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(interval1, interval2):
    """You are given two intervals,
    where each interval is a pair of integers. 	assert f6((1, 2), (2, 3)) == "NO","Test 0"
	assert f6((-1, 1), (0, 4)) == "NO","Test 1"
	assert f6((-3, -1), (-5, 5)) == "YES","Test 2"
	assert f6((-2, 2), (-4, 0)) == "YES","Test 3"
	assert f6((-11, 2), (-1, -1)) == "NO","Test 4"
	assert f6((1, 2), (3, 5)) == "NO","Test 5"
	assert f6((1, 2), (1, 2)) == "NO","Test 6"
	assert f6((-2, -2), (-3, -2)) == "NO","Test 7"
	"""
    def is_prime(num):
        if num == 1 or num == 0:
            return False
        if num == 2:
            return True
        for i in range(2, num):
            if num%i == 0:
                return False
        return True

    l = max(interval1[0], interval2[0])
    r = min(interval1[1], interval2[1])
    length = r - l
    if length > 0 and is_prime(length):
        return "YES"
    return "NO"

# Rust f6 translation

def check(candidate):
    assert candidate((1, 2), (2, 3)) == "NO","Test 0"
    assert candidate((-1, 1), (0, 4)) == "NO","Test 1"
    assert candidate((-3, -1), (-5, 5)) == "YES","Test 2"
    assert candidate((-2, 2), (-4, 0)) == "YES","Test 3"
    assert candidate((-11, 2), (-1, -1)) == "NO","Test 4"
    assert candidate((1, 2), (3, 5)) == "NO","Test 5"
    assert candidate((1, 2), (1, 2)) == "NO","Test 6"
    assert candidate((-2, -2), (-3, -2)) == "NO","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(arr):
    """
    You are given an array arr of integers and you need to return
    sum of magnitudes of integers multiplied by product of all signs
    of each number in the array, represented by 1, -1 or 0.
    Note: return None for empty arr. 	assert True,"Test 0"
	assert f6([1, 2, 2, -4]) == -9,"Test 1"
	assert f6([0, 1]) == 0,"Test 2"
	assert f6([1, 1, 1, 2, 3, -1, 1]) == -10,"Test 3"
	assert f6([]) == None,"Test 4"
	assert f6([2, 4,1, 2, -1, -1, 9]) == 20,"Test 5"
	assert f6([-1, 1, -1, 1]) == 4,"Test 6"
	assert f6([-1, 1, 1, 1]) == -4,"Test 7"
	assert f6([-1, 1, 1, 0]) == 0,"Test 8"
	assert True,"Test 9"
	"""
    if not arr: return None
    prod = 0 if 0 in arr else (-1) ** len(list(filter(lambda x: x < 0, arr)))
    return prod * sum([abs(i) for i in arr])

# Rust f6 translation

def check(candidate):
    assert True,"Test 0"
    assert candidate([1, 2, 2, -4]) == -9,"Test 1"
    assert candidate([0, 1]) == 0,"Test 2"
    assert candidate([1, 1, 1, 2, 3, -1, 1]) == -10,"Test 3"
    assert candidate([]) == None,"Test 4"
    assert candidate([2, 4,1, 2, -1, -1, 9]) == 20,"Test 5"
    assert candidate([-1, 1, -1, 1]) == 4,"Test 6"
    assert candidate([-1, 1, 1, 1]) == -4,"Test 7"
    assert candidate([-1, 1, 1, 0]) == 0,"Test 8"
    assert True,"Test 9"


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

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

    return False

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

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

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

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

    return result

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

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

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

    return result;
}

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

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

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

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

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

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

def f6(grid, k):
    """
    Given a grid with N rows and N columns (N >= 2) and a positive integer k,
    each cell of the grid contains a value. Every integer in the range [1, N * N]
    inclusive appears exactly once on the cells of the grid.

    You have to find the minimum path of length k in the grid. You can start
    from any cell, and in each step you can move to any of the neighbor cells,
    in other words, you can go to cells which share an edge with you current
    cell.
    Please note that a path of length k means visiting exactly k cells (not
    necessarily distinct).
    You CANNOT go off the grid.
    A path A (of length k) is considered less than a path B (of length k) if
    after making the ordered lists of the values on the cells that A and B go
    through (let's call them lst_A and lst_B), lst_A is lexicographically less
    than lst_B, in other words, there exist an integer index i (1 <= i <= k)
    such that lst_A[i] < lst_B[i] and for any j (1 <= j < i) we have
    lst_A[j] = lst_B[j].
    It is guaranteed that the answer is unique.
    Return an ordered list of the values on the cells that the minimum path go through. 	assert f6([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 3) == [1, 2, 1],"Test 0"
	assert f6([[5, 9, 3], [4, 1, 6], [7, 8, 2]], 1) == [1],"Test 1"
	assert f6([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], 4) == [1, 2, 1, 2],"Test 2"
	assert f6([[6, 4, 13, 10], [5, 7, 12, 1], [3, 16, 11, 15], [8, 14, 9, 2]], 7) == [1, 10, 1, 10, 1, 10, 1],"Test 3"
	assert f6([[8, 14, 9, 2], [6, 4, 13, 15], [5, 7, 1, 12], [3, 10, 11, 16]], 5) == [1, 7, 1, 7, 1],"Test 4"
	assert f6([[11, 8, 7, 2], [5, 16, 14, 4], [9, 3, 15, 6], [12, 13, 10, 1]], 9) == [1, 6, 1, 6, 1, 6, 1, 6, 1],"Test 5"
	assert f6([[12, 13, 10, 1], [9, 3, 15, 6], [5, 16, 14, 4], [11, 8, 7, 2]], 12) == [1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6],"Test 6"
	assert f6([[2, 7, 4], [3, 1, 5], [6, 8, 9]], 8) == [1, 3, 1, 3, 1, 3, 1, 3],"Test 7"
	assert f6([[6, 1, 5], [3, 8, 9], [2, 7, 4]], 8) == [1, 5, 1, 5, 1, 5, 1, 5],"Test 8"
	assert f6([[1, 2], [3, 4]], 10) == [1, 2, 1, 2, 1, 2, 1, 2, 1, 2],"Test 9"
	assert f6([[1, 3], [3, 2]], 10) == [1, 3, 1, 3, 1, 3, 1, 3, 1, 3],"Test 10"
	"""
    n = len(grid)
    val = n * n + 1
    for i in range(n):
        for j in range(n):
            if grid[i][j] == 1:
                temp = []
                if i != 0:
                    temp.append(grid[i - 1][j])

                if j != 0:
                    temp.append(grid[i][j - 1])

                if i != n - 1:
                    temp.append(grid[i + 1][j])

                if j != n - 1:
                    temp.append(grid[i][j + 1])

                val = min(temp)

    ans = []
    for i in range(k):
        if i % 2 == 0:
            ans.append(1)
        else:
            ans.append(val)
    return ans

# Rust f6 translation


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

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

    return False

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

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

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

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

    return result

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

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

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

    return result;
}

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

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

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

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

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

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

def f6(n):
    """Everyone knows Fibonacci sequence, it was studied deeply by mathematicians in
    the last couple centuries. However, what people don't know is Tribonacci sequence.
    Tribonacci sequence is defined by the recurrence:
    f6(1) = 3
    f6(n) = 1 + n / 2, if n is even.
    f6(n) =  f6(n - 1) + f6(n - 2) + f6(n + 1), if n is odd. 	assert f6(3) == [1, 3, 2.0, 8.0],"Test 0"
	assert f6(4) == [1, 3, 2.0, 8.0, 3.0],"Test 1"
	assert f6(5) == [1, 3, 2.0, 8.0, 3.0, 15.0],"Test 2"
	assert f6(6) == [1, 3, 2.0, 8.0, 3.0, 15.0, 4.0],"Test 3"
	assert f6(7) == [1, 3, 2.0, 8.0, 3.0, 15.0, 4.0, 24.0],"Test 4"
	assert f6(8) == [1, 3, 2.0, 8.0, 3.0, 15.0, 4.0, 24.0, 5.0],"Test 5"
	assert f6(9) == [1, 3, 2.0, 8.0, 3.0, 15.0, 4.0, 24.0, 5.0, 35.0],"Test 6"
	assert f6(20) == [1, 3, 2.0, 8.0, 3.0, 15.0, 4.0, 24.0, 5.0, 35.0, 6.0, 48.0, 7.0, 63.0, 8.0, 80.0, 9.0, 99.0, 10.0, 120.0, 11.0],"Test 7"
	assert f6(0) == [1],"Test 8"
	assert f6(1) == [1, 3],"Test 9"
	"""
    if n == 0:
        return [1]
    my_tri = [1, 3]
    for i in range(2, n + 1):
        if i % 2 == 0:
            my_tri.append(i / 2 + 1)
        else:
            my_tri.append(my_tri[i - 1] + my_tri[i - 2] + (i + 3) / 2)
    return my_tri

# 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):
    """Given a positive integer n, return the product of the odd f6.
    Return 0 if all f6 are even. 	assert f6(5) == 5,"Test 0"
	assert f6(54) == 5,"Test 1"
	assert f6(120) ==1,"Test 2"
	assert f6(5014) == 5,"Test 3"
	assert f6(98765) == 315,"Test 4"
	assert f6(5576543) == 2625,"Test 5"
	assert f6(2468) == 0,"Test 6"
	"""
    product = 1
    odd_count = 0
    for digit in str(n):
        int_digit = int(digit)
        if int_digit%2 == 1:
            product= product*int_digit
            odd_count+=1
    if odd_count ==0:
        return 0
    else:
        return product

# Rust f6 translation

def check(candidate):
    assert candidate(5) == 5,"Test 0"
    assert candidate(54) == 5,"Test 1"
    assert candidate(120) ==1,"Test 2"
    assert candidate(5014) == 5,"Test 3"
    assert candidate(98765) == 315,"Test 4"
    assert candidate(5576543) == 2625,"Test 5"
    assert candidate(2468) == 0,"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(string):
    '''
    Create a function that takes a string as input which contains only square brackets.
    where at least one bracket in the subsequence is nested.

    '''
	assert f6('[[]]') == True,"Test 0"
	assert f6('[]]]]]]][[[[[]') == False,"Test 1"
	assert f6('[][]') == False,"Test 2"
	assert f6(('[]')) == False,"Test 3"
	assert f6('[[[[]]]]') == True,"Test 4"
	assert f6('[]]]]]]]]]]') == False,"Test 5"
	assert f6('[][][[]]') == True,"Test 6"
	assert f6('[[]') == False,"Test 7"
	assert f6('[]]') == False,"Test 8"
	assert f6('[[]][[') == True,"Test 9"
	assert f6('[[][]]') == True,"Test 10"
	assert f6('') == False,"Test 11"
	assert f6('[[[[[[[[') == False,"Test 12"
	assert f6(']]]]]]]]') == False,"Test 13"
	"""
    opening_bracket_index = []
    closing_bracket_index = []
    for i in range(len(string)):
        if string[i] == '[':
            opening_bracket_index.append(i)
        else:
            closing_bracket_index.append(i)
    closing_bracket_index.reverse()
    cnt = 0
    i = 0
    l = len(closing_bracket_index)
    for idx in opening_bracket_index:
        if i < l and idx < closing_bracket_index[i]:
            cnt += 1
            i += 1
    return cnt >= 2

# Rust f6 translation

def check(candidate):
    assert candidate('[[]]') == True,"Test 0"
    assert candidate('[]]]]]]][[[[[]') == False,"Test 1"
    assert candidate('[][]') == False,"Test 2"
    assert candidate(('[]')) == False,"Test 3"
    assert candidate('[[[[]]]]') == True,"Test 4"
    assert candidate('[]]]]]]]]]]') == False,"Test 5"
    assert candidate('[][][[]]') == True,"Test 6"
    assert candidate('[[]') == False,"Test 7"
    assert candidate('[]]') == False,"Test 8"
    assert candidate('[[]][[') == True,"Test 9"
    assert candidate('[[][]]') == True,"Test 10"
    assert candidate('') == False,"Test 11"
    assert candidate('[[[[[[[[') == False,"Test 12"
    assert candidate(']]]]]]]]') == False,"Test 13"


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(lst):
    """You are given a list of numbers.
    You need to return the sum of squared numbers in the given list,
    round each element in the list to the upper int(Ceiling) first. 	assert f6([1,2,3])==14,"Test 0"
	assert f6([1.0,2,3])==14,"Test 1"
	assert f6([1,3,5,7])==84,"Test 2"
	assert f6([1.4,4.2,0])==29,"Test 3"
	assert f6([-2.4,1,1])==6,"Test 4"
	assert f6([100,1,15,2])==10230,"Test 5"
	assert f6([10000,10000])==200000000,"Test 6"
	assert f6([-1.4,4.6,6.3])==75,"Test 7"
	assert f6([-1.4,17.9,18.9,19.9])==1086,"Test 8"
	assert f6([0])==0,"Test 9"
	assert f6([-1])==1,"Test 10"
	assert f6([-1,1,0])==2,"Test 11"
	"""
    import math
    squared = 0
    for i in lst:
        squared += math.ceil(i)**2
    return squared

# 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(txt):
    '''
    of a given string is an alphabetical character and is not
    Note: "word" is a group of characters separated by space. 	assert f6("apple") == False,"Test 0"
	assert f6("apple pi e") == True,"Test 1"
	assert f6("eeeee") == False,"Test 2"
	assert f6("A") == True,"Test 3"
	assert f6("Pumpkin pie ") == False,"Test 4"
	assert f6("Pumpkin pie 1") == False,"Test 5"
	assert f6("") == False,"Test 6"
	assert f6("eeeee e ") == False,"Test 7"
	assert f6("apple pie") == False,"Test 8"
	assert f6("apple pi e ") == False,"Test 9"
	assert True,"Test 10"
	"""

    check = txt.split(' ')[-1]
    return True if len(check) == 1 and (97 <= ord(check.lower()) <= 122) else False

# Rust f6 translation

def check(candidate):
    assert candidate("apple") == False,"Test 0"
    assert candidate("apple pi e") == True,"Test 1"
    assert candidate("eeeee") == False,"Test 2"
    assert candidate("A") == True,"Test 3"
    assert candidate("Pumpkin pie ") == False,"Test 4"
    assert candidate("Pumpkin pie 1") == False,"Test 5"
    assert candidate("") == False,"Test 6"
    assert candidate("eeeee e ") == False,"Test 7"
    assert candidate("apple pie") == False,"Test 8"
    assert candidate("apple pi e ") == False,"Test 9"
    assert True,"Test 10"


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(arr):
    """Create a function which returns the largest index of an element which
    is not greater than or equal to the element immediately preceding it. If
    no such element exists then return -1. The given array will not contain
    duplicate values. 	assert f6([1,2,4,3,5])==3,"Test 0"
	assert f6([1,2,4,5])==-1,"Test 1"
	assert f6([1,4,2,5,6,7,8,9,10])==2,"Test 2"
	assert f6([4,8,5,7,3])==4,"Test 3"
	assert f6([])==-1,"Test 4"
	"""
    ind=-1
    i=1
    while i<len(arr):
      if arr[i]<arr[i-1]:
        ind=i
      i+=1
    return ind

# Rust f6 translation

def check(candidate):
    assert candidate([1,2,4,3,5])==3,"Test 0"
    assert candidate([1,2,4,5])==-1,"Test 1"
    assert candidate([1,4,2,5,6,7,8,9,10])==2,"Test 2"
    assert candidate([4,8,5,7,3])==4,"Test 3"
    assert candidate([])==-1,"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(lst):
    '''
    Create a function that returns a tuple (a, b), where 'a' is
    the largest of negative integers, and 'b' is the smallest
    of positive integers in a list.
    If there is no negative or positive integers, return them as None. 	assert f6([2, 4, 1, 3, 5, 7]) == (None, 1),"Test 0"
	assert f6([2, 4, 1, 3, 5, 7, 0]) == (None, 1),"Test 1"
	assert f6([1, 3, 2, 4, 5, 6, -2]) == (-2, 1),"Test 2"
	assert f6([4, 5, 3, 6, 2, 7, -7]) == (-7, 2),"Test 3"
	assert f6([7, 3, 8, 4, 9, 2, 5, -9]) == (-9, 2),"Test 4"
	assert f6([]) == (None, None),"Test 5"
	assert f6([0]) == (None, None),"Test 6"
	assert f6([-1, -3, -5, -6]) == (-1, None),"Test 7"
	assert f6([-1, -3, -5, -6, 0]) == (-1, None),"Test 8"
	assert f6([-6, -4, -4, -3, 1]) == (-3, 1),"Test 9"
	assert f6([-6, -4, -4, -3, -100, 1]) == (-3, 1),"Test 10"
	assert True,"Test 11"
	"""
    smallest = list(filter(lambda x: x < 0, lst))
    largest = list(filter(lambda x: x > 0, lst))
    return (max(smallest) if smallest else None, min(largest) if largest else None)

# 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(a, b):
    """
    Create a function that takes integers, floats, or strings representing
    real numbers, and returns the larger variable in its given variable type.
    Return None if the values are equal.
    Note: If a real number is represented as a string, the floating point might be . or ,

    f6(1, 2.5) ➞ 2.5
    f6(1, "2,3") ➞ "2,3"
    f6("5,1", "6") ➞ "6"
    f6("1", 1) ➞ None
    	assert f6(1, 2) == 2, "Test 0"
	assert f6(1, 2.5) == 2.5, "Test 1"
	assert f6(2, 3) == 3, "Test 2"
	assert f6(5, 6) == 6, "Test 3"
	assert f6(1, "2,3") == "2,3", "Test 4"
	assert f6("5,1", "6") == "6", "Test 5"
	assert f6("1", "2") == "2", "Test 6"
	"""
    temp_a, temp_b = a, b
    if isinstance(temp_a, str): temp_a = temp_a.replace(',','.')
    if isinstance(temp_b, str): temp_b = temp_b.replace(',','.')
    if float(temp_a) == float(temp_b): return None
    return a if float(temp_a) > float(temp_b) else b

# Rust f6 translation

def check(candidate):
    assert candidate(1, 2) == 2, "Test 0"
    assert candidate(1, 2.5) == 2.5, "Test 1"
    assert candidate(2, 3) == 3, "Test 2"
    assert candidate(5, 6) == 6, "Test 3"
    assert candidate(1, "2,3") == "2,3", "Test 4"
    assert candidate("5,1", "6") == "6", "Test 5"
    assert candidate("1", "2") == "2", "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):
    """Evaluate whether the given number n can be written as the sum of exactly 4 positive even numbers. 	assert f6(4) == False,"Test 0"
	assert f6(6) == False,"Test 1"
	assert f6(8) == True,"Test 2"
	assert f6(10) == True,"Test 3"
	assert f6(11) == False,"Test 4"
	assert f6(12) == True,"Test 5"
	assert f6(13) == False,"Test 6"
	assert f6(16) == True,"Test 7"
	"""
    return n%2 == 0 and n >= 8

# Rust f6 translation

def check(candidate):
    assert candidate(4) == False,"Test 0"
    assert candidate(6) == False,"Test 1"
    assert candidate(8) == True,"Test 2"
    assert candidate(10) == True,"Test 3"
    assert candidate(11) == False,"Test 4"
    assert candidate(12) == True,"Test 5"
    assert candidate(13) == False,"Test 6"
    assert candidate(16) == 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(n):
    """The Brazilian factorial is defined as:
    brazilian_factorial(n) = n! * (n-1)! * (n-2)! * ... * 1!
    where n > 0. 	assert f6(4) == 288, "Test 4"
	assert f6(5) == 34560, "Test 5"
	assert f6(7) == 125411328000, "Test 7"
	assert f6(1) == 1, "Test 1"
	"""
    fact_i = 1
    special_fact = 1
    for i in range(1, n+1):
        fact_i *= i
        special_fact *= fact_i
    return special_fact

# Rust f6 translation

def check(candidate):
    assert candidate(4) == 288, "Test 4"
    assert candidate(5) == 34560, "Test 5"
    assert candidate(7) == 125411328000, "Test 7"
    assert candidate(1) == 1, "Test 1"


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

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

    return False

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

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

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

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

    return result

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

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

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

    return result;
}

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

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

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

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

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

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

def f6(text):
    """
    Given a string text, replace all spaces in it with underscores,
    and if a string has more than 2 consecutive spaces,
    then replace all consecutive spaces with -
. 	assert f6("Example") == "Example","Test 0"
	assert f6("Mudasir Hanif ") == "Mudasir_Hanif_","Test 1"
	assert f6("Yellow Yellow  Dirty  Fellow") == "Yellow_Yellow__Dirty__Fellow","Test 2"
	assert f6("Exa   mple") == "Exa-mple","Test 3"
	assert f6("   Exa 1 2 2 mple") == "-Exa_1_2_2_mple","Test 4"
	"""
    new_text = ""
    i = 0
    start, end = 0, 0
    while i < len(text):
        if text[i] == " ":
            end += 1
        else:
            if end - start > 2:
                new_text += "-"+text[i]
            elif end - start > 0:
                new_text += "_"*(end - start)+text[i]
            else:
                new_text += text[i]
            start, end = i+1, i+1
        i+=1
    if end - start > 2:
        new_text += "-"
    elif end - start > 0:
        new_text += "_"
    return new_text

# Rust f6 translation

def check(candidate):
    assert candidate("Example") == "Example","Test 0"
    assert candidate("Mudasir Hanif ") == "Mudasir_Hanif_","Test 1"
    assert candidate("Yellow Yellow  Dirty  Fellow") == "Yellow_Yellow__Dirty__Fellow","Test 2"
    assert candidate("Exa   mple") == "Exa-mple","Test 3"
    assert candidate("   Exa 1 2 2 mple") == "-Exa_1_2_2_mple","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(file_name):
    """Create a function which takes a string representing a file's name, and returns
    'Yes' if the the file's name is valid, and returns 'No' otherwise.
    A file's name is considered to be valid if and only if all the following conditions
    are met:
    - There should not be more than three digits ('0'-'9') in the file's name.
    - The file's name contains exactly one dot '.'
    - The substring before the dot should not be empty, and it starts with a letter from
    the latin alphapet ('a'-'z' and 'A'-'Z').
    - The substring after the dot should be one of these: ['txt', 'exe', 'dll']. 	assert f6("example.txt") == 'Yes',"Test 0"
	assert f6("1example.dll") == 'No',"Test 1"
	assert f6('s1sdf3.asd') == 'No',"Test 2"
	assert f6('K.dll') == 'Yes',"Test 3"
	assert f6('MY16FILE3.exe') == 'Yes',"Test 4"
	assert f6('His12FILE94.exe') == 'No',"Test 5"
	assert f6('_Y.txt') == 'No',"Test 6"
	assert f6('?aREYA.exe') == 'No',"Test 7"
	assert f6('/this_is_valid.dll') == 'No',"Test 8"
	assert f6('this_is_valid.wow') == 'No',"Test 9"
	assert f6('this_is_valid.txt') == 'Yes',"Test 10"
	assert f6('this_is_valid.txtexe') == 'No',"Test 11"
	assert f6('#this2_i4s_5valid.ten') == 'No',"Test 12"
	assert f6('@this1_is6_valid.exe') == 'No',"Test 13"
	assert f6('this_is_12valid.6exe4.txt') == 'No',"Test 14"
	assert f6('all.exe.txt') == 'No',"Test 15"
	assert f6('I563_No.exe') == 'Yes',"Test 16"
	assert f6('Is3youfault.txt') == 'Yes',"Test 17"
	assert f6('no_one#knows.dll') == 'Yes',"Test 18"
	assert f6('1I563_Yes3.exe') == 'No',"Test 19"
	assert f6('I563_Yes3.txtt') == 'No',"Test 20"
	assert f6('final..txt') == 'No',"Test 21"
	assert f6('final132') == 'No',"Test 22"
	assert f6('_f4indsartal132.') == 'No',"Test 23"
	assert f6('.txt') == 'No',"Test 24"
	assert f6('s.') == 'No',"Test 25"
	"""
    suf = ['txt', 'exe', 'dll']
    lst = file_name.split(sep='.')
    if len(lst) != 2:
        return 'No'
    if not lst[1] in suf:
        return 'No'
    if len(lst[0]) == 0:
        return 'No'
    if not lst[0][0].isalpha():
        return 'No'
    t = len([x for x in lst[0] if x.isdigit()])
    if t > 3:
        return 'No'
    return 'Yes'

# Rust f6 translation

def check(candidate):
    assert candidate("example.txt") == 'Yes',"Test 0"
    assert candidate("1example.dll") == 'No',"Test 1"
    assert candidate('s1sdf3.asd') == 'No',"Test 2"
    assert candidate('K.dll') == 'Yes',"Test 3"
    assert candidate('MY16FILE3.exe') == 'Yes',"Test 4"
    assert candidate('His12FILE94.exe') == 'No',"Test 5"
    assert candidate('_Y.txt') == 'No',"Test 6"
    assert candidate('?aREYA.exe') == 'No',"Test 7"
    assert candidate('/this_is_valid.dll') == 'No',"Test 8"
    assert candidate('this_is_valid.wow') == 'No',"Test 9"
    assert candidate('this_is_valid.txt') == 'Yes',"Test 10"
    assert candidate('this_is_valid.txtexe') == 'No',"Test 11"
    assert candidate('#this2_i4s_5valid.ten') == 'No',"Test 12"
    assert candidate('@this1_is6_valid.exe') == 'No',"Test 13"
    assert candidate('this_is_12valid.6exe4.txt') == 'No',"Test 14"
    assert candidate('all.exe.txt') == 'No',"Test 15"
    assert candidate('I563_No.exe') == 'Yes',"Test 16"
    assert candidate('Is3youfault.txt') == 'Yes',"Test 17"
    assert candidate('no_one#knows.dll') == 'Yes',"Test 18"
    assert candidate('1I563_Yes3.exe') == 'No',"Test 19"
    assert candidate('I563_Yes3.txtt') == 'No',"Test 20"
    assert candidate('final..txt') == 'No',"Test 21"
    assert candidate('final132') == 'No',"Test 22"
    assert candidate('_f4indsartal132.') == 'No',"Test 23"
    assert candidate('.txt') == 'No',"Test 24"
    assert candidate('s.') == 'No',"Test 25"


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(lst):
    """"
    This function will take a list of integers. For all entries in the list, the function shall square the integer entry if its index is a
    multiple of 3 and will cube the integer entry if its index is a multiple of 4 and not a multiple of 3. The function will not
    change the entries in the list whose indexes are not a multiple of 3 or 4. The function shall then return the sum of all entries. 	assert f6([1,2,3]) == 6,"Test 0"
	assert f6([1,4,9]) == 14,"Test 1"
	assert f6([]) == 0,"Test 2"
	assert f6([1,1,1,1,1,1,1,1,1]) == 9,"Test 3"
	assert f6([-1,-1,-1,-1,-1,-1,-1,-1,-1]) == -3,"Test 4"
	assert f6([0]) == 0,"Test 5"
	assert f6([-1,-5,2,-1,-5]) == -126,"Test 6"
	assert f6([-56,-99,1,0,-2]) == 3030,"Test 7"
	assert f6([-1,0,0,0,0,0,0,0,-1]) == 0,"Test 8"
	assert f6([-16, -9, -2, 36, 36, 26, -20, 25, -40, 20, -4, 12, -26, 35, 37]) == -14196,"Test 9"
	assert f6([-1, -3, 17, -1, -15, 13, -1, 14, -14, -12, -5, 14, -14, 6, 13, 11, 16, 16, 4, 10]) == -1448,"Test 10"
	"""
    result =[]
    for i in range(len(lst)):
        if i %3 == 0:
            result.append(lst[i]**2)
        elif i % 4 == 0 and i%3 != 0:
            result.append(lst[i]**3)
        else:
            result.append(lst[i])
    return sum(result)

# 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(sentence):
    """
    You are given a string representing a sentence,
    the sentence contains some words separated by a space,
    and you have to return a string that contains the words from the original sentence,
    whose lengths are prime numbers,
    the order of the words in the new string should be the same as the original one. 	assert f6("This is a test") == "is","Test 0"
	assert f6("lets go for swimming") == "go for","Test 1"
	assert f6("there is no place available here") == "there is no place","Test 2"
	assert f6("Hi I am Hussein") == "Hi am Hussein","Test 3"
	assert f6("go for it") == "go for it","Test 4"
	assert f6("here") == "","Test 5"
	assert f6("here is") == "is","Test 6"
	"""
    new_lst = []
    for word in sentence.split():
        flg = 0
        if len(word) == 1:
            flg = 1
        for i in range(2, len(word)):
            if len(word)%i == 0:
                flg = 1
        if flg == 0 or len(word) == 2:
            new_lst.append(word)
    return " ".join(new_lst)

# Rust f6 translation

def check(candidate):
    assert candidate("This is a test") == "is","Test 0"
    assert candidate("lets go for swimming") == "go for","Test 1"
    assert candidate("there is no place available here") == "there is no place","Test 2"
    assert candidate("Hi I am Hussein") == "Hi am Hussein","Test 3"
    assert candidate("go for it") == "go for it","Test 4"
    assert candidate("here") == "","Test 5"
    assert candidate("here is") == "is","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(x, n):
    """Your task is to implement a function that will f6 the expression
    otherwise. Both x and n, are string representation of a fraction, and have the following format,
    <numerator>/<denominator> where both numerator and denominator are positive whole numbers.

    You can assume that x, and n are valid fractions, and do not have zero as denominator.

    	assert f6("1/5", "5/1") == True, "Test 0"
	assert f6("1/6", "2/1") == False, "Test 1"
	assert f6("5/1", "3/1") == True, "Test 2"
	assert f6("7/10", "10/2") == False, "Test 3"
	assert f6("2/10", "50/10") == True, "Test 4"
	assert f6("7/2", "4/2") == True, "Test 5"
	"""
    a, b = x.split("/")
    c, d = n.split("/")
    numerator = int(a) * int(c)
    denom = int(b) * int(d)
    if (numerator/denom == int(numerator/denom)):
        return True
    return False

# Rust f6 translation

def check(candidate):
    assert candidate("1/5", "5/1") == True, "Test 0"
    assert candidate("1/6", "2/1") == False, "Test 1"
    assert candidate("5/1", "3/1") == True, "Test 2"
    assert candidate("7/10", "10/2") == False, "Test 3"
    assert candidate("2/10", "50/10") == True, "Test 4"
    assert candidate("7/2", "4/2") == True, "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(nums):
    """
    Write a function which sorts the given list of integers
    in ascending order according to the sum of their digits.
    Note: if there are several items with similar sum of their digits,
    order them based on their index in original list. 	assert f6([1, 11, -1, -11, -12]) == [-1, -11, 1, -12, 11],"Test 0"
	assert f6([1234,423,463,145,2,423,423,53,6,37,3457,3,56,0,46]) == [0, 2, 3, 6, 53, 423, 423, 423, 1234, 145, 37, 46, 56, 463, 3457],"Test 1"
	assert f6([]) == [],"Test 2"
	assert f6([1, -11, -32, 43, 54, -98, 2, -3]) == [-3, -32, -98, -11, 1, 2, 43, 54],"Test 3"
	assert f6([1,2,3,4,5,6,7,8,9,10,11]) == [1, 10, 2, 11, 3, 4, 5, 6, 7, 8, 9],"Test 4"
	assert f6([0,6,6,-76,-21,23,4]) == [-76, -21, 0, 4, 23, 6, 6],"Test 5"
	assert True,"Test 6"
	"""
    def digits_sum(n):
        neg = 1
        if n < 0: n, neg = -1 * n, -1
        n = [int(i) for i in str(n)]
        n[0] = n[0] * neg
        return sum(n)
    return sorted(nums, key=digits_sum)

# Rust f6 translation