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Statement

 Goal

You must determine whether a given expression's bracketing can be made valid by flipping them in-place. An expression has a valid bracketing when all the parentheses (), square brackets [], curly braces {} and angle brackets <> are correctly paired and nested.

You can flip a bracketing element in-place by replacing it with its counterpart, e.g. replace a ( with a ), or a > with a <. For example, converting the second parenthesis in the expression below would make it valid:
<{[(abc(]}> → <{[(abc)]}>

(This is a harder version of community puzzle “Brackets, Extended Edition”. You may want to complete that one first.)
Input
Line 1: the number N of expressions
Next N lines: an expression
Output
N lines: true if the expression can be made valid by flipping elements in-place; false otherwise.
Constraints
N ≤ 100
number of bracketing elements ≤ 500
expression length ≤ 10000
The expression contains no whitespace.
Example
Input
2
<{[(abc(]}>
<{[(abc>}])
Output
true
false
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