≤ n) — how many people can be leaders. In the next line, print k integers in the increasing order — the numbers of the people who can be leaders.

If the data is such that no member of the team can be a leader, print a single number 0.


-----Examples-----
Input
5 4
+ 1
+ 2
- 2
- 1

Output
4
1 3 4 5 
Input
3 2
+ 1
- 2

Output
1
3 
Input
2 4
+ 1
- 1
+ 2
- 2

Output
0

Input
5 6
+ 1
- 1
- 3
+ 3
+ 4
- 4

Output
3
2 3 5 
Input
2 4
+ 1
- 2
+ 2
- 1

Output
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a big positive number x represented as string, find value of x % 11 or x mod 11. Output is expected as an integer.
Example 1:
Input: x = 1345
Output: 3
Explanation: 1345 % 11 = 3 
Example 1:
Input: x = 231456786543567898765
Output: 1
Explanation: 231456786543567898765 % 11 = 1
Your Task:  
You don't need to read input or print anything. Your task is to complete the function xmod11() which takes string x as the input parameter and returns the integer value of x%11.
Expected Time Complexity: O(length of string x)
Expected Space Complexity: O(1)
Constraints:
1 ≤ length of string x ≤ 100000

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
In one of the games Arkady is fond of the game process happens on a rectangular field. In the game process Arkady can buy extensions for his field, each extension enlarges one of the field sizes in a particular number of times. Formally, there are *n* extensions, the *i*-th of them multiplies the width or the length (by Arkady's choice) by *a**i*. Each extension can't be used more than once, the extensions can be used in any order.

Now Arkady's field has size *h*<=×<=*w*. He wants to enlarge it so that it is possible to place a rectangle of size *a*<=×<=*b* on it (along the width or along the length, with sides parallel to the field sides). Find the minimum number of extensions needed to reach Arkady's goal.

Input Specification:
The first line contains five integers *a*, *b*, *h*, *w* and *n* (1<=≤<=*a*,<=*b*,<=*h*,<=*w*,<=*n*<=≤<=100<=000) — the sizes of the rectangle needed to be placed, the initial sizes of the field and the number of available extensions.

The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (2<=≤<=*a**i*<=≤<=100<=000), where *a**i* equals the integer a side multiplies by when the *i*-th extension is applied.

Output Specification:
Print the minimum number of extensions needed to reach Arkady's goal. If it is not possible to place the rectangle on the field with all extensions, print -1. If the rectangle can be placed on the initial field, print 0.

Demo Input:
['3 3 2 4 4\n2 5 4 10\n', '3 3 3 3 5\n2 3 5 4 2\n', '5 5 1 2 3\n2 2 3\n', '3 4 1 1 3\n2 3 2\n']

Demo Output:
['1\n', '0\n', '-1\n', '3\n']

Note:
In the first example it is enough to use any of the extensions available. For example, we can enlarge *h* in 5 times using the second extension. Then *h* becomes equal 10 and it is now possible to place the rectangle on the field.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a linked list of n nodes and a key , the task is to check if the key is present in the linked list or not.
Example:
Input:
n = 4
1->2->3->4
Key = 3
Output:
True
Explanation:
3 is present in Linked List, so the function returns true.
Your Task:
Your task is to complete the given function searchKey(), which takes a head reference and key as Input and returns true or false boolean value by checking the key is present or not in the linked list.
Constraint:
1 <= n <= 10^{5}
1 <= key <= 10^{5}
Expected Time Complexity: O(n)
Expected Space Complexity: O(1)

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
"QAQ" is a word to denote an expression of crying. Imagine "Q" as eyes with tears and "A" as a mouth.

Now Diamond has given Bort a string consisting of only uppercase English letters of length *n*. There is a great number of "QAQ" in the string (Diamond is so cute!).

Bort wants to know how many subsequences "QAQ" are in the string Diamond has given. Note that the letters "QAQ" don't have to be consecutive, but the order of letters should be exact.

Input Specification:
The only line contains a string of length *n* (1<=≤<=*n*<=≤<=100). It's guaranteed that the string only contains uppercase English letters.

Output Specification:
Print a single integer — the number of subsequences "QAQ" in the string.

Demo Input:
['QAQAQYSYIOIWIN\n', 'QAQQQZZYNOIWIN\n']

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

Note:
In the first example there are 4 subsequences "QAQ": "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN".

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Evlampiy has found one more cool application to process photos. However the application has certain limitations.

Each photo i has a contrast v_{i}. In order for the processing to be truly of high quality, the application must receive at least k photos with contrasts which differ as little as possible.

Evlampiy already knows the contrast v_{i} for each of his n photos. Now he wants to split the photos into groups, so that each group contains at least k photos. As a result, each photo must belong to exactly one group.

He considers a processing time of the j-th group to be the difference between the maximum and minimum values of v_{i} in the group. Because of multithreading the processing time of a division into groups is the maximum processing time among all groups.

Split n photos into groups in a such way that the processing time of the division is the minimum possible, i.e. that the the maximum processing time over all groups as least as possible.


-----Input-----

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3·10^5) — number of photos and minimum size of a group.

The second line contains n integers v_1, v_2, ..., v_{n} (1 ≤ v_{i} ≤ 10^9), where v_{i} is the contrast of the i-th photo.


-----Output-----

Print the minimal processing time of the division into groups.


-----Examples-----
Input
5 2
50 110 130 40 120

Output
20

Input
4 1
2 3 4 1

Output
0



-----Note-----

In the first example the photos should be split into 2 groups: [40, 50] and [110, 120, 130]. The processing time of the first group is 10, and the processing time of the second group is 20. Maximum among 10 and 20 is 20. It is impossible to split the photos into groups in a such way that the processing time of division is less than 20.

In the second example the photos should be split into four groups, each containing one photo. So the minimal possible processing time of a division is 0.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Lucky Number 2

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Petya loves long lucky numbers very much. He is interested in the minimum lucky number *d* that meets some condition. Let *cnt*(*x*) be the number of occurrences of number *x* in number *d* as a substring. For example, if *d*<==<=747747, then *cnt*(4)<==<=2, *cnt*(7)<==<=4, *cnt*(47)<==<=2, *cnt*(74)<==<=2. Petya wants the following condition to fulfil simultaneously: *cnt*(4)<==<=*a*1, *cnt*(7)<==<=*a*2, *cnt*(47)<==<=*a*3, *cnt*(74)<==<=*a*4. Petya is not interested in the occurrences of other numbers. Help him cope with this task.

Input Specification:
The single line contains four integers *a*1, *a*2, *a*3 and *a*4 (1<=≤<=*a*1,<=*a*2,<=*a*3,<=*a*4<=≤<=106).

Output Specification:
On the single line print without leading zeroes the answer to the problem — the minimum lucky number *d* such, that *cnt*(4)<==<=*a*1, *cnt*(7)<==<=*a*2, *cnt*(47)<==<=*a*3, *cnt*(74)<==<=*a*4. If such number does not exist, print the single number "-1" (without the quotes).

Demo Input:
['2 2 1 1\n', '4 7 3 1\n']

Demo Output:
['4774\n', '-1\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You have recently been promoted to lead scientist at NASA, the National Association for Sorting Algorithms. Congratulations! Your primary responsibility is testing the sorting algorithms that your team produces. Fortunately, NASA has a large budget this year, and you were able to buy some state-of-the-art integers you can use to test the sorting algorithms.

As the lead scientist, you are well aware that algorithms are tested by their behaviour on worst case inputs. So, to test sorting algorithms, you need sequences that are as unsorted as possible.

Given a sequence of numbers $(a_1,\ldots ,a_ n)$ we say that an element $a_ k$ is sorted if for all indices $j$ such that $j > k$, $a_ j \geq a_ k$ and for all indices $j$ such that $j < k$, $a_ j \leq a_ k$. For example, in\[ (1, 3, 2, 3, 4, 6, 5, 5) \]

the sorted elements are the $1$, the second occurrence of $3$, and the $4$. Note that a sequence is sorted if and only if all its elements are sorted. A sequence is called entirely unsorted if none of its elements are sorted.

Given a sequence of integers, what is the number of entirely unsorted sequences you can make by permuting its elements? Two sequences $(b_1, \dots , b_ n)$ and $(c_1, \dots , c_ n)$ are considered to be different if there is some index $i \in \left\{ 1, \dots , n \right\} $ for which $b_ i \neq c_ i$. Because the number of permutations may be very large, please give it modulo $10^9 + 9$.

-----Input-----
The input starts with an integer $1 \leq n \leq 5000$. Then follows a single line with $n$ integers $a_1, \ldots , a_ n$, with $0 \leq a_ i \leq 10^9$ for all $i$.

-----Output-----
Print a single integer: the number of entirely unsorted sequences you can make by permuting the $a_ i$, modulo $10^9 + 9$.

-----Examples-----
Sample Input 1:
4
0 1 2 3
Sample Output 1:
14

Sample Input 2:
5
1 1 2 1 1
Sample Output 2:
1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A Magic Fraction for N is one that has the following properties:
It is a proper fraction (The value is < 1)
It cannot be reduced further (The GCD of the numerator and the denominator is 1)
The product of the numerator and the denominator is factorial of N. i.e. if a/b is the fraction, then a*b = N!

Examples of Magic Fractions are:

1/2      [ gcd(1,2) = 1 and 1*2=2! ]

2/3      [ gcd(2,3) = 1 and 2*3=3! ]

3/8      [ gcd(3,8) = 1 and 3*8=4! ]

2/12  for example, is not a magic fraction, as even though 2*12=4!, gcd(2,12) != 1

And Magic fractions for number 3 are: 2/3 and 1/6 (since both of them satisfy the above criteria, are of the form a/b where a*b = 3!)

Now given a number N, you need to print the total number of magic fractions that exist, for all numbers between 1 and N (include magic fractions for N, too).

Note:
The number N will be in the range [1, 500]. (1 and 500 inclusive)
You'll have to read the input from STDIN, and print the output to STDOUT

Examples:

1)

Input: 1

Output: 0

Explanation: There is no fraction < 1 whose numerator * denominator = 1!

2)

Input: 3

Output: 3

Explanation: 0 for 1 + 1 for 2 [1/2] + 2 for 3 [1/6, 2/3]

3)

Input: 5

Output: 9 

SAMPLE INPUT
8

SAMPLE OUTPUT
29

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
One day Kefa found n baloons. For convenience, we denote color of i-th baloon as s_{i} — lowercase letter of the Latin alphabet. Also Kefa has k friends. Friend will be upset, If he get two baloons of the same color. Kefa want to give out all baloons to his friends. Help Kefa to find out, can he give out all his baloons, such that no one of his friens will be upset — print «YES», if he can, and «NO», otherwise. Note, that Kefa's friend will not upset, if he doesn't get baloons at all.


-----Input-----

The first line contains two integers n and k (1 ≤ n, k ≤ 100) — the number of baloons and friends.

Next line contains string s — colors of baloons.


-----Output-----

Answer to the task — «YES» or «NO» in a single line.

You can choose the case (lower or upper) for each letter arbitrary.


-----Examples-----
Input
4 2
aabb

Output
YES

Input
6 3
aacaab

Output
NO



-----Note-----

In the first sample Kefa can give 1-st and 3-rd baloon to the first friend, and 2-nd and 4-th to the second.

In the second sample Kefa needs to give to all his friends baloons of color a, but one baloon will stay, thats why answer is «NO».

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