vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Title: Delete from the Left

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given two strings $s$ and $t$. In a single move, you can choose any of two strings and delete the first (that is, the leftmost) character. After a move, the length of the string decreases by $1$. You can't choose a string if it is empty.

For example:
 -  by applying a move to the string "where", the result is the string "here", -  by applying a move to the string "a", the result is an empty string "". 
You are required to make two given strings equal using the fewest number of moves. It is possible that, in the end, both strings will be equal to the empty string, and so, are equal to each other. In this case, the answer is obviously the sum of the lengths of the initial strings.

Write a program that finds the minimum number of moves to make two given strings $s$ and $t$ equal.

Input Specification:
The first line of the input contains $s$. In the second line of the input contains $t$. Both strings consist only of lowercase Latin letters. The number of letters in each string is between 1 and $2\cdot10^5$, inclusive.

Output Specification:
Output the fewest number of moves required. It is possible that, in the end, both strings will be equal to the empty string, and so, are equal to each other. In this case, the answer is obviously the sum of the lengths of the given strings.

Demo Input:
['test\nwest\n', 'codeforces\nyes\n', 'test\nyes\n', 'b\nab\n']

Demo Output:
['2\n', '9\n', '7\n', '1\n']

Note:
In the first example, you should apply the move once to the first string and apply the move once to the second string. As a result, both strings will be equal to "est".

In the second example, the move should be applied to the string "codeforces" $8$ times. As a result, the string becomes "codeforces" $\to$ "es". The move should be applied to the string "yes" once. The result is the same string "yes" $\to$ "es".

In the third example, you can make the strings equal only by completely deleting them. That is, in the end, both strings will be empty.

In the fourth example, the first character of the second string should be deleted.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Let's define a split of $n$ as a nonincreasing sequence of positive integers, the sum of which is $n$. 

For example, the following sequences are splits of $8$: $[4, 4]$, $[3, 3, 2]$, $[2, 2, 1, 1, 1, 1]$, $[5, 2, 1]$.

The following sequences aren't splits of $8$: $[1, 7]$, $[5, 4]$, $[11, -3]$, $[1, 1, 4, 1, 1]$.

The weight of a split is the number of elements in the split that are equal to the first element. For example, the weight of the split $[1, 1, 1, 1, 1]$ is $5$, the weight of the split $[5, 5, 3, 3, 3]$ is $2$ and the weight of the split $[9]$ equals $1$.

For a given $n$, find out the number of different weights of its splits.


-----Input-----

The first line contains one integer $n$ ($1 \leq n \leq 10^9$).


-----Output-----

Output one integer — the answer to the problem.


-----Examples-----
Input
7

Output
4

Input
8

Output
5

Input
9

Output
5



-----Note-----

In the first sample, there are following possible weights of splits of $7$:

Weight 1: [$\textbf 7$] 

Weight 2: [$\textbf 3$, $\textbf 3$, 1] 

Weight 3: [$\textbf 2$, $\textbf 2$, $\textbf 2$, 1] 

Weight 7: [$\textbf 1$, $\textbf 1$, $\textbf 1$, $\textbf 1$, $\textbf 1$, $\textbf 1$, $\textbf 1$]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Find the longest substring in alphabetical order.

Example: the longest alphabetical substring in `"asdfaaaabbbbcttavvfffffdf"` is `"aaaabbbbctt"`.

There are tests with strings up to `10 000` characters long so your code will need to be efficient.

The input will only consist of lowercase characters and will be at least one letter long.

If there are multiple solutions, return the one that appears first.

Good luck :)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Alice and Bob dream about future summer vacations where travel is unconstrained by pandemics, budgetary constraints, or other mundane problems. Since they love winter, they want to visit the Southern Hemisphere, in particular Chile. Chile is, geographically speaking, a rather one-dimensional country, and can be represented as an infinitely long $y$-axis. There are $N$ cities in Chile, numbered from $1$ to $N$, where the $i$th city is located at $y$-coordinate $y_ i$. Alice and Bob will start their journey in city number $1$, and travel to some other city from there.

Each city has an airport with a direct connection to other cities. However, flights cannot be arbitrarily short: For each city $i$ there is a minimal distance $d_ i$ such that there is a flight to city $j$ if and only if $|y_ i-y_ j|\geq d_ i$. The time for a flight is $|y_ i - y_ j|$ minutes, but it also takes time to travel to the airport, check in, pass security, etc. Thus, for each city there is an additional time $r_ i$ such that the total time to fly from $i$ to $j$ is $r_ i + |y_ i - y_ j|$ minutes.

Find the shortest possible time to get to each of the other cities, provided that Alice and Bob start in city $1$. Flights are the only means of transportation, but Alice and Bob can take as many flights as they like.

-----Input-----
The first line contains an integer $N$, the number of cities, where $2 \leq N \leq 2 \cdot 10^5$. The following $N$ lines each consist of three integers $y_ i$, $d_ i$, and $r_ i$, where $0 \leq y_ i, d_ i, r_ i \leq 10^9$. All $y$-coordinates are distinct.

-----Output-----
Print $N-1$ lines, each containing an integer. On the $i$th line, print the shortest possible total time for getting from city 1 to city $i+1$, if possible. If there is no way to get to city $i+1$, print $-1$ instead.

-----Examples-----
Sample Input:
5
1 3 2
2 5 2
3 0 0
4 2 4
5 3 0
Sample Output:
9
-1
5
6

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Tod is very much focus about his English subject but now he is in trouble because he have to do his Math homework but also have to go for English classes so he asks you for help to solve his Math homework question.

You are given a  Natural number(N) you have to print Factorial of the Prime number present in the (S) series(1 ≤ S ≤ N)
INPUT

Natural number N ( 1 ≤ N ≤ 100)

OUTPUT

Factorial of all the prime number present in the series

Series contain all  element between (1 ≤ S ≤ N) 

SAMPLE INPUT
4

SAMPLE OUTPUT
2
6

Explanation

INPUT

4

OUTPUT

2 

6

In this problem series will be (1,2,3,4)

So, Prime number are(2,3)

Factorial of 2 (2*1)=2

Factorial of 3 (321)=6

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.

You are given $N$ sets of integers $A_{1}, A_{2}, \ldots, A_{N}$. For each valid $i$, let's denote the elements of the set $A_{i}$ by $\{c_{i,1}, c_{i,2}, \ldots, c_{i,|A_{i}|}\}$.

Find the number of ways to choose a sequence $(a_{1}, a_{2}, \ldots, a_{N})$ such that:
$a_{i} \in A_{i}$ for each valid $i$
$a_{i} \neq a_{i+1}$ for each valid $i$ and $a_{1} \neq a_{N}$

Since this number may be large, compute it modulo $998,244,353$.

------  Input ------
The first line of the input contains a single integer $N$.
$N$ lines follow. For each valid $i$, the $i$-th of these lines contains an integer $|A_{i}|$ followed by a space and $|A_{i}|$ space-separated non-negative integers $c_{i,1}, c_{i,2}, \ldots, c_{i,|A_{i}|}$.

------  Output ------
Print a single line containing one integer ― the number of ways to choose $(a_{1}, a_{2}, \ldots, a_{N})$, modulo $998,244,353$.

------  Constraints  ------
$2 ≤ N ≤ 200,000$
$|A_{i}| ≥ 1$ for each valid $i$
$|A_{1}| + |A_{2}| + \ldots + |A_{N}| ≤ 200,000$
$1 ≤ c_{i,j} ≤ 200000$ for each valid $i, j$

------  Subtasks ------
Subtask #1 (20 points): $N ≤ 100$

Subtask #2 (80 points): original constraints

----- Sample Input 1 ------ 
3

3 1 2 3

2 1 2

2 2 3
----- Sample Output 1 ------ 
3
----- explanation 1 ------ 
There are three possible sequences: $(1, 2, 3)$, $(2, 1, 3)$ and $(3, 1, 2)$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Russian version of the problem can be read here.

There are two cats playing, and each of them has a set of strings consisted of lower case English letters.

The first cat has N strings, while the second one has M strings. Both the first and the second cat will choose one of it's strings and give it to you. After receiving two strings, you will count the number of pairs of equal substrings that you can choose in both strings, and send this number back to the cats. (Note that two occurences of the same substring are considered different. For example, strings "bab" and "aba" have 6 such pairs.)

The cats are going to give you all N * M possible pairs. They are interested in the total sum of numbers received from you. Your task is to find this number.

Input format

The first line of the input contains the integer N. The next N lines contain the first cat's strings, one string per line. The next line contain the integer M, and after that the next M lines contain the second cat's strings, one string per line as well.

Output format

In one line print the answer to the problem.

Constraints

1 ≤ N, M ≤ 100,000
, the total length of each cat strings set will not exceed 100,000.
All strings in the input will be non-empty.

SAMPLE INPUT
2
ab
bab
2
bab
ba

SAMPLE OUTPUT
18

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
For long time scientists study the behavior of sharks. Sharks, as many other species, alternate short movements in a certain location and long movements between locations.

Max is a young biologist. For $n$ days he watched a specific shark, and now he knows the distance the shark traveled in each of the days. All the distances are distinct. Max wants to know now how many locations the shark visited. He assumed there is such an integer $k$ that if the shark in some day traveled the distance strictly less than $k$, then it didn't change the location; otherwise, if in one day the shark traveled the distance greater than or equal to $k$; then it was changing a location in that day. Note that it is possible that the shark changed a location for several consecutive days, in each of them the shark traveled the distance at least $k$.

The shark never returned to the same location after it has moved from it. Thus, in the sequence of $n$ days we can find consecutive nonempty segments when the shark traveled the distance less than $k$ in each of the days: each such segment corresponds to one location. Max wants to choose such $k$ that the lengths of all such segments are equal.

Find such integer $k$, that the number of locations is as large as possible. If there are several such $k$, print the smallest one.

Input Specification:
The first line contains a single integer $n$ ($1 \leq n \leq 10^5$) — the number of days.

The second line contains $n$ distinct positive integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — the distance traveled in each of the day.

Output Specification:
Print a single integer $k$, such that 
 1.  the shark was in each location the same number of days, 1.  the number of locations is maximum possible satisfying the first condition, 1.  $k$ is smallest possible satisfying the first and second conditions.

Demo Input:
['8\n1 2 7 3 4 8 5 6\n', '6\n25 1 2 3 14 36\n']

Demo Output:
['7', '2']

Note:
In the first example the shark travels inside a location on days $1$ and $2$ (first location), then on $4$-th and $5$-th days (second location), then on $7$-th and $8$-th days (third location). There are three locations in total.

In the second example the shark only moves inside a location on the $2$-nd day, so there is only one location.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Flatland is inhabited by pixels of three colors: red, green and blue. We know that if two pixels of different colors meet in a violent fight, only one of them survives the fight (that is, the total number of pixels decreases by one). Besides, if pixels of colors *x* and *y* (*x*<=≠<=*y*) meet in a violent fight, then the pixel that survives the fight immediately changes its color to *z* (*z*<=≠<=*x*; *z*<=≠<=*y*). Pixels of the same color are friends, so they don't fight.

The King of Flatland knows that his land will be peaceful and prosperous when the pixels are of the same color. For each of the three colors you know the number of pixels of this color that inhabit Flatland. Help the king and determine whether fights can bring peace and prosperity to the country and if it is possible, find the minimum number of fights needed to make the land peaceful and prosperous.

Input Specification:
The first line contains three space-separated integers *a*, *b* and *c* (0<=≤<=*a*,<=*b*,<=*c*<=≤<=231; *a*<=+<=*b*<=+<=*c*<=&gt;<=0) — the number of red, green and blue pixels, correspondingly.

Output Specification:
Print a single number — the minimum number of pixel fights before the country becomes peaceful and prosperous. If making the country peaceful and prosperous is impossible, print -1.

Demo Input:
['1 1 1\n', '3 1 0\n']

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

Note:
In the first test sample the country needs only one fight to achieve peace and prosperity. Besides, it can be any fight whatsoever. For example, let's assume that the green and the blue pixels fight, then the surviving pixel will be red. As a result, after the fight there are two red pixels. There won't be other pixels.

In the second sample the following sequence of fights is possible: red and blue, green and red, red and blue. As a result, after all fights there is one green pixel left.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: k-th divisor

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
You are given two integers *n* and *k*. Find *k*-th smallest divisor of *n*, or report that it doesn't exist.

Divisor of *n* is any such natural number, that *n* can be divided by it without remainder.

Input Specification:
The first line contains two integers *n* and *k* (1<=≤<=*n*<=≤<=1015, 1<=≤<=*k*<=≤<=109).

Output Specification:
If *n* has less than *k* divisors, output -1.

Otherwise, output the *k*-th smallest divisor of *n*.

Demo Input:
['4 2\n', '5 3\n', '12 5\n']

Demo Output:
['2\n', '-1\n', '6\n']

Note:
In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Lumpy is a bus driver. Today, the conductor is absent so Lumpy has to do the conductor's job as well. There are N creatures in the bus. Sometimes the creatures don't carry change and can't pay the exact amount of the fare. Each creature in the bus today has paid an amount
greater than his/her fare. You are given information about the extra amount paid by each creature, by an array A of size N, where Ai denotes the extra amount paid by the i-th creature, in rupees.
After the end of the trip, Lumpy noticed that he had P one rupee coins and Q two rupee coins. He wants to pay back the creatures using this money. Being a kind hearted moose, Lumpy wants to pay back as many creatures as he can. Note that Lumpy will 
not pay back the i-th creature if he can't pay the exact amount that the i-th creature requires with the coins that he possesses. 
Lumpy is busy driving the bus and doesn't want to calculate the maximum number of creatures he can satisfy - He will surely cause an accident if he tries to do so. Can you help him out with this task? 

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
- For each test case, first line consists of three space separated integers N, P and Q.
- Second line consists of N space separated integers A containing N space integers, where i-th integer denotes Ai.

-----Output-----
- For each test case, output a single line containing an integer corresponding to maximum number of creatures that Lumpy can pay back.

-----Constraints-----
- 1 ≤ T ≤ 106
- 1 ≤ N ≤ 105
- 1 ≤ Ai ≤ 109
- 0 ≤ P, Q ≤ 1014
- Sum of N over all the cases does not exceed 106

-----Subtasks-----
- Subtask #1 (15 points): P = 0
- Subtask #2 (15 points): Q = 0
- Subtask #3 (70 points): Original constraints

-----Example-----
Input:3
3 3 0
1 2 2
3 2 1
1 2 1
4 5 4
2 3 4 5

Output:2
3
3

-----Explanation-----
Example 1. Lumpy has just 3 one rupee coins. 

He can pay creatures numbered {1, 2} or creatures numbered {1, 3} with these coins. Thus, answer is 2. 
Example 2. Lumpy has 2 one rupee coins and 1 two rupee coin. 

In the optimal solution, Lumpy can give the two rupee coin to creature 2 and the one rupee coins to creatures 1 and 3. Thus, answer is 3.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Walter and Jesse's friend Mike had helped them in making Crymeth and hence, they wanted to give him a share.
For deciding the share, they both decided to choose one number each, X and Y and found out that K^th Highest Common Factor of their two numbers is a good amount of Crymeth that can be given to Mike .
Walter and Jesse did this activity for D days in total. For each day, find out what quantity of Crymeth they decided to give to Mike.

Input:

First line contains a natural number D - the total number of days.
D lines follow. Each line contains three natural numbers - X, Y and K.

Output:

For each day, print the quantity given to Mike on a new line.
If the K^th HCF of X and Y does not exist, simply print "No crymeth today" (Without the quotes)

Constraints:
1 ≤ D ≤ 10^3
1 ≤ X, Y, K ≤ 10^10

SAMPLE INPUT
3
8 16 2
8 16 4
8 16 5

SAMPLE OUTPUT
4
1
No crymeth today

Explanation

1st Highest Common Factor of 8 and 16 = 8
2nd Highest Common Factor of 8 and 16 = 4
3rd Highest Common Factor of 8 and 16 = 2
4th Highest Common Factor of 8 and 16 = 1

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 $n$ integers. Let's denote monotonic renumeration of array $a$ as an array $b$ consisting of $n$ integers such that all of the following conditions are met:

  $b_1 = 0$;  for every pair of indices $i$ and $j$ such that $1 \le i, j \le n$, if $a_i = a_j$, then $b_i = b_j$ (note that if $a_i \ne a_j$, it is still possible that $b_i = b_j$);  for every index $i \in [1, n - 1]$ either $b_i = b_{i + 1}$ or $b_i + 1 = b_{i + 1}$. 

For example, if $a = [1, 2, 1, 2, 3]$, then two possible monotonic renumerations of $a$ are $b = [0, 0, 0, 0, 0]$ and $b = [0, 0, 0, 0, 1]$.

Your task is to calculate the number of different monotonic renumerations of $a$. The answer may be large, so print it modulo $998244353$.


-----Input-----

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

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).


-----Output-----

Print one integer — the number of different monotonic renumerations of $a$, taken modulo $998244353$.


-----Examples-----
Input
5
1 2 1 2 3

Output
2

Input
2
100 1

Output
2

Input
4
1 3 3 7

Output
4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are N dominoes in a line, and we place each domino vertically upright.
In the beginning, we simultaneously push some of the dominoes either to the left or to the right.

After each second, each domino that is falling to the left pushes the adjacent domino on the left.
Similarly, the dominoes falling to the right push their adjacent dominoes standing on the right.
When a vertical domino has dominoes falling on it from both sides, it stays still due to the balance of the forces.
For the purposes of this question, we will consider that a falling domino expends no additional force to a falling or already fallen domino.
Given a string "S" representing the initial state. S[i] = 'L', if the i-th domino has been pushed to the left; S[i] = 'R', if the i-th domino has been pushed to the right; S[i] = '.', if the i-th domino has not been pushed.
Return a string representing the final state. 
Example 1:
Input: ".L.R...LR..L.."
Output: "LL.RR.LLRRLL.."

Example 2:
Input: "RR.L"
Output: "RR.L"
Explanation: The first domino expends no additional force on the second domino.

Note:

0 <= N <= 10^5
String dominoes contains only 'L', 'R' and '.'

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Bizon the Champion isn't just friendly, he also is a rigorous coder.

Let's define function *f*(*a*), where *a* is a sequence of integers. Function *f*(*a*) returns the following sequence: first all divisors of *a*1 go in the increasing order, then all divisors of *a*2 go in the increasing order, and so on till the last element of sequence *a*. For example, *f*([2,<=9,<=1])<==<=[1,<=2,<=1,<=3,<=9,<=1].

Let's determine the sequence *X**i*, for integer *i* (*i*<=≥<=0): *X*0<==<=[*X*] ([*X*] is a sequence consisting of a single number *X*), *X**i*<==<=*f*(*X**i*<=-<=1) (*i*<=&gt;<=0). For example, at *X*<==<=6 we get *X*0<==<=[6], *X*1<==<=[1,<=2,<=3,<=6], *X*2<==<=[1,<=1,<=2,<=1,<=3,<=1,<=2,<=3,<=6].

Given the numbers *X* and *k*, find the sequence *X**k*. As the answer can be rather large, find only the first 105 elements of this sequence.

Input Specification:
A single line contains two space-separated integers — *X* (1<=≤<=*X*<=≤<=1012) and *k* (0<=≤<=*k*<=≤<=1018).

Output Specification:
Print the elements of the sequence *X**k* in a single line, separated by a space. If the number of elements exceeds 105, then print only the first 105 elements.

Demo Input:
['6 1\n', '4 2\n', '10 3\n']

Demo Output:
['1 2 3 6 \n', '1 1 2 1 2 4 \n', '1 1 1 2 1 1 5 1 1 2 1 5 1 2 5 10 \n']

Note:
none

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