Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def below_zero(operations: List[int]) -> bool:
    """ You're given a list of deposit and withdrawal operations on a bank account that starts with
    zero balance. Your task is to detect if at any point the balance of account fallls below zero, and
    at that point function should return True. Otherwise it should return False.
    >>> below_zero([1, 2, 3])
    False
    >>> below_zero([1, 2, -4, 5])
    True
    """

Response:

Output:
    balance = 0

    for op in operations:
        balance += op
        if balance < 0:
            return True

    return False


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def mean_absolute_deviation(numbers: List[float]) -> float:
    """ For a given list of input numbers, calculate Mean Absolute Deviation
    around the mean of this dataset.
    Mean Absolute Deviation is the average absolute difference between each
    element and a centerpoint (mean in this case):
    MAD = average | x - x_mean |
    >>> mean_absolute_deviation([1.0, 2.0, 3.0, 4.0])
    1.0
    """

Response:

Output:
    mean = sum(numbers) / len(numbers)
    return sum(abs(x - mean) for x in numbers) / len(numbers)


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def intersperse(numbers: List[int], delimeter: int) -> List[int]:
    """ Insert a number 'delimeter' between every two consecutive elements of input list `numbers'
    >>> intersperse([], 4)
    []
    >>> intersperse([1, 2, 3], 4)
    [1, 4, 2, 4, 3]
    """

Response:

Output:
    if not numbers:
        return []

    result = []

    for n in numbers[:-1]:
        result.append(n)
        result.append(delimeter)

    result.append(numbers[-1])

    return result


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def parse_nested_parens(paren_string: str) -> List[int]:
    """ Input to this function is a string represented multiple groups for nested parentheses separated by spaces.
    For each of the group, output the deepest level of nesting of parentheses.
    E.g. (()()) has maximum two levels of nesting while ((())) has three.

    >>> parse_nested_parens('(()()) ((())) () ((())()())')
    [2, 3, 1, 3]
    """

Response:

Output:
    def parse_paren_group(s):
        depth = 0
        max_depth = 0
        for c in s:
            if c == '(':
                depth += 1
                max_depth = max(depth, max_depth)
            else:
                depth -= 1

        return max_depth

    return [parse_paren_group(x) for x in paren_string.split(' ') if x]


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def filter_by_substring(strings: List[str], substring: str) -> List[str]:
    """ Filter an input list of strings only for ones that contain given substring
    >>> filter_by_substring([], 'a')
    []
    >>> filter_by_substring(['abc', 'bacd', 'cde', 'array'], 'a')
    ['abc', 'bacd', 'array']
    """

Response:

Output: return [x for x in strings if substring in x]


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List, Tuple

def sum_product(numbers: List[int]) -> Tuple[int, int]:
    """ For a given list of integers, return a tuple consisting of a sum and a product of all the integers in a list.
    Empty sum should be equal to 0 and empty product should be equal to 1.
    >>> sum_product([])
    (0, 1)
    >>> sum_product([1, 2, 3, 4])
    (10, 24)
    """

Response:

Output:
    sum_value = 0
    prod_value = 1

    for n in numbers:
        sum_value += n
        prod_value *= n
    return sum_value, prod_value


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List, Tuple

def rolling_max(numbers: List[int]) -> List[int]:
    """ From a given list of integers, generate a list of rolling maximum element found until given moment
    in the sequence.
    >>> rolling_max([1, 2, 3, 2, 3, 4, 2])
    [1, 2, 3, 3, 3, 4, 4]
    """

Response:

Output:
    running_max = None
    result = []

    for n in numbers:
        if running_max is None:
            running_max = n
        else:
            running_max = max(running_max, n)

        result.append(running_max)

    return result


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.

def is_palindrome(string: str) -> bool:
    """ Test if given string is a palindrome """
    return string == string[::-1]

def make_palindrome(string: str) -> str:
    """ Find the shortest palindrome that begins with a supplied string.
    Algorithm idea is simple:
    - Find the longest postfix of supplied string that is a palindrome.
    - Append to the end of the string reverse of a string prefix that comes before the palindromic suffix.
    >>> make_palindrome('')
    ''
    >>> make_palindrome('cat')
    'catac'
    >>> make_palindrome('cata')
    'catac'
    """

Response:

Output:
    if not string:
        return ''

    beginning_of_suffix = 0

    while not is_palindrome(string[beginning_of_suffix:]):
        beginning_of_suffix += 1

    return string + string[:beginning_of_suffix][::-1]


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def string_xor(a: str, b: str) -> str:
    """ Input are two strings a and b consisting only of 1s and 0s.
    Perform binary XOR on these inputs and return result also as a string.
    >>> string_xor('010', '110')
    '100'
    """

Response:

Output:
    def xor(i, j):
        if i == j:
            return '0'
        else:
            return '1'

    return ''.join(xor(x, y) for x, y in zip(a, b))


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List, Optional

def longest(strings: List[str]) -> Optional[str]:
    """ Out of list of strings, return the longest one. Return the first one in case of multiple
    strings of the same length. Return None in case the input list is empty.
    >>> longest([])

    >>> longest(['a', 'b', 'c'])
    'a'
    >>> longest(['a', 'bb', 'ccc'])
    'ccc'
    """

Response:

Output:
    if not strings:
        return None

    maxlen = max(len(x) for x in strings)
    for s in strings:
        if len(s) == maxlen:
            return s


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.

def greatest_common_divisor(a: int, b: int) -> int:
    """ Return a greatest common divisor of two integers a and b
    >>> greatest_common_divisor(3, 5)
    1
    >>> greatest_common_divisor(25, 15)
    5
    """

Response:

Output:
    while b:
        a, b = b, a % b
    return a


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def all_prefixes(string: str) -> List[str]:
    """ Return list of all prefixes from shortest to longest of the input string
    >>> all_prefixes('abc')
    ['a', 'ab', 'abc']
    """

Response:

Output:
    result = []

    for i in range(len(string)):
        result.append(string[:i+1])
    return result


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.

def string_sequence(n: int) -> str:
    """ Return a string containing space-delimited numbers starting from 0 upto n inclusive.
    >>> string_sequence(0)
    '0'
    >>> string_sequence(5)
    '0 1 2 3 4 5'
    """

Response:

Output: return ' '.join([str(x) for x in range(n + 1)])


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.

def count_distinct_characters(string: str) -> int:
    """ Given a string, find out how many distinct characters (regardless of case) does it consist of
    >>> count_distinct_characters('xyzXYZ')
    3
    >>> count_distinct_characters('Jerry')
    4
    """

Response:

Output: return len(set(string.lower()))


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def parse_music(music_string: str) -> List[int]:
    """ Input to this function is a string representing musical notes in a special ASCII format.
    Your task is to parse this string and return list of integers corresponding to how many beats does each
    not last.

    Here is a legend:
    'o' - whole note, lasts four beats
    'o|' - half note, lasts two beats
    '.|' - quater note, lasts one beat

    >>> parse_music('o o| .| o| o| .| .| .| .| o o')
    [4, 2, 1, 2, 2, 1, 1, 1, 1, 4, 4]
    """

Response:

Output:
    note_map = {'o': 4, 'o|': 2, '.|': 1}
    return [note_map[x] for x in music_string.split(' ') if x]


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.

def how_many_times(string: str, substring: str) -> int:
    """ Find how many times a given substring can be found in the original string. Count overlaping cases.
    >>> how_many_times('', 'a')
    0
    >>> how_many_times('aaa', 'a')
    3
    >>> how_many_times('aaaa', 'aa')
    3
    """

Response:

Output:
    times = 0

    for i in range(len(string) - len(substring) + 1):
        if string[i:i+len(substring)] == substring:
            times += 1

    return times


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def sort_numbers(numbers: str) -> str:
    """ Input is a space-delimited string of numberals from 'zero' to 'nine'.
    Valid choices are 'zero', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight' and 'nine'.
    Return the string with numbers sorted from smallest to largest
    >>> sort_numbers('three one five')
    'one three five'
    """

Response:

Output:
    value_map = {
        'zero': 0,
        'one': 1,
        'two': 2,
        'three': 3,
        'four': 4,
        'five': 5,
        'six': 6,
        'seven': 7,
        'eight': 8,
        'nine': 9
    }
    return ' '.join(sorted([x for x in numbers.split(' ') if x], key=lambda x: value_map[x]))


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List, Tuple

def find_closest_elements(numbers: List[float]) -> Tuple[float, float]:
    """ From a supplied list of numbers (of length at least two) select and return two that are the closest to each
    other and return them in order (smaller number, larger number).
    >>> find_closest_elements([1.0, 2.0, 3.0, 4.0, 5.0, 2.2])
    (2.0, 2.2)
    >>> find_closest_elements([1.0, 2.0, 3.0, 4.0, 5.0, 2.0])
    (2.0, 2.0)
    """

Response:

Output:
    closest_pair = None
    distance = None

    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                if distance is None:
                    distance = abs(elem - elem2)
                    closest_pair = tuple(sorted([elem, elem2]))
                else:
                    new_distance = abs(elem - elem2)
                    if new_distance < distance:
                        distance = new_distance
                        closest_pair = tuple(sorted([elem, elem2]))

    return closest_pair


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List

def rescale_to_unit(numbers: List[float]) -> List[float]:
    """ Given list of numbers (of at least two elements), apply a linear transform to that list,
    such that the smallest number will become 0 and the largest will become 1
    >>> rescale_to_unit([1.0, 2.0, 3.0, 4.0, 5.0])
    [0.0, 0.25, 0.5, 0.75, 1.0]
    """

Response:

Output:
    min_number = min(numbers)
    max_number = max(numbers)
    return [(x - min_number) / (max_number - min_number) for x in numbers]


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.
from typing import List, Any

def filter_integers(values: List[Any]) -> List[int]:
    """ Filter given list of any python values only for integers
    >>> filter_integers(['a', 3.14, 5])
    [5]
    >>> filter_integers([1, 2, 3, 'abc', {}, []])
    [1, 2, 3]
    """

Response:

Output: return [x for x in values if isinstance(x, int)]


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.

def strlen(string: str) -> int:
    """ Return length of given string
    >>> strlen('')
    0
    >>> strlen('abc')
    3
    """

Response:

Output: return len(string)


Input:
Answer the following question. Break down your reasoning process into small steps. Each step should represent a single, minimal reasoning action, and each step must logically follow the previous one.
Use the following format for each step:
Step i: [Your reasoning process in one cohesive response]
After completing all the steps, conclude with:
Final Answer: \boxed{[Your final answer here without the unit or any additional text]} ####
Stop generation immediately after outputing the Final Answer.

The following are 3 examples:

Question: Complete the implementation of the function below.
from typing import List

def has_close_elements(numbers: List[float], threshold: float) -> bool:
    """ Check if in given list of numbers, are any two numbers closer to each other than
    given threshold.
    >>> has_close_elements([1.0, 2.0, 3.0], 0.5)
    False
    >>> has_close_elements([1.0, 2.8, 3.0, 4.0, 5.0, 2.0], 0.3)
    True
    """

Response:
Step 1: Use a nested loop to compare each number in the list with every other number.
Step 2: Calculate the absolute difference between each pair of distinct elements.
Step 3: Return True if any difference is less than the threshold; otherwise, return False after checking all pairs.
Final Answer: \boxed{
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False
} ####

Question: Complete the implementation of the function below.
from typing import List

def separate_paren_groups(paren_string: str) -> List[str]:
    """ Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
    separate those group into separate strings and return the list of those.
    Separate groups are balanced (each open brace is properly closed) and not nested within each other
    Ignore any spaces in the input string.
    >>> separate_paren_groups('( ) (( )) (( )( ))')
    ['()', '(())', '(()())']
    """

Response:
Step 1: Initialize a `result` list for groups, a `current_string` buffer, and a `current_depth` counter to track nesting levels.
Step 2: Iterate through the string, incrementing depth for `'('` and decrementing for `')'`, while appending brackets to the buffer (ignoring spaces).
Step 3: When `current_depth` returns to zero, a balanced group is complete; join the buffer into a string, add it to `result`, and reset the buffer.
Final Answer: \boxed{
    result = []
    current_string = []
    current_depth = 0

    for c in paren_string:
        if c == '(':
            current_depth += 1
            current_string.append(c)
        elif c == ')':
            current_depth -= 1
            current_string.append(c)

            if current_depth == 0:
                result.append(''.join(current_string))
                current_string.clear()

    return result
} ####

Question: Complete the implementation of the function below.

def truncate_number(number: float) -> float:
    """ Given a positive floating point number, it can be decomposed into
    and integer part (largest integer smaller than given number) and decimals
    (leftover part always smaller than 1).

    Return the decimal part of the number.
    >>> truncate_number(3.5)
    0.5
    """

Response:
Step 1: Use the modulo operator (`%`) with `1.0` to isolate the remainder after division by 1, which represents the decimal component.
Step 2: Alternatively, subtract the integer cast of the number (`int(number)`) from the original float to extract the leftover fractional part.
Final Answer: \boxed{
    return number % 1.0
} ####

Ensure that your response strictly follows the format to maintain clarity and consistency.
Question: Complete the implementation of the function below.

def largest_divisor(n: int) -> int:
    """ For a given number n, find the largest number that divides n evenly, smaller than n
    >>> largest_divisor(15)
    5
    """

Response:

Output:
    for i in reversed(range(n)):
        if n % i == 0:
            return i