Evaluate Expressions with Strictly Positive Integer Intermediate Results

Evaluate a string arithmetic expression whose literals are positive integers and whose binary operators are `+`, `-`, `*`, and `/`. Return its integer value if every evaluated subexpression has a strictly positive integer result. If any literal, operand, or intermediate result fails that rule, return Boolean `false` for the whole expression; later operations cannot make that subexpression valid. ### Supplied Decomposition Helper Assume a helper `split(s)` is provided for expressions in this task. It decomposes an expression at its outermost operation and returns either a one-element tuple containing a literal expression or a three-element tuple `(left_expression, operator, right_expression)`. The returned operand expressions may themselves need evaluation. ```text split("3 / 5") -> ("3", "/", "5") split("5") -> ("5",) split("(10 / 2) / 5") -> ("(10 / 2)", "/", "5") ``` The helper determines the decomposition of a valid input expression. This task does not ask you to implement a parser. The source does not specify the helper's behavior for malformed expressions or every unparenthesized operator combination. ### Arithmetic and Output Rules - A literal must be a positive integer after permitted surrounding whitespace and enclosing parentheses are removed. Zero is invalid. - Addition and multiplication use exact integer arithmetic. Subtraction is invalid if its result is zero or negative. - Division is invalid if the divisor is zero or if the dividend is not exactly divisible by the divisor. Do not round or truncate a fractional quotient. - Return the final positive integer, or Boolean `false` when any subexpression is invalid. ### Examples ```text expression = "(3 + (3 * 5)) / 2" result = 9 expression = "((3 - 5) + 12) / 2" result = false expression = "8 / 12" result = false expression = "3 - 3" result = false ``` In the second example, the subtraction yields a negative intermediate result. In the third, division is not exact. The fourth is invalid because this task requires strictly positive results; zero from subtraction is invalid too.