#include<bits/stdc++.h>
using namespace std;

int T;

int n,ansbase;
struct data{
	int a,b;
	bool operator < (const data w) const{
		return a + max(0,w.a - b) < w.a + max(0,a - w.b);
	}
}a[100050];

void work(data &t){
	string s;
	cin >> s;
	t.a = t.b = 0;
	int l = 0;
	for (int i = 0; i < s.size(); ++i){
		if (s[i] == '(') ++l;
		else{
			if (l > 0) ansbase += 2,--l;
			else ++t.a;
		}
	}
	t.b = l;
}

void solve(){
	ansbase = 0;
	int suma = 0,sumb = 0;
	cin >> n;
	for (int i = 1; i <= n; ++i) work(a[i]),suma += a[i].a,sumb += a[i].b;
	sort(a + 1,a + n + 1);
	int now = 0,premax = 0;
	for (int i = 1; i <= n; ++i){
		now += a[i].a,premax = max(premax,a[i].a);
		now -= a[i].b;
	}
	ansbase += 2*(suma-premax);
	cout<<ansbase<<'\n';
}

int main(){
	ios::sync_with_stdio(0);
	cin >> T;
	while (T--) solve();
	return 0;
}