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 any_int(x, y, z):
    '''
    Create a function that takes 3 numbers.
    Returns true if one of the numbers is equal to the sum of the other two, and all numbers are integers.
    Returns false in any other cases.

    Examples
    any_int(5, 2, 7) ➞ True

    any_int(3, 2, 2) ➞ False

    any_int(3, -2, 1) ➞ True

    any_int(3.6, -2.2, 2) ➞ False

    '''

Response:

Output:
    if isinstance(x,int) and isinstance(y,int) and isinstance(z,int):
        if (x+y==z) or (x+z==y) or (y+z==x):
            return True
        return False
    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.

def encode(message):
    """
    Write a function that takes a message, and encodes in such a
    way that it swaps case of all letters, replaces all vowels in
    the message with the letter that appears 2 places ahead of that
    vowel in the english alphabet.
    Assume only letters.

    Examples:
    >>> encode('test')
    'TGST'
    >>> encode('This is a message')
    'tHKS KS C MGSSCGG'
    """

Response:

Output:
    vowels = "aeiouAEIOU"
    vowels_replace = dict([(i, chr(ord(i) + 2)) for i in vowels])
    message = message.swapcase()
    return ''.join([vowels_replace[i] if i in vowels else i for i in message])


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 skjkasdkd(lst):
    """You are given a list of integers.
    You need to find the largest prime value and return the sum of its digits.

    Examples:
    For lst = [0,3,2,1,3,5,7,4,5,5,5,2,181,32,4,32,3,2,32,324,4,3] the output should be 10
    For lst = [1,0,1,8,2,4597,2,1,3,40,1,2,1,2,4,2,5,1] the output should be 25
    For lst = [1,3,1,32,5107,34,83278,109,163,23,2323,32,30,1,9,3] the output should be 13
    For lst = [0,724,32,71,99,32,6,0,5,91,83,0,5,6] the output should be 11
    For lst = [0,81,12,3,1,21] the output should be 3
    For lst = [0,8,1,2,1,7] the output should be 7
    """

Response:

Output:
    def isPrime(n):
        for i in range(2,int(n**0.5)+1):
            if n%i==0:
                return False

        return True
    maxx = 0
    i = 0
    while i < len(lst):
        if(lst[i] > maxx and isPrime(lst[i])):
            maxx = lst[i]
        i+=1
    result = sum(int(digit) for digit in str(maxx))
    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 check_dict_case(dict):
    """
    Given a dictionary, return True if all keys are strings in lower
    case or all keys are strings in upper case, else return False.
    The function should return False is the given dictionary is empty.
    Examples:
    check_dict_case({"a":"apple", "b":"banana"}) should return True.
    check_dict_case({"a":"apple", "A":"banana", "B":"banana"}) should return False.
    check_dict_case({"a":"apple", 8:"banana", "a":"apple"}) should return False.
    check_dict_case({"Name":"John", "Age":"36", "City":"Houston"}) should return False.
    check_dict_case({"STATE":"NC", "ZIP":"12345" }) should return True.
    """

Response:

Output:
    if len(dict.keys()) == 0:
        return False
    else:
        state = "start"
        for key in dict.keys():

            if isinstance(key, str) == False:
                state = "mixed"
                break
            if state == "start":
                if key.isupper():
                    state = "upper"
                elif key.islower():
                    state = "lower"
                else:
                    break
            elif (state == "upper" and not key.isupper()) or (state == "lower" and not key.islower()):
                    state = "mixed"
                    break
            else:
                break
        return state == "upper" or state == "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 count_up_to(n):
    """Implement a function that takes an non-negative integer and returns an array of the first n
    integers that are prime numbers and less than n.
    for example:
    count_up_to(5) => [2,3]
    count_up_to(11) => [2,3,5,7]
    count_up_to(0) => []
    count_up_to(20) => [2,3,5,7,11,13,17,19]
    count_up_to(1) => []
    count_up_to(18) => [2,3,5,7,11,13,17]
    """

Response:

Output:
    primes = []
    for i in range(2, n):
        is_prime = True
        for j in range(2, i):
            if i % j == 0:
                is_prime = False
                break
        if is_prime:
            primes.append(i)
    return primes


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 multiply(a, b):
    """Complete the function that takes two integers and returns
    the product of their unit digits.
    Assume the input is always valid.
    Examples:
    multiply(148, 412) should return 16.
    multiply(19, 28) should return 72.
    multiply(2020, 1851) should return 0.
    multiply(14,-15) should return 20.
    """

Response:

Output: return abs(a % 10) * abs(b % 10)


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_upper(s):
    """
    Given a string s, count the number of uppercase vowels in even indices.

    For example:
    count_upper('aBCdEf') returns 1
    count_upper('abcdefg') returns 0
    count_upper('dBBE') returns 0
    """

Response:

Output:
    count = 0
    for i in range(0,len(s),2):
        if s[i] in "AEIOU":
            count += 1
    return 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 closest_integer(value):
    '''
    Create a function that takes a value (string) representing a number
    and returns the closest integer to it. If the number is equidistant
    from two integers, round it away from zero.

    Examples
    >>> closest_integer("10")
    10
    >>> closest_integer("15.3")
    15

    Note:
    Rounding away from zero means that if the given number is equidistant
    from two integers, the one you should return is the one that is the
    farthest from zero. For example closest_integer("14.5") should
    return 15 and closest_integer("-14.5") should return -15.
    '''

Response:

Output:
    from math import floor, ceil

    if value.count('.') == 1:
        # remove trailing zeros
        while (value[-1] == '0'):
            value = value[:-1]

    num = float(value)
    if value[-2:] == '.5':
        if num > 0:
            res = ceil(num)
        else:
            res = floor(num)
    elif len(value) > 0:
        res = int(round(num))
    else:
        res = 0

    return res


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 make_a_pile(n):
    """
    Given a positive integer n, you have to make a pile of n levels of stones.
    The first level has n stones.
    The number of stones in the next level is:
        - the next odd number if n is odd.
        - the next even number if n is even.
    Return the number of stones in each level in a list, where element at index
    i represents the number of stones in the level (i+1).

    Examples:
    >>> make_a_pile(3)
    [3, 5, 7]
    """

Response:

Output: return [n + 2*i for i in range(n)]


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 words_string(s):
    """
    You will be given a string of words separated by commas or spaces. Your task is
    to split the string into words and return an array of the words.

    For example:
    words_string("Hi, my name is John") == ["Hi", "my", "name", "is", "John"]
    words_string("One, two, three, four, five, six") == ["One", "two", "three", "four", "five", "six"]
    """

Response:

Output:
    if not s:
        return []

    s_list = []

    for letter in s:
        if letter == ',':
            s_list.append(' ')
        else:
            s_list.append(letter)

    s_list = "".join(s_list)
    return s_list.split()


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 choose_num(x, y):
    """This function takes two positive numbers x and y and returns the
    biggest even integer number that is in the range [x, y] inclusive. If
    there's no such number, then the function should return -1.

    For example:
    choose_num(12, 15) = 14
    choose_num(13, 12) = -1
    """

Response:

Output:
    if x > y:
        return -1
    if y % 2 == 0:
        return y
    if x == y:
        return -1
    return y - 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 rounded_avg(n, m):
    """You are given two positive integers n and m, and your task is to compute the
    average of the integers from n through m (including n and m).
    Round the answer to the nearest integer and convert that to binary.
    If n is greater than m, return -1.
    Example:
    rounded_avg(1, 5) => "0b11"
    rounded_avg(7, 5) => -1
    rounded_avg(10, 20) => "0b1111"
    rounded_avg(20, 33) => "0b11010"
    """

Response:

Output:
    if m < n:
        return -1
    summation = 0
    for i in range(n, m+1):
        summation += i
    return bin(round(summation/(m - 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 unique_digits(x):
    """Given a list of positive integers x. return a sorted list of all
    elements that hasn't any even digit.

    Note: Returned list should be sorted in increasing order.

    For example:
    >>> unique_digits([15, 33, 1422, 1])
    [1, 15, 33]
    >>> unique_digits([152, 323, 1422, 10])
    []
    """

Response:

Output:
    odd_digit_elements = []
    for i in x:
        if all (int(c) % 2 == 1 for c in str(i)):
            odd_digit_elements.append(i)
    return sorted(odd_digit_elements)


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 by_length(arr):
    """
    Given an array of integers, sort the integers that are between 1 and 9 inclusive,
    reverse the resulting array, and then replace each digit by its corresponding name from
    "One", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine".

    For example:
      arr = [2, 1, 1, 4, 5, 8, 2, 3]
            -> sort arr -> [1, 1, 2, 2, 3, 4, 5, 8]
            -> reverse arr -> [8, 5, 4, 3, 2, 2, 1, 1]
      return ["Eight", "Five", "Four", "Three", "Two", "Two", "One", "One"]

      If the array is empty, return an empty array:
      arr = []
      return []

      If the array has any strange number ignore it:
      arr = [1, -1 , 55]
            -> sort arr -> [-1, 1, 55]
            -> reverse arr -> [55, 1, -1]
      return = ['One']
    """

Response:

Output:
    dic = {
        1: "One",
        2: "Two",
        3: "Three",
        4: "Four",
        5: "Five",
        6: "Six",
        7: "Seven",
        8: "Eight",
        9: "Nine",
    }
    sorted_arr = sorted(arr, reverse=True)
    new_arr = []
    for var in sorted_arr:
        try:
            new_arr.append(dic[var])
        except:
            pass
    return new_arr


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 f(n):
    """ Implement the function f that takes n as a parameter,
    and returns a list of size n, such that the value of the element at index i is the factorial of i if i is even
    or the sum of numbers from 1 to i otherwise.
    i starts from 1.
    the factorial of i is the multiplication of the numbers from 1 to i (1 * 2 * ... * i).
    Example:
    f(5) == [1, 2, 6, 24, 15]
    """

Response:

Output:
    ret = []
    for i in range(1,n+1):
        if i%2 == 0:
            x = 1
            for j in range(1,i+1): x *= j
            ret += [x]
        else:
            x = 0
            for j in range(1,i+1): x += j
            ret += [x]
    return ret


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_palindrome(n):
    """
    Given a positive integer n, return a tuple that has the number of even and odd
    integer palindromes that fall within the range(1, n), inclusive.

    Example 1:

        Input: 3
        Output: (1, 2)
        Explanation:
        Integer palindrome are 1, 2, 3. one of them is even, and two of them are odd.

    Example 2:

        Input: 12
        Output: (4, 6)
        Explanation:
        Integer palindrome are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11. four of them are even, and 6 of them are odd.

    Note:
        1. 1 <= n <= 10^3
        2. returned tuple has the number of even and odd integer palindromes respectively.
    """

Response:

Output:
    def is_palindrome(n):
        return str(n) == str(n)[::-1]

    even_palindrome_count = 0
    odd_palindrome_count = 0

    for i in range(1, n+1):
        if i%2 == 1 and is_palindrome(i):
                odd_palindrome_count += 1
        elif i%2 == 0 and is_palindrome(i):
            even_palindrome_count += 1
    return (even_palindrome_count, odd_palindrome_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 count_nums(arr):
    """
    Write a function count_nums which takes an array of integers and returns
    the number of elements which has a sum of digits > 0.
    If a number is negative, then its first signed digit will be negative:
    e.g. -123 has signed digits -1, 2, and 3.
    >>> count_nums([]) == 0
    >>> count_nums([-1, 11, -11]) == 1
    >>> count_nums([1, 1, 2]) == 3
    """

Response:

Output:
    def digits_sum(n):
        neg = 1
        if n < 0: n, neg = -1 * n, -1
        n = [int(i) for i in str(n)]
        n[0] = n[0] * neg
        return sum(n)
    return len(list(filter(lambda x: x > 0, [digits_sum(i) for i in arr])))


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 move_one_ball(arr):
    """We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N].The
    numbers in the array will be randomly ordered. Your task is to determine if
    it is possible to get an array sorted in non-decreasing order by performing
    the following operation on the given array:
        You are allowed to perform right shift operation any number of times.

    One right shift operation means shifting all elements of the array by one
    position in the right direction. The last element of the array will be moved to
    the starting position in the array i.e. 0th index.

    If it is possible to obtain the sorted array by performing the above operation
    then return True else return False.
    If the given array is empty then return True.

    Note: The given list is guaranteed to have unique elements.

    For Example:

    move_one_ball([3, 4, 5, 1, 2])==>True
    Explanation: By performin 2 right shift operations, non-decreasing order can
                 be achieved for the given array.
    move_one_ball([3, 5, 4, 1, 2])==>False
    Explanation:It is not possible to get non-decreasing order for the given
                array by performing any number of right shift operations.

    """

Response:

Output:
    if len(arr)==0:
      return True
    sorted_array=sorted(arr)
    my_arr=[]

    min_value=min(arr)
    min_index=arr.index(min_value)
    my_arr=arr[min_index:]+arr[0:min_index]
    for i in range(len(arr)):
      if my_arr[i]!=sorted_array[i]:
        return False
    return True


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 exchange(lst1, lst2):
    """In this problem, you will implement a function that takes two lists of numbers,
    and determines whether it is possible to perform an exchange of elements
    between them to make lst1 a list of only even numbers.
    There is no limit on the number of exchanged elements between lst1 and lst2.
    If it is possible to exchange elements between the lst1 and lst2 to make
    all the elements of lst1 to be even, return "YES".
    Otherwise, return "NO".
    For example:
    exchange([1, 2, 3, 4], [1, 2, 3, 4]) => "YES"
    exchange([1, 2, 3, 4], [1, 5, 3, 4]) => "NO"
    It is assumed that the input lists will be non-empty.
    """

Response:

Output:
    odd = 0
    even = 0
    for i in lst1:
        if i%2 == 1:
            odd += 1
    for i in lst2:
        if i%2 == 0:
            even += 1
    if even >= odd:
        return "YES"
    return "NO"


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 histogram(test):
    """Given a string representing a space separated lowercase letters, return a dictionary
    of the letter with the most repetition and containing the corresponding count.
    If several letters have the same occurrence, return all of them.

    Example:
    histogram('a b c') == {'a': 1, 'b': 1, 'c': 1}
    histogram('a b b a') == {'a': 2, 'b': 2}
    histogram('a b c a b') == {'a': 2, 'b': 2}
    histogram('b b b b a') == {'b': 4}
    histogram('') == {}

    """

Response:

Output:
    dict1={}
    list1=test.split(" ")
    t=0

    for i in list1:
        if(list1.count(i)>t) and i!='':
            t=list1.count(i)
    if t>0:
        for i in list1:
            if(list1.count(i)==t):

                dict1[i]=t
    return dict1


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 reverse_delete(s,c):
    """Task
    We are given two strings s and c, you have to deleted all the characters in s that are equal to any character in c
    then check if the result string is palindrome.
    A string is called palindrome if it reads the same backward as forward.
    You should return a tuple containing the result string and True/False for the check.
    Example
    For s = "abcde", c = "ae", the result should be ('bcd',False)
    For s = "abcdef", c = "b"  the result should be ('acdef',False)
    For s = "abcdedcba", c = "ab", the result should be ('cdedc',True)
    """

Response:

Output:
    s = ''.join([char for char in s if char not in c])
    return (s,s[::-1] == s)