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(x: int, base: int):
    """Change numerical base of input number x to base.
    return string representation after the conversion.
    base numbers are less than 10. 	assert f6(8, 3) == "22","Test 0"
	assert f6(9, 3) == "100","Test 1"
	assert f6(234, 2) == "11101010","Test 2"
	assert f6(16, 2) == "10000","Test 3"
	assert f6(8, 2) == "1000","Test 4"
	assert f6(7, 2) == "111","Test 5"
	"""
    ret = ""
    while x > 0:
        ret = str(x % base) + ret
        x //= base
    return ret

# Rust f6 translation

def check(candidate):
    assert candidate(8, 3) == "22","Test 0"
    assert candidate(9, 3) == "100","Test 1"
    assert candidate(234, 2) == "11101010","Test 2"
    assert candidate(16, 2) == "10000","Test 3"
    assert candidate(8, 2) == "1000","Test 4"
    assert candidate(7, 2) == "111","Test 5"


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(a, h):
    """Given length of a side and high return area for a triangle. 	assert f6(5, 3) == 7.5,"Test 0"
	assert f6(2, 2) == 2.0,"Test 1"
	assert f6(10, 8) == 40.0,"Test 2"
	"""
    return a * h / 2.0

# Rust f6 translation

def check(candidate):
    assert candidate(5, 3) == 7.5,"Test 0"
    assert candidate(2, 2) == 2.0,"Test 1"
    assert candidate(10, 8) == 40.0,"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):
    """The Fib4 number sequence is a sequence similar to the Fibbonacci sequnece that's defined as follows:
    f6(0) -> 0
    f6(1) -> 0
    f6(2) -> 2
    f6(3) -> 0
    f6(n) -> f6(n-1) + f6(n-2) + f6(n-3) + f6(n-4).
    Please write a function to efficiently compute the n-th element of the f6 number sequence.  Do not use recursion. 	assert f6(5) == 4,"Test 0"
	assert f6(8) == 28,"Test 1"
	assert f6(10) == 104,"Test 2"
	assert f6(12) == 386,"Test 3"
	"""
    results = [0, 0, 2, 0]
    if n < 4:
        return results[n]

    for _ in range(4, n + 1):
        results.append(results[-1] + results[-2] + results[-3] + results[-4])
        results.pop(0)

    return results[-1]

# Rust f6 translation

def check(candidate):
    assert candidate(5) == 4,"Test 0"
    assert candidate(8) == 28,"Test 1"
    assert candidate(10) == 104,"Test 2"
    assert candidate(12) == 386,"Test 3"


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 f6 of elements in the list l. 	assert f6([3, 1, 2, 4, 5]) == 3,"Test 0"
	assert f6([-10, 4, 6, 1000, 10, 20]) == 8.0,"Test 1"
	assert f6([5]) == 5,"Test 2"
	assert f6([6, 5]) == 5.5,"Test 3"
	assert f6([8, 1, 3, 9, 9, 2, 7]) == 7 ,"Test 4"
	"""
    l = sorted(l)
    if len(l) % 2 == 1:
        return l[len(l) // 2]
    else:
        return (l[len(l) // 2 - 1] + l[len(l) // 2]) / 2.0

# Rust f6 translation

def check(candidate):
    assert candidate([3, 1, 2, 4, 5]) == 3,"Test 0"
    assert candidate([-10, 4, 6, 1000, 10, 20]) == 8.0,"Test 1"
    assert candidate([5]) == 5,"Test 2"
    assert candidate([6, 5]) == 5.5,"Test 3"
    assert candidate([8, 1, 3, 9, 9, 2, 7]) == 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();
}

def f6(text: str):
    """
    Checks if given string is a palindrome 	assert f6('') == True,"Test 0"
	assert f6('aba') == True,"Test 1"
	assert f6('aaaaa') == True,"Test 2"
	assert f6('zbcd') == False,"Test 3"
	assert f6('xywyx') == True,"Test 4"
	assert f6('xywyz') == False,"Test 5"
	assert f6('xywzx') == False,"Test 6"
	"""
    for i in range(len(text)):
        if text[i] != text[len(text) - 1 - i]:
            return False
    return True

# Rust f6 translation

def check(candidate):
    assert candidate('') == True,"Test 0"
    assert candidate('aba') == True,"Test 1"
    assert candidate('aaaaa') == True,"Test 2"
    assert candidate('zbcd') == False,"Test 3"
    assert candidate('xywyx') == True,"Test 4"
    assert candidate('xywyz') == False,"Test 5"
    assert candidate('xywzx') == False,"Test 6"


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, p: int):
    """Return 2^n modulo p (be aware of numerics). 	assert f6(3, 5) == 3,"Test 0"
	assert f6(1101, 101) == 2,"Test 1"
	assert f6(0, 101) == 1,"Test 2"
	assert f6(3, 11) == 8,"Test 3"
	assert f6(100, 101) == 1,"Test 4"
	assert f6(30, 5) == 4,"Test 5"
	assert f6(31, 5) == 3,"Test 6"
	"""
    ret = 1
    for i in range(n):
        ret = (2 * ret) % p
    return ret

# Rust f6 translation

def check(candidate):
    assert candidate(3, 5) == 3,"Test 0"
    assert candidate(1101, 101) == 2,"Test 1"
    assert candidate(0, 101) == 1,"Test 2"
    assert candidate(3, 11) == 8,"Test 3"
    assert candidate(100, 101) == 1,"Test 4"
    assert candidate(30, 5) == 4,"Test 5"
    assert candidate(31, 5) == 3,"Test 6"


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_shift(s: str):
    """
    returns encoded string by shifting every character by 5 in the alphabet.
    """
    return "".join([chr(((ord(ch) + 5 - ord("a")) % 26) + ord("a")) for ch in s])

def f6(s: str):
    """
    takes as input string encoded with encode_shift function. Returns decoded string.
    	assert f6(copy.deepcopy(encoded_str)) == str,"Test 0"
	"""
    return "".join([chr(((ord(ch) - 5 - ord("a")) % 26) + ord("a")) for ch in s])

# Rust f6 translation

def check(candidate):
        assert candidate(copy.deepcopy(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(text):
    """
    f6 is a function that takes string and returns string without vowels. 	assert f6('') == '',"Test 0"
	assert f6("abcdef\nghijklm") == 'bcdf\nghjklm',"Test 1"
	assert f6('fedcba') == 'fdcb',"Test 2"
	assert f6('eeeee') == '',"Test 3"
	assert f6('acBAA') == 'cB',"Test 4"
	assert f6('EcBOO') == 'cB',"Test 5"
	assert f6('ybcd') == 'ybcd',"Test 6"
	"""
    return "".join([s for s in text if s.lower() not in ["a", "e", "i", "o", "u"]])

# Rust f6 translation

def check(candidate):
    assert candidate('') == '',"Test 0"
    assert candidate("abcdef\nghijklm") == 'bcdf\nghjklm',"Test 1"
    assert candidate('fedcba') == 'fdcb',"Test 2"
    assert candidate('eeeee') == '',"Test 3"
    assert candidate('acBAA') == 'cB',"Test 4"
    assert candidate('EcBOO') == 'cB',"Test 5"
    assert candidate('ybcd') == 'ybcd',"Test 6"


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, t: int):
	assert f6([1, 2, 4, 10], 100),"Test 0"
	assert not f6([1, 20, 4, 10], 5),"Test 1"
	assert f6([1, 20, 4, 10], 21),"Test 2"
	assert f6([1, 20, 4, 10], 22),"Test 3"
	assert f6([1, 8, 4, 10], 11),"Test 4"
	assert not f6([1, 8, 4, 10], 10),"Test 5"
	"""
    for e in l:
        if e >= t:
            return False
    return True

# Rust f6 translation

def check(candidate):
    assert candidate([1, 2, 4, 10], 100),"Test 0"
    assert not candidate([1, 20, 4, 10], 5),"Test 1"
    assert candidate([1, 20, 4, 10], 21),"Test 2"
    assert candidate([1, 20, 4, 10], 22),"Test 3"
    assert candidate([1, 8, 4, 10], 11),"Test 4"
    assert not candidate([1, 8, 4, 10], 10),"Test 5"


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(x: int, y: int):
    """Add two numbers x and y. 	assert f6(0, 1) == 1,"Test 0"
	assert f6(1, 0) == 1,"Test 1"
	assert f6(2, 3) == 5,"Test 2"
	assert f6(5, 7) == 12,"Test 3"
	assert f6(7, 5) == 12,"Test 4"
	"""
    return x + y

# Rust f6 translation

def check(candidate):
    assert candidate(0, 1) == 1,"Test 0"
    assert candidate(1, 0) == 1,"Test 1"
    assert candidate(2, 3) == 5,"Test 2"
    assert candidate(5, 7) == 12,"Test 3"
    assert candidate(7, 5) == 12,"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(s0: str, s1: str):
    """
    Check if two words have the same characters. 	assert f6('eabcdzzzz', 'dddzzzzzzzddeddabc') == True,"Test 0"
	assert f6('abcd', 'dddddddabc') == True,"Test 1"
	assert f6('dddddddabc', 'abcd') == True,"Test 2"
	assert f6('eabcd', 'dddddddabc') == False,"Test 3"
	assert f6('abcd', 'dddddddabcf') == False,"Test 4"
	assert f6('eabcdzzzz', 'dddzzzzzzzddddabc') == False,"Test 5"
	assert f6('aabb', 'aaccc') == False,"Test 6"
	"""
    return set(s0) == set(s1)

# Rust f6 translation

def check(candidate):
    assert candidate('eabcdzzzz', 'dddzzzzzzzddeddabc') == True,"Test 0"
    assert candidate('abcd', 'dddddddabc') == True,"Test 1"
    assert candidate('dddddddabc', 'abcd') == True,"Test 2"
    assert candidate('eabcd', 'dddddddabc') == False,"Test 3"
    assert candidate('abcd', 'dddddddabcf') == False,"Test 4"
    assert candidate('eabcdzzzz', 'dddzzzzzzzddddabc') == False,"Test 5"
    assert candidate('aabb', 'aaccc') == False,"Test 6"


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 n-th Fibonacci number. 	assert f6(10) == 55,"Test 0"
	assert f6(1) == 1,"Test 1"
	assert f6(8) == 21,"Test 2"
	assert f6(11) == 89,"Test 3"
	assert f6(12) == 144,"Test 4"
	"""
    if n == 0:
        return 0
    if n == 1:
        return 1
    return fib(n - 1) + fib(n - 2)

# Rust f6 translation

def check(candidate):
    assert candidate(10) == 55,"Test 0"
    assert candidate(1) == 1,"Test 1"
    assert candidate(8) == 21,"Test 2"
    assert candidate(11) == 89,"Test 3"
    assert candidate(12) == 144,"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(brackets: str):
    """ brackets is a string of "<" and ">".
	assert f6("<>"),"Test 0"
	assert f6("<<><>>"),"Test 1"
	assert f6("<><><<><>><>"),"Test 2"
	assert f6("<><><<<><><>><>><<><><<>>>"),"Test 3"
	assert not f6("<<<><>>>>"),"Test 4"
	assert not f6("><<>"),"Test 5"
	assert not f6("<"),"Test 6"
	assert not f6("<<<<"),"Test 7"
	assert not f6(">"),"Test 8"
	assert not f6("<<>"),"Test 9"
	assert not f6("<><><<><>><>><<>"),"Test 10"
	assert not f6("<><><<><>><>>><>"),"Test 11"
	"""
    depth = 0
    for b in brackets:
        if b == "<":
            depth += 1
        else:
            depth -= 1
        if depth < 0:
            return False
    return depth == 0

# Rust f6 translation

def check(candidate):
    assert candidate("<>"),"Test 0"
    assert candidate("<<><>>"),"Test 1"
    assert candidate("<><><<><>><>"),"Test 2"
    assert candidate("<><><<<><><>><>><<><><<>>>"),"Test 3"
    assert not candidate("<<<><>>>>"),"Test 4"
    assert not candidate("><<>"),"Test 5"
    assert not candidate("<"),"Test 6"
    assert not candidate("<<<<"),"Test 7"
    assert not candidate(">"),"Test 8"
    assert not candidate("<<>"),"Test 9"
    assert not candidate("<><><<><>><>><<>"),"Test 10"
    assert not candidate("<><><<><>><>>><>"),"Test 11"


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, 2, 4, 10]) == True,"Test 0"
	assert f6([1, 2, 4, 20]) == True,"Test 1"
	assert f6([1, 20, 4, 10]) == False,"Test 2"
	assert f6([4, 1, 0, -10]) == True,"Test 3"
	assert f6([4, 1, 1, 0]) == True,"Test 4"
	assert f6([1, 2, 3, 2, 5, 60]) == False,"Test 5"
	assert f6([1, 2, 3, 4, 5, 60]) == True,"Test 6"
	assert f6([9, 9, 9, 9]) == True,"Test 7"
	"""
    if l == sorted(l) or l == sorted(l, reverse=True):
        return True
    return False

# Rust f6 translation

def check(candidate):
    assert candidate([1, 2, 4, 10]) == True,"Test 0"
    assert candidate([1, 2, 4, 20]) == True,"Test 1"
    assert candidate([1, 20, 4, 10]) == False,"Test 2"
    assert candidate([4, 1, 0, -10]) == True,"Test 3"
    assert candidate([4, 1, 1, 0]) == True,"Test 4"
    assert candidate([1, 2, 3, 2, 5, 60]) == False,"Test 5"
    assert candidate([1, 2, 3, 4, 5, 60]) == True,"Test 6"
    assert candidate([9, 9, 9, 9]) == True,"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(l1: list, l2: list):
    """Return sorted unique f6 elements for two lists. 	assert f6([1, 4, 3, 34, 653, 2, 5], [5, 7, 1, 5, 9, 653, 121]) == [1, 5, 653],"Test 0"
	assert f6([5, 3, 2, 8], [3, 2]) == [2, 3],"Test 1"
	assert f6([4, 3, 2, 8], [3, 2, 4]) == [2, 3, 4],"Test 2"
	assert f6([4, 3, 2, 8], []) == [],"Test 3"
	"""
    ret = set()
    for e1 in l1:
        for e2 in l2:
            if e1 == e2:
                ret.add(e1)
    return sorted(list(ret))

# 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 largest prime factor of n. Assume n > 1 and is not a prime. 	assert f6(15) == 5,"Test 0"
	assert f6(27) == 3,"Test 1"
	assert f6(63) == 7,"Test 2"
	assert f6(330) == 11,"Test 3"
	assert f6(13195) == 29,"Test 4"
	"""
    def is_prime(k):
        if k < 2:
            return False
        for i in range(2, k - 1):
            if k % i == 0:
                return False
        return True
    largest = 1
    for j in range(2, n + 1):
        if n % j == 0 and is_prime(j):
            largest = max(largest, j)
    return largest

# Rust f6 translation

def check(candidate):
    assert candidate(15) == 5,"Test 0"
    assert candidate(27) == 3,"Test 1"
    assert candidate(63) == 7,"Test 2"
    assert candidate(330) == 11,"Test 3"
    assert candidate(13195) == 29,"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(n: int):
    """f6 is a function that sums numbers from 1 to n. 	assert f6(1) == 1,"Test 0"
	assert f6(6) == 21,"Test 1"
	assert f6(11) == 66,"Test 2"
	assert f6(30) == 465,"Test 3"
	assert f6(100) == 5050,"Test 4"
	"""
    return sum(range(n + 1))

# Rust f6 translation

def check(candidate):
    assert candidate(1) == 1,"Test 0"
    assert candidate(6) == 21,"Test 1"
    assert candidate(11) == 66,"Test 2"
    assert candidate(30) == 465,"Test 3"
    assert candidate(100) == 5050,"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 correct_bracketing(brackets: str):
    """ brackets is a string of "(" and ")".
	assert f6("()"),"Test 0"
	assert f6("(()())"),"Test 1"
	assert f6("()()(()())()"),"Test 2"
	assert f6("()()((()()())())(()()(()))"),"Test 3"
	assert not f6("((()())))"),"Test 4"
	assert not f6(")(()"),"Test 5"
	assert not f6("("),"Test 6"
	assert not f6("(((("),"Test 7"
	assert not f6(")"),"Test 8"
	assert not f6("(()"),"Test 9"
	assert not f6("()()(()())())(()"),"Test 10"
	assert not f6("()()(()())()))()"),"Test 11"
	"""
    depth = 0
    for b in brackets:
        if b == "(":
            depth += 1
        else:
            depth -= 1
        if depth < 0:
            return False
    return depth == 0

# Rust f6 translation

def check(candidate):
    assert candidate("()"),"Test 0"
    assert candidate("(()())"),"Test 1"
    assert candidate("()()(()())()"),"Test 2"
    assert candidate("()()((()()())())(()()(()))"),"Test 3"
    assert not candidate("((()())))"),"Test 4"
    assert not candidate(")(()"),"Test 5"
    assert not candidate("("),"Test 6"
    assert not candidate("(((("),"Test 7"
    assert not candidate(")"),"Test 8"
    assert not candidate("(()"),"Test 9"
    assert not candidate("()()(()())())(()"),"Test 10"
    assert not candidate("()()(()())()))()"),"Test 11"


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(xs: list):
    """ xs represent coefficients of a polynomial.
    xs[0] + xs[1] * x + xs[2] * x^2 + ....
     Return f6 of this polynomial in the same form. 	assert f6([3, 1, 2, 4, 5]) == [1, 4, 12, 20],"Test 0"
	assert f6([1, 2, 3]) == [2, 6],"Test 1"
	assert f6([3, 2, 1]) == [2, 2],"Test 2"
	assert f6([3, 2, 1, 0, 4]) == [2, 2, 0, 16],"Test 3"
	assert f6([1]) == [],"Test 4"
	"""
    return [(i * x) for i, x in enumerate(xs)][1:]

# 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):
    """The FibFib number sequence is a sequence similar to the Fibbonacci sequnece that's defined as follows:
    f6(0) == 0
    f6(1) == 0
    f6(2) == 1
    f6(n) == f6(n-1) + f6(n-2) + f6(n-3).
    Please write a function to efficiently compute the n-th element of the f6 number sequence. 	assert f6(2) == 1,"Test 0"
	assert f6(1) == 0,"Test 1"
	assert f6(5) == 4,"Test 2"
	assert f6(8) == 24,"Test 3"
	assert f6(10) == 81,"Test 4"
	assert f6(12) == 274,"Test 5"
	assert f6(14) == 927,"Test 6"
	"""
    if n == 0:
        return 0
    if n == 1:
        return 0
    if n == 2:
        return 1
    return fibfib(n - 1) + fibfib(n - 2) + fibfib(n - 3)

# Rust f6 translation

def check(candidate):
    assert candidate(2) == 1,"Test 0"
    assert candidate(1) == 0,"Test 1"
    assert candidate(5) == 4,"Test 2"
    assert candidate(8) == 24,"Test 3"
    assert candidate(10) == 81,"Test 4"
    assert candidate(12) == 274,"Test 5"
    assert candidate(14) == 927,"Test 6"


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();
}

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

def f6(s):
    """Write a function f6 which takes a string representing
    a word as input and returns the number of vowels in the string.
    Vowels in this case are 'a', 'e', 'i', 'o', 'u'. Here, 'y' is also a
    vowel, but only when it is at the end of the given word. 	assert f6("abcde") == 2, "Test 1"
	assert f6("Alone") == 3, "Test 2"
	assert f6("key") == 2, "Test 3"
	assert f6("bye") == 1, "Test 4"
	assert f6("keY") == 2, "Test 5"
	assert f6("bYe") == 1, "Test 6"
	assert f6("ACEDY") == 3, "Test 7"
	assert True,"Test 7"
	"""
    vowels = "aeiouAEIOU"
    n_vowels = sum(c in vowels for c in s)
    if s[-1] == 'y' or s[-1] == 'Y':
        n_vowels += 1
    return n_vowels

# Rust f6 translation

def check(candidate):
    assert candidate("abcde") == 2, "Test 1"
    assert candidate("Alone") == 3, "Test 2"
    assert candidate("key") == 2, "Test 3"
    assert candidate("bye") == 1, "Test 4"
    assert candidate("keY") == 2, "Test 5"
    assert candidate("bYe") == 1, "Test 6"
    assert candidate("ACEDY") == 3, "Test 7"
    assert True,"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(x, shift):
    """Circular shift the digits of the integer x, shift the digits right by shift
    and return the result as a string.
    If shift > number of digits, return digits reversed. 	assert f6(100, 2) == "001","Test 0"
	assert f6(12, 2) == "12","Test 1"
	assert f6(97, 8) == "79","Test 2"
	assert f6(12, 1) == "21","Test 3"
	assert f6(11, 101) == "11","Test 4"
	"""
    s = str(x)
    if shift > len(s):
        return s[::-1]
    else:
        return s[len(s) - shift:] + s[:len(s) - shift]

# Rust f6 translation

def check(candidate):
    assert candidate(100, 2) == "001","Test 0"
    assert candidate(12, 2) == "12","Test 1"
    assert candidate(97, 8) == "79","Test 2"
    assert candidate(12, 1) == "21","Test 3"
    assert candidate(11, 101) == "11","Test 4"