#include<algorithm>
#include<iostream>
#include<vector>
using namespace std;
typedef long long lint;
typedef vector<int>vi;
typedef pair<int,int>pii;
#define rep(i,n)for(int i=0;i<(int)(n);++i)

struct cmp{
  bool operator()(pii a,pii b)const{
    int f=a.first-a.second;
    f=b.first+max(f,-b.second);
    int s=b.first-b.second;
    s=a.first+max(s,-a.second);
    return f==s?-a.second<-b.second:f<s;
  }
};

int main(){
  int n;
  string s;
  cin>>n>>s;
  int mi=0,cur=0;
  vector<pii> kenchon(n);
  rep(i,n){
    cur+=s[i]=='('?1:-1;
    mi=min(mi,cur);
    kenchon[i]=pii(cur,mi);
  }
  sort(kenchon.begin(),kenchon.end(),cmp());
  lint sum=(lint)n*(lint)(n+1)/2;
  lint ans=0;
  lint cursum=0;
  rep(i,n){
    ans=kenchon[i].first+max(ans,(lint)-kenchon[i].second);
    cursum+=kenchon[i].first;
  }
  cout<<sum+(cursum-ans-ans)<<endl;
}