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You are given a string of 2N characters consisting of N ‘[‘ brackets and N ‘]’ brackets. A string is considered balanced if it can be represented in the for S2[S1] where S1 and S2 are balanced strings. We can make an unbalanced string balanced by swapping adjacent characters. Calculate the minimum number of swaps necessary to make a string balanced.
Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains an integer N denoting the length of the string.
The second line of each test case contains the string consisting of '[' and ']'.
Output:
Print the minimum number of swaps to make the string balanced for each test case in a new line.
Constraints:
1<= T <=100
1<= N <=100000
Example:
Input : []][][
Output : 2
First swap: Position 3 and 4
[][]][
Second swap: Position 5 and 6
[][][]
Input : [[][]]
Output : 0
String is already balanced.
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