vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
To help those contestants who struggle a lot in contests, the headquarters of Codeforces are planning to introduce Division 5. In this new division, the tags of all problems will be announced prior to the round to help the contestants.

The contest consists of $n$ problems, where the tag of the $i$-th problem is denoted by an integer $a_i$.

You want to AK (solve all problems). To do that, you must solve the problems in some order. To make the contest funnier, you created extra limitations on yourself. You do not want to solve two problems consecutively with the same tag since it is boring. Also, you are afraid of big jumps in difficulties while solving them, so you want to minimize the number of times that you solve two problems consecutively that are not adjacent in the contest order.

Formally, your solve order can be described by a permutation $p$ of length $n$. The cost of a permutation is defined as the number of indices $i$ ($1\le i<n$) where $|p_{i+1}-p_i|>1$. You have the requirement that $a_{p_i}\ne a_{p_{i+1}}$ for all $1\le i< n$.

You want to know the minimum possible cost of permutation that satisfies the requirement. If no permutations meet this requirement, you should report about it.


-----Input-----

The first line contains a single integer $t$ ($1\leq t\leq 10^4$) — the number of test cases.

The first line of the description of each test case contains a single integer $n$ ($1 \le n \le 10^5$) — the number of problems in the contest.

The next line contains $n$ integers $a_1,a_2,\ldots a_n$ ($1 \le a_i \le n$) — the tags of the problems.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.


-----Output-----

For each test case, if there are no permutations that satisfy the required condition, print $-1$. Otherwise, print the minimum possible cost of a permutation that satisfies the required condition.


-----Examples-----

Input
4
6
2 1 2 3 1 1
5
1 1 1 2 2
8
7 7 2 7 7 1 8 7
10
1 2 3 4 1 1 2 3 4 1
Output
1
3
-1
2


-----Note-----

In the first test case, let $p=[5, 4, 3, 2, 1, 6]$. The cost is $1$ because we jump from $p_5=1$ to $p_6=6$, and $|6-1|>1$. This permutation is valid because we don't solve problems with the same tag twice in a row. We cannot find a permutation with a cost smaller than $1$.

In the second test case, let $p=[1,5,2,4,3]$. The cost is $3$ because $|p_2-p_1|>1$, $|p_3-p_2|>1$, and $|p_4-p_3|>1$. The permutation is valid because we don't solve problems with the same tag twice in a row. We cannot find a permutation with a cost smaller than $3$.

In the third test case, for any order of solving the problems, we will solve two problems with the same tag consecutively, so the answer is $-1$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Program a function `sumAverage(arr)` where `arr` is an array containing arrays full of numbers, for example:

```python
sum_average([[1, 2, 2, 1], [2, 2, 2, 1]])
```

First, determine the average of each array. Then, return the sum of all the averages.

- All numbers will be less than 100 and greater than -100.
- `arr` will contain a maximum of 50 arrays.
- After calculating all the averages, add them **all** together, **then** round down, as shown in the example below:

The example given: `sumAverage([[3, 4, 1, 3, 5, 1, 4], [21, 54, 33, 21, 77]])`, the answer being 44.
1. Calculate the average of each individual array:
```
[3, 4, 1, 3, 5, 1, 4] = (3 + 4 + 1 + 3 + 5 + 1 + 4) / 7 = 3
[21, 54, 33, 21, 77] = (21 + 54 + 33 + 21 + 77) / 5 = 41.2
```
2. Add the average of each array together:
```
3 + 41.2 = 44.2
```
3. Round the final average down:

~~~if:julia
In Julia, the `Statistics` package is preloaded.
~~~
```python
import math
math.floor(44.2) = 44
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Let’s define a grid to be a set of tiles with 2 rows and 13 columns. Each tile has an English letter written in it. The letters don't have to be unique: there might be two or more tiles with the same letter written on them. Here is an example of a grid:
    
    
    ABCDEFGHIJKLM  
    NOPQRSTUVWXYZ

We say that two tiles are adjacent if they share a side or a corner. In the example grid above, the tile with the letter 'A' is adjacent only to the tiles with letters 'B', 'N', and 'O'. A tile is not adjacent to itself.

A sequence of tiles is called a path if each tile in the sequence is adjacent to the tile which follows it (except for the last tile in the sequence, which of course has no successor). In this example, "ABC" is a path, and so is "KXWIHIJK". "MAB" is not a path because 'M' is not adjacent to 'A'. A single tile can be used more than once by a path (though the tile cannot occupy two consecutive places in the path because no tile is adjacent to itself).

You’re given a string s which consists of 27 upper-case English letters. Each English letter occurs at least once in s. Find a grid that contains a path whose tiles, viewed in the order that the path visits them, form the string s. If there’s no solution, print "Impossible" (without the quotes).

Input

The only line of the input contains the string s, consisting of 27 upper-case English letters. Each English letter occurs at least once in s.

Output

Output two lines, each consisting of 13 upper-case English characters, representing the rows of the grid. If there are multiple solutions, print any of them. If there is no solution print "Impossible".

Examples

Input

ABCDEFGHIJKLMNOPQRSGTUVWXYZ


Output

YXWVUTGHIJKLM
ZABCDEFSRQPON


Input

BUVTYZFQSNRIWOXXGJLKACPEMDH


Output

Impossible

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In universe Earth C-137, Rick discovered a special form of magnetic force between two balls if they are put in his new invented basket. Rick has n empty baskets, the ith basket is at position[i], Morty has m balls and needs to distribute the balls into the baskets such that the minimum magnetic force between any two balls is maximum.
Rick stated that magnetic force between two different balls at positions x and y is |x - y|.
Given the integer array position and the integer m. Return the required force.
 
Example 1:

Input: position = [1,2,3,4,7], m = 3
Output: 3
Explanation: Distributing the 3 balls into baskets 1, 4 and 7 will make the magnetic force between ball pairs [3, 3, 6]. The minimum magnetic force is 3. We cannot achieve a larger minimum magnetic force than 3.

Example 2:
Input: position = [5,4,3,2,1,1000000000], m = 2
Output: 999999999
Explanation: We can use baskets 1 and 1000000000.

 
Constraints:

n == position.length
2 <= n <= 10^5
1 <= position[i] <= 10^9
All integers in position are distinct.
2 <= m <= position.length

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Having recently been hired by Netwerc Industries as a network engineer, your first task is to assess their large and dated office network. After mapping out the entire network, which consists of network switches and cables between them, you get a hunch that, not only are some of the switches redundant, some of them are not used at all! Before presenting this to your boss, you decide to make a program to test your claims. 

The data you have gathered consists of the map of the network, as well as the length of each cable. While you do not know the exact time it takes to send a network packet across each cable, you know that it can be calculated as $\ell / v + c$, where
 - $\ell $ is the length of the cable,
 - $v$ is the propagation speed of the cable, and
 - $c$ is the overhead of transmitting the packet on and off the cable.

You have not been able to measure $v$ and $c$. The only thing you know about them is that they are real numbers satisfying $v > 0$ and $c \ge 0$, and that they are the same for all cables. You also know that when a network packet is being transmitted from one switch to another, the network routing algorithms will ensure that the packet takes an optimal path—a path that minimises the total transit time.

Given the map of the network and the length of each cable, determine which switches could never possibly be part of an optimal path when transmitting a network packet from switch $1$ to switch $n$, no matter what the values of $v$ and $c$ are.

-----Input-----
The input consists of:
 - One line with two integers $n$, $m$ ($2 \leq n \leq 2000$, $1 \leq m \leq 10^4$), the number of switches and the number of cables in the network. The switches are numbered from $1$ to $n$.
 - $m$ lines, each with three integers $a$, $b$ and $\ell $ ($1 \leq a, b \leq n$, $1\leq \ell \leq 10^9$), representing a network cable of length $\ell $ connecting switches $a$ and $b$.

There is at most one cable connecting a given pair of switches, and no cable connects a switch to itself. It is guaranteed that there exists a path between every pair of switches.

-----Output-----
First output a line with an integer $k$, the number of switches that could never possibly be part of an optimal path when a packet is transmitted from switch $1$ to switch $n$. Then output a line with $k$ integers, the indices of the $k$ unused switches, in increasing order.

-----Examples-----
Sample Input 1:
7 8
1 2 2
1 3 1
1 4 3
2 6 1
2 7 2
3 5 1
4 7 2
5 7 1
Sample Output 1:
2
4 6

Sample Input 2:
5 6
1 2 2
2 3 2
3 5 2
1 4 3
4 5 3
1 5 6
Sample Output 2:
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The weekend is coming soon and you want to spend some time without worrying about your younger son Tommy. He is 6 years old and likes playing computer games a lot. Knowing that, you have written a special computer game for him. 

The game is about exploring labyrinths. You have prepared big dungeons to keep him busy for a long time. More specifically, the dungeons consists of R rooms and P portals between them. The rooms are numbered from 1 to R. The portals are one directional and each of them have assigned a time needed to teleport Tommy from one room to another.  In order to prevent Tommy from being scared of losing himself in the dungeons, you designed them in such a way that if a player is in a room A, then there is no possibility to use a sequence of portals from A which will teleport him again to A. In order to make Tommy happy, you created some number of rooms without any outgoing portal. Each such room contains a treasure and the game ends as soon as Tommy is teleported to such a room. For any other room, he will take some time to explore it, and you know that the maximum time that he can spend exploring a single room is 2 time units.

Tommy can start the game in any room he wants and you are interested in the maximum number of time units he can spend exploring the dungeons until he finds any treasure. 

Input format:

In the first line there are two integers R and P denoting the number of rooms and the number of portals between them.
P lines follow. Each of them consists of 3 integers r1, r2, and t. Where r1 and r2 denote respectively the starting and the ending room of a single portal in the dungeons, while t denotes the time needed to travel through this portal.

Output format:

Output exactly one integer denoting the maximum number of time units that Tommy can spend in the game.

Constraints:

1 ≤ R ≤ 10^6
1 ≤ P ≤ 10^6
1 ≤ r1, r2 ≤ R
1 ≤ t ≤ 10^9

SAMPLE INPUT
3 3
3 1 2
3 2 4
1 2 3

SAMPLE OUTPUT
9

Explanation

The longest game is possible when Tommy starts exploring dungeons in room 3, explore it for 2 time units, then use a portal to get to room 1, explore it for another 2 time units and use a portal in order to get to room 2, where he finds a treasure.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a non-empty integer array, find the minimum number of moves required to make all array elements equal, where a move is incrementing a selected element by 1 or decrementing a selected element by 1.

You may assume the array's length is at most 10,000.

Example:

Input:
[1,2,3]

Output:
2

Explanation:
Only two moves are needed (remember each move increments or decrements one element):

[1,2,3]  =>  [2,2,3]  =>  [2,2,2]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Polycarp has an integer $n$ that doesn't contain the digit 0. He can do the following operation with his number several (possibly zero) times:

Reverse the prefix of length $l$ (in other words, $l$ leftmost digits) of $n$. So, the leftmost digit is swapped with the $l$-th digit from the left, the second digit from the left swapped with ($l-1$)-th left, etc. For example, if $n=123456789$ and $l=5$, then the new value of $n$ will be $543216789$.

Note that for different operations, the values of $l$ can be different. The number $l$ can be equal to the length of the number $n$ — in this case, the whole number $n$ is reversed.

Polycarp loves even numbers. Therefore, he wants to make his number even. At the same time, Polycarp is very impatient. He wants to do as few operations as possible.

Help Polycarp. Determine the minimum number of operations he needs to perform with the number $n$ to make it even or determine that this is impossible.

You need to answer $t$ independent test cases.


-----Input-----

The first line contains the number $t$ ($1 \le t \le 10^4$) — the number of test cases.

Each of the following $t$ lines contains one integer $n$ ($1 \le n < 10^9$). It is guaranteed that the given number doesn't contain the digit 0.


-----Output-----

Print $t$ lines. On each line print one integer — the answer to the corresponding test case. If it is impossible to make an even number, print -1.


-----Examples-----

Input
4
3876
387
4489
3
Output
0
2
1
-1


-----Note-----

In the first test case, $n=3876$, which is already an even number. Polycarp doesn't need to do anything, so the answer is $0$.

In the second test case, $n=387$. Polycarp needs to do $2$ operations:

Select $l=2$ and reverse the prefix $\underline{38}7$. The number $n$ becomes $837$. This number is odd.

Select $l=3$ and reverse the prefix $\underline{837}$. The number $n$ becomes $738$. This number is even.

It can be shown that $2$ is the minimum possible number of operations that Polycarp needs to do with his number to make it even.

In the third test case, $n=4489$. Polycarp can reverse the whole number (choose a prefix of length $l=4$). It will become $9844$ and this is an even number.

In the fourth test case, $n=3$. No matter how hard Polycarp tried, he would not be able to make an even number.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
We have a string S of length N consisting of uppercase English letters.
How many times does ABC occur in S as contiguous subsequences (see Sample Inputs and Outputs)?

-----Constraints-----
 - 3 \leq N \leq 50
 - S consists of uppercase English letters.

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

-----Output-----
Print number of occurrences of ABC in S as contiguous subsequences.

-----Sample Input-----
10
ZABCDBABCQ

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

Two contiguous subsequences of S are equal to ABC: the 2-nd through 4-th characters, and the 7-th through 9-th characters.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Write a function that takes a single array as an argument (containing multiple strings and/or positive numbers and/or arrays), and returns one of four possible string values, depending on the ordering of the lengths of the elements in the input array:

Your function should return...

- “Increasing” - if the lengths of the elements increase from left to right (although it is possible that some neighbouring elements may also be equal in length)
- “Decreasing” - if the lengths of the elements decrease from left to right (although it is possible that some neighbouring elements may also be equal in length)
- “Unsorted” - if the lengths of the elements fluctuate from left to right
- “Constant” - if all element's lengths are the same.



Numbers and Strings should be evaluated based on the number of characters or digits used to write them.

Arrays should be evaluated based on the number of elements counted directly in the parent array (but not the number of elements contained in any sub-arrays).

Happy coding! :)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The Fibonacci sequence $F_0, F_1, \ldots$ is a special infinite sequence of non-negative integers, where $F_0 = 0$, $F_1 = 1$ and for each integer $n \ge 2$, $F_n = F_{n-1} + F_{n-2}$.
Consider the sequence $D$ of the last decimal digits of the first $N$ Fibonacci numbers, i.e. $D = (F_0 \% 10, F_1 \% 10, \ldots, F_{N-1} \% 10)$. Now, you should perform the following process:
- Let $D = (D_1, D_2, \ldots, D_l)$.
- If $l = 1$, the process ends.
- Create a new sequence $E = (D_2, D_4, \ldots, D_{2 \lfloor l/2 \rfloor})$. In other words, $E$ is the sequence created by removing all odd-indexed elements from $D$.
- Change $D$ to $E$.
When this process terminates, the sequence $D$ contains only one number. You have to find this number.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single integer $N$.

-----Output-----
For each test case, print a single line containing one integer ― the last remaining number.

-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le N \le 10^{18}$

-----Subtasks-----
Subtask #1 (20 points):
- $1 \le T \le 10^5$
- $1 \le N \le 10^7$
Subtask #2 (80 points): original constraints

-----Example Input-----
1
9

-----Example Output-----
3

-----Explanation-----
Example case 1: The first $N$ Fibonacci numbers are $(0, 1, 1, 2, 3, 5, 8, 13, 21)$. The sequence $D$ is $(0, 1, 1, 2, 3, 5, 8, 3, 1) \rightarrow (1, 2, 5, 3) \rightarrow (2, 3) \rightarrow (3)$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The recent vote in Puerto Rico favoring United States statehood has made flag makers very excited. An updated flag with $51$ stars rather than the current one with $50$ would cause a huge jump in U.S. flag sales. The current pattern for $50$ stars is five rows of $6$ stars, interlaced with four offset rows of $5$ stars. The rows alternate until all stars are represented. 

    * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

This pattern has the property that adjacent rows differ by no more than one star. We represent this star arrangement compactly by the number of stars in the first two rows: 6,5.

A $51$-star flag that has the same property can have three rows of $9$ stars, interlaced with three rows of $8$ stars (with a compact representation of 9,8). Conversely, if a state were to leave the union, one appealing representation would be seven rows of seven stars (7,7).

A flag pattern is visually appealing if it satisfies the following conditions:
 - Every other row has the same number of stars.
 - Adjacent rows differ by no more than one star.
 - The first row cannot have fewer stars than the second row.

Your team sees beyond the short-term change to $51$ for the US flag. You want to corner the market on flags for any union of three or more states. Given the number $S$ of stars to draw on a flag, find all possible visually appealing flag patterns.

-----Input-----
The input consists of a single line containing the integer $S$ ($3\le S\le 32767$).

-----Output-----
On the first line, print $S$, followed by a colon. Then, for each visually appealing flag of $S$ stars, print its compact representation, one per line.

This list of compact representations should be printed in increasing order of the number of stars in the first row; if there are ties, print them in order of the number of stars in the second row. The cases $1$-by-$S$ and $S$-by-$1$ are trivial, so do not print those arrangements.

The compact representations must be printed in the form “x,y”, with exactly one comma between x and y and no other characters.

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

Sample Input 2:
50
Sample Output 2:
50:
2,1
2,2
3,2
5,4
5,5
6,5
10,10
13,12
17,16
25,25

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a binary string S of length N. 

You have to perform the following operation exactly once:
Select an index i (1 ≤ i ≤ N) and delete S_{i} from S. The remaining parts of S are concatenated in the same order.

How many distinct binary strings of length N-1 can you get after applying this operation?

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

- The first line of input contains a single integer T - the number of test cases. The description of T test cases follow.
- The first line of each test case contains N - the length of the binary string S.
- The second line contains the binary string S.

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

For each test case, output the number of distinct binary strings that you can get after applying the operation exactly once.

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

$1 ≤ T ≤ 10^{5}$
$2 ≤ N ≤ 10^{5}$
- Sum of $N$ does not exceed $2 \cdot 10^{5}$ over all testcases.

----- Sample Input 1 ------ 
3
3
100
4
1111
5
10110
----- Sample Output 1 ------ 
2
1
4

----- explanation 1 ------ 
Test Case 1: We have $S = 100$. Now, we can get $00$ (on deleting $S_{1}$), $10$ (on deleting $S_{2}$) and $10$ (on deleting $S_{3}$). Therefore, we can get $2$ distinct strings.

Test Case 2: We have $S = 1111$. Now, we will always get $111$ irrespective of the index $i$ on which we apply the operation. Therefore, we can get $1$ distinct string.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# Task
 Consider a string of lowercase Latin letters and space characters (" "). 
 
 First, rearrange the letters in each word `alphabetically`. 
 
 And then rearrange the words in ascending order of the sum of their characters' `ASCII` values. 
 
 If two or more words have the same `ASCII` value, rearrange them by their length in ascending order; If their length still equals to each other, rearrange them `alphabetically`.
 
 Finally, return the result.

# Example

 For `s = "batman is bruce wayne"`, the result should be `"is bceru aenwy aamntb"`.
``` 
After rearranging the letters the string turns into
"aamntb is bceru aenwy".
The ASCII values of each word are: [627, 220, 529, 548].
After sorting the words the following string is obtained:
"is bceru aenwy aamntb" (with ASCII values of [220, 529, 548, 627]).```

 For `s = "peter parker is spiderman"`, the result should be `"is eeprt aekprr adeimnprs"`

 `(ASCII values: [220, 554, 645, 963])`

# Input/Output


 - `[input]` string `s`

  A string of lowercase words. Each word is separated by exactly one space character.


 - `[output]` a string

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