Bracket Logic

Brackets and parentheses in mathematical expressions have to conform to certain logical rules. Every opening bracket must have a closing mate somewhere further down the line. Although brackets can be nested, different types cannot overlap:

• ([<x+y>+3]-1) makes sense because each set of brackets contains or is contained by another set.
• ([<x+y>+3)-1] makes no sense because the parentheses and the square brackets overlap.

Given a string expression that can contain four types of brackets: () <> [] {}, create a function that returns true if the bracket logic is valid and false if it is not.

Examples

bracketLogic("[<>()]") ➞ true

bracketLogic("[<(>)]") ➞ false

bracketLogic("[(a*b+<7-c>+9]") ➞ false
// Opening parenthesis has no mate.

bracketLogic("[{(h*i+3)-12]/4*x+2}") ➞ false
// Square and curly brackets overlap.

bracketLogic("[ab(c/d<e-f+(7*6)>)+2]") ➞ true

Notes

Any characters other than the brackets can be ignored.