vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
And while Mishka is enjoying her trip...

Chris is a little brown bear. No one knows, where and when he met Mishka, but for a long time they are together (excluding her current trip). However, best friends are important too. John is Chris' best friend.

Once walking with his friend, John gave Chris the following problem:

At the infinite horizontal road of width w, bounded by lines y = 0 and y = w, there is a bus moving, presented as a convex polygon of n vertices. The bus moves continuously with a constant speed of v in a straight Ox line in direction of decreasing x coordinates, thus in time only x coordinates of its points are changing. Formally, after time t each of x coordinates of its points will be decreased by vt.

There is a pedestrian in the point (0, 0), who can move only by a vertical pedestrian crossing, presented as a segment connecting points (0, 0) and (0, w) with any speed not exceeding u. Thus the pedestrian can move only in a straight line Oy in any direction with any speed not exceeding u and not leaving the road borders. The pedestrian can instantly change his speed, thus, for example, he can stop instantly.

Please look at the sample note picture for better understanding.

We consider the pedestrian is hit by the bus, if at any moment the point he is located in lies strictly inside the bus polygon (this means that if the point lies on the polygon vertex or on its edge, the pedestrian is not hit by the bus).

You are given the bus position at the moment 0. Please help Chris determine minimum amount of time the pedestrian needs to cross the road and reach the point (0, w) and not to be hit by the bus.


-----Input-----

The first line of the input contains four integers n, w, v, u (3 ≤ n ≤ 10 000, 1 ≤ w ≤ 10^9, 1 ≤ v,  u ≤ 1000) — the number of the bus polygon vertices, road width, bus speed and pedestrian speed respectively.

The next n lines describes polygon vertices in counter-clockwise order. i-th of them contains pair of integers x_{i} and y_{i} ( - 10^9 ≤ x_{i} ≤ 10^9, 0 ≤ y_{i} ≤ w) — coordinates of i-th polygon point. It is guaranteed that the polygon is non-degenerate.


-----Output-----

Print the single real t — the time the pedestrian needs to croos the road and not to be hit by the bus. The answer is considered correct if its relative or absolute error doesn't exceed 10^{ - 6}.


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

Output
5.0000000000


-----Note-----

Following image describes initial position in the first sample case:

[Image]

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

Time Limit: 0 seconds

Memory Limit: 64 megabytes

Problem Description:
You are given undirected weighted graph. Find the length of the shortest cycle which starts from the vertex 1 and passes throught all the edges at least once. Graph may contain multiply edges between a pair of vertices and loops (edges from the vertex to itself).

Input Specification:
The first line of the input contains two integers *n* and *m* (1<=≤<=*n*<=≤<=15,<=0<=≤<=*m*<=≤<=2000), *n* is the amount of vertices, and *m* is the amount of edges. Following *m* lines contain edges as a triples *x*,<=*y*,<=*w* (1<=≤<=*x*,<=*y*<=≤<=*n*,<=1<=≤<=*w*<=≤<=10000), *x*,<=*y* are edge endpoints, and *w* is the edge length.

Output Specification:
Output minimal cycle length or -1 if it doesn't exists.

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

Demo Output:
['3\n', '14\n']

Note:
none

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Polycarpus develops an interesting theory about the interrelation of arithmetic progressions with just everything in the world. His current idea is that the population of the capital of Berland changes over time like an arithmetic progression. Well, or like multiple arithmetic progressions.

Polycarpus believes that if he writes out the population of the capital for several consecutive years in the sequence *a*1,<=*a*2,<=...,<=*a**n*, then it is convenient to consider the array as several arithmetic progressions, written one after the other. For example, sequence (8,<=6,<=4,<=2,<=1,<=4,<=7,<=10,<=2) can be considered as a sequence of three arithmetic progressions (8,<=6,<=4,<=2), (1,<=4,<=7,<=10) and (2), which are written one after another.

Unfortunately, Polycarpus may not have all the data for the *n* consecutive years (a census of the population doesn't occur every year, after all). For this reason, some values of *a**i* ​​may be unknown. Such values are represented by number -1.

For a given sequence *a*<==<=(*a*1,<=*a*2,<=...,<=*a**n*), which consists of positive integers and values ​​-1, find the minimum number of arithmetic progressions Polycarpus needs to get *a*. To get *a*, the progressions need to be written down one after the other. Values ​​-1 may correspond to an arbitrary positive integer and the values *a**i*<=&gt;<=0 must be equal to the corresponding elements of sought consecutive record of the progressions.

Let us remind you that a finite sequence *c* is called an arithmetic progression if the difference *c**i*<=+<=1<=-<=*c**i* of any two consecutive elements in it is constant. By definition, any sequence of length 1 is an arithmetic progression.

Input Specification:
The first line of the input contains integer *n* (1<=≤<=*n*<=≤<=2·105) — the number of elements in the sequence. The second line contains integer values *a*1,<=*a*2,<=...,<=*a**n* separated by a space (1<=≤<=*a**i*<=≤<=109 or *a**i*<==<=<=-<=1).

Output Specification:
Print the minimum number of arithmetic progressions that you need to write one after another to get sequence *a*. The positions marked as -1 in *a* can be represented by any positive integers.

Demo Input:
['9\n8 6 4 2 1 4 7 10 2\n', '9\n-1 6 -1 2 -1 4 7 -1 2\n', '5\n-1 -1 -1 -1 -1\n', '7\n-1 -1 4 5 1 2 3\n']

Demo Output:
['3\n', '3\n', '1\n', '2\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
"It does not matter how slowly you go as long as you do not stop." - Confucius
You are given an array $A_1, A_2, \ldots, A_N$ and an integer $K$. For each subarray $S = [A_l, A_{l+1}, \ldots, A_r]$ ($1 \le l \le r \le N$):
- Let's define an array $B$ as $S$ concatenated with itself $m$ times, where $m$ is the smallest integer such that $m(r-l+1) \ge K$.
- Next, let's sort $B$ and define $X = B_K$, i.e. as a $K$-th smallest element of $B$. Note that $|B| \ge K$.
- Then, let's define $F$ as the number of occurrences of $X$ in $S$.
- The subarray $S$ is beautiful if $F$ occurs in $S$ at least once.
Find the number of beautiful subarrays of $A$. Two subarrays $A_l, A_{l+1}, \ldots, A_r$ and $A_p, A_{p+1}, \ldots, A_q$ are different if $l \neq p$ or $r \neq q$.

-----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 line of each test case contains two space-separated integers $N$ and $K$. 
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer - the number of beautiful subarrays.

-----Constraints-----
- $1 \le T \le 5$
- $1 \le N \le 2,000$
- $1 \le K \le 10^9$
- $1 \le A_i \le 2000$ for each valid $i$

-----Subtasks-----
Subtask #1 (20 points): $1 \le N \le 200$
Subtask #2 (80 points): original constraints

-----Example Input-----
1
3 3
1 2 3

-----Example Output-----
3

-----Explanation-----
Example case 1: There are six subarrays of $A$: $[1]$, $[2]$, $[3]$, $[1, 2]$, $[2, 3]$, $[1, 2, 3]$. The corresponding arrays $B$ are $[1, 1, 1]$, $[2, 2, 2]$, $[3, 3, 3]$, $[1, 2, 1, 2]$, $[2, 3, 2, 3]$, $[1, 2, 3]$.
Three of the subarrays are beautiful: $[1]$, $[1, 2]$ and $[1, 2, 3]$. For these subarrays, $X$ is $1$, $2$ and $3$ respectively (for example, for $S = [1, 2]$, $B = [1, 2, 1, 2]$ is sorted to $[1, 1, 2, 2]$ and $X = 2$ is the $3$-rd element). Then, $F = 1$ for each of these subarrays, and each of these subarrays contains $1$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given are integers L and R. Find the number, modulo 10^9 + 7, of pairs of integers (x, y) (L \leq x \leq y \leq R) such that the remainder when y is divided by x is equal to y \mbox{ XOR } x.What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

 - When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.
For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)


-----Constraints-----
 - 1 \leq L \leq R \leq 10^{18}

-----Input-----
Input is given from Standard Input in the following format:
L R

-----Output-----
Print the number of pairs of integers (x, y) (L \leq x \leq y \leq R) satisfying the condition, modulo 10^9 + 7.

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

-----Sample Output-----
3

Three pairs satisfy the condition: (2, 2), (2, 3), and (3, 3).

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

An IP address contains four numbers(0-255) and separated by dots. It can be converted to a number by this way:


Given a string `s` represents a number or an IP address. Your task is to convert it to another representation(`number to IP address` or `IP address to number`).

You can assume that all inputs are valid.

# Example

Example IP address: `10.0.3.193`

Convert each number to a 8-bit binary string
(may needs to pad leading zeros to the left side):
```
10  -->  00001010
0   -->  00000000
3   -->  00000011
193 -->  11000001
```
Combine these four strings: `00001010 00000000 00000011 11000001` and then convert them to a decimal number:
`167773121`


# Input/Output


`[input]` string `s`

A number or IP address in string format.

`[output]` a string

A converted number or IP address in string format.

# Example

For `s = "10.0.3.193"`, the output should be `"167773121"`.

For `s = "167969729"`, the output should be `"10.3.3.193"`.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Vasya has *n* days of vacations! So he decided to improve his IT skills and do sport. Vasya knows the following information about each of this *n* days: whether that gym opened and whether a contest was carried out in the Internet on that day. For the *i*-th day there are four options:
 1.  on this day the gym is closed and the contest is not carried out; 1.  on this day the gym is closed and the contest is carried out; 1.  on this day the gym is open and the contest is not carried out; 1.  on this day the gym is open and the contest is carried out. 
On each of days Vasya can either have a rest or write the contest (if it is carried out on this day), or do sport (if the gym is open on this day).

Find the minimum number of days on which Vasya will have a rest (it means, he will not do sport and write the contest at the same time). The only limitation that Vasya has — he does not want to do the same activity on two consecutive days: it means, he will not do sport on two consecutive days, and write the contest on two consecutive days.

Input Specification:
The first line contains a positive integer *n* (1<=≤<=*n*<=≤<=100) — the number of days of Vasya's vacations.

The second line contains the sequence of integers *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=3) separated by space, where: 
 -  *a**i* equals 0, if on the *i*-th day of vacations the gym is closed and the contest is not carried out; -  *a**i* equals 1, if on the *i*-th day of vacations the gym is closed, but the contest is carried out; -  *a**i* equals 2, if on the *i*-th day of vacations the gym is open and the contest is not carried out; -  *a**i* equals 3, if on the *i*-th day of vacations the gym is open and the contest is carried out.

Output Specification:
Print the minimum possible number of days on which Vasya will have a rest. Remember that Vasya refuses:
 -  to do sport on any two consecutive days, -  to write the contest on any two consecutive days.

Demo Input:
['4\n1 3 2 0\n', '7\n1 3 3 2 1 2 3\n', '2\n2 2\n']

Demo Output:
['2\n', '0\n', '1\n']

Note:
In the first test Vasya can write the contest on the day number 1 and do sport on the day number 3. Thus, he will have a rest for only 2 days.

In the second test Vasya should write contests on days number 1, 3, 5 and 7, in other days do sport. Thus, he will not have a rest for a single day.

In the third test Vasya can do sport either on a day number 1 or number 2. He can not do sport in two days, because it will be contrary to the his limitation. Thus, he will have a rest for only one day.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
## Task
 In your favorite game, you must shoot a target with a water-gun to gain points. Each target can be worth a different amount of points. 
 
 You are guaranteed to hit every target that you try to hit. You cannot hit consecutive targets though because targets are only visible for one second (one at a time) and it takes you a full second to reload your water-gun after shooting (you start the game already loaded).

 Given an array `vals` with the order of each target's point value, determine the maximum number of points that you can win.

## Example
 For `vals = [1, 2, 3, 4]`, the result should be `6`.
 
 your optimal strategy would be to let the first one pass and shoot the second one with value 2 and the 4th one with value 4 thus:

 `vals[1](2) + vals[3](4) = 6`
 
 For `vals = [5, 5, 5, 5, 5]`, the result should be `15`.
 
 your optimal strategy would be to shoot the 1st, 3rd and 5th value:
 
 `5 + 5 + 5 = 15`
 
 You haven't shoot the 2nd, 4th value because you are reloading your water-gun after shooting other values.
 
 Note that the value can be zero or negative, don't shoot them ;-)
 
 For `vals = [0, 0, -1, -1]`, the result should be `0`.
 
 For `vals = [5, -2, -9, -4]`, the result should be `5`.
 
 Shoot the first one is enough.
 
## Input/Output


 - `[input]` integer array `vals`

  The point values (negative or non-negative) of the targets (in order of appearance).


 - `[output]` an integer

  The maximum number of points that you can score.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Today, Yasser and Adel are at the shop buying cupcakes. There are $n$ cupcake types, arranged from $1$ to $n$ on the shelf, and there are infinitely many of each type. The tastiness of a cupcake of type $i$ is an integer $a_i$. There are both tasty and nasty cupcakes, so the tastiness can be positive, zero or negative.

Yasser, of course, wants to try them all, so he will buy exactly one cupcake of each type.

On the other hand, Adel will choose some segment $[l, r]$ $(1 \le l \le r \le n)$ that does not include all of cupcakes (he can't choose $[l, r] = [1, n]$) and buy exactly one cupcake of each of types $l, l + 1, \dots, r$.

After that they will compare the total tastiness of the cupcakes each of them have bought. Yasser will be happy if the total tastiness of cupcakes he buys is strictly greater than the total tastiness of cupcakes Adel buys regardless of Adel's choice.

For example, let the tastinesses of the cupcakes be $[7, 4, -1]$. Yasser will buy all of them, the total tastiness will be $7 + 4 - 1 = 10$. Adel can choose segments $[7], [4], [-1], [7, 4]$ or $[4, -1]$, their total tastinesses are $7, 4, -1, 11$ and $3$, respectively. Adel can choose segment with tastiness $11$, and as $10$ is not strictly greater than $11$, Yasser won't be happy :(

Find out if Yasser will be happy after visiting the shop.


-----Input-----

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains $n$ ($2 \le n \le 10^5$).

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($-10^9 \le a_i \le 10^9$), where $a_i$ represents the tastiness of the $i$-th type of cupcake.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $10^5$.


-----Output-----

For each test case, print "YES", if the total tastiness of cupcakes Yasser buys will always be strictly greater than the total tastiness of cupcakes Adel buys regardless of Adel's choice. Otherwise, print "NO".


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

Output
YES
NO
NO



-----Note-----

In the first example, the total tastiness of any segment Adel can choose is less than the total tastiness of all cupcakes.

In the second example, Adel will choose the segment $[1, 2]$ with total tastiness $11$, which is not less than the total tastiness of all cupcakes, which is $10$.

In the third example, Adel can choose the segment $[3, 3]$ with total tastiness of $5$. Note that Yasser's cupcakes' total tastiness is also $5$, so in that case, the total tastiness of Yasser's cupcakes isn't strictly greater than the total tastiness of Adel's cupcakes.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
As Sherlock Holmes was investigating a crime, he identified *n* suspects. He knows for sure that exactly one of them committed the crime. To find out which one did it, the detective lines up the suspects and numbered them from 1 to *n*. After that, he asked each one: "Which one committed the crime?". Suspect number *i* answered either "The crime was committed by suspect number *a**i*", or "Suspect number *a**i* didn't commit the crime". Also, the suspect could say so about himself (*a**i*<==<=*i*).

Sherlock Holmes understood for sure that exactly *m* answers were the truth and all other answers were a lie. Now help him understand this: which suspect lied and which one told the truth?

Input Specification:
The first line contains two integers *n* and *m* (1<=≤<=*n*<=≤<=105,<=0<=≤<=*m*<=≤<=*n*) — the total number of suspects and the number of suspects who told the truth. Next *n* lines contain the suspects' answers. The *i*-th line contains either "+*a**i*" (without the quotes), if the suspect number *i* says that the crime was committed by suspect number *a**i*, or "-*a**i*" (without the quotes), if the suspect number *i* says that the suspect number *a**i* didn't commit the crime (*a**i* is an integer, 1<=≤<=*a**i*<=≤<=*n*).

It is guaranteed that at least one suspect exists, such that if he committed the crime, then exactly *m* people told the truth.

Output Specification:
Print *n* lines. Line number *i* should contain "Truth" if suspect number *i* has told the truth for sure. Print "Lie" if the suspect number *i* lied for sure and print "Not defined" if he could lie and could tell the truth, too, depending on who committed the crime.

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

Demo Output:
['Truth\n', 'Not defined\nNot defined\nNot defined\n', 'Lie\nNot defined\nLie\nNot defined\n']

Note:
The first sample has the single person and he confesses to the crime, and Sherlock Holmes knows that one person is telling the truth. That means that this person is telling the truth.

In the second sample there are three suspects and each one denies his guilt. Sherlock Holmes knows that only two of them are telling the truth. Any one of them can be the criminal, so we don't know for any of them, whether this person is telling the truth or not.

In the third sample the second and the fourth suspect defend the first and the third one. But only one is telling the truth, thus, the first or the third one is the criminal. Both of them can be criminals, so the second and the fourth one can either be lying or telling the truth. The first and the third one are lying for sure as they are blaming the second and the fourth one.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Variation of this nice kata, the war has expanded and become dirtier and meaner; both even and odd numbers will fight with their pointy `1`s. And negative integers are coming into play as well, with, ça va sans dire, a negative contribution (think of them as spies or saboteurs).

Again, three possible outcomes: `odds win`, `evens win` and `tie`.

Examples:

```python
bits_war([1,5,12]) => "odds win" #1+101 vs 1100, 3 vs 2
bits_war([7,-3,20]) => "evens win" #111-11 vs 10100, 3-2 vs 2
bits_war([7,-3,-2,6]) => "tie" #111-11 vs -1+110, 3-2 vs -1+2
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef bought an electronic board and pen. He wants to use them to record his clients' signatures.
The board is a grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$) of pixels. Initially, all pixels are white. A client uses the electronic pen to sign on the board; whenever the pen touches a pixel, this pixel becomes black. Note that a signature may be non-continuous (a client may lift the pen while signing).
Chef stores a typical signature of his current client as a matrix of characters $A_{i, j}$, where for each valid $i$ and $j$, $A_{i, j}$ is either '1' (if the cell in the $i$-th row and $j$-th column is black) or '0' (if this cell is white). The client just signed on the board; this signature is stored in the same form as a matrix $B_{i, j}$. Chef wants to know how close this signature is to this client's typical signature.
Two signatures are considered the same if it is possible to choose (possibly negative) integers $dr$ and $dc$ such that for each $1 \le i \le N$ and $1 \le j \le M$, $A_{i, j} = B_{i + dr, j + dc}$. Here, if $B_{i + dr, j + dc}$ does not correspond to a valid cell, it is considered to be '0'.
To compare the signatures, the colours of zero or more cells must be flipped in such a way that the signatures become the same (each flipped cell may be in any matrix). The error in the client's current signature is the minimum number of cells whose colours must be flipped. Find the error in the signature.

-----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 line of each test case contains two space-separated integers $N$ and $M$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains a string with length $M$ describing the $i$-th row of the matrix $A$.
- $N$ more lines follow. For each valid $i$, the $i$-th of these lines contains a string with length $M$ describing the $i$-th row of the matrix $B$.

-----Output-----
For each test case, print a single line containing one integer — the error in the current signature.

-----Constraints-----
- $1 \le T \le 50$
- $2 \le N, M \le 25$

-----Example Input-----
5
3 3
100
010
000
000
010
001
4 4
0000
0110
0000
0011
1100
0000
1100
0000
3 3
100
000
001
000
010
000
3 3
000
010
000
100
000
001
3 3
111
000
000
001
001
001

-----Example Output-----
0
2
1
0
2

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