# 3212. 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, ].

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.

### 输入格式

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

Each line $i$ of the $n$ subsequent lines consists of a single string, $s$, denoting a sequence of brackets.

• $1 \leq n \leq 10^3$
• $1 \leq len_s \leq 10^3$, where $len_s$ is the length of the sequence.
• Each character in the sequence will be a bracket (i.e., {, }, (, ), [, and ]).

### 输出格式

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.

### 样例

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

Output
YES
NO
YES


### 提示

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 pairs [(] and (]) are not balanced.

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

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