Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

from typing import List, Any

def f6(values: List[Any]) -> List[int]:
    """ Filter given list of any python values only for integers 	assert f6([]) == [],"Test 0"
	assert f6([4, {}, [], 23.2, 9, 'adasd']) == [4, 9],"Test 1"
	assert f6([3, 'c', 3, 3, 'a', 'b']) == [3, 3, 3],"Test 2"
	"""
    return [x for x in values if isinstance(x, int)]

# Rust f6 translation

def check(candidate):
    assert candidate([]) == [],"Test 0"
    assert candidate([4, {}, [], 23.2, 9, 'adasd']) == [4, 9],"Test 1"
    assert candidate([3, 'c', 3, 3, 'a', 'b']) == [3, 3, 3],"Test 2"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(string: str) -> int:
    """ Return length of given string 	assert f6('') == 0,"Test 0"
	assert f6('x') == 1,"Test 1"
	assert f6('asdasnakj') == 9,"Test 2"
	"""
    return len(string)

# Rust f6 translation

def check(candidate):
    assert candidate('') == 0,"Test 0"
    assert candidate('x') == 1,"Test 1"
    assert candidate('asdasnakj') == 9,"Test 2"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(n: int) -> int:
    """ For a given number n, find the largest number that divides n evenly, smaller than n 	assert f6(3) == 1,"Test 0"
	assert f6(7) == 1,"Test 1"
	assert f6(10) == 5,"Test 2"
	assert f6(100) == 50,"Test 3"
	assert f6(49) == 7,"Test 4"
	"""
    for i in reversed(range(n)):
        if n % i == 0:
            return i

# Rust f6 translation

def check(candidate):
    assert candidate(3) == 1,"Test 0"
    assert candidate(7) == 1,"Test 1"
    assert candidate(10) == 5,"Test 2"
    assert candidate(100) == 50,"Test 3"
    assert candidate(49) == 7,"Test 4"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

from typing import List

def f6(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 	assert f6(2) == [2],"Test 0"
	assert f6(4) == [2, 2],"Test 1"
	assert f6(8) == [2, 2, 2],"Test 2"
	assert f6(3 * 19) == [3, 19],"Test 3"
	assert f6(3 * 19 * 3 * 19) == [3, 3, 19, 19],"Test 4"
	assert f6(3 * 19 * 3 * 19 * 3 * 19) == [3, 3, 3, 19, 19, 19],"Test 5"
	assert f6(3 * 19 * 19 * 19) == [3, 19, 19, 19],"Test 6"
	assert f6(3 * 2 * 3) == [2, 3, 3],"Test 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

# Rust f6 translation


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

from typing import List

def f6(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. 	assert f6([]) == [],"Test 0"
	assert f6([1, 2, 3, 4]) == [1, 2, 3, 4],"Test 1"
	assert f6([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5],"Test 2"
	"""
    import collections
    c = collections.Counter(numbers)
    return [n for n in numbers if c[n] <= 1]

# Rust f6 translation

def check(candidate):
    assert candidate([]) == [],"Test 0"
    assert candidate([1, 2, 3, 4]) == [1, 2, 3, 4],"Test 1"
    assert candidate([1, 2, 3, 2, 4, 3, 5]) == [1, 4, 5],"Test 2"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(string: str) -> str:
    """ For a given string, flip lowercase characters to uppercase and uppercase to lowercase. 	assert f6('') == '',"Test 0"
	assert f6('Hello!') == 'hELLO!',"Test 1"
	assert f6('These violent delights have violent ends') == 'tHESE VIOLENT DELIGHTS HAVE VIOLENT ENDS',"Test 2"
	"""
    return string.swapcase()

# Rust f6 translation

def check(candidate):
    assert candidate('') == '',"Test 0"
    assert candidate('Hello!') == 'hELLO!',"Test 1"
    assert candidate('These violent delights have violent ends') == 'tHESE VIOLENT DELIGHTS HAVE VIOLENT ENDS',"Test 2"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

from typing import List

def f6(strings: List[str]) -> str:
    """ Concatenate list of strings into a single string 	assert f6([]) == '',"Test 0"
	assert f6(['x', 'y', 'z']) == 'xyz',"Test 1"
	assert f6(['x', 'y', 'z', 'w', 'k']) == 'xyzwk',"Test 2"
	"""
    return ''.join(strings)

# Rust f6 translation

def check(candidate):
    assert candidate([]) == '',"Test 0"
    assert candidate(['x', 'y', 'z']) == 'xyz',"Test 1"
    assert candidate(['x', 'y', 'z', 'w', 'k']) == 'xyzwk',"Test 2"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

from typing import List

def f6(strings: List[str], prefix: str) -> List[str]:
    """ Filter an input list of strings only for ones that start with a given prefix. 	assert f6([], 'john') == [],"Test 0"
	assert f6(['xxx', 'asd', 'xxy', 'john doe', 'xxxAAA', 'xxx'], 'xxx') == ['xxx', 'xxxAAA', 'xxx'],"Test 1"
	"""
    return [x for x in strings if x.startswith(prefix)]

# Rust f6 translation

def check(candidate):
    assert candidate([], 'john') == [],"Test 0"
    assert candidate(['xxx', 'asd', 'xxy', 'john doe', 'xxxAAA', 'xxx'], 'xxx') == ['xxx', 'xxxAAA', 'xxx'],"Test 1"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l: list):
    """Return only positive numbers in the list. 	assert f6([-1, -2, 4, 5, 6]) == [4, 5, 6],"Test 0"
	assert f6([5, 3, -5, 2, 3, 3, 9, 0, 123, 1, -10]) == [5, 3, 2, 3, 3, 9, 123, 1],"Test 1"
	assert f6([-1, -2]) == [],"Test 2"
	assert f6([]) == [],"Test 3"
	"""
    return [e for e in l if e > 0]

# Rust f6 translation


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(n):
    """Return true if a given number is prime, and false otherwise. 	assert f6(6) == False,"Test 0"
	assert f6(101) == True,"Test 1"
	assert f6(11) == True,"Test 2"
	assert f6(13441) == True,"Test 3"
	assert f6(61) == True,"Test 4"
	assert f6(4) == False,"Test 5"
	assert f6(1) == False,"Test 6"
	assert f6(5) == True,"Test 7"
	assert f6(11) == True,"Test 8"
	assert f6(17) == True,"Test 9"
	assert f6(5 * 17) == False,"Test 10"
	assert f6(11 * 7) == False,"Test 11"
	assert f6(13441 * 19) == False,"Test 12"
	"""
    if n < 2:
        return False
    for k in range(2, n - 1):
        if n % k == 0:
            return False
    return True

# Rust f6 translation

def check(candidate):
    assert candidate(6) == False,"Test 0"
    assert candidate(101) == True,"Test 1"
    assert candidate(11) == True,"Test 2"
    assert candidate(13441) == True,"Test 3"
    assert candidate(61) == True,"Test 4"
    assert candidate(4) == False,"Test 5"
    assert candidate(1) == False,"Test 6"
    assert candidate(5) == True,"Test 7"
    assert candidate(11) == True,"Test 8"
    assert candidate(17) == True,"Test 9"
    assert candidate(5 * 17) == False,"Test 10"
    assert candidate(11 * 7) == False,"Test 11"
    assert candidate(13441 * 19) == False,"Test 12"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

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 f6(xs: list):
    """ xs are coefficients of a polynomial.
    f6 find x such that poly(x) = 0.
    f6 returns only only zero point, even if there are many.
    Moreover, f6 only takes list xs having even number of coefficients
    and largest non zero coefficient as it guarantees
    a solution. 	assert math.fabs(poly(coeffs, solution)) < 1e-4,"Test 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

# Rust f6 translation

def check(candidate):
        assert math.fabs(poly(coeffs, solution)) < 1e-4,"Test 0"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l: list):
    """This function takes a list l and returns a list l' such that
    l' is identical to l in the indicies that are not divisible by three, while its values at the indicies that are divisible by three are equal
    to the values of the corresponding indicies of l, but sorted. 	assert tuple(f6([1, 2, 3])) == tuple(sort_third([1, 2, 3])),"Test 0"
	assert tuple(f6([5, 3, -5, 2, -3, 3, 9, 0, 123, 1, -10])) == tuple(sort_third([5, 3, -5, 2, -3, 3, 9, 0, 123, 1, -10])),"Test 1"
	assert tuple(f6([5, 8, -12, 4, 23, 2, 3, 11, 12, -10])) == tuple(sort_third([5, 8, -12, 4, 23, 2, 3, 11, 12, -10])),"Test 2"
	assert tuple(f6([5, 6, 3, 4, 8, 9, 2])) == tuple([2, 6, 3, 4, 8, 9, 5]),"Test 3"
	assert tuple(f6([5, 8, 3, 4, 6, 9, 2])) == tuple([2, 8, 3, 4, 6, 9, 5]),"Test 4"
	assert tuple(f6([5, 6, 9, 4, 8, 3, 2])) == tuple([2, 6, 9, 4, 8, 3, 5]),"Test 5"
	assert tuple(f6([5, 6, 3, 4, 8, 9, 2, 1])) == tuple([2, 6, 3, 4, 8, 9, 5, 1]),"Test 6"
	"""
    l = list(l)
    l[::3] = sorted(l[::3])
    return l

# Rust f6 translation


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l: list):
    """Return sorted f6 elements in a list. 	assert f6([5, 3, 5, 2, 3, 3, 9, 0, 123]) == [0, 2, 3, 5, 9, 123],"Test 0"
	"""
    return sorted(list(set(l)))

# Rust f6 translation


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l: list):
    """Return maximum element in the list. 	assert f6([1, 2, 3]) == 3,"Test 0"
	assert f6([5, 3, -5, 2, -3, 3, 9, 0, 124, 1, -10]) == 124,"Test 1"
	"""
    m = l[0]
    for e in l:
        if e > m:
            m = e
    return m

# Rust f6 translation


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(n: int):
    """Return the number of times the digit 7 appears in integers less than n which are divisible by 11 or 13. 	assert f6(50) == 0,"Test 0"
	assert f6(78) == 2,"Test 1"
	assert f6(79) == 3,"Test 2"
	assert f6(100) == 3,"Test 3"
	assert f6(200) == 6,"Test 4"
	assert f6(4000) == 192,"Test 5"
	assert f6(10000) == 639,"Test 6"
	assert f6(100000) == 8026,"Test 7"
	"""
    ns = []
    for i in range(n):
        if i % 11 == 0 or i % 13 == 0:
            ns.append(i)
    s = ''.join(list(map(str, ns)))
    ans = 0
    for c in s:
        ans += (c == '7')
    return ans

# Rust f6 translation

def check(candidate):
    assert candidate(50) == 0,"Test 0"
    assert candidate(78) == 2,"Test 1"
    assert candidate(79) == 3,"Test 2"
    assert candidate(100) == 3,"Test 3"
    assert candidate(200) == 6,"Test 4"
    assert candidate(4000) == 192,"Test 5"
    assert candidate(10000) == 639,"Test 6"
    assert candidate(100000) == 8026,"Test 7"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l: list):
    """This function takes a list l and returns a list l' such that
    l' is identical to l in the odd indicies, while its values at the even indicies are equal
    to the values of the even indicies of l, but sorted. 	assert tuple(f6([1, 2, 3])) == tuple([1, 2, 3]),"Test 0"
	assert tuple(f6([5, 3, -5, 2, -3, 3, 9, 0, 123, 1, -10])) == tuple([-10, 3, -5, 2, -3, 3, 5, 0, 9, 1, 123]),"Test 1"
	assert tuple(f6([5, 8, -12, 4, 23, 2, 3, 11, 12, -10])) == tuple([-12, 8, 3, 4, 5, 2, 12, 11, 23, -10]),"Test 2"
	"""
    evens = l[::2]
    odds = l[1::2]
    evens.sort()
    ans = []
    for e, o in zip(evens, odds):
        ans.extend([e, o])
    if len(evens) > len(odds):
        ans.append(evens[-1])
    return ans

# Rust f6 translation


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def encode_cyclic(s: str):
    """
    returns encoded string by cycling groups of three characters.
    """
    # split string to groups. Each of length 3.
    groups = [s[(3 * i):min((3 * i + 3), len(s))] for i in range((len(s) + 2) // 3)]
    # cycle elements in each group. Unless group has fewer elements than 3.
    groups = [(group[1:] + group[0]) if len(group) == 3 else group for group in groups]
    return "".join(groups)

def f6(s: str):
    """
    takes as input string encoded with encode_cyclic function. Returns decoded string.
    	assert f6(encoded_str) == str,"Test 0"
	"""
    return encode_cyclic(encode_cyclic(s))

# Rust f6 translation

def check(candidate):
        assert candidate(encoded_str) == str,"Test 0"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(n: int):
    """
    f6 returns n-th number that is a Fibonacci number and it's also prime. 	assert f6(1) == 2,"Test 0"
	assert f6(2) == 3,"Test 1"
	assert f6(3) == 5,"Test 2"
	assert f6(4) == 13,"Test 3"
	assert f6(5) == 89,"Test 4"
	assert f6(6) == 233,"Test 5"
	assert f6(7) == 1597,"Test 6"
	assert f6(8) == 28657,"Test 7"
	assert f6(9) == 514229,"Test 8"
	assert f6(10) == 433494437,"Test 9"
	"""
    import math

    def is_prime(p):
        if p < 2:
            return False
        for k in range(2, min(int(math.sqrt(p)) + 1, p - 1)):
            if p % k == 0:
                return False
        return True
    f = [0, 1]
    while True:
        f.append(f[-1] + f[-2])
        if is_prime(f[-1]):
            n -= 1
        if n == 0:
            return f[-1]

# Rust f6 translation

def check(candidate):
    assert candidate(1) == 2,"Test 0"
    assert candidate(2) == 3,"Test 1"
    assert candidate(3) == 5,"Test 2"
    assert candidate(4) == 13,"Test 3"
    assert candidate(5) == 89,"Test 4"
    assert candidate(6) == 233,"Test 5"
    assert candidate(7) == 1597,"Test 6"
    assert candidate(8) == 28657,"Test 7"
    assert candidate(9) == 514229,"Test 8"
    assert candidate(10) == 433494437,"Test 9"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l: list):
    	assert f6([1, 3, 5, 0]) == False,"Test 0"
	assert f6([1, 3, 5, -1]) == False,"Test 1"
	assert f6([1, 3, -2, 1]) == True,"Test 2"
	assert f6([1, 2, 3, 7]) == False,"Test 3"
	assert f6([1, 2, 5, 7]) == False,"Test 4"
	assert f6([2, 4, -5, 3, 9, 7]) == True,"Test 5"
	assert f6([1]) == False,"Test 6"
	assert f6([1, 3, 5, -100]) == False,"Test 7"
	assert f6([100, 3, 5, -100]) == False,"Test 8"
	"""
    for i in range(len(l)):
        for j in range(i + 1, len(l)):
            for k in range(j + 1, len(l)):
                if l[i] + l[j] + l[k] == 0:
                    return True
    return False

# Rust f6 translation

def check(candidate):
    assert candidate([1, 3, 5, 0]) == False,"Test 0"
    assert candidate([1, 3, 5, -1]) == False,"Test 1"
    assert candidate([1, 3, -2, 1]) == True,"Test 2"
    assert candidate([1, 2, 3, 7]) == False,"Test 3"
    assert candidate([1, 2, 5, 7]) == False,"Test 4"
    assert candidate([2, 4, -5, 3, 9, 7]) == True,"Test 5"
    assert candidate([1]) == False,"Test 6"
    assert candidate([1, 3, 5, -100]) == False,"Test 7"
    assert candidate([100, 3, 5, -100]) == False,"Test 8"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(n: int):
    """
    Imagine a road that's a perfectly straight infinitely long line.
    n cars are driving left to right;  simultaneously, a different set of n cars
    are driving right to left.   The two sets of cars start out being very far from
    each other.  All cars move in the same speed.  Two cars are said to collide
    when a car that's moving left to right hits a car that's moving right to left.
    However, the cars are infinitely sturdy and strong; as a result, they continue moving
    in their trajectory as if they did not collide.

    This function outputs the number of such collisions.
    	assert f6(2) == 4,"Test 0"
	assert f6(3) == 9,"Test 1"
	assert f6(4) == 16,"Test 2"
	assert f6(8) == 64,"Test 3"
	assert f6(10) == 100,"Test 4"
	"""
    return n**2

# Rust f6 translation

def check(candidate):
    assert candidate(2) == 4,"Test 0"
    assert candidate(3) == 9,"Test 1"
    assert candidate(4) == 16,"Test 2"
    assert candidate(8) == 64,"Test 3"
    assert candidate(10) == 100,"Test 4"


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l: list):
    """Return list with elements incremented by 1. 	assert f6([]) == [],"Test 0"
	assert f6([3, 2, 1]) == [4, 3, 2],"Test 1"
	assert f6([5, 2, 5, 2, 3, 3, 9, 0, 123]) == [6, 3, 6, 3, 4, 4, 10, 1, 124],"Test 2"
	"""
    return [(e + 1) for e in l]

# Rust f6 translation


Prompt:
from typing import List, Dict, Tuple, Union, Optional

def f1(numbers: List[float], threshold: float) -> bool:
    """
    f1: List[float] -> float -> bool
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.3) == True
    assert f1([1.0, 2.0, 3.9, 4.0, 5.0, 2.2], 0.05) == False
    assert f1([1.0, 2.0, 5.9, 4.0, 5.0], 0.95) == True
    """
    for idx, elem in enumerate(numbers):
        for idx2, elem2 in enumerate(numbers):
            if idx != idx2:
                distance = abs(elem - elem2)
                if distance < threshold:
                    return True

    return False

#  Rust f1 translation
fn has_close_elements(numbers: Vec<f64>, threshold: f64) -> bool {
    for idx in 0..numbers.len() {
        for idx2 in 0..numbers.len() {
            if idx != idx2 {
                let distance = (numbers[idx] - numbers[idx2]).abs();
                if distance < threshold {
                    return true;
                }
            }
        }
    }

    return false;
}
def f2(paren_string: str) -> List[str]:
    """
    f2: str -> List[str]
    assert f2('(()()) ((())) () ((())()())') == [
        '(()())', '((()))', '()', '((())()())'
    ]
    assert f2('() (()) ((())) (((())))') == [
        '()', '(())', '((()))', '(((())))'
    ]
    assert f2('(()(())((())))') == [
        '(()(())((())))'
    ]
    assert f2('( ) (( )) (( )( ))') == ['()', '(())', '(()())']
    """
    result = []
    current_string = []
    current_depth = 0

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

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

    return result

# Rust f2 translation
fn f2(paren_string: &str) -> Vec<String> {
    let mut result = Vec::new();
    let mut current_string = String::new();
    let mut current_depth = 0;

    for c in paren_string.chars() {
        if c == '(' {
            current_depth += 1;
            current_string.push(c);
        } else if c == ')' {
            current_depth -= 1;
            current_string.push(c);

            if current_depth == 0 {
                result.push(current_string);
                current_string = String::new();
            }
        }
    }

    return result;
}

def f3(number: float) -> float:
    """
    f3: float -> float
    assert f3(3.5) == 0.5
    assert abs(f3(1.33) - 0.33) < 1e-6
    assert abs(f3(123.456) - 0.456) < 1e-6
    """
    return number % 1.0

# Rust f3 translation
fn f3(number: f64) -> f64 {
    return number % 1.0;
}

def f4(a, b):
    """
    Complete the function that takes two integers and returns the product of their unit digits.
    f4: int -> int -> int
    assert f4(148, 412) == 16,
    assert f4(19, 28) == 72,
    assert f4(2020, 1851) == 0
    assert f4(3,3) == 9
    assert f4(12,33) == 6
    """
    return abs(a % 10) * abs(b % 10)

# Rust f4 translation
fn f4(a: i32, b: i32) -> i32 {
    return (a % 10).abs() * (b % 10).abs();
}

def f5(xs: List[int]) -> List[int]:
    """
    xs represent coefficients of a polynomial.
    f5: List[int] -> List[int]
    assert f5([3, 1, 2, 4, 5]) == [1, 4, 12, 20]
    assert f5([1, 2, 3]) == [2, 6]
    assert f5([3, 2, 1]) == [2, 2]
    assert f5([3, 2, 1, 0, 4]) == [2, 2, 0, 16]
    assert f5([1]) == []
    """
    return [(i * x) for i, x in enumerate(xs)][1:]

# Rust f5 translation
fn f5(xs: Vec<i32>) -> Vec<i32> {
    return xs.iter().enumerate().map(|(i, x)| i as i32 * x).skip(1).collect();
}

def f6(l):
    	assert f6([1, 3, 5, 0]) == False,"Test 0"
	assert f6([1, 3, -2, 1]) == False,"Test 1"
	assert f6([1, 2, 3, 7]) == False,"Test 2"
	assert f6([2, 4, -5, 3, 5, 7]) == True,"Test 3"
	assert f6([1]) == False,"Test 4"
	assert f6([-3, 9, -1, 3, 2, 30]) == True,"Test 5"
	assert f6([-3, 9, -1, 3, 2, 31]) == True,"Test 6"
	assert f6([-3, 9, -1, 4, 2, 30]) == False,"Test 7"
	assert f6([-3, 9, -1, 4, 2, 31]) == False,"Test 8"
	"""
    for i, l1 in enumerate(l):
        for j in range(i + 1, len(l)):
            if l1 + l[j] == 0:
                return True
    return False

# Rust f6 translation

def check(candidate):
    assert candidate([1, 3, 5, 0]) == False,"Test 0"
    assert candidate([1, 3, -2, 1]) == False,"Test 1"
    assert candidate([1, 2, 3, 7]) == False,"Test 2"
    assert candidate([2, 4, -5, 3, 5, 7]) == True,"Test 3"
    assert candidate([1]) == False,"Test 4"
    assert candidate([-3, 9, -1, 3, 2, 30]) == True,"Test 5"
    assert candidate([-3, 9, -1, 3, 2, 31]) == True,"Test 6"
    assert candidate([-3, 9, -1, 4, 2, 30]) == False,"Test 7"
    assert candidate([-3, 9, -1, 4, 2, 31]) == False,"Test 8"