vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Having passed the Hunter Exam, Gon is now officially a Hunter! Gon is now saying goodbye to his best friend, Killua, as Gon wants to visit his home in ‘While Island’.

Gon and Killua plan to use the online chat application, Olaz, to keep in touch. However, they are not confident with Olaz’s security: some imposters may be able to login to Gon’s account and send messages to Killua! To prevent this, they have decided to use the following method:
 - Before starting a conversation, Gon must send Killua a number $X$ with exactly $n$ digits.
 - Killua must reply with an integer $Y$ with exactly $n$ digits, where $X$ and $Y$ form a best friend pair.
 - Each time they start a conversation, they must use a different best friend pair. This would avoid imposters from simply reusing the previous best friend pairs.

To define a best friend pair, first we define a friendly operation on a number $X$ as follow:
 - Select two adjacent digits of $X$.
 - Either add $1$ to both digits, or subtract $1$ from both digits.
 - It is forbidden to add $1$ to digit $9$, or subtract $1$ from digit $0$.
 - It is also forbidden to subtract $1$ from the first digit of $X$, if the first digit of $X$ is $1$.

Note that the last two conditions guarantee that the new number is valid and does not have leading zero. The new and old numbers will also have the same length.

Two numbers $X$ and $Y$ without leading zeros are called best friends, if we can obtain $Y$ from $X$, by applying a finite number of friendly operations. Note that a number $X$ is best friend with itself.

For example, $666$ and $875$ are best friends because we can apply the operations as follow:
 - $666 \rightarrow 776$
 - $776 \rightarrow 886$
 - $886 \rightarrow 875$

Now Gon is wondering how many conversation can they have, before running out of best friend pairs.

-----Input-----
The input contains exactly one integer $n$ $(1 \le n \le 10^5)$.

-----Output-----
The output contains exactly one integer — the number of pairs of best friend numbers with exactly $n$ digits, modulo $998244353$.

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

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Fake News (easy)

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
As it's the first of April, Heidi is suspecting that the news she reads today are fake, and she does not want to look silly in front of all the contestants. She knows that a newspiece is fake if it contains heidi as a subsequence. Help Heidi assess whether the given piece is true, but please be discreet about it...

Input Specification:
The first and only line of input contains a single nonempty string *s* of length at most 1000 composed of lowercase letters (a-z).

Output Specification:
Output YES if the string *s* contains heidi as a subsequence and NO otherwise.

Demo Input:
['abcheaibcdi\n', 'hiedi\n']

Demo Output:
['YES', 'NO']

Note:
A string *s* contains another string *p* as a subsequence if it is possible to delete some characters from *s* and obtain *p*.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Scooby is stuck in a cave in barren islands. Shaggy decided to play a prank on scooby.
in his ghostly voice shaggy asks a question to the scared scooby. 
the ghost(shaggy) will make scooby's way out only if he answers the following problem. 
since scooby is not a nerd help him get out of the cave. the question is as follows.
Given a set S .
value of subset of s is sum of numbers in that subset.
Find sum of value of all subsets mod 10^9+7. 

Note :- value of null set is 0

Input

first line contains T . no of test cases 

first line of every test cases is n (set size) 

second line of every test cases contains n numbers of the set  x(i).

Output

print on a new line sum of value of all subsets of S mod 10^9+7 for each test case

Constraint

0 < T < 10

0 < n ≤ 100

0 ≤ x(i) ≤ 100000

SAMPLE INPUT
1
3
1 2 3

SAMPLE OUTPUT
24

Explanation

for set {1,2,3}

posssible subsets are {1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}

sum of value of all subset is 24

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Making Sequences is Fun

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
We'll define *S*(*n*) for positive integer *n* as follows: the number of the *n*'s digits in the decimal base. For example, *S*(893)<==<=3, *S*(114514)<==<=6.

You want to make a consecutive integer sequence starting from number *m* (*m*,<=*m*<=+<=1,<=...). But you need to pay *S*(*n*)·*k* to add the number *n* to the sequence.

You can spend a cost up to *w*, and you want to make the sequence as long as possible. Write a program that tells sequence's maximum length.

Input Specification:
The first line contains three integers *w* (1<=≤<=*w*<=≤<=1016), *m* (1<=≤<=*m*<=≤<=1016), *k* (1<=≤<=*k*<=≤<=109).

Please, do not write the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output Specification:
The first line should contain a single integer — the answer to the problem.

Demo Input:
['9 1 1\n', '77 7 7\n', '114 5 14\n', '1 1 2\n']

Demo Output:
['9\n', '7\n', '6\n', '0\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A linear congruential generator produces a series R(⋅) of pseudo-random numbers by the following for- mulas:

<image>

where S, A, C, and M are all parameters. In this problem, 0 ≤ S, A, C ≤ 15 and M = 256.

Now suppose we have some input string I(⋅), where each character in the string is an integer between 0 and (M - 1). Then, using the pseudo-random number series R(⋅), we obtain another string O(⋅) as the output by the following formula:

<image>

Your task is to write a program that shows the parameters S, A, and C such that the information entropy of the output string O(⋅) is minimized. Here, the information entropy H is given by the following formula:

<image>

where N is the length of the string and #(x) is the number of occurences of the alphabet x.



Input

The input consists of multiple datasets. Each dataset has the following format:

N
I(1) I(2) ... I(N)


N does not exceed 256.

The last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.

Output

For each dataset, print in a line the values of the three parameters S, A, and C separated by a single space. If more than one solution gives the same minimum entropy, choose the solution with the smallest S, A, and then C.

Example

Input

5
5 4 3 2 1
5
7 7 7 7 7
10
186 8 42 24 154 40 10 56 122 72
0


Output

0 1 1
0 0 0
8 7 14

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a tree with N vertices.

Here, a tree is a kind of graph, and more specifically, a connected undirected graph with N-1 edges, where N is the number of its vertices.

The i-th edge (1≤i≤N-1) connects Vertices a_i and b_i, and has a length of c_i.
You are also given Q queries and an integer K. In the j-th query (1≤j≤Q):
 - find the length of the shortest path from Vertex x_j and Vertex y_j via Vertex K.

-----Constraints-----
 - 3≤N≤10^5 
 - 1≤a_i,b_i≤N (1≤i≤N-1) 
 - 1≤c_i≤10^9 (1≤i≤N-1) 
 - The given graph is a tree.
 - 1≤Q≤10^5 
 - 1≤K≤N 
 - 1≤x_j,y_j≤N (1≤j≤Q) 
 - x_j≠y_j (1≤j≤Q) 
 - x_j≠K,y_j≠K (1≤j≤Q) 

-----Input-----
Input is given from Standard Input in the following format:  
N  
a_1 b_1 c_1  
:  
a_{N-1} b_{N-1} c_{N-1}
Q K
x_1 y_1
:  
x_{Q} y_{Q}

-----Output-----
Print the responses to the queries in Q lines.

In the j-th line j(1≤j≤Q), print the response to the j-th query.

-----Sample Input-----
5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5

-----Sample Output-----
3
2
4

The shortest paths for the three queries are as follows:
 - Query 1: Vertex 2 → Vertex 1 → Vertex 2 → Vertex 4 : Length 1+1+1=3 
 - Query 2: Vertex 2 → Vertex 1 → Vertex 3 : Length 1+1=2 
 - Query 3: Vertex 4 → Vertex 2 → Vertex 1 → Vertex 3 → Vertex 5 : Length 1+1+1+1=4

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Brave Ponta has finally arrived at the final dungeon. This is a dark wilderness in front of the fort of the evil emperor Boromos, with fairly strong monsters guarding their territories.

<image>


Figure 1: Wilderness

As shown in Fig. 1, the wilderness is represented by a 4 × 4 square region with the southwest as the origin (0, 0). Inside this area are monsters, as shown by the dots in the figure. Brave Ponta must cross this area from west to east (W to E). That is, you must start from the point where the x coordinate is 0.0 and the y coordinate is 0.0 or more and 4.0 or less, and move to the point where the x coordinate is 4.0 and the y coordinate is 0.0 or more and 4.0 or less.

When an enemy enters the area, the monster attacks the enemy if the distance between him and the enemy is shorter than the distance between any other monster and the enemy.

Now that there are not enough items, it was Ponta who really wanted to avoid fighting as much as possible before fighting Boromos. There, Ponta noticed: If you follow the path where there are always two or more monsters with the shortest distance to you, you won't be attacked by monsters.

Whether the brave Ponta can reach Boromos unscathed depends on your control. Create a program to find the shortest distance through the dark wilderness.

For reference, the shortest path in FIG. 1 is shown in FIG.

<image>


Figure 2: Shortest path



Input

Multiple datasets are given as input. Each dataset is given in the following format:

n (number of monsters: integer)
x1 y1 (Position of the first monster: Real number separated by blanks)
x2 y2 (Position of the second monster: Real number separated by blanks)
..
..
xn yn (position of nth monster: real number separated by blanks)


n is 1 or more and 20 or less. The x and y coordinate values ​​that indicate the position of the monster are 0.0 or more and 4.0 or less.

When n is 0, it indicates the end of input.

Output

Output the shortest distance on one line for each dataset. If you can't cross the wilderness without being attacked by a monster, print "impossible".

The distance output may have an error of 0.00001 or less.

Example

Input

2
1 1
3 3
4
1.0 0.5
1.0 2.5
3.0 1.5
3.0 3.5
1
2.0 2.0
0


Output

5.656854249492
4.618033988750
impossible

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

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Problem Description:
Igor K. always used to trust his favorite Kashpirovsky Antivirus. That is why he didn't hesitate to download the link one of his groupmates sent him via QIP Infinium. The link was said to contain "some real funny stuff about swine influenza". The antivirus had no objections and Igor K. run the flash application he had downloaded. Immediately his QIP Infinium said: "invalid login/password".

Igor K. entered the ISQ from his additional account and looked at the info of his main one. His name and surname changed to "H1N1" and "Infected" correspondingly, and the "Additional Information" field contained a strange-looking binary code 80 characters in length, consisting of zeroes and ones. "I've been hacked" — thought Igor K. and run the Internet Exploiter browser to quickly type his favourite search engine's address.

Soon he learned that it really was a virus that changed ISQ users' passwords. Fortunately, he soon found out that the binary code was actually the encrypted password where each group of 10 characters stood for one decimal digit. Accordingly, the original password consisted of 8 decimal digits.

Help Igor K. restore his ISQ account by the encrypted password and encryption specification.

Input Specification:
The input data contains 11 lines. The first line represents the binary code 80 characters in length. That is the code written in Igor K.'s ISQ account's info. Next 10 lines contain pairwise distinct binary codes 10 characters in length, corresponding to numbers 0, 1, ..., 9.

Output Specification:
Print one line containing 8 characters — The password to Igor K.'s ISQ account. It is guaranteed that the solution exists.

Demo Input:
['01001100100101100000010110001001011001000101100110010110100001011010100101101100\n0100110000\n0100110010\n0101100000\n0101100010\n0101100100\n0101100110\n0101101000\n0101101010\n0101101100\n0101101110\n', '10101101111001000010100100011010101101110010110111011000100011011110010110001000\n1001000010\n1101111001\n1001000110\n1010110111\n0010110111\n1101001101\n1011000001\n1110010101\n1011011000\n0110001000\n']

Demo Output:
['12345678\n', '30234919\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given two integer sequences $A_1, A_2, \ldots, A_N$ and $B_1, B_2, \ldots, B_M$. For any two sequences $U_1, U_2, \ldots, U_p$ and $V_1, V_2, \ldots, V_q$, we define
Score(U,V)=∑i=1p∑j=1qUi⋅Vj.Score(U,V)=∑i=1p∑j=1qUi⋅Vj.Score(U, V) = \sum_{i=1}^p \sum_{j=1}^q  U_i \cdot V_j \,.
You should process $Q$ queries of three types:
- $1$ $L$ $R$ $X$: Add $X$ to each of the elements $A_L, A_{L+1}, \ldots, A_R$.
- $2$ $L$ $R$ $X$: Add $X$ to each of the elements $B_L, B_{L+1}, \ldots, B_R$.
- $3$: Print $Score(A, B)$ modulo $998,244,353$.

-----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 line of each test case contains two integers, $N$ and $M$, denoting the length of $A$ and $B$ respectively.
- The second line contains $N$ integers, elements of $A$.
- The third line contains $M$ integers, elements of $B$.
- The next line will contain an integer, $Q$, number of queries.
- Each of the next $Q$ lines will contain one of $3$ kinds of updates as mentioned in the statement
It’s guaranteed that each update is a valid update operation.

-----Output-----
For each query of the third type, print a single line containing one integer - the answer to that query.

-----Constraints-----
- $1 \le T \le 10$
- $2 \le N, M, Q \le 10^5$
- $0 \le |A_i|, |B_i|, |X| \le 10^5$

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

-----Example Output-----
72
24
90

-----Explanation-----
Before the first operation, $A = [2, -1, 5],\ B = [3, 3, 2, 4]$
So, for the first operation,
$Score(A,\ B) = 2*3 + 2*3 + 2*2 + 2*4$ $+ (-1)*3$ $+ (-1)*3$ $+ (-1)*2$ $+$ $(-1)*4$ $+  5*3$ $+ 5*3$ $+ 5*2$ $+ 5*4$ $= 72.$
After the second query $A = [2, -3, 3]$, $B = [3, 3, 2, 4]$
So, for the third query, $Score(A, B) = 2*3 + 2*3 + 2*2$ $+ 2*4$ $+ (-3)*3$ $+ (-3)*3$ $+ (-3)*2$ $+ (-3)*4$ $+  3*3$ $+ 3*3$ $+ 3*2$ $+ 3*4$ $= 24$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
According to an old legeng, a long time ago Ankh-Morpork residents did something wrong to miss Fortune, and she cursed them. She said that at some time n snacks of distinct sizes will fall on the city, and the residents should build a Snacktower of them by placing snacks one on another. Of course, big snacks should be at the bottom of the tower, while small snacks should be at the top.

Years passed, and once different snacks started to fall onto the city, and the residents began to build the Snacktower. [Image] 

However, they faced some troubles. Each day exactly one snack fell onto the city, but their order was strange. So, at some days the residents weren't able to put the new stack on the top of the Snacktower: they had to wait until all the bigger snacks fell. Of course, in order to not to anger miss Fortune again, the residents placed each snack on the top of the tower immediately as they could do it.

Write a program that models the behavior of Ankh-Morpork residents.


-----Input-----

The first line contains single integer n (1 ≤ n ≤ 100 000) — the total number of snacks.

The second line contains n integers, the i-th of them equals the size of the snack which fell on the i-th day. Sizes are distinct integers from 1 to n. 


-----Output-----

Print n lines. On the i-th of them print the sizes of the snacks which the residents placed on the top of the Snacktower on the i-th day in the order they will do that. If no snack is placed on some day, leave the corresponding line empty.


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

Output
3
 
2 1
Input
5
4 5 1 2 3

Output
 
5 4
 
 
3 2 1



-----Note-----

In the example a snack of size 3 fell on the first day, and the residents immediately placed it. On the second day a snack of size 1 fell, and the residents weren't able to place it because they were missing the snack of size 2. On the third day a snack of size 2 fell, and the residents immediately placed it. Right after that they placed the snack of size 1 which had fallen before.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# Task
 You have two sorted arrays `a` and `b`, merge them to form new array of unique items.

 If an item is present in both arrays, it should be part of the resulting array if and only if it appears in both arrays the same number of times.

# Example

  For `a = [1, 3, 40, 40, 50, 60, 60, 60]` and `b = [2, 40, 40, 50, 50, 65]`, the result should be `[1, 2, 3, 40, 60, 65]`.
```
Number 40 appears 2 times in both arrays, 
thus it is in the resulting array.
Number 50 appears once in array a and twice in array b, 
therefore it is not part of the resulting array.```

# Input/Output


 - `[input]` integer array `a`

 A sorted array.
 
 1 ≤ a.length ≤ 500000
 
 
 - `[input]` integer array `b`

 A sorted array.
 
 `1 ≤ b.length ≤ 500000`
 

- `[output]` an integer array

  The resulting sorted array.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an $n\times n\times n$ cube, let $f(x,y,z)$ (where $1\leq x,y,z\leq n$) denote the value stored in cell $(x,y,z)$. 

A $k\times k\times k$ sub-cube (where $1\leq k\leq n$) of an $n\times n\times n$ cube is considered to be special if the maximum value stored in any cell in the sub-cube is equal to $\boldsymbol{\mbox{k}}$.

For each $\boldsymbol{\mbox{k}}$ in the inclusive range $[1,n]$, calculate the number of special sub-cubes. Then print each $\textit{count}_k$ as a single line of space-separated integers (i.e., $\textit{count}_1\ \textit{count}_2\ \textbf{.... count}_n$).

Input Format

The first line contains an integer, $\textit{q}$, denoting the number of queries. The $2\cdot q$ subsequent lines describe each query over two lines:

The first line contains an integer, $n$, denoting the side length of the initial cube.
The second line contains $n^{3}$ space-separated integers describing an array of $n^{3}$ integers in the form $a_0,a_1,\ldots,a_{n^3-1}$. The integer in some cell $(x,y,z)$ is calculated using the formula $a[(x-1)\cdot n^2+(y-1)\cdot n+z]$.

Constraints

$1\leq q\leq5$
$1\leq n\leq50$
$1\leq f(x,y,z)\leq n$ where $1\leq x,y,z\leq n$

Output Format

For each query, print $n$ space-separated integers where the $i^{\mbox{th}}$ integer denotes the number of special sub-cubes for $k=i$.

Sample Input
2
2
2 1 1 1 1 1 1 1
2
1 1 1 1 2 1 1 2

Sample Output
7 1
6 1

Explanation

We must perform the following $q=2$ queries:

We have a cube of size $n=2$ and must calculate the number of special sub-cubes for the following values of $\boldsymbol{\mbox{k}}$:

$k=1$: There are $2^3=8$ sub-cubes of size $1$ and seven of them have a maximum value of $1$ written inside them. So, for $k=1$, the answer is $7$. 
$k=2$: There is only one sub-cube of size $2$ and the maximum number written inside it is $2$. So, for $k=2$, the answer is $1$.    

We then print the respective values for each $\boldsymbol{\mbox{k}}$ as a single line of space-separated integers (i.e., 7 1).

We have a cube of size $n=2$ and must calculate the number of special sub-cubes for the following values of $\boldsymbol{\mbox{k}}$:   

$k=1$: There are $2^3=8$ sub-cubes of size $1$ and six of them have a maximum value of $1$ written inside them. So, for $k=1$, the answer is $\boldsymbol{6}$. 
$k=2$: There is only one sub-cube of size $2$ and the maximum number written inside it is $2$. So, for $k=2$, the answer is $1$.        

We then print the respective values for each $\boldsymbol{\mbox{k}}$ as a single line of space-separated integers (i.e., 6 1).

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The main city magazine offers its readers an opportunity to publish their ads. The format of the ad should be like this:

There are space-separated non-empty words of lowercase and uppercase Latin letters.

There are hyphen characters '-' in some words, their positions set word wrapping points. Word can include more than one hyphen. 

It is guaranteed that there are no adjacent spaces and no adjacent hyphens. No hyphen is adjacent to space. There are no spaces and no hyphens before the first word and after the last word. 

When the word is wrapped, the part of the word before hyphen and the hyphen itself stay on current line and the next part of the word is put on the next line. You can also put line break between two words, in that case the space stays on current line. Check notes for better understanding.

The ad can occupy no more that k lines and should have minimal width. The width of the ad is the maximal length of string (letters, spaces and hyphens are counted) in it.

You should write a program that will find minimal width of the ad.


-----Input-----

The first line contains number k (1 ≤ k ≤ 10^5).

The second line contains the text of the ad — non-empty space-separated words of lowercase and uppercase Latin letters and hyphens. Total length of the ad don't exceed 10^6 characters.


-----Output-----

Output minimal width of the ad.


-----Examples-----
Input
4
garage for sa-le

Output
7

Input
4
Edu-ca-tion-al Ro-unds are so fun

Output
10



-----Note-----

Here all spaces are replaced with dots.

In the first example one of possible results after all word wraps looks like this:

garage.

for.

sa-

le



The second example:

Edu-ca-

tion-al.

Ro-unds.

are.so.fun

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. All houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, adjacent houses have security system connected and it will automatically contact the police if two adjacent houses were broken into on the same night.

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonight without alerting the police.

Example 1:


Input: [2,3,2]
Output: 3
Explanation: You cannot rob house 1 (money = 2) and then rob house 3 (money = 2),
             because they are adjacent houses.


Example 2:


Input: [1,2,3,1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
             Total amount you can rob = 1 + 3 = 4.

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