Balanced Sequence

괄호 문자열 n개를 임의 순서로 이어 붙인 뒤 만들 수 있는 가장 긴 균형 부분 수열의 길이를 구한다.

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문제 설명

예제1

문제

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 $t$ .

입력

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 $5 \times 10^6$ .

출력

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