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

The following are 3 examples:

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

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

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

    return False
} ####

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

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

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

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

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

    return result
} ####

Question: Complete the implementation of the function below.

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

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

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

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

def is_palindrome(text: str):
    """
    Checks if given string is a palindrome
    >>> is_palindrome('')
    True
    >>> is_palindrome('aba')
    True
    >>> is_palindrome('aaaaa')
    True
    >>> is_palindrome('zbcd')
    False
    """

Response:

Output:
    for i in range(len(text)):
        if text[i] != text[len(text) - 1 - 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 modp(n: int, p: int):
    """Return 2^n modulo p (be aware of numerics).
    >>> modp(3, 5)
    3
    >>> modp(1101, 101)
    2
    >>> modp(0, 101)
    1
    >>> modp(3, 11)
    8
    >>> modp(100, 101)
    1
    """

Response:

Output:
    ret = 1
    for i in range(n):
        ret = (2 * ret) % p
    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 encode_shift(s: str):
    """
    returns encoded string by shifting every character by 5 in the alphabet.
    """
    return "".join([chr(((ord(ch) + 5 - ord("a")) % 26) + ord("a")) for ch in s])

def decode_shift(s: str):
    """
    takes as input string encoded with encode_shift function. Returns decoded string.
    """

Response:

Output: return "".join([chr(((ord(ch) - 5 - ord("a")) % 26) + ord("a")) for ch in s])


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

The following are 3 examples:

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

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

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

    return False
} ####

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

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

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

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

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

    return result
} ####

Question: Complete the implementation of the function below.

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

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

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

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

def remove_vowels(text):
    """
    remove_vowels is a function that takes string and returns string without vowels.
    >>> remove_vowels('')
    ''
    >>> remove_vowels("abcdef\nghijklm")
    'bcdf\nghjklm'
    >>> remove_vowels('abcdef')
    'bcdf'
    >>> remove_vowels('aaaaa')
    ''
    >>> remove_vowels('aaBAA')
    'B'
    >>> remove_vowels('zbcd')
    'zbcd'
    """

Response:

Output: return "".join([s for s in text if s.lower() not in ["a", "e", "i", "o", "u"]])


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 below_threshold(l: list, t: int):
    """Return True if all numbers in the list l are below threshold t.
    >>> below_threshold([1, 2, 4, 10], 100)
    True
    >>> below_threshold([1, 20, 4, 10], 5)
    False
    """

Response:

Output:
    for e in l:
        if e >= t:
            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 add(x: int, y: int):
    """Add two numbers x and y
    >>> add(2, 3)
    5
    >>> add(5, 7)
    12
    """

Response:

Output: return x + y


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 same_chars(s0: str, s1: str):
    """
    Check if two words have the same characters.
    >>> same_chars('eabcdzzzz', 'dddzzzzzzzddeddabc')
    True
    >>> same_chars('abcd', 'dddddddabc')
    True
    >>> same_chars('dddddddabc', 'abcd')
    True
    >>> same_chars('eabcd', 'dddddddabc')
    False
    >>> same_chars('abcd', 'dddddddabce')
    False
    >>> same_chars('eabcdzzzz', 'dddzzzzzzzddddabc')
    False
    """

Response:

Output: return set(s0) == set(s1)


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 fib(n: int):
    """Return n-th Fibonacci number.
    >>> fib(10)
    55
    >>> fib(1)
    1
    >>> fib(8)
    21
    """

Response:

Output:
    if n == 0:
        return 0
    if n == 1:
        return 1
    return fib(n - 1) + fib(n - 2)


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 correct_bracketing(brackets: str):
    """ brackets is a string of "<" and ">".
    return True if every opening bracket has a corresponding closing bracket.

    >>> correct_bracketing("<")
    False
    >>> correct_bracketing("<>")
    True
    >>> correct_bracketing("<<><>>")
    True
    >>> correct_bracketing("><<>")
    False
    """

Response:

Output:
    depth = 0
    for b in brackets:
        if b == "<":
            depth += 1
        else:
            depth -= 1
        if depth < 0:
            return False
    return depth == 0


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

The following are 3 examples:

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

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

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

    return False
} ####

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

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

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

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

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

    return result
} ####

Question: Complete the implementation of the function below.

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

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

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

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

def monotonic(l: list):
    """Return True is list elements are monotonically increasing or decreasing.
    >>> monotonic([1, 2, 4, 20])
    True
    >>> monotonic([1, 20, 4, 10])
    False
    >>> monotonic([4, 1, 0, -10])
    True
    """

Response:

Output:
    if l == sorted(l) or l == sorted(l, reverse=True):
        return True
    return False


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

The following are 3 examples:

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

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

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

    return False
} ####

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

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

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

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

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

    return result
} ####

Question: Complete the implementation of the function below.

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

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

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

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

def common(l1: list, l2: list):
    """Return sorted unique common elements for two lists.
    >>> common([1, 4, 3, 34, 653, 2, 5], [5, 7, 1, 5, 9, 653, 121])
    [1, 5, 653]
    >>> common([5, 3, 2, 8], [3, 2])
    [2, 3]

    """

Response:

Output:
    ret = set()
    for e1 in l1:
        for e2 in l2:
            if e1 == e2:
                ret.add(e1)
    return sorted(list(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 largest_prime_factor(n: int):
    """Return the largest prime factor of n. Assume n > 1 and is not a prime.
    >>> largest_prime_factor(13195)
    29
    >>> largest_prime_factor(2048)
    2
    """

Response:

Output:
    def is_prime(k):
        if k < 2:
            return False
        for i in range(2, k - 1):
            if k % i == 0:
                return False
        return True
    largest = 1
    for j in range(2, n + 1):
        if n % j == 0 and is_prime(j):
            largest = max(largest, j)
    return largest


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 sum_to_n(n: int):
    """sum_to_n is a function that sums numbers from 1 to n.
    >>> sum_to_n(30)
    465
    >>> sum_to_n(100)
    5050
    >>> sum_to_n(5)
    15
    >>> sum_to_n(10)
    55
    >>> sum_to_n(1)
    1
    """

Response:

Output: return sum(range(n + 1))


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

The following are 3 examples:

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

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

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

    return False
} ####

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

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

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

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

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

    return result
} ####

Question: Complete the implementation of the function below.

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

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

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

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

def correct_bracketing(brackets: str):
    """ brackets is a string of "(" and ")".
    return True if every opening bracket has a corresponding closing bracket.

    >>> correct_bracketing("(")
    False
    >>> correct_bracketing("()")
    True
    >>> correct_bracketing("(()())")
    True
    >>> correct_bracketing(")(()")
    False
    """

Response:

Output:
    depth = 0
    for b in brackets:
        if b == "(":
            depth += 1
        else:
            depth -= 1
        if depth < 0:
            return False
    return depth == 0


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

The following are 3 examples:

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

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

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

    return False
} ####

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

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

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

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

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

    return result
} ####

Question: Complete the implementation of the function below.

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

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

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

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

def derivative(xs: list):
    """ xs represent coefficients of a polynomial.
    xs[0] + xs[1] * x + xs[2] * x^2 + ....
     Return derivative of this polynomial in the same form.
    >>> derivative([3, 1, 2, 4, 5])
    [1, 4, 12, 20]
    >>> derivative([1, 2, 3])
    [2, 6]
    """

Response:

Output: return [(i * x) for i, x in enumerate(xs)][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 fibfib(n: int):
    """The FibFib number sequence is a sequence similar to the Fibbonacci sequnece that's defined as follows:
    fibfib(0) == 0
    fibfib(1) == 0
    fibfib(2) == 1
    fibfib(n) == fibfib(n-1) + fibfib(n-2) + fibfib(n-3).
    Please write a function to efficiently compute the n-th element of the fibfib number sequence.
    >>> fibfib(1)
    0
    >>> fibfib(5)
    4
    >>> fibfib(8)
    24
    """

Response:

Output:
    if n == 0:
        return 0
    if n == 1:
        return 0
    if n == 2:
        return 1
    return fibfib(n - 1) + fibfib(n - 2) + fibfib(n - 3)


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.

FIX = """
Add more test cases.
"""

def vowels_count(s):
    """Write a function vowels_count which takes a string representing
    a word as input and returns the number of vowels in the string.
    Vowels in this case are 'a', 'e', 'i', 'o', 'u'. Here, 'y' is also a
    vowel, but only when it is at the end of the given word.

    Example:
    >>> vowels_count("abcde")
    2
    >>> vowels_count("ACEDY")
    3
    """

Response:

Output:
    vowels = "aeiouAEIOU"
    n_vowels = sum(c in vowels for c in s)
    if s[-1] == 'y' or s[-1] == 'Y':
        n_vowels += 1
    return n_vowels


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 circular_shift(x, shift):
    """Circular shift the digits of the integer x, shift the digits right by shift
    and return the result as a string.
    If shift > number of digits, return digits reversed.
    >>> circular_shift(12, 1)
    "21"
    >>> circular_shift(12, 2)
    "12"
    """

Response:

Output:
    s = str(x)
    if shift > len(s):
        return s[::-1]
    else:
        return s[len(s) - shift:] + s[:len(s) - shift]


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 digitSum(s):
    """Task
    Write a function that takes a string as input and returns the sum of the upper characters only'
    ASCII codes.

    Examples:
        digitSum("") => 0
        digitSum("abAB") => 131
        digitSum("abcCd") => 67
        digitSum("helloE") => 69
        digitSum("woArBld") => 131
        digitSum("aAaaaXa") => 153
    """

Response:

Output:
    if s == "": return 0
    return sum(ord(char) if char.isupper() else 0 for char in s)


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

The following are 3 examples:

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

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

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

    return False
} ####

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

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

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

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

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

    return result
} ####

Question: Complete the implementation of the function below.

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

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

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

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

def fruit_distribution(s,n):
    """
    In this task, you will be given a string that represents a number of apples and oranges
    that are distributed in a basket of fruit this basket contains
    apples, oranges, and mango fruits. Given the string that represents the total number of
    the oranges and apples and an integer that represent the total number of the fruits
    in the basket return the number of the mango fruits in the basket.
    for examble:
    fruit_distribution("5 apples and 6 oranges", 19) ->19 - 5 - 6 = 8
    fruit_distribution("0 apples and 1 oranges",3) -> 3 - 0 - 1 = 2
    fruit_distribution("2 apples and 3 oranges", 100) -> 100 - 2 - 3 = 95
    fruit_distribution("100 apples and 1 oranges",120) -> 120 - 100 - 1 = 19
    """

Response:

Output:
    lis = list()
    for i in s.split(' '):
        if i.isdigit():
            lis.append(int(i))
    return n - sum(lis)


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 pluck(arr):
    """
    "Given an array representing a branch of a tree that has non-negative integer nodes
    your task is to pluck one of the nodes and return it.
    The plucked node should be the node with the smallest even value.
    If multiple nodes with the same smallest even value are found return the node that has smallest index.

    The plucked node should be returned in a list, [ smalest_value, its index ],
    If there are no even values or the given array is empty, return [].

    Example 1:
        Input: [4,2,3]
        Output: [2, 1]
        Explanation: 2 has the smallest even value, and 2 has the smallest index.

    Example 2:
        Input: [1,2,3]
        Output: [2, 1]
        Explanation: 2 has the smallest even value, and 2 has the smallest index.

    Example 3:
        Input: []
        Output: []

    Example 4:
        Input: [5, 0, 3, 0, 4, 2]
        Output: [0, 1]
        Explanation: 0 is the smallest value, but  there are two zeros,
                     so we will choose the first zero, which has the smallest index.

    Constraints:
        * 1 <= nodes.length <= 10000
        * 0 <= node.value
    """

Response:

Output:
    if(len(arr) == 0): return []
    evens = list(filter(lambda x: x%2 == 0, arr))
    if(evens == []): return []
    return [min(evens), arr.index(min(evens))]


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 search(lst):
    '''
    You are given a non-empty list of positive integers. Return the greatest integer that is greater than
    zero, and has a frequency greater than or equal to the value of the integer itself.
    The frequency of an integer is the number of times it appears in the list.
    If no such a value exist, return -1.
    Examples:
        search([4, 1, 2, 2, 3, 1]) == 2
        search([1, 2, 2, 3, 3, 3, 4, 4, 4]) == 3
        search([5, 5, 4, 4, 4]) == -1
    '''

Response:

Output:
    frq = [0] * (max(lst) + 1)
    for i in lst:
        frq[i] += 1;

    ans = -1
    for i in range(1, len(frq)):
        if frq[i] >= i:
            ans = i

    return ans