#include <stdio.h>

 #include <iostream>

 #include <cstdlib>

 #include <cmath>

 #include <string>

 #include <cstring>

 #include <algorithm>

 #include <stack>

 #include <queue>

 #include <set>

 #include <map>

 #include <vector>

 using namespace std;

 typedef long long ll;

 typedef unsigned long long ull;

 #define Faster ios::sync_with_stdio(false),cin.tie(0)

 #define Read freopen("in.txt", "r", stdin),freopen("out.txt", "w", stdout)

 const int INF = 0x3f3f3f3f;

 const int maxn = 1e5 + ;

 const int MOD = 1e9 + ;

 struct node{

     int left, right;

     bool operator < (const node& x) const {

         if(left <= right && x.right < x.left) return false;

         else if(left > right && x.right >= x.left) return true;

         if(left <= right && x.right >= x.left) return left > x.left;

         else return right < x.right;

     }

 }a[maxn];

 int main()

 {

     Faster;

     int t;

     cin >> t;

     while(t--){

         int n;

         cin >> n;

         int ans = ;

         for(int i = ;i < n;i++){

             string s;

             cin >> s;

             a[i].left = a[i].right = ;

             for(int j = ;j < s.size();j++){

                 if(s[j] == '('){

                     a[i].left++;

                 }

                 else if(s[j] == ')'){

                     if(a[i].left > ){

                         a[i].left--;

                         ans += ;

                     }

                     else{

                         a[i].right++;

                     }

                 }

             }

         }

         sort(a, a+n);

         int now = ;    //记录有多少左括号没有匹配

         for(int i = ;i < n;i++){

             if(a[i].right > now)

                 a[i].right = now;

             ans += a[i].right*;

             now -= a[i].right;

             now += a[i].left;

         }

         cout << ans << endl;

     }

     return ;

 }