Stacks: Balanced Brackets

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, ].

Some examples of balanced brackets are []{}(), [({})]{}() and ({(){}[]})[].

By this logic, we say a sequence of brackets is considered to be 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 strings of brackets, determine whether each sequence of brackets is balanced. If a string is balanced, print YES on a new line; otherwise, print NO on a new line.

Input Format

The first line contains a single integer, , denoting the number of strings.
Each line of the subsequent lines consists of a single string, , denoting a sequence of brackets.

Constraints

, where is the length of the sequence.
Each character in the sequence will be a bracket (i.e., {, }, (, ), [, and ]).

Output Format

For each string, print whether or not the string of brackets is balanced on a new line. If the brackets are balanced, print YES; otherwise, print NO.

Sample Input

3
{[()]}
{[(])}
{{[[(())]]}}

Sample Output

YES
NO
YES

Explanation

The string {[()]} meets both criteria for being a balanced string, so we print YES on a new line.
The string {[(])} is not balanced, because the brackets enclosed by the matched pairs [(] and (]) are not balanced. Thus, we print NO on a new line.
The string {{[[(())]]}} meets both criteria for being a balanced string, so we print YES on a new line.