A bracket is considered to be any one of the following characters: (, ), {, }, [, or ].

Two brackets are considered to be a matched pair if the an opening bracket (i.e., (, [, or {) occurs to the left of a closing bracket (i.e., ), ], or }) of the exact same type. There are three types of matched pairs of brackets: [], {},and ().

A matching pair of brackets is not balanced if the set of brackets it encloses are not matched. For example, {[(])} is not balanced because the contents in between { and } are not balanced. The pair of square brackets encloses a single, unbalanced opening bracket, (, and the pair of parentheses encloses a single, unbalanced closing square bracket, ].

By this logic, we say a sequence of brackets is balanced if the following conditions are met:

It contains no unmatched brackets.

The subset of brackets enclosed within the confines of a matched pair of brackets is also a matched pair of brackets.

Given n strings of brackets, determine whether each sequence of

brackets is balanced. If a string is balanced, return YES. Otherwise, return NO.

**INPUT:**

The first line contains a single integer n, the number of strings.

Each of the next n lines contains a single string s, a sequence of brackets.

**CONSTRAINTS:**

1<=n<=10^3

1<=|s|<=10^3, where is the length of the sequence.

All chracters in the sequences ? { {, }, (, ), [, ] }.

**OUTPUT:**

For each string, return YES or NO.

Explanation

1.The string {[()]} meets both criteria for being a balanced string, so we print YES on a new line.

2.The string {[(])} is not balanced because the brackets enclosed by the matched pair { and } are not balanced: [(]).

3.The string {{[[(())]]}} meets both criteria for being a balanced string, so we print YES on a new line.

Time Limit:
5.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

Marking Scheme:
Marks are awarded when all the testcases pass.

Allowed Languages:
Bash,
C,
C++,
C++14,
C++17,
Clojure,
C#,
D,
Erlang,
F#,
Go,
Groovy,
Haskell,
Java,
Java 8,
Java 14,
JavaScript(Rhino),
JavaScript(Node.js),
Julia,
Kotlin,
Lisp,
Lisp (SBCL),
Lua,
Objective-C,
OCaml,
Octave,
Pascal,
Perl,
PHP,
Python,
Python 3,
Python 3.8,
R(RScript),
Racket,
Ruby,
Rust,
Scala,
Swift-4.1,
Swift,
TypeScript,
Visual Basic

Initializing Code Editor...

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