#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int n;
string s[100005];
int sum[100005] , mn[100005];
vector<pair<int,int> > pos , neg;
bool check(int x)
{
    int s = 0;
    for(int i = 0;i < pos.size();i++) {
        if(s + pos[i].first < -x) return 0;
        s += pos[i].second ;
    }
   //printf("HERE %d\n" , s);
    int t = 0 , mn = 0;
    for(int i = 0;i < neg.size();i++) {
        mn = min(mn , t + neg[i].first);
        t += neg[i].second;
    }
    mn = min(mn , t);
    int delta = -x - mn;
   // printf("here %d %d , %d\n",t,mn,delta);
    t += delta ;
    return (t <= s);
}
void solve()
{
    cin >> n; pos.clear() ; neg.clear() ;
    int l = 0 , r = 0 , sm = 0, len = 0;
    for(int i = 1;i <= n;i++) {
        cin >> s[i]; r += s[i].size(); len += s[i].size();
        sum[i] = 0;
        mn[i] = 0;
        for(int j = 0;j < s[i].size();j++) {
            if(s[i][j] == '(') sum[i]++;
            else sum[i]--;
            mn[i] = min(mn[i] , sum[i]);
        }
        sm += sum[i];
        if(sum[i] >= 0) {
            pos.push_back(pair<int,int>{mn[i] , sum[i]});
        }
        else {
            sum[i] = 0; mn[i] = 0;
            for(int j = s[i].size() - 1;j >= 0;j--) {
                if(s[i][j] == '(') sum[i]--;
                else sum[i]++;
                mn[i] = min(mn[i] , sum[i]);
            }
            neg.push_back(pair<int,int>{mn[i] , sum[i]});
        }
    }
    sort(pos.begin() , pos.end()); reverse(pos.begin() , pos.end());
    sort(neg.begin()  ,neg.end()); reverse(neg.begin() , neg.end());
    //for(auto [x,y] : pos) printf("pos %d %d\n",x,y);
   // for(auto [x,y] : neg) printf("neg %d %d\n",x,y);
    //check(0) ; return ;
    while(l < r) {
        int md = (l + r >> 1);
        if(check(md)) r = md;
        else l = md + 1;
    }
  //  cout << len <<' ' << sm <<' ' << l << '\n';
    cout << len - (abs(sm + l) + l) << '\n';
}
int main()
{
//    freopen("in.txt","r",stdin);
    ios::sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0);
    int t;cin >> t;
    while(t--) {
            solve();
    }
    return 0;
}