apaz/codeforces-genesys huggingface dataset:
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 5.0 seconds
Memory limit: 512.0 MB

# Problem
You are given a string $$$s$$$ of length $$$n$$$, consisting of lowercase Latin letters.

You are allowed to replace at most one character in the string with an arbitrary lowercase Latin letter.

Print the lexicographically minimal string that can be obtained from the original string and contains the maximum number of palindromes as substrings. Note that if a palindrome appears more than once as a substring, it is counted the same number of times it appears.

The string $$$a$$$ is lexicographically smaller than the string $$$b$$$ if and only if one of the following holds:

- $$$a$$$ is a prefix of $$$b$$$, but $$$a \ne b$$$;
- in the first position where $$$a$$$ and $$$b$$$ are different, the string $$$a$$$ contains a letter that appears earlier in the alphabet than the corresponding letter in $$$b$$$.

## Input Format
The first line contains one integer $$$n$$$ ($$$1 \leq n \leq 3 \cdot 10^5$$$) — the number of characters in the string.

The second line contains the string $$$s$$$ itself, consisting of exactly $$$n$$$ lowercase Latin letters.

## Output Format
In the first line, print one integer — the maximum number of palindromic substrings that can be obtained using the operation described in the statement at most once.

In the second line, print the string that can be obtained from $$$s$$$ and has the maximum possible number of palindromic substrings. If there are multiple answers, print the lexicographically smallest one.

## Examples
```input
5
aabaa
```
```output
15
aaaaa
```
-----
```input
5
aaaaa
```
```output
15
aaaaa
```
-----
```input
4
awoo
```
```output
7
aooo
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
You are given an integer $$$n$$$ and three strings $$$a, b, c$$$, each consisting of $$$n$$$ lowercase Latin letters.

Let a template be a string $$$t$$$ consisting of $$$n$$$ lowercase and/or uppercase Latin letters. The string $$$s$$$ matches the template $$$t$$$ if the following conditions hold for all $$$i$$$ from $$$1$$$ to $$$n$$$:

- if the $$$i$$$-th letter of the template is lowercase, then $$$s_i$$$ must be the same as $$$t_i$$$;
- if the $$$i$$$-th letter of the template is uppercase, then $$$s_i$$$ must be different from the lowercase version of $$$t_i$$$. For example, if there is a letter 'A' in the template, you cannot use the letter 'a' in the corresponding position of the string.

Accordingly, the string doesn't match the template if the condition doesn't hold for at least one $$$i$$$.

Determine whether there exists a template $$$t$$$ such that the strings $$$a$$$ and $$$b$$$ match it, while the string $$$c$$$ does not.

## Input Format
The first line contains an integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 20$$$) — the length of the given strings.

The next three lines contain the strings $$$a, b$$$ and $$$c$$$. Each string consists of exactly $$$n$$$ lowercase Latin letters.

## Output Format
For each testcase, print "YES" if there exists a template $$$t$$$ such that the strings $$$a$$$ and $$$b$$$ match it, while the string $$$c$$$ does not. Otherwise, print "NO".

## Examples
```input
4
1
a
b
c
2
aa
bb
aa
10
mathforces
luckforces
adhoccoder
3
acc
abd
abc
```
```output
YES
NO
YES
NO
```

## Note
In the first test case, you can use the template "C". The first letter of strings $$$a$$$ and $$$b$$$ differ from 'c', so they match the template. The first letter of string $$$c$$$ equals 'c', so it doesn't match.

In the third test case, you can use the template "CODEforces".

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Let's recall that an increasing subsequence of the array $$$a$$$ is a sequence that can be obtained from it by removing some elements without changing the order of the remaining elements, and the remaining elements are strictly increasing (i. e $$$a_{b_1} < a_{b_2} < \dots < a_{b_k}$$$ and $$$b_1 < b_2 < \dots < b_k$$$). Note that an empty subsequence is also increasing.

You are given a positive integer $$$X$$$. Your task is to find an array of integers of length at most $$$200$$$, such that it has exactly $$$X$$$ increasing subsequences, or report that there is no such array. If there are several answers, you can print any of them.

If two subsequences consist of the same elements, but correspond to different positions in the array, they are considered different (for example, the array $$$[2, 2]$$$ has two different subsequences equal to $$$[2]$$$).

## Input Format
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The only line of each test case contains a single integer $$$X$$$ ($$$2 \le X \le 10^{18}$$$).

## Output Format
For each query, print the answer to it. If it is impossible to find the required array, print -1 on the first line. Otherwise, print a positive integer $$$n$$$ on the first line — the length of the array. On the second line, print $$$n$$$ integers — the required array itself. If there are several answers, you can print any of them. All elements of the array should be in the range $$$[-10^9; 10^9]$$$.

## Examples
```input
4
2
5
13
37
```
```output
1
0
3
0 1 0
5
2 2 3 4 2
7
-1 -1 0 0 2 3 -1
```

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Given an array $$$a$$$ of $$$n$$$ elements, find the maximum value of the expression:

$$$$$$|a_i - a_j| + |a_j - a_k| + |a_k - a_l| + |a_l - a_i|$$$$$$

where $$$i$$$, $$$j$$$, $$$k$$$, and $$$l$$$ are four distinct indices of the array $$$a$$$, with $$$1 \le i, j, k, l \le n$$$.

Here $$$|x|$$$ denotes the absolute value of $$$x$$$.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$4 \le n \le 100$$$) — the length of the given array.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^6 \le a_i \le 10^6$$$).

## Output Format
For each test case, print a single integer — the maximum value.

## Examples
```input
5
4
1 1 1 1
5
1 1 2 2 3
8
5 1 3 2 -3 -1 10 3
4
3 3 1 1
4
1 2 2 -1
```
```output
0
6
38
8
8
```

## Note
In the first test case, for any selection of $$$i$$$, $$$j$$$, $$$k$$$, $$$l$$$, the answer will be $$$0$$$. For example, $$$|a_1 - a_2| + |a_2 - a_3| + |a_3 - a_4| + |a_4 - a_1| = |1 - 1| + |1 - 1| + |1 - 1| + |1 - 1| = 0 + 0 + 0 + 0 = 0$$$.

In the second test case, for $$$i = 1$$$, $$$j = 3$$$, $$$k = 2$$$, and $$$l = 5$$$, the answer will be $$$6$$$. $$$|a_1 - a_3| + |a_3 - a_2| + |a_2 - a_5| + |a_5 - a_1| = |1 - 2| + |2 - 1| + |1 - 3| + |3 - 1| = 1 + 1 + 2 + 2 = 6$$$.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
You have $$$5$$$ different types of coins, each with a value equal to one of the first $$$5$$$ triangular numbers: $$$1$$$, $$$3$$$, $$$6$$$, $$$10$$$, and $$$15$$$. These coin types are available in abundance. Your goal is to find the minimum number of these coins required such that their total value sums up to exactly $$$n$$$.

We can show that the answer always exists.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 10^9$$$) — the target value.

## Output Format
For each test case, output a single number — the minimum number of coins required.

## Examples
```input
14
1
2
3
5
7
11
12
14
16
17
18
20
98
402931328
```
```output
1
2
1
3
2
2
2
3
2
3
2
2
8
26862090
```

## Note
In the first test case, for $$$n = 1$$$, the answer is $$$1$$$ since only one $$$1$$$ value coin is sufficient. $$$1 = 1 \cdot 1$$$.

In the fourth test case, for $$$n = 5$$$, the answer is $$$3$$$, which can be achieved using two $$$1$$$ value coins and one $$$3$$$ value coin. $$$5 = 2 \cdot 1 + 1 \cdot 3$$$.

In the seventh test case, for $$$n = 12$$$, the answer is $$$2$$$, which can be achieved using two $$$6$$$ value coins.

In the ninth test case, for $$$n = 16$$$, the answer is $$$2$$$, which can be achieved using one $$$1$$$ value coin and one $$$15$$$ value coin or using one $$$10$$$ value coin and one $$$6$$$ value coin. $$$16 = 1 \cdot 1 + 1 \cdot 15 = 1 \cdot 6 + 1 \cdot 10$$$.

Now solve the problem and return the code.