Balanced Sequence

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 $t$.

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 $5 \times 10^6$.

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

2
1
)()(()(
2
)
)(

4
2

2018 Multi-University Training Contest 1