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# Balanced Sequence

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 8946    Accepted Submission(s): 2310

Problem Description
Chiaki has $n$ strings $s_1,s_2,\dots,s_n$ consisting of '(' and ')'. A string of this type is said to be balanced:

+ if it is the empty string
+ if $A$ and $B$ are balanced, $AB$ is balanced,
+ if $A$ is balanced, $(A)$ is balanced.

Chiaki can reorder the strings and then concatenate them get a new string $t$. Let $f(t)$ be the length of the longest balanced subsequence (not necessary continuous) of $t$. Chiaki would like to know the maximum value of $f(t)$ for all possible $t$.

Input
There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:
The first line contains an integer $n$ ($1 \le n \le 10^5$) -- the number of strings.
Each of the next $n$ lines contains a string $s_i$ ($1 \le |s_i| \le 10^5$) consisting of (' and )'.
It is guaranteed that the sum of all $|s_i|$ does not exceeds $5 \times 10^6$.

Output
For each test case, output an integer denoting the answer.

Sample Input
2
1
)()(()(
2
)
)(


Sample Output
4
2


Source

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