vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Devu has an array A consisting of N positive integers. He would like to perform following operation on array.

- Pick some two elements a, b in the array (a could be same as b, but their corresponding indices in the array should not be same).
Remove both the elements a and b and instead add a number x such that x lies between min(a, b) and max(a, b), both inclusive, (i.e. min(a, b) ≤ x ≤ max(a, b)).

Now, as you know after applying the above operation N - 1 times, Devu will end up with a single number in the array. He is wondering whether it is possible to do the operations in such a way that he ends up a number t. 

He asks your help in answering Q such queries, each of them will contain an integer t and you have to tell whether it is possible to end up t. 

-----Input-----
There is only one test case per test file.
First line of the input contains two space separated integers N, Q denoting number of elements in A and number of queries for which Devu asks your help, respectively
Second line contains N space separated integers denoting the content of array A.

Each of the next Q lines, will contain a single integer t corresponding to the query.

-----Output-----
Output Q lines, each containing "Yes" or "No" (both without quotes) corresponding to the answer of corresponding query.

-----Constraints-----
- 1 ≤ N, Q ≤ 105
- 0 ≤ t ≤ 109

-----Subtasks-----
Subtask #1 : 30 points
- 1 ≤ Ai ≤ 2

Subtask #2 : 70 points
- 1 ≤ Ai ≤ 109

-----Example-----
Input 1:
1 2
1
1
2

Output:
Yes
No

Input 2:
2 4
1 3
1
2
3
4

Output:
Yes
Yes
Yes
No

-----Explanation-----
In the first example, Devu can't apply any operation. So the final element in the array will be 1 itself. 

In the second example,
Devu can replace 1 and 3 with any of the numbers among 1, 2, 3. Hence final element of the array could be 1, 2 or 3.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In this problem you operate on two arrays of $N$ integers. We will call them the ${0}^{t h}$ and the $1^{st}$ respectively. 

Your goal is just to maintain them under the modification operations, such as:   

1 $\mbox{id}$ $\boldsymbol{l}$ $\textbf{r}$: Reverse the subarray of the $\text{id}^{\text{th}}$ array, starting at the ${l}^{\mbox{th}}$ number, ending at the $r^{\mbox{th}}$ number, inclusively;  
2 $\mbox{id}$ $\boldsymbol{l}_{1}$ $r_1$ $l_2$ $r_2$: Swap two consecutive fragments of the $\text{id}^{\text{th}}$ array, the first is from the $l_1^{th}$ number to the $r_1^{th}$, the second is from the $l_{2}^{t h}$ number to the $r_2^{th}$;  
3 $\boldsymbol{l}$ $\textbf{r}$: Swap the piece that starts at the ${l}^{\mbox{th}}$ number and end at the $r^{\mbox{th}}$ one between the ${0}^{t h}$ and the $1^{st}$ array;  
4 $\boldsymbol{l}$ $\textbf{r}$: We consider only the piece from the ${l}^{\mbox{th}}$ number to the $r^{\mbox{th}}$ one. The numbers in the ${0}^{t h}$ array are $\mbox{X}$-coordinates of some set of points and the numbers in the $1^{st}$ array are $\mathbf{Y}$-coordinates of them. For the obtained set of points we would like to place such a circle on a plane that would contain all the points in it and would have the minimal radius. Find this minimal radius.  

Input Format 

The first line of input contains two space separated integers $N$ and $\mbox{M}$ denoting the number of integers in arrays and the number of queries respectively. 

The second line contains $N$ space separated integers: the initial elements of the ${0}^{t h}$ array. 

The third line contains $N$ space separated integers: the initial elements of the $1^{th}$ array. 

Then there are $\mbox{M}$ lines containing queries in the format listed above.  

Output Format 

For each type-4 query output the sought minimal radius with exactly two symbols after the decimal point precision.  

Constraints 

$1\leq N,M\leq10^5$ 

All the numbers in arrays are non-negative and don't exceed $10^{6}$. 

The sum of $R-L$ over the type-4 queries won't exceed $10^{6}$. 

In the query of the type 2, $1\leq l_1\leq r_1<l_2\leq r_2\leq N$. 

In the queries of the types 1, 3, 4, $1\leq l\leq r\leq N$; $0\leq id<2$.

Sample Input

10 10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
3 2 6
1 0 9 9
4 6 9
2 0 2 7 9 9
1 0 3 6
2 1 2 3 4 5
1 1 7 10
2 1 8 8 9 10
4 6 9
2 0 2 2 4 6

Example Output

2.12
2.50

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given an array A, consisting of N distinct integers.  
Calculate number of pairs (i,j) (1 ≤ i < j ≤ N), such that 2 \cdot (A_{i} \oplus A_{j}) = A_{i} + A_{j}, where \oplus denotes [bitwise XOR].

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

- The first line contains two integers N - the size of the array. 
- The second line contains N space-separated integers A_{1}, \ldots, A_{N} - the elements of the array A.

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

For each test case, output the number of pairs satisfying constraints.

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

$2 ≤ N ≤ 10^{6}$
$1 ≤ A_{i} ≤ 2^{60}-1$

------ subtasks ------ 

Subtask $1$ (20 points): $2 ≤ N ≤ 2000$
Subtask $2$ (40 points): $1 ≤ A_{i} ≤ 2^{20}-1$
Subtask $3$ (40 points): Original constraints.

----- Sample Input 1 ------ 
4
1 2 3 6

----- Sample Output 1 ------ 
2

----- explanation 1 ------ 
There are $2$ pairs $(i,j)$ satisfying all the conditions.
- $(i,j)= (1, 3)$. Thus, $2\cdot (A_{1}\oplus A_{3}) = 2\cdot (1\oplus 3) = 2\cdot 2 = 4$. Also, $A_{1}+A_{3} = 1+3 = 4$.
- $(i,j)= (2, 4)$. Thus, $2\cdot (A_{2}\oplus A_{4}) = 2\cdot (2\oplus 6) = 2\cdot 4 = 8$. Also, $A_{2}+A_{4} = 2+6 = 8$.

----- Sample Input 2 ------ 
5
4 3 9 7 1
----- Sample Output 2 ------ 
1
----- explanation 2 ------ 
There is only one pair $(i,j)$ satisfying all the conditions:
- $(i,j) = (2, 5)$. Thus, $2\cdot (A_{2}\oplus A_{5}) = 2\cdot (3\oplus 1) = 2\cdot 2 = 4$. Also, $A_{2}+A_{5} = 3+1 = 4$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Monocarp plays a computer game. There are $n$ different sets of armor and $m$ different weapons in this game. If a character equips the $i$-th set of armor and wields the $j$-th weapon, their power is usually equal to $i + j$; but some combinations of armor and weapons synergize well. Formally, there is a list of $q$ ordered pairs, and if the pair $(i, j)$ belongs to this list, the power of the character equipped with the $i$-th set of armor and wielding the $j$-th weapon is not $i + j$, but $i + j + 1$.

Initially, Monocarp's character has got only the $1$-st armor set and the $1$-st weapon. Monocarp can obtain a new weapon or a new set of armor in one hour. If he wants to obtain the $k$-th armor set or the $k$-th weapon, he must possess a combination of an armor set and a weapon that gets his power to $k$ or greater. Of course, after Monocarp obtains a weapon or an armor set, he can use it to obtain new armor sets or weapons, but he can go with any of the older armor sets and/or weapons as well.

Monocarp wants to obtain the $n$-th armor set and the $m$-th weapon. What is the minimum number of hours he has to spend on it?


-----Input-----

The first line contains two integers $n$ and $m$ ($2 \le n, m \le 2 \cdot 10^5$) — the number of armor sets and the number of weapons, respectively.

The second line contains one integer $q$ ($0 \le q \le \min(2 \cdot 10^5, nm)$) — the number of combinations that synergize well.

Then $q$ lines follow, the $i$-th line contains two integers $a_i$ and $b_i$ ($1 \le a_i \le n$; $1 \le b_i \le m$) meaning that the $a_i$-th armor set synergizes well with the $b_i$-th weapon. All pairs $(a_i, b_i)$ are distinct.


-----Output-----

Print one integer — the minimum number of hours Monocarp has to spend to obtain both the $n$-th armor set and the $m$-th weapon.


-----Examples-----

Input
3 4
0
Output
3
Input
3 4
2
1 1
1 3
Output
2


-----Note-----

In the first example, Monocarp can obtain the strongest armor set and the strongest weapon as follows:

Obtain the $2$-nd weapon using the $1$-st armor set and the $1$-st weapon;

Obtain the $3$-rd armor set using the $1$-st armor set and the $2$-nd weapon;

Obtain the $4$-th weapon using the $3$-rd armor set and the $2$-nd weapon.

In the second example, Monocarp can obtain the strongest armor set and the strongest weapon as follows:

Obtain the $3$-rd armor set using the $1$-st armor set and the $1$-st weapon (they synergize well, so Monocarp's power is not $2$ but $3$);

Obtain the $4$-th weapon using the $3$-rd armor set and the $1$-st weapon.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The organizers of a programming contest have decided to present t-shirts to participants. There are six different t-shirts sizes in this problem: S, M, L, XL, XXL, XXXL (sizes are listed in increasing order). The t-shirts are already prepared. For each size from S to XXXL you are given the number of t-shirts of this size.

During the registration, the organizers asked each of the n participants about the t-shirt size he wants. If a participant hesitated between two sizes, he could specify two neighboring sizes — this means that any of these two sizes suits him.

Write a program that will determine whether it is possible to present a t-shirt to each participant of the competition, or not. Of course, each participant should get a t-shirt of proper size:   the size he wanted, if he specified one size;  any of the two neibouring sizes, if he specified two sizes. 

If it is possible, the program should find any valid distribution of the t-shirts.


-----Input-----

The first line of the input contains six non-negative integers — the number of t-shirts of each size. The numbers are given for the sizes S, M, L, XL, XXL, XXXL, respectively. The total number of t-shirts doesn't exceed 100 000.

The second line contains positive integer n (1 ≤ n ≤ 100 000) — the number of participants.

The following n lines contain the sizes specified by the participants, one line per participant. The i-th line contains information provided by the i-th participant: single size or two sizes separated by comma (without any spaces). If there are two sizes, the sizes are written in increasing order. It is guaranteed that two sizes separated by comma are neighboring.


-----Output-----

If it is not possible to present a t-shirt to each participant, print «NO» (without quotes).

Otherwise, print n + 1 lines. In the first line print «YES» (without quotes). In the following n lines print the t-shirt sizes the orginizers should give to participants, one per line. The order of the participants should be the same as in the input.

If there are multiple solutions, print any of them.


-----Examples-----
Input
0 1 0 1 1 0
3
XL
S,M
XL,XXL

Output
YES
XL
M
XXL

Input
1 1 2 0 1 1
5
S
M
S,M
XXL,XXXL
XL,XXL

Output
NO

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

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Problem Description:
Recently, Vladimir got bad mark in algebra again. To avoid such unpleasant events in future he decided to train his arithmetic skills. He wrote four integer numbers *a*, *b*, *c*, *d* on the blackboard. During each of the next three minutes he took two numbers from the blackboard (not necessarily adjacent) and replaced them with their sum or their product. In the end he got one number. Unfortunately, due to the awful memory he forgot that number, but he remembers four original numbers, sequence of the operations and his surprise because of the very small result. Help Vladimir remember the forgotten number: find the smallest number that can be obtained from the original numbers by the given sequence of operations.

Input Specification:
First line contains four integers separated by space: 0<=≤<=*a*,<=*b*,<=*c*,<=*d*<=≤<=1000 — the original numbers. Second line contains three signs ('+' or '*' each) separated by space — the sequence of the operations in the order of performing. ('+' stands for addition, '*' — multiplication)

Output Specification:
Output one integer number — the minimal result which can be obtained.

Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).

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

Demo Output:
['3\n', '8\n', '9\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Cowboy Beblop is a funny little boy who likes sitting at his computer. He somehow obtained two elastic hoops in the shape of 2D polygons, which are not necessarily convex. Since there's no gravity on his spaceship, the hoops are standing still in the air. Since the hoops are very elastic, Cowboy Beblop can stretch, rotate, translate or shorten their edges as much as he wants.

For both hoops, you are given the number of their vertices, as well as the position of each vertex, defined by the X , Y and Z coordinates. The vertices are given in the order they're connected: the 1st vertex is connected to the 2nd, which is connected to the 3rd, etc., and the last vertex is connected to the first one. Two hoops are connected if it's impossible to pull them to infinity in different directions by manipulating their edges, without having their edges or vertices intersect at any point – just like when two links of a chain are connected. The polygons' edges do not intersect or overlap. 

To make things easier, we say that two polygons are well-connected, if the edges of one polygon cross the area of the other polygon in two different directions (from the upper and lower sides of the plane defined by that polygon) a different number of times.

Cowboy Beblop is fascinated with the hoops he has obtained and he would like to know whether they are well-connected or not. Since he’s busy playing with his dog, Zwei, he’d like you to figure it out for him. He promised you some sweets if you help him! 


-----Input-----

The first line of input contains an integer n (3 ≤ n ≤ 100 000), which denotes the number of edges of the first polygon. The next N lines each contain the integers x, y and z ( - 1 000 000 ≤ x, y, z ≤ 1 000 000) — coordinates of the vertices, in the manner mentioned above. The next line contains an integer m (3 ≤ m ≤ 100 000) , denoting the number of edges of the second polygon, followed by m lines containing the coordinates of the second polygon’s vertices.

It is guaranteed that both polygons are simple (no self-intersections), and in general that the obtained polygonal lines do not intersect each other. Also, you can assume that no 3 consecutive points of a polygon lie on the same line.


-----Output-----

Your output should contain only one line, with the words "YES" or "NO", depending on whether the two given polygons are well-connected. 


-----Example-----
Input
4
0 0 0
2 0 0
2 2 0
0 2 0
4
1 1 -1
1 1 1
1 3 1
1 3 -1

Output
YES



-----Note-----

On the picture below, the two polygons are well-connected, as the edges of the vertical polygon cross the area of the horizontal one exactly once in one direction (for example, from above to below), and zero times in the other (in this case, from below to above). Note that the polygons do not have to be parallel to any of the xy-,xz-,yz- planes in general. [Image]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
When simulating x-ray imaging different energy photons interact differently and therefore needs to be simulated separetly. Often one has an x-ray spectrum with thousands of bins, so that it is impractical to do a simulation for each bin. We want to do simulations only for a few energies, but want to choose these energies in an optimal way. Energies for the simulation should be chosen to minimize the sum over all photons of the square of the distance between the energy of that photon and its closest simulation energy.

-----Input-----
The input will start with two integers $1\leq n\leq 200$ and $1\leq m \leq n$ denoting the number of energies in the input spectrum and the number of simulation energies, respectively. This is followed by a line of $n$ integers $0\leq k_ i\leq 10^6$, where $k_ i$ ($1\leq i \leq n$) is the number of photons with energy $i$ in the x-ray spectrum. Simulation energies $E_ j$ ($1\leq j \leq m$) should be selected so as to minimize\[ \sum _{i=1}^n k_ i\min _ j\left((i-E_ j)^2\right). \]

-----Output-----
Output one number, the minimum value of the sum above, with a relative or absolute error less than $10^{-4}$.

-----Example-----
In sample input 1 we are have $n=3$, $m=2$, $k_1=3$, $k_2=1$, and $k_3=1$. Optimal simulation energies will be $E_1=1$ and $E_2=2.5$, since this will remove the contribution from bin 1 and minimize the contribution from bins 2 and 3. The sum will be $k_1(1-E_1)^2+k_2(2-E_2)^2+k_3(3-E_2)^2=3\cdot 0^2+1\cdot 0.5^2+1\cdot 0.5^2=0.5$.

-----Examples-----
Sample Input:
3 2
3 1 1
Sample Output:
0.5

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are n cities in Berland, each of them has a unique id — an integer from 1 to n, the capital is the one with id 1. Now there is a serious problem in Berland with roads — there are no roads.

That is why there was a decision to build n - 1 roads so that there will be exactly one simple path between each pair of cities.

In the construction plan t integers a_1, a_2, ..., a_{t} were stated, where t equals to the distance from the capital to the most distant city, concerning new roads. a_{i} equals the number of cities which should be at the distance i from the capital. The distance between two cities is the number of roads one has to pass on the way from one city to another. 

Also, it was decided that among all the cities except the capital there should be exactly k cities with exactly one road going from each of them. Such cities are dead-ends and can't be economically attractive. In calculation of these cities the capital is not taken into consideration regardless of the number of roads from it. 

Your task is to offer a plan of road's construction which satisfies all the described conditions or to inform that it is impossible.


-----Input-----

The first line contains three positive numbers n, t and k (2 ≤ n ≤ 2·10^5, 1 ≤ t, k < n) — the distance to the most distant city from the capital and the number of cities which should be dead-ends (the capital in this number is not taken into consideration). 

The second line contains a sequence of t integers a_1, a_2, ..., a_{t} (1 ≤ a_{i} < n), the i-th number is the number of cities which should be at the distance i from the capital. It is guaranteed that the sum of all the values a_{i} equals n - 1.


-----Output-----

If it is impossible to built roads which satisfy all conditions, print -1.

Otherwise, in the first line print one integer n — the number of cities in Berland. In the each of the next n - 1 line print two integers — the ids of cities that are connected by a road. Each road should be printed exactly once. You can print the roads and the cities connected by a road in any order.

If there are multiple answers, print any of them. Remember that the capital has id 1.


-----Examples-----
Input
7 3 3
2 3 1

Output
7
1 3
2 1
2 6
2 4
7 4
3 5

Input
14 5 6
4 4 2 2 1

Output
14
3 1
1 4
11 6
1 2
10 13
6 10
10 12
14 12
8 4
5 1
3 7
2 6
5 9

Input
3 1 1
2

Output
-1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Iahub got bored, so he invented a game to be played on paper.
 He writes n integers a1, a2, ..., an. Each of those integers can be either 0 or 1. He's allowed to do exactly one move: he chooses two indices i and j (1 ≤ i ≤ j ≤ n) and flips all values ak for which their positions are in range [i, j] (that is i ≤ k ≤ j). Flip the value of x means to apply operation x = 1 - x.
 The goal of the game is that after exactly one move to obtain the maximum number of ones. Write a program to solve the little game of Iahub.
```
@param {Array} line of the input there are n integers: a1, a2, ..., an. 1 ≤ n ≤ 100. It is guaranteed that each of those n values is either 0 or 1
@return {Integer} the maximal number of 1s that can be obtained after exactly one move
```
Examples :
```
[1, 0, 0, 1, 0, 0]  =>  5
[1, 0, 0, 1]  =>  4

```
Note:
 In the first case, flip the segment from 2 to 6 (i = 2, j = 6). That flip changes the sequence, it becomes: [1 1 1 0 1 1]. So, it contains four ones. There is no way to make the whole sequence equal to [1 1 1 1 1 1].
 In the second case, flipping only the second and the third element (i = 2, j = 3) will turn all numbers into 1.

(c)ll931110 & fchirica

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Today the Intergalactic Council of Pebble Coins (ICPC) conducted an intergalactic auction of the Neutronium Chaos Pebble Coin (NCPC). This coin, which was forged in the Ancient Coin Machine (ACM), is rumored to be the key to ruling the universe. 

Due to the extremely competitive nature of the auction, as well as the odd mechanics of the intergalactic currency used (far too advanced for mere mortals to understand), the auction was conducted with the following rules:
 - only one participant was allowed to make a bid at a time,
 - each participant was only allowed to make one bid, and
 - a participant making a bid had to bid at least twice the amount of the highest bid at the time.

The first participant making a bid was allowed to make a bid of any positive amount.

After the auction there were a lot of sore losers – understandably, having just lost their chance at world domination. To make the losers feel a little better and prevent possible rioting, the ICPC has decided to hold a lottery for the participants. The winners of the lottery are determined as follows. The ICPC picks a random number $s$. A group of participants is called winning if the sum of their bets from the auction is equal to $s$. A participant wins the lottery and receives a prize – a shiny Pebble Coin – if they belong to any winning group of participants.

Given the names of the participants, the bets that they made, and the random number $s$ chosen by the ICPC, help them determine which participants won the lottery.

-----Input-----
The first line of input contains two integers $n$ and $s$, where $1 \le n \le 1000$ is the number of participants, and $1 \le s < 10^{1000}$ is the random number chosen by the ICPC.

Then follow $n$ lines describing the participants. Each line contains a string $t$ and an integer $b$, where $t$ is the name of a participant, and $1 \le b < 10^{1000}$ is the amount of his bet. The name of each participant is unique and consists of between $1$ and $20$ letters from the English alphabet.

-----Output-----
Output an integer $k$ denoting the number of participants that won the lottery. Then output $k$ lines containing the names of the participants that won the lottery, one per line, in any order.

-----Examples-----
Sample Input:
5 63
Vader 3
Voldemort 7
BorgQueen 20
Terminator 40
Megatron 101
Sample Output:
3
BorgQueen
Terminator
Vader

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