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 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, return YES. Otherwise, return NO.

Function Description

Complete the function isBalanced in the editor below. It must return a string: YES if the sequence is balanced or NO if it is not.

isBalanced has the following parameter(s):

• s: a string of brackets

Input Format

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

Constraints

• , where  is the length of the sequence.
• All chracters in the sequences ∈ { {, }, (, ), [, ] }.

Output Format

For each string, return YES or NO.

Sample Input

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

Sample Output

YES
NO
YES

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.

---

쉽게 생각하면 { 와 [ 와 ( 에 대한 가중치? 계산을 해서 하나씩 더하고 빼고 하면 되겠지만, 중요한건 Balance 를 맞춰야만 "YES"가 된다는 것이다.

문제는 의외로 쉽게 풀 수 있다.