There are n brackets, and you want to know whether they are matched. The brackets will only contain {, }, (, ), [, ]. Here is the matching rules. For example, {{[}]} is not matching, but [{{}}()] is matching. Please write a program to check whether the given string is matched or not. 

The first line will be an integer T, which is the number of test cases. (1 <= T <= 10)
For each test case, the first line will be an integer n ( 1 <= n <= 30000)
Then there is a line with n brackets. 

For each test case, print YES if the test case is a matching case. Otherwise, print NO. 

7
1
(
2
()
2
{]
6
[(){}]
4
(])[
8
[[{{}}]]
6
[][{]]

NO
YES
NO
YES
NO
YES
NO