Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2

    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

        if n % i == 0:
            fact.append(i)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

        if n % i == 0:
            fact.append(i)
            n //= i

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

            i += 1

    if n > 1:
        fact.append(n)
    return fact

        if n % i == 0:
            fact.append(i)
            n //= i
        else:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

    if n > 1:
        fact.append(n)
    return fact

        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):

        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:

            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:

        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

            fact.append(i)
            n //= i

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:

            i += 1

    if n > 1:
        fact.append(n)
    return fact

            fact.append(i)
            n //= i
        else:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:

    if n > 1:
        fact.append(n)
    return fact

            fact.append(i)
            n //= i
        else:
            i += 1

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:

            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:

            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:

            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)

        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)

            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)

    if n > 1:
        fact.append(n)
    return fact

            n //= i
        else:
            i += 1

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)

            n //= i
        else:
            i += 1

    if n > 1:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)

            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)

            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i

            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i

        else:
            i += 1

    if n > 1:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i

        else:
            i += 1

    if n > 1:
        fact.append(n)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i

        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:

            i += 1

    if n > 1:
        fact.append(n)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:

            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)
    return fact

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def factorize(n: int) -> List[int]:
    """ Return list of prime factors of given integer in the order from smallest to largest.
    Each of the factors should be listed number of times corresponding to how many times it appeares in factorization.
    Input number should be equal to the product of all factors
    >>> factorize(8)
    [2, 2, 2]
    >>> factorize(25)
    [5, 5]
    >>> factorize(70)
    [2, 5, 7]
    """
    import math
    fact = []
    i = 2
    while i <= int(math.sqrt(n) + 1):
        if n % i == 0:
            fact.append(i)
            n //= i
        else:
            i += 1

    if n > 1:
        fact.append(n)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate(2) == [2]
    assert candidate(4) == [2, 2]
    assert candidate(8) == [2, 2, 2]
    assert candidate(3 * 19) == [3, 19]
    assert candidate(3 * 19 * 3 * 19) == [3, 3, 19, 19]
    assert candidate(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19]
    assert candidate(3 * 19 * 19 * 19) == [3, 19, 19, 19]
    assert candidate(3 * 2 * 3) == [2, 3, 3]


Prompt:
from typing import List

def remove_duplicates(numbers: List[int]) -> List[int]:
    """ From a list of integers, remove all elements that occur more than once.
    Keep order of elements left the same as in the input.
    >>> remove_duplicates([1, 2, 3, 2, 4])
    [1, 3, 4]
    """

    c = collections.Counter(numbers)
    return [n for n in numbers if c[n] <= 1]

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([]) == []
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4]
    assert candidate([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5]


Prompt:
from typing import List

def remove_duplicates(numbers: List[int]) -> List[int]:
    """ From a list of integers, remove all elements that occur more than once.
    Keep order of elements left the same as in the input.
    >>> remove_duplicates([1, 2, 3, 2, 4])
    [1, 3, 4]
    """

return [n for n in numbers if c[n] <= 1]

    import collections
    c = collections.Counter(numbers)

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([]) == []
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4]
    assert candidate([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5]


Prompt:
from typing import List

def remove_duplicates(numbers: List[int]) -> List[int]:
    """ From a list of integers, remove all elements that occur more than once.
    Keep order of elements left the same as in the input.
    >>> remove_duplicates([1, 2, 3, 2, 4])
    [1, 3, 4]
    """

    import collections
    c = collections.Counter(numbers)
    return [n for n in numbers if c[n] <= 1]

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([]) == []
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4]
    assert candidate([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5]


Prompt:
from typing import List

def remove_duplicates(numbers: List[int]) -> List[int]:
    """ From a list of integers, remove all elements that occur more than once.
    Keep order of elements left the same as in the input.
    >>> remove_duplicates([1, 2, 3, 2, 4])
    [1, 3, 4]
    """
    import collections

return [n for n in numbers if c[n] <= 1]

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([]) == []
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4]
    assert candidate([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5]


Prompt:
from typing import List

def remove_duplicates(numbers: List[int]) -> List[int]:
    """ From a list of integers, remove all elements that occur more than once.
    Keep order of elements left the same as in the input.
    >>> remove_duplicates([1, 2, 3, 2, 4])
    [1, 3, 4]
    """
    import collections

    c = collections.Counter(numbers)
    return [n for n in numbers if c[n] <= 1]

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([]) == []
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4]
    assert candidate([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5]


Prompt:
from typing import List

def remove_duplicates(numbers: List[int]) -> List[int]:
    """ From a list of integers, remove all elements that occur more than once.
    Keep order of elements left the same as in the input.
    >>> remove_duplicates([1, 2, 3, 2, 4])
    [1, 3, 4]
    """
    import collections
    c = collections.Counter(numbers)

return [n for n in numbers if c[n] <= 1]

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([]) == []
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4]
    assert candidate([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5]


Prompt:
def flip_case(string: str) -> str:
    """ For a given string, flip lowercase characters to uppercase and uppercase to lowercase.
    >>> flip_case('Hello')
    'hELLO'
    """

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate('') == ''
    assert candidate('Hello!') == 'hELLO!'
    assert candidate('These violent delights have violent ends') == 'tHESE VIOLENT DELIGHTS HAVE VIOLENT ENDS'


Prompt:
from typing import List

def concatenate(strings: List[str]) -> str:
    """ Concatenate list of strings into a single string
    >>> concatenate([])
    ''
    >>> concatenate(['a', 'b', 'c'])
    'abc'
    """

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([]) == ''
    assert candidate(['x', 'y', 'z']) == 'xyz'
    assert candidate(['x', 'y', 'z', 'w', 'k']) == 'xyzwk'


Prompt:
from typing import List

def filter_by_prefix(strings: List[str], prefix: str) -> List[str]:
    """ Filter an input list of strings only for ones that start with a given prefix.
    >>> filter_by_prefix([], 'a')
    []
    >>> filter_by_prefix(['abc', 'bcd', 'cde', 'array'], 'a')
    ['abc', 'array']
    """

return [x for x in strings if x.startswith(prefix)]

METADATA = {
    'author': 'jt',
    'dataset': 'test'
}

def check(candidate):
    assert candidate([], 'john') == []
    assert candidate(['xxx', 'asd', 'xxy', 'john doe', 'xxxAAA', 'xxx'], 'xxx') == ['xxx', 'xxxAAA', 'xxx']


Prompt:
def get_positive(l: list):
    """Return only positive numbers in the list.
    >>> get_positive([-1, 2, -4, 5, 6])
    [2, 5, 6]
    >>> get_positive([5, 3, -5, 2, -3, 3, 9, 0, 123, 1, -10])
    [5, 3, 2, 3, 9, 123, 1]
    """


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """

        return False
    for k in range(2, n - 1):
        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """

    for k in range(2, n - 1):
        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """

        if n % k == 0:
            return False
    return True

    if n < 2:
        return False
    for k in range(2, n - 1):

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """

            return False
    return True

    if n < 2:
        return False
    for k in range(2, n - 1):
        if n % k == 0:

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """

    if n < 2:
        return False
    for k in range(2, n - 1):
        if n % k == 0:
            return False

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """

    if n < 2:
        return False
    for k in range(2, n - 1):
        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:

    for k in range(2, n - 1):
        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:

        if n % k == 0:
            return False
    return True

        return False
    for k in range(2, n - 1):

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:

            return False
    return True

        return False
    for k in range(2, n - 1):
        if n % k == 0:

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:

        return False
    for k in range(2, n - 1):
        if n % k == 0:
            return False

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:

        return False
    for k in range(2, n - 1):
        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False

        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False

            return False
    return True

    for k in range(2, n - 1):
        if n % k == 0:

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False

    for k in range(2, n - 1):
        if n % k == 0:
            return False

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False

    for k in range(2, n - 1):
        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False
    for k in range(2, n - 1):

            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False
    for k in range(2, n - 1):

        if n % k == 0:
            return False

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False
    for k in range(2, n - 1):

        if n % k == 0:
            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False
    for k in range(2, n - 1):
        if n % k == 0:

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False
    for k in range(2, n - 1):
        if n % k == 0:

            return False
    return True

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
def is_prime(n):
    """Return true if a given number is prime, and false otherwise.
    >>> is_prime(6)
    False
    >>> is_prime(101)
    True
    >>> is_prime(11)
    True
    >>> is_prime(13441)
    True
    >>> is_prime(61)
    True
    >>> is_prime(4)
    False
    >>> is_prime(1)
    False
    """
    if n < 2:
        return False
    for k in range(2, n - 1):
        if n % k == 0:
            return False

METADATA = {}

def check(candidate):
    assert candidate(6) == False
    assert candidate(101) == True
    assert candidate(11) == True
    assert candidate(13441) == True
    assert candidate(61) == True
    assert candidate(4) == False
    assert candidate(1) == False
    assert candidate(5) == True
    assert candidate(11) == True
    assert candidate(17) == True
    assert candidate(5 * 17) == False
    assert candidate(11 * 7) == False
    assert candidate(13441 * 19) == False


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

            begin = center
        else:
            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

        else:
            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

            end = center
    return begin

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """

    begin, end = -1., 1.
    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

while poly(xs, begin) * poly(xs, end) > 0:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

            begin = center
        else:
            end = center
    return begin

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

        else:
            end = center
    return begin

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

            end = center
    return begin

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4


Prompt:
import math

def poly(xs: list, x: float):
    """
    Evaluates polynomial with coefficients xs at point x.
    return xs[0] + xs[1] * x + xs[1] * x^2 + .... xs[n] * x^n
    """
    return sum([coeff * math.pow(x, i) for i, coeff in enumerate(xs)])

def find_zero(xs: list):
    """ xs are coefficients of a polynomial.
    find_zero find x such that poly(x) = 0.
    find_zero returns only only zero point, even if there are many.
    Moreover, find_zero only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution.
    >>> round(find_zero([1, 2]), 2) # f(x) = 1 + 2x
    -0.5
    >>> round(find_zero([-6, 11, -6, 1]), 2) # (x - 1) * (x - 2) * (x - 3) = -6 + 11x - 6x^2 + x^3
    1.0
    """
    begin, end = -1., 1.

    while poly(xs, begin) * poly(xs, end) > 0:
        begin *= 2.0
        end *= 2.0
    while end - begin > 1e-10:
        center = (begin + end) / 2.0
        if poly(xs, center) * poly(xs, begin) > 0:
            begin = center
        else:
            end = center
    return begin

METADATA = {}

def check(candidate):
    import math
    import random
    rng = random.Random(42)
    import copy
    for _ in range(100):
        ncoeff = 2 * rng.randint(1, 4)
        coeffs = []
        for _ in range(ncoeff):
            coeff = rng.randint(-10, 10)
            if coeff == 0:
                coeff = 1
            coeffs.append(coeff)
        solution = candidate(copy.deepcopy(coeffs))
        assert math.fabs(poly(coeffs, solution)) < 1e-4