Simplify Linear Constraints

You are given a single variable x and a set of constraints in the form of $x \geq a$ or $x \leq a$, where a is an integer. The constraints are separated by ||. Your task is to simplify these constraints by combining them into a single, equivalent constraint.

For the simplification, consider the following:

• For all constraints of the form $x \geq a$, choose the maximum a as the effective lower bound.
• For all constraints of the form $x \leq a$, choose the minimum a as the effective upper bound.
• If both a lower bound and an upper bound exist and the lower bound is greater than the upper bound, then the constraints are contradictory; output false.
• If only one type of constraint is present, output that constraint alone.
• If both are valid, output the simplified constraint in the form x >= L and x <= U where L and U are the simplified bounds.

inputFormat

The input consists of a single line containing one or more constraints separated by ||. Each constraint is in one of the following LaTeX formats:

$x \geq a$ or $x \leq a$, where a is an integer.

outputFormat

Output the simplified constraint. The output should be one of the following formats:

• If both lower and upper bounds are applicable and valid, output: x >= L and x <= U
• If only a lower bound is provided, output: x >= L
• If only an upper bound is provided, output: x <= U
• If the constraints are contradictory, output: false

sample

x >= 3||x <= 7

x >= 3 and x <= 7