vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
В самолёте есть n рядов мест. Если смотреть на ряды сверху, то в каждом ряду есть 3 места слева, затем проход между рядами, затем 4 центральных места, затем ещё один проход между рядами, а затем ещё 3 места справа.

Известно, что некоторые места уже заняты пассажирами. Всего есть два вида пассажиров — статусные (те, которые часто летают) и обычные. 

Перед вами стоит задача рассадить ещё k обычных пассажиров так, чтобы суммарное число соседей у статусных пассажиров было минимально возможным. Два пассажира считаются соседями, если они сидят в одном ряду и между ними нет других мест и прохода между рядами. Если пассажир является соседним пассажиром для двух статусных пассажиров, то его следует учитывать в сумме соседей дважды.


-----Входные данные-----

В первой строке следуют два целых числа n и k (1 ≤ n ≤ 100, 1 ≤ k ≤ 10·n) — количество рядов мест в самолёте и количество пассажиров, которых нужно рассадить.

Далее следует описание рядов мест самолёта по одному ряду в строке. Если очередной символ равен '-', то это проход между рядами. Если очередной символ равен '.', то это свободное место. Если очередной символ равен 'S', то на текущем месте будет сидеть статусный пассажир. Если очередной символ равен 'P', то на текущем месте будет сидеть обычный пассажир. 

Гарантируется, что количество свободных мест не меньше k. Гарантируется, что все ряды удовлетворяют описанному в условии формату.


-----Выходные данные-----

В первую строку выведите минимальное суммарное число соседей у статусных пассажиров.

Далее выведите план рассадки пассажиров, который минимизирует суммарное количество соседей у статусных пассажиров, в том же формате, что и во входных данных. Если в свободное место нужно посадить одного из k пассажиров, выведите строчную букву 'x' вместо символа '.'. 


-----Примеры-----
Входные данные
1 2
SP.-SS.S-S.S

Выходные данные
5
SPx-SSxS-S.S

Входные данные
4 9
PP.-PPPS-S.S
PSP-PPSP-.S.
.S.-S..P-SS.
P.S-P.PP-PSP

Выходные данные
15
PPx-PPPS-S.S
PSP-PPSP-xSx
xSx-SxxP-SSx
P.S-PxPP-PSP



-----Примечание-----

В первом примере нужно посадить ещё двух обычных пассажиров. Для минимизации соседей у статусных пассажиров, нужно посадить первого из них на третье слева место, а второго на любое из оставшихся двух мест, так как независимо от выбора места он станет соседом двух статусных пассажиров. 

Изначально, у статусного пассажира, который сидит на самом левом месте уже есть сосед. Также на четвёртом и пятом местах слева сидят статусные пассажиры, являющиеся соседями друг для друга (что добавляет к сумме 2).

Таким образом, после посадки ещё двух обычных пассажиров, итоговое суммарное количество соседей у статусных пассажиров станет равно пяти.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Jon Snow and his Favourite Number

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Jon Snow now has to fight with White Walkers. He has *n* rangers, each of which has his own strength. Also Jon Snow has his favourite number *x*. Each ranger can fight with a white walker only if the strength of the white walker equals his strength. He however thinks that his rangers are weak and need to improve. Jon now thinks that if he takes the bitwise XOR of strengths of some of rangers with his favourite number *x*, he might get soldiers of high strength. So, he decided to do the following operation *k* times: 
1.  Arrange all the rangers in a straight line in the order of increasing strengths.1.  Take the bitwise XOR (is written as ) of the strength of each alternate ranger with *x* and update it's strength.1.  The strength of first ranger is updated to , i.e. 7.1.  The strength of second ranger remains the same, i.e. 7.1.  The strength of third ranger is updated to , i.e. 11.1.  The strength of fourth ranger remains the same, i.e. 11.1.  The strength of fifth ranger is updated to , i.e. 13.
Now, Jon wants to know the maximum and minimum strength of the rangers after performing the above operations *k* times. He wants your help for this task. Can you help him?

Input Specification:
First line consists of three integers *n*, *k*, *x* (1<=≤<=*n*<=≤<=105, 0<=≤<=*k*<=≤<=105, 0<=≤<=*x*<=≤<=103) — number of rangers Jon has, the number of times Jon will carry out the operation and Jon's favourite number respectively.

Second line consists of *n* integers representing the strengths of the rangers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=103).

Output Specification:
Output two integers, the maximum and the minimum strength of the rangers after performing the operation *k* times.

Demo Input:
['5 1 2\n9 7 11 15 5\n', '2 100000 569\n605 986\n']

Demo Output:
['13 7', '986 605']

Note:
none

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

Carol wants to sort an array of n integers. The array contains a permutation of {1,2,..,n}. 

Carol can only sort subarrays at a time. More specifically, she has a list of m subarrays in order that she will sort by. A subarray is a contiguous portion of the original array, which can be specified by a start and end index. 

She wonders if the list she has will sort every permutation correctly. If so, print the phrase "All ok!". If not, determine the lexicographically smallest permutation that will not be correctly sorted.

Input format:

The first line of input will contain two integers n,m.
The following m lines of input will contain two integers li,ri describing the start and end indices of the subarray that Carol will sort.

Output format:

If every permutation is correctly sorted, print the string "All ok!" (without quotes). Otherwise, print n space separated integers, representing the lexicographically smallest permutation of {1,2,..,n} that can't be sorted. 

Constraints:

For all subtasks
1 ≤ li ≤ ri ≤ n

40 pts:
1 ≤ n ≤ 10
1 ≤ m ≤ 3

60 pts:
1 ≤ n ≤ 50
1 ≤ m ≤ 50

SAMPLE INPUT
9 2
1 6
4 9

SAMPLE OUTPUT
1 2 4 5 6 7 3 8 9

Explanation

In this case, Carol has a list of 9 integers, and she sorts the subarray from the 1st to 6th element, then the 4rd to 9th element. We can see that this will not correctly sort the permutation {1,2,4,5,6,7,3,8,9}, since the first subarray will make the array become {1,2,4,5,6,7,3,8,9}, and the second will make it {1,2,4,3,5,6,7,8,9}, which is not in sorted order. This is also the lexicographically smallest permutation that can't be sorted.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has X 5 rupee coins and Y 10 rupee coins. Chef goes to a shop to buy chocolates for Chefina where each chocolate costs Z rupees. Find the maximum number of chocolates that Chef can buy for Chefina.

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

- The first line contains a single integer T — the number of test cases. Then the test cases follow.
- The first and only line of each test case contains three integers X, Y and Z — the number of 5 rupee coins, the number of 10 rupee coins and the cost of each chocolate.

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

For each test case, output the maximum number of chocolates that Chef can buy for Chefina.

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

$1 ≤ T ≤ 100$ 
$1 ≤ X,Y,Z ≤ 1000$

----- Sample Input 1 ------ 
4
10 10 10
3 1 8
8 1 3
4 4 1000
----- Sample Output 1 ------ 
15
3
16
0

----- explanation 1 ------ 
Test case $1$: Chef has $10 \cdot 5 + 10 \cdot 10 = 150$ rupees in total. Since each chocolate costs $10$ rupees, Chef can spend all $150$ rupees and buy $15$ chocolates for Chefina.

Test case $2$: Chef has $3 \cdot 5 + 1 \cdot 10 = 25$ rupees in total. Since each chocolate costs $8$ rupees, Chef can buy a maximum of $3$ chocolates for Chefina, leaving him with $1$ rupee.

Test case $3$: Chef has $8 \cdot 5 + 1 \cdot 10 = 50$ rupees in total. Since each chocolate costs $3$ rupees, Chef can buy a maximum of $16$ chocolates for Chefina, leaving him with $2$ rupee.

Test case $4$: Chef has $4 \cdot 5 + 4 \cdot 10 = 60$ rupees in total. Since each chocolate costs $1000$ rupees, Chef can buy no chocolate for Chefina, leaving him with $60$ rupees.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Cirno_9baka has a tree with $n$ nodes. He is willing to share it with you, which means you can operate on it.

Initially, there are two chess pieces on the node $1$ of the tree. In one step, you can choose any piece, and move it to the neighboring node. You are also given an integer $d$. You need to ensure that the distance between the two pieces doesn't ever exceed $d$.

Each of these two pieces has a sequence of nodes which they need to pass in any order, and eventually, they have to return to the root. As a curious boy, he wants to know the minimum steps you need to take.


-----Input-----

The first line contains two integers $n$ and $d$ ($2 \le d \le n \le 2\cdot 10^5$).

The $i$-th of the following $n - 1$ lines contains two integers $u_i, v_i$ $(1 \le u_i, v_i \le n)$, denoting the edge between the nodes $u_i, v_i$ of the tree.

It's guaranteed that these edges form a tree.

The next line contains an integer $m_1$ ($1 \le m_1 \le n$) and $m_1$ integers $a_1, a_2, \ldots, a_{m_1}$ ($1 \le a_i \le n$, all $a_i$ are distinct)  — the sequence of nodes that the first piece needs to pass.

The second line contains an integer $m_2$ ($1 \le m_2 \le n$) and $m_2$ integers $b_1, b_2, \ldots, b_{m_2}$ ($1 \le b_i \le n$, all $b_i$ are distinct)  — the sequence of nodes that the second piece needs to pass.


-----Output-----

Output a single integer  — the minimum steps you need to take.


-----Examples-----

Input
4 2
1 2
1 3
2 4
1 3
1 4
Output
6
Input
4 2
1 2
2 3
3 4
4 1 2 3 4
1 1
Output
8


-----Note-----

In the first sample, here is one possible sequence of steps of length $6$.

The second piece moves by the route $1 \to 2 \to 4 \to 2 \to 1$.

Then, the first piece moves by the route $1 \to 3 \to 1$.

In the second sample, here is one possible sequence of steps of length $8$:

The first piece moves by the route $1 \to 2 \to 3$.

Then, the second piece moves by the route $1 \to 2$.

Then, the first piece moves by the route $3 \to 4 \to 3 \to 2 \to 1$.

Then, the second piece moves by the route $2 \to 1$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are $n$ pillars aligned in a row and numbered from $1$ to $n$.

Initially each pillar contains exactly one disk. The $i$-th pillar contains a disk having radius $a_i$.

You can move these disks from one pillar to another. You can take a disk from pillar $i$ and place it on top of pillar $j$ if all these conditions are met:

  there is no other pillar between pillars $i$ and $j$. Formally, it means that $|i - j| = 1$;  pillar $i$ contains exactly one disk;  either pillar $j$ contains no disks, or the topmost disk on pillar $j$ has radius strictly greater than the radius of the disk you move. 

When you place a disk on a pillar that already has some disks on it, you put the new disk on top of previously placed disks, so the new disk will be used to check the third condition if you try to place another disk on the same pillar.

You may take any disk and place it on other pillar any number of times, provided that every time you do it, all three aforementioned conditions are met. Now you wonder, is it possible to place all $n$ disks on the same pillar simultaneously?


-----Input-----

The first line contains one integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the number of pillars.

The second line contains $n$ integers $a_1$, $a_2$, ..., $a_i$ ($1 \le a_i \le n$), where $a_i$ is the radius of the disk initially placed on the $i$-th pillar. All numbers $a_i$ are distinct.


-----Output-----

Print YES if it is possible to place all the disks on the same pillar simultaneously, and NO otherwise. You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).


-----Examples-----
Input
4
1 3 4 2

Output
YES

Input
3
3 1 2

Output
NO



-----Note-----

In the first case it is possible to place all disks on pillar $3$ using the following sequence of actions:

  take the disk with radius $3$ from pillar $2$ and place it on top of pillar $3$;  take the disk with radius $1$ from pillar $1$ and place it on top of pillar $2$;  take the disk with radius $2$ from pillar $4$ and place it on top of pillar $3$;  take the disk with radius $1$ from pillar $2$ and place it on top of pillar $3$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In a small but very proud high school it was decided to win ACM ICPC. This goal requires to compose as many teams of three as possible, but since there were only 6 students who wished to participate, the decision was to build exactly two teams.

After practice competition, participant number i got a score of a_{i}. Team score is defined as sum of scores of its participants. High school management is interested if it's possible to build two teams with equal scores. Your task is to answer that question.


-----Input-----

The single line contains six integers a_1, ..., a_6 (0 ≤ a_{i} ≤ 1000) — scores of the participants


-----Output-----

Print "YES" (quotes for clarity), if it is possible to build teams with equal score, and "NO" otherwise.

You can print each character either upper- or lowercase ("YeS" and "yes" are valid when the answer is "YES").


-----Examples-----
Input
1 3 2 1 2 1

Output
YES

Input
1 1 1 1 1 99

Output
NO



-----Note-----

In the first sample, first team can be composed of 1st, 2nd and 6th participant, second — of 3rd, 4th and 5th: team scores are 1 + 3 + 1 = 2 + 1 + 2 = 5.

In the second sample, score of participant number 6 is too high: his team score will be definitely greater.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There is a prison that can be represented as a rectangular matrix with $n$ rows and $m$ columns. Therefore, there are $n \cdot m$ prison cells. There are also $n \cdot m$ prisoners, one in each prison cell. Let's denote the cell in the $i$-th row and the $j$-th column as $(i, j)$.

There's a secret tunnel in the cell $(r, c)$, that the prisoners will use to escape! However, to avoid the risk of getting caught, they will escape at night.

Before the night, every prisoner is in his own cell. When night comes, they can start moving to adjacent cells. Formally, in one second, a prisoner located in cell $(i, j)$ can move to cells $( i - 1 , j )$ , $( i + 1 , j )$ , $( i , j - 1 )$ , or $( i , j + 1 )$, as long as the target cell is inside the prison. They can also choose to stay in cell $(i, j)$.

The prisoners want to know the minimum number of seconds needed so that every prisoner can arrive to cell $( r , c )$ if they move optimally. Note that there can be any number of prisoners in the same cell at the same time.


-----Input-----

The first line contains an integer $t$ $(1 \le t \le 10^4)$, the number of test cases.

Each of the next $t$ lines contains four space-separated integers $n$, $m$, $r$, $c$ ($1 \le r \le n \le 10^9$, $1 \le c \le m \le 10^9$).


-----Output-----

Print $t$ lines, the answers for each test case.


-----Examples-----

Input
3
10 10 1 1
3 5 2 4
10 2 5 1
Output
18
4
6


-----Note-----

None

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You've got a string $a_1, a_2, \dots, a_n$, consisting of zeros and ones.

Let's call a sequence of consecutive elements $a_i, a_{i<=+<=1}, \ldots,<=a_j$ ($1\leq<=i\leq<=j\leq<=n$) a substring of string $a$. 

You can apply the following operations any number of times:
 -  Choose some substring of string $a$ (for example, you can choose entire string) and reverse it, paying $x$ coins for it (for example, «0101101» $\to$ «0111001»); -  Choose some substring of string $a$ (for example, you can choose entire string or just one symbol) and replace each symbol to the opposite one (zeros are replaced by ones, and ones — by zeros), paying $y$ coins for it (for example, «0101101» $\to$ «0110001»). 
You can apply these operations in any order. It is allowed to apply the operations multiple times to the same substring.

What is the minimum number of coins you need to spend to get a string consisting only of ones?

Input Specification:
The first line of input contains integers $n$, $x$ and $y$ ($1<=\leq<=n<=\leq<=300\,000, 0 \leq x, y \leq 10^9$) — length of the string, cost of the first operation (substring reverse) and cost of the second operation (inverting all elements of substring).

The second line contains the string $a$ of length $n$, consisting of zeros and ones.

Output Specification:
Print a single integer — the minimum total cost of operations you need to spend to get a string consisting only of ones. Print $0$, if you do not need to perform any operations.

Demo Input:
['5 1 10\n01000\n', '5 10 1\n01000\n', '7 2 3\n1111111\n']

Demo Output:
['11\n', '2\n', '0\n']

Note:
In the first sample, at first you need to reverse substring $[1 \dots 2]$, and then you need to invert substring $[2 \dots 5]$. 

Then the string was changed as follows:

«01000» $\to$ «10000» $\to$ «11111».

The total cost of operations is $1 + 10 = 11$.

In the second sample, at first you need to invert substring $[1 \dots 1]$, and then you need to invert substring $[3 \dots 5]$. 

Then the string was changed as follows:

«01000» $\to$ «11000» $\to$ «11111».

The overall cost is $1 + 1 = 2$.

In the third example, string already consists only of ones, so the answer is $0$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Eugeny loves listening to music. He has n songs in his play list. We know that song number i has the duration of t_{i} minutes. Eugeny listens to each song, perhaps more than once. He listens to song number i c_{i} times. Eugeny's play list is organized as follows: first song number 1 plays c_1 times, then song number 2 plays c_2 times, ..., in the end the song number n plays c_{n} times.

Eugeny took a piece of paper and wrote out m moments of time when he liked a song. Now for each such moment he wants to know the number of the song that played at that moment. The moment x means that Eugeny wants to know which song was playing during the x-th minute of his listening to the play list.

Help Eugeny and calculate the required numbers of songs.


-----Input-----

The first line contains two integers n, m (1 ≤ n, m ≤ 10^5). The next n lines contain pairs of integers. The i-th line contains integers c_{i}, t_{i} (1 ≤ c_{i}, t_{i} ≤ 10^9) — the description of the play list. It is guaranteed that the play list's total duration doesn't exceed 10^9 $(\sum_{i = 1}^{n} c_{i} \cdot t_{i} \leq 10^{9})$.

The next line contains m positive integers v_1, v_2, ..., v_{m}, that describe the moments Eugeny has written out. It is guaranteed that there isn't such moment of time v_{i}, when the music doesn't play any longer. It is guaranteed that v_{i} < v_{i} + 1 (i < m).

The moment of time v_{i} means that Eugeny wants to know which song was playing during the v_{i}-th munite from the start of listening to the playlist.


-----Output-----

Print m integers — the i-th number must equal the number of the song that was playing during the v_{i}-th minute after Eugeny started listening to the play list.


-----Examples-----
Input
1 2
2 8
1 16

Output
1
1

Input
4 9
1 2
2 1
1 1
2 2
1 2 3 4 5 6 7 8 9

Output
1
1
2
2
3
4
4
4
4

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
In the game Lizard Era: Beginning the protagonist will travel with three companions: Lynn, Meliana and Worrigan. Overall the game has *n* mandatory quests. To perform each of them, you need to take exactly two companions.

The attitude of each of the companions to the hero is an integer. Initially, the attitude of each of them to the hero of neutral and equal to 0. As the hero completes quests, he makes actions that change the attitude of the companions, whom he took to perform this task, in positive or negative direction.

Tell us what companions the hero needs to choose to make their attitude equal after completing all the quests. If this can be done in several ways, choose the one in which the value of resulting attitude is greatest possible.

Input Specification:
The first line contains positive integer *n* (1<=≤<=*n*<=≤<=25) — the number of important tasks. 

Next *n* lines contain the descriptions of the tasks — the *i*-th line contains three integers *l**i*,<=*m**i*,<=*w**i* — the values by which the attitude of Lynn, Meliana and Worrigan respectively will change towards the hero if the hero takes them on the *i*-th task. All the numbers in the input are integers and do not exceed 107 in absolute value.

Output Specification:
If there is no solution, print in the first line "Impossible".

Otherwise, print *n* lines, two characters is each line — in the *i*-th line print the first letters of the companions' names that hero should take to complete the *i*-th task ('L' for Lynn, 'M' for Meliana, 'W' for Worrigan). Print the letters in any order, if there are multiple solutions, print any of them.

Demo Input:
['3\n1 0 0\n0 1 0\n0 0 1\n', '7\n0 8 9\n5 9 -2\n6 -8 -7\n9 4 5\n-4 -9 9\n-4 5 2\n-6 8 -7\n', '2\n1 0 0\n1 1 0\n']

Demo Output:
['LM\nMW\nMW\n', 'LM\nMW\nLM\nLW\nMW\nLM\nLW\n', 'Impossible\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given an array (which will have a length of at least 3, but could be very large) containing integers. The array is either entirely comprised of odd integers or entirely comprised of even integers except for a single integer `N`. Write a method that takes the array as an argument and returns this "outlier" `N`.

## Examples

```python
[2, 4, 0, 100, 4, 11, 2602, 36]
Should return: 11 (the only odd number)

[160, 3, 1719, 19, 11, 13, -21]
Should return: 160 (the only even number)
```

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