vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Write a function ```convert_temp(temp, from_scale, to_scale)``` converting temperature from one scale to another. 
Return converted temp value. 

Round converted temp value to an integer(!).

Reading: http://en.wikipedia.org/wiki/Conversion_of_units_of_temperature

```
possible scale inputs:
    "C"  for Celsius
    "F"  for Fahrenheit
    "K"  for Kelvin
    "R"  for Rankine
    "De" for Delisle
    "N"  for Newton
    "Re" for Réaumur
    "Ro" for Rømer
```

```temp``` is a number, ```from_scale``` and ```to_scale``` are strings. 

```python
convert_temp(   100, "C",  "F") # => 212
convert_temp(    40, "Re", "C") # => 50
convert_temp(    60, "De", "F") # => 140
convert_temp(373.15, "K",  "N") # => 33
convert_temp(   666, "K",  "K") # => 666
```

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

There are the following games.

N characters are lined up in a vertical row. The color of these characters is red, blue, or yellow, and in the initial state, four or more characters of the same color are not lined up in a row. The player can select a character at a certain position and change it to another color. By this operation, if four or more characters of the same color are lined up in a row, those characters will disappear. When four or more characters of the same color are lined up in a row due to the disappearance of the characters, those characters also disappear, and this chain continues until there are no more places where four or more characters of the same color are lined up in a row. .. The purpose of this game is to reduce the number of characters remaining without disappearing.

For example, if the color of the sixth character from the top is changed from yellow to blue in the state at the left end of the figure below, five blue characters will disappear in a row, and finally three characters will remain without disappearing.

<image>


Given the color sequence of N characters in the initial state, create a program that finds the minimum value M of the number of characters that remain without disappearing when the color of the character is changed in only one place.



input

The input consists of multiple datasets. Each dataset is given in the following format.

The first line consists of only the number of characters N (1 ≤ N ≤ 10000). The following N lines contain one of 1, 2, and 3 integers, and the i + 1st line (1 ≤ i ≤ N) represents the color of the i-th character from the top in the initial state (1). Is red, 2 is blue, and 3 is yellow).

When N is 0, it indicates the end of input. The number of datasets does not exceed 5.

output

For each dataset, output the minimum value M of the number of characters remaining without disappearing on one line.

Examples

Input

12
3
2
1
1
2
3
2
2
2
1
1
3
12
3
2
1
1
2
3
2
1
3
2
1
3
0


Output

3
12


Input

None


Output

None

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Lesha plays the recently published new version of the legendary game hacknet. In this version character skill mechanism was introduced. Now, each player character has exactly *n* skills. Each skill is represented by a non-negative integer *a**i* — the current skill level. All skills have the same maximum level *A*.

Along with the skills, global ranking of all players was added. Players are ranked according to the so-called Force. The Force of a player is the sum of the following values:
 -  The number of skills that a character has perfected (i.e., such that *a**i*<==<=*A*), multiplied by coefficient *c**f*.-  The minimum skill level among all skills (*min* *a**i*), multiplied by coefficient *c**m*. 
Now Lesha has *m* hacknetian currency units, which he is willing to spend. Each currency unit can increase the current level of any skill by 1 (if it's not equal to *A* yet). Help him spend his money in order to achieve the maximum possible value of the Force.

Input Specification:
The first line of the input contains five space-separated integers *n*, *A*, *c**f*, *c**m* and *m* (1<=≤<=*n*<=≤<=100<=000, 1<=≤<=*A*<=≤<=109, 0<=≤<=*c**f*,<=*c**m*<=≤<=1000, 0<=≤<=*m*<=≤<=1015).

The second line contains exactly *n* integers *a**i* (0<=≤<=*a**i*<=≤<=*A*), separated by spaces, — the current levels of skills.

Output Specification:
On the first line print the maximum value of the Force that the character can achieve using no more than *m* currency units.

On the second line print *n* integers *a*'*i* (*a**i*<=≤<=*a*'*i*<=≤<=*A*), skill levels which one must achieve in order to reach the specified value of the Force, while using no more than *m* currency units. Numbers should be separated by spaces.

Demo Input:
['3 5 10 1 5\n1 3 1\n', '3 5 10 1 339\n1 3 1\n']

Demo Output:
['12\n2 5 2 \n', '35\n5 5 5 \n']

Note:
In the first test the optimal strategy is to increase the second skill to its maximum, and increase the two others by 1.

In the second test one should increase all skills to maximum.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
For each string *s* consisting of characters '0' and '1' one can define four integers *a*00, *a*01, *a*10 and *a*11, where *a**xy* is the number of subsequences of length 2 of the string *s* equal to the sequence {*x*,<=*y*}. 

In these problem you are given four integers *a*00, *a*01, *a*10, *a*11 and have to find any non-empty string *s* that matches them, or determine that there is no such string. One can prove that if at least one answer exists, there exists an answer of length no more than 1<=000<=000.

Input Specification:
The only line of the input contains four non-negative integers *a*00, *a*01, *a*10 and *a*11. Each of them doesn't exceed 109.

Output Specification:
If there exists a non-empty string that matches four integers from the input, print it in the only line of the output. Otherwise, print "Impossible". The length of your answer must not exceed 1<=000<=000.

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

Demo Output:
['Impossible\n', '0110\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A long time ago, in a galaxy far far away two giant IT-corporations Pineapple and Gogol continue their fierce competition. Crucial moment is just around the corner: Gogol is ready to release it's new tablet Lastus 3000.

This new device is equipped with specially designed artificial intelligence (AI). Employees of Pineapple did their best to postpone the release of Lastus 3000 as long as possible. Finally, they found out, that the name of the new artificial intelligence is similar to the name of the phone, that Pineapple released 200 years ago. As all rights on its name belong to Pineapple, they stand on changing the name of Gogol's artificial intelligence.

Pineapple insists, that the name of their phone occurs in the name of AI as a substring. Because the name of technology was already printed on all devices, the Gogol's director decided to replace some characters in AI name with "#". As this operation is pretty expensive, you should find the minimum number of characters to replace with "#", such that the name of AI doesn't contain the name of the phone as a substring.

Substring is a continuous subsequence of a string.


-----Input-----

The first line of the input contains the name of AI designed by Gogol, its length doesn't exceed 100 000 characters. Second line contains the name of the phone released by Pineapple 200 years ago, its length doesn't exceed 30. Both string are non-empty and consist of only small English letters.


-----Output-----

Print the minimum number of characters that must be replaced with "#" in order to obtain that the name of the phone doesn't occur in the name of AI as a substring.


-----Examples-----
Input
intellect
tell

Output
1
Input
google
apple

Output
0
Input
sirisiri
sir

Output
2


-----Note-----

In the first sample AI's name may be replaced with "int#llect".

In the second sample Gogol can just keep things as they are.

In the third sample one of the new possible names of AI may be "s#ris#ri".

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Alica and Bob are playing a game.

Initially they have a binary string $s$ consisting of only characters 0 and 1.

Alice and Bob make alternating moves: Alice makes the first move, Bob makes the second move, Alice makes the third one, and so on. During each move, the current player must choose two different adjacent characters of string $s$ and delete them. For example, if $s = 1011001$ then the following moves are possible:   delete $s_1$ and $s_2$: $\textbf{10}11001 \rightarrow 11001$;  delete $s_2$ and $s_3$: $1\textbf{01}1001 \rightarrow 11001$;  delete $s_4$ and $s_5$: $101\textbf{10}01 \rightarrow 10101$;  delete $s_6$ and $s_7$: $10110\textbf{01} \rightarrow 10110$. 

If a player can't make any move, they lose. Both players play optimally. You have to determine if Alice can win.


-----Input-----

First line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases.

Only line of each test case contains one string $s$ ($1 \le |s| \le 100$), consisting of only characters 0 and 1.


-----Output-----

For each test case print answer in the single line.

If Alice can win print DA (YES in Russian) in any register. Otherwise print NET (NO in Russian) in any register.


-----Example-----
Input
3
01
1111
0011

Output
DA
NET
NET



-----Note-----

In the first test case after Alice's move string $s$ become empty and Bob can not make any move.

In the second test case Alice can not make any move initially.

In the third test case after Alice's move string $s$ turn into $01$. Then, after Bob's move string $s$ become empty and Alice can not make any move.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Valera has got a rectangle table consisting of n rows and m columns. Valera numbered the table rows starting from one, from top to bottom and the columns – starting from one, from left to right. We will represent cell that is on the intersection of row x and column y by a pair of integers (x, y).

Valera wants to place exactly k tubes on his rectangle table. A tube is such sequence of table cells (x_1, y_1), (x_2, y_2), ..., (x_{r}, y_{r}), that:   r ≥ 2;  for any integer i (1 ≤ i ≤ r - 1) the following equation |x_{i} - x_{i} + 1| + |y_{i} - y_{i} + 1| = 1 holds;  each table cell, which belongs to the tube, must occur exactly once in the sequence. 

Valera thinks that the tubes are arranged in a fancy manner if the following conditions are fulfilled:   no pair of tubes has common cells;  each cell of the table belongs to some tube. 

Help Valera to arrange k tubes on his rectangle table in a fancy manner.


-----Input-----

The first line contains three space-separated integers n, m, k (2 ≤ n, m ≤ 300; 2 ≤ 2k ≤ n·m) — the number of rows, the number of columns and the number of tubes, correspondingly. 


-----Output-----

Print k lines. In the i-th line print the description of the i-th tube: first print integer r_{i} (the number of tube cells), then print 2r_{i} integers x_{i}1, y_{i}1, x_{i}2, y_{i}2, ..., x_{ir}_{i}, y_{ir}_{i} (the sequence of table cells).

If there are multiple solutions, you can print any of them. It is guaranteed that at least one solution exists. 


-----Examples-----
Input
3 3 3

Output
3 1 1 1 2 1 3
3 2 1 2 2 2 3
3 3 1 3 2 3 3

Input
2 3 1

Output
6 1 1 1 2 1 3 2 3 2 2 2 1



-----Note-----

Picture for the first sample:  [Image] 

Picture for the second sample:  [Image]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Chef has an array A of length N. In one operation, Chef can:

Choose any subarray [L, R] (1 ≤ L ≤ R ≤ N);
Add 1 to A_{L}, subtract 1 from A_{L+1}, add 1 to A_{L+2}, subtract 1 from A_{L+3} and so on, till A_{R}.

Chef performed Q such operations where the i^{th} operation was performed on the subarray [L_{i}, R_{i}].

Determine the final sum of the array after these Q operations.

Note that a subarray is formed by deleting some (possibly zero) elements from the beginning and some (possibly zero) elements from the end of the array.

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

- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of multiple lines of input.
- The first line of each test case contains two integers N, Q, number of elements and the number of queries.
- The next line contains N space-separated integers A_{1}, A_{2}, \dots A_{N} - denoting the array A.
- The next Q lines contains two space-separated integers with i^{th} line containing L_{i}, R_{i}.

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

For each test case, output the final sum of the array after performing all the Q operations.

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

$1 ≤ T ≤ 1000$
$1 ≤ N, Q ≤ 3 \cdot 10^{5}$
$1 ≤ A_{i} ≤ 100$
- The sum of $N$ over all test cases won't exceed $3 \cdot 10^{5}$.
- The sum of $Q$ over all test cases won't exceed $3 \cdot 10^{5}$.

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

----- Sample Output 1 ------ 
16
6

----- explanation 1 ------ 
Test case $1$: The queries are as follows:

- Query $1$: The chosen subarray is $[1, 3, 4, 4, 2]$ which changes to $[1+1, 3-1, 4+1, 4-1, 2+1] = [2, 2, 5, 3, 3]$. Thus, the array becomes $[2, 2, 5, 3, 3]$.
- Query $2$: The chosen subarray is $[5, 3]$ which changes to $[5+1, 3-1] = [6, 2]$. Thus, the array becomes $[2, 2, 6, 2, 3]$.
- Query $3$: The chosen subarray is $[2]$ which changes to $[2+1] = [3]$. Thus, the array becomes $[2, 3, 6, 2, 3]$.

The sum of final array is $2+3+6+2+3 = 16$.

Test case $2$: The queries are as follows:

- Query $1$: The chosen subarray is $[4]$ which changes to $[4+1] = [5]$. Thus, the array becomes $[5]$.
- Query $2$: The chosen subarray is $[5]$ which changes to $[5+1] = [6]$. Thus, the array becomes $[6]$.

The sum of final array is $6$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Your friend has n cards.

You know that each card has a lowercase English letter on one side and a digit on the other.

Currently, your friend has laid out the cards on a table so only one side of each card is visible.

You would like to know if the following statement is true for cards that your friend owns: "If a card has a vowel on one side, then it has an even digit on the other side." More specifically, a vowel is one of 'a', 'e', 'i', 'o' or 'u', and even digit is one of '0', '2', '4', '6' or '8'.

For example, if a card has 'a' on one side, and '6' on the other side, then this statement is true for it. Also, the statement is true, for example, for a card with 'b' and '4', and for a card with 'b' and '3' (since the letter is not a vowel). The statement is false, for example, for card with 'e' and '5'. You are interested if the statement is true for all cards. In particular, if no card has a vowel, the statement is true.

To determine this, you can flip over some cards to reveal the other side. You would like to know what is the minimum number of cards you need to flip in the worst case in order to verify that the statement is true.


-----Input-----

The first and only line of input will contain a string s (1 ≤ |s| ≤ 50), denoting the sides of the cards that you can see on the table currently. Each character of s is either a lowercase English letter or a digit.


-----Output-----

Print a single integer, the minimum number of cards you must turn over to verify your claim.


-----Examples-----
Input
ee

Output
2

Input
z

Output
0

Input
0ay1

Output
2



-----Note-----

In the first sample, we must turn over both cards. Note that even though both cards have the same letter, they could possibly have different numbers on the other side.

In the second sample, we don't need to turn over any cards. The statement is vacuously true, since you know your friend has no cards with a vowel on them.

In the third sample, we need to flip the second and fourth cards.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are the boss of ACM (Association for the Country of Mububa), an upstanding company with a single goal of world domination.

Today, you have conquered the unnamed country of Mububa (how an unnamed country has a name is, of course, outside the scope of this problem). Mububa is known for its great, great, bananas. In light of this monumental achievement, you have decided to reward your executives with Mububa’s greatest treasure (which is obviously, bananas). You have prepared $N$ briefcases, each contains a number of bananas. These briefcases are numbered from $1$ through $N$.

You reward your executives one by one in order from the least evil executive, to the most evil executive (still not comparably evil to you, of course). No two executives are equally evil. For each executive, you first decide how many briefcases you want to give him. If you decide to give an executive $a$ briefcases, you give him the $a$ briefcases with lowest numbers that you still have. Each executive you reward must receive at least one briefcase.

It is important to be fair when distributing rewards. You do not want your executives to stage a hunger strike, after all. Thus, the rewards the executives received must reflect how evil they are. More rigorously, if executive $A$ is more evil than executive $B$, then the total number of bananas received by executive $A$ must be at least as large as the total number of bananas received by executive $B$.

You know the number of bananas inside all of the briefcases. You want to reward as many executives as possible, but wants the distribution to still be fair (i.e. following the previous requirement) amongst them. What is the maximum number of executives you can reward this way?

-----Input-----
The first line contains a non-negative integer $2 \leq N \leq 3000$, giving the number of briefcases you have. Then follows a line with $N$ integers, the $i$-th of which denotes the number of bananas in briefcase number $i$. Each briefcase contains between $1$ and $10^9$ bananas, inclusively.

-----Output-----
Print the maximum number of executives you can reward with bananas.Sample Data explanation

In the first example, give briefcase $1$ to the least evil executive, briefcase $2$ to the second least evil executive, and briefcases $3$ and $4$ to the most evil executive.

In the second example, give briefcase $1$ to the least evil executive, briefcases $2$ and $3$ to the second least evil executive, and briefcases $4$, $5$, and $6$ to the most evil executive.

-----Examples-----
Sample Input:
4
1 2 1 2
Sample Output:
3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Splendid matrices are square matrices with dimensions 2^n X 2^n filled in a particular manner. Splendid matrices for n=1, n=2 and n=3 are shown below: 

n=1
1 2
3 4

n=2 
1  2  5  6
3  4  7  8
9  10 13 14
11 12 15 16

n=3 
1  2  5  6  17 18 21 22 
3  4  7  8  19 20 23 24 
9  10 13 14 25 26 29 30 
11 12 15 16 27 28 31 32 
33 34 37 38 49 50 53 54 
35 36 39 40 51 52 55 56 
41 42 45 46 57 58 61 62 
43 44 47 48 59 60 63 64

You will be given q queries, each query being of either of the 2 types : 
Type 1 : 1 n k , for the splendid matrix M with dimensions 2^n X 2^n, what are the values of i and j such that M(i,j)=k , i.e the value k is present in which cell of the matrix M ? 
Type 2 : 2 n i j , for the splendid matrix M with dimensions 2^n X 2^n, what is the value of M(i,j) , i.e what value is present in the cell which lies in the i th row and j th column of the matrix M?
Input
First line consists of q denoting the number of queries. The next q lines contain either queries of type 1 (3 space separated integers 1 n k) or queries of type 2 (4 space separated integers 2 n i j ).
Output
q lines. The answer to queries of type 1 should contain 2 space separated integers i and j such that M(i,j)=k. The answer to queries of type 2 should contain a single integer denoting the value at M(i,j).
Constraints
1 < = q < = 10^5
1 < = n < = 15
1 < = k < = 2^2n 
1< = i , j < = 2^n

SAMPLE INPUT
6
1 1 3
2 1 1 2
1 2 14
2 2 4 3
2 3 5 3
1 3 29

SAMPLE OUTPUT
2 1
2
3 4
15
37
3 7

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given two $n \times m$ matrices containing integers. A sequence of integers is strictly increasing if each next number is greater than the previous one. A row is strictly increasing if all numbers from left to right are strictly increasing. A column is strictly increasing if all numbers from top to bottom are strictly increasing. A matrix is increasing if all rows are strictly increasing and all columns are strictly increasing. 

For example, the matrix $\begin{bmatrix} 9&10&11\\ 11&12&14\\ \end{bmatrix}$ is increasing because each individual row and column is strictly increasing. On the other hand, the matrix $\begin{bmatrix} 1&1\\ 2&3\\ \end{bmatrix}$ is not increasing because the first row is not strictly increasing.

Let a position in the $i$-th row (from top) and $j$-th column (from left) in a matrix be denoted as $(i, j)$. 

In one operation, you can choose any two numbers $i$ and $j$ and swap the number located in $(i, j)$ in the first matrix with the number in $(i, j)$ in the second matrix. In other words, you can swap two numbers in different matrices if they are located in the corresponding positions.

You would like to make both matrices increasing by performing some number of operations (possibly none). Determine if it is possible to do this. If it is, print "Possible", otherwise, print "Impossible".


-----Input-----

The first line contains two integers $n$ and $m$ ($1 \leq n,m \leq 50$) — the dimensions of each matrix.

Each of the next $n$ lines contains $m$ integers $a_{i1}, a_{i2}, \ldots, a_{im}$ ($1 \leq a_{ij} \leq 10^9$) — the number located in position $(i, j)$ in the first matrix.

Each of the next $n$ lines contains $m$ integers $b_{i1}, b_{i2}, \ldots, b_{im}$ ($1 \leq b_{ij} \leq 10^9$) — the number located in position $(i, j)$ in the second matrix.


-----Output-----

Print a string "Impossible" or "Possible".


-----Examples-----
Input
2 2
2 10
11 5
9 4
3 12

Output
Possible

Input
2 3
2 4 5
4 5 6
3 6 7
8 10 11

Output
Possible

Input
3 2
1 3
2 4
5 10
3 1
3 6
4 8

Output
Impossible



-----Note-----

The first example, we can do an operation on the top left and bottom right cells of the matrices. The resulting matrices will be $\begin{bmatrix} 9&10\\ 11&12\\ \end{bmatrix}$ and $\begin{bmatrix} 2&4\\ 3&5\\ \end{bmatrix}$.

In the second example, we don't need to do any operations.

In the third example, no matter what we swap, we can't fix the first row to be strictly increasing in both matrices.

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