Mismatched Brackets

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Best White is a mathematics graduate student at T1 University. Recently, he finished writing a paper and he decided to polish it. As he started to read it from the beginning, he realized that some of the formulas have problems: some of the brackets are mismatched! Since there are so many formulas in his paper, he decided to check their validity with a computer program.

The following kinds of brackets are included in Best White’s paper.

  • Round brackets are opened by a ( and closed by a ).
  • Curly brackets are opened by a { and closed by a }.
  • Square brackets are opened by a [ and closed by a ].

A formula is said well-matched when the following conditions are met:

  1. Every bracket has a corresponding pair. ( corresponds to ), [ corresponds to ], et cetera.
  2. Every bracket pair is opened first, and closed later.
  3. No two pairs "*cross*" each other. For example, [(]) is not well-matched.

Write a program to help Best White by checking if each of his formulas is well-matched. To make the problem easier, everything other than brackets are removed from the formulas.


The first line of the input will contain the number of test cases C\ (1 \le C \le 100). Each test is given in a single line as a character string. The strings will only include characters in "[](){}" (quotes for clarity). The length of the string will not exceed 10,000.


For each test case, print a single line "YES" when the formula is well-matched; print "NO" otherwise. (quotes for clarity)

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