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 even_odd_count(num):
    """Given an integer. return a tuple that has the number of even and odd digits respectively.

     Example:
        even_odd_count(-12) ==> (1, 1)
        even_odd_count(123) ==> (1, 2)
    """

Response:

Output:
    even_count = 0
    odd_count = 0
    for i in str(abs(num)):
        if int(i)%2==0:
            even_count +=1
        else:
            odd_count +=1
    return (even_count, odd_count)


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 int_to_mini_roman(number):
    """
    Given a positive integer, obtain its roman numeral equivalent as a string,
    and return it in lowercase.
    Restrictions: 1 <= num <= 1000

    Examples:
    >>> int_to_mini_roman(19) == 'xix'
    >>> int_to_mini_roman(152) == 'clii'
    >>> int_to_mini_roman(426) == 'cdxxvi'
    """

Response:

Output:
    num = [1, 4, 5, 9, 10, 40, 50, 90,
           100, 400, 500, 900, 1000]
    sym = ["I", "IV", "V", "IX", "X", "XL",
           "L", "XC", "C", "CD", "D", "CM", "M"]
    i = 12
    res = ''
    while number:
        div = number // num[i]
        number %= num[i]
        while div:
            res += sym[i]
            div -= 1
        i -= 1
    return res.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.

def right_angle_triangle(a, b, c):
    '''
    Given the lengths of the three sides of a triangle. Return True if the three
    sides form a right-angled triangle, False otherwise.
    A right-angled triangle is a triangle in which one angle is right angle or
    90 degree.
    Example:
    right_angle_triangle(3, 4, 5) == True
    right_angle_triangle(1, 2, 3) == False
    '''

Response:

Output: return a*a == b*b + c*c or b*b == a*a + c*c or c*c == a*a + b*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.

def find_max(words):
    """Write a function that accepts a list of strings.
    The list contains different words. Return the word with maximum number
    of unique characters. If multiple strings have maximum number of unique
    characters, return the one which comes first in lexicographical order.

    find_max(["name", "of", "string"]) == "string"
    find_max(["name", "enam", "game"]) == "enam"
    find_max(["aaaaaaa", "bb" ,"cc"]) == ""aaaaaaa"
    """

Response:

Output: return sorted(words, key = lambda x: (-len(set(x)), x))[0]


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 eat(number, need, remaining):
    """
    You're a hungry rabbit, and you already have eaten a certain number of carrots,
    but now you need to eat more carrots to complete the day's meals.
    you should return an array of [ total number of eaten carrots after your meals,
                                    the number of carrots left after your meals ]
    if there are not enough remaining carrots, you will eat all remaining carrots, but will still be hungry.

    Example:
    * eat(5, 6, 10) -> [11, 4]
    * eat(4, 8, 9) -> [12, 1]
    * eat(1, 10, 10) -> [11, 0]
    * eat(2, 11, 5) -> [7, 0]

    Variables:
    @number : integer
        the number of carrots that you have eaten.
    @need : integer
        the number of carrots that you need to eat.
    @remaining : integer
        the number of remaining carrots thet exist in stock

    Constrain:
    * 0 <= number <= 1000
    * 0 <= need <= 1000
    * 0 <= remaining <= 1000

    Have fun :)
    """

Response:

Output:
    if(need <= remaining):
        return [ number + need , remaining-need ]
    else:
        return [ number + remaining , 0]


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 do_algebra(operator, operand):
    """
    Given two lists operator, and operand. The first list has basic algebra operations, and
    the second list is a list of integers. Use the two given lists to build the algebric
    expression and return the evaluation of this expression.

    The basic algebra operations:
    Addition ( + )
    Subtraction ( - )
    Multiplication ( * )
    Floor division ( // )
    Exponentiation ( ** )

    Example:
    operator['+', '*', '-']
    array = [2, 3, 4, 5]
    result = 2 + 3 * 4 - 5
    => result = 9

    Note:
        The length of operator list is equal to the length of operand list minus one.
        Operand is a list of of non-negative integers.
        Operator list has at least one operator, and operand list has at least two operands.

    """

Response:

Output:
    expression = str(operand[0])
    for oprt, oprn in zip(operator, operand[1:]):
        expression+= oprt + str(oprn)
    return eval(expression)


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 solve(s):
    """You are given a string s.
    if s[i] is a letter, reverse its case from lower to upper or vise versa,
    otherwise keep it as it is.
    If the string contains no letters, reverse the string.
    The function should return the resulted string.
    Examples
    solve("1234") = "4321"
    solve("ab") = "AB"
    solve("#a@C") = "#A@c"
    """

Response:

Output:
    flg = 0
    idx = 0
    new_str = list(s)
    for i in s:
        if i.isalpha():
            new_str[idx] = i.swapcase()
            flg = 1
        idx += 1
    s = ""
    for i in new_str:
        s += i
    if flg == 0:
        return s[len(s)::-1]
    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 string_to_md5(text):
    """
    Given a string 'text', return its md5 hash equivalent string.
    If 'text' is an empty string, return None.

    >>> string_to_md5('Hello world') == '3e25960a79dbc69b674cd4ec67a72c62'
    """

Response:

Output:
    import hashlib
    return hashlib.md5(text.encode('ascii')).hexdigest() if text else None


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 generate_integers(a, b):
    """
    Given two positive integers a and b, return the even digits between a
    and b, in ascending order.

    For example:
    generate_integers(2, 8) => [2, 4, 6, 8]
    generate_integers(8, 2) => [2, 4, 6, 8]
    generate_integers(10, 14) => []
    """

Response:

Output:
    lower = max(2, min(a, b))
    upper = min(8, max(a, b))

    return [i for i in range(lower, upper+1) if i % 2 == 0]