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

template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  auto start=clock();
  Int n;
  string s;
  cin>>n>>s;
  

  using P = pair<Int, Int>;
  vector<P> v;
  Int a=0,b=0,c=0,ans=0;
  for(Int i=0;i<n;i++){
    if(s[i]=='(') a++;
    else if(a) a--,c++;
    else b++;
    ans+=c;
    v.emplace_back(a,b);
  }
  
  Int res=0;
  while((double)(clock()-start)/CLOCKS_PER_SEC<1.9){
    Int tmp=0;
    a=0;b=0;
    for(Int i=0;i<n;i++){
      Int x,y;
      tie(x,y)=v[i];
      if(min(a,y)<min(x,b)) swap(a,x),swap(b,y);
      Int z=min(a,y);
      b+=y-z;
      a=x+a-z;
      tmp+=z;
    }
    chmax(res,tmp);
    random_shuffle(v.begin(),v.end());
  }

  ans+=res;
  ans<<=1;
  cout<<ans<<endl;
  return 0;
}