vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Title: Multithreading

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Emuskald is addicted to Codeforces, and keeps refreshing the main page not to miss any changes in the "recent actions" list. He likes to read thread conversations where each thread consists of multiple messages.

Recent actions shows a list of *n* different threads ordered by the time of the latest message in the thread. When a new message is posted in a thread that thread jumps on the top of the list. No two messages of different threads are ever posted at the same time.

Emuskald has just finished reading all his opened threads and refreshes the main page for some more messages to feed his addiction. He notices that no new threads have appeared in the list and at the *i*-th place in the list there is a thread that was at the *a**i*-th place before the refresh. He doesn't want to waste any time reading old messages so he wants to open only threads with new messages.

Help Emuskald find out the number of threads that surely have new messages. A thread *x* surely has a new message if there is no such sequence of thread updates (posting messages) that both conditions hold: 
 1.  thread *x* is not updated (it has no new messages); 1.  the list order 1, 2, ..., *n* changes to *a*1, *a*2, ..., *a**n*.

Input Specification:
The first line of input contains an integer *n*, the number of threads (1<=≤<=*n*<=≤<=105). The next line contains a list of *n* space-separated integers *a*1, *a*2, ..., *a**n* where *a**i* (1<=≤<=*a**i*<=≤<=*n*) is the old position of the *i*-th thread in the new list. It is guaranteed that all of the *a**i* are distinct.

Output Specification:
Output a single integer — the number of threads that surely contain a new message.

Demo Input:
['5\n5 2 1 3 4\n', '3\n1 2 3\n', '4\n4 3 2 1\n']

Demo Output:
['2\n', '0\n', '3\n']

Note:
In the first test case, threads 2 and 5 are placed before the thread 1, so these threads must contain new messages. Threads 1, 3 and 4 may contain no new messages, if only threads 2 and 5 have new messages.

In the second test case, there may be no new messages at all, since the thread order hasn't changed.

In the third test case, only thread 1 can contain no new messages.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Appu doesn't like maths.He was always intimidated by its calculations and stuff.To make matters worse,his Maths teacher is very strict.He gives him tough Home Work problems to him at the end of each chapter.If Appu fails to do the homework correctly,he punishes him.
Today Appu's teacher finished teaching him Set Theory,and he gave Appu the following problem:

" Lists are just like sets the only difference being that in lists a number can appear many time unlike  in sets.For example {4,5,5} is a list,but not a set because 5 appears twice.But {4,5} is both a list and set.A list of size n has (2^n)-1 non-empty sublists. For example, {1,3,3} has 7 sublists : {1},{3},{3},{1,3},{3,3},1,3},{1,3,3} . Lets define sublist sum of a list as sum of all the elements in the sub-list. Lets denote sublist sums of a list S  as SS[1],SS[2],SS[3]...... ,SS[ 2^n -1]. Lets also define a All Sublists Sum as ASS,

       ASS= (2^SS[1])+(2^(SS[2]) ..... + 2^(SS[2^n -1])  . Now given a list S,find the  ASS of that list. "

Looking at this statement, Appu was horrified.He has no clue whatsover on how to proceed.Can you help Appu from his punishment the next day in the class?

Input
The first line contains an integer N - the size of list S.Then next line contains N elements of list S.

Output
Output the (ASS of the list S)%(10^9+7)

Constraints
1 ≤ N ≤ 10^5
Each element of the list can be from 0 and 10^10 (inclusive)

SAMPLE INPUT
3
6 4 5

SAMPLE OUTPUT
36464

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Marut loves good strings. According to him, good strings are those which contain either all alphabets of uppercase or lowercase.
While he is preparing for his exams, he finds many bad strings in his book and wants to convert them to good strings.
But he wants to do this in minimum number of operations.
 In one operation, he can pick only one character of any case and convert it 
to any other case.

As his exams are going on, he wants your help.

Input:
The first line contains an integer T, denoting the number of test cases.
Each test case consists of only one line with a string S which contains uppercase and lowercase alphabets..

Output:
Print the minimum number of operations, in which Marut can obtain a good string.
Print the answer for each test case in new line.

Constraints:
1 ≤ T ≤ 10
If T is not in this range, print "Invalid Test" (without the quotes)
1 ≤ Length of S ≤ 100
S can contain numbers, special characters but no spaces.
If the length of string is not in the above range or it does not contain any alphabets, print "Invalid Input" (without the quotes)  

For Example, if the input is:
0
TestString  

Print "Invalid Test" (without the quotes)

SAMPLE INPUT
3
abcEfg
!@6#2
123A

SAMPLE OUTPUT
1
Invalid Input
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has a sequence of $N$ integers, $A_1, A_2, ... , A_N$. He likes this sequence if it contains a  subsequence of $M$ integers, $B_1, B_2, ... , B_M$ within it.
A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.
You will be given a sequence of $N$ integers, $A_1, A_2, ..., A_N$ followed by another sequence of $M$ integers, $B_1, B_2, ..., B_M$. Given these, you have to tell whether Chef likes the sequence of $N$ integers($A_1, A_2, ..., A_N$) or not. 
Formally, output "Yes" if
$\exists idx_1, idx_2, ..., idx_M | 1 \le idx_1 < idx_2 < ... < idx_M \le N$ and $A_{idx_i} = B_i \forall i, 1 \le i \le M$
Otherwise output "No". Note that the quotes are for clarity.

-----Input-----
The first line contains a single integer, $T$.
$T$ test cases follow where each test case contains four lines:
- The first line of a test case contains a single integer $N$
- The second line of the test case contains $N$ space separated integers, $A_1, A_2, ..., A_N$
- The third line of the test case contains a single integer $M$.
- The fourth line contains $M$ space separated integers, $B_1, B_2, ..., B_M$
Symbols have usual meanings as described in the statement.

-----Output-----
For each test case, output a single line containing the output. Output is "Yes" if Chef likes the sequence $A$. Output is "No" if Chef dislikes the sequence $A$.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N \le 10^3$
- $1 \le M \le 10^3$
- $1 \le A_i, B_i \le 10^9$

-----Sample Input-----
3
6
1 2 3 4 5 6
3
2 3 4
6
22 5 6 33 1 4
2
4 15
4
1 3 4 2
2
1 2

-----Sample Output-----
Yes
No
Yes

-----Explanation:-----
In sample test case $1$, the sequence $1,2,3,4,5,6$ contains the subsequence $2, 3, 4$. The subsequence is present at indices $1, 2, 3$ of the original sequence.
Hence, $1,2,3,4,5,6$ is a sequence which Chef likes it. Therefore, we output "Yes".
In sample test case $2$, the subsequence $4, 15$ is not present in sequence $22, 5, 6, 33, 1, 4$. Hence, we output "No".
In sample test case $3$, the sequence $1, 3, 4, 2$ contains the subsequence $1, 2$. The subsequence is present at indices $0, 3$. Therefore, we output "Yes".

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef and his best friend Aleksa are into mathematical games these days. Today, they have some ( ≥ 0 ) black cells represented as B, and a white cell represented as W, lying randomly in a straight line.
They have decided to play with these cells. In a move, a player chooses some ( > 0 ) black cells lying on any one side of the white cell and remove them. It should be noted that a player is not allowed to choose black cells from both side of the given white cell. Both the players alternate their moves, and play optimally. The player who is unable to move in his respective turn will lose the game.
Aleksa, being a girl, has a habit of playing first. But Chef is fairly smart himself, and will not play the game if he is going to lose it. Therefore, he wants to know the winner beforehand. Can you tell him who is going to win the game for the given configuration of cells?

-----Input-----
First line of input contains a single integer T denoting the number of test cases. First and the only line of each test case contains a string S consisting of the characters 'B' and 'W', denoting black and white cells, respectively.

-----Output-----
For each test case, output "Chef" if chef wins the game for the given configuration. Else print "Aleksa". (quotes for clarity only).

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ |S| ≤ 10000
- S contains exactly 1 white cell.

-----Scoring-----
-  Subtask 1:  1 ≤ T ≤ 10, 1 ≤ |S| ≤ 10 : ( 30 pts )
-  Subtask 2:  1 ≤ T ≤ 10, 1 ≤ |S| ≤ 100 : ( 30 pts )
-  Subtask 3:  1 ≤ T ≤ 10, 1 ≤ |S| ≤ 10000 : ( 40 pts )

-----Example-----
Input
3
W
BW
BWBB

Output
Chef
Aleksa
Aleksa

----- Explanation-----
-  Test 1 : Aleksa cannot make a move in her first turn as there is no black cell in the given configuration.
-  Test 2 : Aleksa can remove 1 black cell lying on the left of white cell in her turn. But then, Chef cannot make a move in his turn as there will be no black cells left.
-  Test 3 : Figure out yourself.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a 32 bit unsigned integer num and an integer i. Perform following operations on the number - 
1. Get ith bit
2. Set ith bit
3. Clear ith bit
Note : For better understanding, we are starting bits from 1 instead 0. (1-based)
Example 1:
Input: 70 3
Output: 1 70 66
Explanation: Bit at the 3rd position from LSB is 1. (1 0 0 0 1 1 0)
The value of the given number after setting the 3rd bit is 70. 
The value of the given number after clearing 3rd bit is 66. (1 0 0 0 0 1 0)
Example 2:
Input: 8 1
Output: 0 9 8
Explanation: Bit at the first position from LSB is 0. (1 0 0 0)
The value of the given number after setting the 1st bit is 9. (1 0 0 1)
The value of the given number after clearing 1st bit is 8. (1 0 0 0)
 
Your Task:
Complete the function bitManipulation() which takes two integers num and i as input and prints the results after each operation separted by a space in the same line. You don't have to print any new lines after printing the output, that will be handled by driver code.
 
Constraints:
0<=num<=10^{9}
1<=i<=32

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Recently personal training sessions have finished in the Berland State University Olympiad Programmer Training Centre. By the results of these training sessions teams are composed for the oncoming team contest season. Each team consists of three people. All the students of the Centre possess numbers from 1 to 3n, and all the teams possess numbers from 1 to n. The splitting of students into teams is performed in the following manner: while there are people who are not part of a team, a person with the best total score is chosen among them (the captain of a new team), this person chooses for himself two teammates from those who is left according to his list of priorities. The list of every person's priorities is represented as a permutation from the rest of 3n - 1 students who attend the centre, besides himself.

You are given the results of personal training sessions which are a permutation of numbers from 1 to 3n, where the i-th number is the number of student who has won the i-th place. No two students share a place. You are also given the arrangement of the already formed teams in the order in which they has been created. Your task is to determine the list of priorities for the student number k. If there are several priority lists, choose the lexicographically minimal one.

Input

The first line contains an integer n (1 ≤ n ≤ 105) which is the number of resulting teams. The second line contains 3n space-separated integers from 1 to 3n which are the results of personal training sessions. It is guaranteed that every student appears in the results exactly once.

Then follow n lines each containing three integers from 1 to 3n — each line describes the members of a given team. The members of one team can be listed in any order, but the teams themselves are listed in the order in which they were created. It is guaranteed that the arrangement is correct, that is that every student is a member of exactly one team and those teams could really be created from the given results using the method described above.

The last line contains number k (1 ≤ k ≤ 3n) which is the number of a student for who the list of priorities should be found.

Output

Print 3n - 1 numbers — the lexicographically smallest list of priorities for the student number k. 

The lexicographical comparison is performed by the standard < operator in modern programming languages. The list a is lexicographically less that the list b if exists such an i (1 ≤ i ≤ 3n), that ai < bi, and for any j (1 ≤ j < i) aj = bj. Note, that the list 1 9 10 is lexicographically less than the list 1 10 9. That is, the comparison of lists is different from the comparison of lines.

Examples

Input

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


Output

2 3 5 6 9 1 7 8 

Input

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


Output

1 2 3 4 5 6 7 9 

Input

2
4 1 3 2 5 6
4 6 5
1 2 3
4


Output

5 6 1 2 3 

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Convert a non-negative integer to its english words representation. Given input is guaranteed to be less than 231 - 1.

Example 1:


Input: 123
Output: "One Hundred Twenty Three"


Example 2:


Input: 12345
Output: "Twelve Thousand Three Hundred Forty Five"

Example 3:


Input: 1234567
Output: "One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven"


Example 4:


Input: 1234567891
Output: "One Billion Two Hundred Thirty Four Million Five Hundred Sixty Seven Thousand Eight Hundred Ninety One"

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: `2332, 110011, 54322345`

For a given number ```num```, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed.

In this kata, single digit numbers and numbers which start or end with zeros (such as `010` and `00`) are **NOT** considered valid numerical palindromes.  

If `num` contains no valid palindromes, return `"No palindromes found"`. 
Otherwise, return `"Not valid"` if the input is not an integer or is less than `0`.


## Examples

```
palindrome(1221)      =>  [22, 1221]
palindrome(34322122)  =>  [22, 212, 343, 22122]
palindrome(1001331)   =>  [33, 1001, 1331]
palindrome(1294)      =>  "No palindromes found"
palindrome("1221")    =>  "Not valid"
```

---

### Other Kata in this Series:

Numerical Palindrome #1
Numerical Palindrome #1.5
Numerical Palindrome #2
Numerical Palindrome #3
Numerical Palindrome #3.5
Numerical Palindrome #4
Numerical Palindrome #5

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Today on a math lesson the teacher told Vovochka that the Euler function of a positive integer φ(*n*) is an arithmetic function that counts the positive integers less than or equal to n that are relatively prime to n. The number 1 is coprime to all the positive integers and φ(1)<==<=1.

Now the teacher gave Vovochka an array of *n* positive integers *a*1,<=*a*2,<=...,<=*a**n* and a task to process *q* queries *l**i* *r**i* — to calculate and print  modulo 109<=+<=7. As it is too hard for a second grade school student, you've decided to help Vovochka.

Input Specification:
The first line of the input contains number *n* (1<=≤<=*n*<=≤<=200<=000) — the length of the array given to Vovochka. The second line contains *n* integers *a*1,<=*a*2,<=...,<=*a**n* (1<=≤<=*a**i*<=≤<=106).

The third line contains integer *q* (1<=≤<=*q*<=≤<=200<=000) — the number of queries. Next *q* lines contain the queries, one per line. Each query is defined by the boundaries of the segment *l**i* and *r**i* (1<=≤<=*l**i*<=≤<=*r**i*<=≤<=*n*).

Output Specification:
Print *q* numbers — the value of the Euler function for each query, calculated modulo 109<=+<=7.

Demo Input:
['10\n1 2 3 4 5 6 7 8 9 10\n7\n1 1\n3 8\n5 6\n4 8\n8 10\n7 9\n7 10\n', '7\n24 63 13 52 6 10 1\n6\n3 5\n4 7\n1 7\n2 4\n3 6\n2 6\n']

Demo Output:
['1\n4608\n8\n1536\n192\n144\n1152\n', '1248\n768\n12939264\n11232\n9984\n539136\n']

Note:
In the second sample the values are calculated like that:
 -  φ(13·52·6) = φ(4056) = 1248 -  φ(52·6·10·1) = φ(3120) = 768 -  φ(24·63·13·52·6·10·1) = φ(61326720) = 12939264 -  φ(63·13·52) = φ(42588) = 11232 -  φ(13·52·6·10) = φ(40560) = 9984 -  φ(63·13·52·6·10) = φ(2555280) = 539136

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are n cities numbered from 1 to n in Berland. Some of them are connected by two-way roads. Each road has its own length — an integer number from 1 to 1000. It is known that from each city it is possible to get to any other city by existing roads. Also for each pair of cities it is known the shortest distance between them. Berland Government plans to build k new roads. For each of the planned road it is known its length, and what cities it will connect. To control the correctness of the construction of new roads, after the opening of another road Berland government wants to check the sum of the shortest distances between all pairs of cities. Help them — for a given matrix of shortest distances on the old roads and plans of all new roads, find out how the sum of the shortest distances between all pairs of cities changes after construction of each road.

Input

The first line contains integer n (2 ≤ n ≤ 300) — amount of cities in Berland. Then there follow n lines with n integer numbers each — the matrix of shortest distances. j-th integer in the i-th row — di, j, the shortest distance between cities i and j. It is guaranteed that di, i = 0, di, j = dj, i, and a given matrix is a matrix of shortest distances for some set of two-way roads with integer lengths from 1 to 1000, such that from each city it is possible to get to any other city using these roads.

Next line contains integer k (1 ≤ k ≤ 300) — amount of planned roads. Following k lines contain the description of the planned roads. Each road is described by three space-separated integers ai, bi, ci (1 ≤ ai, bi ≤ n, ai ≠ bi, 1 ≤ ci ≤ 1000) — ai and bi — pair of cities, which the road connects, ci — the length of the road. It can be several roads between a pair of cities, but no road connects the city with itself.

Output

Output k space-separated integers qi (1 ≤ i ≤ k). qi should be equal to the sum of shortest distances between all pairs of cities after the construction of roads with indexes from 1 to i. Roads are numbered from 1 in the input order. Each pair of cities should be taken into account in the sum exactly once, i. e. we count unordered pairs.

Examples

Input

2
0 5
5 0
1
1 2 3


Output

3 

Input

3
0 4 5
4 0 9
5 9 0
2
2 3 8
1 2 1


Output

17 12

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# Task
 "AL-AHLY" and "Zamalek" are the best teams in Egypt, but "AL-AHLY" always wins the matches between them. "Zamalek" managers want to know what is the best match they've played so far.
 
 The best match is the match they lost with the minimum goal difference. If there is more than one match with the same difference, choose the one "Zamalek" scored more goals in.
 
 Given the information about all matches they played, return the `index` of the best match (`0-based`). If more than one valid result, return the smallest index.

# Example

 For `ALAHLYGoals = [6,4] and zamalekGoals = [1,2]`, the output should be 1.
 
 Because `4 - 2` is less than `6 - 1`
 
 For `ALAHLYGoals = [1,2,3,4,5] and zamalekGoals = [0,1,2,3,4]`, the output should be 4.
 
 The goal difference of all matches are 1, but at 4th match "Zamalek" scored more goals in. So the result is `4`.
 
# Input/Output


 -  `[input]` integer array `ALAHLYGoals`

  The number of goals "AL-AHLY" scored in each match.


 - `[input]` integer array `zamalekGoals`

  The number of goals "Zamalek" scored in each match. It is guaranteed that zamalekGoals[i] < ALAHLYGoals[i] for each element.


 - `[output]` an integer

  Index of the best match.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.

-----Constraints-----
 - 1 \leq N < 10^{100}
 - 1 \leq K \leq 3

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

-----Output-----
Print the count.

-----Sample Input-----
100
1

-----Sample Output-----
19

The following 19 integers satisfy the condition:
 - 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100

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