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.

Function Description

Complete the function isBalanced in the editor below.

isBalanced has the following parameter(s):

string s: a string of brackets

Returns

string: either YES or NO

Input Format

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

$1\leq n\leq10^3$
$1\leq|s|\leq10^3$, where $|s|$ is the length of the sequence.
All chracters in the sequences ∈ { {, }, (, ), [, ] }.

Output Format

For each string, return YES or NO.

Sample Input
STDIN Function
----- --------
3 n = 3
{[()]} first s = '{[()]}'
{[(])} second s = '{[(])}'
{{[[(())]]}} third s ='{{[[(())]]}}'

Sample Output
YES
NO
YES

Explanation

The string {[()]} meets both criteria for being a balanced string.
The string {[(])} is not balanced because the brackets enclosed by the matched pair { and } are not balanced: [(]).
The string {{[[(())]]}} meets both criteria for being a balanced string.

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