#include<cstdio>

 #include<cstring>

 #include<string>

 #include<cmath>

 #include<iostream>

 #include<algorithm>

 #include<map>

 #include<set>

 #include<queue>

 #include<vector>

 using namespace std;

 typedef long long ll;

 typedef unsigned int uint;

 typedef unsigned long long ull;

 typedef pair<int,int> PII;

 typedef vector<int> VI;

 #define fi first

 #define se second

 #define MP make_pair

 int read()

 {

     int v=, f=;

     char c=getchar();

     while (c<||<c) {if(c=='-') f=-; c=getchar();}

     while (<=c&&c<=) v=(v<<)+v+v+c-, c=getchar();

     return v*f;

 }

 const int N=;

 int a[N],b[N],n,ans;

 char ch[N];

 PII A[N],B[N],C[N]; 

 bool cmp1(const PII &a,const PII &b)

 {

     return a.fi<b.fi;

 }

 bool cmp2(const PII &a,const PII &b)

 {

     return a.se>b.se;

 }

 int main()

 {

     int cas=read();

     while(cas--)

     {

         n=read();

         int ans=;

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

         {

             scanf("%s",ch+);

             a[i]=b[i]=;

             int now=;

             for(int j=;ch[j];j++)

              if(ch[j]==')')

              {

               if(now) now--,ans++;

                else a[i]++;

              }

               else now++;

             b[i]=now;

             for(int j=;ch[j];j++) ch[j]=;

         }

         for(int i=;i<=n;i++) A[i]=MP(a[i],b[i]);

         int len1=,len2=;

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

          if(a[i]<b[i]) B[++len1]=A[i];

           else C[++len2]=A[i];

         sort(B+,B+len1+,cmp1);

         sort(C+,C+len2+,cmp2);

         int now=;

         for(int i=;i<=len1;i++)

         {

             ans+=min(now,B[i].fi);

             now-=min(now,B[i].fi);

             now+=B[i].se;

         }

         for(int i=;i<=len2;i++)

         {

             ans+=min(now,C[i].fi);

             now-=min(now,C[i].fi);

             now+=C[i].se;

         }

         printf("%d\n",ans*);

     }

     return ;

 }