vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
It is the easy version of the problem. The difference is that in this version, there are no nodes with already chosen colors.

Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?

You have a perfect binary tree of $2^k - 1$ nodes — a binary tree where all vertices $i$ from $1$ to $2^{k - 1} - 1$ have exactly two children: vertices $2i$ and $2i + 1$. Vertices from $2^{k - 1}$ to $2^k - 1$ don't have any children. You want to color its vertices with the $6$ Rubik's cube colors (White, Green, Red, Blue, Orange and Yellow).

Let's call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik's cube.

A picture of Rubik's cube and its 2D map.

More formally:

a white node can not be neighboring with white and yellow nodes;

a yellow node can not be neighboring with white and yellow nodes;

a green node can not be neighboring with green and blue nodes;

a blue node can not be neighboring with green and blue nodes;

a red node can not be neighboring with red and orange nodes;

an orange node can not be neighboring with red and orange nodes;

You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color.

The answer may be too large, so output the answer modulo $10^9+7$.


-----Input-----

The first and only line contains the integers $k$ ($1 \le k \le 60$) — the number of levels in the perfect binary tree you need to color.


-----Output-----

Print one integer — the number of the different colorings modulo $10^9+7$.


-----Examples-----

Input
3
Output
24576
Input
14
Output
934234


-----Note-----

In the picture below, you can see one of the correct colorings of the first example.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You've just recently been hired to calculate scores for a  Dart Board game!

Scoring specifications:

* 0 points - radius above 10
* 5 points - radius between 5 and 10 inclusive
* 10 points - radius less than 5

**If all radii are less than 5, award 100 BONUS POINTS!**

Write a function that accepts an array of radii (can be integers and/or floats), and returns a total score using the above specification.

An empty array should return 0.

## Examples:

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

Write a program that accepts sets of three numbers, and prints the second-maximum number among the three.

------ Input ------ 

First line contains the number of triples, N.
The next N lines which follow each have three space separated integers.

------ Output ------ 

For each of the N triples, output one new line which contains the second-maximum integer among the three.

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

$1 ≤ N ≤ 6$
$1 ≤ every integer ≤ 10000$
$The three integers in a single triplet are all distinct. That is, no two of them are equal.

----- Sample Input 1 ------ 
3
1 2 3
10 15 5
100 999 500
----- Sample Output 1 ------ 
2
10
500

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Now-a-days, Manish is becoming  famous for bank robbery in the country because of his cleverness, he never robs own his own.He has four workers A , B, C, and D , all working under him.All of the four take some amount for that. There are total N banks in the country and Manish wants to rob all the banks with minimum

amount spent on workers.Only one worker is allowed to rob the ith bank but following a condition that if one worker robs ith bank, then he can't rob (i+1) th bank.

So ,Manish wants you to calculate minimum amount that he has to spend on all workers to rob all N banks.

-----Input Format-----
First line consists number of test cases T.For each test case,

first line consists an integer N, number of banks in the country

and the next N line consists 4 integers amount taken by A,B,C and D respectively to rob ith bank.

-----Output format-----
For each test case ,output an integer, minimum amount paid  by Manish in separate line .

-----Constraint-----
- 1<=T<=1000
- 1<=N<=100000
- 1<=amount<=100000

-----Subtasks-----
Subtask-1 (10 points)
- 1<=T<=5
- 1<=N<=10
- 1<=amount<=10
Subtask-1 (30 points)
- 1<=T<=100
- 1<=N<=1000
- 1<=amount<=1000
Subtask-1 (60 points)
Original Constraints 
Sample Input
1
3
4 7 2 9
5 6 4 7
2 6 4 3

Sample Output
10

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
My colleague Elisabeth is lazy, both at work and when going to work. She never wants to do more than necessary, which also applies to her journey to work. Her goal is to use a minimum amount of energy, which she achieves by braking and accelerating as little as possible. This method applies to all wheel-based transport means she owns.

Elisabeth has earlier optimized her route by trial and error, but now wants your help to find the optimal path. She has provided a map with $N$ junctions and $R$ straight one-way roads between the junctions. If a road is dual way, it is represented as two one-way roads.

Fortunately, Elisabeth often works night shifts, so braking and acceleration are only needed when turning in a junction, as there is no other traffic on the roads. Her goal is to find a route where the maximum turning angle in the junctions is minimized, as this means maximized speed. However, the route can not be too long.

-----Input-----
The first line of input contains three space separated integers $J, R, D$ ($2 \leq J \leq 200, 1 \leq R \leq 40000, 1 \leq D \leq 1000000$). $J$ is the number of junctions, $R$ is the number of one-way roads which are connecting two junctions, and $D$ is the maximum distance, in meters, that Elisabeth wants to travel. The road network is such that there is no path, that Elisabeth may want to use, which has the length $L$ such that $D < L < D (1 + 10^{-6})$.

Then follow $J$ lines with two integers $x$ and $y$, ($-100000 \leq x, y \leq 100000$), the distinct coordinates in meters on a flat ground. Elisabeth lives at junction $1$ and her work is at junction $J$.

After that, $R$ lines follow with two integers $a$ and $b$. This should be interpreted as the one-way road between the one-indexed source and destination junctions $a$ and $b$ ($1\leq a, b\leq J$).

-----Output-----
Output one line with the maximum turning angle of the route that thas the maximum turning angle as low as possible. The turning angle must be output in degrees and have an absolute or relative error at most $10^{-6}$. If there is no such route that is short enough, output “Impossible” on a single line.

-----Examples-----
Sample Input 1:
5 6 500
-100 0
-100 100
0 200
100 100
100 0
1 2
1 3
2 3
3 4
3 5
4 5
Sample Output 1:
90.00000000

Sample Input 2:
5 6 450
-100 0
-100 100
0 200
100 100
100 0
1 2
1 3
2 3
3 4
3 5
4 5
Sample Output 2:
126.86989765

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The count-and-say sequence is the sequence of integers with the first five terms as following:

1.     1
2.     11
3.     21
4.     1211
5.     111221



1 is read off as "one 1" or 11.
11 is read off as "two 1s" or 21.
21 is read off as "one 2, then one 1" or 1211.



Given an integer n, generate the nth term of the count-and-say sequence.



Note: Each term of the sequence of integers will be represented as a string.


Example 1:

Input: 1
Output: "1"



Example 2:

Input: 4
Output: "1211"

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a graph with $3 \cdot n$ vertices and $m$ edges. You are to find a matching of $n$ edges, or an independent set of $n$ vertices.

A set of edges is called a matching if no two edges share an endpoint.

A set of vertices is called an independent set if no two vertices are connected with an edge.


-----Input-----

The first line contains a single integer $T \ge 1$ — the number of graphs you need to process. The description of $T$ graphs follows.

The first line of description of a single graph contains two integers $n$ and $m$, where $3 \cdot n$ is the number of vertices, and $m$ is the number of edges in the graph ($1 \leq n \leq 10^{5}$, $0 \leq m \leq 5 \cdot 10^{5}$).

Each of the next $m$ lines contains two integers $v_i$ and $u_i$ ($1 \leq v_i, u_i \leq 3 \cdot n$), meaning that there is an edge between vertices $v_i$ and $u_i$.

It is guaranteed that there are no self-loops and no multiple edges in the graph.

It is guaranteed that the sum of all $n$ over all graphs in a single test does not exceed $10^{5}$, and the sum of all $m$ over all graphs in a single test does not exceed $5 \cdot 10^{5}$.


-----Output-----

Print your answer for each of the $T$ graphs. Output your answer for a single graph in the following format.

If you found a matching of size $n$, on the first line print "Matching" (without quotes), and on the second line print $n$ integers — the indices of the edges in the matching. The edges are numbered from $1$ to $m$ in the input order.

If you found an independent set of size $n$, on the first line print "IndSet" (without quotes), and on the second line print $n$ integers — the indices of the vertices in the independent set.

If there is no matching and no independent set of the specified size, print "Impossible" (without quotes).

You can print edges and vertices in any order.

If there are several solutions, print any. In particular, if there are both a matching of size $n$, and an independent set of size $n$, then you should print exactly one of such matchings or exactly one of such independent sets.


-----Example-----
Input
4
1 2
1 3
1 2
1 2
1 3
1 2
2 5
1 2
3 1
1 4
5 1
1 6
2 15
1 2
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6
4 5
4 6
5 6

Output
Matching
2
IndSet
1
IndSet
2 4
Matching
1 15



-----Note-----

The first two graphs are same, and there are both a matching of size 1 and an independent set of size 1. Any of these matchings and independent sets is a correct answer.

The third graph does not have a matching of size 2, however, there is an independent set of size 2. Moreover, there is an independent set of size 5: 2 3 4 5 6. However such answer is not correct, because you are asked to find an independent set (or matching) of size exactly $n$.

The fourth graph does not have an independent set of size 2, but there is a matching of size 2.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
“Peter Pan frames” are a way of decorating text in which every character is framed by a diamond- shaped frame, with frames of neigbhouring characters interleaving. A Peter Pan frame for one letter looks like this (‘X’ is the letter we are framing):

..#..
.#.#.
#.X.#
.#.#.
..#..

However, such a framing would be somewhat dull so we’ll frame every third letter using a “Wendy frame”. A Wendy frame looks like this:

..*..
.*.*.
*.X.*
.*.*.
..*..

When a Wendy frame interleaves with a Peter Pan frame, the Wendy frame (being much nicer) is put on top. For an example of the interleaving check the sample cases.

-----Input-----
The first and only line of input will contain at least $1$ and at most $15$ capital letters of the English alphabet.

-----Output-----
Output the word written using Peter Pan and Wendy frames on $5$ lines.

-----Examples-----
Sample Input 1:
A
Sample Output 1:
..#..
.#.#.
#.A.#
.#.#.
..#..

Sample Input 2:
DOG
Sample Output 2:
..#...#...*..
.#.#.#.#.*.*.
#.D.#.O.*.G.*
.#.#.#.#.*.*.
..#...#...*..

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Luka found a very unusual game board in his attic. Surprisingly, it consists of $R \cdot C$ square cells. The rows are numbered $0$ to $R-1$ top to bottom and the columns $0$ to $C-1$ left to right.

What makes the board unusual is the way in which the cells are coloured. Each cell is either grey or white:
 - white, if the row and column numbers of the cell, when represented in binary, have at least one digit 1 in the same position. For example, the cell $(4, 5)$ would be white.
 - grey, otherwise. For example, the cell $(2, 5)$ would be grey.

The following image shows a board of size 10·10. 

Luka’s hedgehog likes walking on this unusual board and does it in an unusual way. The hedgehog starts his walk in the cell $(0, 0)$ and continues in the zig-zag pattern as in the second image above. While the hedgehog is walking, Luka counts how many grey squares it visited.

After visiting $K$ squares, the hedgehog gets tired and falls asleep. Luka then goes to bed too, happy that he was able count the grey squares.

Knowing the dimensions of the board and the number $K$ beforehand, however, it is possible to write a program that calculates the result faster. This is your task.

-----Input-----
The first line contains two integers $R$ ($1 \le R \le 1000000$) and $C$ ($1 \le C \le 1000000$), the dimensions of the board.

The second line contains the integer $K$ ($1 \le K \le R \cdot C$), the total number of squares the hedgehog visits.

Note that this number may not fit in a 32-bit integer.

-----Output-----
Output the number of grey cells the hedgehog visits.

-----Examples-----
Sample Input 1:
10 10
6
Sample Output 1:
5

Sample Input 2:
3 5
11
Sample Output 2:
8

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Luba is surfing the Internet. She currently has *n* opened tabs in her browser, indexed from 1 to *n* from left to right. The mouse cursor is currently located at the *pos*-th tab. Luba needs to use the tabs with indices from *l* to *r* (inclusive) for her studies, and she wants to close all the tabs that don't belong to this segment as fast as possible.

Each second Luba can either try moving the cursor to the left or to the right (if the cursor is currently at the tab *i*, then she can move it to the tab *max*(*i*<=-<=1,<=*a*) or to the tab *min*(*i*<=+<=1,<=*b*)) or try closing all the tabs to the left or to the right of the cursor (if the cursor is currently at the tab *i*, she can close all the tabs with indices from segment [*a*,<=*i*<=-<=1] or from segment [*i*<=+<=1,<=*b*]). In the aforementioned expressions *a* and *b* denote the minimum and maximum index of an unclosed tab, respectively. For example, if there were 7 tabs initially and tabs 1, 2 and 7 are closed, then *a*<==<=3, *b*<==<=6.

What is the minimum number of seconds Luba has to spend in order to leave only the tabs with initial indices from *l* to *r* inclusive opened?

Input Specification:
The only line of input contains four integer numbers *n*, *pos*, *l*, *r* (1<=≤<=*n*<=≤<=100, 1<=≤<=*pos*<=≤<=*n*, 1<=≤<=*l*<=≤<=*r*<=≤<=*n*) — the number of the tabs, the cursor position and the segment which Luba needs to leave opened.

Output Specification:
Print one integer equal to the minimum number of seconds required to close all the tabs outside the segment [*l*,<=*r*].

Demo Input:
['6 3 2 4\n', '6 3 1 3\n', '5 2 1 5\n']

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

Note:
In the first test Luba can do the following operations: shift the mouse cursor to the tab 2, close all the tabs to the left of it, shift the mouse cursor to the tab 3, then to the tab 4, and then close all the tabs to the right of it.

In the second test she only needs to close all the tabs to the right of the current position of the cursor.

In the third test Luba doesn't need to do anything.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Harsh, like usual, started studying 6 months before for his end semester examinations. He was going to complete his 8th revision of the whole syllabus, when suddenly Pranav showed up in his room with the last year's question paper for their algorithms course. This paper contains a problem which both of them couldn't solve. Frustrated he asked you for help. But you declined him and instead try to do this problem instead:
You are given an array $A_1,A_2,\dots,A_N$, a positive integer $K$, and a function $F(x)=\displaystyle\sum_{i=1}^{N}{\left|{\left({x-A_i}\right)^K}\right|}$. Find the smallest integer $x$ such that $F(x)$ is minimum.Input
- The first line contains two space-seperated integers , $N$ and $K$
- The second line contains $N$ space-seperated integers $A_1,A_2,\dots,A_N$. Output
In the first and only line print the smallest integer $x$ such that $F(x)$ is minimumConstraints
- $1 \leq N \leq {10}^{5}$
- $1 \leq K \leq {3}$
- $1 \leq A_i \leq {5}\times{10}^{4}$ for each valid $i$Sample Input 1
3 1
6 1 7
Sample Output 1
6
Explanation 1
$F(6) = \displaystyle\sum_{i=1}^{N}{\left|{\left({6-A_i}\right)^K}\right|} \\ F(6) = \left|{\left({6-6}\right)^1}\right| + \left|{\left({6-1}\right)^1}\right| + \left|{\left({6-7}\right)^1}\right| \\ F(6)  = 0 + 5+ 1 \\ F(6)  = 6 $
Here $6$ is the minumum value for $F(x)$ for any integer value of $x$.Sample Input 2
3 2
6 1 7
Sample Output 2
5
Explanation 2
$F(5) = \displaystyle\sum_{i=1}^{N}{\left|{\left({5-A_i}\right)^K}\right|} \\F(5) = \left|{\left({5-6}\right)^2}\right| + \left|{\left({5-1}\right)^2}\right| + \left|{\left({5-7}\right)^2}\right| \\F(5) = 1 + 16 + 4 \\F(5) = 21$ 
Here $21$ is the minumum value for $F(x)$ for any integer value of $x$.Sample Input 3
3 3
6 1 7
Sample Output 3
4
Explanation 3
$F(4) = \displaystyle\sum_{i=1}^{N}{\left|{\left({4-A_i}\right)^K}\right|} \\F(4) = \left|{\left({4-6}\right)^3}\right| + \left|{\left({4-1}\right)^3}\right| + \left|{\left({4-7}\right)^3}\right| \\F(4) = 8 + 27 + 27 \\F(4) = 62 $
Here $62$ is the minumum value for $F(x)$ for any integer value of $x$.

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

Time Limit: 2 seconds

Memory Limit: 64 megabytes

Problem Description:
After a terrifying forest fire in Berland a forest rebirth program was carried out. Due to it *N* rows with *M* trees each were planted and the rows were so neat that one could map it on a system of coordinates so that the *j*-th tree in the *i*-th row would have the coordinates of (*i*,<=*j*). However a terrible thing happened and the young forest caught fire. Now we must find the coordinates of the tree that will catch fire last to plan evacuation.

The burning began in *K* points simultaneously, which means that initially *K* trees started to burn. Every minute the fire gets from the burning trees to the ones that aren’t burning and that the distance from them to the nearest burning tree equals to 1.

Find the tree that will be the last to start burning. If there are several such trees, output any.

Input Specification:
The first input line contains two integers *N*,<=*M* (1<=≤<=*N*,<=*M*<=≤<=2000) — the size of the forest. The trees were planted in all points of the (*x*,<=*y*) (1<=≤<=*x*<=≤<=*N*,<=1<=≤<=*y*<=≤<=*M*) type, *x* and *y* are integers.

The second line contains an integer *K* (1<=≤<=*K*<=≤<=10) — amount of trees, burning in the beginning. 

The third line contains *K* pairs of integers: *x*1,<=*y*1,<=*x*2,<=*y*2,<=...,<=*x**k*,<=*y**k* (1<=≤<=*x**i*<=≤<=*N*,<=1<=≤<=*y**i*<=≤<=*M*) — coordinates of the points from which the fire started. It is guaranteed that no two points coincide.

Output Specification:
Output a line with two space-separated integers *x* and *y* — coordinates of the tree that will be the last one to start burning. If there are several such trees, output any.

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

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

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Andrew and Jerry are playing a game with Harry as the scorekeeper. The game consists of three rounds. In each round, Andrew and Jerry draw randomly without replacement from a jar containing n balls, each labeled with a distinct positive integer. Without looking, they hand their balls to Harry, who awards the point to the player with the larger number and returns the balls to the jar. The winner of the game is the one who wins at least two of the three rounds.

Andrew wins rounds 1 and 2 while Jerry wins round 3, so Andrew wins the game. However, Jerry is unhappy with this system, claiming that he will often lose the match despite having the higher overall total. What is the probability that the sum of the three balls Jerry drew is strictly higher than the sum of the three balls Andrew drew?


-----Input-----

The first line of input contains a single integer n (2 ≤ n ≤ 2000) — the number of balls in the jar.

The second line contains n integers a_{i} (1 ≤ a_{i} ≤ 5000) — the number written on the ith ball. It is guaranteed that no two balls have the same number.


-----Output-----

Print a single real value — the probability that Jerry has a higher total, given that Andrew wins the first two rounds and Jerry wins the third. Your answer will be considered correct if its absolute or relative error does not exceed 10^{ - 6}. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if $\frac{|a - b|}{\operatorname{max}(1, b)} \leq 10^{-6}$.


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

Output
0.0000000000

Input
3
1 2 10

Output
0.0740740741



-----Note-----

In the first case, there are only two balls. In the first two rounds, Andrew must have drawn the 2 and Jerry must have drawn the 1, and vice versa in the final round. Thus, Andrew's sum is 5 and Jerry's sum is 4, so Jerry never has a higher total.

In the second case, each game could've had three outcomes — 10 - 2, 10 - 1, or 2 - 1. Jerry has a higher total if and only if Andrew won 2 - 1 in both of the first two rounds, and Jerry drew the 10 in the last round. This has probability $\frac{1}{3} \cdot \frac{1}{3} \cdot \frac{2}{3} = \frac{2}{27}$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Create a function that takes a string and returns that
string with the first half lowercased and the last half uppercased.

eg: foobar == fooBAR

If it is an odd number then 'round' it up to find which letters to uppercase. See example below.

    sillycase("brian")  
    //         --^-- midpoint  
    //         bri    first half (lower-cased)  
    //            AN second half (upper-cased)

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