vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
1000000000000001 dogs suddenly appeared under the roof of Roger's house, all of which he decided to keep. The dogs had been numbered 1 through 1000000000000001, but he gave them new names, as follows:
 - the dogs numbered 1,2,\cdots,26 were respectively given the names a, b, ..., z;
 - the dogs numbered 27,28,29,\cdots,701,702  were respectively given the names aa, ab, ac, ..., zy, zz;
 - the dogs numbered 703,704,705,\cdots,18277,18278  were respectively given the names aaa, aab, aac, ..., zzy, zzz;
 - the dogs numbered 18279,18280,18281,\cdots,475253,475254  were respectively given the names aaaa, aaab, aaac, ..., zzzy, zzzz;
 - the dogs numbered 475255,475256,\cdots  were respectively given the names aaaaa, aaaab, ...;
 - and so on.
To sum it up, the dogs numbered 1, 2, \cdots were respectively given the following names:
a, b, ..., z, aa, ab, ..., az, ba, bb, ..., bz, ..., za, zb, ..., zz, aaa, aab, ..., aaz, aba, abb, ..., abz, ..., zzz, aaaa, ...
Now, Roger asks you:
"What is the name for the dog numbered N?"

-----Constraints-----
 - N is an integer.
 -  1 \leq N \leq 1000000000000001

-----Input-----
Input is given from Standard Input in the following format:
N

-----Output-----
Print the answer to Roger's question as a string consisting of lowercase English letters.

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

-----Sample Output-----
b


Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
"How did you get the deal,how did he agree?"
"Its's simple Tom I just made him an offer he couldn't refuse" 
Ayush is the owner of a big construction company and a close aide of Don Vito The Godfather, recently with the help of the Godfather his company has been assigned a big contract according to the contract he has to make n number of V shaped infinitely long roads(two V shaped roads may or  not intersect) on an infinitely large field.
Now the company assigning the contract needs to know the maximum number of regions they can get after making n such roads.
Help Ayush by answering the above question.

-----Input:-----
- The first line consists of the number of test cases $T$. 
- Next T lines consists of the number of V shaped roads $n$.

-----Output:-----
For each test case print a single line consisting of the maximum regions obtained.

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq n \leq 10^9$

-----Sample Input:-----
2
1
2

-----Sample Output:-----
2
7

-----EXPLANATION:-----
Test case 1:       For one V shaped road there will be 2 regions

Test case 2:       For n=2 the following figure depicts the case of maximum regions:

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has invested his money at an interest rate of X percent per annum while the current inflation rate is Y percent per annum. 

An investment is called *good* if and only if the interest rate of the investment is at least twice of the inflation rate.  
Determine whether the investment made by Chef is *good* or not.

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

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of two integers X and Y, the interest rate and the current inflation rate respectively.

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

For each test case, output YES if the investment is good, NO otherwise.

You can output any letter in any case. For example YES, yes, yES are all considered same.

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

$1 ≤ T ≤ 400$
$1 ≤ X, Y ≤ 20$

----- Sample Input 1 ------ 
5
7 4
6 3
2 4
10 10
20 1

----- Sample Output 1 ------ 
NO
YES
NO
NO
YES

----- explanation 1 ------ 
Test case $1$: The interest rate is $7$ and the current inflation rate is $4$. Since the interest rate is less than twice of current inflation rate, the investment is not good.

Test case $2$: The interest rate is $6$ and the current inflation rate is $3$. Since the interest rate is equal to twice of current inflation rate, the investment is good.

Test case $3$: The interest rate is $2$ and the current inflation rate is $4$. Since the interest rate is less than twice of current inflation rate, the investment is not good.

Test case $4$: The interest rate is $10$ and the current inflation rate is $10$. Since the interest rate is less than twice of current inflation rate, the investment is not good.

Test case $5$: The interest rate is $20$ and the current inflation rate is $1$. Since the interest rate is greater than twice of current inflation rate, the investment is good.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Teiji is a number theory lover. All numbers are his friends - so long as they are integers. One day, while preparing for the next class as a teaching assistant, he is interested in a number-theoretical function called the divisor function. The divisor function σ(n) is defined as the sum of all positive divisors of n. “How fast does this σ(n) grow?” he asked himself. Apparently, σ(n) grows fast as n increases, but it is hard to estimate the speed of the growth. He decided to calculate the maximum value of σ(n)/n on 1 ≤ n ≤ k, for various k.

While it is easy for small numbers, it is tough to calculate many values of the divisor function by hand. Tired of writing thousands of digits, he decided to solve the problem with the help of a computer. But there is a problem: he is not familiar with computer programming. He asked you, a talented programmer, for help.

Please write a program to help him.



Input

The input contains a series of test cases. Each test case is described by a line, which contains a single integer k (1 ≤ k ≤ 1015 ). The input ends with a line containing a zero, which should not be processed.

Output

For each test case, output the maximum value of σ(n)/n where 1 ≤ n ≤ k in a line. Each value should be printed with six digits after the decimal point, and should not contain an absolute error greater than 10-6.

Example

Input

1
2
3
10
50
0


Output

1.000000
1.500000
1.500000
2.000000
2.583333

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
After acquiring an extraordinary amount of knowledge through programming contests, Malvika decided to harness her expertise to train the next generation of Indian programmers. So, she decided to hold a programming camp. In the camp, she held a discussion session for n members (n-1 students, and herself). They are sitting in a line from left to right numbered through 1 to n.

Malvika is sitting in the nth spot. She wants to teach m topics of competitive programming to the students. As the people taking part in the camp are all newbies, they know none of the topics being taught, i.e., initially, the first n - 1 people in the line know none of the topics, while the nth knows all of them.

It takes one hour for a person to learn a topic from his neighbour. Obviously, one person cannot both teach a topic as well as learn one during the same hour. That is, in any particular hour, a person can either teach a topic that he knows to one of his neighbors, or he can learn a topic from one of his neighbors, or he can sit idly. It is also obvious that if person x is learning from person y at a particular hour, then person y must be teaching person x at that hour.

Also, note that people can work parallely too, i.e., in the same hour when the 4th person is teaching the 3rd person, the 1st person can also teach the 2nd or learn from 2nd.

Find out the minimum number of hours needed so that each person learns all the m topics.

-----Input-----
- The first line of input contains a single integer T denoting number of test cases.
- The only line of each test case contains two space separated integers n, m as defined in the statement.

-----Output-----
- For each test case, output a single integer in a line corresponding to the answer of the problem.

-----Constraints-----
- 1 ≤ T, n, m ≤ 100

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

Output:
1
4

-----Explanation-----
In the first example, there are two people. Second person is Malvika and she has to teach only one topic to the first person. It will take only one hour to do so.

In the second example, there are three people. The 3rd person is Malvika and she has to teach only two topics to 1st and 2nd person. In the 1st hour, she teaches the 1st topic to the 2nd person. Now, in the 2nd hour, the 2nd person will teach the 1st topic to the 1st person. In the 3rd hour, Malvika will teach the 2nd topic to the 2nd person. Now the 2nd person will teach that topic to the 1st in the 4th hour. So, it takes a total of 4 hours for all the people to know all the topics.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
So, the Berland is at war with its eternal enemy Flatland again, and Vasya, an accountant, was assigned to fulfil his duty to the nation. 

Right now the situation in Berland is dismal — their both cities are surrounded! The armies of flatlanders stand on the borders of circles, the circles' centers are in the surrounded cities. At any moment all points of the flatland ring can begin to move quickly in the direction of the city — that's the strategy the flatlanders usually follow when they besiege cities.

The berlanders are sure that they can repel the enemy's attack if they learn the exact time the attack starts. For that they need to construct a radar that would register any movement at the distance of at most *r* from it. Thus, we can install a radar at such point, that at least one point of the enemy ring will be in its detecting range (that is, at a distance of at most *r*). Then the radar can immediately inform about the enemy's attack. 

Due to the newest technologies, we can place a radar at any point without any problems. But the problem is that the berlanders have the time to make only one radar. Besides, the larger the detection radius (*r*) is, the more the radar costs.

That's why Vasya's task (that is, your task) is to find the minimum possible detection radius for the radar. In other words, your task is to find the minimum radius *r* (*r*<=≥<=0) such, that a radar with radius *r* can be installed at some point and it can register the start of the movements of both flatland rings from that point. 

In this problem you can consider the cities as material points, the attacking enemy rings - as circles with centers in the cities, the radar's detection range — as a disk (including the border) with the center at the point where the radar is placed.

Input Specification:
The input files consist of two lines. Each line represents the city and the flatland ring that surrounds it as three space-separated integers *x**i*, *y**i*, *r**i* (|*x**i*|,<=|*y**i*|<=≤<=104; 1<=≤<=*r**i*<=≤<=104) — the city's coordinates and the distance from the city to the flatlanders, correspondingly.

It is guaranteed that the cities are located at different points.

Output Specification:
Print a single real number — the minimum detection radius of the described radar. The answer is considered correct if the absolute or relative error does not exceed 10<=-<=6.

Demo Input:
['0 0 1\n6 0 3\n', '-10 10 3\n10 -10 3\n']

Demo Output:
['1.000000000000000', '11.142135623730951']

Note:
The figure below shows the answer to the first sample. In this sample the best decision is to put the radar at point with coordinates (2, 0). 

The figure below shows the answer for the second sample. In this sample the best decision is to put the radar at point with coordinates (0, 0).

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Roma and Changing Signs

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Roma works in a company that sells TVs. Now he has to prepare a report for the last year.

Roma has got a list of the company's incomes. The list is a sequence that consists of *n* integers. The total income of the company is the sum of all integers in sequence. Roma decided to perform exactly *k* changes of signs of several numbers in the sequence. He can also change the sign of a number one, two or more times.

The operation of changing a number's sign is the operation of multiplying this number by -1.

Help Roma perform the changes so as to make the total income of the company (the sum of numbers in the resulting sequence) maximum. Note that Roma should perform exactly *k* changes.

Input Specification:
The first line contains two integers *n* and *k* (1<=≤<=*n*,<=*k*<=≤<=105), showing, how many numbers are in the sequence and how many swaps are to be made.

The second line contains a non-decreasing sequence, consisting of *n* integers *a**i* (|*a**i*|<=≤<=104).

The numbers in the lines are separated by single spaces. Please note that the given sequence is sorted in non-decreasing order.

Output Specification:
In the single line print the answer to the problem — the maximum total income that we can obtain after exactly *k* changes.

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

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

Note:
In the first sample we can get sequence [1, 1, 1], thus the total income equals 3.

In the second test, the optimal strategy is to get sequence [-1, 1, 1], thus the total income equals 1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
`{a, e, i, o, u, A, E, I, O, U}`

Natural Language Understanding is the subdomain of Natural Language Processing where people used to design AI based applications have ability to understand the human languages. HashInclude Speech Processing team has a project named Virtual Assistant. For this project they appointed you as a data engineer (who has good knowledge of creating clean datasets by writing efficient code). As a data engineer your first task is to make vowel recognition dataset. In this task you have to find the presence of vowels in all possible substrings of the given string. For each given string you have to return the total number of vowels.

## Example

Given a string `"baceb"` you can split it into substrings: `b, ba, bac, bace, baceb, a, ac, ace, aceb, c, ce, ceb, e, eb, b`. The number of vowels in each of these substrings is `0, 1, 1, 2, 2, 1, 1, 2, 2, 0, 1, 1, 1, 1, 0`; if you sum up these number, you get `16` - the expected output.

**Note**: your solution should have linear time complexity.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Complete the function that counts the number of unique consonants in a string (made up of printable ascii characters).

Consonants are letters used in English other than `"a", "e", "i", "o", "u"`. We will count `"y"` as a consonant.

Remember, your function needs to return the number of unique consonants - disregarding duplicates. For example, if the string passed into the function reads `"add"`, the function should return `1` rather than `2`, since `"d"` is a duplicate.

Similarly, the function should also disregard duplicate consonants of differing cases. For example, `"Dad"` passed into the function should return `1` as `"d"` and `"D"` are duplicates.

## Examples

```
"add" ==> 1
"Dad" ==> 1
"aeiou" ==> 0
"sillystring" ==> 7
"abcdefghijklmnopqrstuvwxyz" ==> 21
"Count my unique consonants!!" ==> 7
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Old Farmer Ranjan works on the farm of landlord Mittal Sahab. On the occasion of Diwali, Mittal Sahab decided to give some bonus to the hardworking farmer Ranjan. Mittal Sahab promised him to offer all the dragon fruits that Ranjan collects in one go from the right side of the farm returning back to the same side, such that he can take exactly 2 left turns.
Ranjan farmer can start plowing from any cell $A[i][N]$ where 1 ≤$ i$ ≤ N. 
The farm is represented as a 2D matrix, each cell consisting of some units of dragon fruit. Ranjan farmer wants to collect as much amount of dragon fruits as possible, but he is illiterate so he gave this job to his son, the great coder Rishi.
Please refer to the image below for more clarification on how to traverse the farm.

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

The first line contains single integer $T$, denoting the number of test cases.
The next line consists of 2 space separated integers $N$ and $M$, denoting the dimension of the farm.
The next $N$ lines consist of $M$ space separated integers each denoting the amount of dragon fruit in the cell.

------ Output: ------
Output a single integer denoting the maximum amount of vegetable Ranjan farmer could collect.

------ Constraints  ------
$1 ≤ T ≤ 5$
$2 ≤ N,M ≤ 10^{3}$
$2 ≤ A[i][j] ≤ 10^{9}$ for  $1 ≤ i,j ≤ N,M respectively$

------ Sample Input: ------
	2
	3 3
	1 2 3
	3 3 1
	4 1 6
	3 3
	3 7 4
	1 9 6
	1 7 7

------ Sample Output: ------
	20
	34

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You might know some pretty large perfect squares.  But what about the NEXT one?

Complete the `findNextSquare` method that finds the next integral perfect square after the one passed as a parameter.  Recall that an integral perfect square is an integer n such that sqrt(n) is also an integer.  

If the parameter is itself not a perfect square then `-1` should be returned.  You may assume the parameter is positive.


**Examples:**

```
findNextSquare(121) --> returns 144
findNextSquare(625) --> returns 676
findNextSquare(114) --> returns -1 since 114 is not a perfect
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef recently took a course in linear algebra and learned about linear combinations of vectors. Therefore, in order to test his intelligence, Raj gave him a "fuzzy" problem to solve.
A sequence of integers $B_1, B_2, \ldots, B_M$ generates an integer $K$ if it is possible to find a sequence of integers $C_1, C_2, \ldots, C_M$ such that $C_1 \cdot B_1 + C_2 \cdot B_2 + \ldots + C_M \cdot B_M = K$.
In this problem, Chef has a sequence $A_1, A_2, \ldots, A_N$ and he should answer $Q$ queries. In each query, he is given an integer $K$; the answer to this query is the number of pairs $(l, r)$ such that $1 \le l \le r \le N$ and the subsequence $(A_l, A_{l+1}, \ldots, A_r)$ generates $K$.
Chef has no idea how to solve this problem ― can you help him find the answers to all queries?

-----Input-----
- The first line of the input contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- The third line contains a single integer $Q$.
- The following $Q$ lines describe queries. Each of these lines contains a single integer $K$.

-----Output-----
For each query, print a single line containing one integer ― the number of contiguous subsequences that generate $K$.

-----Constraints-----
- $1 \le N, Q \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- $1 \le K \le 10^6$

-----Subtasks-----
Subtask #1 (10 points): $1 \le N \le 1,000$
Subtask #2 (90 points): original constraints

-----Example Input-----
2
2 4
3
1
2
8

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

-----Explanation-----
The sequence $(2, 4)$ has three contiguous subsequences: $(2)$, $(4)$ and $(2, 4)$. 
- In the first query, $1$ cannot be generated by any subsequence.
- In the second query, $2$ is generated by subsequences $(2)$ and $(2, 4)$. For example, for the subsequence $(2, 4)$, we can choose $C_1 = 1$ and $C_2 = 0$.
- In the third query, $8$ is generated by all three subsequences.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
One day Squidward, Spongebob and Patrick decided to go to the beach. Unfortunately, the weather was bad, so the friends were unable to ride waves. However, they decided to spent their time building sand castles.

At the end of the day there were n castles built by friends. Castles are numbered from 1 to n, and the height of the i-th castle is equal to h_{i}. When friends were about to leave, Squidward noticed, that castles are not ordered by their height, and this looks ugly. Now friends are going to reorder the castles in a way to obtain that condition h_{i} ≤ h_{i} + 1 holds for all i from 1 to n - 1.

Squidward suggested the following process of sorting castles:   Castles are split into blocks — groups of consecutive castles. Therefore the block from i to j will include castles i, i + 1, ..., j. A block may consist of a single castle.  The partitioning is chosen in such a way that every castle is a part of exactly one block.  Each block is sorted independently from other blocks, that is the sequence h_{i}, h_{i} + 1, ..., h_{j} becomes sorted.  The partitioning should satisfy the condition that after each block is sorted, the sequence h_{i} becomes sorted too. This may always be achieved by saying that the whole sequence is a single block. 

Even Patrick understands that increasing the number of blocks in partitioning will ease the sorting process. Now friends ask you to count the maximum possible number of blocks in a partitioning that satisfies all the above requirements.


-----Input-----

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of castles Spongebob, Patrick and Squidward made from sand during the day.

The next line contains n integers h_{i} (1 ≤ h_{i} ≤ 10^9). The i-th of these integers corresponds to the height of the i-th castle.


-----Output-----

Print the maximum possible number of blocks in a valid partitioning.


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

Output
3

Input
4
2 1 3 2

Output
2



-----Note-----

In the first sample the partitioning looks like that: [1][2][3].

 [Image] 

In the second sample the partitioning is: [2, 1][3, 2]

 [Image]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Your retro heavy metal band, VÄxën, originally started as kind of a joke, just because why would anyone want to use the crappy foosball table in your startup's game room when they could be rocking out at top volume in there instead? Yes, a joke, but now all the top tech companies are paying you top dollar to play at their conferences and big product-release events. And just as how in the early days of the Internet companies were naming everything "i"-this and "e"-that, now that VÄxënmänïä has conquered the tech world, any company that doesn't use Hëävÿ Mëtäl Ümläüts in ëvëry pössïblë pläcë is looking hopelessly behind the times.

Well, with great power chords there must also come great responsibility! You need to help these companies out by writing a function that will guarantee that their web sites and ads and everything else will RÖCK ÄS MÜCH ÄS PÖSSÏBLË! Just think about it -- with the licensing fees you'll be getting from Gööglë, Fäcëböök, Äpplë, and Ämäzön alone, you'll probably be able to end world hunger, make college and Marshall stacks free to all, and invent self-driving bumper cars. Sö lët's gët röckïng and röllïng! Pëdal tö thë MËTÄL!

Here's a little cheatsheet that will help you write your function to replace the so-last-year letters a-e-i-o-u-and-sometimes-y with the following totally rocking letters:

```
A = Ä = \u00c4     E = Ë = \u00cb     I = Ï = \u00cf
O = Ö = \u00d6     U = Ü = \u00dc     Y = Ÿ = \u0178
a = ä = \u00e4     e = ë = \u00eb     i = ï = \u00ef
o = ö = \u00f6     u = ü = \u00fc     y = ÿ = \u00ff
```
### Python issues
First, Python in the Codewars environment has some codec/encoding issues with extended ASCII codes like the umlaut-letters required above. With Python 2.7.6, when writing your solution you can just copy the above umlaut-letters (instead of the unicode sequences) and paste them into your code, but I haven't found something yet that will work for *both* 2.7.6 and 3.4.3 -- hopefully I will find something soon (answers/suggestions are welcome!), and hopefully that part will also be easier with other languages when I add them.

Second, along the same lines, don't bother trying to use string translate() and maketrans() to solve this in Python 2.7.6, because maketrans will see the character-mapping strings as being different lengths. Use a different approach instead.

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