

Balanced SequenceTime 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
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