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

bracket_logic("[<>()]") ➞ true

bracket_logic("[<(>)]") ➞ false

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

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

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

Notes

Any characters other than the brackets can be ignored.